Kybernetes
ISSN 0368-492X
The International Journal of Systems & Cybernetics
Volume 31 Number 9/10 2002
Special double issue: Systems and cybernetics: new theories and applications — Part I Guest Editor Yi Lin Paper format Kybernetes includes ten issues in traditional paper format. The contents of this issue are detailed below.
Internet Online Publishing with Archive, Active Reference Linking, Key Readings, Non-article Content, Institution-wide Licence, E-mail Alerting Service and Usage Statistics. Access via the Emerald Web site: http://www.emeraldinsight.com/ft See p. 1186 for full details of subscriber entitlements.
Contents of Part II _______________________________ 1184 Access to Kybernetes online ______________________ 1186 Editorial advisory board __________________________ 1187 Abstracts and keywords __________________________ 1188 Awards for Excellence ____________________________ 1203 Preface __________________________________________ 1205 Editorial _________________________________________ 1208 Creative idea generation via interpretative approach to analogical reasoning Kambiz Badie _________________________________________________ 1210
CLCR optimal input design for IS and IU plants Cs. Ba´nya´sz and L. Keviczky _____________________________________ 1220
Universe as a self-observable, self-ethical, life-embedding mathematical system Michel Bounias ________________________________________________ 1236
A synergetics approach to disruptive innovation Gerrit Broekstra _______________________________________________ 1249
Uncertain variables and their applications for control systems Z. Bubnicki ___________________________________________________ 1260
This issue is part of a comprehensive multiple access information service
CONTENTS
CONTENTS continued
Control synthesis of a class of DEDS Frantisˇek Cˇapkovicˇ _____________________________________________ 1274
Incentives: mechanisms for the consistency of the Colombian educational system Mario Castillo, Gabriel Duque and Fernando Beltra´n _________________ 1282
Modelling, prototyping, and verifying concurrent and distributed applications using object-oriented Petri nets Milan Cˇesˇka, Vladimı´r Janousˇek and Toma´sˇ Vojnar __________________ 1289
Fuzzy algorithms of problem solving O.G. Chorayan and G.O. Chorayan ________________________________ 1300
Towards autonomous application interfaces Miche`le Courant and Ste´phane Le Peutrec __________________________ 1306
Can the system idea help promote critical thinking and intellectual autonomy in pedagogy? D. Andre´s Mejı´a _______________________________________________ 1313
A systemic look at educational development programs: two perspectives on a recent Colombian experience Angela Espinosa and Mike C. Jackson______________________________ 1324
The bridge to humanity’s future: text of a multimedia address Willard R. Fey and Ann C.W. Lam ________________________________ 1336
What is ‘‘engineering systems thinking?’’ Moti Frank ___________________________________________________ 1350
The ‘‘Roundtable’’ for school learning and planning groups: planting a seed for systemic renewal Susan Farr Gabriele ____________________________________________ 1361
Epidemiologic modelling of HIV and CD4 cellular/molecular population dynamics T. Habtemariam, B. Tameru, D. Nganwa, L. Ayanwale, A. Ahmed, D. Oryang and H. AbdelRahman __________________________________ 1369
Application of systems analysis in modelling the risk of bovine spongiform encephalopathy (BSE) T. Habtemariam, B. Tameru, D. Nganwa, L. Ayanwale, A. Ahmed, D. Oryang, H. AbdelRahman, G. Gray, J. Cohen and S. Kreindel ________ 1380
Tools for creation of multimodels Martin Hruby´, Radek Kocˇ´ı, Petr Peringer and Zdena Ra´bova´ ___________ 1391
Optimal control and approximation of variational inequalities Hrubina Kamil and Jadlovska´ Anna _______________________________ 1401
Thorough numerical entropy analysis of some substitutive sequences by lumping K. Karamanos and I. Kotsireas ___________________________________ 1409
Mathematical bios Louis Kauffman and Hector Sabelli________________________________ 1418
On the reachable robustness limits for time delay control systems L. Keviczky and Cs. Ba´nya´sz _____________________________________ 1429
‘‘Physics’’ approach to general systems theory J. Korn_______________________________________________________ 1442
A systems approach to self-organization in the dreaming brain Stanley Krippner and Allan Combs ________________________________ 1452
Asymptotic models and methods in complex systems dynamics (General approach) Lyudmila K. Kuzmina __________________________________________ 1463
Relonics: balascopy-based systems-specific technology Vadim I. Kvitash_______________________________________________ 1471
The cruel blow to the biomedical paradigm not based on systems sciences and cybernetics Vadim I. Kvitash_______________________________________________ 1481
Categorical prediction of acute chest pain outcome by relonics Vadim I. Kvitash_______________________________________________ 1487
Note from the publisher ___________________________ 1494 Index to volume 31, 2002 _________________________ 1497
CONTENTS continued
Kybernetes 31,9/10
Special double issue: Systems and cybernetics: new theories and applications — Part II (to be published in Vol. 32, No. 5/6, 2003) Guest Editor Yi Lin
1184 Specific relonic patterns from non-specific or useless laboratory data Vadim I. Kvitash Raster space with relativity Zhilin Li, Yong-qi Chen, Yongli Li, Xiaoxia Li and Yi Lin Normal sum decomposition of general systems Guoyang Liu Communities of learning: a case in local development Ernesto Lleras A biocultural model of aging Mario E. Martinez Adaptive dual control in one biomedical problem Konstantin N. Nechval, Nicholas A. Nechval and Edgars K. Vasermanis Effective state estimation of stochastic systems Nicholas A. Nechval, Konstantin N. Nechval and Edgars K. Vasermanis A learning model for the dual evolution of human social behaviors M. Nemiche and Rafael Pla-Lopez Autocorrelation and frequency analysis differentiate cardiac and economic bios from 1/f noise M. Patel and H. Sabelli A holistic approach towards the validation and legitimisation of information systems O. Petkova and D. Petkov Development of an autonomous spacecraft for planetary exploration Gianmarco Radice ‘‘How much cybernetics can you handle?’’ James N. Rose Axiomatic combinatorial world theory with emergent intelligence: simplifying understanding and professionalizing general education Donald O. Rudin Mathematical development: a theory of natural creation H. Sabelli Aging and social systems H. Sabelli, M. Patel, L. Carlson-Sabelli, J. Konecki, J. Nagib and A. Sugerman
Life-long creation in the prevention of premature aging H. Sabelli and A. Sugerman
Contents of Part II
Inside communication in nanostructured evolutionary automata nanophysics and an information concept for viable technologies Salvatore Santoli System dynamics modelling, simulation and optimization of integrated urban systems: a soft computing approach P.S. Satsangi, D.S. Mishra, S.K. Gaur, B.K. Singh and D.K. Jain Model following PID control system Stanislaw Skoczowski, Stefan Domek and Krzysztof Pietrusewicz Novelty, diversification and nonrandom complexity define creative processes A. Sugerman and H. Sabelli On the criterion of optimal product structure in the microeconomic system (enterprise) and adjustment of product structure Lixin Tao Smarter computer intrusion detection utilizing decision modeling Christopher C. Valentino Cybernetics and systems, from past to future Robert Valle´e Statistical validation of simulation models of observable systems Edgars K. Vasermanis, Konstantin N. Nechval and Nicholas A. Nechval SWARM based study on spatial-temporal emergence in flood Yiming Wei, Linpeng Zhang and Ying Fan Towards a cybernetics of value, presence, and anticipation John Wood Pansystems mathematics: an analysis of panweighted fieldnetwork Xiaolong Wu, Dinghe Guo, Jinghong Pan and Xuemou Wu On stochastic optimal control for stock price volatility Ying Yi-rong, Lin Yi and Wu Chong-feng Pansystems GuanKong technology and information quantization Yu Hong-yi, Leon (Xiangjun) Feng and Yu Ran Randomization and eventual reordering: a number theoretic approach Barry Zeeberg Data self-create in data storage system Zhou ke, Zhang Jiangling and Feng Dan
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EDITORIAL ADVISORY BOARD A. Bensoussan President of INRIA, France V. Chavchanidze Institute of Cybernetics, Tbilisi University, Georgia A.B. Engel IMECC-Unicamp, Universidad Estadual de Campinas, Brazil R.L. Flood Hull University, UK F. Geyer The Netherlands Universities Institute for Co-ordination of Research in Social Sciences, Amsterdam, The Netherlands A. Ghosal Honorary Fellow, World Organisation of Systems and Cybernetics, New Delhi, India R. Glanville Royal Melbourne Institute of Technology University, Australia R.W. Grubbstro¨m Linko¨ping University, Sweden Chen Hanfu Institute of Systems Science, Academia Sinica, People’s Republic of China G.J. Klir State University of New York, USA Yi Lin International Institute for General Systems Studies Inc., USA
K.E. McKee IIT Research Institute, Chicago, IL, USA M. Ma˘nescu Academician Professor, Bucharest, Romania M. Mansour Swiss Federal Institute of Technology, Switzerland
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K.S. Narendra Yale University, New Haven, CT, USA C.V. Negoita City University of New York, USA W. Pearlman Technion Haifa, Israel A. Raouf Pro-Rector, Ghulam Ishaq Khan (GIK) Institute of Engineering Sciences & Technology, Topi, Pakistan Y. Sawaragi Kyoto University, Japan B. Scott Cranfield University, Royal Military College of Science, Swindon, UK D.J. Stewart Human Factors Research, UK I.A. Ushakov Moscow, Russia J. van der Zouwen Free University, Amsterdam, The Netherlands
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Creative idea generation via interpretative approach to analogical reasoning Kambiz Badie Keywords Cybernetics, Reasoning To add the flavor of creativity to analogical reasoning, an intermediate space has been proposed to be included between source and target, so that the inputs in the source can be interpreted in terms of some navigating concepts in this layer for further reinterpretation in the target space. In this paper, as the extension of this approach, interpretation schemes have been addressed emphasizing on the co-working of interpretation and reinterpretation mechanisms for idea generation with respect to different types of situations in the source. Within this respect, hypothesis generation in the scientific domains, has been emphasized as a tangible application of an interpretative approach to interdomain analogical reasoning. As the final remarks, the proposed approach has been compared with both the classical approach to analogical reasoning and the related works as well. CLCR optimal input design for IS and IU plants Cs. Ba´nya´sz and L. Keviczky Keywords Cybernetics, Design The paper deals with the optimal reference signal excitation for closed-loop-controlrelevant (CLCR) identification for inverse stable (IS) and inverse unstable (IU) processes. For the IS case the optimal excitation depends only on the performance design goal, however, for the IU case it depends on the invariant factors of the plant, so only learning algorithms can be applied.
Kybernetes, Vol. 31 No. 9/10, 2002, Abstracts and keywords. # MCB UP Limited, 0368-492X
Universe as a self-observable, self-ethical, life-embedding mathematical system Michel Bounias Keywords Cybernetics, Perception, Evolution strategies The non-well-founded properties of the empty set provide existence to abstract topological spaces, in which intersections of subspaces with non-equal dimensions give topologically
closed structures. This let space-time emerge as an ordered sequence of sections upon a defined combination rule, in which interactivity between observable structures is allowed and conditions for conscious perception phenomena are fulfilled. Conditions for evolution and rules for optimal evolution of ecosystems also infer as corollaries. A physical universe and life constitute one single self-organized and self managed system where life appears as the physical-like realization of conditions of functionality of the embedding mathematical spaces. The system includes self-ethical and moral guidelines which should inspire human behavior on Planet Earth. A synergetics approach to disruptive innovation Gerrit Broekstra Keywords Cybernetics, Technological innovation Emery and Trist were the first to design an influential taxonomy of four social fields to accommodate the perceived emergence of a new type of business environment, the type 4 turbulent field. This captured the predicament of leading companies suddenly confronted with, what Christensen called much later, disruptive change. Their taxonomy was based on the study of adaptive behavior on linear dynamical systems. This paper proposes a modification of the taxonomy on the basis of Synergetics to enable dealing with the nonlinear evolutionary dynamics of complex probabilistic business systems. Synergetics focuses on what happens in phase transitions or bifurcations which appear to be the essential nature of turbulent fields. Furthermore, Haken’s slaving principle and the concept of the order parameter are remarkably well-suited to review the Christensen’s findings of companies held captive by customers and, particularly, the puzzling delay shown by leading companies in responding to newcomers. These newcomers typically change the nature of the order parameters of type 3 established fields, as represented by Christensen’s product performance characteristics, which may cause customers to switch their preferences and buying behavior. Thus the apparent stability of an established field can
be quite deceptive. As such, this paper suggests the existence of a lock-out principle complementary to the lock-in principle described by Arthur in his work. Uncertain variables and their applications for control systems Z. Bubnicki Keywords Cybernetics, Control systems, Stability The definitions and basic properties of so called uncertain variables are presented. The uncertain variables are described by certainty distributions given by an expert and characterizing approximate values of the variables. Control problems for uncertain systems with static and dynamic plants are considered. A method of the stability analysis for a system with uncertain parameters is described. Simple examples illustrate the presented approaches. Control synthesis of a class of DEDS Frantisˇek Cˇapkovicˇ Keywords Cybernetics, Dynamic modelling, Control systems A new control synthesis method suitable for a special kind of discrete event dynamic systems (DEDS) is presented in this paper. The systems to be controlled are modelled by a special class of Petri nets (PN) named state machine (SM). The class is distinctive by the fact that each PN transition has only one input place and only one output place. Bipartite directed graphs (BDG) are utilized in the control synthesis process. Namely, PN in general are (from the structure point of view) the BDG. Both the state reachability tree and the corresponding control one are developed in the straight-line procedure starting from the given initial state and directed to the desirable terminal one as well as in the backtracking procedure starting from the terminal state and directed to the initial one. After a suitable intersection of both the straight-lined state reachability tree and the backtracking one the state trajectories of the system are obtained. After the intersection of both the straight-lined control reachability tree and the backtracking one the control interferences corresponding to the state trajectories are obtained.
Incentives: mechanisms for the consistency of the Colombian educational system Mario Castillo, Gabriel Duque and Fernando Beltra´n Keywords Cybernetics, Education, Quality, Efficiency This paper focuses on a project to develop a methodology for diagnosing and designing incentives to improve the colombian basic education system’s performance. We describe the system and then the model identifying the agents characterized and the relationships between them. With these elements we construct an Incentives map. In order to connect the decisions of the individual or institution agents to the performance of the system, we build a way of illustrating them. Finally, we present the results. Modelling, prototyping, and verifying concurrent and distributed applications using object-oriented Petri nets Milan Cˇesˇka, Vladimı´r Janousˇek and Toma´sˇ Vojnar Keywords Cybernetics, Distributed applications, Rapid prototyping, Object-oriented computing This paper presents several research issues associated with the PNtalk language that is based on a certain kind of object-oriented Petri nets (OOPNs) and intended mainly for modelling, prototyping, and verifying concurrent and distributed applications. The paper reviews the main concepts of PNtalk and OOPNs followed by a proposal of a system allowing prototypes based on PNtalk to be run in a distributed way. Furthermore, the first step made towards state spacesbased formal analysis and verification over PNtalk OOPNs are also briefly mentioned in the paper. Fuzzy algorithms of problem solving O.G. Chorayan and G.O. Chorayan Keywords Cybernetics, Fuzzy systems Labyrinth test psychophysiological experiment is elaborated to analyze possible mechanism of the probabilistic prognosis forming and realizing in the condition of essential information uncertainty. The
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dynamics of the probabilistic prognosis construction and improvement during multistage labyrinth test solving is established. This dynamics is characterized by considerable changes of the subjective probabilities and membership function quantitative indices apparently used in the fuzzy logic of mental activity being applied in decision-making processes realized in the condition of uncertainty. The possible link between probabilistic prognosis efficiency and some functional peculiarities of cortical hemisphere asymmetry has also been studied. Towards autonomous application interfaces Miche`le Courant and Ste´phane Le Peutrec Keywords Cybernetics, Human-computer interaction, Computer networks, Software engineering A global change resulting from a convergence between communication technologies – namely Internet, and other devices technologies – namely robotics, mobile communication, and domotics – is presently affecting Information and Communication Technology (ICT). This situation, denoted by the so-called Intelligent Networks and Ubiquitous Computing fields, is characterized by a high diversity and promiscuity of equipments and applications, together with a great variability of using contexts. In order to address this variability, we propose a new kind of interaction schema, separating the application interface from the application itself. The paper describes this schema and its central concept of virtual instrument, allowing the users to initiate observation processes with the running applications, and to construct their own points of view upon their activities. Can the system idea help promote critical thinking and intellectual autonomy in pedagogy? D. Andre´s Mejı´a Keywords Cybernetics, System design Some problems have been pointed out in the literature, regarding how the various critical approaches to pedagogy have failed to properly promote autonomy of thinking and
to prevent the imposition of knowledge. The criticisms include the incapacity of some approaches to highlight and question subtle or tacit forms of knowledge, and the implicit active imposition of knowledge by some others. With the possible use of critical systems thinking in pedagogy in mind, here we examine how the forms of critique used by three different approaches within this strand can deal with these criticisms. We will argue that, as presently conceived, the critical use of the system idea is susceptible of being criticised in the same way. A systemic look at educational development programs: two perspectives on a recent Colombian experience Angela Espinosa and Mike C. Jackson Keywords Cybernetics, System design education There has been considerable agreement among researchers and practitioners, working on development issues, that unless we improve the education infrastructure in less-developed countries they will never be able to improve their development indices. Innumerable educational reform programs in many different countries, over the last century, have been driven by this aim but few have had the desired impact on local educational systems in terms of coverage, quality and equity. Taking as an example a project recently undertaken in Colombia, we argue in this paper that a significant reason for this may well be the inappropriate theoretical paradigms and methodological approaches underpinning the majority of educational reform programs. The bridge to humanity’s future: text of a multimedia address Willard R. Fey and Ann C.W. Lam Keywords Cybernetics, Environment, Economic growth Human life on Earth is threatened by the growth of world human consumption which quadruples every 35 years. Major environmental imbalances may soon severely deplete our planetary life-support system. However, the world economy is designed to create and depend on
consumption growth. If this growth were to stop, major economic, social and military crises could result. We call this tragic dilemma the Ecocosm Paradox. Powerful human instincts drive the positive feedbackloop processes that generate consumption growth. This growth involves many human, technological, and natural environmental variables whose separate study has given rise to specialized intellectual disciplines. However, in order to address our current dilemma, these variables must be analyzed together as a single, complex process. A new method of analysis, synthesis, and implementation based on a new transdisciplinary field, ‘ ‘Ecocosm Dynamics’ ’, is herein proposed for this analysis. What is ‘ ‘engineering systems thinking’ ’? Moti Frank Keywords Cybernetics, Systems design As technological systems grow larger, more complex, and interdisciplinary, electronics and hi-tech industries face a growing demand for engineers with a capacity for ‘ ‘engineering systems thinking’ ’. This paper presents a multifunctional definition and 30 laws of ‘ ‘engineering systems thinking’ ’. The definition and the laws are based on a study that its purpose was to identify the characteristics of engineers who are able to think in the manner called ‘ ‘engineering systems thinking’ ’. A thorough understanding of ‘ ‘engineering systems thinking’ ’ on both the theoretical and operational levels will prove useful in the design of curricula to improve and develop thinking of this sort. The ‘ ‘Roundtable’ ’ for school learning and planning groups: planting a seed for systemic renewal Susan Farr Gabriele Keywords Cybernetics, Education, Organizational change Current public education, overwhelmed by piece-meal reform efforts, is in need of systemic renewal. An investigation of key literature – systems methods, instructional design, and group process models – yields
the conditions necessary for systemic change and a suitable base model. Namely, a successful systemic educational change effort is ideal-based, holistic, continuing, participatory, user-friendly, easy to adjust/ improve, and emancipatory. A suitable base model is discovered in the learning systems of Alcoholics Anonymous and then built on for a new model: the Roundtable (RT) for secular learning. Briefly, the RT session is designed so that leadership and learning opportunities are distributed among all participants, who have equal time to present their ideas. Pilot studies in professional scientific organizations allowed refinement of the model. This study investigated sought the seven conditions in four RT applications in 4th-grade classrooms in California. Participants at each site were the teacher and their 30 ^ 1 students. Each teacher held ten RT sessions, with students leading two to three of the last four sessions. Evidence was sought in the RT texts, session recordings, and users’ views. The criteria were met in the following ways. The RT applications were: ideal-based in the RT texts; user-friendly as they were user-ready and engaging; easy to adjust/improve in the simple revision session tasks, and emancipatory as users learned in important, positive and unanticipated ways. The RT applications were holistic: found suitable for all classroom levels at both schools, and for all school groups at one school. They were continuing after the study in 2 or 3 of the four classrooms. They were very participatory in the roles of listener, reader, and speaker; somewhat participatory in the leader and coplanner roles. Contributions to organizational /educational change theory and future projects are promising. Epidemiologic modelling of HIV and CD4 cellular/molecular population dynamics T. Habtemariam, B. Tameru, D. Nganwa, L. Ayanwale, A. Ahmed, D. Oryang and H. AbdelRahman Keywords AIDS, Cybernetics, Computational model Computational models can facilitate the understanding of complex biomedical systems such as in HIV/AIDS. Untangling the dynamics between HIV and CD4+ cellular
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populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we have developed a state transition systems dynamics and stochastic model that can be used to examine various alternatives for the control and treatment of HIV/AIDS. The specific objectives of our study were to use a cellular/molecular model to study optimal chemotherapies for reducing the HIV viral load, and b) to use the model to study the pattern of mutant viral populations and resistance to drug therapies. The model considers major state variables (uninfected CD4+ lymphocytes, infected CD4+ cells, replicated virions) along with their respective state transition rates (viz. CD4+ replacement rate, infection rate, replication rate, depletion rate). The state transitions are represented by ordinary differential equations. The systems dynamics model was used for a variety of computational experimentations to evaluate HIV mutations, and to evaluate effective strategies in HIV drug therapy interventions. Application of systems analysis in modelling the risk of bovine spongiform encephalopathy (BSE) T. Habtemariam, B. Tameru, D. Nganwa, L. Ayanwale, A. Ahmed, D. Oryang, H. AbdelRahman, G. Gray, J. Cohen and S. Kreindel Keywords Cybernetics, Risk, Modelling, Bovine spongiform encephalopathy Bovine spongiform encephalopathy (BSE), widely known as ‘ ‘mad cow disease’ ’, has virtually crippled the British livestock industry. Even though, no cases of BSE have been reported in the United States (US), a similar epidemic in the US would be catastrophic. The added concern for the risk of introduction of the human disease called variant Creutzfeldt-Jacob disease that has been linked to eating meat of BSE infected cattle compounds the risk of BSE. Systems dynamics models based on the underlying transmission pathways of BSE can help to anticipate the spread of this disease in different cattle populations and assist in the evaluation of potential risk mitigations for preventing its introduction or controlling its spread if it was introduced. With this in
mind, an age and health status structured systems dynamics model was developed. The model assesses potential risk pathways for entry of the BSE causative agent into US cattle and the US food supply as well as to how the agent’s infectivity measured in ID50s may spread in human and cattle populations. By making assumptions and setting up feasible scenarios, the model can be used to examine potential prevalence and incidences rates of BSE; the effect of mitigations including changes in feeding habits or rendering processes and/or other policies and regulations designed to prevent the introduction of BSE. The systems dynamics simulation model enabled us to create virtual experiments whose real-world analogues would otherwise be expensive, dangerous, or even impossible to carryout.
Tools for creation of multimodels Martin Hruby´, Radek Kocˇ´i, Petr Peringer and Zdena Ra´bova´ Keywords Cybernetics, Simulation The process of creating complex models often requires different modelling methods and tools to be integrated. This paper provides a concise description of an object-oriented environment for creating composite models. The proposed approach is based on using simulation abstractions as basic model building blocks. The basic environment is built up of a Prolog interpreter, SIMLIB and object-oriented Petri nets.
Optimal control and approximation of variational inequalities Hrubina Kamil and Jadlovska´ Anna Keywords Cybernetics, Control systems, Approximation concepts The paper deals with the problems of numerical approximation of the variational inequalities solution which occur in the optimal control problems. The Ky Fan-Sion theorem of the saddle point is used for the solution of variational inequalities. The theoretical results form the basis for the algorithms creation.
Thorough numerical entropy analysis of some substitutive sequences by lumping K. Karamanos and I. Kotsireas Keywords Cybernetics, Entropy, Analysis In this work we perform a detailed entropy analysis of some substitutive sequences using the technique of lumping. The basic novelty of the entropy analysis by lumping is that, unlike the Fourier transform or the conventional entropy analysis by gliding, it gives results that can be related to algorithmic aspects of the sequences and in particular with the important property of automaticity. All computations in this paper have been performed with TOOLS FOR SYMBOLIC DYNAMICS a Maple package developed by the authors. Mathematical bios Louis Kauffman and Hector Sabelli Keywords Chaos, Cybernetics In this paper we report on a mathematical pattern that we call bios, and its generation by recursions of bipolar feedback. Bios is a newly found form of organization, that resembles chaos in its aperiodic pattern and its extreme sensitivity to initial conditions, but has additional properties (diversification, novelty, nonrandom complexity, life-limited patterning, 1/f power spectrum) found in natural creative processes, and absent in chaos. The process equation At+1 ¼ At+gtsin(At) generates convergence to p, a cascade of bifurcations, chaos, bios and infinitation, as the value of the feedback gain gt increases. In the complex plane, series generated by orthogonal process equations display fractal organic patterns. On the reachable robustness limits for time delay control systems L. Keviczky and Cs. Ba´nya´sz Keywords Cybernetics, Control systems The paper presents a new decomposition method to handle optimal control design for two-degree of freedom time delay control systems. In this approach exact relationships between the actuator, process and design parameters and also robustness measures are developed. The ultimate robustness limit of any control can be explicitly calculated by this approach.
‘ ‘Physics’ ’ approach to general systems theory J. Korn Keywords Cybernetics, General living systems theory A number of empirical statements intended to capture features of ‘ ‘systems’ ’ considered to be pervasive, is given. A symbolism based on processed natural language is outlined. The symbolism can be used for analysis of scenarios with predominantly qualitative properties i.e. human activity situations. It is capable of carrying the appropriate mathematics and uncertainties associated with operation of human and other types of components, is based on a kind of predicate logic and exhibits changes of states in time. The approach has led to a definition of information and product and systems design. A systems approach to self-organization in the dreaming brain Stanley Krippner and Allan Combs Keywords Cybernetics, Brain, Self-development This systems model of dreaming consciousness examines the self-organizing properties of the sleeping brain, offering a step towards reconciling brain-based and content-based attempts to understand the nature of dreaming. We argue that the brain can be understood as a complex selforganizing system that, in dreaming, responds to subtle influences such as residual feelings and memories. The hyperresponsiveness of the brain during dreaming is viewed in terms of the tendency of complex chaotic-like systems to respond to small variations in initial conditions (the butterfly effect) and to the amplification of subtle emotional and cognitive signals through the mechanism of stochastic resonance, all in combination with psychophysiological changes in the brain during both slow wave sleep and rapid eye movement (REM) sleep dreaming. These changes include the active inhibition of extroceptive stimulation and, especially in REM sleep, alterations in the brain’s dominant neuromodulatory systems, bombardment of the visual cortex with bursts of PGO activity, increases in limbic system activity, and a reduction of activity in the prefrontal regions.
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Asymptotic models and methods in complex systems dynamics (General approach) Lyudmila K. Kuzmina Keywords Cybernetics, Stability, Modelling The paper is concerned with the different aspects of mathematical modelling and analysis in dynamics of complex non-linear systems, that are generated by applied problems of engineering practice. Main aims are the problems of optimal (in some sense) mechanical-mathematical modelling and the regular schemes of decomposition. The critical step in the use of mathematics for solving complex engineering problems is the building of a suitable mathematical model, that, generally speaking, is the result of combining the mathematical formalized procedures as well as heuristic (nonformalized) manners (conjunction of rigorous science and free art). This work advocates a novel approach to the building process of mathematical models, presenting an overview of concepts and techniques needed for modelling, via comprehension of modelling problem as singularly perturbed one. Here uniform methodology, based on methods of Lyapunov theory, Perturbations theory [Asymptotic method in theory of non-linear oscillations (1963)] in accordance with Stability postulate and Singularity postulate is developed. This asymptotic approach (called – LPSS approach) allows to elaborate the general conception of the modelling; to determine the conditions of qualitative equivalence between full model and simplified model. As applications, the different examples of concrete physical nature are considered.
Relonics: balascopy-based systems-specific technology Vadim I. Kvitash Keywords Cybernetics, Control, Coordination Relonics is a systems-specific technology based on a complete scientific theory of control, regulation and coordination in super-complex systems which allows generation of a new class of relational systemic information currently not available from any existing technologies. The cruel blow to the biomedical paradigm not based on systems sciences and cybernetics Vadim I. Kvitash Keywords Cybernetics, Biomedical Systems-Specific Technology can detect, identify, evaluate and represent previously unknown patterns of multi-dimensional networks which underline clinically significant metabolic disorders not identifiable by currently available diagnostic modalities. Categorical prediction of acute chest pain outcome by relonics Vadim I. Kvitash Keywords Cybernetics, Biomedical Relonics, for the first time, identifies previously unknown multi-dimensional patterns of biochemical meta-networks which can serve as specific and sensitive systemic markers for categorical prediction of acute chest pain outcome in individual patients at the time of admission in Intensive Care Unit.
Abstracts and keywords of papers for Part II (to be published in Vol. 32, No 5/6 2003) Specific relonic patterns from non-specific or useless laboratory data Vadim I. Kvitash Keywords Cybernetics, Biomedical, Liver diseases, Relonic meta-network Discusses how in 20 different hepato-biliary diseases, relonics for the first time, identifies previously unknown systemic relational networks of biochemical imbalances/ dysbalances which can be used as prototype patterns for early diagnosis, instant monitoring of treatment response, and individualized treatment adjustments. Raster space with relativity Zhilin Li, Yong-qi Chen, Yongli Li, Xiaoxia Li and Yi Lin Keywords Cybernetics, Approximation concepts, Geographical information systems Practical needs in geographical information systems (GIS) have led to the investigation of formal, sound and computational methods for spatial analysis. Since models based on topology of R2 have a serious problem of incapability of being applied directly for practical computations, we have noticed that models developed on the raster space can overcome this problem. Because some models based on vector spaces have been effectively used in practical applications, we then introduce the idea of using the raster space as our platform to study spatial entities of vector spaces. In this paper, we use raster spaces to study not only morphological changes of spatial entities of vector spaces, but also equal relations and connectedness of spatial entities of vector spaces. Based on the discovery that all these concepts contain relativity, we then introduce several new concepts, such as observable equivalence, strong connectedness, and weak connectedness. Additionally, we present a possible method of employing raster spaces to study spatial relations of spatial entities of vector spaces. Since the traditional raster spaces could not be used directly, we first construct a new model, called pansystems
model, for the concept of raster spaces, then develop a procedure to convert a representation of a spatial entity in vector spaces to that of the spatial entity in a raster space. Such conversions are called approximation mappings.
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Normal sum decomposition of general systems Guoyang Liu Keywords Cybernetics, General systems This paper introduces normal systems and the normal sum of general systems. A system S ¼ ðM ; RÞ is normal if and only if any two relations in R are not contained in the same Cartesian product Mn for any ordinary number n. Normal sum is a new kind of decomposition (composition) of general systems. Given a normal system S ¼ ðM ; RÞ; and two subsets A1 # M and A2 # M : One of the main results is that the normal sum of the A1-related subsystem and the A2-related subsystem of S equals the (A1 < A2)-related subsystem of S. This implies that every normal system is a normal sum of its subsystems which are non-trivial and non-discrete.
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Communities of learning: a case in local development Ernesto Lleras Keywords Cybernetics, Learning With the help of some notions developed by us, such as ‘ ‘community of learning’ ’, ‘ ‘powerover relations’ ’, ‘ ‘power-for relations’ ’, learning as observing relations and practices, and others, we describe an intervention in a community with a research-action methodology, aiming at creating learning spaces in different realms of everyday life like enterprise creation and operation, self-government and selfmanagement, and relationships with a traditional learning community as is the case of a high school. A biocultural model of aging Mario E. Martinez Keywords Cybernetics, Older people Addresses how the life sciences have concentrated on the pathology of aging while
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ignoring the biocultural aspects of health in the process of growing older. Argues that growing older is a dynamic cognitive, biological and cultural coauthoring of health rather than a hopeless unfolding of progressive pathology. Proposes that this fragmented concept of aging precludes operationalizing and understanding the cultural markers that affect longevity. These cultural milestones, or biocultural portals include middle age markers, retirement markers, perceived wisdom, sexuality, status in the community, transcendental beliefs, sense of empowerment vs helplessness and any other biocultural phase in human development. Suggests that the biocultural portals define and trigger the phase transitions of life as well as influence how they are accommodated. For example, the markers for middle age established by a culture, strongly influence the cognitive and biological expectations for the second half of life. Adaptive dual control in one biomedical problem Konstantin N. Nechval, Nicholas A. Nechval and Edgars K. Vasermanis Keywords Cybernetics, Pharmaceuticals In this paper, the following biomedical problem is considered. People are subjected to a certain chemotherapeutic treatment. The optimal dosage is the maximal dose for which an individual patient will have toxicity level that does not cross the allowable limit. We discuss sequential procedures for searching the optimal dosage, which are based on the concept of dual control and the principle of optimality. According to the dual control theory, the control has two purposes that might be conflicting: one is to help learning about unknown parameters and/or the state of the system (estimation); the other is to achieve the control objective. Thus the resulting control sequence exhibits the closed-loop property, i.e. it anticipates how future learning will be accomplished and how it can be fully utilized. Thus, in addition to being adaptive, this control also plans its future learning according to the control objective. Results are obtained for a priori uniform distribution of the unknown dosage. Because answers can be obtained analytically without approximation, the optimum policy
can be compared with the non-optimum policy of optimizing stage by stage. An illustrative example is given. Effective state estimation of stochastic systems Nicholas A. Nechval, Konstantin N. Nechval and Edgars K. Vasermanis Keywords Cybernetics, Stochastic modelling In the present paper, for constructing the minimum risk estimators of state of stochastic systems, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant estimator, which has smaller risk than any of the well-known estimators. There exists a class of control systems where observations are not available at every time due to either physical impossibility and/or the costs involved in taking a measurement. In this paper, the problem of how to select the total number of the observations optimally when a constant cost is incurred for each observation taken is discussed. To illustrate the proposed technique, an example is given and comparison between the maximum likelihood estimator (MLE), minimum variance unbiased estimator (MVUE), minimum mean square error estimator (MMSEE), median unbiased estimator (MUE), and the best invariant estimator (BIE) is discussed. A learning model for the dual evolution of human social behaviors M. Nemiche and Rafael Pla-Lopez Keywords Cybernetics, Modelling, Individual behaviour In this work we modelize, with an abstract mathematical model by computer simulation, the processes that have made to appear in the world a strong duality between orient and occident, by combining changes in conditions of initialization, natural system and the
opposition gregarious/individualism of the social behaviors.Finally we present a statistical study of the influence of the repression adaptability, resignation and recycling on the ecological destruction and social evolution.This model can help us to analyze if the current capitalist globalization can be stopped, changed or regulated, and if it is possible to overcome it towards a Free Scientific Society. Autocorrelation and frequency analysis differentiate cardiac and economic bios from 1/f noise M. Patel and H. Sabelli Keywords Chaos, Economics, Cybernetics Mathematical bios and heartbeat series show an inverse relation between frequency and power; the time series of differences between successive terms of cardiac and mathematical chaos shows a direct relation between frequency and power. Other statistical analyses differentiate these biotic series from stochastically generated 1/f noise. The time series of complex biological and economic processes as well as mathematical bios show asymmetry, positive autocorrelation, and extended partial autocorrelation. Random, chaotic and stochastic models show symmetric statistical distributions, and no partial autocorrelation. The percentage of continuous proportions is high in cardiac, economic, and mathematical biotic series, and scarce in pink noise and chaos. These findings differentiate creative biotic processes from chaotic and stochastic series. We propose that the widespread 1/f power spectrum found in natural processes represents the integration of the fundamental relation between frequency and energy stated in Planck’s law. Natural creativity emerges from determined interactions rather than from the accumulation of accidental random changes. A holistic approach towards the validation and legitimisation of information systems O. Petkova and D. Petkov Keywords Cybernetics, Information systems The research aims to show that validation and legitimisation of an information systems
(IS) project need to be treated simultaneously to improve software project management. A starting assumption is that traditional aspects of model validity and legitimisation in operational research can be applicable to the field of IS. However, non-traditional types of IS are more suitable to be viewed from an interpretive viewpoint. Validation is explored both from hard systems and also from soft systems point of view. Some extensions on the notion of validation for soft systems are provided for that purpose. Issues regarding both validation and legitimisation in IS are illustrated on a case study regarding the management of an academic research management IS project. Issues related both validation and legitimisation in IS are illustrated on a case study regarding the management of an academic research IS project. The latter had eventually to be abandoned. The case study shows how the non-adherence to the principles of validation and legitimisation lead to that situation. Development of an autonomous spacecraft for planetary exploration Gianmarco Radice Keywords Cybernetics, Autonomy The purpose of this paper is to present a new approach in the concept and implementation of autonomous microspacecraft. The one true ‘ ‘artificial agent’ ’ approach to autonomy requires the microspacecraft to interact in a direct manner with the environment through the use of sensors and actuators. As such, little computational effort is required to implement such an approach, which is clearly of great benefit for limited micro-satellites. Rather than using complex world models, which have to be updated, the agent is allowed to exploit the dynamics of its environment for cues as to appropriate actions to achieve mission goals. The particular artificial agent implementation used here has been borrowed from studies of biological systems, where it has been used successfully to provide models of motivation and opportunistic behaviour. The so-called ‘ ‘cue-deficit’ ’ action selection algorithm considers the micro-spacecraft to be a non-linear dynamical system with a
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number of observable states. Using optimal control theory rules are derived which determine which of a finite repertoire of behaviours the satellite should select and perform. The principal benefits of this approach is that the micro-spacecraft is endowed with self-sufficiency, defined here to be the ability to achieve mission goals, while never placing itself in an irrecoverable position.
group opposition, and topological transformation are generators necessary and sufficient to construct mathematics (Bourbaki, 1946). Homologous cognitive structures generate human mental development (Piaget, 1949). Process theory proposes that these mathematical generators also create nature. Lattice order is embodied as action, group opposition as two-valued information, and topological transformation as spatial organization.
‘ ‘How much cybernetics can you handle?’ ’ James N. Rose Keywords Cybernetics, Human-computer interaction Humanity is innately a composition of primitive cybernetic translations/ transmissions to begin with, from atoms through organizations of civilization. The last 75 years has seen us recognize and then extend those relations into sentience and sociological practicalities. It is the author’s intention with this paper to shed some new light and introduce new concepts into the field and understandings.
Aging and social systems H. Sabelli, M. Patel, L. Carlson-Sabelli, J. Konecki, J. Nagib and A. Sugerman Keywords Social systems, Age discrimination In our society, medical care and economic progress have improved the duration and quality of life, but aging is accelerated by social norms and their psychological introjection. Healthy aging involves the continuing pursuit of creative activity. Changes in self-view and behavior will require and promote a change in social roles, and the emancipatory mobilization of senior adults of both sexes and all classes.
Axiomatic combinatorial world theory with emergent intelligence: simplifying understanding and professionalizing general education Donald O. Rudin Keywords Cybernetics, Evolution A theory of knowledge shows that all four systems of nature are recursive combinatorial-hamiltonian self-programmed flow-wave systems that can be deduced from the usual Conservation Law promoted to the Axiom of Science.
Life-long creation in the prevention of premature aging H. Sabelli and A. Sugerman Keywords Cybernetics, Health Aging is a continuous process of growth and decay, both of which start at birth and continue throughout life. Activity develops muscles and neurons; inactivity atrophies them. Here we propose lifelong creative activity as a method to deal with aging. Decreased creative and learning capacity is a self-fulfilling prophecy. Changing personal perceptions and expectations can promote health care and productive behavior.
Mathematical development: a theory of natural creation H. Sabelli Keywords Systems theory, Chaos, Cybernetics The physical universe is the embodiment of necessary mathematical forms by everpresent flux. Interaction of these forms generates diversity, novelty, complexity, and higher levels of organization. Lattice order,
Inside communication in nanostructured evolutionary automata nanophysics and an information concept for viable technologies Salvatore Santoli Keywords Cybernetics, General systems On the background of previous research work concerning a nanoscale approach to a theory
of biomimetic evolutionary systems and biomimetic information processing it is shown that strictly formal-logic based, ‘ ‘hard-wired’ ’ electronic hardware misses the very physical nature of bioevolvability. A new, physics-base concept of information, and a new concept of hierarchical, open and dissipative ‘ ‘evolware’ ’, much like biosystems ‘ ‘wetware’ ’, are required for developing an actually biomimetic ‘ ‘evolutionary automata’ ’ technology, but a basic inter- and intra-level communication problem is shown to affect the whole automaton’s nanostructure. The problem consists in the difficulty of setting forth causal links bridging the whole hierarchy, from the nanoscale up to the macroscopic structure-functions.
Systems dynamics modelling, simulation and optimization of integrated urban systems: a soft computing approach P.S. Satsangi, D.S. Mishra, S.K. Gaur, B.K. Singh and D.K. Jain Keywords Cybernetics, Modelling, Simulation, Optimization A systems dynamics (SD) simulation model has been developed to analyse dynamics of system behaviour in terms of various performance indicators representing city problems, on one hand, and city development, on the other, with three types of policy interventions: changes in the level of sectoral activities, structural changes in different sectors; and changes in the tolerable city problems index. An artificial neurals network (ANN) model has been successfully trained and used as a quick response model for fast feature extraction of the dynamics of the integrated urban energy-economyenvironment system such that the outputs are within reasonable acceptable error for values of inputs covered by the input space of training patterns. For the sake of further convenience and effectiveness in policy decision making, optimised simulation trajectories are generated by applying genetic algorithms (GAs) search and optimisation methods for alternative policy
scenarios of input variables. An application is shown in the context of the city of Jaipur.
Model following PID control system Stanisław Skoczowski, Stefan Domek and Krzysztof Pietrusewicz Keywords Cybernetics, Control systems The paper deals with robustness to plant parameter perturbations and sensitivity to disturbances of two-loop control structures containing a model of the controlled plant and two PID controllers. Special attention is paid to high robustness of considered structure to perturbations of the controlled plant in relation to its nominal model and to good reduction of disturbances. On the basis of presented simulation results one can compare properties of the proposed structure with properties of the Smith predictor and classic control system structure with single feedback loop. The proposed model following control structures may find wide application to robust control of parameter-varying plants.
Novelty, diversification and nonrandom complexity define creative processes A. Sugerman and H. Sabelli Keywords Cybernetics, Creativity We describe a theory of creative activity through the development and use of mathematical tools in the analysis of time series. The time series analyzed include empirical series and biotic and chaotic series generated by recurrent functions. Embeddings are used to measure the dimensionality of a series, and analyses of isometries of Euclidean norms at various embeddings reveal the relatively simple processes that generate and combine with complex structures. These tools identify and measure diversity, novelty, and complexity in complex natural processes and in mathematical bios. The presence of these properties shows that creative processes result from deterministic interactions among relatively simple components, not only from random accident.
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On the criterion of optimal product structure in the micro-economic system (enterprise) and adjustment of product structure Lixin Tao Keywords Cybernetics, Product structure In order to make a thorough inquiry into the criterion of optimal product structure in the micro-economic system (enterprise), this paper has proposed and demonstrated the benefit-type linear programming model, and based on it, the concepts of enterprise’s product structure, feasible structure and optimal structure have been discussed and the criterion of optimal structure has been revealed. In this paper, the methods of simplex iteration and sensitivity analysis are both used to approach necessarily the adjustment of product structure under the circumstances of varied or invaried environment inside and outside the system, and as a final, it has come to a conclusion that the variation of resource price vector P would not affect the optimal product structure in enterprise, but the variation of resourceconstrained vector b will cause negative effects both on optimal product structure in enterprise and on determination of criterion for optimal structure.
Smarter computer intrusion detection utilizing decision modeling Christopher C. Valentino Keywords Cybernetics, Decision making, Security Addresses specific problems within the area of performing computer system intrusion detection, and presents the reader with an effective decision model to addressing these problems. Current intrusion detection analysis methods are reluctant to properly evaluate the results of decisions made based on their analysis outcomes. These analysis outcomes influence the decision making process involved in response to an intrusion. Utilizing basic decision modeling methods we can develop a model that is both effective and easy to use. To form this model we must have the following within our environment; standard analysis procedure and the classification of information elements. These
will feed into our structured decision model and aid in our final decision outcome. Cybernetics and systems, from past to future Robert Valle´e Keywords Cybernetics, Systems The founders of cybernetics and systems are presented, among them N. Wiener, W.S. Mc Culloch and L. von Bertalanffy. Some precursors are cited from antiquity to 20th century. The basic concepts are exposed: feedback, quantity of information, requisite variety, homeostasis, local and global points of view, oprn systems, autopoiesis. The roles of the observer and of the actor are emphasized. Future is considered in three directions: development of epistemology and of praxiology, symbiosis of man and machine, role of requisite variety in the survival of mankind. Statistical validation of simulation models of observable systems Edgars K. Vasermanis, Konstantin N. Nechval and Nicholas A. Nechval Keywords Cybernetics, Systems, Simulation, Risk In this paper, for validating computer simulation models of real, observable systems, an uniformly most powerful invariant (UMPI) test is developed from the generalized maximum likelihood ratio (GMLR). This test can be considered as a result of a new approach to solving the Behrens-Fisher problem when covariance matrices of two multivariate normal populations (compared with respect to their means) are different and unknown. The test is based on invariant statistic whose distribution, under the null hypothesis, does not depend on the unknown (nuisance) parameters. The sample size and threshold of the UMPI test are determined from minimization of the weighted sum of the model builder’s risk and the model user’s risk. The proposed test could result in the saving of sample items, if the items of the sample are observed sequentially. In this paper we present the exact form of the proposed curtailed procedure and examine the
expected sample size savings under the null hypothesis. The sample size savings can be bounded by a constant, which is independent of the sample size. Tables are given for the expected sample size savings and maximum sample size saving under the null hypothesis for a range of significance levels (a), dimensions (p) and sample sizes (n). The curtailed test considered in this paper represents improvement over the noncurtailed or standard fixed sample tests. SWARM based study on spatial-temporal emergence in flood Yiming Wei, Linpeng Zhang and Ying Fan Keywords Cybernetics, Simulation, Disaster management In complex adaptive system (CAS), the complex behavior of system is emerged from the bottom, that agents’ adaptability bottomup the complexity of the entire system. This idea can be simulated by the method of computer aid simulation. SWARM, which is developed by Santa Fe Institute, is such a tools kit based on the bottom-up modeling method that can be used in CAS simulation on computer. This paper presented a Swarm based simulation platform for the study on complexity in flood disaster. Its application is illustrated with a SWARM based model and program for simulating spatial and temporal emergence of flooding. This model offers virtually unlimited possibilities to simulate the emergence of flooding. Some rules have been elicited from the experimental results, which could provide useful information for the disaster reduction and management. Towards a cybernetics of value, presence, and anticipation John Wood Keywords Cybernetics, Values The paper asks whether we can popularise a cybernetics of human presence. It suggests that, despite its implicit critique of mechanistic thinking, cybernetics inherited its mindset from classical science, and therefore played a part in the evolution of technologically induced forms of alienation. Cybernetics also upholds a strongly western model of ‘ ‘self’ ’ that, given the technological
power implicit in established cybernetic principles, reinforces instrumentalist, solipsistic, and cynical modes of reasoning in the economically ‘ ‘advanced’ ’ nations. These effects, in turn, continue to precipitate ecological damage. In discussing more recent developments, the paper notes the possibilities for modes of cybernetics that could become operative at the site of our selfworld interface. At this level, it argues, our human ontology becomes more synonymous with our senses. This can also be shown by reminding ourselves of the crucial role of our ‘ ‘creative presence’ ’, in which a greater acknowledgement of anticipatory reasoning might inform an actative, flow-based grammar of cybernetics. It concludes that clocks need to be radically re-designed within terms that are in accord with (at least) secondorder cybernetics.
Pansystems mathematics: an analysis of panweighted field-network Xiaolong Wu, Dinghe Guo, Jinghong Pan and Xuemou Wu Keywords Cybernetics, Topology, Mathematics In this paper, we will introduce charm pansystems and provide mathematical models for panweighted field-network. Various mathematical models of pansystems will be discussed. Some traditional mathematical concepts such as topology space and rough sets theory will be analyzed within this framework.
On stochastic optimal control for stock price volatility Ying Yi-rong, Lin Yi and Wu Chong-feng Keywords Cybernetics, Risk, Stochastic modelling The dynamic measure of risk problem in incomplete market is discussed when stock appreciation rates are uncertain. Meanwhile, a related stochastic game problem is studied. The value of a stochastic optimal control is regarded as a reasonable measure of the risk. The form of the optimal objective is obtained by employing the tools of BSDE theory.
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Pansystems Guankong technology and information quantization Yu Hong-Yi, Leon (Xiangjun) Feng and Yu Ran Keywords Cybernetics, Systems theory A basic pansystems scientific view about the physical world is presented. The principle and methodology of pansystems GuanKong technology are introduced. Simple metrics for the quantization of information, risk and gain by comparison (GBC) are established and discussed, and the practical and simple membership function which realizes the transformation from qualitative to quantitative order are given, and an example showing the pansystems GuanKong in detail is also given. Randomization and eventual reordering: a number theoretic approach Barry Zeeberg Keywords Cybernetics, Computational methods Shuffling a deck of cards is normally used for randomization. An imperfect shuffle would not produce the desired randomization, since there would be residual correlation with the original order. On the other hand, from the classical card magic literature it is known that eight successive perfect riffle shuffles returns
the deck to the original order. The question addressed here is whether this observation is in fact unusual and surprising. Although a general closed-form analytical solution does not appear to be possible, a simple program could be written to determine deck sizes and numbers of shuffles for which eventual reordering occurs. This computational approach correctly predicts the original observation of eight shuffles for a deck of 52 cards; in fact if the trivial solutions of integral multiples of eight shuffles are discarded, eight shuffles appears to be the unique solution for a 52 card deck.
Data self-create in data storage system Zhou ke, Zhang Jiangling and Feng Dan Keywords Cybernetics, Data storage When the controller of storage system becomes more and more powerful, it sometimes creates new data and stores those data in system, just like parity information in RAID level 5 described by Chen and Lee (993). We call these phenomena data self-create. This paper provides a theory about data self-create which separates data self-create phenomena into 16 kinds. Three applications are introduced. From a pansystems (Wu XueMou, 1993) view, this paper also gives an explanation of data self-create.
Preface Special double issue: systems and cybernetics: new theories and applications – Part I Guest Editor: Yi Lin
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This Special Double Issue contains selected papers from the 12th International Congress of the World Organization of Systems and Cybernetics (WOSC) held jointly with the 4th Workshop of the International Institute of General Systems Studies (IIGSS). The Co-Chairs of the conference and workshop were Professor Robert Vallee´, the Director-General of WOSC, and Professor Yi Lin, the President of IIGSS. It is fitting that Kybernetes the officially chosen publication of WOSC should be invited to publish selected contributions and, in particular, the winners of the Kybernetes Research Award, which was sponsored by the journal’s publisher, Emerald. We are also pleased to include in this selection of contributions some of the papers that were ‘‘highly commended’’ by the judging panel for this award. We are grateful to Dr. Yi Lin for accepting our invitation to be the Guest Editor of this specially compiled collection of papers, that were presented at the congress and workshop. Some 59 papers have been selected, refereed and edited to present the new theories and applications in systems and cybernetics that have emerged from the presentations and discussions that contributed to the success of the endeavor. Reports of the congress and workshop have already appeared in Kybernetes Volume 31 Nos 7 and 8, 2002 together with full details of the awards presented. We are pleased, however, to include here a summary of the highlights of the occasion which in itself also serves to provide the scenario for the contributions that have been selected for publication. Professor Robert Vallee´ in his summarized report writes that: The 12th International Congress of Cybernetics and Systems of the WOSC and the 4th IIGSS Workshop were held, as a joint event, in Pittsburgh, Pensylvania, from 23 to 26 March, 2002 at Sheraton Station Square Hotel. The honorary chair was Professor Stafford Beer, President of WOSC, who unfortunately was not able to come, and the two Co-Chairs were Professor Yi Lin, President of IIGSS and Professor Robert Vallee´, Director-General of WOSC. Other officers of WOSC who could not come, despite their former intentions, were Professor J. Rose, Honorary Director and founder of WOSC and Professor Brian H. Rudall, Director of the Norbert Wiener Institute of WOSC. After the welcome reception, on Saturday evening, the Conference opened on Sunday morning by an address followed by a plenary lecture on Cybernetics and Systems from Past to Future by R. Vallee´. There were about 90 participants, coming from the Americas (mainly USA and also Colombia, Venezuela . . .), from Europe (UK, Switzerland, France, The Netherlands, Poland, Slovakia, Bulgaria, Romania . . .), from Russia, from the Far East (an important delegation from China . . .). The Symposia were devoted to: Systemic and Cybernetics Oriented Learning Experiences (Angela Espinosa), Reconstructability Analysis (Martin Zwick), Reconstructability, Instant Modeling and Data-Knowledge
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Analysis (Guangfu Shu), Creative Development and Processes, Systemic Approach to Health and Aging (Hector Sa belli), Control Theory and Engineering (Zdzislaw Bubnicki), Grey Systems : Theory and Applications ( Julong Deng, Sifeng Liu), Grey Systems : Methodology and Applications (Mian-Yu Chen), Pan Systems Theory and Technology (Leon Feng, Xuemou Wu), New Theories about Space-Time (Leon Feng), Systems-Specific Technology and Balascopy-Based General Systems Theory (Vadim I. Kvitash). On Sunday there were two other plenary lectures : The ‘‘Roundtable’’ for School Learning and Planning Groups : Planting a Seed for Systemic Renewal by Susan Farr Gabriele and ‘‘Reconstructability Analysis. An Overview’’ by Martin Zwick. On Monday the plenary lecture was about ‘‘The Bridge to Humanity’s Future’’ by Willard R. Fey and Ann C. W. Lam. The last plenary lecture was delivered on Tuesday by Vadim. I. Kvitash on ‘‘Relonics : Balascopy Based Systems-Specific Technology’’. On Monday an hour was devoted to the presentation of awards by the two representatives of WOSC : Robert Vallee´, Director General and Dr. Alex Andrew, Director for International Affairs. The first awards were two Honorary Fellowships of WOSC (already 37 such fellowships have been attributed). One for Professor Acad. Zdzislaw Bubnicki, Technical University of Wroclaw (Poland), for his renowned works on the theory of systems, the creation of the journal Systems Science and the organization of a long series of International congresses on systems held in Poland, UK and USA. The other Honorary Fellowship was given to Professor Yi Lin, Slippery Rock University (Pennsylvania), President and founder of IIGSS, for his excellent researches on systems science and the organization IIGSS Workshops. The four other awards were offered by Emerald, publishers of Kybernetes, WOSC official journal (Editor-in-Chief: Brian H. Rudall). The Kybernetes Research Award was presented to M. Nemiche and Rafael PlaLopez (Department of Applied Mathematics, Universitat de Vale`ncia, Spain) for their communication on ‘‘A Learning Model for the Dual Evolution of Human Social Behaviors’’. They will receive a check of £ 300 and a 1 year subscription to Kybernetes. The three Highly Commended Awards were given to: Willard R. Fey and Ann C. W. Lam for (Ecocosm Dynamics Ltd, USA) for ‘‘The Bridge to Humanity’s Future Test of Multimedia Address’’. Sifeng Liu (College of Economics and Management, Nanjing University of Aeronautics and Astronautics, China), Yi Lin (Mathematics Department, Slippery Rock University, Pennsylvania), Yaguo Dang and Bingjun Li (Institute of Management Science, Henan Agricultural University, China) for ‘‘The Technical Change and the Funds for Science and Technology’’, Gary P. Shaffer (Department of Biological Sciences, Saint Louis University, Louisiana) for ‘‘Simulating Ecosytem Dynamics by Isolating Events Comprised of only a Few Variables. Needs for a K-Systems Granulation Methodology’’. Proceedings containing the abstracts of the communications were distributed at the beginning of the Conference. Selected complete papers will be published in Kybernetes.
The convenors of the congress symposia are also engaged in preparing special features and issues for inclusion with our regular journal sections – for publication in the coming Volume 32. In particular the subjects of current interest in the systems and cybernetics fields: ‘‘Reconstructability Analysis’’ ‘‘Some New Theories about Space-Time’’ and ‘‘Grey Systems Theory, Methodology and Applications’’ are being scheduled as special issue topics in this volume. In addition, Volume 32 will also have a special double issue devoted to ‘‘Artificial Life’’ that will include contributions from some of the leading researchers in this field.
Part II of this specially selected collection of papers will be published in Kybernetes Vol. 32, Nos 5/6, 2003. The titles of these papers are listed in the contents pages and the abstracts are also included in this issue. The selected contributions collected here from the prestigious WOSC and IIGSS Congress and Workshop confirm the importance of the role of cybernetics and systems in both research and development worldwide by introducing new theories and applications that once again illustrate the essential interdisciplinary nature of our studies. Brian H. Rudall Editor-in-Chief
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Editorial Our Heartfelt Appreciation
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The 12th International World Organization of Systems and Cybernetics (WOSC) Congress and the 4th International Institute for General Systems Studies (IIGSS) Workshop, 24-26 March, 2002, co-chaired by Yi Lin (USA) and Robert Vallee´ (France), had been recorded in the scientific history as an important event with a great many new theories and discoveries presented. The event, held in Sheraton Station Square Hotel, Pittsburgh, and sponsored by the United Nations and the Encyclopedia of Life Support Systems, attracted over 150 scholars from 32 nations and regions around the globe, including, Belams, Brazil, Bulgaria, Canada, Colombia, Czeck Republic, Egypt, France, Hong Kong, Hungary, India, Iran, Israel, Italy, Japan, Kuwait, Latvia, Mongolia, People’s Republic of China, Poland, Romania, South Africa, Russia, Scotland, Slovakia, Spain, Switzerland, Taiwan, The Netherlands, United Kingdom, USA, Venezuela. Over 40 classical scientific areas were represented at the conference. These scientific areas include aerospace engineering, artificial intelligence, atmospheric physics, automation, biological science, business administration, communication, computer science, control and systems engineering, cybernetics, digital engineering, dynamics, earth science, economics, education, electric and computer engineering, electrical engineering, electronic physics, finance, geographical science, health and epidemiology, industrial design, industrial engineering, informatics, information systems, law, law and policies of organizations, management, mathematics (pure and applied), mechanical engineering, mechanics, medical technology, medicine, military science, planetary science, physiology, political science, public administration, regional economic planning, sociology, statistics (mathematical and applied), systems science and theoretical physics. Participants of the joint event consisted mainly of scholars from academia, administrations of higher education and research institutions. Also, some government officers, bankers, scientific practitioners in industry participated in the three-day event. Thanks go to Professor Brian Rudall, the editor-in-chief of ‘‘Kybernetes: The International Journal of Systems and Cybernetics’’, and the entire editorial board of the journal, for inviting us to publish selected papers of the joint Conference as two double issues of this internationally prestigious publication. It is our hope that with these special issues in print, we can help to raise the more than half century old systems movement to a higher level by introducing
the bold challenges facing the traditional science and our new theories and methodologies to overcome some of the weaknesses existing in the traditional science. Yi Lin Guest Editor President and Director International Institute for General Systems Studies 23 Kings Lane, Grove City PA 16127, USA E-mail: jeffrey:
[email protected]
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Creative idea generation via interpretative approach to analogical reasoning Kambiz Badie Info Society Group, Iran Telecom Research Center Keywords Cybernetics, Reasoning Abstract To add the flavor of creativity to analogical reasoning, an intermediate space has been proposed to be included between source and target, so that the inputs in the source can be interpreted in terms of some navigating concepts in this layer for further reinterpretation in the target space. In this paper, as the extension of this approach, interpretation schemes have been addressed emphasizing on the co-working of interpretation and reinterpretation mechanisms for idea generation with respect to different types of situations in the source. Within this respect, hypothesis generation in the scientific domains, has been emphasized as a tangible application of an interpretative approach to interdomain analogical reasoning. As the final remarks, the proposed approach has been compared with both the classical approach to analogical reasoning and the related works as well.
The basic view Classical approach to analogy is not sufficiently capable of suggesting a framework for creativity, mainly due to the following reasons. (a) Creativity seems to be based on a sort of divergent thinking within which numerous alternatives are to be generated in the target space, whereas, in case of classical analogy, due to the monologue nature of structure mapping between the source and the target, such an objective seems to be hardly achievable. (b) Creativity is a sort of clue-oriented process, within which new ideas are to be generated based on some clues from a previously structured relevant source(s), however, classical analogy restricts itself to a predefined concept of similarity between the source and the target. In other words, in case of classical analogy, source has been assumed to be similar to the target in a predefined manner. (c) In classical analogy, purpose of analogy is almost explicitly defined, whereas creative issues are not directly concerned with an explicit involvement of purpose. Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1210-1219. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443428
For a detailed discussion on limitation of creativity in the classical analogy (predictive analogy) with predefined ontology of similarity between source and target see Indurkhya (1992). To add the flavor of creativity to analogical
reasoning, an intermediate space was proposed to be included between source and target, so that the inputs in the source can be interpreted in terms of some navigating concepts in this layer for further reinterpretation in the target space (Badie and Hejazi, 2001). This yields the possibility of producing numerous alternatives as the final ideas. Moreover, the co-working of the two interpretation and reinterpretation actions, one from the source into the intermediate space and the other from the intermediate space into the target space, eliminates the urgency for depending on inherent similarity between the source and the target. Within the above discourse, it was found out that interpretation schemes can play a central role in making the analogical reasoning tend to creative idea generation. Obviously, the more sophisticated an interpretation scheme, the more creative the final ideas are expected to be.
Some related works An integrated analogy model for creative reasoning Within the framework of this model, creativity is interpreted as the search for some source analogue with which to reinterpret a given target domain. A prime benefit of observing integration in analogy is due to the fact that focusing on an individual stage in it eliminates the influence of interactions between stages. Furthermore, indirect interactions between non-sequential stages may not be identified by the constrained models such as the requirements placed up on retrieval by the validation process. The computational model of creative reasoning proposed by O’Donoghue (1997) is a three - stage process, where the validation phase is divided into two; the first part validates the structure of the transferred knowledge, and the second half requires domain specific expert reasoning within the target domain using the transferred knowledge. We can see that, the creativity within the framework of this model is a timeconsuming process, requiring much iteration through the filtering mechanism outlined in the model. The output of any iteration is some new interpretation of the problem domain, but may prove to be one with no discernible advantage over previous interpretations. However, such apparently fruitless interpretation may ultimately prove useful by providing the inspiration for a further retrieval episode, which delivers an all-encompassing explanation (O’Donoghue, 1997).
Conceptual integration network Within the framework of this network, traditional spaces associated with analogical or metaphoric mapping, the source and the target, combine via some structural mapping to produce another independent blended space that provides the local point for the resultant integration (Fauconnier and Turner,
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1998a). The basic peculiarity of this model is the use of an additional distinct coordinating space, known as generic space. This space contains the low-level conceptual structures that serve to mediate between the contents of the input spaces, thus enabling them to be structurally reconciled. Structural reconciliation involves mapping the conceptual structure of one input space onto another so as to ascertain a coherent alignment of elements from each. For instance, in the example of “love as a great teacher”, the generic space provides low-level structures that are relevant to the process of personification, and which serve to mediate between the input space of a psychological concept “love”, and a physical concept “teacher”.
Interpretation schemes To step toward potential interpretation schemes, the concepts in the intermediate space should be selected as generic as possible and should be able to show the major mental modes the reasoner may exhibit within the reasoning process. These mental modes include all categories with respect to human perception of the surrounding environment as well as emotions and ethics, whose significance has been clarified within the frame of reasoner’s phenomenological experiences. With respect to this, a variety of rules are required to illustrate how co-existence of some lower-level (concrete) concepts can be interpreted in terms of higher-level (abstract) concepts that are significant to the reasoner. With respect to interpretation schemes, defaults rules which are the products of experience (and may also be derived analytically using a meta-domain theory) can take the responsibility of mapping the concepts in the source, onto some concepts which are ready to be translated into abstract concepts in the intermediate space. For instance, in the case where a statement is raised by a person saying “I don’t want to swim”, and this statement is faced by another statement saying “Why don’t you take your swimming pants then?”, a strange situation will eventually come out, whose manifestation in the reasoner (the person listening to all these statements)’s mind would be in terms of emergence of the navigating concept of “strangeness”. It is this navigating concept that can later be reinterpreted in terms of new concepts in the target, based upon reasoner’s previous experiences as well as his/her very tendency in performing analogy (Figure 1). An interesting aspect in interpreting a situation into the abstract concepts in the intermediate space is the very possibility/freedom each emerged concept can hold with respect to a subsequent reinterpretation in the target space. For instance, in an earlier example, the concepts “not liking to do an action” and “calling for the tool for that action”, and the concept “strangeness” that is a higher – level concept emerged as a result of “aggregation” of these two concepts, can be subject to reinterpretation based on the urgency and
Creative idea to analogical reasoning 1213
Figure 1. An example showing the emergence of the two navigating concepts “strangeness” and “silliness”
significance the reasoner has toward them in his/her mind. Let us say, if the reasoner is particularly alert and conscious toward the concept of “strangeness” with no particular emphasis on how it has been emerged, that would be the navigating concept “strangeness”, which will later be reinterpreted into some new concepts in the target space, with no particular emphasis on the conjunction of “not liking to do an action” and “calling for the tool for that action” as its causality. For instance, the reasoner may finally end up with a situation where “some body is doing an obvious favor to another person”, however “the other person tries to act in a way as if he/she has done some thing insulting to him/her”. It is seen that, in this example, the etiology for strangeness with respect to the target domain has no relevance with those respecting the source. One reason that different people may show different reactions in interpreting a similar situation may be the difference that they do have in the way they are
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Figure 2. Co-working of interpretation and reinterpretation for generating new ideas in the target space
conscious / alert toward the navigating concepts emerged within the process of analogical reasoning. Figure 2 demonstrates the different formats for co-working of interpretation and reinterpretation for generating new ideas in the target space. As it is seen from the figure, the first format is the same as structure mapping (Gentner, 1983), which is based on a simple carry over of basic structure, with no emphasis on numerousness of the ideas in the target space. Within this format, search is done among a number of predefined concepts in the target in order to find those concepts whose relational structures are the same as those in the source. The second format has something to say more than structure mapping, and is benefited by a deep knowledge to generate relatively creative concepts in the target through reinterpreting the navigating concepts related to the major concepts in the source.
The third format, which is the most creative in comparison with the first and the second formats, is benefited by a deep knowledge to generate creative concepts through reinterpreting the navigating concepts related to both the major concepts and their relational structures in the source.
Creative idea to analogical reasoning 1215
Types of situation and its influence on analogical reasoning Distinction should be made between situations with declarative and implicational descriptions. Transferring knowledge from source to the target can therefore be performed in four possible manners, out of which three manners have been explained as follows. (1) From “declarative situation” to “declarative situation” . . . In this case, the navigating concepts already produced in the intermediate space, are reinterpreted into appropriate concepts in the target space, through implementing reinterpretation to both the major concepts and the concepts on relational structures, in such a way that the resulted idea can be consistent with respect to the target domain. In the example of Figure 1, within which the two statements are in counter position with each other leading to emergence of the concept “strangeness” in the intermediate space, both action and tool illustrated in the figure can be reinterpreted into appropriate concepts in the target domain. For instance, if the reasoner is interested in the domain of eating foods, an idea coming to mind through listening to this example would be a situation within which somebody says “today I am not interested in eating grilled meat” but his/her statement is followed by another statement saying “why don’t you bring your favorite tartar sauce with you then?”, which is quite odd and strange respecting the first statement. Other ideas may be created in the reasoner’s mind based on the type of the domain which is particularly significant for them at a certain stage of time. (2) From “implicational situation” to “implicational situation”. . .. In this case, relational structures concretely used in describing a situation are supposed to be interpretation – free, and only the major concepts are subject to interpretation in the intermediate space. Obviously, relations are kept intact, when the navigating concepts are reinterpreted into appropriate concepts in the target space. As an example, suppose that we have the following statement: “If you listen to the music with a high volume, your ears will get painful, and if you listen to the music with low volume, you will not be able to hear the music.”
The above statement can be reinterpreted into an appropriate form, for instance in the domain of eating, in the following way.
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“If you eat too much, you will have stomach pain, and if you don’t eat enough you still will feel hungry.”
In an earlier example, relational structures “high”, “painful”, “low”, and “not being able”, which have been used in describing the source situation, are semantically preserved in the structure of the final idea produced in the target space, only with the difference that their syntax is somehow subject to modification based on the aesthetics required for describing the idea in the target space. (3) From “declarative situation” to “implicational situation”. . .. This is the case a scientist or a researcher is faced, when formulating a hypothetical model with respect to a specific target, based on environmental facts, is taken into account. Another interesting aspect in interpretative analogical reasoning is the very hierarchy in describing a source situation that in turn calls for an inherent hierarchy in deriving the navigating concepts in the intermediate space. Going back to the example of Figure 1, suppose that the situation in the source gets little complicated in the sense that a listener or an observer is added to it, listening to the situation at which “not liking to swim” is associated with a back-comment “calling for swimming pants”. Suppose that the listener does not show any particular reaction against this situation, which according to interpretation has been shown to be strange. Here, from the view point of an external reasoner, such a new situation may be interpreted into a new navigating concept in the intermediate space that is “silliness”. As is seen from the figure, the aggregation of the concepts “strangeness” and “not showing any particular reaction” leads to emergence of the concept “silliness” at a higher level of hierarchy. It is to be noted that, the more the interpretation depth, the more sophisticated the creativity for performing the interpretation in a meaningful manner is expected to be. Obviously, the interpretative analogical reasoning performed with a higher depth in interpretation, is as well more creative.
Hypothesis generation as an application for interpretative analogical reasoning Hypothesis generation based on an inter-domain analogical reasoning is an issue that helps realize the significance of applying interpretative analogy to well-established scientific domains to produce hypotheses in these domains. In this respect it is both crucial and delicate to describe a new domain in a way such that abstract concepts can be reinterpreted in terms of some concrete concepts in that domain. In other words, a domain should essentially include an ability, based on which the navigating concepts shown up through the process of interpreting the concepts in the source domain, can be translated into
passible concepts in it. As an example, consider the case of producing new hypotheses in the domain of “sociology”, based on transferring possible knowledge in the domain of “physics”. The most important issue within this respect is to see first what are the abstract concepts in the space intermediating “physics” and “sociology”, that can be equally significant to both of them. It is under such a condition that the events in the domain of “physics” can be interpreted into some abstract concepts that can later be reinterpreted into new hypotheses in the domain of “sociology”. Examples can be mentioned for the physical laws like “the pressure applied to liquid is equally transferred to all its parts” and “gas has the tendency to be diffused inside the vacuum”, which can respectively lead to final ideas “the pressure applied to a community with uniform characteristics is equally transferred to all its members” and “ an idea has the tendency to be diffused (or propagated) inside a vacuum community (a community within which no remarkable idea is governing)”. With respect to the first example, the major concept “liquid” in the source is first interpreted into the navigating concept “group of members with uniform characteristics” and is then reinterpreted into the concept “community with uniform characteristics in the target”, while regarding the second example, the concept “gas” in the source is first interpreted into the navigating concept “fluid entity” and is finally reinterpreted into the concept “idea” in the target. The emergence of the ideas in this way, can subsequently help the researcher in sociology develop sophisticated postulates in his/her field based on possible contexts.
Comparing with the classical approach to analogical reasoning In comparison with the classical approach to analogical reasoning, the interpretative approach is benefited by the following characteristics. .
Co-working of interpretation and reinterpretation, instead of a simple monologue between source and target, provides a chance for generating some new ideas (or hypotheses) in the target space, in the cases where no explicit similarity has been presupposed between the two. In this manner, interpreting the content of the source within the context of the target is taken into consideration, instead of a direct knowledge transference from the source to the target.
.
One does not need to be conscious toward a specific purpose for transferring the knowledge to the target. Instead the thing important is to be conscious toward the total domain within which new ideas are expected to be generated based on some clues from the source.
.
No predefined correspondence is necessary to exist between the concepts in the source and those in the target. Instead, that is the co-working of
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the two interpretation and reinterpretation actions which decides on the status of correspondence for both the major concepts and their relational structures at the two spaces. Within this context, non causal relational structures are open to carry over, to provide the possibility of generating helpful hypotheses in the target space.
1218 Comparing the proposed approach with the related works Comparing with the integrated model of analogy, no effort is done to search for the appropriate source, it has rather been assumed that the objective of analogical reasoning in our approach is to make a creative use of whatever which has been offered as a source. In fact it is due to the very flexibility in the interpretation processes that the possibility of creative generation of ideas increases. Also no effort is done to explain anomalies in the target interpretation. As a conclusion, in contrast with the integrated model of analogy whose objective is to select appropriate source(s) via many iterations through the related filtering mechanism, the proposed approach has the ability to compensate for the probable deficiencies in a given source via the interpretation mechanisms, respectively from the given source to the intermediate space, and oppositely from the intermediate space to the target. It is due to these interpretation mechanisms that the total analogical reasoning can exhibit more creative behavior. Comparing the proposed approach with concept integration and blending, one can claim that the proposed approach can be viewed as a particular version of concept integration wherein the acting generic space includes a number of highly abstract concepts that simultaneously dominate the concepts both in the source and the target space. However, no explicit blending occurs, since the intermediate space in our approach is responsible for one – way transference of the source concepts to the target space whereas in case of blending, both source and target are simultaneously fed into the blending mode under coordination of the generic space. Regarding this, we observe that the main role of intermediate space is converting the concepts in the source, while generic space is in charge of coordinating the very interaction, which is essential to blending process. In this sense, it seems that the two interpretational actions – one from the source to the intermediate space, and the other from the intermediate space to the target – can compensate for the deficiency which may come about due to lack of coordination in these interactions. References Badie, K. and Hejazi M. (2001), “Creative idea generation via passing through an intermediate space between the source and the target”, Proceedings of the Workshop Program at the Fourth International Conference on Case-Based Reasoning, Vancouver, Canada, pp. 125-8.
Fauconnier, G. and Turner, M. (1998a), “Conceptual integration networks”, Cognitive Science, Vol. 22 No. 2, pp. 133-87. Fauconnier, G., and Turner, M. (1998b), “Conceptual integration networks”, in Jean-Piere Koenig (Ed.), Discourse and Cognition, Center for the Study of Language and Information(CSLI), Stanford, pp. 269-83. Gentner, D. (1983), “Structure mapping: A theoretical framework for analogy”, Cognitive Science, Vol. 7 No. 2, pp. 155-70. Indurkhya, B. 1992. “Predictive analogy and cognition”, Analogical and Inductive Inference, AII’92, Lecture Notes in Artificial Intelligence, Springer-Verlag, pp. 214-31. O’Donoghue, D. 1997. “Towards a computational model of creative reasoning”, Proceedings of the Conference on Computational Models of Creative Cognition, 30 June-2 July, Dublin, Ireland.
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The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/0368-492X.htm
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CLCR optimal input design for IS and IU plants Cs. Ba´nya´sz and L. Keviczky Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Kende u, Hungary Keywords Cybernetics, Design Abstract The paper deals with the optimal reference signal excitation for closed-loop-controlrelevant (CLCR ) identification for inverse stable (IS) and inverse unstable (IU) processes. For the IS case the optimal excitation depends only on the performance design goal, however, for the IU case it depends on the invariant factors of the plant, so only learning algorithms can be applied.
Introduction The authors introduced a special scheme (Keviczky, 1995), which proved to be good to handle combined identification and control problems (Keviczky and Ba´nya´sz, 1999a). The scheme (which was later named as a generic two-degree of freedom (G2DF ) system) is based on a special Keviczky-Ba´nya´sz- (or shortly K-B- ) parametrization, shown in Figure 1 for exact model matching. Here S [ S and R are the process and regulator, respectively, where S is the closed set of all stable proper real-rational systems, having all poles within the closed unit disc. In this study we will not deal with open-loop unstable plants and it is reasonable, but not necessary, to assume that Sðv ¼ 1Þ ¼ 0: A G2DF control system is shown in Figure 2 for exact model matching, where yr, u, y and w are the reference, process input, output and disturbance signals, respectively. Here the former r is an internal signal. S is the process and M the model of the process. Assume that the process and its model are factorizable as S ¼ S þ S 2 z 2d ¼
Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1220-1235. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443437
B 2d z ; A
M ¼ M þ M 2 z 2dm ¼
B^ 2dm z ^ A
ð1Þ
where S+ and M+ mean the inverse stable (IS ), S 2 and M 2 the inverse unstable (IU ) factors, respectively. z 2 d and z 2 dm correspond to discrete time delays, which are the integer multiple of the sampling time, usually z 2d ¼ z 2dm is assumed. (To get a unique factorization it is reasonable to ensure that S 2 and M 2 are monic, i.e. S 2 ð1Þ ¼ M 2 ð1Þ ¼ 1; having unity gain.) It is important that the inverse of the term z 2 d is not realizable, because it would mean an ideal This work was supported by the Hungarian NSF (OTKA).
predictor z d. These assumptions mean that S 2 ¼ S 2 z 2d and M 2 ¼ M 2 z 2dm are uncancelable invariant factors for any design procedure. The optimal all realisable stabilizing (ARS ) regulator (Maciejowski, 1989) of the G2DF scheme (Keviczky and Ba´nya´sz, 1999b) is given by Ropt ¼ Ro ¼
P w Gw S 21 P wK w Qo þ ¼ ¼ 1 2 P w K w S 1 2 Qo S 1 2 P w Gw S 2 z 2d
ð2Þ
Qo ¼ Qw ¼ P w K w ¼ P w Gw S 21 þ
ð3Þ
Optimal design for IS and IU plants 1221
where
is the associated Youla-parameter (Keviczky and Ba´nya´sz, 1999b; Maciejowski, 1989), furthermore Qr ¼ P r K r ¼ P r Gr S 21 þ ;
K w ¼ Gw S 21 þ ;
K r ¼ Gr S 21 þ
ð4Þ
It was shown (Keviczky and Ba´nya´sz, 1999a, b) that the optimization of the G2DF scheme can be performed in H2 and H1 norm spaces by the proper selection of the serial Kr and embedded Kw filters (compensators). These optimizations will be reduced to the optimal computation of the Gr and Gw filters. If Gr and Gw are optimally selected, then Ropt denotes the optimal ARS regulator of equation 2. It is interesting to see how the transfer characteristics of this system looks like: y ¼ P r Gr S 2 z 2d yr 2 ð1 2 P w Gw S 2 z 2d Þw ¼ yt þ yd
ð5Þ
where yt is the tracking (servo) and yd is the regulating (or disturbance rejection) independent behaviors of the closed-loop response, respectively. Here Pr and Pw are stable and proper transfer functions, which are partly capable to place desired poles in the servo and the regulatory transfer functions,
Figure 1. A K-B-parametrized 2DF system with noise model
Figure 2. The generic 2DF control system
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furthermore they are usually referred as reference signal and output disturbance predictors. We will see that they can even be called as reference models, so reasonably P r ðv ¼ 0Þ ¼ 1 and P w ðv ¼ 0Þ ¼ 1 are selected. While Ro is the true theoretically existing but unknown ARS regulator, generally the regulator R^ o is designed on the basis of a nominal model M of the true process S. Consider the practical form of R^ o (using M in equation 2) of the G2DF system ^o P w G^ w M 21 Q þ R^ o ¼ ¼ ð6Þ ^ oM 1 2 P w G^ w M 2 z 2d 1 2 Q where ^ o ¼ P w G^ w M 21 Q þ
ð7Þ
is the nominal Y-parameter depending on the model of the plant, which gives ^ back (equation 3) as Qo ¼ P w Gw S 21 þ ¼ Qo jM ¼S : The dependence on the inverse stable part is direct and visible, however, Gw generally depends on the inverse unstable part. The G^ r and G^ w notations denote the model based version of Gr and Gw. (One can use the same notations for the Kr and Kw, denoting the K^ r and K^ w compensators in a similar way.) Figure 3 using the G2DF structure shows an obvious way of how to perform the ID step in a combined ID and control scheme (Keviczky, 1995), i.e. a regular ID algorithm between the auxiliary variable u~^ and the measured controlled variable y should be used. Note that u~^ and y must be obtained from the closedloop operated by the generic optimal controller structure with the optimal regulator R^ and compensator K^ r (which is now also model based). Because u~^ depends on the model M, only an iterative control refinement procedure can be performed. (The sub- and superscripts i 2 1 refer to the apriori state of knowledge at the i-th step in an iterative procedure.)
Figure 3. Model based version of the G2DF scheme for iterative controller refinement
Optimal design for IS and IU plants
Error properties Introduce the additive and relative model errors D ¼ S 2 M;
‘¼
D S2M ¼ M M
ð8Þ
One could see in Figure 3, that the model based version of the K-B-parametrized G2DF scheme is a special system for the combined ID and control paradigm, because the control and modeling errors are identical. This common error is P r G^ r M 2 z 2d ‘ 1 2~e ¼ 1~ ¼ y 2 y~^ ¼ w yr þ ^ ^ 1 þ RS 1 þ RS
1223
ð9Þ
The related uncertainty model is shown in Figure 4. Straightforward calculations give the following equivalent form of the common error 1~ 1~ ¼
G^ r M 2 ‘ G^ w M 2 ‘ P r yr 2 P w w þ ð1 2 P w G^ w M 2 Þw ^ ^ |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} 1 þ RS 1 þ RS |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} 1~o 1~r 1~w
ð10Þ
Here 1~r and 1~w are the contributions of yr and w to the error 1; ~ furthermore 1~o is the remaining uncompensable error (in case of ideal process model matching: ‘ ¼ 0). Because generally Pw is also not ideal, it is only an estimate of the true (or optimal) P ow predictor, the above formula can be further rewritten as 1~ ¼
G~ r M 2 ‘ G~ w M 2 ‘ P r yr 2 P w w þ ‘w G~ w M 2 P w w þ ð1 2 P ow G~ w M 2 Þw ð11Þ ~ ~ |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} 1 þ RS 1 þ RS |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} 1~DP w 1~oo 1~r 1~w
Figure 4. The uncertainty model of a K-B-parametrized G2DF system
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Here 1~DP w occurred due to the non ideal predictor Pw and 1~oo is the theoretical residual error (when both ‘ ¼ 0 and ‘w ¼ 0), where P ow 2 P w Dw ¼ Pw Pw
ð12Þ
1~r ¼
M 2‘ G^ r M 2 ‘ P r yr ¼ y^ ^ ^ r 1 þ RS 1 þ RS
ð13Þ
1~w ¼
M 2‘ G^ w M 2 ‘ P ww ¼ w^ ^ ^ 1 þ RS 1 þ RS
ð14Þ
‘w ¼
1224
1~oo ¼ ð1 2 P ow G^ w M 2 Þw
ð15Þ
are introduced, furthermore y^ r ¼ P r G^ r yr
w^ ¼ P w G^ w w
ð16Þ
are filtered predicted variables based on the Pr and Pw reference models. Finally M 2‘ ^ þ 1~DP w þ 1~oo ðy^ r 2 wÞ ~ 1 þ RS
ð17Þ
1~DP w ¼ G^ w M 2 ‘w P w w ¼ M 2 ‘w w^
ð18Þ
1~ ¼ is obtained, where
CLCR optimal input design The formal description of the procedure how to combine modeling and control if the ID is performed in a closed-loop experiment is very simple: ^ yr ; DÞ ¼ M c* ðM; yr ; SÞ M * ¼ arg min J ic ð1^c Þ ¼ arg min J ic ðM ; R; M [M
M [M
ð19Þ
where the identification criterion J ic ð1^c Þ is now the function of the closed-loop ID error 1^c ; and the regulator is designed by equation (6). (It is possible to form many other different combined schemes depending on the structure of the optimal control and the combination of the sequential identification and control steps (Ljung, 1987).) In the framework of the G2DF controller scheme, because the control and identification errors are identical, the most obvious way to realize an optimal
closed-loop-control-relevant (CLCR ) identification (Ljung, 1987) procedure is the following: .
maximize a proper measure of the identification (prediction) error by an input design algorithm optimizing the external excitation reference signal yr
.
minimize the identification error by an appropriate parameter estimation method, obtaining the best model.
The optimal input design procedure (Goodwin and Payne, 1977) should be performed in the iterative control refinement procedure. In this procedure the external excitation to be designed is the y r reference signal series, while the actual input signal is the auxiliary signal u^~ series in the modeling step. The formal calculation of y r to increase the robustness of the CLCR identification by determining an optimal input excitation is sometimes called “optimal input design” (OID ). So in this procedure, (equation 19) has to be reformulated by the following extension: M CLCR ¼ arg min sup J ic ð1Þ ~ M [M yr [U
ð20Þ
where U is the (mostly amplitude: U : jyr j # 1) constrained input signal domain. This general task is very difficult to solve in the original form. Therefore it is interesting to further analyze the error 1~ ¼ 2~e in (equation 9). It is easy to see that 1~r and 1~w represent the systematic model errors, contributed by yr and w, respectively: however, only 1~r can be influenced externally through yr 1~r ¼ ‘
Gr M 2 ~ 1 yr P r yr ¼ ‘H~ 1 Gr M 2 P r yr ¼ ‘W ^ 1 þ RS
ð21Þ
where H~ 1 is H~ 1 ¼
1 ^ 1 þ RS
¼
1 2 P w Gw M 2 1 þ P w Gw M 2 ‘
ð22Þ
and ~ 1 ¼ Gr M 2 P r ¼ H~ 1 Gr M 2 P r ¼ 1 2 P w Gw M 2 Gr M 2 P r W ^ 1 þ P w Gw M 2 ‘ 1 þ RS ~ 1 ð‘; P r ; P w ; Gr ; Gw ; M 2 Þ ¼W ~ 1 for ‘ ! 0 is The limit value of W
ð23Þ
Optimal design for IS and IU plants 1225
Gr M 2 ~ P r ¼ ð1 2 P w Gw S 2 ÞP r Gr S 2 W1 ð‘ ¼ 0Þ ¼ ^ 1 þ RS ‘¼0
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¼ W 1 ðP r ; P w ; Gr ; Gw ; S 2 Þ ¼ W 1
ð24Þ
1226 p of (equation 20) can be It is easy to see that an approximate solution M s obtained by
M CLCR ¼ arg min sup k1k ~ ¼ arg min k1k ~ M [M yr [U
M [M
yr ¼arg supk1~r k
< M sp
yr [U
~ 1 yr k ¼ arg min sup k1~r k ¼ arg min sup k‘W M [M yr [U
M [M yr [U
ð25Þ
where the applied norm is not specified yet. So the optimal CLCR identification procedure can be formulated quite generally by ~ 1 yr k M sp ¼ arg min sup k1~r k ¼ arg min sup k‘W M [M yr [U
M [M yr [U
ð26Þ
An usual simple solution of such minimax problems is to find certain visible ~1 separability, if there are any. Thus (equation 26) can be further simplified, if W is independent of ‘, then
M
s p
~ 1 yr k ¼ arg min ‘ supkH~ 1 Gr M 2 P r yr k ¼ arg min ‘ supkW M [M yr [U M [M yr [U ( ¼ arg
!) min k‘k sup kH~ 1 Gr M 2 P r yr k
M [M
yr [U
¼ arg min k‘k M [M
yr ¼arg
sup kH~ 1 Gr M 2 P r yr k
yr [U
so the OID is obtained from the supremum problem
ð27Þ
p ~ ~ ys r ¼ arg sup kW1 yr k ¼ arg sup kH1 Gr M 2 P r yr k yr [U
ð28Þ
yr [U
Optimal design for IS and IU plants
and the optimal model is obtained by minimizing k‘k:
1227 OID for IS processes For IS processes, when Gw M 2 ¼ 1 and Gr M 2 ¼ 1 H~ 1; IS ¼
1 ^ 1 þ RS
¼
1 2 Pw 1 þ P w‘
ð29Þ
and ~ 1; IS ¼ 1 2 P w P r W 1 þ P w‘
ð30Þ
The first difficulty in (equation 27) is that H~ 1 ¼ H~ 1; IS now depends on ‘, i.e. on the true process S, which is the well known “catch-22” problem of OID for dynamic systems, when the optimal input depends on the process itself to be identified. In this case, when our ultimate goal is to find optimal CLCR identification this problem can be overcome, because assuming that the iterative refinement converges, H~ 1; IS can be substituted by H 1; IS ¼ H~ 1; IS ð‘ ¼ ~ 1; IS by W 1; IS ¼ W ~ 1; IS ð‘ ¼ 0Þ: It is interesting to observe that for IS 0Þ and W processes W 1; IS ¼ ð1 2 P w ÞP r and can completely be calculated from our design requirements Pw and Pr. This fact, anyway means that a CLCR optimal p exciting reference signal ys r for IS processes can be generated a priori in the knowledge of the design requirements. Because W1, IS is now independent of ‘ the approximate optimal solution M sp also equals to the true MCLCR one and the separability condition required for (equation 20) is fulfilled. OID for IU processes The previous statements, however, are not valid for the general IU processes, where H 1 ¼ H 1; IU and W 1 ¼ W 1; IU still depend on the invariant factor S2 of the plant and the serial filters Gr and Gw obtained from the optimization, so only an iterative “learning” procedure can be applied. The best way is to use the available last (best) model Mi in an iterative scheme. Applying this principle an ˜ 1 should be applied instead of the true H1 one, where estimate H H~ 1 ¼ 1 2 P w Gw M 2 ø H 1 ¼ H 1; IU ¼ H~ 1; IU ð‘ ¼ 0Þ ¼ 1 2 P w Gw S 2 can be used giving the approximate
ð31Þ
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~ 1 ¼ H~ 1 P r Gr M 2 ¼ ð1 2 P w Gw M 2 ÞP r Gr M 2 ø W 1 ¼ W 1; IU W ~ 1; IS ð‘ ¼ 0Þ ¼ ð1 2 P w Gw S 2 ÞP r Gr S 2 ¼W
1228
ð32Þ
Thus for the i-th iteration ~ i yr k ¼ arg sup kð1 2 P w G i M i ÞP r G i M i yr k yriþ1 ¼ arg sup kW w 2 r 2 yr [U
ð33Þ
yr [U
On the basis of (equation 33) the OID task obtained is to maximize a proper norm of the auxiliary signal ~ r ¼ ð1 2 P w Gw M 2 z 2dm ÞP r Gr M 2 z 2dm yr v ¼ Wy ¼
~ 21 Þ g0 þ Gðz z 2dm yr ~ 21 Þ 1 þ Dðz
ð34Þ
where the same notation is used for M as in equation (1). Equation (34) can be rewritten in a linear-in-the-parameters form as ~ 21 Þyr ðk 2 1Þ þ Dðz ~ 21 Þvðk þ dm 2 1Þ vðk þ dm Þ ¼ g 0 yr ðkÞ þ Gðz ð35Þ T
¼ g 0 yr ðkÞ þ g ðk 2 1Þq ¼ g0 yr ðkÞ þ b wherez g ðk 2 1Þ ¼ ½yr ðk 2 1Þ; yr ðk 2 2Þ; . . .; 2vðk þ d m 2 1Þ; ð36Þ 2 vðk þ d m 2 2Þ; . . .T q ¼ ½ g0 ; g1 ; . . .; d1 ; d2 ; . . .T and the length of these vectors depend on the orders of the polynomials in Pr, Pw, Gr, Gw, M 2 and on dm. Selecting the ‘2-norms for the signals yr and v, one looks for an energy-constrained reference signal first. Assume that {yr } [ ‘2 ~ is stable, i.e. W ~ [ H1 : This implies that {v} [ ‘2 ; too and kvk‘ # and W 2 ~ ~ 1 is the H1-norm of W: ~ So a kWk1 kyr k‘2 ; where the induced ‘2-norm kWk simple “local” strategy can now be obtained to generate a locally optimal p sequence { ys r } using the criterion
p vðk þ d m Þ ¼ arg sup jvðk þ dm Þj2 ys r ðkÞ ¼ arg sup ‘ 2
k yr k‘2 ¼1
jyr j2 #1
ð37Þ
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k ¼1; 2; . . .; n
1229
Since yr(k ) and vðk þ d m Þ are scalars, the above problem reduces to p ys r ðkÞ ¼ arg sup jvðk þ d m Þj
k ¼ 1; 2; . . .; n
ð38Þ
* g T ðk 2 1Þq ¼ 2sign yr ¼ 2sign 2 g0
ð39Þ
jyr j#1
The solution gives p ys r ðkÞ
(see Figure 5 for an illustration). Finally, the optimal input generating step in the iterative refinement is T i yiþ1 k ¼ 1; . . .; n ð40Þ r ðkÞ ¼ signðg 0 Þ sign g i ðk 2 1Þq i It is interesting to observe that the obtained optimal CLCR input generating strategy is very similar to the open-loop strategy introduced by the authors (Keviczky and Ba´nya´sz, 1973; Keviczky, 1975), i.e. in case of amplitude constraint the optimal input generated by the location of the minimum of a parabola, is calculated from a prediction model. However, the generating filters are completely different. Note that one can find a much simpler and perhaps more convincing derivation for the above input generating strategy by using the powers of the signals v and yr. (Do not forget that “power” rather than “energy” is required for the consistent parameter estimation.) It is well known that the “transfer” relationship between these powers is
Figure 5. Derivation of the optimal input generating strategy
~ powðyr Þ powðvÞ # W 1
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ð41Þ
and it is easy to obtain
1230
~ yr ¼ W ~ ~ sup{powðyr Þ} ¼ W sup{powðvÞ} ¼ W 1 1 1 1
ð42Þ
under the amplitude constraint jyr j # 1; when kyr k1 ¼ kyr k‘1 ¼ 1: So the locally optimal generating law (equation 40) maximizes the instantaneous increment of the power (variance) of v. That is, the worst-case CLCR input design procedure forms a maximum variance strategy. This is a very interesting result, and shows the special dialectics of identification and ˜ for control. It is also interesting to see that the input generating function W M ¼ S is ~ jM ¼S ¼ W ¼ gðY Þ ¼ Y =ð1 þ Y Þ2 ¼ H~ 2 jM ¼S W
Y ¼ RS
ð43Þ
which means that the input design at the generic scheme concentrates the input excitation around the crossover frequency vc , where jY j ¼ 1 and jW ð jvÞj ¼ jg ðY Þj is maximal. The adaptive control refinement procedure described earlier corresponds to the classical adaptive dual-control strategy where one parameter estimation step is followed by an optimal regulator computation step. The other calculations are to compute the auxiliary input u~^ðkÞ specific for the generic scheme and the actual input u~ ðkÞ to the process. In order to extend the adaptive dual-control procedure by the reference signal optimization step, this can be performed by ~ r ; P w ; G k ; G k ; M k Þyr ðkÞ vðkÞ ¼ WðP r w 2
ð44Þ
g ðk 2 1Þ ¼ ½ yr ðk 2 1Þ; yr ðk 2 2Þ; . . .; 2vðk þ d m 2 1Þ; ð45Þ 2 vðk þ d m 2 2Þ; . . .T qk ¼ ½ g k0 ; g k1 ; . . .d k1 ; d k2 ; . . .T yr ðkÞ ¼ signð gk0 Þ sign g T ð k 2 1Þq k
ð46Þ
This combined extended dual-control procedure can also be seen in Figure 3, where k K^ r ¼ Gkr ðM kþ Þ21
ð47Þ
Optimal design for IS and IU plants
was introduced based on the notations in equations (1) and (4).
1231 Example 1. Let the IS process be given by S¼
0:001ð1:1 þ 1z 21 Þ z 22 ð1 2 1:6693z 21 þ 0:7788z 22 Þ
ð48Þ
Apply the unity gain tracking and disturbance rejection reference models Pr ¼
0:5z 21 ; 1 2 0:5z 21
Pw ¼
0:2z 21 1 2 0:8z 21
ð49Þ
and start the iterative control refinement by the model M0 ¼
0:1ð1 þ 4:0z 21 Þ z 22 ð1 2 0:2z 21 Þð1 2 0:9z 21 Þ
ð50Þ
i.e. d m ¼ d ¼ 2: In the simulation runs an additive white noise was used as output disturbance with a standard deviation l ¼ 0:01: A simple off-line LS method was used for parameter estimation, only to demonstrate the operation p of the iterative algorithm. The optimal reference signal ys r was generated by (equation 40) in each step. The outputs of the reference model (continuous) and the controlled process (dashed) are shown in Figure 6, before and after the iterative refinement. ~ The frequency characteristics (continuous) of the input-generating weight W s p and the spectrum (dashed) of the obtained optimal yr reference signal are shown in Figure 7 for n ¼ 200: The effectiveness of the optimal reference signal can be seen in Figure 8, where the control loss function (variance) is shown for three input excitations: unit step (dotted), unit square wave (dashed), maximum variance optimal (continuous) in the function of iterations. It is easy to see how much faster the iteration is, when applying OID. Example 2. Let the IU process be given by S¼
0:125ð1 þ 1:6z 21 Þ z 22 ð1 2 0:5z 21 Þð1 2 0:8z 21 Þ
and use the same Pr, Pw, l applied in Example 1. The initial model be
ð51Þ
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Figure 6. Outputs of the reference model and the controlled process before and after the iteration (LS, optimal input )
M0 ¼
0:1ð1 2 4:0z 21 Þ z 22 ð1 2 0:2z 21 Þð1 2 0:9z 21 Þ
ð52Þ
i.e. d m ¼ d ¼ 2: The outputs of the reference model (continuous) and the controlled process (dashed), as well as the control (continuous) and modeling (dashed) error signals are shown in Figure 9 for n ¼ 200 samples using the optimal reference signal excitation in an adaptive control refinement p scheme. Here the optimal reference signal ys r was generated by the adaptive algorithm (46), in each sampling instance. The figure shows the fast learning (adaptation) property of the combined CLCR input design and adaptive identification and control algorithms.
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Figure 7. Frequency ~ and characteristics of W the optimal input spectrum
Figure 8. Control loss function for three reference signals
Conclusions The paper gives the generating law for the computation of the optimal reference signal excitation for CLCR identification. The resulting relationships are considerably different for IS and IU processes. For the IS case the optimal excitation depends only on the performance design goal, which means that the optimal reference signal excitation can be apriori generated in the knowledge of a reference model Pw for the desired disturbance rejection behaviour of the closed-loop. However, for the IU case it depends on the invariant factors of the plant, so only learning algorithms can be applied, which iteratively estimate the IU part of the process model.
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Figure 9. Operation of the adaptive algorithm
Two simple simulation examples, one for the iterative refinement and the other for the adaptive case, are also given to show the operation of the developed algorithms. References Goodwin, G.C. and Payne, R.L. (1977), Dynamic System Identification: Experiment Design and Data Analysis, Academic Press, p. 291. Keviczky, L. (1975), “Design of Experiments for the identification of linear dynamic systems”, Technometrics, Vol. 17 No. 3, pp. 303-8. Keviczky, L. (1995), “Combined identification and control: another way (Invited plenary paper.)”, 5th IFAC Symp. on Adaptive Control and Signal Processing, ACASP’95, Budapest, Hungary, pp. 13-30.
Keviczky, L. and Ba´nya´sz, Cs. (1973), “On input signal synthesis for linear discrete-time systems”, 3rd IFAC symp. on Ident. and Syst. Par. Est., Hague/Delft, The Netherlands, pp. 93-102. Keviczky, L. and Ba´nya´sz, Cs. (1999a), “Optimality of two-degree of freedom controllers in H2and H1-norm space, their robustness and minimal sensitivity”, 14th IFAC World Congress, Beijing, People’s Republic of China, Vol. F, pp. 331-6. Keviczky, L. and Ba´nya´sz, Cs. (1999b), “Dialectics of identification and control”, Report ESF COSY Course, Valencia, Spain, pp. 107. Ljung, L. (1987), System Identification: Theory for the User, Prentice-Hall, p. 519. Maciejowski, J.M. (1989), Multivariable Feedback Design, Addison-Wesley, p. 424.
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The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/0368-492X.htm
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Universe as a self-observable, self-ethical, life-embedding mathematical system Michel Bounias INRA-DSPE, Avignon University, The Alexandria Institute of Medicine, New York, USA BioMathematics Unit, Domain of Sagne-Soulier, 07470 Le Lac d’Issarle`s, France Keywords Cybernetics, Perception, Evolution strategies Abstract The non-well-founded properties of the empty set provide existence to abstract topological spaces, in which intersections of subspaces with non-equal dimensions give topologically closed structures. This let space-time emerge as an ordered sequence of sections upon a defined combination rule, in which interactivity between observable structures is allowed and conditions for conscious perception phenomena are fulfilled. Conditions for evolution and rules for optimal evolution of ecosystems also infer as corollaries. A physical universe and life constitute one single self-organized and self managed system where life appears as the physical-like realization of conditions of functionality of the embedding mathematical spaces. The system includes self-ethical and moral guidelines which should inspire human behavior on Planet Earth.
Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1236-1248. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443446
Introduction Life has long appeared as a specific phenomenon to physicists. Some like Schro¨dinger (1944) even questioned the relevance of physical laws to biology. This situation still feeds polemics in terms of the assessment of biological risk from physical factors (Marino, 2000) and even more at planetary level, about how human societies should behave with respect to Earth’s ecosystems (Cairns, 2000). The actual nature of life has not yet been elucidated, but life apparently occurs within a physical universe, and our works originally raised the following founding question: “do conditions for existence of a physical universe also provide clues for the apparition of the living phenomenon”? In other words, could life and universe constitute a Global System (GS), and which organization laws are provided to this system by its fundamental structure ? The very primary goal formerly raised (Bounias, 1990) was to assess what would be the formal conditions supporting the concept of the existence of Universe(s). Two conjectures were proposed by mathematician Bonaly (1992):
(1) a physical universe should in some way be observable (2) only topologically closed structures would be physically observable, and such objects should be found at intersection of spaces with non-equal dimensions. One inferring condition was therefore that abstract topological spaces should be primarily available. However, no such things as numbers and other sets could be taken for granted at the beginning. Instead, their existence should be justified, likely by some primary axioms that remained to be identified through formal reasoning. However, a demonstration requires a reasoning system to be applied to probationary spaces where propositions should be proved to be valid (Bounias, 1997, 2001). Here, we had to identify a space supporting the proposition: “a physical universe exists”, but the reasoning system had to be stated. For this purpose, the theory of sets extended to non-well-founded sets – associated to the general topology extended to fuzzy settings – provide the most powerful reasoning system available. Main results The following statement will be proved from a sequence of steps. Theorem. The existence of the empty set provides existence to physical universes in which the following features of life are embedded: conscious perception, ecosystem’s optimal organization laws and evolutionary processes. The described system will be referred to as the (GS). 1. Lemmas of Space-time The following Lemmas identify the foundations of spaces needed for existence of a physical universe. Lemma 1.1. The empty set is a non-well-founded set or hyperset, whose existence gives rise to existence of abstract mathematical spaces endowed with the power of continuum (Bounias and Bonaly, 1997a). The complementary of Ø in Ø is Ø. Thus set (Ø) is self-contained. The axiom of availability (Bounias, 2001) is required for getting the power set of parts of (Ø), that is the infinite sequence of sets of parts of sets of parts {Pn(Ø)}. This set contains the Von Neuman set {Ø, {Ø,{Ø}},. . .} equipotent to N and all pairs of integers, that is all members of set Q and their sequences. The latter in turn provide existence to a set equipotent to reals R. Importantly, that (Ø) is a non-well-founded set or hyperset solves antinomies affecting Ø and formerly let unaddressed, e.g.: indexation on I ¼ Ø of intersections of families of parts of sets, and the boundary problem in {Ø, R} since (Ø) becomes equipotent to R. Corollary 1.1. The hyperset (Ø) is bounded by a unique set noted (¢), identifiable as the set with neither members nor parts. In contrast with (Ø) having empty parts, and being contained in all well-defined sets, (¢) is
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contained in no set. Thus it represents the greatest lower bound or infimum of the GS. Lemma 1.2. The intersection of subspaces with non-equal dimensions is topologically closed (Bounias and Bonaly, 1994). Let (E m, ’) and (E n, ’) be two open spaces. If m ¼ n; their intersection A ¼ fE n > E m } is open. Let {S kk+1} be the manifold of k-simplices constructed from k þ 1 points in E k. Consider n points of a n-simplex included in E n and belonging to A. Add one point y belonging to E m to (S nn+1) which becomes a polygon with n þ 2 faces or a loop (Ln+2): since E m, E n are open, all neighborhoods of y meet A and y is an accumulation point of A. However if m . n; then the obtained n þ 2 points get dimension n þ 1: Thus the n-loop n (Ln+2) becomes a (S n+1 n+2) simplex and cannot belong to (E \A ). Therefore y must belong to A and since A contains all its accumulation points, it is closed. Condition m – n is sufficient, though settings can be constructed in which it would be not necessary. Corollary 1.2.1. Our space-time appears as an ordered sequence of intersections {S}i ¼ fW 4 > ðW 3Þi }i ; upon rules (’ i) holding on mappings of section (Si) into (Si+1) (Bonaly and Bounias, 1995). There exists as many different space-time sequences as there are such rules. Regarding our observable spacetime, Bounias (2001) proposed the following properties for (’ i): (1) topologies should be conserved; (2) for any (Si), ðS iþ1 Þ – ðS i Þ and ðS iþ1 Þ – Ø; (3) for any ðS iþ1 Þ : ðS i Þ > ðS iþ1 Þ ¼ max{ðS i Þ > ðS iþk Þ;k$1 }
ð1Þ
This predicts the occurrence of geodesic trajectories and the least action principle (work in progress). Corollary 1.2.2. The empty hyperset (Ø) constitutes a lattice of cells whose sizes are determined by successive intervals provided by subdivisions in its equipotent integer sets. Since (1) all these cells are similarly empty and constructed from the same generator (Ø) and the complementarity law as the initiator; (2) the union of two empty parts is an empty part; (3) all parts are similar at all scales, then the empty lattice owns a fractal structure. Work in progress demonstrates how particles can be generated from this lattice up to quantum and relativistic properties. Corollary 1.2.3. The existence of the lattice of self-containing empty cells provides support to the inertons theory (Krasnoholovets, 1997) which proves that exchanges of elementary deformations give rise to a system of particle-tospace interactions. Formal development of this system allows logical derivation
of both of quantum and relativistic/gravitational properties of matter (Krasnoholovets, 2000). Corollarily, the possibility of identifying a wave function emerges for a complex system like a living organism (Krasnoholovets, 2001). Lemma 1.3. The composition rule of objects and distances from one to next sections is a non-linear convolution of morphisms endowed with the structure of a moment. From (Si) to (Si+1) a composed indicatrix function f(i,i+1) accounts for the localization of all points belonging to distances (D{Xj}j) and to objects (mkYj l called ‘instans’) in topological sets mapped from one to the next section. The compositions (D{Xj}j) o f(i,i+1) and (mkYjl) o f(i,i+1) are called “moments of junction” (Bounias, 1997). Let M denote the morphisms of distances and topological frames, and J the morphisms of objects. Then, with (’) and (S) denoting two kinds of mappings, k indexing the sequence of sections of spacetime and T(’ ) the mapping connecting section (Sk) to (Sk+q) so that combination rule (’) substitutes for (S): ðM ’ JÞkþq ¼ T ð’Þ ðMSJÞk
ð2Þ
Relation (2) depicts a non-linear convolution which can be derived into a classical convolution upon restrictive conditions. Remark 1.3. The moment of junction stands for a strict differential element of both space and time. It connects space sections (Si) to (Si+1) in such a way that the increment of time is empty if (Si+1)¼(Si) while it is a positive infinitesimal element if ðS i Þ – ðS iþ1 Þ even by one single point in one single subset. The corresponding increments of space are determined by the topological distances of the position of objects in (Si) with their position in (Si+1) relatively to the same topological frames mapped from (Si) to (Si+1). Lemmas of physical interactions The above provided abstract space allows interactions to occur between objects. This section describes interactions between inert structures. Lemma 2.1. In an embedding lattice W, (1) closed subspaces represent physical objects and open parts contribute to distances. (2) Interactions necessarily occur through a connected “separating distance”. The Jordan-Veblen’s theorem states that a path connecting the interior of a space to the interior of another space has a non-empty intersection with the frontiers of these spaces (denoted as Jordan’s point or set of points). Then, the Jordan’s points stand for the trace of the interaction. Collisions are represented by A > B – Ø; which is considered later, or by the path being reduced to a
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point or a finite set of limited size. Connectivity must be fulfilled in the embedding space, which is the case of the earlier lattice. Let A, B, be two closed spaces in an embedding part E of W. If A > B – Ø; then the symmetric difference DðA; BÞ ¼ ðA < BÞ \ ðA > BÞ is compatible both with the definition of a topology and with the definition of a distance. Since A and B are closed, their intersection is closed and its complementary D is open. Therefore, it represents a natural topological distance and the lattice is called a delta-metric space. Lemma 2.2. Interactions necessarily occur through a connected “separating distance”. If A > B ¼ Ø; there must exist at least one connected set C intersecting both A and B, such that A,B,C belong to the same topology as involved in the interaction. Then, a path wE(A, B ) can be plunged into the distance between A and B inside E defined as follows: DE ðA; BÞ ¼ DðA; CÞ > DðB; CÞ
ð3:1Þ
If several sets {C 1, C 2,. . ., Ci,. . ., Cn} are involved, then: DE ðA; BÞ ¼ DðA; DðCiÞÞ > DðB; DðCiÞÞ
ð3:2Þ
Consequently, a continued path can be provided a definition space between A and B within E. This space has been called a “separating distance” (Bounias, 2001). Lemma 2.3. A path connecting two interacting objects provides a physical measurement device if its dimension is not equal to the dimension of the scanned objects. For the purpose of physical measurements, the path lE ( A, B ) must itself be a physical object. Then, following Lemma 1.2, it must have a dimension notequal to the dimension of DE (A, B ) nor of A and B. This should have applications in the measure of unknown physical spaces. Remark 2. All these properties need not be artificially introduced; they emerge as natural consequences from the primary axiom and logical conditions for the functionality of the abstract mathematical space embedding the GS.
Lemmas of perception and biological self The availability of the above abstract mathematical structures embeds some features which are essential for the phenomenon of life to occur. The former Lemma 2.1 provided the intermediate step of inert matter interactions while inert-to-living interactions will be considered now. Living-to-living interactions will be examined in the Lemmas 5.1-5.3 and Proposition 5.
Lemma 3.1. The perception function is founded on the existence of Banach type fixed points in the mappings of the trace of perceived object to the interior of the perceiving one. A path w(A, B ) connecting the interior of a closed B taken as the perceived object to a closed A considered as the perceiver, carries to a point or subset (a ) of the frontier of A the mapping of a point or subset (b ) of the frontier of B if the following conditions are fulfilled: (1) the path is a continued sequence of functions f n (2) the mapping converges to a fixed point in the interior of A so that a stable configuration can be used as the endpoint of the perceptive flow. The space of this interaction is finite and discrete: thus it is compact, and since it is metric, it is complete. Then, it suffices that the sequence of mappings is Cauchy inside the closed A. Since inside A the mappings of f n(a) range in a bounded subspace, contraction mappings provide a simple combination rule determining converging sequences of the Banach type. Then, the image of a Jordan’s point will be a fixed point and two corollaries follow: Remarks 3.1. The fixed points standing in the interior of a perceiving object as the mapping (or image by f n) of outside information provide the reference data for feedback reaction of perceiver A to perceived object B. This is enough to support lower levels of life organization. However, such fixed points can stand for mental images in a space organized as a brain-type system (Bounias and Bonaly, 1997b; Bounias, 2000, Sharma et al., 2001). This denotes a higher level of organization in which greater levels are required: (1) in accuracy in the evaluation of environmental topologies; (2) in the assessment of the unicity of the self-perception in a more complicated structure. This introduces the next Lemma 3.2 concerning the foundations of the biological self. Lemma 3.2. The Biological Self is founded on Brouwer’s type fixed points. In a closed topological structure, all continued functions own a fixed point of the Brouwer’s type. Therefore Brouwer’s fixed points exist for all internal functions, including: (1) mental images and (2) metabolic and related processes. The union of Brouwer’s with Banach type fixed points associate the signals from outside perception to stable parts representative of perception from the inside. Therefore, organisms provided by evolutionary construction of structures associating these two classes of fixed points will be endowed with the capacity of conscious perception.
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Lemma 3.3. Unicity of the Biological Self is determined through fulfillment by biological anatomy and physiology of mathematical conditions for the unicity of fixed points. Unicity of fixed points involves compatibility and semi-compatibility of mappings, which is materialized in biological anatomy by chiasm structures. These conditions allow fixed points to exist also in presence of fuzzy components and] discontinuity of some parts (Singh et al., 1997; Sharma et al., 2001). Corollary 3.3. The biological time is irreversible. Given sequences of mappings, fixed points are not identical for surjective and non-surjective mappings. Since in a sequence of contractive mappings at least some iterates must be surjective, the reciprocal mapping of a sequence leading from a perceptive pre-image to a mental image would not associate the same self to the same perceptions. Corollary 3.4. The space of the brain system owns anticipatory and fractal properties. Since a mental image should be sustained up to the installment of the next one, the system involves a succession of sustained fixed points. Because the corresponding sequences of neuronal connections do not necessarily have the same duration, then the system is represented by an equation in which: (1) state at (t ) is function of a state at (t+k ), denoting hyperincursivity, and (2) the equation is similar with the relation depicting a construction endowed with self-similarity ratios (Bounias and Bonaly, 2001).
Lemmas of brain management and supply services Lemma 4.1. The intersection of Brouwer’s and Banach fixed points lays the foundations of brain-controlled homeostasy. Feedback loops connect the state of the organism to the unconscious-type mental images that reflect a normal functioning of the body (see Lemma 4.5 for justification) through appropriate receptors. The adjustment of the inside-body functions and the whole-body (outside) behavior, as directed by mental images constituted from both conscious and unconscious perceptions, establishes the foundations of total homeostasy (Bounias et al., 2001). In a diseased organism, these feedback loops are altered. The following Lemma 4.2 raises the possibility of further introducing a correction to this situation. Lemma 4.2. The brain system is able to connect neuronal groups into an arrangement corresponding to a mental image of a still unrealized situation. Then, the activity of the organism can be considerably improved in its accuracy by progressive adjustment to the goal represented by the anticipatory mental image. This capacity represents a major homeostatic resource at both
outside-to-inside level and inside regulation processes. This indeed leads to possibilities such as intuition and abstract creativity, and to the following: Lemma 4.3. Anticipatory properties of brain provide the foundations of a theory of the NeuroBioFeedback (NBF) medical technology (Bounias, 2002). A normal pattern of activity of the brain is bijectively associated with correct reference mental images and correct control of body functions. In presence of patients with altered homeostasy, NBF training induces the restoration of normal brain activity and substitutes new corrected mental images to the previously altered ones. Then, conditions of rehabilitation of patients can be predicted, and predictions have been verified in clinical setting on groups of patients with brain injury (Bounias et al., 2001b). New insights to neurotoxicology are also opened by the experimentally supported prediction of Lemma 4.1 (Bounias et al., 2001a). In the earlier Lemma 4.1 - 4.3, the term of body has been used without former justification. This gap is now filled. Lemma 4.4. The body is a mechanical construction needed for filling with the appropriate energy supply the material realization of the functionality of the underlying mathematical spaces. Interactions between closed objects involve: (1) connective paths between them; (2) feedback loops between perception of outside signals and reaction allowing an object to keep its integrity against entropic trends; and (3) storage of information is optionally used within organisms and between organisms. The latter is imposed by limited resistance of organisms to entropy, which implies education, and therefore reproduction. The goal of keeping integrity has been interpreted as a teleonomic factor (i.e. a belief): here, it will further be explained by logical properties of the GS. Higher levels of perception functions are provided by the presence of sensory organs or equivalent structures, and further by a physiological organization providing associate unicity of the self. All these functions can be operating upon construction and maintenance of appropriate physical supports. The brain, as a primary functional entity, must be fueled with energy and the surrounding system must be provided with motility allowing the search for fuel sources: this justifies the body. Corollary 4.4. The surrounding body must not need more energy than the brain. If the contrary occurred, organs and tissues surrounding the brain could consume too much to allow the brain to work. It is meaningful that in higher organisms, the brain needs more energy than any other organ: however this statement should be more correctly expressed in the reverse form: the body organs consistently consume less than the brain. This will further be strengthened later with introduction of the bio-Hamiltonian concept.
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Since such systems can wear a host of various forms, their interactions with the environmental milieu will in turn wear a diversity of forms. This found the basis for ecosystem features as inferring from the above sequence of concepts. Accordingly, two other steps take place here. Foundations of ecosystem interactions and evolution Lemma 5.1. Increasing diversity is a fundamental feature of our observable space-time. Among the infinitely many fundamental combination rules governing space-time sequences as mappings T n : ðS i Þ 7 ! ðS iþ1 Þ one precludes the possibility of loops by including the additional clause: ;n . 0j;kj T n ðS k Þ – ðS k Þ ð4Þ If condition (4) was not fulfilled, there could occur short loops in the space-time sequence. In contrast, under holding of this condition, there can occur an alternance of increasing and decreasing diversity of the GS structure and functions, but decreasing phases would necessarily be limited while increasing phases are endowed with the potential of the power set of parts. This law therefore favors an increase of diversity of all types of structures, functions and species: it is consistent with a neguentropic trends and should be added to relation (1). Interestingly, conditions (1) and (2) coincide with the “exploration function” proposed as a way to explore an unknown space: here it represents a way of self-exploration of universe. This could provide support to some aspects of the anthropic theory (with exception to any priviledged position of humans) and stands like a kind of “driving force”. Lemma 5.2. There exists a Hamiltonian for a living organism. Characteristics can be defined as follows: (1) The accompanying wave function is supported by Corollary 1.2.3. (2) The kinetic component includes members working at corpuscular, molecular, organ and macroscopic scales. (3) The potential component includes interaction of the former members, and also genetical and evolutionary potentialities. In effect (Corollary 1.2.1), the living phenomenon actually represents a continuum through the four-manifold which embeds our space-time (Bounias, 2001). These properties fill a formerly deplored gap about the absence of Hamiltonian for living systems (Rosen, 1989). Corollary 5.2. Morphisms of continuous mappings connect the stability of genomic materials to the functionality of coded structures (Bounias et al., 2001b). This result provides justification to the motor of evolution and allows the Darwinian theory to be partly supported and partly refined.
Lemma 5.3. The evolution of ecosystem spaces as topological spaces toward optimum states involves three necessary conditions: (1) continuity of functions;
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(2) maximal complementarity of species for habitat and resources; (3) mutualism. Proof. Components (species and habitat) and combination rules (flows of matter, energy and species) fulfill stability upon union and finite intersection and form topological spaces. The space of orbits of all members by the set of functions (or functional) is finite and discrete, thus it is compact, and at least delta-metric thus complete. Mappings of compact into topological spaces are continuous. The Weierstrass theorem states that this system reaches its boundaries, that is, at the present state, it can reach its maximum. No point of the space of orbits is a isolated one, so that this space is connected. Then, the Bolzano theorem states that it will reach its maximum on the condition that it meets all intermediate states. Last, the Heine-Borel-Lebesgue property imposes nonempty intersections of sets of components with sets of functions, i.e. each specie should contribute to some level to the constitution of habitat and resources of others, which defines ecological mutualism (QED). A Corollary 5.3.1. Intermediate interactions examined at various scales integrate toxicity, parasitism, criminality, terrorism and war into a single concept (Bounias and Bonaly, 2000). This provides clues to further management of human societies within the living community on Planet Earth. Corollary 5.3.2. Genetical adaptative variability must confer higher mutability to further generations. The condition for growing diversity of ecological niches, inferring from Lemma 5.1 and relation (4) imposes a correlated diversification of species. This meets with former conjectures which have recently received experimental support (Brookfield, 2001). Figure 1 summarizes the steps marked by the continued sequence of demonstrations presented above. Proposition 5. A kind of objective spirituality can infer from properties of the GS. Since as many universes are putatively existing as there exists sequences of intersections Wm > Wn ðm – njðm; nÞ – ð4; 3ÞÞ and their rules of the (’ i) type, and that none of these universes are totally independent in the embedding four-manifold, action in one universe may impact on others, even if the involved reactants remain inaccessible to mutual perception. Therefore, an ethics of universal respect of all forms of known and unknown forms of life and biotopes should be emphasized.
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Figure 1. The sequence of logical implications inferring from the primary axiom of the existence of the empty set and the availability of set theory and topology
Discussion and conclusions This paper provides an opportunity of shedding light on the works remaining to do about connections between the various Lemmas and in raising points which are still missing. The above results imply a clause of respect of all known and unknown forms of life as defined earlier. It explains why all species should be protected, including those not directly useful for humans, in appearance, and suggests that even species considered as pests should not be matter of attempts to eradication, since they all have a role in the GS. Furthermore, a behavior of complementarity should prevail over competition and struggle for elimination of competitors. Accordingly, the management of our Planet Earth should be assigned some natural guiding principles and boundaries which may contrast with the usual standard paradigms edicted by political economy, since whatever is decided by human power, in the last instance, the laws holding on the existence and functions of the life-embedding GS will prevail over the human “Runes”. Since all parts of all possible universe embedded in the same four-space can be somewhat connected by one or more dimensions, unwanted interactions may occur between worlds: these considerations could open the way to a rationally founded form of “spirituality”, in terms of analysis of the implications of human behavior with regard to the respect of the fate of the entire living community - either knowable or for ever unknowable – of the GS. Where repression, persuasion and education failed, human societies could escape war, destruction and criminality through one’s perception of other’s pain and distress, (including species and biotopes) either from direct feeling of by analytical identification. Both ways are made available by properties of the GS. References Bonaly, A. (1992), Personal communication. Bonaly, A. and Bounias, M. (1995), “The trace of time in Poincare´ sections of a topological space”, Physics Essays, Vol. 8 No. 2, pp. 236-44. Bounias, M. (1990), “The Global Project: towards a theory of existence, structuration and organization”. University of Avignon, Biomathematics and Toxicology Unit Research Project, p. 14 Bounias, M. (2000), “A theorem proving the irreversibility of the biological time, based on fixed points in the brain as a compact delta-complete topological space”, in Dubois, D.M. (Ed.), CASYS’99 third Int. Conf., CP517 American Institute of Physics, pp. 233-43. Bounias, M. (2001), On the Hamiltonian of Living Organisms. In: CASYS’2000 fifth Int. Conf., ed. D.M. Dubois, Lie`ge, Belgium, Int. J. Comput. Anticip. Syst., p. 17 (in press). Bounias, M. and Bonaly, A. (1994), “On mathematical links between physical existence, observability and information: towards a Theorem of Something”, J. Ultra Scientist of Physical Sciences, Vol. 6 No. 2, pp. 251-9. Bounias, M. and Bonaly, A. (1996), “On metrics and scaling: physical co-ordinates in topological spaces”, Indian Journal of Theoretical Physics, Vol. 44 No. 4, pp. 303-21.
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Bounias, M. and Bonaly, A. (1997a), “Some theorems on the empty set as necessary and sufficient for the primary topological axioms of physical existence”, Physics Essays, Vol. 10 No. 4, pp. 633-43. Bounias, M. and Bonaly, A. (1997b), “The topology of perceptive functions as a corollary of the theorem of existence in closed spaces”, BioSystems, Vol. 42, pp. 191-205. Bounias, M. and Bonaly, A. (2000), “The future of life on Earth: ecosystems as topological spaces”, in Burdyuzha, V. and Khozin, G. (Eds), The Future of Universe and The Future of Our Civilization, World Scientific, Singapore, pp. 206-24. Bounias, M. and Bonaly, A. (2001), “A formal link of anticipatory mental imaging with fractal features of biological time”, in Dubois, D.M. (Ed.), CASYS’2000 fourth Int. Conf., CP573 American Institute of Physics, pp. 422-36. Bounias, M., Laibow, R.E. and Stubblebine, A.N. (2001a), “NeuroBioFeedback, Mathematics and Neurotoxicology”, in, The environmental aspects of neurotoxicity, Proceedings of the 19th Annu. Symp. American Environmental Health Foundation, Dallas, 7-11 June 2001, AEHF, Dallas, Vol. 4, pp. 14-18. Bounias, M., Laibow, R.E., Stubblebine, A.N. and Bonaly, A. (2001b), “EEGNeuroBioFeedback treatment of patients with brain injury”, J. Neurotherapy, Parts 1 to 4 (in press). Bounias, M., Bonaly, A., Santoli, S., Magnon, A., Ansari, A.H., Laibow, R.E., Stubblebine, A.N., Sharma, B.K. and Me´hois, M.J. (1999), “At the least upper bound of accessible knowledge. A global project on whole-scale existence and properties of universe and its components”, J. Ultra Scientist of Physical Sciences, Vol. 11 No. 3, pp. 295-311. Brookfield, J.F.Y. (2001), “The evolvability enigma”, Current Biology, Vol. 11, pp. R106-8. Cairns, J. Jr (2000), “The quest for immortality on an unsustainable planet”, in Burdyuzha, V. and Khozin, G. (Eds), The Future of Universe and The Future of Our Civilization, World Scientific, Singapore, pp. 3-11. Krasnoholovets, V. (1997), “Motion of a relativistic particle and the vacuum”, Physics Essays, Vol. 10 No. 3, pp. 407-16. Krasnoholovets, V. (2000), “On the nature of spin, inertia and gravity of a moving canonical particle”, Indian J. Theor. Phys., Vol. 48 No. 2, pp. 97-132. Krasnoholovets, V. (2001), Gravitation as deduced from submicroscopic quantum mechanics, p. 12. (Communication to Author) Marino, A.A. (2000), “In the eye of the beholder: the role of style of thought in the determination of health risks from electromagnetic fields”, Frontier Perspectives, Vol. 9 No. 2, pp. 22-7. Rosen, R. (1989), “Some epistemological issues in physics and biology” (dedicated to David Bohm), p. 28. (Communication to Author) Schro¨dinger, E. (1944), What is life? Cambridge University Press, Cambridge, UK. Sharma, B.K., Sahu, D. and Bounias, M. (2001), “Common fixed point theorems for a mixed family of fuzzy and crisp mappings”, Fuzzy sets and Systems (in press). Singh, T.B., Banerjee, A., Bounias, M. and Bonaly, A. (1999), “Fixed points in the mathematical brain that do not need continuity in neuronal chaining”, J. Ultra Scientist of Physical Sciences, Vol. 11 No. 2, pp. 191-5.
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A synergetics approach to disruptive innovation Gerrit Broekstra Nyenrode University, Breukelen, The Netherlands
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Keywords Cybernetics, Technological innovation Abstract Emery and Trist were the first to design an influential taxonomy of four social fields to accommodate the perceived emergence of a new type of business environment, the type 4 turbulent field. This captured the predicament of leading companies suddenly confronted with, what Christensen called much later, disruptive change. Their taxonomy was based on the study of adaptive behavior on linear dynamical systems. This paper proposes a modification of the taxonomy on the basis of Synergetics to enable dealing with the nonlinear evolutionary dynamics of complex probabilistic business systems. Synergetics focuses on what happens in phase transitions or bifurcations which appear to be the essential nature of turbulent fields. Furthermore, Haken’s slaving principle and the concept of the order parameter are remarkably well-suited to review the Christensen’s findings of companies held captive by customers and, particularly, the puzzling delay shown by leading companies in responding to newcomers. These newcomers typically change the nature of the order parameters of type 3 established fields, as represented by Christensen’s product performance characteristics, which may cause customers to switch their preferences and buying behavior. Thus the apparent stability of an established field can be quite deceptive. As such, this paper suggests the existence of a lock-out principle complementary to the lock-in principle described by Arthur in his work.
A bit of synergetics Let us study the buying behavior or evolution of customer demand as a function of time in a population of 2N customers in a business sector for two competing products, technologies or business concepts with, following Christensen (1997), two different performance characteristics P1 and P2. Assume there are at a given time t n1(t ) P1-type customers forming a subpopulation 1 and n2(t ) P2-type customers in subpopulation 2. If the total number of customers is a constant 2N, we can introduce as an order parameter the single macroscopic state variable n(t ) to describe the state of the synergetic field, such that n1 ¼ N þ n and n2 ¼ N 2 n while 2N # n # N : To describe the evolution of the state variable n(t ) as a function of time, we can be sure that, due to the enormous complexity of the factors underlying individual customer motivations at the microlevel to favor a particular product or technology, which translates into random fluctuations influencing the macrostate, the macrovariable n can not be known exactly and is therefore to be regarded as a probabilistic variable from the start. This entails that a dynamic description of customer demand evolution over time will necessarily have to be in terms of the probability distribution p(n; t ), representing the probability of finding a field in state n at a time t. The mathematics of the
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evolution of the distribution function over time as applied here can be found in a lucidly written and inspiring book by Weidlich and Haag (1983, 2000) on a Synergetics approach to, for example, opinion formation in politics and investment strategies in economics. Since we will closely follow their results here, we will restrict ourselves to the basics and focus on the interpretations of our own computer simulations. The evolution equation of the probability distribution p(n; t ) is given by the so-called discrete Master Equation. This can be converted into an approximate description in terms of continuous variables, called the Fokker-Planck equation, but here all results are derived by using the exact master equation. Basically, the latter straightforwardly balances the accounts for the probability fluxes that occur when members of population 1 change their demands for product 1 to 2 and, likewise, members of population 2 change from 2 to 1. The master equation is given by dpðn; tÞ ¼ ½w" ðn 2 1Þpðn 2 1; tÞ 2 w# ðnÞpðn; tÞ 2 ½w" ðnÞpðn; tÞ dt 2 w# ðn þ 1Þpðn þ 1; tÞ
ð1Þ
where the first bracketed term refers to the net probability flux between “neighboring” states ðn 2 1Þ and n, and the second to the net flux between (n ) and ðn þ 1Þ: Further, in (1) w" and w# stand for the transition probabilities for the whole field state variable n, such that w" ðnÞ ¼ n2 p12 ðnÞ and w# ðnÞ ¼ n1 p21 ðnÞ
ð2Þ
where p12 (n ) is the individual transition probability per unit time for a P2-type customer who switches to the P1 population, and p21 (n ) the transition probability per unit time for a P1-type customer switching to the P2 population. These transition probabilities will be assumed to be a function of n only and to be the same for all customers. For their study on the political opinion formation process Weidlich and Haag (1983, p. 41) introduced two trend parameters that influence the individual transition probabilities. They appear to be equally applicable to customers of a business sector involved in a collective performance demand formation process. First, assuming that customers have individual preferences for either products which are independent of the demands of other customers, we introduce a preference parameter d. Second, customers are also assumed to have a propensity to conform to the majority buying habits and adapt their attitude towards the prevailing demands whether voluntarily or “pressured” by media campaigns and group controls. Clear evidence of such conformity trends is the increasingly worldwide demand for certain brand names and the occasional hypes arising around novelties. To take into account this basic
readiness of individuals to conform, Weidlich and Haag (1983) introduced a conformity parameter k. The individual transition probabilities in (2) are now defined by p12 ðnÞ ¼ n expðd þ knÞ and p21 ðnÞ ¼ n exp½2ðd þ knÞ
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ð3Þ
where n is some flexibility parameter determining the switching frequency, which is absorbed in the scaling of the time t. From (3) it is readily seen that a positive trend parameter d increases the probability of individuals switching from a preference for P2 to P1, while at the same time reducing the probability of switching from P1 to P2. The reverse applies for negative d. Similarly, a positive k increases the transition probability of conforming to the majority and reduces it for the minority. As indicated, this effect is assumed to be stronger for a larger value of the state variable n. A stability analysis of the stationary field created by the master equation reveals that kc ¼ 1 is a critical value at which a bifurcation can be expected as will be seen later (Weidlich and Haag, 1983, p. 44).
Locking into a type 3 established field We are now ready for a preliminary exploration of the behavior of the successive fields as discussed by Emery and Trist (1965) by looking into the effects on the probability distributions of changing values of the trend parameters d and k. The numerical integration of (1) has been performed by applying a second-order Runge-Kutta scheme. The computer programs have been written in Qbasic. For purposes of clarity all discrete points p (n; t ) in the figures have been connected by line segments which gives the appearance of continuous distribution curves. Looking at the results, let us start with the stationary distribution pst(n) of a type 1 embryonic field consisting of two competing new products or technologies which may look like the bell-shaped curve at t ¼ 0 in Figure 1(a). This is interpreted here as the playing field of startup companies where products are looking for customer needs. Corresponding to Ashby’s (1952) iterated systems which are unconnected, Emery and Trist (1965) called this a “placid, randomized environment”. Individual preferences for one or the other product are absent ðd ¼ 0Þ; and the inclination to conform to majority demand is relatively small and subcritical ðk ¼ 0:5Þ: The most probable state of the embryonic business sector is one where n ¼ 0; or n1 ¼ n2 ¼ N ; i.e. an equal number of customers are buying product 1 or 2. The dispersion of the distribution pst ðnÞ is a measure of the fluctuations around this mean state n ¼ 0 originating in unpredictable microevents. At t ¼ 0 it is assumed that while individual preferences remain zero ðd ¼ 0Þ; the conformity trend parameter is raised stepwise above the critical value
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Figure 1. (a) Evolution of a symmetrical distribution associated with a type 1 embryonic field at t ¼ 0 to one of a type 2 emerging field by changing k stepwise from 0.5 to 1.5 while d remains 0 ðN ¼ 25Þ; (b) Evolution of a type 3 established field showing the transformation of the final stationary symmetrical distribution of Figure 2(a) towards an asymmetrical “monopoly peak” by increasing d stepwise from 0 to 0.3 while k remains at 1.5 ðN ¼ 25Þ
kc ¼ 1-1:5 indicating a much greater readiness of customers to align their buying decisions to what the prevalent majority wants. As shown in Figure 1(a), a bifurcation occurs from the monostable form at t ¼ 0 to a bistable form which attains it final shape at about t ¼ 5: Initially fluctuations increase rapidly as shown by the large dispersion exemplified by the distribution at t ¼ 0:5: Once the two symmetrical humps start to take shape the distribution drifts more slowly towards its final bistable form. The phase transition shown in Figure 1(a) may be thought of as representing a type 2 emerging field where the final bistable form indicates the emergence of one or the other product, and not both, where each has equal probability of
being realized in an actual sample business sector (replacing Emery and Trist’s placid, clustered environment). The most remarkable thing to note is that although there is still no individual preference for one or the other product, the above-critical tendency to conform to the majority customer demand will unpredictably lock the business sector into one or the other product which becomes the dominant design. This “lock-in through fluctuation” principle has been discussed by Brian Arthur (1994). Weidlich and Haag (1983, p. 47) referred to this apparently autocatalytic process as “collective self-stabilization” of one particular option. Evidently, in terms of choice, entrepreneurs can greatly enhance the odds of their product becoming selected by trying to influence the individual preference parameter through intensive marketing campaigns thus creating first-mover advantages. Instead of discussing the asymmetry that a positive or negative d introduces in the probability distribution of a type 2 field (see also Weidlich and Haag, 1983), for simplicity reasons let us take one step at a time and, starting from the final stationary distribution in Figure 1(a), proceed by increasing d stepwise from 0 to +0.3. The result is shown in Figure 1(b) and may be thought of as representing the evolutionary formation of a type 3 established field in which one product, technology or business concept essentially comes to dominate the field (originally, Emery and Trist’s disturbed-reactive environment). As shown, the left hump initially being in a diminishing minority position disappears entirely. The distribution drifts towards a large, narrow single peak on the extreme right of the scale, indicating that with little variation virtually every customer buys product 1 (likewise a negative d would have produced a symmetric curve on the left side of the diagram). In politics, Weidlich and Haag (1983, p. 47) refer to this type of distribution as representing the establishment of a totalitarian state in a society where a strong conformity trend tends to drive a given preference gradually to extreme values by a self-reinforcing process resembling a self-fulfilling prophecy. This is not such an inappropriate term indeed for those familiar business situations where, once locked into a particular product performance definition or technological design, “the winner takes all”, and eventually one or a few leading companies, understanding these critical success factors best, monopolize customer demand. The inefficient QWERTY typing keyboard we are stuck with, designed in 1873 “as a feat of anti-engineering” forcing typists to type as slowly as possible to prevent typewriters to become jammed, is a famous case in point (Diamond, 1998, p. 248). Switching customers, hysteresis and lock-out in a type 4 turbulent field Instead of changing the preference parameter d step-wise, we will now show what happens when, starting from the same bimodal distribution at the beginning of a type 3 field as in Figure 1(b), d slowly increases from zero to
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reach a maximum value and then slowly decreases, goes through zero and reaches a negative maximum value, and so on. This can best be realized by assuming that d depends on time according to a sinus wave with amplitude d0 and period T in the following way (see Weidlich and Haag, 1983, p. 50):
dðtÞ ¼ d0 sinð2pt=TÞ
ð4Þ
It is thus hypothesized here that in the business world the individual preference parameter d shows slow periodic changes due to the fact that customer demand for a particular performance, say P1, gradually becomes saturated and that emerging new products or technologies with new performance characteristics, say P2 (or with a different rank ordering of performance characteristics), gradually gain attractiveness. It is also hypothesized that customer demand typically shows “flocking behavior” meaning that the conformity parameter k remains relatively high above the critical value at 1.5. Introducing a normalized variable x ¼ n=N ; so that 21:0 # x # 1:0; we will study the behavior of the mean value kxl and the variance s as a function of time. The parameter d(t ) is shown in Figure 2(a)as the dotted wave-like curve. What happens initially to the probability distribution is basically what we already saw in Figure 1(b). The bimodal distribution evolves into an narrow spike on the right-hand side so that kxl is close to 1.0. When d(t ) then swings over to its opposite value, the distribution eventually transforms into a narrow spike on the left-hand side with kxl close to 21.0, and so on. The initial shape of the mean value kxl in Figure 2(a) is the familiar S-shaped growth curve representing the maturing of a type 3 established field. Shapiro and Varian (1999) referred here to the adoption dynamics typical for the lock-in adoption of new technologies: flat during launch, steep rise during takeoff as positive feedback kicks in, and leveling off as saturation is reached. As to the lock-out process, it is noteworthy that, when d starts to decline from its maximum value, kxl initially remains stable and it is not until d is well below zero that kxl starts to change appreciably. Remarkably, this is followed by a sudden breakdown of collective customer demand for product 1 towards the opposite state representing a high demand for product 2 which, rightly so, can be called a disruptive innovation. Apparently the stability of kxl is deceptive and we witness a phase transition or bifurcation of a type 4 turbulent field (honoring Emery and Trist’s (1973) designation) which is, in locking out the established product 1, of a revolutionary nature. As Weidlich and Haag (1983, p. 53) have noted for the political opinion formation process, sudden revolutionary breakdowns are typical for a totalitarian state where “even after delusively stable periods hard, revolutionary and in their details unpredictable transitions” occur. Similarly, monopolistic “captivity” (Christensen, 1997) situations in business where a dominant design strongly determines the rules of the game are prone to be subject to the same deceptive stability and revolutionary breakdowns as well. Miller’s (1990) idea of “excess” and
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Figure 2. (a) Development of a type 4 turbulent field; upper part shows the evolution of the mean value kxl (closed curve) and d (dotted curve) as functions of time, and the lower part shows the variance s for d0 ¼ 0:3; T ¼ 200; k ¼ 1:5 and N ¼ 25; (b) Corresponding hysteresis loop for kxl as a function of d showing alternating lock-in and lock-out
Christensen’s (1997) “delay” empirically suggest support for what occurs in this simulation. The “turbulence” in the bifurcation phase caused by a disruptive product becomes conspicuously clear when we look at the behavior of the variance s as a function of time at the lower part of Figure 2(a). Being negligibly small when kxl is relatively stable near its maximum 1.0 and minimum 2 1.0 values, it becomes suddenly very high during the breakdown corresponding to large fluctuations indicating large-scale unpredictability typical for a type 4 field. By analogy with Arthur’s (1994) lock-in-by-fluctuation mechanism in a type 2 emerging field, we are here witnessing a lock-out-by-fluctuation mechanism of the established product, technology or business concept by a newly emerging product acting as the “fluctuation”. As shown in Figure 2(a), repeated bifurcations caused by the continuing alternation of d yield an overall image of
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disruptive “allopatric” change as a punctuated equilibrium process, where relatively long periods of convergence and quasi-stability are punctuated by brief periods of dramatic frame-breaking changes (Tushman and Romanelli, 1985). In evolutionary biology, incidentally, this process is known to concur with the allopatric model of speciation, where new species originate in geographical isolation (Eldredge and Gould, 1972). This is exactly what we observe when new-comers originate in business sectors which are originally isolated from the established markets. Finally, it is of interest to note that when time is eliminated, kxl as a function of d shows the conspicuous form of an hysteresis loop. In Figure 2(b), we first see the initial transient starting from the origin in the kxl, d-diagram where the bistable form transforms in a monostable form of a type 3 field as shown in Figure 1(b). Subsequently, the “large revolutionary cycle containing the quasistable as well as the breakdown behavior” (Weidlich and Haag, 1983, p. 53) due to customer demands switching to a disruptive product or technology is shown quite pronounced. Of course, further interesting extensions may be incorporated, such as assuming d to be dependent on x and introducing time-varying behavior of k (see also Weidlich and Haag, 1983, on the “Schumpeter Clock”, p. 156). The few examples given here may suffice to illustrate the potential of a quantitative approach to uncovering the underlying self-reinforcing mechanism and principles, Christensen’s (1997, p. xviii) “laws of organizational nature”, that govern the behavior of synergetic fields as applied to business dynamics. Fields and the slaving principle It is generally believed that companies have a lot of strategic choice in determining their future courses. Top managers are celebrated and, sometimes outrageously, rewarded for manoeuvring their companies into market leadership. This belief of managerial control is fed by deeply anchored myths of individuality and freedom of action. The above results seriously question this prevalent system of beliefs. As Haken (2000) has shown, the assumption of the presence of synergetic fields with self-reinforcing, positivefeedback mechanisms leads to the conclusion that macroscopic field variables, called “order parameters”, govern the behavior of the microscopic parts by the “slaving principle”, In short, the parts, for example, companies in a business sector, are enslaved by a field in the same manner as atoms are in a laser, where above a critical threshold self-organization sets in creating a coherent field which serves as an order parameter which enslaves the atoms. The process is essentially similar to the lock-in dynamics as discussed earlier in the creation of a type 3 established field from a type 2 bifurcation. This is a case of circular causality where the parts generate the field and the field, in turn, acts as an order parameter enslaving the parts (Haken, 2000, p. 25). The room for manoeuvring by top management of an established leading firm
is basically restricted to an improvement trajectory defined by the existing order parameter, the prevailing customer performance demand, which may eventually initiate the very instability it attempts to avoid. As Shapiro and Varian (1999) have argued, lock-in has become even more important in the information economy. They confirm that here the underlying self-reinforcing, positive feedback mechanism appears to be a more “virulent” phenomena since companies’ dominance is based on demand-side economies of scale. Microsoft’s monopolization of the operating systems markets exemplifies this phenomenon. Customers value its systems because they are widely used and switching costs become relatively high. The above simulation of the evolutionary dynamics of customer demand by the methods of Synergetics appears to be an appropriate tool for a quantitative study of the effects of demand-side economies of scale in the information economy. While lock-in has received ample attention here, this paper has shown that its counterpart, lockout, is an equally important facet of the evolutionary process. Christensen (1997, p. xix) argued that his observations of the effects of disruptive innovations on established business sectors, as the cause of lock-out, support the theory of resource dependence. Briefly, this theory states that “while managers may think they control the flow of resources in their firms, in the end it is really customers and investors who dictate how money will be spent”. Or, corresponding to Haken’s slaving principle and strongly corroborated by the above simulation results, “leading firms were held captive by their customers” (Christensen, 1997, p. 24). However, it would be epistemologically more correct not to attribute control to any part, but to hypothesize the existence of a synergetic field described by an order parameter, such as above the customer performance demand, which essentially enslaves the behavior of all the parts, managers, customers and investors alike. The Western managerial culture is so heavily influenced by the biological metaphors of Darwinian competition, selfish strategies and survival of the fittest that it has ignored alternative explanations of dynamical business phenomena. Particularly where the dynamics of emergent processes are the focus of attention, a theory of business dynamics based on the recent findings of the sciences of complexity may open new vistas of evolutionary explanations. Field theories are not so unfamiliar as they may sound. We have no problem in accepting that the earth goes around the sun enslaved in an elliptical orbit because this is the most probable solution in a gravitational field. As Brian Goodwin has shown in a compelling monograph on the theory of biological morphogenesis – the origin of complex order and form from simple beginnings – generative fields provide a powerful holistic and rigorous approach to the study of “creative emergence as the central quality of the evolutionary process” (Goodwin, 1994, p. xii). In the process of dynamic stabilization, non-linear fields that have the capacity to generate patterns spontaneously, order out of nothing, and give rise to surprises due the
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emergence of unexpected behavior may provide entirely new and exciting insights into the evolutionary dynamics of business as the above simulations indicate.
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Conclusions Our simulation results indicate that for long-term growth and to avoid surprise by disruptive newcomers and lock-out it is imperative that firms develop a three-pronged approach to strategy (cf. Baghai et al., 1999). Apart from focusing on sustaining the core business in a type 3 established, and as we have seen deceptively stable field, renewal strategies should emphasize orientations towards type 1 embryonic and type 2 emerging business sectors which may be potentially disruptive. This requires a kind of innovative entrepreneurship that is by no means an established practice among leading firms. Established companies are usually quite reluctant to initiate innovations particularly those that may prove disruptive and may cannibalize existing products. Top management and corporate staff are usually too far removed from customers and rewarded for increasing performance in the established business. Innovations that tend to develop in the periphery of the core business are often smothered by these conservative forces. Corporate venturing by companies like Nokia or timely acquisitions of innovators like Ben and Jerry’s by Unilever have the potential of overcoming the notorious lack of innovative entrepreneurship in established firms and prevent future lock-out. In times of economic recession these lessons tend soon to be forgotten being replaced by indiscriminate cost-cutting which in itself is a self-reinforcing destabilizing mechanism. References Arthur, W.B. (1994), Increasing Returns and Path Dependence in the Economy, The University of Michigan Press, Ann Arbor. Ashby, W.R. (1952), Design for a Brain: The Origin of Adaptive Behaviour, Chapman and Hall, London. Baghai, M., Coley, S. and White, D. (1999), The Alchemy of Growth, Perseus, Reading. Broekstra, G. (1998), “An organization is a conversation”, in Grant, D., Keenoy, T. and Oswick, C. (Eds), Discourse and Organization, Sage, London, pp. 152-76. Christensen, C.M. (1997), The Innovators Dilemma, Harvard Business School Press, Boston. Diamond, J. (1998), Guns, Germs and Steel, Vintage, London. Eldredge, N. and Gould, S.J. (1972), “Punctuated equilibrium: an alternative to phyletic gradualism”, in Schopf, T.J.M. (Ed.), Models in Paleobiology, Freeman, San Francisco. Emery, F.E. and Trist, E.L. (1965), “The causal texture of organizational environments”, Human Relations, Vol. 18, pp. 21-31. Emery, F.E. and Trist, E.L. (1973), Towards a Social Ecology, Plenum Press, London. Goodwin, B. (1994), How the Leopard Changed its Spots: The Evolution of Complexity, Scribner’s Sons, New York.
Haken, H. (1983), Synergetics, Springer-Verlag, Berlin. Haken, H. (2000), Information and Self-Organization: A Macroscopic Approach to Complex Systems, Springer, Berlin. Miller, D. (1990), The Icarus Paradox, Harper, New York. Shapiro, C. and Varian, H.R. (1999), Information Rules, Harvard Business School Press, Boston. Tushman, M.L. and Romanelli, E. (1985), “Organizational evolution: a metamorphosis model of convergence and reorientation”, Research in Organizational Behavior, Vol. 7, pp. 171-222. Weidlich, W. and Haag, G. (1983, 2000), Concepts and Models of a Quantitative Sociology, Springer-Verlag, Berlin.
A synergetics approach
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Uncertain variables and their applications for control systems Z. Bubnicki Institute of Control and Systems Engineering, Wroclaw University of Technology, Wrocław, Poland Keywords Cybernetics, Control systems, Stability Abstract The definitions and basic properties of so called uncertain variables are presented. The uncertain variables are described by certainty distributions given by an expert and characterizing approximate values of the variables. Control problems for uncertain systems with static and dynamic plants are considered. A method of the stability analysis for a system with uncertain parameters is described. Simple examples illustrate the presented approaches.
1. Introduction For the analysis and decision making in a class of uncertain knowledge-based systems an idea of so called uncertain variables based on uncertain logics has been developed (Bubnicki, 2000a, 2001a, b, 2002b). The uncertain variables, related to random and fuzzy variables, are described by their certainty distributions given by an expert and expressing his/her knowledge on approximate values of the variables. The uncertain variables may be applied to the analysis and decision making in systems with unknown parameters in their mathematical descriptions (in classical models or in relational knowledge representations). The purpose of this paper is to show how the uncertain variables may be applied to selected analysis and design problems for control systems. After a short presentation of the uncertain variables in section 2, an open-loop control system with a static uncertain plant is considered in section 3. The application of the uncertain variables for the design of a closed-loop control system with a dynamic plant containing unknown parameters is presented in section 4, and section 5 describes a method of estimation of the certainty index that the system is stable.
Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1260-1273. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443464
2. Uncertain variables The uncertain variable is defined by a set of values X (a real number vector space), the function hx ðxÞ ¼ vðx ø xÞ (i.e. the certainty index that x is approximately equal to x, given by an expert) and the following definitions:
Variables for control systems
~ Dx Þ ¼ max hx ðxÞ; vðx [ x[Dx
~ Dx Þ ¼ 1 2 vðx [ ~ Dx Þ; vðx
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~ D2 Þ ¼ max{vðx [ ~ D1 Þ; vðx [ ~ D2 Þ}; ~ D1 _ x [ vðx [ ~ D2 Þ ¼ min{vðx [ ~ D1 Þ; vðx [ ~ D2 Þ}; ~ D1 ^ x [ vðx [ ~ Dx denotes a soft property: “x approximately where Dx ; D1 ; D2 , X; x [ belongs to Dx” or “the approximate value of x belongs to Dx ”, and ~ Dx Þ [ ½0; 1 denotes the certainty index of this property. The vðx [ function hx(x ) is called a certainty distribution, the maximum value of hx(x ) is equal to 1. It may be useful to apply another version of the uncertain variable called ~ Dx is C-uncertain variable, for which the certainty index of the property x [ defined as follows ~ Dx Þ ¼ 12 ½vðx [ ~ Dx Þ þ 1 2 vðx [ ~ Dx Þ vc ðx [
ð1Þ
where Dx ¼ X 2 Dx : It may be shown that ~ Dx Þ; ~ Dx Þ $ vðx vðx [
~ Dx Þ: ~ Dx Þ ¼ vðx vc ðx [
The mean value of x is defined as follows Z 21 Z hx ðxÞ dx : M x ðxÞ ¼ xhx ðxÞ dx · X
X
3. Open-loop control system with a static plant Let us consider a static plant with input vector u [ U and output vector y [ Y ; described by a function y ¼ Fðu; z; xÞ where z [ Z is a vector of disturbances which can be measured and x [ X is an unknown vector parameter which is assumed to be a value of an uncertain variable x with a certainty distribution hx(x ) given by an expert. The control problem for the given z and the given desirable value y^ may be formulated as follows: Version I: To find the decision u^ maximizing vðy ø y^ Þ: Version II: To find u^ minimizing M s ðs ; u; zÞ
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where s ¼ wðy; y^ Þ is a quality index, e.g. s ¼ ðy 2 y^ ÞT ðy 2 y^ Þ where y and y^ are column vectors, and Ms is the mean value of s: In both versions hy ðy ; u; zÞshould be determined: hy ðy ; u; zÞ ¼ vðy ø yÞ ¼
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max
x [ Dx ðy ;u;zÞ
hx ðxÞ
ð2Þ
where Dx ðy ; u; zÞ ¼ {x [ X : Fðu; z; xÞ ¼ y}: Then in version I u^ is the value of u maximizing hy ðy ; u; zÞ: In version II for the determination of M s ðs ; uÞ one should find hs ðs ; u; zÞ ¼ max hy ðy ; uÞ y [ Dy ðsÞ
where Dy ðsÞ ¼ {y [ Y : wðy; y^ Þ ¼ s}: The problem formulations for C-uncertain variables have an analogous form but the considerations are much more complicated (Bubnicki, 2001a, b). When the problem in version I D and II have one solution, as a result we obtain the function u^ ¼ CðzÞ; i.e. the control algorithm in an open-loop control system. Now let us consider a plant described by a relation Rðu; y; z ; xÞ , U £ Y £ Z : The relation R is not reduced to a function and describes a relational knowledge representation of the plant. This is a description of a nondeterministic plant and for the given (u, z ) we may determine the set of possible outputs Dy ðu; z ; xÞ ¼ {y [ Y : ðu; y; zÞ [ Rðu; y; z ; xÞ}: The control problem may be formulated as follows: for the given R, hx and z find ~ Dy : u^ ¼ arg max v½Dy ðu; z ; x Þ # u In this formulation Dy , Y is a set given by a user, the property y [ Dy ~ means that Dy ðu; z ; xÞ # Dy where x is denotes the user’s requirement and # an approximate value of x : It is easy to note that D ~ Dy ¼ v½u [ ~ Du ðz ; x Þ ¼ v½Dy ðu; z ; x Þ # vðu; zÞ
where Du ðz ; xÞ ¼ {u [ U : Dy ðu; z ; xÞ # Dy }: Consequently, ~ Dx ðDy ; u; zÞ vðu; zÞ ¼ v½x [ where
Dx ðDy ; u; zÞ ¼ {x [ X : u [ Du ðz ; xÞ}
Variables for control systems
and u^ ¼ arg max u
max
x[Dx ðDy ;u;zÞ
D hx ðxÞ ¼ CðzÞ:
As a result we obtain the control algorithm C(z ) if v(u, z ) is maximized by one value u^ ¼ CðzÞ: In general, we can obtain a set of the decisions Du(z ) maximizing v(u, z ). Then the deterministic control algorithm may be obtained by using the mean value of u for the given z. It is easy to see that if x* is the value maximizing hx(x ) and there are no constraints for u then: Du ðzÞ ¼ {u [ U : x* [ Dx ðDy ; u; zÞ}: If x is considered as C-uncertain variable then according to (1) one should determine ~ Dx ðDy ; u; zÞ ¼ 12 {v½x [ ~ Dx ðDy ; u; zÞ þ 1 2 v½x [ ~ Dx ðDy ; u; zÞ} vc ½x [ where ~ Dx ðDy ; u; zÞ ¼ v½x [
max x[Dx ðDy ;u;zÞ
hx ðxÞ:
The optimal decision u^ c is obtained by maximization of vc. Example 1. Let u; y; z; x [ R 1 (one-dimensional variables), the relation R is given by inequality xu þ z # y # 2xu þ z; Dy ¼ ½y1 ; y2 ; y1 . 0; y2 . 2y1 ; x . 0: Then Du ðz ; xÞ ¼
hy 2 z y 2 z i 1 2 ; ; x 2x
Dx ðDy ; u; zÞ ¼
hy 2 z y 2 z i 1 2 ; : u 2u
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Assume that x has a triangular certainty distribution presented in Figure 1 with a ¼ d ¼ 12 : Then 8 > > > > > > > <
y2 2 z u 1 vðu; zÞ ¼ y1 2 z > > 2 1 2 > > u > > > : 0
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for
y2 2 z # u
for
2ðy1 2 zÞ # u and y2 2 z $ u
for
2ðy1 2 zÞ $ u and y1 2 z # u
for
y1 2 z $ u:
Thus, u^ is any value from ½2ð y1 2 zÞ; y2 2 z and vðu^ Þ ¼ 1: In the case of C-uncertain variable, using (1) we obtain 8 > > > > > <
y2 2 z 2u vc ðuÞ ¼ 1 2 y1 2 z > u > > > > : 0
for
u $ y1 þ 0:5y2 2 1:5z
for y1 2 z # u # y1 þ 0:5y2 2 1:5z for
u # y1 2 z:
It is easy to see that u^ c ¼ y1 þ 0:5y2 2 1:5z and vc ðu^ c Þ ¼
Figure 1. Example 1: Triangular certainty Distribution
y2 2 z : 2y1 þ y2 2 3z
For example, for y1 ¼ 3; y2 ¼ 13; z ¼ 1 we obtain u^ [ ½4; 12 and v ¼ 1; u^ c ¼ 8 and vc ¼ 0:75: The function vc(u ) is shown in Figure 2. 4. Closed-loop control system with a dynamic plant The approach based on uncertain variables may be applied to closed-loop control systems containing continuous dynamic plant with unknown parameters which are assumed to be the values of uncertain variables. The plant may be described by a classical model or by a relational knowledge representation. Now let us consider two control algorithms for the classical model of the plant. The plant is described by the equations
Variables for control systems
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s_ðtÞ ¼ f ½sðtÞ; uðtÞ ; x; yðtÞ ¼ h½sðtÞ where s is a state vector, or by the transfer function K P ðp; xÞ in the linear case. The controller with the input y (or the control error 1 ) is described by the analogous model with a vector of parameters b which is to be determined. Consequently, the performance index Q¼
Z
T
D wðy; uÞ dt ¼ Fðb; xÞ
0
for the given T and w is a function of b and x. In particular, for one-dimensional plant: Q¼
Z
1
1 2 ðtÞ dt ¼ Fðb; xÞ:
0
Figure 2. Example 1: Function v3(m)
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The closed-loop control system is then considered as a static plant with the input b, the output Q and the unknown parameter x, for which we can formulate and solve the decision problem described in Section 3. The control problem consisting in the determination of b in the known form of the control algorithm may be formulated as follows: for the given models of the plant and the controller find the value b^ minimizing M ðQÞ; i.e. the mean value of the performance index. The procedure for solving the problem is then the following. 1. To determine the function Q ¼ Fðb; xÞ: 2. To determine the certainty distribution hq ðq; bÞ for Q using the function F and the distribution hx(x ) in the same way as in the formula (2) for y : 3. To determine the mean value M ðQ; bÞ: 4. To find b^ minimizing M ðQ; bÞ: In the second approach it is necessary to find the value b(x ) minimizing Q ¼ Fðb; xÞ for the fixed x. The control algorithm with the uncertain parameter b(x ) may be considered as a knowledge of the control in our case, and the controller with this parameter may be called an uncertain controller. The deterministic control algorithm may be obtained in two ways, giving different results. The first way consists in substituting M ðbÞ in the place of b(x ) in the uncertain control algorithm, where M ðbÞ should be determined using the function b(x ) and the certainty distribution hx ðxÞ: The second way consists in determination of the relationship between ud ¼ M ð u Þ and the input of the controller, using the form of the uncertain control algorithm and the certainty distribution hx ðxÞ: This may be very difficult for the dynamic controller. The problem may be easier if the state of the plant s(t ) is put at the input of the controller. Then the uncertain controller has the form u ¼ Cðs; xÞ which may be obtained as a result of nonparametric optimization, i.e. C is the optimal control algorithm for the given model of the plant with the fixed x and for the given form of a performance index. Then D ud ¼ M ðu; sÞ ¼ Cd ðsÞ
where M ðu ; sÞ is determined using the distribution ~ Dx ðu ; sÞ ¼ max hx ðxÞ hu ðu ; sÞ ¼ v½x [ x [ Dx ðu ; sÞ
and Dx ðu ; sÞ ¼ {x [ X : u ¼ Cðs; xÞ}:
Example 2. The data for the linear control system under consideration (Figure 3) are the following:
K P ð p ; xÞ ¼
x ; ðpT 1 þ 1ÞðpT 2 þ 1Þ
K C ð p ; bÞ ¼
b p
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zðtÞ ¼ 0 for t , 0; zðtÞ ¼ 1 for t $ 0; hx(x ) has a triangular form presented in Figure 1. It is easy to determine
Q¼
Z
1
1 2 ðtÞ dt ¼
0
x 2 ðT 1 þ T 2 Þ ¼ Fðb; xÞ: 2xbðT 1 þ T 2 2 xbT 1 T 2 Þ
ð3Þ
The minimization of Q with respect to b gives
bðxÞ ¼
a ; x
a¼
T1 þ T2 ; T 1T 2
i.e. the uncertain controller is described by
K C ð pÞ ¼
bðxÞ a ¼ : xp p
Figure 3. Example 2: Linear Control System
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The certainty distribution hb(b ) is as follows: 8 > 0 for > > > > > > > ab 2 a > > > < db þ 1 for hb ðbÞ ¼ 2ab þ a > > > þ 1 for > > db > > > > > > 0 for :
a aþd a a #b# aþd a a a #b# a a2d a # b , 1: a2d 0,b#
From the definition of a mean value we obtain M ðbÞ ¼
adðd 2 þ 2a 2 Þ : a2 2 2a ln 2 a 2 d2
ð4Þ
Finally, the deterministic controller is described by K C;d ð pÞ ¼
M ðbÞ : p
To apply the first approach described in this section, it is necessary to find the certainty distribution for Q using formula (3) and the distribution hx ðxÞ; then to determine M ðQ ; bÞ and to find the value b^ minimizing M ðQ ; bÞ: It may given by the formula (4). be shown that b^ – M ðbÞ 5. Stability of dynamical systems with uncertain parameters The uncertain variables may be used in the investigation of the stability of a control system containing unknown parameter x which is assumed to be a value of an uncertain variable. Consider the nonlinear and/or time-varying system with one equilibrium state equal to 0 (a vector with zero components), described by snþ1 ¼ Aðsn ; cn ; xÞsn
ð5Þ
where sn [ S [ R k is a state vector, cn [ C is a vector of time-varying parameters and the uncertainty concerning cn is formulated as follows ^ ð6Þ cn [ Dc n$0
where Dc is a given set in C. The system (5) is globally asymptotically stable (GAS) iff sn converges to 0 for any s0 : For the fixed x, the uncertain system (5),
(6) is GAS iff the system (5) is GAS for every sequence cn satisfying (6). Let W(x ) and P(x ) denote properties concerning x such that W(x ) is a sufficient condition and P(x ) is a necessary condition of the global asymptotic stability for the system (5), (6), i.e. W ðxÞ ! the system ð5Þ; ð6Þ is GAS; the system ð5Þ; ð6Þ is GAS ! PðxÞ: Then the certainty index vs that the system (5), (6) is GAS may be estimated by the inequality vw # vs # vp where vw ¼ max hx ðxÞ; x[Dxw
Dxw ¼ {x [ X : W ðxÞ};
vp ¼ max hx ðxÞ; x[Dxp
Dxp ¼ {x [ X : PðxÞ};
vw is the certainty index that the sufficient condition is approximately satisfied and vp is the certainty index that the necessary condition is approximately satisfied. In general, Dxw # Dxp and Dxp 2 Dxw may be called “a grey zone” which is a result of an additional uncertainty caused by the fact that W ðxÞ – PðxÞ: In particular, if it is possible to determine a sufficient and necessary condition W ðxÞ ¼ PðxÞ then vw ¼ vp and the value vs may be determined exactly. The condition P(x ) may be determined as a negation of a sufficient condition that the system is not GAS, i.e. such a property Pneg(x ) that P neg ðxÞ ! there exists cn satisfying ð6Þ such that ð5Þ is not GAS: For the nonlinear and time-varying system we may use the stability conditions in the form of the theorems presented in Bubnicki (1964, 1968, 2000c, 2002c). Choosing different sufficient and necessary conditions we may obtain the different estimations of the certainty index vs. In particular, we may choose the following conditions presented in Bubnicki (2000c).
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Theorem 1. The system (5), (6) where
^ Dc ¼ c [ C : AðxÞ # Aðs; c; xÞ # AðxÞ
ð7Þ
s[S
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is GAS if all entries of the matrices A(x ) and AðxÞ are nonnegative and kAðxÞk , 1
ð8Þ
where kAk ¼ max
1#j#k
k X
jaij j:
A
i¼1
The inequality in (7) denotes the inequalities for the entries: aij ðxÞ # aij ðs; c; xÞ # a ij ðxÞ: Theorem 2. Assume that all entries of the matrix AðxÞ are nonnegative. If the system (5), (7) is GAS then k _X
a ij ðxÞ , 1:
ð9Þ
j i¼1
From Theorems 1 and 2 we obtain Dxw ¼ {x [ X :
k ^X
a ij ðxÞ , 1};
ð10Þ
j i¼1
Dxp ¼ X 2 Dx; neg where Dx;neg ¼ {x [ X :
k ^X
aij ðxÞ $ 1}:
ð11Þ
j i¼1
Example 3. Consider an uncertain system (5) where k ¼ 2 and " # a11 ðsn ; cn Þ þ x a12 ðsn ; cn Þ Aðsn ; cn ; xÞ ¼ a22 ðsn ; cn Þ þ x a21 ðsn ; cn Þ with the uncertainty (7), i.e. nonlinearities and the sequence cn are such that
^ ^ a ij # aij ðs; cÞ # a ij ;
i ¼ 1; 2;
Variables for control systems
j ¼ 1; 2:
c[Dc s[Ds
Assume that x $ 0 and a ij $ 0: Applying the condition (8) yields a 11 þ x þ a 21 , 1;
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a 12 þ a 22 þ x , 1
and Dxw in (10) is defined by: x , 1 2 maxða11 þ a 21 ; a 12 þ a 22 Þ: Applying the negation of the condition (9) yields a11 þ x þ a 21 $ 1;
a12 þ a 22 þ x $ 1:
Then Dx,neg in (11) is determined by x $ 1 2 minða11 þ a 21 ; a12 þ a 22 Þ and the necessary condition (9) defining the set Dxp ¼ X 2 Dx;neg is as follows x , 1 2 minða11 þ a 21 ; a12 þ a 22 Þ: For the given certainty distribution hx(x ) we can determine vw ¼ max hx ðxÞ; 0#x#xw
vp ¼ max hx ðxÞ 0#x#xp
where xw ¼ 1 2 maxða11 þ a 21 ; a 12 þ a 22 Þ; xp ¼ 1 2 minða11 þ a 21 ; a12 þ a 22 Þ: Assume that hx(x ) has parabolic form: hx ðxÞ ¼ 2e 22 ðx 2 dÞ2 þ 1 for d 2 e # x # d þ e and hx ðxÞ ¼ 0 otherwise; 0 , e , d: The results obtained from (12) for the different cases are as follows. 1. For xw $ d vw ¼ vp ¼ 1:
ð12Þ
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2. For d 2 e # xw # d vw ¼ 2e 22 ðxw 2 dÞ2 þ 1; vp ¼ 1 for xp $ d
1272 and
vp ¼ 2e 22 ðxp 2 dÞ2 þ 1 for xp # d: 3. For xw # d 2 e vw ¼ 0; 8 1 > > < 2 22 vp ¼ 2e ðxp 2 dÞ þ 1 > > : 0
for
xp $ d
for d 2 e # xp # d for
xp # d 2 e:
For example, if d 2 e # xw # d and xp # d then the certainty index vs that the system is globally asymptotically stable satisfies the inequality 2e 22 ðxw 2 dÞ2 þ 1 # vs # 2e 22 ðxp 2 dÞ2 þ 1: For the numerical data a 11 ¼ 0:2; a11 ¼ 0:1; a 21 ¼ 0:3; a 21 ¼ 0:2; a 12 ¼ 0:2; a12 ¼ 0:1; a 22 ¼ 0:2; a 22 ¼ 0:1; d ¼ 0:9; e 22 ¼ 3; we obtain vw ¼ 0:52; vp ¼ 0:97 and 0:52 # vs # 0:97: 6. Conclusions The uncertain variables are proved to be a convenient tool for the analysis and design of control systems containing a plant with unknown parameters characterized by an expert. In the case of C-uncertain variable the expert’s knowledge is used in a better way but the calculations are more complicated. The estimation of vs for the system stability may be useful for choosing parameters of the controller to obtain a small value of vw and/or a small value of the grey zone vp 2 vw (Bubnicki, 2000c, 2002c). The applications of the uncertain variables in uncertain control systems may be extended to more complicated cases: multistage decision processes (Bubnicki, 2002b), the control of assembly systems (Bubnicki, 2002a), complex knowledge-based systems (Bubnicki, 2000d), and learning systems (Bubnicki, 2000b).
References Bubnicki, Z. (1964), “On the stability condition of nonlinear sampled-data systems”, IEEE Trans. on AC, Vol. 9, pp. 280-1. Bubnicki, Z. (1968), “On the linear conjecture in the deterministic and stochastic stability of discrete systems”, IEEE Trans. on AC, Vol. 13, pp. 199-200. Bubnicki, Z. (2000a), “Uncertain variables in the computer aided analysis of uncertain systems”, in Pichler, F., Moreno-Diaz, R. and Kopacek, P. (Eds), Computer Aided Systems Theory. Lecture Notes in Computer Science, Springer-Verlag, London, Berlin, Vol. 1798, pp. 528-42. Bubnicki, Z. (2000b), “Learning processes in a class of knowledge-based systems”, Kybernetes, Vol. 29, pp. 1016-28. Bubnicki, Z. (2000c), “General approach to stability and stabilization for a class of uncertain discrete non-linear systems”, Int. J. of Control, Vol. 73, pp. 1298-306. Bubnicki, Z. (2000d), “Knowledge validation and updating in a class of uncertain distributed knowledge systems”, in Shi, Z., Faltings, B. and Musen, M. (Eds), Proc. of 16th IFIP World Computer Congress – IIP (Beijing), Publishing House of Electronics Industry, Beijing, pp. 516-23. Bubnicki, Z. (2001a), “Uncertain variables and their applications for a class of uncertain systems”, International Journal of Systems Science, Vol. 32, pp. 651-9. Bubnicki, Z. (2001b), “Uncertain variables and their application to decision making”, IEEE Trans. on SMC, Part A: Systems and Humans, Vol. 31 No. 6 (in press). Bubnicki, Z. (2002a), “Application of uncertain variables for a class of intelligent knowledgebased assembly systems”, in Sugisaka, M. and Tanaka, H. (Eds), Proc. of the 7th Int. Symposium on Artificial Life and Robotics, Oita. Bubnicki, Z. (2002b), Uncertain Logics, Variables and Systems, Springer-Verlag, London, Berlin (in press). Bubnicki, Z. (2002c), “Stability and stabilization of discrete systems with random and uncertain parameters”, Proc. of 15th IFAC World Congress, Barcelona (in press).
Variables for control systems
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Control synthesis of a class of DEDS Frantisˇek Cˇapkovicˇ Institute of Informatics, Slovak Academy of Sciences, Bratislava, Slovak Republic Keywords Cybernetics, Dynamic modelling, Control systems Abstract A new control synthesis method suitable for a special kind of discrete event dynamic systems (DEDS) is presented in this paper. The systems to be controlled are modelled by a special class of Petri nets (PN) named state machine (SM). The class is distinctive by the fact that each PN transition has only one input place and only one output place. Bipartite directed graphs (BDG) are utilized in the control synthesis process. Namely, PN in general are (from the structure point of view) the BDG. Both the state reachability tree and the corresponding control one are developed in the straight-line procedure starting from the given initial state and directed to the desirable terminal one as well as in the backtracking procedure starting from the terminal state and directed to the initial one. After a suitable intersection of both the straight-lined state reachability tree and the backtracking one the state trajectories of the system are obtained. After the intersection of both the straight-lined control reachability tree and the backtracking one the control interferences corresponding to the state trajectories are obtained.
1. Introduction Last years have seen that the discrete event dynamic systems (DEDS) control synthesis is very important area of modern control theory. Petri nets (PN) are often used (Holloway et al., 1997; Peterson, 1981) for DEDS modelling, analysis and control synthesis. This paper is devoted to DEDS described by the socalled state machines (SM). SM represent a special class of the ordinary PN (OPN) where each PN transition has only one input place and only one output place. Recently (Cˇapkovicˇ, 2000a, b, c), the control synthesis method utilizing directed graphs (DG) was developed for SM. The approach presented here improves and/or simplifies the above mentioned method. Bipartite DG (BDG) (Diestel, 1997) are used in this way. Thus, the process of finding the control vectors is simpler and more effective. SM can be understood to be the DG with the PN places being the DG nodes and the PN transitions being fixed to the DG edges. Hence, the SM state reachability tree can be developed (Cˇapkovicˇ, 1999) as follows xðk þ 1Þ ¼ D k · xðkÞ; k ¼ 0; N where k is the discrete step (the level of the tree); xðkÞ ¼ Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1274-1281. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443473
ð1Þ ðkÞ T ðsðkÞ p1 ðgÞ; . . .; spn ðgÞÞ ;
Partially supported by the Slovak Grant Agency for Science (VEGA) in frame of the project # 2/7145/20
k ¼ 0; N is the n-dimensional state vector in the step k ; sðkÞ pi ðgÞ; i ¼ 1; n is the Control synthesis state of the elementary place pi in the step k. It depends on actual enabling its of DEDS ðkÞ ðkÞ input transitions. g symbolizes this dependency. D k ¼ {dðkÞ ij }n£n ; dij ¼ gt pi jpj ; i ¼ 1; n; j ¼ 1; n: It is the functional matrix where gðkÞ t pi j pj [ {0; 1} is the transition function of the PN transition fixed on the edge oriented from pj to pi. 1275 To avoid problems with computer handling Dk a simple approach to control synthesis was proposed (Cˇapkovicˇ, 2000 a, b, c). It operates with the adjacency matrix D of the DG. The idea is very simple. To obtain possible trajectories from a given initial state x0 to a prescribed terminal state xt a special intersection of both the straight-lined reachability tree (developed from x0 towards xt) and the backtracking reachability tree (developed from the xt towards x0, however, containing the paths oriented towards the terminal state) is performed. The former tree is developed as follows {x1 } ¼ D · x0
ð2Þ
{x2 } ¼ D · {x1 } ¼ D · ðD · x0 Þ ¼ D 2 · x0
ð3Þ
··· ··· ··· {xN } ¼ D · {xN 21 } ¼ D N · x0
ð4Þ
where xN ¼ xt : In general, {xj} is an aggregate of all of the states that are reachable from the previous states. According to graph theory N # ðn 2 1Þ: The latter tree is the following {xN 21 } ¼ D T · xN
ð5Þ
{xN 22 } ¼ D T · {xN 21 } ¼ ðD T Þ2 · xN
ð6Þ
··· ··· ··· {x0 } ¼ D T · {x1 } ¼ ðD T ÞN · xN
ð7Þ
Here, {xj} is an aggregate all of the states from which the next states are reachable. It is clear that x0 – {x0 } and xN – {xN }: It is the consequence of the fact that in general, D · D T – I n as well as D T · D – I n (In is ðn £ nÞ identity matrix). The intersection of the trees is made as follows M 1 ¼ ðx0 ;1{x1 }; . . .;1{xN 21 };1{xN }Þ
ð8Þ
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M 2 ¼ ð2{x0 };2{x1 }; . . .;2{xN 21 }; xN Þ
ð9Þ
M ¼ M1 > M2
ð10Þ
M ¼ ðx0 ; {x1 }; . . .; {xN 21 }; xN }
ð11Þ
1276 where the matrices M
1, M2 represent, respectively, the straight-lined tree and the backtracking one. The special intersection of both the trees is performed by means of the column-to-column intersection both of the matrices. Thus, {xi } ¼ minð1{xi };2{xi }Þ; i ¼ 0; N with 1{x0 } ¼ x0 ;2{xN } ¼ xN : Due to the causality principle any shorter feasible solution is involved in the longer feasible one. It can be found when before the intersection of the matrices M1 and M2 the latter one is shifted to the left for a number of columns. After shifting M2 for one column, the intersection with M1 yields the following matrix2 1M with dimensionality ðn £ N Þ
21
M ¼ ðx0 ; {x1 }; . . .; {xN 22 }; xN 21 Þ
ð12Þ
where xN 21 ¼ xt : In general, the shifting (i.e. finding the ðn £ ðN 2 k þ 1ÞÞ matrices 2k M ; k ¼ 1; 2; . . .Þ can continue until the intersections exists, i.e. until x0 [2 {x0 } and xt [1 {xN 2k }. In M the trajectories from the initial state x0 to the terminal one xN are comprehended. D k contains relations between the trajectories and the control variables. The procedure of the assignment corresponding transitions to the elementary parts of the trajectories consists in finding the final set {Ti} of transitions enable in the steps i¼0, N 2 1. It is the following: {T i } ¼ bt{T i } > sl{T i }
ð13Þ
{T i } ¼ {bt{xi }þ }; sl{T i } ¼ {sl{xi }þ }
ð14Þ
{xi } ¼ DTk · {xiþ1 }
ð15Þ
sl
ð16Þ
bt
bt
{xi } ¼ D k · {xi }
where bt{xi}+, sl{xi}+ denotes respectively the set that consists only of the nonzero elements of the bt{xi} and sl{xi} (sl{·} means straight-lined; bt{·} means back tracking). On this way the composed elements (like, e.g. a+b in general) express in (15) separating the elementary trajectories (i.e. forks) and in (16) their assembling (i.e. joins). Let us denote the former ones as ða þ bÞ_ and the latter ones as ða þ bÞ^ : The global set of the enabled transitions is
{T} ¼ {{T 0 }; {T 1 }; . . .; {T N 21 }}
ð17Þ Control synthesis
Thus, the control problem is resolved. Another problem is how to choose the most suitable trajectory with respect to prescribed control task specifications and the corresponding sequence {U } ¼ {u0 ; u1 ; . . .; uN 21 } of the control vectors. This problem is out of the frame of this approach. The specifications are usually given in nonanalytical terms – e.g. verbally. Hence, a suitable representation of knowledge about them can be useful. The main aim of this paper is to simplify the above method, especially as to the assigning the transitions BDG are used on this way. 2. The new approach The OPN in general (SM as well) can be understood to be BDG. Let S ¼ fP; T} be the set of the BDG nodes where P is the set of the PN places and T is the set of the PN transitions. Let D be the set S £ S of BDG edges. Their occurrence can be expressed by the ððm þ nÞ £ ðm þ nÞÞ matrix 0 1 f m£m G T A D¼@ T ð18Þ F f n£n where f i£j in general is the ði £ jÞ zero matrix; G is the ðm £ nÞ incidence matrix expressing T £ P; F is the ðn £ mÞ incidence matrix representing P £ T. Then, BDG can be understood to be DG and the above described control synthesis procedure can be used. The straight lined development is the following {skþ1 } ¼ D · {sk }; k ¼ 0; 1; . . .; 2N 2 1
ð19Þ
s0 ¼ ðxT0 ; fTm ÞT
ð20Þ
{s1 } ¼ ðfTn ; {u0 }T ÞT
ð21Þ
{s2 } ¼ ð{x1 }T ; fTm ÞT
ð22Þ
{s3 } ¼ ðfTn ; {u1 }T ÞT
ð23Þ
··· ··· ··· {s2 N 21 } ¼ ðfTn ; {uN 21 }T ÞT
ð24Þ
of DEDS
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{s2 N } ¼ ð{xN }T ; fTm ÞT
ð25Þ
where fj in general is the j-dimensional zero vector. The straight-lined reachability tree arising from the initial vector s0 and directed towards the terminal state s2N can be recorded by the matrix M 1 ¼ ðs0 ;1{s1 }; . . .;1{s2 N 21 };1{s2 N }Þ
ð26Þ
The backtracking development is {s2 N 2k21 } ¼ D T · {s2 N 2k }; k ¼ 0; 1; . . .; 2 N 2 1 s2 N ¼ ðxTN ; fTm ÞT
ð27Þ
{s2 N 21 } ¼ ðfTn ; {uN 21 }T ÞT
ð28Þ
{s2 N 22 } ¼ ð{xN 21 }T ; fTm ÞT
ð29Þ
{s2 N 23 } ¼ ðfTn ; {uN 22 }T ÞT
ð30Þ
··· ··· ··· {s1 } ¼ ðfTn ; {u0 }T ÞT
ð31Þ
{s0 } ¼ ð{x0 }T ; fTm ÞT
ð32Þ
The backtracking reachability tree is recorded by M 2 ¼ ð2{s0 };2 {s1 }; . . .;2 {s2N 21 }; s2N Þ
ð33Þ
After the intersection (10) we have M ¼ ðs0 ; {s1 }; . . .; {s2N 21 }; x2N Þ
ð34Þ
where {si } ¼ minð1{si };2 {si }Þ; i ¼ 0; 2N with 1{s0 } ¼ s0 ; 2 {s2N } ¼ s2N : Information about the state vectors is stored in the even columns of M while information about the control vectors is stored in its odd columns. In addition to this, the matrices F and G are numerical constant incidence matrices expressing the relations P £ T and T £ P, respectively. Hence, it is not necessary to use the relatively complicated procedure (13)-(16). This is a big advantage of the proposed approach. On the other hand the dimensionality of the matrix D is ððn þ mÞ £ ðn þ mÞÞ, while in the original method the dimensionality is only ðn £ nÞ: Also the dimensionalities of M1, M2 and M are
greater than those in the original method. However, because of the special block Control synthesis form of both the matrix D and the vectors sk, k ¼ 0; 2 N we can simultaneously of DEDS use (alternate step-by-step) two procedures with dimensionalities n, m, respectively. 3. The peculiarity of the approach What is specific in this approach is the step-by-step alternation of enumerating both the state variables and the control ones. In the sense of the previous section the straight-lined procedure is the following 1
1
X ¼ ðx0 ; f n£N Þ
ð35Þ
1
{u0 } ¼ F T · x0
ð36Þ
U ¼ ð1 {u0 }; f m£ðN 21Þ Þ
ð37Þ
1
1
{x1 } ¼ G T · 1 {u0 }
ð38Þ
X ¼ ðx0 ;1 {x1 }; f n£ðN 21Þ Þ
ð39Þ
1
1
{u1 } ¼ F T · 1 x1
ð40Þ
U ¼ ð1 {u0 };1 {u1 }; f m£ðN 22Þ Þ
ð41Þ
1
1
{x2 } ¼ G T · 1 {u1 }
ð42Þ
X ¼ ðx0 ;1 {x1 };1 {x2 }; f n£ðN 22Þ Þ
ð43Þ
··· ··· ··· 1
1
{uN 21 } ¼ F T · 1 xN 21
ð44Þ
U ¼ ð1 {u0 };1 {u1 }; . . .;1 {uN 21 }Þ
ð45Þ
1
1
{xN } ¼ G T · 1 {uN 21 }
ð46Þ
X ¼ ðx0 ;1 {x1 };1 {x2 }; . . .;1 {xN }Þ
ð47Þ
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where 1U is ðm £ N Þ matrix and 1X is ðn £ ðN þ 1ÞÞ matrix. The left upper index 1( · ) points out performing the straight-lined procedure. The backtracking procedure run as follows 2
X ¼ ðf n£N ; xN Þ
ð48Þ
2
{uN 21 } ¼ G:xN
ð49Þ
U ¼ ðf m£ðN 21Þ ;2 {uN 21 }Þ
ð50Þ
1280 2
2
2
{xN 21 } ¼ F:2 {uN 21 }
ð51Þ
X ¼ ðf n£ðN 21Þ ;2 {xN 21 }; xN Þ
ð52Þ
2
2
{uN22 } ¼ G:2 {xN21 }
ð53Þ
U ¼ ðf m£ðN 21Þ ;2 {uN 22 };2 {uN 21 }Þ
ð54Þ
2
2
{xN 22 } ¼ F · 2 {uN 21 }
ð55Þ
X ¼ ðf n£ðN 22Þ ;2 {xN 22 };2 {xN 21 }; xN Þ ... ... ... 2
2
{u1 } ¼ G · 2 {x2 }
ð56Þ
U ¼ ðf n£1 ;2 {u1 }; . . .;2 {uN 21 }Þ
ð57Þ
2
2
{x1 } ¼ F · 2 {u1 }
ð58Þ
X ¼ ðf n£1 ;2 {x1 };2 {x2 }; . . .; xN Þ
ð59Þ
2
2
{u0 } ¼ G · 2 {x1 }
ð60Þ
U ¼ ð2 {u0 };2 {u1 }; . . .;2 {uN 21 }Þ
ð61Þ
2
{x0 } ¼ F · 2 {x0 }
ð62Þ
X ¼ ð2 {x0 };2 {x1 };2 {x2 }; . . .; xN Þ ð63Þ Control synthesis 2 of DEDS U is ðm £ N Þ matrix and X is ðn £ ðN þ 1ÞÞ matrix. The left upper where 2 index (·) points out performing the backtracking procedure. The final phase of the control problem solving consists in the special intersection described above. In such a way we have both the system state trajectories and corresponding control strategies 1281 2
2
X ¼ 1X > 2 X
ð64Þ
X ¼ ðx0 ; {x1 }; . . .; {xN 21 }; xN Þ
ð65Þ
U ¼ 1 U > 2U
ð66Þ
U ¼ ð{u0 }; {u1 }; . . .; {uN 21 }Þ
ð67Þ
Henceforth, the procedure (13)-(16) need not be used. Using the zero blocks is eliminated as well. References Cˇapkovicˇ, F. (1999), “Automated solving of DEDS control problems”, in El-Dessouki, A., Imam, I., Kodratoff, Y. and Ali, M. (Eds), Multiple Approaches to Intelligent Systems, LNAI, Vol. 1611 of LNCS, Springer, Berlin, Heidelberg, New York, Tokyo, pp. 735-46. Cˇapkovicˇ, F. (2000a), “Intelligent control of discrete event dynamic systems”, Proceedings of 2000 IEEE International Symposium on Intelligent Control (Patras, Greece), IEEE Press, Piscataway, USA, pp. 109-14. Cˇapkovicˇ, F. (2000b), “Modelling and control of discrete event dynamic systems”, Research Report, BRICS Report Series, RS-00-26, University of Aarhus, Denmark, September, p. 58. ˇCapkovicˇ, F. (2000c), “A solution of DEDS control synthesis problems”, Proceedings of IFAC Conference on Control System Design (Bratislava, Slovak Republic), Pergamon, Elsevier Science, Oxford, UK, pp. 343-8. Diestel, R. (1997), Graph Theory, Springer, New York. Holloway, L., Krogh, B. and Giua, A. (1997), “A survey of Petri net methods for controlled discrete event systems”, Discrete Event Dynamic Systems: Theory an Appl., Vol. 7, pp. 151-80. Peterson, J.L. (1981), Petri Net Theory and Modeling the Systems, Prentice Hall, New York.
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Incentives: mechanisms for the consistency of the Colombian educational system Mario Castillo, Gabriel Duque and Fernando Beltra´n Department of Industrial Engineering, Universidad de Los Andes, Bogota´, Colombia Keywords Cybernetics, Education, Quality, Efficiency Abstract This paper focuses on a project to develop a methodology for diagnosing and designing incentives to improve the Colombian basic education system’s performance. We describe the system and then the model identifying the agents characterized and the relationships between them. With these elements we construct an Incentives map. In order to connect the decisions of the individual or institution agents to the performance of the system, we build a way of illustrating them. Finally, we present the results.
1. Introduction This paper was developed under a program[1] that responded to the need of the Colombian basic education system to look for structural changes oriented to improve its quality, coverage, and equity. We participated in a project that developed a methodology for diagnosing and designing incentives to improve the system’s performance. In the conceptual framework we describe the system and our definition of incentives in this context. We then describe the model identifying the agents characterized and the relationships between them. With these elements we construct an Incentives Map. In order to connect the decisions of the individual or institution agents to the performance of the system, we build a way of illustrating them. Finally we present the results.
Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1282-1288. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443482
2. Conceptual framework The main concepts and tools come from the fields of institutional economics, applied microeconomics and decision theory. They proved to be appropriate for the provision of elements to build the analysis of a complex system as the one we studied. We developed a conceptual model representing the economic agents that conform the Colombian basic education system and the main relations among them. In this sense the system is described as a set of economic agents, both institutional and individual, whose relations and interactions are represented as economic contracts. The objective of the analysis was to design a set of mechanisms and policies to restructure the relationships among the agents in the system. It is expected
that in the process of making individual maximizing choices, the agents contribute to the goals set for the system. We seek to generate a consistent set of proposals to ensure some degree of self- regulation. Our definition of incentives is not limited to the idea of assigning prizes and compensations for desirable behavior of the agents. We rather defined them as the set of mechanisms and policies present in the decision variables and interactions of the agents.
Colombian educational system 1283
3. General model and economic agents A graphic representation of the general model can be seen in Figure 1. It identifies the limit of the system analyzed, the agents studied and the relations among them. Each institutional or individual agent was described and characterized in terms of its main objectives and decision variables. The idea behind this specification was that when the agents make their decisions to meet their individual objectives, the relations between them act as restrictions. Each agent was identified and described. Many of these agents required a description of the institutions that make them up to better identify their objectives and the decision variables under their control. As an example, the main institutions considered within the Central Government are the Ministries of Education and Finance, and the National Planning Department. Other agents, like the teachers, were characterized as individuals seeking their well being and a good place in society – as any individual economic agent would seek. The contracts between the economic agents were described in terms of three factors: the exchange, the rules for the exchange, and the motivation for each agent to fulfill its responsibility. These terms were used to characterize the relationships in Figure 1.
Figure 1.
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4. Incentives Map We constructed a table, called Incentives Map, based on the decision variables of each one of the economic agents of the system. The table includes each one of the eight agents with their respective decision variables. This table presents, in an explicit way, the relations between the decisions variables of each agent and the decision variables of each one of the other agents. Each pair of decision variables is rated with a pair of integer numbers, each of which is chosen among 0 and 3. The first number represents how relevant a decision variable is for the relation between the two agents (0 means no relevance at all, and 3 means very relevant). The second number attempts to rate the level of existing incentives in the relation between the two agents through the given decision variable (0 means incentive absence, and 3 means strong incentive presence). This Incentives Map synthesizes the interactions between the different economic agents of the Colombian basic education system. This map is the result of a systematic and detailed analysis about the agent’s characterization (the agents objectives, their decisions variables and their most important interactions with other agents of the system), and the contracts that govern the agent’s interactions. In Table I we present a sample of the Incentives Map, exhibiting the school and its interactions with the community. As an example, let us consider the school. In this case we can understand better the role of the school based on the interpretation of the Incentives Map. We can observe the importance and quantity of interactions between this agent and the others. The analysis lets us conclude that the school is the institutional agent that can generate the most changes in the system; it also allows us to see that this agent provides the most relevant opportunities to improve the system. The school has relations particularly relevant with departments, municipalities, teachers and communities. In our research we made this type of analysis for each one of the economic agents, making clear for each one of them the principal weaknesses in their relations with other agents as well as the most important opportunities for the system improvement. Working in the appropriate way on each one of the interactions must produce a system improvement.
School decision variables
Table I.
Curriculum quality Pertinence of pedagogic methods Quality/achievement level of school institutional education plan School minimal conditions Management quality
Community Interaction relevance Incentives intensity 3 3
0 0
3 3 3
1 1 1
5. Relations between the agents decisions and the variables that affect the performance of the system The Incentives Map is somehow the synthesis of our diagnosis about the public education system using the institutional economics and the decision analysis approach. However, an important issue remains: how to achieve changes in the public education system performance? In order to do this, we adopted the performance variables defined by the New Scholar System Program: quality, coverage, equity, and efficiency. We explicitly defined each dimension of the system performance and we identified a set of 24 variables that can affect some or all the four dimensions. Once we identified explicitly the variables, so called “critical variables”, we turn to the agents’ decision variables in order to learn how the decision variables act upon the critical variables. The rational is quite simple: only through their decision variables can the agents act upon the variables that affect the system performance factors. Based on the rational described earlier, we formulated six sets of propositions oriented to improve the consistency and performance of the Colombian educational system. The propositions were grouped according to the core issues of the education system as: (1) the system of generation and distribution of resources, (2) the stability and harmonization of educational plans, (3) the improvement of teachers potential, (4) the school as the kernel of the system: autonomy and efficiency, (5) a reformulation of the teachers union role, and (6) a reformulation of the community role. Each of the propositions was accompanied of a logical scheme that presented the way, as the agent’s decision variables would affect the critical variables, and these, in turn, would affect the performance factors. We will illustrate the way in which the proposals were presented in our work. This is a specific proposal with its respective logical scheme (Figure 2). Improving the schools principals’ leadership in the academic and administrative management. The school principal is a very important actor for the development of an appropriate educational environment. The principal, as resources manager and school pedagogic mission leader, must be supported by the school government. The school principal must represent the autonomy and authority of the school in the decision of how to achieve the school goals. The school principal must be endowed with management tools. He/she should participate in the appointment and evaluation of the teachers. The fact that the school principal truly assumes his role of academic and management
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Figure 2.
leader will positively influence the development of a responsible autonomy in the school. Following is the logical scheme associated to the proposal described earlier: Variables .
Decision variables: Central government CG1: game rules for teachers CG2: rules for the elaboration of educational plans and budgets School S1: management quality S2: quality and achievement level of the school institutional education plan
.
Critical variables: V1: quality of schools management V2: quality of schools academic management V3: school capacity for interacting with other institutions involved in the educational process V4: school social role and action scope
The scheme shows the relations and causality effects between the variables involved in the proposal related with the school principal’s leadership.
The government decision variables management quality and rules for the elaboration of educational plans and budgets, affect the school decision variables management quality and quality and achievement level of the school institutional education plan. The last two decision variables affect in different ways the critical variables quality of schools management, quality of schools academic management, school capacity for interact with other institutions that produce educational acts, and school social role and action scope. As the scheme shows, these critical variables affect the performance factors of the system. 6. General results The approach and the methodology adopted in our work use concepts coming from institutional economy, applied micro economy and decision analysis. This approach allowed us to carry out, in a structured way, a comprehensive analysis of Colombian public educational system. We arrived to a good detail level of analysis, that enables us to design policies and incentives mechanisms that should improve the consistency of the system and its global performance in terms of quality, coverage, and equity. Our work is a methodological alternative, conceptually robust and consistent, which proved to be practical and effective. This methodology could be used in the analysis of other public systems of a similar complexity to the Colombia educational system. The results of this work represent a solid basis for the construction of an evaluation and control system, which will make possible to measure the impact of the mechanism and policies to be adopted in the future to improve the Colombian educational system. Note 1. The Colombian New Scholar System Program
Further reading Abrile, M.I. (1994), “Nuevas demandas a la educacio´n y a la Institucio´n Escolar, y la profesionalizacio´, n de los docentes”, Revista Iberoamericana de Educacio´n – OEI No. 5, mayo-agosto. BID – The World Bank – PREAL (1999), “Teachers in Latin American: new perspectives on their development and performance”, Report on the Proceedings of the Conference, 28-30 Junio 1999 San Jose´, Costa Rica. Clavijo, S. (1998), Poli´tica Fiscal y Estado en Colombia, Ediciones Uniandes, Bogota´, Colombia. Corte´s, S. (1998), “Giovanni. Informe final del estudio sobre fuentes y usos de recursos pu´blicos para la educacio´n primaria y secundaria”, Technical Report MEN, Bogota´, Colombia. DNP (1998), “Misio´n Social. Evolucio´n de la sociedad Colombiana y construccio´n del desarrollo humano”, Informe de Desarrollo Humano, DNP, Bogota´, Colombia. MEN (1994), Ley General de Educacio´n 115.
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MEN (1997), Programa Nacional de Incentivos. Direccio´n de Organizacio´n Escolar. Enero de 1997. MEN (1999), Plan de Racionalizacio´n del Sector Educativo, Plan Nacional de Desarrollo (1998-2002), Ley 508. Milgrom, P. y Roberts, (1992), Economics, Organizations and Management. Prentice-Hall. Mizala, A., Gonza´lez, P., Romanguera, P. and Guzma´n, A. (2000), “Los maestros en Chile: Carreras e incentivos”, Reporte BID – Red de Centros de Investigacio´n. Mora, H., Ayala, U., Gutie´rrez, C. y Velasco, A. (1999), “Financiamiento de la educacio´n por medio de subsidios a la demanda: evaluacio´n de la viabilidad del sistema de capitacio´n”, Reporte. Fedesarrollo, Bogota´, Colombia. Pen˜a, M. (2000), “Reforma escolar y autonomi´a. Propuesta para el fortalecimiento de las instituciones educativas en Colombia”, Reporte Corpoeducacio´n. Pe´rez, F. (1996), “Ca´lculo de la unidad de pago por capitacio´n, UPC de la educacio´n ba´sica”, Reporte DNP, Bogota´, Colombia. Salanie´,, B. (1998), The Economics of Contracts, The MIT Press, Cambridge, Mass. Sarmiento, E. (1997), “Financiacio´n equitativa y eficiente del sector educativo”, Misio´n Social, DNP, Bogota´, Colombia. Sarmiento, E. (1998), “Perfeccionamiento de la fo´rmula financiera y aplicacio´n a las experiencias demostrativas”, Misio´n Social, DNP, Bogota´, Colombia. Sarmiento, E. (2000), “Situado fiscal y financiacio´n del sector educativo: equidad y eficiencia”, Revista Fecode, No. 53. Unesco (2000), Indicadores: Definiciones, Propo´sitos y Datos Requeridos. Proyecto Regional de Indicadores Educativos II, Cumbre de las Ame´ricas, Santiago, Chile. Wiesner, E. (1997), “La asignacio´n de recursos por capitacio´n y la reforma del sector educativo en Colombia”, Reporte BID.
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Modelling, prototyping, and verifying concurrent and distributed applications using object-oriented Petri nets
Applications using OOPNs
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Milan Cˇesˇka, Vladimı´r Janousˇek and Toma´sˇ Vojnar Department of Computer Science and Engineering, Brno University of Technology, Bozˇeteˇchova, Brno, Czech Republic Keywords Cybernetics, Distributed applications, Rapid prototyping, Object-oriented computing Abstract This paper presents several research issues associated with the PNtalk language that is based on a certain kind of object-oriented Petri nets (OOPNs) and intended mainly for modelling, prototyping, and verifying concurrent and distributed applications. The paper reviews the main concepts of PNtalk and OOPNs followed by a proposal of a system allowing prototypes based on PNtalk to be run in a distributed way. Furthermore, the first step made towards state spaces-based formal analysis and verification over PNtalk OOPNs are also briefly mentioned in the paper.
1. Introduction This paper reviews some of the research activities related to the object-oriented Petri nets (OOPNs) associated with the language and tool called PNtalk (Cˇesˇka and Janousˇek, 1997; Janousˇek, 1998), which have been developed mainly to support modelling, investigating, and prototyping concurrent and distributed object-oriented software systems. PNtalk supports intuitive modelling of all the key features of these systems, including object-orientedness, message sending, parallelism, and synchronisation. The main modelling features of PNtalk and OOPNs are presented at the beginning of this paper. The use of PNtalk should be supported by a tool suite constituting the so-called PNtalk system. A prototype of such a system supporting modelling and simulation of systems by means of OOPNs was already implemented some time ago (Cˇesˇka et al., 1997). Here, we sketch the main principles of a new architecture of the PNtalk system that should allow us to run OOPN-based prototypes in a truly distributed way and with the possibility of creating mobile PNtalk objects. This work was done within the project CEZ:J22/98:262200012 “Research in Information and Control Systems” and within the project of the Grant Agency of the Czech Republic No. 102/00/1017 “Modelling, Verifying, and Prototyping Distributed Applications Using Petri Nets”.
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In the remaining part of this paper there are briefly presented some issues related to generating and using state spaces of OOPNs for formal analysis and verification of the considered systems. These issues are mostly related to the fact that we have to deal with dynamically arising and disappearing instances in state spaces of OOPNs (Vojnar, 2001).
1290 2. PNtalk and the associated OOPNs The OOPN formalism associated with PNtalk is characterized by a Smalltalkbased object-orientation enriched with concurrency and polymorphic transition execution, which allows for message sending, waiting for and accepting responses, creating new objects, and performing primitive computations (Janousˇek, 1998). An example illustrating the notation of PNtalk is shown in Figure 1. It is a fragment of a PNtalk class whose each object represents a session of a user working with a certain graphic object in the system of a cooperative editor for hierarchical diagrams (Bastide et al., 1996; Kocˇ´ı and Vojnar, 2001). We will return to this model in slightly more detail later. The main principles of the structure and behaviour of OOPNs are explained in the following. A deeper introduction to the OOPN formalism can be found in (Cˇesˇka et al., 1997) and the formal definition of OOPNs in (Vojnar, 2001).
2.1 The structure of OOPNs An OOPNs is defined on a collection of elements comprising constants, variables, net elements (i.e. places and transitions), class elements (i.e. object nets, method nets, synchronous ports, and message selectors), classes, object identifiers, and method net instance identifiers. An OOPN has its initial class and initial object identifier, as well. The so-called universe of an OOPN contains (nested) tuples of constants, classes, and object identifiers. Object nets consist of places and transitions. Each place has some (possibly empty) initial marking. Each transition has conditions and preconditions (i.e. inscribed testing and input arcs), a guard, an action, and postconditions (i.e. inscribed output arcs). Method nets are similar to object nets but, additionally, each of them has a set of parameter places and a return place. Method nets can access places of the appropriate object nets, which allows running methods to modify the states of the objects which they are running in. Constructors are method nets intended for initializing objects. Synchronous ports are special transitions which cannot fire alone but only dynamically fused to some regular transitions. These transitions “activate” the ports from their guards via message sending. Every synchronous port embodies a set of conditions, preconditions, and postconditions over places of the appropriate object net, and further a guard, and a set of parameters.
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Figure 1. A fragment of a class demonstrating the notion of PNtalk
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Parameters of an activated port s can be bound to constants or unified with variables defined on the level of the transition or port that activated s. A class is given by its object net, its sets of method nets and synchronous ports, and a set of message selectors corresponding to its methods and ports. Object nets describe what data particular objects encapsulate and what activity they exhibit on their own. Method nets specify how objects asynchronously respond to received messages. Synchronous ports allow to remotely test and change states of objects in an atomic way.
2.2 The dynamic behaviour of OOPNs A state of an OOPN can be encoded as a marking, which can be structured into a system of objects. Thus the dynamic behaviour of OOPNs corresponds to an evolution of a system of objects. An object of a certain class c is a system of net instances that contains exactly one instance of the object net of c and a set of currently running instances of method nets from c. Every net instance entails its identifier and a marking of its places and transitions. A marking of a place is a multiset of elements of the universe. A transition marking is a set of records about method net instances invoked from the appropriate transition. For a given OOPN, its initial making corresponds to a single, initially marked object net instance from the initial class. A change of a marking of an OOPN is a result of an occurrence of some event. Such an OOPN event is given by (1) its type, (2) the identifier of the net instance it takes place in, (3) the transition it is statically represented by, and (4) the binding tree containing the bindings of the variables used on the level of the involved transition as well as within all the synchronous ports (possibly indirectly) activated from that transition. There are four kinds of events according to the way of evaluating the action of the appropriate transition: A – an atomic action involving trivial computations only, N – a new object instantiation via the message new, F – an instantiation of a Petri-net described method, and J – terminating a method net instance. (An invocation of a constructor over a class leads to a sequence built of an N, F, and J event.)
2.3 An example of an OOPN In Figure 1 there is presented a fragment of the class Session from the system of a cooperative editor for hierarchical diagrams (Bastide et al., 1996; Kocˇ´ı and Vojnar, 2001). Let us now return to this class for a moment.
In the model of the locking mechanisms of a cooperative editor (Kocˇ´ı and Vojnar, 2001), if a user wants to view or edit a diagram, the user first has to create a Session over the diagram. The session may be created by means of the constructor user:graphic: whose second parameter has to be the graphic that is the root of the diagram to be opened (in the hierarchy of diagrams managed by the editor). The graphic must be owned for encapsulation by the user. The ownership for encapsulation is checked via the method expand:for: invoked over the graphic. This method returns either a reference to the appropriate diagram or nil. The latter case causes the Session’s constructor to also return ni1 leading to a subsequent deletion of the not successfully created Session by the garbage collector. When a diagram is changed, it sends a message update to all the Sessions currently opened over this diagram. The fact that update is a method allows the appropriate message to be processed in an asynchronous way and makes it easier to implement this mechanism in a distributed environment. The method update ensures that there eventually appears a token #yes in the place update which enables the transition update via the synchronous port mustUpdate. The transition update calls the method goUpdate that implements the internal details of updating a diagram – the method is not presented here. Note that more requests to update may lead to a single physical update of the appropriate diagram.
3. Towards a distributed PNtalk The current version of the PNtalk system that is available on the Internet since 1996 can hardly be considered anything more than a demonstration of the concept of OOPNs. It is based on the 1995 version of OOPNs ( Janousˇek, 1995), and so it does not reflect some of the new features of OOPNs as introduced in ( Janousˇek, 1998), which is especially the case of synchronous ports. Moreover, the closedness and poor interoperability of this PNtalk implementation does not allow for experimenting with applications that are more than some “school examples” (such as different variants of the system of dining philosophers or very simple workflow systems). Currently we are developing a new PNtalk system architecture that is intended for experiments with prototyping more realistic applications. This new PNtalk has to support a seamless evolution of an application from a simple model to a prototype running in real time and, possibly, to final implementation including some parts realized in PNtalk. This goal may be achieved by using encapsulation of model components allowing them to be developed independently of each other. The employed encapsulation and objectorientation have to be platform-independent as well as programming language- and network distribution-independent. Although, we prefer implementations in the Smalltalk and Prolog languages, the language
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independence of components, as well as the network transparency, can be achieved by using some standards for inter-object communication as, e.g. CORBA. Then, each CORBA-compliant component could be connected to an OOPN-based prototype and vice versa. The new PNtalk is not being designed in a form of a compact, integrated environment supporting editing, compiling, simulation, and debugging. It is a set of simple tools, instead. These tools can be used either independently or combined in order to pragmatically support all phases of a model or prototype development. In the early phases, using some integrated environment could be advantageous. In this case, such an environment could be built upon the mentioned tools in a form of a special software layer, as it will be mentioned later. As the new PNtalk system implementation is not finished yet, it has to be stressed that the PNtalk system itself has to be evolvable. Its architecture proposal takes this into account – it is based on the idea that complex systems evolve from simpler ones. The simplest form of the new PNtalk system is based on a number of universal components which themselves could evolve: An OOPN interpreter is a key component. It is intended to be used in all phases of a model or prototype development. It could also participate in the final implementation of a developed software system. The key parts of the interpreter may also be used for state space generation in verification tools. The interpreter should have a form of a library available in several programming languages. The very first versions are being implemented in Prolog and Smalltalk. Moreover, it should be also available as a program which it is possible to communicate with via TCP/IP. This means that the interpreter can become a part of an arbitrary software system, even a distributed one. The OOPN interpreter can be viewed as a virtual machine whose behaviour is defined by the image that it works with. The image is a set of all the currently living objects in a binary form. It contains both compiled class definitions and methods as well as states of all the objects in the form of tokens distributed in Petri nets. A compiler compiles the textual form of the PNtalk language into a binary form acceptable by the interpreter. It may work incrementally. In such a case, it embeds (possibly in cooperation with some supporting tools) the compiled code into an existing image. The compiler could be implemented as a library for some programming languages as well as a standalone program. A source code repository in its simplest form, it could be a file containing all the source code of the classes of the objects contained in an image. More interestingly, it could be a log file containing all changes to the sources of an image, which resembles Smalltalk. In its even more sophisticated form, it could be implemented as a database accessible via TCP/IP. The compiler has to be able to compile the source code of a method independently of the employed realisation of the source code repository.
An editor should allow us to create and modify OOPN classes and methods both in a textual and a graphical way. It interacts with the source code repository. It could possibly interact with the compiler in order to check the source code. The graphical version of the editor has to be able to load the source code obtained from the text editor and to semi-automatically add the missing graphical information to the OOPN diagrams. The source code repository should contain the textual form of OOPN components definitions together with the graphical information associated with the appropriate diagrams if it is available. A shell (debugger) allows a programmer to interact directly with the OOPN interpreter via a TCP/IP connection. It makes it possible to load an image or to add some compiled code or saved object state to the active image. The shell makes it also possible to save the current image or its part to a file or to send it through a network connection to a file or another interpreter. Moreover, it allows a programmer to send a message to an object living in the active image and to inspect the result. It also allows him or her to list all processes, to stop execution of some process and to trace it or let it proceed. The shell has to have both a command-line as well as a graphical form. In both cases, it has to allow for tracing processes and inspecting states of objects on the source code level (textual or graphical). This means that it should also interact with the source code repository. Analysis and verification tools should be available in the form of libraries for some programming languages as well as in the form of a server accessible via TCP/IP. The analysis and verification suite should comprise its own shell making it possible to interactively specify what is to be analysed or verified. All these tools constitute the basic level of the PNtalk system components. These components can interoperate with other software systems. They also allow for a simple form of communication over TCP/IP networks. On top of this basic level components, a distributed PNtalk system could be built in several steps: A simple client-server PNtalk architecture integrates the editor and shell (debugger) enriched with the possibility of invoking the compiler remotely. It connects via HTTP to a server that encapsulates reentrant interpreter, compiler, and analysis and verification tools. All functionality of these tools is offered to each authenticated user. This architecture can exploit powerful computational servers on the network. It allows multiple programmers to develop independent prototypes that can communicate via TCP/IP. A multiuser PNtalk authenticated several users or client applications may interact with a shared PNtalk interpreter. Each user owns some objects and these objects have access rights defined. We obtain a client-server PNtalk that enables a tighter coupling of components developed by various programmers.
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The shared PNtalk interpreter is a modified version of the basic PNtalk interpreter described above. A distributed PNtalk interpreter is modified in such a way that objects can communicate with each other regardless of the interpreter they are living in. This means that the image can be distributed among several interpreters and the distribution is transparent to the objects. To support this mode of PNtalk operation, some name server has to be introduced, allowing an object identified to be located. The interpreter has to decide where the receiver of the processed message lives and to possibly delegate the message delivery to some other interpreter. The distributed PNtalk can also be accessed in a client-server manner in which case the server is built upon a cluster of PNtalk interpreters, a name server, a source code repository, a compiler, and a verification server. Note that the Multiuser PNtalk and the Distributed PNtalk are mutually independent modifications of the basic PNtalk interpreter. Nevertheless, they can be merged. 4. Analysis and verification over OOPNs In this section, we briefly mention the first step made towards exploiting formal analysis and verification methods in the context of OOPNs (Vojnar, 2001). Using formal analysis and verification can be considered complementary to validating systems by simulation because although we need not be able to fully verify or analyse the behaviour of a system, even partial analysis or verification can reveal errors different from the ones found by simulation. Among the different methods of performing formal analysis or verification, generating and exploring suitably represented state spaces – see, e.g. (Valmari, 1998) – appears to be the most straightforward approach for the case of OOPNs. 4.4 Generating state spaces of OOPNs In state spaces of OOPNs, it appears necessary to be beware of the so-called naming problem (Vojnar, 2001). This phenomenon corresponds to the undesirable possibility of generating many states differing only in the identifiers of the involved net instances. Two causes of the naming problem in the domain of state spaces of OOPNs (and other formalisms with dynamic instantiation) may be identified: (1) assigning names to newly arising instances unnecessarily reflecting the history of their creation, and (2) dealing with concurrently existing, uniquely identified instances that play somehow symmetrical roles in the appropriate models (as a reflection of some symmetries existing already on the level of the modelled systems).
Although the naming problem is not exclusively specific to OOPNs (nor to formalisms with dynamic structuring), it manifests itself in an especially severe way here due to the first mentioned source specific to this area. Vojnar (2001) has proposed and compared two methods for dealing with the naming problem in the context of OOPNs, namely sophisticated naming rules and name abstraction. The idea of using sophisticated naming rules is inspired by the approach to identifying processes in Spin (Holzmann, 1997), which has been generalized and modified to suit better the needs of OOPNs. Nameabstraction, on the other hand, is a fully transparent application of the concept of symmetrically reduced state spaces – see, e.g. (Ip and Dill, 1996; Junttila, 1999) – to solving the naming problem. When applying symmetries to solving the naming problem in the context of state spaces of OOPNs, it is necessary to take into account some special issues, such as: garbage collection, encapsulation of method net instances in objects, infinite numbers of the possibilities how to identify a newly arising instance, or providing a sufficiently broad notion of trivial operations over instance identifiers. The most elaborated sophisticated naming rules appear to be applicable when dealing with systems without many system-level symmetries, especially when partial order reduction is used. In the other cases (which do not seem to be only exceptional when applying object orientation), using name abstraction can be more advantageous. Let us add that the naming problem should always be solved together with the problem of removing unnecessary instancesfrom states. This is because that if we do not systematically remove such instances, the number of concurrently existing instances may grow and the naming problem can manifest itself stronger. Moreover, there can be generated redundant, semantically equal states distinguished by the different garbage present in them even when we apply a very good solution of the naming problem. Therefore, it seems to be advantageous to remove all unnecessary instances from states as soon as possible. In the case of the PNtalk OOPNs, we use an immediate garbage collecting mechanism to solve the above problem. In order for this mechanism to work properly, it suffices to create OOPNs such that they do not store references to obsolete instances.
4.5 Using state spaces of OOPNs In the area of formal analysis and verification of concurrent systems there have already been proposed many ways of expressing properties of the systems under investigation to be evaluated over state spaces of their models (Valmari, 1998). They include, e.g. using state space statistics, universal state space query languages, property labels or directives, or temporal logics. Most of the common ways of asking state space analysis or verification questions can be accommodated for dealing with OOPN-based models too (Vojnar, 2001).
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Properties to be evaluated over state spaces of OOPNs should not refer to the concrete identifiers of instances. This is because the concrete names of instances do not normally have any influence upon the behaviour of OOPNbased models, and moreover, it is hard (and sometimes impossible) to predict what identifiers will be used for what instances in what states. Some new useful kinds of system properties to be checked may also be introduced in the area of systems that can be suitably described by OOPNs – e.g. persistence of instances, instance-oriented progress, etc. Generally, analysis or verification questions to be answered over state spaces of OOPNs can ignore or, on the other hand, respect the structuring of running OOPNs into instances. Unfortunately, dealing with instance-oriented analysis or verification queries may lead to higher time and space requirements (Vojnar, 2001). This applies especially in the cases when it is not sufficient to distinguish particular instances within a single state, and we have to track their individual behaviour along some state space paths. The particular specification and query techniques can be applied in the domain of OOPN-based models such that analytical or verification questions described by them could be answered over (possibly name-abstracted) state spaces of OOPNs by means of fairly standard algorithms. In some cases, however, the standard algorithms have to be slightly modified to a certain degree to be able to deal with models structured into sets of net instances and objects, which can be dynamically created and/or discarded (Vojnar, 2001).
5. Conclusions In the paper, we have presented several research issues related to the PNtalk language and system and to the OOPNs associated with them. Firstly, we have outlined the main concepts of the new architecture of the PNtalk system which should allow us to run OOPN-based prototypes in a truly distributed way. Although this architecture is still subject to development, some parts of the new PNtalk system have already been experimentally implemented (a new PNtalk interpreter, a simple client-server variant of the PNtalk system). Now, the distributed architecture of PNtalk is to be further refined, fully implemented, and tested on a suitable case study – for this reason, we have decided to use the cooperative editor case study (Bastide et al., 1996, Kocˇ´ı and Vojnar, 2001). We have also presented the first steps which have been done in the area of generating and using state spaces of OOPNs for formal analysis and verification. A prototype of a generator of state spaces of OOPNs (using name abstraction or, alternatively, sophisticated naming rules) and a processor of a simple state space query language have already been built. In the future, we intend to improve the current state space tool, to augment it with an option of partial-order reduction, and to try to enable export to some already existing
state space tools (possibly slightly extended). We have proposed a technique for automatic type analysis in OOPNs (Krˇena and Vojnar, 2001) as well. References Bastide, R., Lakos, C.A. and Palanque, P. (1996), “A cooperative Petri Net editor”, A Case Study Proposal for the 2nd Workshop on Object-Oriented Programming and models of Concurrency, ICATPN’96, Osaka, http://wrcm.dsi.unimi.it/PetriLab/ws96 Cˇesˇka, M. and Janousˇek, V. (1997), “A formal model for Object-Oriented Petri Nets modeling”, Advances in Systems Science and Applications, An Official Journal of the International Institute for General Systems Studies Special Issue, pp. 119-24. Cˇesˇka, M., Janousˇek, V. and Vojnar, T. (1997), “PNtalk – a computerized tool for Object-Oriented Petri Nets modelling”, Computer Aided Systems Theory - EURO-CAST’97, SpringerVerlag, LNCS, Las Palmas de Gran Canaria, Spain, Vol. 1333, pp. 591-610. Holzmann, G. (1997), “The model checker spin”, IEEE Transactions on Software Engineering, Vol. 23 No. 5. Ip, C. and Dill, D. (1996), “Better verification through symmetry”, Journal of Formal Methods in System Design, Vol. 9 No. 1/2, pp. 41-76. Janousˇek, V. (1995), “PNtalk: object orientation in Petri Nets”, Proceedings of European Simulation Multiconference ESM’95. Czech Technical University, Prague, pp. 196-200. Janousˇek, V. (1998), “Modelling objects by Petri Nets”. PhD thesis, Department of Computer Science and Engineering, FEECS, Brno University of Technology, Czech Republic. (In Czech) Junttila, T. (1999), “Detecting and exploiting data type symmetries of algebraic system nets during reachability analysis”, Technical Report HUT-TCS-A57, Helsinki University of Technology, Laboratory for Theoretical Computer Science, Helsinki, Finland. Kocˇ´ı, R. and Vojnar, T. (2001), “A PNtalk-based model of a cooperative editor”, Proceedings of MOSIS’01 (Hradec nad Moravicı´, Czech Republic) MARQ Ostrava, pp. 165-72. Krˇena, B. and Vojnar, T. (2001), “Type analysis in Object-Oriented Petri Nets”, Proceedings of ISM’01 (Hradec nad Moravicı´, Czech Republic), MARQ Ostrava, pp. 173-80. Valmari, A. (1998), “The state explosion problem”, in Reisig, W. and Rozenberg, G. (Eds), Lectures on Petri Nets I: Basic Models, Springer-Verlag, LNCS, Vol. 1491, pp. 429-528. Vojnar, T. (2001), “Towards formal analysis and verification over state spaces of Object-Oriented Petri Nets” PhD thesis, Department of Computer Science and Engineering, FEECS, Brno University of Technology, Czech Republic.
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Fuzzy algorithms of problem solving O.G. Chorayan and G.O. Chorayan Kogan’s Research Institute of Neurocybernetics, Department of Physiology, Rostov State University, Rostov on Don, Russia Keywords Cybernetics, Fuzzy systems Abstract Labyrinth test psychophysiological experiment is elaborated to analyze possible mechanism of the probabilistic prognosis forming and realizing in the condition of essential information uncertainty. The dynamics of the probabilistic prognosis construction and improvement during multi-stage labyrinth test solving is established. This dynamics is characterized by considerable changes of the subjective probabilities and membership function quantitative indices apparently used in the fuzzy logic of mental activity being applied in decisionmaking processes realized in the condition of uncertainty. The possible link between probabilistic prognosis efficiency and some functional peculiarities of cortical hemisphere asymmetry has also been studied.
Introduction Labyrinth test psychophysiological experiment is elaborated to analyze possible mechanism of the probabilistic prognosis forming and realizing in the condition of essential information uncertainty. The dynamics of the probabilistic prognosis construction and improvement during multi-stage labyrinth test solving is established. This dynamics is characterized by considerable changes of the subjective probabilities and membership function quantitative indices apparently used in the fuzzy logic of mental activity being applied in decision-making processes realized in the condition of uncertainty. The possible link between probabilistic prognosis efficiency and some functional peculiarities of cortical hemisphere asymmetry has also been studied.
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Discussion The probabilistic prognosis phenomenon has a significant role in most cases of human activity while considerable information uncertainty. It consists of the capability of forecasting on the basis of the previous identical situation analysis (Budashevsky and Menitsky, 1973; Chorayan, 1987, 1995; Kogan and Chorayan, 1980; Phaygenberg, 1962, 1972; Phaygenberg and Zhuravlev, 1974). In terms of psychological concepts it implies the formation of subjective models in accordance with the real probabilistic structure of the experience. The latter is ordinary necessary for optimal organization and realization of the individual
behavior in the stochastic condition and his adaptation to the external world Fuzzy characterized by temporal and spatial dynamics. Psychophysiological essence algorithms of of the probabilistic prognosis consists of the comparison of current information problem solving with related information kept in memory and successive appropriate hypothesis, constructing a model of future events with some probability meanings. 1301 Labyrinth method is one of the perspective and much-promised approaches to psychophysiological study of the effective solving of such problems by individuals (Chorayan, 1979; Kyroy, 1979; Lindley, 1971). Peculiarities of problem solving reflected in the psychophysiological manifestation (the word description of the problem situation dynamic model, left-side or right-side cortical hemisphere predominating tests and so on) are analyzed. Considerable information uncertainty of the problem situation presented at labyrinth test solving explains the expediency and adequacy of the information theory methods (Chorayan and Chorayan, 2000; Shannon, 1963) and fuzzy sets theory (Chorayan, 1979, 1995, 2000; Zadeh, 1965, 1994, 1999), numerical values of membership function calculation, and set-theoretical operations of fuzzy sets approximating psychophysiological features of thinking activity that are laying in the basis of the brain higher intelligent behavior. Theory of fuzzy sets is based on the widespread concept that in the real world most events and objects are the classes without strict frontiers. So the membership or nonmembership of each concrete unit, element to such classes may be defined only by some intermediate numerical values between 0 (non-membership) and 1 (full membership). Fuzzy subset A of the universal set U is defined by the membership function: mA ðuÞ ! ½0; 1: In a series of experiments 22 examinees were suggested to solve a few types of labyrinth problems (to find the exit from multistage labyrinth making the minimum steps taking into account existence of some regularity in the labyrinth structure that may be revealed on the basis of the experience (while labyrinth solving). The examples of applied labyrinth are presented in Scheme 1 (Figure 1). Dynamics of the labyrinth task decision by the examinee is shown below: A3! A2!A6 B4! B3! B1! B2 C3! C1! C2! C6! C5!C2!C4 D4! D1! D5! D2 E3 F1 G3! G1
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Figure 1. The examples of labyrinths (A, B, C. . . – labyrinth branches (stages), 1, 2, 3. . . – steps at each branch)
H3 I1 K3! K6!K2!K9!K1 The correct steps are underlined. In addition to evaluating the efficiency of mistaken steps, the functional cortical hemispheres asymmetry index was also studied using the peculiarities of the right- or left-side predominacy on the basis of psychophysiological tests (“leading arm”, “leadind leg”, “leading eye”, “leading ear” and so on). Asymmetry index in the earlier-mentioned case is manifested, so: Eye Leg Ear Arm # # # # RðrightÞ RðrightÞ LðleftÞ RðrightÞ In accordance with the idea that the decision-making process as key moment of problem solving under the essential uncertainty presented by labyrinth test is basically determined by information handling in brain structures and probabilistic or even fuzzy logic of higher mental activity, corresponding methods of the information theory and theory of fuzzy sets approaches are used in analysis and interpretation of the experimental results. Some information methods (entropy and redundancy) H emp ¼ 2SP i log2 P i ;
D ¼ 1 2 H emp =H max
and set-theoretic operations (intersection and concentration)
A > B ¼ min½mA ðuÞ; mB ðuÞ;
Fuzzy algorithms of problem solving
ConA ¼ A a
on fuzzy sets approximating psychophysiological characteristics of the labyrinth problems solving process were applied. The numerical values of the membership function (m) are calculated using the probabilistic index: P1 – the objective probability appropriated to the real labyrinth structure, P2 – empiric probability calculated on the basis of the ratio of the performed steps to the total possible steps at this labyrinth branch, P3 – empiric probability calculated taking into account steps previously performed at this labyrinth branch. Results of such analysis are presented in Table I. The summary fuzzy set as problem characteristics of the labyrinth test is found on the basis of set-theoretic intersection operation of appropriate fuzzy sets: A > B > . . . > K ¼ min{mA ; mB ; . . .mK } So we have the following consequence: H 2 ðA ¼ EÞ 2 F 2 ðI ¼ KÞ 2 C 2 D 2 B: The results of information analysis show average values of empiric entropy calculated on the basis of steps performed during transition from one to the next branch (stage) of the labyrinth tend to improve quantitatively probabilistic prognosis that in turn increase the mental activity efficiency laying on the basis of the psychophysiological mechanism of the probabilistic prognosis construction. It is interesting also to underline the evidence of the subjective probability increase of the realized alternative steps after previous success manifested in the decrease of the number of mistaken steps on the previous stage. Apparently there is the mental activity stimulation for the sake of positive emotion as the result of successive activity. In contrast, there is a decrease of mental activity associated with mistaken steps increase on the previous stage of the labyrinth.
Branch (stage) A B C D E F G H I K
m1(P1)
Membership function for P1, P2, P3 m2(P2)
m3(P3)
0.33 0.75 0.42 0.60 0.42 0.48 1.00 0.33 0.66 0.33
0.33 1.00 1.00 0.80 0.14 0.17 0.33 0.11 0.20 0.56
0.14 1.00 1.00 0.50 0.14 0.17 1.00 0.11 0.20 0.20
1303
Table I. Numerical values of membership function
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The essential factor of such improvement of forecasting probabilistic model is the real problem situation decrease (it is determined by empiric entropy decrease) appropriate to strengthening or loosening of mental activity under influence of positive (or negative) emotions evoked by current success (or nonsuccess) during problem situation solving. Although the results of the functional asymmetry indices point to rather homogenous data (strict predominacy of the right-side asymmetry and a few cases of the left-side asymmetry especially in relation to visual analyzer), it is associated with more higher efficiency of the probabilistic prognosis of wellknown literature data of the psychophysiological nature of the labyrinth problems solving studies which lead to the conclusion of the following probabilistic prognosis algorithm. Apparently the functional asymmetry has some modifying action influenced on fuzzy algorithm of the probabilistic prognosis. For instance in the case of left-side dominacy (particularly in the case of “leading left eye”, “leading left ear”). There is tendency to mistaken steps decrease, to more efficient decision of labyrinth problem. However, small number of such cases does not allow to make substantiated assertion. On the initial stage of problem solving on the basis of input information and results of the first steps evaluation the individual constructs some model, scheme of possible labyrinth structure is constructed. On the next stages this model is cleared, verified on the basis of self-organizing using the subjective probability concepts, numerical values of membership function, fuzzy logic of mental activity. References Budashevsky, B.G. and Menitsky, D.N. (1973), “The peculiarities of the probabilistic patterns recognition under some psychopathology states”, Schizophrenia and Probabilistic Prognosis, Moscow, pp. 5-19. Chorayan, O.G. (1979), Fuzzy Algorithms of Thought Processes, Rostov State University Press, p. 160. Chorayan, O.G. (1987), Concept of Probability and Fuzziness in Brain Activity, Rostov State University Press, p. 158. Chorayan, O.G. (1995), Cybernetics of the Central Nervous System, Rostov State University Press, p. 142. Chorayan, O.G. (2000), “Neurocybernetics: contents and problems”, Kybernetes, Vol. 29 No. 5/6, pp. 803-10. Chorayan, O.G. and Chorayan, G.O. (2000), “Brain organization and informational activity”, Kybernetes, Vol. 29 No. 9/10, pp. 1324-32. Kogan, A.B. and Chorayan, O.G. (1980), Probabilistic Mechanisms of the Nervous Activity, Rostov State University Press, p. 176. Kyroy, V.N. (1979), “Contribution to fuzzy algorithms of human thought problems solving”, Problems of Artificial Intelligence, Elista, pp. 27-34. Lindley, D.M. (1971), Making Decisions, L-n, N-Y, p. 276.
Phaygenberg, I.M. (1962), “Probability prognosis in brain activity”, Problems of Psychology, Vol. 2, pp. 59-65. Phaygenberg, I.M. (1972), Brain, Psychics, Health, Moscow, p. 84. Phaygenberg, I.M. and Zhuravlev, D.E. (1974), Probabilistic Prognosing in Human Activity, Moscow, p. 242. Shannon, S. (1963), A Mathematical Theory of Communication. Information and Cybernetics Theory, Moscow, p. 360. Zadeh, L.A. (1965), “Fuzzy sets”, Inform. a. Control., Vol. 9, pp. 338-53. Zadeh, L.A. (1994), “Fuzzy logic, neural networks and soft computing”, Communication of the ACM, Vol. 37, pp. 77-85. Zadeh, L.A. (1999), “The birth and evolution of fuzzy logic – a perxonal perspective”, J. Jap. Soc. for Fuzzy Theory and Systems, Vol. 11 No. 6, pp. 891-905.
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Towards autonomous application interfaces Miche`le Courant and Ste´phane Le Peutrec Department of lnformatics, University of Fribourg, Fribourg, Switzerland Keywords Cybernetics, Human-computer interaction, Computer networks, Software engineering Abstract A global change resulting from a convergence between communication technologies – namely Internet, and other devices technologies – namely robotics, mobile communication, and domotics – is presently affecting Information and Communication Technology (ICT). This situation, denoted by the so-called Intelligent Networks and Ubiquitous Computing fields, is characterized by a high diversity and promiscuity of equipments and applications, together with a great variability of using contexts. In order to address this variability, we propose a new kind of interaction schema, separating the application interface from the application itself. The paper describes this schema and its central concept of virtual instrument, allowing the users to initiate observation processes with the running applications, and to construct their own points of view upon their activities.
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Introduction Application interfaces in intelligent networks A global change resulting from a convergence between communication technologies – namely Internet and other devices technologies – namely robotics, mobile communication, and domotics – is presently occurring in Information and Communication Technology (ICT). This situation, denoted by the so-called Intelligent Networks and Ubiquitous Computing fields (Hedberg, 2000; Schubiger et al., 2000), is characterized by a high diversity and promiscuity of equipments and applications, together with a great variability of using contexts, which are bringing on new constraints on the design of application interfaces. First, in such networks, the frontiers with the physical world are fuzzy and variable, as far as human activities tend to associate or dissociate to it resources or equipments according to their needs or points of views. A robot for example, may sometimes be considered as an integral part of the network, especially, when used as a terminal node devoted to sensory-motor activity, while it clearly remains a separate entity belonging to the physical world in other cases. Second, there is a marked tendency in network technology for designing artificial entities evolving towards more and more autonomous and adaptive components (be they robots, or software components, like agent-based
Internet services, network management applications, or artificial worlds simulators). In our opinion, these various factors are working together towards a new challenge: human beings are actually facing the need to learn to interact with potentially unknown, changing, heterogeneous, and unpredictable artificial entities. For tackling this problem, two trends may be adopted. The first method aims at categorizing applications as far as possible, and then fitting each category with one ad hoc interfacing model. Such a method has already been successful in the system software or document editing domains with the desktop and toolkits metaphors for example. However, due to the trade-off between the interface adequation and its accessibility, this way of doing generates specialization effects. Moreover, it excludes non categorized applications from opportunistic uses. In opposition to this, our proposal is then to set up a human-system coupling, which goes through diversity – over the jungle of heterogeneous resources and appropriation modes – and remains open to opportunistic uses of the network resources. The solution consists in a middleware, called virtual instrument, allowing the users to construct themselves their own points of view upon these resources, on the only basis of raw information provided under a declarative form by the resources. This work has been carried on inside the FOCALE project, a part of the WELCOME [1] research framework (Le Peutrec and Courant, 2000; Schubiger, 2000; Schubiger et al., 2000; PAI Group, 2001), which aims at developing flexible and adaptive components for designing Intelligent Network infrastructure.
Physical space metaphor Now, establishing the contact with a priori unknown entities in the network appears very similar to the problem of exploration and communication in the physical space: one has to be able to explore the universe in order to identify some entity to interact with, then to find the appropriate way to set up the conditions allowing interaction, to set up these conditions effectively, and finally to interact. Notice that such a way of doing is totally human-centered (Winograd, 1999), for the interaction initiative totally belongs to the user. In addition, the particular interaction that may occur between an entity and a particular user may not be prepared by the entity, except at a very basic level (approximately the same way that a galaxy emits light independently from the telescope that may suddenly capture it). However, if natural physical entities constantly emit and receive signals, artificial entities do not have any spontaneous capability to do so. In order to become observable, and even reachable, by a given user, these entities then have to be put under conditions, where they are also “forced” to emit and/or
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receive signals towards or from any incoming user. Once this prerequisite is achieved, one has simply to use an appropriate device or middleware for capturing (respective sending) these signals (Le Peutrec and Courant, 2000). Hence, the presented work here addresses the realization of a system able to construct these two mechanisms.
1308 System overview Interaction as a three-level problem So formulated, the problem of interacting with an unknown application appears composed of three big stages. .
Exploration is the phase of sounding the universe resulting in the identification of an entity to interact with by the user. This phase can be made possible thanks to an indirection mechanism, assumed by an entity we call an interconnection server. The interconnection server is a kind of universal instrument for sounding the network. It also acts as a mediator by providing the user with the information required for the establishment of a direct interaction.
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Instrumentation is a phase aiming at the interaction protocol settling. On the basis of the received information, and whether he already knows the case or not, the user chooses or builds an ad hoc tool called virtual instrument, which will serve him to interact with the application.
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Interaction is the effective functioning stage of the instrument, mounted or selected at the previous stage, which proceeds through a sensory-motor like coupling between the application and the user, mediated by the instrument.
This structure and the corresponding elements of the system are shown in Figure 1. Application requirements In order to become perceivable by potential users, an application must register itself at the interconnection server, and provide it a description of itself, called the conceptual interface. The conceptual interface consists in three levels of description: the application label, is mainly oriented towards application classification, and is used by the interconnection server for answering further user’s requests. It may consist textual information such as keywords, useful for application functional indexing, and some static features related to implementation (such information may be extracted automatically by a method like the one described in (Schubiger, 2000)). The second level, called contact descriptor, brings on information useful for interaction initialization. For instance, in case of a genetic simulator, it may provide the upper limit of
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Figure 1. Overview of the system
the individual space. The third level is the application’s ontology. It declares in an object-oriented form of concepts that are exploited by the application. Each concept is represented by a class, whose properties denotes the data that an entity instantiating this concept can export, or import. The application’s ontology is the basis upon which the user can start interpreting the application, for attempting to enter its semantic universe. Putting in correspondence his own semantics with the elements of the ontology, he will be able to construct a virtual instrument. This will be achieved through the specification of: (1) a scope: an intentional description of the entities he would like to interact with, and (2) a signal description: the information he would like to exchange with these entities. In order to dynamically accept interaction requests coming from the users, an application must also be equipped with a port server, which is in charge to handle these requests. A request is composed of a scope, a data description, and a temporal law, either referring to a clock, or to the application internal time. For each request received, the port server reacts by dynamically generating a special component, called a port, dedicated to the communication between the application and the user. The port is then in charge (1) to calculate the extension of the scope specified in the request, (2) to extract from this extension the data the user is waiting for or to force the corresponding entities to accept the data coming from the user. These two tasks are not executed just one time, but each time the port receives a temporal signal according to the temporal law specified in
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the request. As shown in Figure 1, note that during the lifetime of interaction, the application is then fitted with a static part, composed of its port server and conceptual interface and a dynamic part composed of as many dedicated ports than needed by the instruments plugged onto it.
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Instrumentation Finally, the virtual instrument is the ultimate component allowing a user to interact with an application. It is in direct contact with the port server, which has been secreted by the application in reaction to the interaction request stimulus. In case of pure observation for example, the virtual instrument is in charge of collecting, analyzing and displaying the concerned perceivable data in a suitable format. The architecture of a virtual instrument dedicated to observation is given in Figure 2. We can distinguish four components: the tuner, the clock, the transformer and the display. The clock is a component allowing to define the time of the observation either in terms of the internal time of the application or in terms of events produced by the user. Hence, it is the temporal bridge between the application and the user’s universes. The transformer is the heart of the instrument. It is in charge to adapt the signals received, into a form appropriate to the display. To find a correspondence with a physical instrument, the transformer could be compared with a succession of lenses inside an optical device. The display is the final component achieving information expression. It can be any device, such as, a classical monitor, or it can belong to the equipment spectrum of ubiquitous computing, typically a wearable device like a heating bracelet used for translating alarms in case of real-time monitoring.
Figure 2. Architecture of an observation virtual instrument
Interaction consists in signal transfer and transformation through the virtual instrument. In case of observation, the signals are first transmitted by the dedicated port of the application to the transformer. There, they are translated into signals appropriate to the display, while the display further conveys them to the user. During all the interaction process, the instrument remains under user’s control. This one can for example tune the instrument online for modifying, either the focus, or the temporal law governing the emission and reception of signals by the application. The port reacts in real-time to these tunings. Concluding remarks A model of the described system has been implemented on top of a Java platform for two prototypical cases of applications (Le Peutrec and Courant, 2000). The first one pertains to artificial biology, and hence is a virtual world application. The second one aims at object following inside a building, and hence belongs to ubiquitous computing. The system allows network exploration and interaction with applications satisfying minimum requirements. The original features of the method lie in a drastical separation between the application and its interface, which releases the application from any specific interaction protocol with the user. Instead, by delivering only conceptual interfaces, applications adopt a declarative approach of their interaction, and the focus is moved onto instruments. The interest of this move is multiple: better abstraction of interaction and reusability of instruments, simplification in application design, openness onto adaptive and evolutionary application design, openness towards exploratory and opportunistic user behaviors, compatibility with heterogeneous devices handling required by ubiquitous computing (Schubiger et al., 2000). Moreover, deeper issues may also be identified for the physical metaphor is a very powerful one (Lakoff and Johnson, 1980; Lakoff and Nunez, 2000). Practically the transposition of the notion of instrument for interfacing entities pertaining to the virtual sphere dissolves their frontier with the physical devices. A true clarification in uses may follow, namely when the physical metaphor will be deployed until its least details concerning component identification and assembling techniques. Our claim is that such a transition could correspond to a radical cognitive evolution, actually to the emergence of a new human space in which the virtual and the physical simply melt for not having any pragmatic reason to be separated. Note 1. “WELCOME – Where Immersion meets Intelligent Networks” is a project supported by the Swiss National Foundation for Scientific. Research under grants No. 2000.53930.98 and No. 2000-057279.99.
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References Hedberg, S.R. (2000), “After desktop computing: a progress report on smart environments”, IEEE Intelligent Systems, Vol. 15 No. 5. Lakoff, G. and Johnson, M. (1980), Conceptual Metaphors in Everyday Language, The University of Chicago. Lakoff, G. and Nunez, R.E. (2000), Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being, Basic Books. Le Peutrec, S. and Courant, M. (2000), “Revisiting HCI for networking computers: a first breakthrough for artificial biology”, Proceedings of the International ICSC Symposium on Biologically Inspired Systems (BIS’2000), 12-15 December 2000, Wollongong, Australia. PAI Group (2001), http://diuf.unifr.ch/pai/research/welcome/, University of Fribourg. Schubiger, S. (2000), “A resource classification system for the WOS”, Proceedings of the Workshop on Distributed Communities on the WEB, July 2000, Quebec, Canada. Schubiger, S., Maffioletti, S., Tafat-Bouzid, A. and Hirsbrunner, B. (2000), “Providing service in a changing ubiquitous computing environment”, Proceedings of the Workshop on Infrastructure for Smart Devices – How to Make Ubiquity an Actuality, (HUC 2000), 27 September 2000, Bristol. Winograd, T.A. (1999), “Human-centered interaction architecture”, Unpublished draft, http:// graphics.Stanford.EDU/projects/iwork/papers/humcent/index.htm
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Can the system idea help promote critical thinking and intellectual autonomy in pedagogy?
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D. Andre´s Mejı´a Depto. de Ingenierı´a Industrial, Universidad de Los Andes, Bogota´, Colombia Keywords Cybernetics, System design Abstract Some problems have been pointed out in the literature, regarding how the various critical approaches to pedagogy have failed to properly promote autonomy of thinking and to prevent the imposition of knowledge. The criticisms include the incapacity of some approaches to highlight and question subtle or tacit forms of knowledge, and the implicit active imposition of knowledge by some others. With the possible use of critical systems thinking in pedagogy in mind, here we examine how the forms of critique used by three different approaches within this strand can deal with these criticisms. We will argue that, as presently conceived, the critical use of the system idea is susceptible of being criticised in the same way.
1. Introduction Beyond the mere acquisition of information and skills, the development of autonomy of thought and action has been repeatedly declared as one of the main objectives of education. Its importance is normally associated with the fact that it is a requirement for central purposes in our societies, like democracy, individuality, and participation. The notion of autonomy of thought is intimately connected with that of Criticality[1]. Criticality is invoked to prevent the imposition of knowledge, thus allowing the students to construct their own. We start here from the idea that autonomy of thought cannot be obtained with a libertarian policy of “leaving students alone”, but by means of a critical engagement with others. That is, by leaving someone alone, by not interacting with her/him, we cannot directly impose our knowledge on her/him. But this does not guarantee that s/he will construct her/his own and not have it imposed from other sources. Several critical approaches in education explicitly seek to promote critical thinking, or to use criticality, and with this to help students develop their thought autonomously and/or to prevent the imposition of knowledge on them. They include various forms of critical pedagogy (Freire, 1972; Giroux, 1997), post-radical pedagogy (Buckingham, 1998), the critical thinking movement (Paul, 1993; Siegel, 1988), feminist pedagogy (Luke and Gore, 1992), and critical
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theory in education (Young, 1992). Nevertheless, various concerns have been voiced regarding either their failure to prevent knowledge imposition and promote autonomy of thinking, or the actual imposition of their views on the students. To name a few, Ellsworth (1989) and Gur-Ze’ev (1998) have argued that critical pedagogy imposes its own particular view of society. Duhan Kaplan (1989) has pointed at the inability of the tools developed by the critical thinking movement to actually identify and question concrete but subtle forms of knowledge which are present, even if tacitly, in the actual lives of students. Maddock (1999) has remarked something similar about Young’s and other authors’ applications of critical theory in education. Salman (1998) has also said something in a similar vein, in respect of Ellsworth’s post-radical pedagogy and her emphasis on the purely textual, failing to acknowledge the material. Duhan Kaplan (1989) and Paul (1992) have criticised the proneness of the critical thinking movement’s critical tools to the use by students of a fancy terminology just to advance their own positions and get them accepted or imposed. None of these critical approaches explicitly makes use of systems ideas. Actually, not many reflections and/or applications in pedagogy from a critical systems thinking perspective have appeared in the literature (for some instances see Gregory, 1993; and, with some critical aspects but not explicitly using critical systems thinking, see Banathy, 1992; Espinosa, 2000; and the special issue of Systems Research and Behavioural Science, Vol. 18 No. 4, 2001 Designing Educational Systems for the 21st Century). It seems then worth examining the potential of various critical uses of systems ideas. The main questions to be addressed in this paper will be the following ones: .
What potential does the system idea have in helping achieve the critical purpose of developing autonomy in students and preventing knowledge imposition on them?
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What forms of knowledge imposition can [and cannot] the system idea help prevent?
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Can the system idea help avoid the imposition of knowledge in the name of critique?
We will examine here three more or less generic strands of systems thinking that present critical elements. One is what can be called a systemically critical approach; that is, one that takes critique to be basically systemic by means of the questioning of systemic boundaries. The second one emphasises something similar to what Jackson has called a “discursive rationality” (2000), we will call it, however, organisation of interactions, as it concentrates on defining the form of the conversations in which knowledge is produced. The third one is a critical pluralist approach, and it attempts to be critical about the various systemic paradigms while promoting the development of all of them.
2. Systemic or boundary critique Critical thinking Its main characteristic consists in the fact that critique is taken to be basically and intellectual systemic, and the central element of criticality the system boundary (Midgley, autonomy 2000; Ulrich, 1983, 1987). Critique here is essentially boundary critique, and the core proposal can be summarised with the idea that forms of knowledge are in principle incomplete or partial; that given the finitude of human beings, 1315 everything that should be taken into account for determining true knowledge cannot be taken[2]. Therefore, humans would draw boundaries that delimit what they will focus on, leaving some elements or aspects inside – and therefore taking them into account – and the rest outside – and therefore somehow excluding them. As concerns pedagogy, tools to disclose the boundaries of any form of knowledge – and with those boundaries the elements that have been included or excluded – could be given to the students so that they could then question the partiality of any form of knowledge. In fact, this is what we take to be Ulrich (1996) proposal of educating the citizens, so that they can become critical and able to participate in debates of issues of public concern. Boundary critique is about detecting boundaries drawn by forms of knowledge over a space of aspects or elements. This demands from the critical person to be able to identify aspects or elements on the one hand, and on the other to independently recognise how forms of knowledge draw boundaries around them. But importantly, the theory of boundary critique does not describe the space of aspects of elements, and therefore it needs the critical person to be able to know it in advance. If this knowledge is not self-evident, or given, then the critical person might fail in the application of boundary critique. Now, does boundary critique impose some form of knowledge itself? The systemic theory that constitutes the proposed basis for critique does not advocate any particular form of knowledge. Instead, it simply suggests that one should be critical of any such forms, and the means to do it is the employment of the system idea. Of course, the very proposal of being critical about forms of knowledge is a form of knowledge in its own right, that could itself be imposed[3]. However, what I am interested here is the question of whether by applying boundary critique one is imposing a particular ideology that is alternative to, and replaces, the form of knowledge about which one is being critical. And in this respect the theory underlying boundary critique can be said to not entail an ideology. Nevertheless, let us pay attention to the kind of knowledge that is required from the critical person in order to determine in a particular case what boundaries a form of knowledge is drawing. That required knowledge must be independent from her/his own beliefs about whatever that form of knowledge is about, for otherwise, critique would itself be ideological. For instance, if the form of knowledge under critical scrutiny is a proposal for a health system in a community, the theory of boundary critique does not advocate any particular
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view of health care. However, what is not clear but is required if boundary critique will not be a vehicle for knowledge imposition, is that someone’s critical appraisal of that proposal will be independent from her/his own views about health care. If the results of any practical application of boundary critique are ideological, then there is a risk that the critical person will impose her/his views in the name of critique. This can be seen in that the results of her/his application of boundary critique may be legitimised by the fact that they are critical. But given that they would be tainted with the critical person’s own ideological views, if someone else accepts those results then s/he would be at the same time accepting [part of] the critical person’s ideological views. 3. The organisation of interactions The idea here is to organise the interactions between persons – in the pedagogical case between teacher and students – in such a way that no single person or group can make her/his voice dominate the conversation, and that all voices are given the chance to be heard. One particular systemic method developed along these lines is Syntegration (Beer, 1995), and it has been used to organise pedagogical interactions (as reported in Espinosa, 2000). It is important to note that these methods do not say anything about the contents of the conversation, because they focus on the form of the interactions. Instead, they attempt to simply make sure that all the participants are given the same chance to talk, advance claims, formulate questions, etc. The application of such methods in pedagogy tries to remove the obstacles that do not let students talk. However, by not dealing with contents, it does not mention the kinds of questions that the participants should formulate in order to identify and question forms of knowledge that may not be so obvious. If it does not provide those tools, it is not making sure that those forms of knowledge will not be imposed, and therefore, it must rely on the students already having those abilities. If that imposition occurs – or has occurred in the past – then under the guise of an apparent genuine dialogue those forms of knowledge will be legitimised or pass undetected. 4. Critical systemic pluralism By acknowledging the potential validity, even if limited, of the various paradigms that have appeared in systems thinking, critical pluralism seeks to encourage the development of all of them while critiquing their limitations and potentialities to aid in the use of their methodologies, methods, and tools (Jackson, 2000). Gregory’s paper on educational systems can to some extent be said to go along these lines. We will examine here the relation between knowledge imposition and the type of critique provided by this form of critical pluralism, rather than
the potential application of its methodologies. The contribution of its Critical thinking application depends largely on the possibilities of the systems paradigms and intellectual whose use it seeks to inform. Two strands within the systemic paradigms have autonomy already been discussed in Sections 2 and 3. In this case, it is perhaps not the system idea which is the basis for critique, but rather an independent analysis of basic assumptions, limitations, and 1317 possible consequences of the acceptance of each of the various paradigms. This analysis is provided by the theory, and the critical person is expected to use these insights to examine particular situations as well as the possibility of applying in them the various systems methodologies, methods or tools. Just like boundary critique, critical pluralism does not advocate any particular form of knowledge – in this case, any particular systemic paradigm – and therefore, it cannot be accused of imposing one. It only seeks to provide more information – critical information – so that their use is better informed. However, it is important to more closely look at what this means. Can some knowledge imposition occur by means of the acceptance of the critical knowledge provided by the critical pluralist theory? we might say that someone could disagree with the critical knowledge of assumptions, strengths, weaknesses, constitutive rules, etc. provided by the theory, and in that sense it could of course be imposed[4]. But the issue I want to examine is whether by accepting this critical knowledge one would be at the same time committing to particular views that might compete with, or be alternative to, those systemic paradigms the theory is critical about. In this respect, for not imposing a particular systemic view the critical pluralist theory would require its critical knowledge to be independent from the forms of knowledge it is critical about, or from any alternative to them. To put it more clearly, the various systemic paradigms are constituted by knowledge about the world, society, knowledge, and so on. Critical pluralist authors have produced some critical knowledge about those systemic paradigms, and specifically about their assumptions, limitations, etc. If this critical knowledge depends on those authors’ views about the world, society, knowledge, etc. then its uncritical acceptance would entail the imposition of [part of] those views. 5. Givenness We want to argue now that what the approaches described above require so that knowledge imposition is prevented, can be described in terms of two elements, which I will call givenness and interpretation independence. This section will be devoted to the givenness requirement, while in the next one we will talk about interpretation independence. The choice of the term givenness intends to acknowledge Wilfrid Sellars (1956) work, and particularly his discussion of the Myth of the Given. In particular, he argued against them in vogue versions of empiricism which
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suggested that secure knowledge ultimately rests on some kind of elements which are given to the mind (e.g. sense data). As such, knowledge of these elements would be inescapable and incorrigible; that is, the mind cannot fail to know them, and it cannot be wrong about them. Sellars effectively showed that any knowledge about anything, as represented in beliefs or propositions, necessarily belongs to the “logical space of reasons”. In that space it is other beliefs or propositions – playing the role of reasons – which participate in the practical activity of justification. No belief or proposition can be, then, given. Now, even though Sellars’ essay attempted to be Kantian through and through, the Kantian distinctions between the synthetic and the analytic, and between the a priori and the a posteriori, are to some extent also susceptible to Sellars’ criticism. As Rorty (1979) has argued, the Kantian idea that the manifold of experience is organised by the human categories of understanding in an act of synthesis, makes sense only if somehow the human mind could have some access to that manifold. For otherwise how can it be known that the mind is presented with a diversity? Why should we think that sensibility “in its original receptivity” presents us with a manifold, a manifold which, however, “cannot be presented as a manifold” until the understanding has used concepts to synthesise it? (. . ..) If we are going to argue that we can only be conscious of synthesised intuitions, how do we get information about intuitions prior to synthesis? (Rorty, 1979, pp. 153-154)
Actually, arguably Quine’s (1953) argument against the analytic-synthetic distinction, and more specially Davidson (1974) against the scheme-content distinction, can be said to more clearly articulate the rejection of the separation between concepts and intuitions. There is no space here to present the whole argument (see for instance Rorty, 1979). However, the important point is that the space of possible elements or aspects of knowledge is not immediately knowable to an inquirer. These elements are not there, in some way given, waiting to be organised, to be chosen from, or to be connected with others. The identification of those very elements is in itself knowledge, and as such it can be changed by reasons. The elements themselves, if one wants to still speak that way, are not incorrigible or inescapable. Now, let us recall from Section 2 that to effectively prevent knowledge imposition, boundary critique required from students, or more generally from the critical person, “to be able to identify aspects or elements on the one hand, and on the other to independently recognise how forms of knowledge draw boundaries around them”. If one accepts the rejection of the Myth of the Given, then the identification of aspects or elements cannot be taken as a basis for critique. That is, the critical knowledge of the elements excluded or included by any form of knowledge, is itself a form of knowledge whose justification has not been secured epistemologically, and can only be justified by reasons, just like any other ideological form of knowledge. If forms of knowledge are problematic, then critical knowledge is problematic in the same way and for the same reasons.
Similarly, in Section 3, I argued that approaches based on the organisation of Critical thinking interactions must rely on the students already having the ability to identify and and intellectual question forms of knowledge. In this case, the requirement of givenness autonomy appears in a stronger way. If the questioning of a form of knowledge depends on the questioning of the various aspects that it has or has not taken into account, as well as of the manner in which it took them into account, then again 1319 the fact that these aspects are not given to the critical person’s mind implies that relevant questions may never be formulated. Therefore, the corresponding knowledge that passed unquestioned may be imposed. Ultimately, this issue boils down to a matter of the questioning competence of teacher and students: Although, they must of course have some competence, it may not be enough for the formulation of certain relevant questions. 6. Interpretation independence The expression interpretation independence refers to the idea that one can produce an interpretation of some form of knowledge in some domain, independently from one’s beliefs about that same domain. Or, in other words, that an interpreter’s knowledge of the meaning of a speaker’s words is independent from her/his knowledge of reality in the domain in question. The issue of interpretation independence is important for the discussion about criticality and knowledge imposition, in so far as a critical analysis of any particular form of knowledge is an interpretation of it. One philosopher who has extensively worked on the problem of interpretation is Donald Davidson (1973, 1974). In his work, interpretation refers to the production, by an interpreter, of a sentence or set of them that s/he knows how to use, that translates – or keeps the meaning of – a sentence or set of them uttered by a speaker. The first point is derived from Quine’s rejection of the analyticsynthetic distinction, and the derived rejection of a distinction between questions of meaning and questions of truth (Quine, 1953). To know the meaning of some sentence it does not mean that one will know something like its definition, or a set of [analytic] sentences that in some sense give its meaning. It is, rather, to know how to use it. This in turn is knowing many other sentences that would be true if that one were true [or false], knowing when to use it – if it is an occasional sentence – , knowing how to produce new sentences – and their truth value – that relate to the translated sentence, and so on. Davidson has shown that an interpreter makes an active use of her/his own beliefs when interpreting a speaker’s sentences. There is no space here to present the argument; but one of its central ideas consists in the inevitability of the application of the charity principle in interpretation (Davidson, 1973). According to this principle, an interpreter will try to maximise the rightness of what the speaker says as far as it is plausible. And being right, of course, means being right according to the interpreter’s beliefs – what else? An interpretation in which the speaker is mostly
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wrong is more likely to be a bad interpretation. Davidson (2000, page 70) expresses this relation between truth and meaning saying that “translation succeeds only if it preserves truth, and the traditional aim of translation is to preserve meaning”. But let us notice now that in order to determine what beliefs the speaker might be wrong or right about, the interpreter needs to use her/his own beliefs. Moreover, they are beliefs about the same domain or objects that the speaker’s beliefs are about. This idea of charity, which is essentially holistic, further suggests that the attribution of a belief to a speaker entails that the interpreter is prepared to attribute her/him many more beliefs, expressed in sentences that relate to the originally translated ones. These related sentences would effectively be ones that the interpreter her/himself takes to be entailed by the translated ones, and that therefore s/he thinks the speaker will – or should – agree with. In fact, given that according to Quine’s rejection of the analytic-synthetic distinction there cannot be a clear separation between questions of meaning and questions of truth, the line that separates translated from related sentences is a fuzzy one. That is, there is no clear way of separating an interpreter’s description of the meaning of a speaker’s utterances from her/his believed implications of the views represented by those utterances. The critical knowledge produced by the theory underlying a critical approach, or by its use in a particular situation, is constituted by sentences that the critical person takes to be entailed by, and in a sense also to describe, the form of knowledge that s/he is being critical of. And, as argued above, this knowledge is necessarily constructed out of her/his beliefs about the same domain or objects that the form of knowledge being critiqued is about. There is, then, no interpretation independence for critical knowledge. But that was exactly what we argued in Sections 2 and 4 was required by both boundary critique and critical systemic pluralism so that they would not actively promote the imposition of knowledge. In boundary critique, the user of the tools provided by the approach will also have to use her own views to be critical about someone else’s – or her/his own –; and in doing this s/he may pass (part of) those views as valid, without a proper critical conversation, because s/he is presumably being critical. In critical systemic pluralism, the same applies to the views of the proponents of the approach.
7. Summary and concluding remarks: systems, holism, and criticality Based on the discussions in the literature on critical thinking in pedagogy, we have tried in this short paper to show some problems that present conceptions of critical systems thinking face, in terms of the problem of knowledge imposition. We examined three strands of systems thinking which propose to use the system idea in a critical way, and which in one way or another are
concerned with the problem of knowledge imposition: boundary critique, Critical thinking organisation of interactions, and critical systemic pluralism. and intellectual Kinds of approaches trying to provide tools for either boundary critique or autonomy organisation of interactions, were found to require givenness; that is, that the aspects that the students are to pay attention to, that the questions that s/he should ask, so that the imposition of knowledge from external sources is 1321 prevented, are given, and require no additional knowledge to that already possessed by them. Approaches within critical systemic pluralism and boundary critique were argued to require interpretation independence; that is, that someone’s critical views about any particular form of knowledge be independent from her/his own beliefs about whatever that form of knowledge is about. Unfortunately, there was no space to appropriately present the arguments for the conclusions that neither givenness nor interpretation independence are possible. The implications are very important, however, because not meeting the givenness requirement would mean that boundary-critique and organisation-of-interactions approaches are unable to guarantee that forms of knowledge that might potentially be imposed will be identified and questioned. In turn, not meeting the interpretation independence requirement would imply that boundary-critique and critical systemic approaches may be vehicles for the active imposition of the critical person’s views, in the name of critique. We take it that the impossibility to obtain givenness and interpretation independence are both consequences of the radically holistic view of language that has been constructed by a number of philosophers, among which Sellars, Quine, and Davidson, are particularly important (Rorty, 1979, 1991). The critical use to which the system idea has been put relies, paradoxically, on a rather reductionistic understanding of meaning and interpretation. The system idea should not then be used to provide ontological descriptions of weltanschauungen, belief systems, theories, designs of social systems, or whatever is the case. What it can only do is help us – those engaged in conversation – enhance the scope of our beliefs and the inclusiveness of our conversations, where neither scope nor inclusiveness should be regarded as absolute terms. Notes 1. Let me clarify that we do not claim that the only or main purpose of critical approaches is the development of autonomy of thought and the prevention of knowledge imposition. It is an important one, though, for most of them. 2. Ulrich only makes this claim in relation to the realm of the practical; that is, of what ought to be, as represented in designs of social systems. Midgley does not seem to take this restriction. 3. One aspect of the well-known Habermas-Gadamer debate can be said to be about this. 4. This issue would be similar to that mentioned in Section 2, and for which the HabermasGadamer debate is relevant.
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References Banathy, B. (1992), A Systems View of Education: Concepts and Principles for Effective Practice, Educational Technology, Englewood Cliffs. Beer, S. (1995), Beyond Dispute: The Invention of Team Syntegrity, Wiley, Chichester. Buckingham, D. (Ed.). (1998), Teaching Popular Culture: Beyond Radical Pedagogy, UCL, London. Davidson, D. (1973), “Radical interpretation”, in, Brandorn, R. (Ed.), Inquiries into Truth and Interpretation, Clarendon, Oxford. Davidson, D. (1974), “On the very idea of a conceptual scheme”, Inquiries into Truth and Interpretation, Clarendon, Oxford. Davidson, D. (2000), “Truth rehabilitated”, Rorty and His Critics, Blackwell, Malden. Duhan Kaplan, L. (1989), “Teaching intellectual autonomy: the failure of the critical thinking movement”, in, Walter K. (Ed.) Re-Thinking Reason. New Perspectives in Critical Thinking, State University of NY, Albany, pp. 205-19. Ellsworth, E. (1989), “Why doesn’t this feel empowering? working through the repressive myths of critical pedagogy”, Harvard Educational Review, Vol. 59, pp. 297-324. Espinosa, A. (2000). “Creating a democratic learning Context: an experience in the use of syntegration for this purpose”, Proceedings of the 2001 ISSS Conference: Understanding Complexity: The Systems Sciences in the New Millennium, Toronto. Freire, P. (1972), Pedagogy of the Oppressed, Sheed and Ward, London. Giroux, H. (1997), Pedagogy and the Politics of Hope: Theory, Culture, and Schooling, Westview, Boulder. Gregory, W. (1993), “Designing educational systems: a critical systems approach”, Systems Practice, Vol. 6, pp. 199-209. Gur-Ze’ev, I. (1998), “Toward a nonrepressive critical pedagogy”, Educational Theory, Vol. 48, pp. 463-86. Jackson, M. (2000), Systems Approaches to Management, Kluwer/Plenum, NY. Luke, C., and Gore, J. (Eds) (1992), Feminisms and Critical Pedagogy, Routledge, London. Maddock, T. (1999), “The nature and limits of critical theory in education”, Educational Philosophy and Theory, Vol. 31, pp. 43-61. Midgley, G. (2000), Systemic Intervention: Philosophy, Methodology, and Practice, Kluwer, N.Y. Paul, R. (1992), “Teaching critical reasoning in the strong sense: getting behind worldviews”, in Talaska, R. (Ed.), Critical Reasoning in Contemporary Culture, State University of NY, Albany, pp. 135-56. Paul, R. (1993), Critical Thinking: What Every Person Needs to Survive in a Rapidly Changing World, 3rd ed., Foundation for Critical Thinking, Santa Ana. Quine, W. (1953), “Two Dogmas of Empiricism”, From a Logical Point of View: Nine LogicoPhilosophical Essays, Harvard University, Cambridge. Rorty, R. (1979), Philosophy and the Mirror of Nature, Princeton University, Princeton. Salman, K. (1998). “Why doesn’t this feel political?” Journal of Critical Pedagogy, Vol. 2. Available at http://www.wmc.edu/academics/library/pub/jcp/issueII-1/saltman.html (December 2001). Sellars, W. (1956), Empiricism and the Philosophy of Mind, Harvard University, Cambridge reprinted in 1997. Siegel, H. (1988), Educating Reason: Rationality, Critical Thinking and Education, Routledge, London.
Ulrich, W. (1983), Critical Heuristics of Social Planning: A New Approach to Practical Philosophy, Wiley, Chichester. Ulrich, W. (1991), “Critical heuristics of social systems design”, in Flood, R. and Jackson, M. (Eds), Critical Systems Thinking: Directed Readings, Wiley, Chichester. Ulrich, W. (1996), “Critical systems thinking for citizens: a research proposal”, Working Paper No. 10, The Centre for Systems Studies, University of Hull. Young, R. (1992), Critical Theory and Classroom Talk, Multilingual Matters, Clevedon.
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A systemic look at educational development programs: two perspectives on a recent Colombian experience Angela Espinosa Los Andes University, Bogota, Colombia
Mike C. Jackson HUBS, University of Hull, Hull, Canada Keywords Cybernetics, System design education Abstract There has been considerable agreement among researchers and practitioners, working on development issues, that unless we improve the education infrastructure in lessdeveloped countries they will never be able to improve their development indices. Innumerable educational reform programs in many different countries, over the last century, have been driven by this aim but few have had the desired impact on local educational systems in terms of coverage, quality and equity. Taking as an example a project recently undertaken in Colombia, we argue in this paper that a significant reason for this may well be the inappropriate theoretical paradigms and methodological approaches underpinning the majority of educational reform programs.
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Educational reform and development Along with the acceptance that human capital is the most valuable resource that a nation possesses, has come the realization that improving the educational infrastructure of a country is one of the most significant development strategies that can be adopted. An improved basic education system can assist competitiveness and hence economic growth. As Carnoy and Castro (1997) have it, “to have a qualified workforce increases the competitivity and exporting possibilities and results in better development rates for a country”. This is especially true given the increasing dependence in many businesses upon new information and communication technologies. Such businesses, they state, need a work force with “a solid mathematical foundation, creativity, effective communication and team working skills”. In general, a more Cartesian education reform agenda seems to be a link between improving the educational system of a country and increasing the efficient and effective utilization of capital, the performance of the workforce and other aspects of production processes. It is assumed that such developments will, in turn, lead to the alleviation of poverty and to greater equality in income distribution. More recent debates on these hypotheses
highlight the social and financial capital formation aspects as relevant as the human capital. The 1980s external debt crisis of Latin American countries resulted in reduced income per capita and a 22 per cent increase in poverty in the region measured in terms of access to the basic prerequisites of life such as public education, health and water supply and housing systems (Morsley et al., 1997). As said by the IDB President, E. Iglesias in 1998, there has been an increase from 90 million people living in poverty in the 1980s to 150 million nowadays, which means 30 per cent of regional population[1]. It is not surprising therefore, given the earlier argument, that there has been a huge interest in Latin America in the idea of initiating educational reform programs as a means of fostering economic development and hence addressing the issue of increased poverty. There have been some examples, where a clear link can be drawn between new educational policies and improved development rates, but in most cases, what might seem like the obvious benefits of educational reform have not been fully realized. Castro et al. (1998) says that, after a decade of reforms the low level of instruction of most of the work force and great inequities in accessing work opportunities are still stopping the development options for the region. The open question is why so many programs and so much investment, aimed at improving educational standards in Latin America, have had such disappointing results. It is the aim of this paper to establish why this might be the case and to eventually influence current strategies in a more useful direction. Our hypothesis is that to get better results it is necessary to look at educational development from a more holistic perspective. Current failures seem to arise from a Cartesian way of understanding socio-economic and educational development processes. A more holistic approach would seek to address attitudes, values and the context of interaction at the level of local educational systems as well as linking these to other societal and institutional systems. New technologies and management structures should support but not dominate this design orientation. We explore this hypothesis by looking first at the theoretical and methodological underpinnings of the usual reform strategy adopted; second at a case involving a recent educational program in Colombia which had a clash of mechanistic and holistic perspectives – The “New School System” program (1998-2002) as seen by an insider of the program; and third by jointly reviewing some possible alternative systemic approaches. Multilateral agencies strategies to educational reform in Latin America The Inter-American Development Bank (IDB) has engaged with many governments in the region to promote educational reform, primarily by
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concentrating on the educational infrastructure and re-orientating educational systems to the new characteristics of international markets. The World Bank has similarly, since 1963, financed more than two hundred projects for educational development in the poorest countries of the region, concentrating on improving the numbers of qualified people leaving educational systems (Ramirez, 2001). In general terms, it is possible to argue that a certain, mechanistic theory of educational development has underpinned the efforts of these banks in the region. The aim has been to achieve the goals of quality, equity and coverage of educational systems with a view to increasing the socio-economic development of each country. It has been assumed that these goals can be pursued in tandem without contradiction. (Wolff and Castro, 2000). The main vehicle for realising change has been seen as increasing the efficacy and efficiency of the institutions managing educational resources. Technology has been perceived as crucial for this and the main measures of performance have been related to delivery at reasonable cost (Ramı´rez, 2001). This theory is then translated down into a methodology, which is most clearly visible in the IDB projects in the region. It can be seen as involving five interrelated elements: rethink the educational system and its structure in relation to the world of work; decentralize educational management and control of resources to local levels in order to ensure better use of resources and more management control and accountability; provide training programs and incentives in order to get better teachers and educational services; make maximum use of technology to improve quality; put quantitative measures of performance in place. (Carnoy and Castro, 1997) Traditional educational reform programs for implementing these strategies usually seek for isolated projects developing each one of the ideas, not necessarily at the same places or institutions. Target goals are precisely linked to detailed projects and are normally related with the way of using the resources and not to the quality of verifiable results. Better use of these resources may result if properly linked to local potentialities and needs. We can now consider an individual case of educational reform in Colombia, relating it to this mechanistic theory and practice.
A recent educational program in Colombia: the “New School System” program Mechanistic beginnings This program to reform the Colombian basic education system was undertaken by the Colombian Ministry of Education and the IDB between 1998 and 2002. It was initially planned and pursued according to the traditional approach suggested for such programs by the IDB, incorporating the main elements of the mechanistic theory and methodology outlined previously.
It was originally aimed at promoting local transformations in effectiveness and efficiency in a group of departments (5-8), municipalities (100-160) and public schools (500-800). There was to be a gradual change process, with the respective authorities joining the program at their own pace, but the hope was that the program would eventually impact on the whole of the basic education system.
A holistic alternative Although the program began by following the traditional approach, between 1998 and August 2000 the Minister of Education, Mr G. Bula, supported its reorientation along a participative action research kind of program. He had supported before other experiences in managing change using organizational cybernetics and second-order cybernetics ideas and tools that also influenced this program’s design and the prototype stage. To this end, he established a Coordinator Unit at the Ministry of Education led by national and international advisors with these and also other academic orientations (economy, social psychology, ethnography, philosophy of language, systems dynamics, among others). Specialized professionals from all relevant fields also staffed this Unit[2]. The basic aim of the “New School System” program remained to fulfil the mission of the basic education system as laid out in the Colombian constitution – to guarantee a quality education for all – but the language used were firstly influenced by organizational and second order cybernetics theory and methodologies. This language was first used to facilitate the initial design stage with participation of all main viewpoints, (the National Planning Department, The Treasury Ministry, the Teachers Trade Union, the IDB, among others). First agreements on main concepts, strategies and organizational design resulted from this stage. The design of the prototypes and implementation stages followed the same philosophy, and were developed through workshops facilitated each time with different kind of systemic and cybernetic tools some of them previously used in the country for diagnosing effectiveness of public sector institutions (Espejo and Reyes, 2001). The educational reform program was premised on promoting single, and double loop learning in the organizations supporting each level of the system. This had to be embedded in a shared identity and improved relationships of cohesion, citizenship and performance within the system as a whole, at each level of organization. In this educational reform system, cohesion implied the need to encourage the autonomy of the parts while keeping a stable relationship with the organization they belong to. Citizenship referred to the autonomous acting according to agreed values, resources and game rules. Performance referred to the need for accountability in delivering services to clients or to other organizational levels.
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Organizational learning was to be promoted by changing the way of thinking, acting and relating to each other among the actors at the various levels of the system. The aim was the one of rebuilding the language and practices in use in the way of managing the social and working relationships among the main actors. The knowledge of teachers and authorities at the local level had to be respected as valid and legitimate, and had to become the basis on which the “New School System” program was constructed. Education had to be more closely related to community development and to improving the way of living in order that it made sense to people and gained their support. These and other changes would contribute to development of teachers and schools capable of second order learning. Guided by this cybernetic theory, the Co-ordinator Unit agreed a number of strategies in pursuit of the “New School System” program, being some of the most relevant ones: .
increasing the participation of children and parents in developing knowledge and ensuring links to community development;
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developing improved relationships, for example between the educational community and the municipal authorities responsible for education;
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developing “Complete Schools”, associations of geographically close schools which together could offer a complete basic education service and thus become more autonomous;
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concentrating educational management initiatives on providing resources for meeting local needs;
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ensuring that those organizations responsible for education at the municipal and national levels added value by facilitating and complementing initiatives at the school level;
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developing an incentive program based on understanding the system as a set of economic agents, both institutional and individual, whose relations and interactions were represented as economic contracts and then stating a set of changes, actions, and incentive mechanisms oriented to improve the consistency of the system and its global performance in terms of quality, coverage, and equity (Castillo et al., 2002);
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involving the local community in social mobilization processes around collectively agreed initiatives for local educational transformation.
To reiterate, this design of program emphasised achieving the educational mission of the country by encouraging actor participation in setting educational priorities and policies; the development of more autonomous individuals and institutions with a strengthened capacity for learning and action; and a growth in the cohesion of the system by ensuring citizenship and performance in pursuit of locally agreed goals aligned with the nationally agreed ones.
The program could best be supported, it was felt, by offering technical assistance in the formulation of educational transformation plans, encouraging the development of “Complete Schools”, ensuring participatory practices and involvement of the community, improving negotiation skills at the local level, providing for feedback and the follow-up of initiatives, ensuring permanent and effective communication between all educational levels, and by synthesizing the learning process from the Program and ensuring diffusion to the rest of the country. What happened? The first stage of the project was in the period 1998-1999 when the new Minister team managed to agree with the IDB and other members of the Board, as well as with the technical staff, the first stage of the program’s design. From 1999 to August 2000 main efforts of the Co-ordinator Unit were concerned with the make-up of the technical teams, which were to assist at each organizational level (national, departments, municipalities and public schools). Also with establishing, educational development strategies with the departments involved in the prototype scheme, Quindı´o and Risaralda, that started in September 1999. In each one, technical teams from the National, Departmental and municipal levels (about 60 people) participated actively in the development work, mostly through workshops with the Co-ordinator Unit. These teams made progress, not without having to deal with huge tensions and conflicting views. The workshops facilitated the process for agreeing the conceptual, methodological, instrumental and financial guidelines for planning and implementing the program and also tried to create a context for dialectic solution of current tensions through participative action. By July 2000, there was a detailed design available to present to the Board of Directors of the program. (SECAB, 2000) In July 2000 there was a following up mission from the IDB to check preliminary conditions fulfilment for first investment approval for the program. In this meeting, the resulting design and implementation proposal was presented and discussed. There were representatives from the Ministry of Education, the National Planning Department, the Finance Ministry and the IDB (the USA and Colombian representatives). It was at this meeting that some significant disagreements surfaced. Some present, wedded to the traditional IDB approach, felt that the new design might not produce visible and measurable enough results in the short term. Nevertheless the proposal was accepted but on proviso that, before formal approval of the credit resources, more details would have to be provided in terms of action plans, mechanisms for using the resources and specific transformation plans for the departments where the prototype activity was taking place. It was while these additional details were being prepared that events took a dramatic turn. In August 2000 the President appointed a new Minister of
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Education Mr. F.J. Lloreda. This allowed all of the theoretical and methodological tensions present in the Board to come to the surface. The perspectives of the National Planning Department and the Treasury Ministry coincided with the preferred model and strategies of the IDB. It was their view that what was required was a more effective and speedy process for improving efficiency in the distribution and use of resources at the national level of the educational system, as well as more concrete attention to improve the efficiency of the educational institutions. The new Minister’s team also preferred this view and decided to move forward with the program on the basis of these success criteria. Without the political support they had before, some of the experts left the Co-ordinator Unit at that stage. It was easier to take the detailed design back to more traditional expected results and procedures. Although many elements of the cybernetic oriented design and strategies remained in place, while they were already part of the agreed language and strategies, the final detailed plan, which is now being implemented, adhered much more closely to the traditional, mechanistic approach. Gone was the centrality of creating a learning context in which local institutions participated in formulating their own educational transformation plans at their own levels and developed new kinds of relationships with local communities to promote citizenship and performance in realising deeper educational reform. Instead, the focus was on defining the instruments that the national technical teams considered the Secretariats of Education and the public schools themselves required in order to properly manage their resources, according to pre-established goals for the territorial level, agreed by the national authorities at the program’s board. A systematic procedure for training the officials involved in the program from the departments and other levels was to be established, employing formal workshops where the Co-ordinator Unit offered initial technical assistance to the local teams and then left them developing agreed specific projects (e.g. improving filing systems, management information systems, control systems; all according to the suggested methodologies and tools). In a word, what was abandoned was any commitment to generating a proper learning context for promoting second order learning.
Critical review of the Colombian case We will present this critical review of the case study from two perspectives. First, from the point of view of someone (Angela Espinosa) centrally involved in the development of the alternative cybernetic approach. Second, from that of someone (Mike Jackson) taking an external, critical systems thinking, look at events.
In defence of the cybernetic oriented alternative The account provided above allows an easy comparison between the more mechanistic approach to educational reform and the alternative more systemic oriented approach. It does so in terms of different theories of educational development, the main hypotheses supporting these alternative theories, the main purpose sought, the key transformations supported, the main actions encouraged and the primary results expected. In general, it can be argued that the traditional, philosophical and methodological approach, favored by the IDB, concentrates on increasing the efficacy and efficiency of the institutions managing resources provided for education as the best means of improving the delivery of those services. Predetermined managerial support schemes and instruments are employed in order to improve efficacy and efficiency, especially in terms of the use made of financial resources. The risk with this scheme is that there may be less effort at the changing schools for developing innovative practices in education, but emphasis in demonstrating proper resources management and information management. Efficiency in the short term, even if essential for organizational performance does not guarantee sustainable performance, as said in Espejo et al., 1996. The changing institutions may end up managing efficiently the resources for the wrong purposes if they are not fulfilling the goals of offering quality education for the students. Their sustainability as an educational institution may still be at risk. They may still need to learn how to behave also intelligently and be valuable contributors to their social milieu. The cybernetic alternative[3], by contrast, tried to concentrate on increasing the “potentiality” (as defined by Beer, 1981) of the educational system by focusing on actions that would add value and improve the capacity of educational services at each organizational level of the system. It argued that transforming the quality and equity of the educational system depends as much on involving teachers, pupils and communities as upon the financial, technological and managerial resources available to the educational authorities. They as the real change actors required to develop their core potentialities and the organization must provide the required societal, technical and management milieu for developing these new kind of social and working practices. It was essential therefore to create appropriate learning contexts, at each level of the system, capable of facilitating change for those involved in the educational process, and thus enabling them to learn how to cope with complexity and change while developing their own educational transformation process. From the cybernetic standpoint, the possibilities of impacting with significant changes on the educational system, changes sustainable in the medium and long term, are much greater if design proceeds according to these
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principles than if it is conditioned by more mechanistic assumptions. It would change investment criteria and priorities. For instance, successful implementation and scale of impact depend upon transformation plans being developed at the local level in the light of perceived needs and potentials, and being aligned with national policies, strategies and available resources. These things are less likely if a mechanistic, top-down methodological framework is adopted where each institution receives agreed resources and has to expend them on the basis of pre-determined guidelines, without explicit actions and resources to also develop a proper learning context for sustainable change. Simply providing management tools cannot ensure a better quality educational system. Summarizing more Cartesian approaches may improve the management of a system that is doing the wrong things and serving the wrong purposes – only now it is using its resources more efficiently in pursuing them.
Some questions from a critical systems perspective The point of raising some critical systems questions is not to denounce the cybernetic oriented program design, which can only be applauded from a systemic viewpoint. Rather it is to put on the agenda whether taking other holistic approaches (as well as the cybernetic) into account, might allow greater learning to take place concerning the Colombian case and might improve the chances of success in seeking the transformation of educational systems in the future. Some of the questions that would occur to a critical systems thinker (many based on previous critiques of the cybernetic approaches ( Jackson, 1998)) would be as follows. (1) Does not the cybernetic approach equate to a form of “utopian engineering”, which seeks to change the whole system at once? Is not this dangerous and likely to be unacceptable to many? (2) Does not the cybernetic approach simply seek to replace the “one best way” of mechanistic thinking with the “one best way” of organismic and neuro-cybernetic thinking? (3) Because of its adherence to the organismic and brain metaphors, do not cybernetics misuse concepts such as cohesion, purpose, citizenship, accountability and participation, seeing them always in terms of the parts functioning to serve the whole? (4) Does not cybernetics pretend to be underpinned by some expert knowledge regarding the proper design of complex systems and so lend itself to authoritarian usage?
If the answer to these questions is yes, as critical systems thinkers suspect, it could explain a number of things about the Colombian case. (1) Why, for example, the original Co-ordinator Unit could not give space to the mechanistic concerns of the IDB as well as to their own “organismic” and “brain” directives. (2) Why the achievement of the cybernetic goals was perceived in terms of a one-off design rather than in terms of a process of building a coalition among decision-makers. (3) Why opposing value and cultural perspectives were not better taken into account. (4) Why there appeared to be an insufficient appreciation of the political difficulties of implementing the cybernetic design. (5) Why a number of the cybernetic insights and initiatives were easily accommodated into the revised mechanistic design.
An unfinished conversation In order to deepen the conversation that both authors have started while developing this analysis from both systemic approaches, there follows a first reply from the cybernetic approach to the critical enquiry. (1) There is never an attempt to “change the whole system at once”. On the contrary we understand change as an evolutionary learning process, structurally and culturally based, impossible to be produced from outside and less to be produced at once. Instead of engineering an utopia, we try to facilitate the learning process of an organization in the direction it decides to go and to help them finding proper cultural and structural adjustments for advancing in the agreed change direction. (2) One best way suggests following a pre-fixed model. The VSM is not seen as a model to be followed up but as a language offering useful distinctions to talk about the viability and performance of a learning organization. About the organismic and neuro-cybernetic thinking that you relate to the cybernetic proposal, I shall rather invite you to invent a new metaphor beyond these ones (even including them); a socio cybernetic inspired metaphor, for instance, that may take more fairly current organizational cybernetic developments that you have even classified as emancipatory thinking in Jackson (2000) and that I feel would better describe the state of the art of these approaches. (3) The idea of homeostasis in social relationships differs from this idea of parts functioning to serve the whole. It refers to relationships that keep stable over a time period while agreeing on certain purposes and game
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rules that fit both. It is in this understanding that we use the VSM to create structural contexts more able to cope with the required variety of these negotiations and interactions, at each organizational level. This is a recursive property and not exclusive to the whole. In this understanding (beyond the biological and closer to a social metaphor) we interpret cohesion and so on. (4) It may or may not happen and design of the change process must properly acknowledge the risk and use the required tools to prevent it. One is by understanding the role of the expert, as a facilitator of the change process who is not longer required once the change process is engrained in current practices and made sustainable through proper incentives sponsored by the changing organization. Proper design of learning teams and their political interactions with the organization may also prevent the risk, but not avoid it totally. About the Colombian case. (1) It did give all the space. There was not a pre-fixed program design but what resulted was the result of hard negotiations with the main actors including the trade union and the IDB who played an important role all way around. (2) The story told the result of the coalition, which was pre-dominantly cybernetic oriented, at the conceptual and methodological levels, while there was the political and technical support for it. It has been my work to try and differentiate the initial agreements and viewpoints, the suggested cybernetic orientations and the way it finished. (3) Opposing value and cultural perspectives were important criteria for designing the conversational spaces when advancing the reform prototypes. Maybe we should have used them also as criteria for designing the political and management spaces of the program but other design criteria (more politically oriented) prevailed on these spaces. (4) The appreciation was permanently handled by the technical team – while developing the prototypes, the tensions were felt all the time. Most political difficulties were solved through the process and might have kept controlled if implementation carried on the cybernetic oriented design. (5) What remained, as said was the language already engrained by most actors in terms of strategies and program orientations. It was already part of the agreements. To get agreements on them was a permanent negotiation process. Later interpretations on implementation details changed the initial focus and translated the final projects into more instrumental and mechanistic oriented ones. These issues will be taken up specifically in another paper.
Conclusion We have reviewed two alternative approaches to managing educational development programmes and the way they played out in the particular political and cultural context of a Colombian case. The story told echoes similar stories in other countries and we hope that lessons can be learned about the design of educational systems more generally. We believe that a deeper understanding of the paradigmatic, theoretical and methodological underpinnings of reform programmes, and the tensions between them, should enable us to generate sufficient learning to improve on current practice and design more successful strategies for educational development. Notes 1. http://www.iadb.org/exr/prensa/speeches/s15399c.htm 2. The views and definitions presented in this paper by the insider of the Program (A. Espinosa) do not attempt to represent the views or definitions of other leaders of the Program, but come from her own experience as technical coordinator of the program, from August 1999 to December 2000 and as an academic researcher in organizational change from a cybernetic approach. 3. When we refer to the cybernetic alternative we refer to the pre-dominating conceptual basis underpinning most of the programs design and implementation criteria, which integrated both organizational cybernetics and second order cybernetics concepts and tools, but also other systemic oriented concepts as tools as described. References Carnoy, M. and Castro. (1997), “Que´ rumbo debe tomar el mejoramiento de la educacio´n en Ame´rica Latina?”, BID, Washington DC, pp. 1-5. Castro, C., Navarro, J.C., Wolf, L. and Carbol, M. (1998), “Making education a catalyst for progress: the contributions of the IDB Bank”, BID, Washington DC, p. 1. Castillo, M., Duque, G. and Beltra´n, F. (2002), “Incentives: mechanisms for the consistency of the Colombian education system”, Kybernetes, (in press). Espejo, R. and Reyes, A. (Eds.) (2001), “The state of the state. Systemic practice and action research”, Vol. 14, No. 2. Espejo, R., Schumann, W., Schwaninger, M. and Billelo, U. (1996), Organizational transformation and learning: A cybernetic approach to management, John Wiley and Sons, Chichester, Chapters 3-10. Jackson, M.C. (1988), “An appreciation of Stafford Beer’s ‘viable systems’ viewpoint on managerial practice”, J. Mgt. Stud., Vol. 25, pp. 557-73. Jackson, M.C. (2000), Systems Approaches to Management, Kluwer/Plenum, New York, pp. 174-6. Morsley, S. et al. (1997), Estrategia Para Reducir la Pobreza, BID, Washington, DC, p. 1. SECAB (2000), Andres Bello Agreement, Ministry of Education, Bogota´, Colombia, Final Report -A. Espinosa. Ramı´rez, J.F. (2001), “Education evaluation as a learning tool: a systemic view”, Thesis Report Industrial Engineering Department, Los Andes University, Bogota´, pp. 14-22. Wolff, L. and Castro de M., C. (2000), “Secondary Education in Latin America and the Caribbean. The Challenge of Growth and Reform”, BID, Washington, DC, p. 30.
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The bridge to humanity’s future: text of a multimedia address Willard R. Fey and Ann C.W. Lam Ecocosm Dynamics, Ltd 1830 Cameo Court, Tucker, Georgia, USA Keywords Cybernetics, Environment, Economic growth Abstract Human life on Earth is threatened by the growth of world human consumption which quadruples every 35 years. Major environmental imbalances may soon severely deplete our planetary life-support system. However, the world economy is designed to create and depend on consumption growth. If this growth were to stop, major economic, social and military crises could result. We call this tragic dilemma the Ecocosm Paradox. Powerful human instincts drive the positive feedback-loop processes that generate consumption growth. This growth involves many human, technological, and natural environmental variables whose separate study has given rise to specialized intellectual disciplines. However, in order to address our current dilemma, these variables must be analyzed together as a single, complex process. A new method of analysis, synthesis, and implementation based on a new transdisciplinary field, “Ecocosm Dynamics”, is herein proposed for this analysis.
Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1336-1349. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443545
Introduction We are all involuntary passengers on a small, open spacecraft. All that stands between us and the frigid vacuum of space is a thirty-mile-thick blanket of air that we must breathe to live and a higher layer of ionized atoms that solar radiation heats to more than a thousand degrees Kelvin. All life on the craft depends on sunlight converted to nourishment by plant photosynthesis. In land plants grow in a thin layer of living soil. Plants absorb carbon dioxide and exhale oxygen, while animals do the reverse. Widespread, diverse plant and animal life forms regenerate the elements necessary for life support and provide flexibility under stressful conditions. This fragile balance of water, atmosphere, soil, and life forms necessary for human survival took more than two billion years to create. In the last five thousand years, one species alone out of millions has altered the evolution of life on Earth and compromised its life support system. Formerly, all species were created and modified by mutation or long-term natural selection to survive in local environments which created the global atmospheric, soil, and water balances necessary to support all life for eons. Now the local and global balances are being destroyed as the evolutionary process that changed species to fit their local environments is being Highly commended Paper (judged by the Kybernetes Research Award Panel).
transformed into the destruction of the global environment to realize the shortterm desires of this one species. Humanity is so ignorant of and apathetic toward the details of the automatic natural life support balances that it is threatening its own survival as it allows its acquisitive leaders to become wealthy.
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The ecocosm paradox The Ecocosm is the whole Earth system including the planet, the natural nonhuman living systems, and the human presence, all constantly interacting. The Ecocosm Paradox postulates that the environmental crisis arises from the growth of world human consumption, the link between the natural environment and the human presence. Human consumption draws resources from the environment and turns them into waste. When people cut the trees of a forest or pump oil from a well, they do it to provide products for humans to consume. Tragically, the world human system is so dependent on consumption growth that, if growth were to stop to alleviate the environmental crisis, major economic, financial, social, and military disasters would threaten human survival. Human warfare developed over time from local, weaponless, nonlethal, territorial combat between individual animals to global nuclear war between allied blocks of nations representing billions of people. The weapons in the early human conflicts were primitive stone spears, knives, and arrows. When horses were domesticated, they were used to pull chariots and carry riders. At sea, wooden, oar-powered galleys used catapults to hurl projectiles. As technology advanced, bronze replaced stone, then iron replaced bronze; guns and cannons replaced catapults, spears, and arrows; and armored vehicles replaced chariots. Galleys were replaced by sail-driven frigates; then by metal, steam-powered battleships, submarines, and aircraft carriers. Recently, atomic weapons delivered by aircraft and missiles brought war to everyone. Now computers, wireless communications, the Internet, and smart, miniaturized, biological, chemical, and nuclear superweapons have created the potential for a species-threatening, pervasive, global killing field with no battle lines. This escalation in the power and extent of human aggression has occurred in an evolutionary twinkling. The horrors of humanity’s military history were demonstrated in many battles that benefited from advances in weapons’ technology and changed the course of history: Gaugamela, Actium, Agincourt, Yorktown, Gettysburg, Midway, and Hiroshima. If the environmental crisis created by humanity’s growing intervention in the natural life support system cannot be effectively resolved soon; humans will use modern warfare, their ultimate conflict resolution method, to decide the issues arising from water and materials shortages, environmental catastrophes, leadership power struggles, worldwide financial collapse, and failures of the production, distribution, utility, and
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Figure 1. World human population growth
Figure 2. World per capita consumption growth
service functions. Humanity’s insensitivity to and acceptance of the massive death and destruction of modern war must end to prevent a violent resolution of the Ecocosm Paradox. UN data (Figure 1) for world human population are plotted on a logarithmic scale. The exponential shape on the log scale depicts an exponential function whose doubling time is getting shorter. We call it a “hyper-exponential.” Human population is now six billion. An additional billion people is added about every 10 years. As the annual growth rate has increased, population doubling time has fallen in the last 500 years from 650 years to its present doubling time of 34 years. The acceleration of population growth is caused by technology-driven health advances that reduce the death rate. Though births per year have fallen also, the world human birth rate is still more than twice the death rate; and major new health advances appear imminent. Strong population growth is not over. UN data (Figure 2) shows the growth of the world per capita GDP index. This linear time history on the log scale from 1950 to 1980 indicates exponential per capita consumption. World consumption is the algebraic
product of average annual per capita consumption and human population. In this graph, per capita consumption doubles in about 30 years. With population doubling every 35 years, their product, world consumption, quadruples in 30 to 35 years. Stopping population growth will not stop consumption growth. If current population growth and per capita consumption growth continue, by the end of the 21st century world human consumption will be 50 times as large as it is today. Since even today’s consumption clearly is unsustainable, such growth will devastate the environment. Both population and per capita consumption have positive feedback loops that force them to grow (Figure 3). Population growth is driven by a natural reproduction loop and a biotechnology loop that extends life expectancy (Figure 3, right). Per capita consumption growth is caused by technology loops reinforced by world economics and government action loops (Figure 3, left). Environmental collapse, resource exhaustion, and toxic pollution constraints may create negative loops that will finally stop the growth. The causal-loop diagram for human population (Figure 4) shows one positive and five negative loops. Today, human fertility produces new humans faster than deaths and shifts to the non-reproductive state can remove people from the childbearing population that energizes the positive loop. This is the first positive loop that forces consumption growth. In most nations, both birth and death rates are falling. Death rates are falling as public health measures and medical technology extend human lifespan. Funds and benefits from medical consumption motivate biotechnologists to increase research to find more medical products that lower death probabilities even further.
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Figure 3. The ecocosm paradox diagram
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Figure 4. Population causal loop diagram
This biotechnology loop is the second positive population loop. It makes population’s exponential growth hyper. Technology (Figure 5) conceives and produces virtually all the products humans consume. Most technological advances result from organized research by highly-trained people working for governments or private organizations. In the upper part of the technology causal-loop diagram, research and design effort leads to new knowledge and products. These motivate higher per capita consumption that increases consumption. Increased consumption of technological products provides many benefits and disbenefits. Both motivate more research. Technology is a positive feedback process in which theories and products developed by scientific research produce results that lead to more research and more trained people to do more research.
Figure 5. Technology causal loop diagram
The interaction of human instincts and technology that drives per capita consumption growth is reinforced by economics and governments. Consumption is the closure point for all major economic loops (Figure 6). It connects the producer and consumer roles of each person and focuses the attitudes and actions of producers and consumers to reinforce consumption. Consumption also relates the financial aspects to the physical aspects of the economy. To increase consumption producers design and produce technological products, market them, advertise them, invest in production capacity, hire workers, and provide credit to customers (Figure 7). To increase their ability to consume, consumers work and invest to obtain income. They borrow, perceive advertising that makes them desire more, and use and then discard their purchases when they are used up or better new products appear. Positive feedback loops reinforce all of these actions and, thereby, reinforce consumption. Speculative operations in securities markets are driven by positive investment loops (Figure 8). Consumption growth stimulates price increases for securities that attract speculative funds to finance producer operations that reinforce consumption. If consumption growth were to stop and speculators believed that it would not restart, securities prices would collapse. Most government revenues come from taxes on income, sales, capital gains, and value added (Figure 9); so, governments encourage consumption growth through their own consumption, the creation of money and credit, depletion allowances and monetary policy. To encourage consumption growth, commercial banks also create money through credit expansion. The operation of positive technology loops reinforced by positive economic, financial and government loops drives the exponential growth of per capita consumption.
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Figure 6. Production/Consumption causal loop diagram
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Figure 7. Marketing causal loop diagram
The Ecocosm Paradox hypothesizes that the growth of world human consumption, which quadruples consumption every 35 years, must stop to avoid an environmental catastrophe. A seemingly small 4 per cent per year increase in consumption produces this rapid expansion. Human instincts to reproduce and to consume are enormously amplified by technology, economics, and politics to cause devastating growth. The natural planetary life support system cannot absorb this accelerating destruction and continue to function effectively. The activities of almost all persons, businesses, and governments depend on, create, and demand consumption growth; so it is unlikely that growth can be stopped. But, if, somehow, growth could be stopped to save the environment; societies would become unstable, the world economy and securities markets would collapse, and wars would follow. Thus, humanity’s
Figure 8. Investment causal loop diagram
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Figure 9. Government causal loop diagram
destiny seems to be continued explosive growth until some kind of catastrophe devastatingly ends the growth; and, perhaps, humanity itself. No currently proposed solution to the environmental crisis faces the reality that the Earth is finite and human consumption growth must not only stop, but it must be reduced to a long-term sustainable annual amount. This can only be done by changing human attitudes and restructuring the socio-economic system, so it is not dependent on expansion and does not create it. The current piecemeal attempts to improve efficiencies, and to encourage conservation and recycling may postpone the environmental collapse; but they will not stop growth nor produce a sustainable Ecocosm.
A method to find a solution A method of analysis, synthesis, and implementation is needed to discover and institute a realizable higher-level human consciousness to support a new, sustainable human socio-economic system structure in interaction with a modified natural life support system. This must achieve a long-term, stable, balanced Ecocosm. It must be in harmony with human instincts, desires, and capabilities; with plant and animal community functions; and with planetary dimensions and resources. It must automatically and quickly limit human consumption, without unacceptable laws or force, to the gradually changing planetary carrying capacity as technology progresses and as resources are exhausted. The new system must be achievable with “tolerable” damage to human life, freedom, and property. A “painless” solution is impossible. Even today, people are starving and dying in wars. Living systems are extremely complex,
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internally self-organizing, and respond to depravation and conflict with violence. Humans are not passive and precisely responsive to forces as masses and electrons are. Thus, the success of science in manipulating the physical world is not easily duplicated in the living world, and there is no known algorithm to synthesize a sustainable world human system. Therefore, the solution method proposed here is a science-aided, creative art; not a mathematically derivable, experimentally reproducible science that most scientists would desire. Designing the adaptive-sustainable Ecocosm and the implementation process necessary to bring it into reality is the most important and the most difficult task ever undertaken in the history of humanity. The method must perform an incredibly difficult analysis to produce a new Ecocosm system paradigm of unprecedented creativity. It can only begin to implement its changes with the cooperation of a substantial fraction of influential human leaders and groups who, in the past have rarely agreed, even on trivial issues. If any of the recommendations are wrong, a catastrophe rather than an improvement may occur. There may be no second chance because changes will have been made that cannot be reversed. Science has produced such toxic materials, powerful forces, and destructive weapons that immense planetary damage can arise from small errors in the planned interventions or from aggression by terrorists, criminals, or warlords. Thus, the method’s task is extremely difficult; the time available to do it is unknown, but short; the margin for error is tiny; and the likelihood of a second chance is small. This is not a task that anyone would want to perform unless humanity’s survival depends on it. We believe that it does. The method involves assembling a multifaceted group of people that will create an essential new intellectual discipline as it designs the adaptivesustainable Ecocosm and then implements the changes in human consciousness and system structure that the design requires. In order to understand and modify the Ecocosm, the designers must be able to conceptualize and analyze the Ecocosm as a whole, living, noisy, feedback control system. While human decisions control the major forces, a diverse nonhuman living community must flourish to provide human life support. The conceptualization and analysis must include critical aspects of human and living nonhuman behaviors as they interact on local and global levels to preserve the life support system and the living participants. Knowledge from the sciences and other disciplines such as biology, ecology, psychology, theology, economics, sociology, political science, geology, and meteorology will be needed. None of these disciplines was created to study the whole earth system with all its forms of interaction, especially not in the pathological state of the current environmental and social crisis. Each focuses on a specific, manageable, clearly related set of variables whose properties are isolated from the complexity and incommensurate units of the others. Each is sufficiently
complex by itself that it takes years of study for a person to learn the field’s principles in depth. Understanding the Ecocosm will require knowledge from all of these disciplines and others, but seldom in a form the field provides. A new, holistic, statistical-feedback-control discipline is required to combine the essential knowledge of all relevant fields with new knowledge discovered by the group, so the contents of and the relationships between the fields can be applied to the study of the whole Ecocosm as it was, as it is now, and as it will become in the future. The creators of the new field will have to bring available and new information together in one place or reference where it can be obtained from media centers and the Internet. We suggest the field to be called as Ecocosm Dynamics. Ecocosm is taken from the Greek words “oikos”, a house or environment, and “kosmos”, a complex, orderly, self-inclusive universe. Ecocosm is the whole, orderly, home planetary system of humanity. Dynamics is the analysis and control of patterns of change through time of critical variables. A group of people is needed to create the Ecocosm Dynamics discipline and to design the adaptive-sustainable Ecocosm. All members will contribute to discipline development and system design. Most will produce their own models and design recommendations. The group will evaluate and consolidate the recommendations and present the best to the world community. In order to accomplish this task, the members must be willing and able to learn about the whole Ecocosm, learn about each others disciplines, share their insights and analysis with the others, and keep open, honest minds. The team must be totally committed to solving the Paradox properly, not to becoming wealthy, powerful, or famous, or to winning prestigious prizes. It is likely that doing this analysis correctly and honestly will attract animosity from many. The team will be trying to discover a planetary system that will stop consumption growth. Almost everyone is committed to growth and hopes to become rich from it, so no one wants to hear about reducing it. If the team overcomes these obstacles and produces a promising system design, world leaders may not accept it nor allow implementation because the recommendations may seem counter-intuitive to people unfamiliar with the nature of complex, human, feedback control processes. Also, detrimental effects will be expected during the implementation period that few will be willing to accept. If the team’s recommendations are approved, any adversity during implementation will appear intolerable to many; and the team will be blamed for it. Once the research work begins, it will soon become clear to the team just how difficult its assignments really are to do properly with reasonable assurance of success in the short time available. Finding financial support for the group and its tasks will be extraordinarily difficult for similar reasons. Since there is so much at stake for so many growth-dependent people and organizations, both during the final stages of
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Figure 10. The bridge to humanity’s future
the expansion and in the trade-offs and losses arising from the adversities of the transition period; there will be great pressure on any research group that seeks to influence these outcomes. Those who hold power will not give it up for the good of posterity or for the good of other, less influential, people or life forms. Even if the Ecocosm design is successful, it will only succeed long after the group members are dead. To create the new discipline, to do the Ecocosm analysis, to modify the existing planetary system, and to wait for the transition time pattern to lead to the eventual stable pattern will take at least one hundred years. Only very unusual people will be willing to undertake such a difficult task knowing that their only reward will be antagonism and that they will never know whether they were successful. As consumption grows faster and faster beyond its sustainable annual amount, humanity will move higher and higher on the precipice above many possible future valleys of disintegration, two of which are shown in the graph of future consumption with and without an implemented solution to the Paradox (Figure 10). The successful development and application of the method; with its research group, new discipline, and design of the sustainable Ecocosm; is symbolized by a bridge over this valley from the unsustainable peak of consumption to a lower sustainable consumption plateau. If an effective design is implemented properly and in time, the Ecocosm will avoid the environmental and social catastrophes that quickly would force the critical variables into the depths of the valley. The design’s consumption transition time patterns will also decline; but not as far, nor as fast, with less destruction, and with faster recovery. Therefore, a well-constructed bridge, the method that provides the successful design and implementation, will save many lives and prevent much devastation.
We call the effort to design an adaptive-sustainable Ecocosm: Operation Rainbow Bridge. The rainbow, in the traditions of many cultures, symbolizes hope for future well-being after adversity and/or cooperative diversity. It suggests that dishonest and destructive forms of competition will be eliminated; that all of Earth’s diverse people will equitably share information, resources and influence; that the adversity of the implementation will be tolerable; that a sustainable Ecocosm will be achieved; and that the result of the reformation process will be to unify all people in their resolve to maintain their stable Ecocosm. Perhaps the most difficult aspect of the Ecocosm Paradox solution will be the planning and implementation of the transition to the sustainable Ecocosm. In order to stop consumption growth and to obtain long-term stable consumption, certain changes must occur in humanity’s consciousness and in the Ecocosm’s feedback structure. The design effort must identify these changes. In order to obtain improved performance in the real Ecocosm, these changes must actually be realized in the operating structure. The Ecocosm’s operating feedback structure is created and maintained by the thoughts and actions of humans. Therefore, changes in collective human higher-consciousness must be substantially established before any new loop structure will function properly. The elements of the new higher-consciousness are not all clear; but, at least, humans must overcome their selfishness, vengefulness, and aggression. We must be able instinctively to forgive, to share, and to treat others with honesty, consideration and respect. In a closely interdependent, crowded Ecocosm, trust is the fundamental interpersonal attitude necessary for long-term social survival. Trust cannot persist between people and groups, and the violent resolution of conflicts will not end, unless humanity develops these higher instincts. When efforts to change consciousness and loop structure begin, transient patterns will arise. These time patterns will be different from old system patterns and different from eventual improved system patterns. Transients will dominate during the transition time period, which begins when structure changes are initiated and ends with the clear beginning of improved patterns as the transients disappear. Changes that are actually implemented are seldom exactly the same as the proposed changes. Unplanned structure changes may be made by system participants who are coping with the system’s crises or by those who are trying to evade, circumvent or take advantage of the proposed system changes. Such incorrect, unconscious, and unplanned structure changes may cause serious implementation problems. The result may be chaotic, violent, conflicting, unpredictable, counter-intuitive, and/or uncontrollable time patterns that complicate and lengthen the transition period. At worst, sustainable time patterns may never be achieved. On January 16th, 1920 the 18th Amendment to the United States Constitution banned the manufacture, sale, and transportation of intoxicating
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liquors. American reformers wanted to improve people’s physical health, family happiness, and social well-being. Instead, consumption of alcohol greatly increased and social stability was upset by the growth of organized crime fueled by bootlegging profits. Thousands died nationwide in the resulting gangland wars and enforcement operations. On December 5th, 1933, the 21st Amendment repealed Prohibition, but the power of organized crime still remains. Counter-intuitive disasters often result from well-meaning reforms. Conclusion Massive human intervention in the natural environment has created Earth’s environmental crisis with its Ecocosm Paradox. The intractability of the Paradox and the speed of the environmental disintegration present humanity with a supreme and unprecedented challenge. To create a realizable, collective higher-consciousness that will support a sustainable Ecocosm system structure that will stabilize human consumption, and maintain an adaptable life support system for present living beings and their progeny indefinitely; and to do it before the environment or the socio-economic system collapses. We cannot offer a solution at this time. An effective solution, if one can be found, will be counter-intuitive, even to experienced systems analysts. It is not wise to guess in the face of great complexity with such enormous consequences for humanity at stake. Others who do make recommendations sometimes have little concept of the true nature and severity of the problems, and little idea of what will be required to solve the problems in the real world. The virtual worlds of television, computers, mathematical abstractions, positive thinking, managed news, psychological advertising, and unprecedented economic prosperity in the midst of escalating environmental destruction have decoupled science and humanity from reality that the real nature of life on our small planet is almost totally obscured. As Walter Truett Anderson warned in To Govern Evolution, “The central political problem of our time is not that people in power do the wrong things, or that some people have more power than others, or that there is a lack of clarity and honesty in political dialogue; all of these are real and serious, but they are only dim reflections of a larger problem, which is that we literally do not know what we are doing.” We have presented here the nature of the Ecocosm, its problems, and the Paradox; with recommendations for finding a solution and implementing it. These are offered as our understanding of the only reasonable chance humanity has to save itself from itself. Virtually all of the prophetic traditions of religions and cultures worldwide, ancient and modern, forecast a catastrophic “end time”. Now, a crisis that could threaten humanity’s survival is upon us in the form of the intractable dilemma of the Ecocosm Paradox. How will we respond? How will you respond?
References Anderson, W.T. (1987), To Govern Evolution: Further Adventures of the Political Animal, Harcourt Brace Jovanovich, Boston, MA. Andrey, R. (1966), The Territorial Imperative, Atheneum, New York, NY. Brundtland, G.H. and Chair (1987), Our Common Future, Oxford University Press, New York, NY. Fey, W.R. (2002), “Intellectual roots and philosophy of system dynamics”, Encyclopedia of Life Support Systems, Internet, United Nations. Fey, W.R. and Lam, A.C.W. (2000), “The bridge to humanity’s future”, Proceedings of the World Congress of the Systems Sciences and ISSS 2000, (full paper). Fey, W.R. and Lam, A.C.W. (2001), “The bridge to humanity’s future”, Understanding Complexity, (plenary address) Kluwer/Plenum, London, England. Gutierrez, L.T. and Fey, W.R. (1980), Ecosystem Succession, MIT Press, Cambridge, MA. Meadows, D.H. et al. (1972), The Limits to Growth, Universe, New York, NY. Parent, J. (1984), A Survey of United States and Total World Production, Proved Resources, and Remaining Recoverable Resources of Fossil Fuels and Uranium, Institute of Gas Technology, Chicago, IL. Tutu, D. (1994), The Rainbow People of God, Doubleday, New York, NY. Tutu, D. (1999), No Future Without Forgiveness, Doubleday, New York, NY.
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What is “engineering systems thinking”? Moti Frank Technion – Israel Institute of Technology, Haifa, Israel Keywords Cybernetics, Systems design Abstract As technological systems grow larger, more complex, and interdisciplinary, electronics and hi-tech industries face a growing demand for engineers with a capacity for “engineering systems thinking”. This paper presents a multifunctional definition and 30 laws of “engineering systems thinking”. The definition and the laws are based on a study that its purpose was to identify the characteristics of engineers who are able to think in the manner called “engineering systems thinking”. A thorough understanding of “engineering systems thinking” on both the theoretical and operational levels will prove useful in the design of curricula to improve and develop thinking of this sort.
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Introduction As technological systems grow larger, more complex, and interdisciplinary, electronics and hi-tech industries face a growing demand for engineers with a capacity for “engineering systems thinking”. But, what is engineering systems thinking? Acknowledging the widespread use of the term “engineering systems thinking” in the engineering community, it was decided to examine the subject in the context of a study (Frank, 1999). Based on this study, a multifunctional definition (Frank and Waks, 2001) and 30 laws (Frank, 2000) of “engineering systems thinking” were extracted. “Systems thinking”, according to Senge (1990), “is a discipline for seeing wholes”. It is a framework for seeing interrelationships rather than things, for seeing patterns of change rather than static “snapshots”. Systems thinking offers us a flexible language that might expand, change, and shape our ordinary way of thinking in regard to complex issues. The systems thinking literature deals mainly with living, economic, management and social systems, as well as with the analysis of complex organizations (Ackoff, 1981; Bertalanffy, 1968; Checkland, 1981, 1989; Chen and Stroup, 1993; Cleland and King, 1972; Hoefler and Mar, 1992; Graczyk, 1993; Katz and Kahn, 1978; Kim, 1995; Klir, 1985; O’Connor and McDermont, 1997; Richmond, 2000; Senge, 1990; Senge et al., 1994 and Waring, 1996). This paper, however, deals with something slightly different – “engineering systems thinking”. A thorough understanding of engineering systems thinking on both the theoretical and operational levels will prove useful in the design of curricula intended to improve and develop thinking of this sort. The main purpose of the study (Frank, 1999) was to identify the characteristics of engineers with a capacity for engineering systems thinking.
The research was carried out in three stages. The qualitative-naturalistic Engineering inquiry paradigm, in which data collection is principally based on interviews systems thinking and observations, was found to be suitable for the first and second stages (Guba and Lincoln, 1985). The third stage of the research consisted of a survey based on a pilot questionnaire ðN ¼ 31Þ and a final questionnaire ðN ¼ 276Þ: The great amount of “raw data” collected in the study have been sorted to 83 1351 categories: ten categories referred to the definition of engineering systems thinking; four categories dealt with various types of systems thinking; 15 categories related to the knowledge demanded of system engineers; 31 categories referred to the skills demanded of system engineers; 15 categories dealt with the behavioral competencies demanded of system engineers; eight categories referred to the processes by which systems thinking capability is acquired. Based on the research findings and a literature review, a multifunctional definition (Frank and Waks, 2001) and 30 laws (Frank, 2000) of “engineering systems thinking” were proposed. First, I will present the definition of “engineering systems thinking” based on the first ten categories. A multifunctional definition of engineering systems thinking A multifunctional definition is a collection of facets combined through informal connectives. It is a framework that is constructed from detailed sub-definitions, each specifying uniquely the entity under consideration in a certain set of relevant aspects (Waks, 1995). Each aspect is represented by a facet, which in turn involves the labeling of conceptual categories that define the relevant universe of contents. Figure 1 shows the proposal for the multifunctional definition of engineering systems thinking (Frank and Waks, 2001). In this case we have seven facets A-G, each of which has its own labeling unique elements. Let me now discuss the main categories of the multifunctional definition (Figure 1): Understanding the whole system Most of the subjects defined engineering systems thinking as the ability to understand the whole system or the ability to perceive how the component or the card functions as part of a system. According to Kim (1995), Senge (1994) and Waring (1996), a problem may not be solved by breaking it down into elements and finding a separate solution for each of those elements. One must be able to see the whole picture. Some problems stem from the structure of the system itself. All system components (persons, parts) share responsibility for system problems. Thus, an engineer with a capacity for systems thinking understands how sub-systems integrate into a whole single system and understands the whole – the entire system and the whole picture beyond its single components.
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Figure 1. A multifunctional definition of engineering systems thinking (Frank and Waks, 2001)
Understanding the synergy of the system Engineering Many subjects were of the opinion that the systems engineer required to systems thinking understand the synergy of a given system. According to many authors (Graczyk, 1993; Kahn and Katz, 1966; Waring, 1996), a system is more than just a collection of parts. “The whole is more than the sum of its parts”. This synergistic effect is one of the central and most important attributes of a 1353 system, but it is, at times, hard to identify. The general systems theory holds that all systems are similar in certain ways. According to this view, if the synergy attribute exists in all systems, then it certainly exists in man-made technological systems. The systems engineer must, therefore, be capable of deriving the synergy of a system from the very integration of the sub-systems under his responsibility. Understanding the system from multiple perspectives In the opinion of many interviewees, an engineer with engineering systems thinking capability must understand and be able to describe a system from all relevant perspectives beyond the level of engineering (i.e. technological, economical, managerial, social, electrical, mechanical, and operational perspectives). A successful systems engineer would avoid adopting a one-dimensional view and would examine a specific subject or problem from different angles and points of view. Understanding the implications of modification to the system It turns out that modifications are central to the work of the systems engineer. The systems engineer must understand the system as a whole and be capable of anticipating and detailing all implications (including side effects) of changes in the system – engineering and non-engineering alike – both those initiated by the contractor and those required by the end user after freezing the design. In many cases, the systems engineer must be able to take care of every stage of the change starting from the conception of the idea and proceeding through the paper work (forms and approvals) and on to the execution and documentation of the introduced modification. Understanding a new system immediately upon presentation An engineer with a good grasp of the system understands and is able to describe the operation, purposes, applications, advantages, and limitations of an unknown system immediately after receiving an initial explanation. System complexity level According to O’Connor and McDermott (1997) and Senge (1990) systems showing complexity of detail may be treated by categorization, classification,
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ordering, and a systemic-algorithmic approach. A system has dynamic complexity, however, when its parts have multiple modes of operation and each part may be connected, according to need, to a different part. Dynamic complexity exists when a certain operation results in a certain series of consequences in one part of the system and a totally different series of consequences in other parts of the system. Dynamic complexity also exists when regular intervention produces results that are irregular. Regular methods of design and analysis are not structured to cope with dynamic complexity. In real life, most situations deal with dynamic complexity and not complexity of detail. Simulations with thousands of variables and complex alignments of components are likely to divert our attention from seeing the main patterns and interactions. Thus, a system becomes more complex with the growing number of subsystems within it, causing an increase in the number of interconnections between its components. A successful systems engineer will be better equipped to describe the functionality of complex systems. Interconnections The issue of interconnections between system parts is common to all definitions of the concept “system” (Cleland and King, 1972; Graczyk, 1993; O’Connor and McDermott, 1997; Whitner, 1985). In the opinion of many subjects, engineering systems thinking involves an understanding of the interconnections between system components. A successful systems engineer must understand and be able to describe the interconnections (even when some of them are hidden) and the mutual influences between sub-systems (and neighboring systems). Remedies for failures and system problems Systems engineers are sometimes required to remedy/solve/analyze system failures or system problems. Engineering systems thinking a priori could, perhaps, prevent the appearance of a system failure or a system problem. Therefore the treatment of system failures/problems is a significant component of engineering systems thinking. Analysis and synthesis System analysis is the disassembly of the system to its components with the purpose of analyzing its operation. Synthesis is the connection of components or sub-systems into a whole system. An engineer with a capacity for engineering systems thinking must be able to move from the whole to its parts, and analyze the system by breaking it down to its components. He or she must be able to track signals from the input
through every sub-system, and interface to the output. In addition to this, Engineering however, the systems engineer must be able to synthesize. He or she must be systems thinking able to assemble or connect sub-systems into a complete system and provide end-to-end solutions. Don’t get stuck on details There are engineers who have to thoroughly understand all the details involved in a given problem in order to be able to form a decision and come up with a solution. Engineers of this sort usually find it difficult to develop engineering systems thinking. A successful systems engineer must be able to see the whole picture and not get stuck on details. He or she should be able to act without understanding fully all of the system’s details. Such engineers usually feel comfortable working in unclear conditions and in an uncertain environment. Multidisciplinary and interdisciplinary knowledge The single most prominent characteristic of an engineer with a capacity for engineering systems thinking is multidisciplinary knowledge, as well as interdisciplinary knowledge. Knowledge of this sort makes one comfortable with multi-tasking activities. By “multidisciplinary knowledge”, however, I do not mean that one knows “a little of everything”. The systems engineer must acquire specialization in at least one main area (an “anchor”); in addition, he or she must be knowledgeable in all other relevant areas. The engineer’s knowledge in those other areas need not be equal to that of a specialist. In the additional content areas, the systems engineer must possess general knowledge and understanding on the overall level. He or she must be familiar with the jargon of the other disciplines (relevant to his occupation and tasks), and be able to communicate with people from different areas. Wide knowledge is required for the systems engineer also in order to be able to understand and derive significance from the answers and reports of others, i.e. “specialists” from outside his own main area of expertise. Such wide knowledge may also enable the systems engineer to cope with new disciplines. The 30 laws Let me now present 30 engineering systems thinking laws (Frank, 2000), based on the research findings, a literature review and Senge’s (1990) laws for systems thinking: (1) In all the project’s phases/stages and along the system’s life, the systems engineer has to take into account the customer organization vision, goals and tasks, the customer requirements and preferences, and the problems to be solved by the system and the customer needs.
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(2) The whole has to be seen as well as the interaction between the system’s elements. For this purpose a circular thinking has to be developed, to replace the traditional linear thinking. A problem should not be solved by just dismantling it to parts but all its implications have to be taken into account. Each activity in a system’s certain element affects the other elements and the whole. (3) Consider that every action could have implications also in another place or at another time. (4) One should always look for the synergy and the relative advantages stemming from the integration of sub-systems. (5) The solution is not always only engineering one. The systems engineer has also to take into account cost, re-use, organizational, managerial, and personal considerations. (6) The system’s engineer should take as many different perspectives as possible, of every subject or problem, and other aspects have to be reviewed from all points of view. (7) Always take into account electrical considerations, mechanical considerations, environmental conditions constraints, quality assurance considerations, and benefit indices, such as reliability, availability, maintainability, testability and productibility. (8) In all development phases the future logistic requirements have to be taken into account (spare parts, maintenance infrastructures, support, service, maintenance levels, worksheets, technical documentation and various manuals). (9) When a need arises to carry out a modification in the system, take into account: the engineering and non-engineering implications in any place and at any time; the effects on the Form, Fit and Function; the delays and the time durations of the modification incorporation; the system’s response time to the changes; the needs, difficulties and attitudes of those supposed live with the modification; that the change could bring short-term benefit but long-term damage. (10) Each problem may have more than one possible working solution. All possible alternatives should be examined and compared to each other by quantitative and qualitative measurements. The optimal alternative should be chosen. (11) Engineering design is not necessarily maximal. One should not always aspire to achieve maximum performances. At every stage engineering trade-offs and cost-effectiveness considerations should be considered. One could always improve more. One has to know when to “cut” and freeze a configuration for production. Excessive pressure in a certain
point could cause a collapse at another point. Over stressing one part in Engineering the system could weaken another part and thus the entire system. systems thinking Maximum performance design is expensive and not always results in maximizing entire system performance. (12) In case of system’s malfunction, problem or failure, repeated structures and patterns should be looked for and analyzed, and lessons drawn accordingly (repeated failure is a failure that keeps returning, after the repairs, until the true malfunction is found and repaired. A repeated-nonverified failure is a failure that the user complained about, the technician inspected and could not verify and the failure reappeared again in the next operation). (13) Look always for the leverage point – changes that might introduce significant improvements by minimum effort. (14) Pay attention to and take into account slow or gradual processes. (15) Avoid adapting a known solution for the current problem – it might not be suitable. (16) Take into account development risks. In each project uncertainty prevails on the level of scheduling, cost, resources, scope, environmental conditions and technology. Therefore, the strategy of eliminating uncertainties has to be taken – e.g. experiments, tests, verifications, analyses, comparisons, simulations, awareness of possible risks, planning ways of retreat and risk deployment among the partners. (17) It is impossible to run a project without control, configuration management, milestones and management and scheduling methods. Possible bottlenecks and potential critical paths have to be examined constantly. (18) The operator/user person must be considered as major part of the system. Hence at each stage, the human element has to be considered. The engineering design should include MMI (Man-Machine-Interface) considerations. (19) The engineering design is a top-down design (excluding certain “open systems”, for which the bottom-up approach is preferable). The integration and tests are bottom-up. (20) At every stage, systemic design considerations should be used (such as decentralized or centralized design, minimum dependency between subsystems, etc.). The systems engineer should be familiar with system malfunction analysis methods and tools. (21) Engineering systems thinking requires the use of simulations. The simulation limitations should be taken into account.
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(22) Engineering systems thinking requires the integration of expertise from different disciplines. As the systems become more complex and dynamic, one person, as competent as he may be, is inadequate to understand and see it all. Systems thinking, by its nature requires the examination of different perspectives, calling for teamwork to cover the various perspectives. When setting up the team proper representation has to be given to all the system’s functions. Control and status discussions and meetings as well as “brain storming” may have to be more frequent. (23) Try to anticipate the future at every stage. Take into account anticipated technological developments, future market needs, difficulties, problems and expected changes in the project. (24) Selecting partners and sub-contractors could be critical. Before signing agreements refer to considerations such as the “engineering/economic history” of the potential partner, manpower (quality, stability, human capital) that he is capable of investing at the project’s disposal, division of work and responsibility and proper arrangements for status meetings, integration tests and experiments of all kind. (25) When selecting the software language or software development tools and platforms, make sure that they are usable and supportable, or changeable, throughout the system’s life. (26) When selecting components for production, take into account their shelf life. Select components whose supply is guaranteed throughout all the system’s life. In case of likely obsolescence of component, make sure of having sufficient stock. (27) In order to win a tender, many companies reduce the development price in their offer, assuming that they will be compensated by the serial production and by the cost of modifications (if required). Therefore, in engineering systems thinking, it is recommended not to start development at all, if the serial production budgets are not guaranteed in advance. (28) Always examine the external threats against the system (for example, electro-magnetic-interference, environment conditions, etc.). (29) Engineering systems thinking resorts probability and statistical terms, both when defining the system specifications and when determining the project targets (costs, performance, time and scope). (30) In engineering systems thinking it is advisable to limit the responsibility assigned to an external factor (such as external counselor), since this increases the dependency on it.
Conclusion Engineering In this paper, I presented a multifunctional definition and 30 laws of a concept I systems thinking call “Engineering Systems Thinking”. The concept emerges from research that was carried out in the field. I claim that a successful systems engineer must possess a developed capacity for engineering systems thinking, a type of thinking that has many of the classic characteristics of systems thinking, but 1359 which also has unique characteristics that distinguish it from the term that is currently used in the field (systems thinking). The proposed definition and laws are important on the theoretical and practical level alike. On the theoretical level they may contribute to the theoretical body of knowledge of the General Systems Theory. On the practical level the definition may constitute a basis for further research, to develop a curriculum for engineering systems thinking. References Ackoff, R.L. (1981), Creating the Corporate Future, Wiley, New York. Bertalanffy, L.V. (1968), General System Theory: Foundations, Development, Applications, George Braziller, New York. Checkland, P. (1981), Systems Thinking, Systems Practice, Wiley, Chichester. Checkland, P. (1989), “Soft systems methodology”, in Rosenhead, J. (Ed.), Rational Analysis for a Problematic World, Wiley, Chichester, pp. 71-100. Chen, D. and Stroup, W. (1993), “General system theory: toward a conceptual framework for science and technology education for all”, Journal of Science Education and Technology, Vol. 2, pp. 447-59. Cleland, D. and King, W. (1972), Management: A System Approach, McGraw-Hill, New York. Denzin, N.K. and Lincoln, Y.S. (1994), Handbook of Qualitative Research, Sage, London. Frank, M. (1996), Evaluating Outcomes of an Engineering Curriculum, unpublished MSc thesis, Department of Education in Technology and Science, Technion – Israel Institute of Technology, Haifa, Israel (In Hebrew, abstract in English). Frank, M. (1999), Engineering Systems Thinking – Characteristics and Learning Processes, unpublished PhD thesis, Department of Education in Technology and Science, Technion – Israel Institute of Technology, Haifa, Israel (In Hebrew, abstract in English). Frank, M. (2000), “Engineering systems thinking and systems thinking”, Systems Engineering, Vol. 3 No. 3, pp. 163-8. Frank, M. and Waks, S. (2001), “Engineering systems thinking: a multifunctional definition”, Systemic Practice and Action Research, Vol. 14, pp. 361-9. Graczyk, S.L. (1993), “Get with the system: general systems theory for business officials”, School Business Affairs, Vol. 59, pp. 16-20. Guba, E.G. and Lincoln, Y.S. (1985), Naturalistic Inquiry, Sage, Beverly Hills. Hoefler, B.G. and Mar, B.W. (1992), “Systems engineering methodology for engineering planning applications”, The Journal of Professional Issues in Engineering Education and Practice, Vol. 118, pp. 113-28. Katz, D. and Kahn, R.L. (1978), The Social Psychology of Organizations, Wiley, New York. Kim, D.H. (1995), Systems Thinking Tools, Pegasus Communications, Cambridge.
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Klir, G.J. (1985), Architecture of Systems Problem Solving, Plenum, New York. Morse, J.M. (1994), “Designing funded qualitative research”, in Denzin, N.K. and Lincoln, Y.S. (Eds), Handbook of Qualitative Research, Sage, Thousand Oaks. O’Connor, J. and McDermott, I. (1997), The Art of Systems Thinking, Thorsons, San Francisco. Richmond, B. (2000), The Thinking in Systems Thinking: Seven Essential Skills, Pegasus, Waltham. Senge, P.M. (1994), The Fifth Discipline: The Art and Practice of the Learning Organization, Doubleday, New York. Senge, P. et al. (1994), The Fifth Discipline Fieldbook, Doubleday, New York. Waks, S. (1995), Curriculum Design – From an Art Towards a Science, Tempus Publications, Hamburg. Waring, A. (1996), Practical Systems Thinking, Thomson Business Press, Boston. Whitner, P.A. (1985), Gestalt Therapy and General System Theory, The University of Toledo, Ohio.
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The “Roundtable” for school learning and planning groups: planting a seed for systemic renewal
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Susan Farr Gabriele GEMS: Gabriele Educational Materials and Systems, Stevenson Ranch, California, USA Keywords Cybernetics, Education, Organizational change Abstract Current public education, overwhelmed by piece-meal reform efforts, is in need of systemic renewal. An investigation of key literature – systems methods, instructional design, and group process models – yields the conditions necessary for systemic change and a suitable base model. Namely, a successful systemic educational change effort is ideal-based, holistic, continuing, participatory, user-friendly, easy to adjust/improve, and emancipatory. A suitable base model is discovered in the learning systems of Alcoholics Anonymous and then built on for a new model: the Roundtable (RT) for secular learning. Briefly, the RT session is designed so that leadership and learning opportunities are distributed among all participants, who have equal time to present their ideas. Pilot studies in professional scientific organizations allowed refinement of the model. This study investigated sought the seven conditions in four RT applications in 4th-grade classrooms in California. Participants at each site were the teacher and their 30 ^ 1 students. Each teacher held ten RT sessions, with students leading two to three of the last four sessions. Evidence was sought in the RT texts, session recordings, and users’ views. The criteria were met in the following ways. The RT applications were: ideal-based in the RT texts; user-friendly as they were user-ready and engaging; easy to adjust/improve in the simple revision session tasks, and emancipatory as users learned in important, positive and unanticipated ways. The RT applications were holistic: found suitable for all classroom levels at both schools, and for all school groups at one school. They were continuing after the study in 2 or 3 of the four classrooms. They were very participatory in the roles of listener, reader, and speaker; somewhat participatory in the leader and co-planner roles. Contributions to organizational /educational change theory and future projects are promising.
Introduction This paper reports on a formal study of the “Roundtable” (RT) model in four 4th grade public school classrooms in Los Angeles County. The RT is an activity for classrooms of all ages and also for professional and community meetings. Briefly, the activity is named the RT to contrast it with the well known “lecture” model in two ways. First, the RT is “co-operated” because of its shift from leader-operation to co-operation (shared operation). In the RT session, leadership is distributed and rotating among all participants. Second, during a RT session all participants have equal time to present and develop their ideas.
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My interest in this model was first motivated by my teaching career experience in urban schools where I found current educational systems to be overwhelmed and overworked, in a state of social decline and in need of “systemic” renewal. This aggravated decline is reported in the descriptive educational literature as increasing participant isolation and disconnection (Erickson, 1989; Maeroff, 1986), urban school staff struggling for survival (Rogers, 1989); and increasing school-site violence (Walker, 1995). Taking a wider perspective, Gardner (1991) explains that the deficiencies in our schools reflect deficiencies in our wider society. Bracey (1992), too, avers that the “true crisis of education in America is that it is trying to function not only in an era of disinformation but also in a time of social decline that looks like collapse”, (p. 104). The terrorist bombings in New York and Washington D. C. on September 11, 2001, are further evidence of social decline world-wide (Thomas et al., 2001). Banathy’s comparison of systemic and traditional educational change is helpful to show the meaning and value of systemic change or “systems” thinking. SYSTEMIC CHANGE is based on a systems view of an organization, and it is guided by the principle that any change in a part of the system affects the whole system, and change in the whole affects all of its parts. Second, the system is more than the sum of its parts, more by the interaction among the parts and the emergent effects produced by the interaction. Third, change occurs by purposeful design. Fourth, a systemic change – even the smallest one – is contemplated in view of the relationship between the system and its environment. PIECEMEAL CHANGE allows tinkering with or changing parts in an effort to improve the system. Change is not “mapped” into the whole system. Changing parts happens without consideration of the effect on the relationships that operate among parts and between the system and its environment. On account of the “non-systemic” nature of piecemeal change, change is usually short-lived because it was not accomplished with the involvement of other parts and lacks their cooperation. (Banathy, 1991, p. 149). The RT interested me because it had the potential value of an emancipatory learning system and because it appeared to realize the seven necessary conditions of a successful systemic educational activity system (EAS) change model. Specifically, it appeared to be ideal-based, holistic, continuing, participatory, very user-friendly, easy to adjust and improve, and emancipatory for all EAS members. Theoretical and empirical foundation There were six steps to the construction of the knowledge base, the theoretical and empirical foundation, of the RT and this study. First, I reviewed
organizational systems methods (Jackson, 2000) and EAS and EAS systemic change research (Carr, 1998; Collinson and Cook, 2000; Fuhrman et al., 1993; Goertz et al., 1996; Grant, 1998; Jenlink, 1995; Raywid, 1993; Whitford and Jones, 2000; Seels, 1995) to find these seven conditions. Second, I enhanced and specified these conditions drawing from current group process models – the lecture model (Kemp, 1994), cooperative learning (Johnson, 1984, 1975), whole language (Cross, 1995; Goodman, 1986; Smith, 1988), advance-organizer and review methods (Banathy, 1991; Berliner, 1984; Rosenshine, 1986; Saettler, 1990), dialogue (Bohm, 1996 Freire, 1970); design conversation (Banathy, 1996), and an intriguing and surprising lay reading club model gleaned out of the meetings of Alcoholics Anonymous or AA (Daniell, 1992, 1994; Gabriele, 1996; Hough, 1992; Lave and Wenger, 1992; Makela et al., 1996; Reed-Jones, 1992). From this a new activity called the RT for emancipatory learning was drafted. Third, I conduct pilot studies of the RT which support its value in professional settings and prompt an improvement of model. The pilot studies include applications in the Asilomar Conversation Community, an affiliate of the International Systems Institute (isiconversations.org), and the International Society for the Systems Sciences (isss.org). Fourth, I prepare the RT to be embedded in formal EAS, with a view to protecting the new system from being consumed by, or threatening to, the existing EAS. Lastly, the hypothetical RT model is created and described as possessing the seven conditions in abundance. The resulting RT Model (Figure 1) is comprised of four components. First, the RT room is set up with chairs in a circle, participant guides at each seat, a resource center, and wall charts (Figure 1(a)). Second, the RT folder (Figure 1(b)) cues the session with the RT texts (the Leader’s guide, five Basic readings, a suggested topic-of-the-day). In a 60 min RT (Figure 1(c)), 10 min of the RT session are devoted to five Readings/Reviews of New Basics and/or Subject Matter Basics and the suggested topic and 50 min to No-Response Learner Reports, time divided equally among all present, and listeners are not to respond. Third, the RT sessions fit into existing school groups and meetings of
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Figure 1. The RT session: a time view (a) and space views (b, c)
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all school participants. Fourth, there is the occasional separate RT revision session where users are to modify and upgrade the Leader’s guide by consensus. By consensus it is meant that if all do not agree on a change, the RT texts remain the same for the time being. These components are proposed as the independent variable in the traditional scientific method, also the designed variable in “systems” thinking. The hypothetical RT is constructed to possess these seven conditions identified in the literature as potentially valuable for changing (accelerating learning in) individuals and the organizations in which they work. (cf. the dependent or emerging variable). Specifically, the RT is ideal-based as it focuses users on the ideal state rather than just problems; it is holistic as all EAS members can opt to use it in one of their existing groups; it is continuing, requiring only 1 h a week (a day, a month); it is participative as users have equal time and opportunity in a variety of learning roles; it is user-friendly because it is user-ready and engaging; it is easy to adjust and improve because of its very simple revision session tasks; it is emancipatory because it is based on a time-tested well-researched model (AA) where individuals, and even spinoff organizations, have demonstrated self-transformation and goal transcendence. The purpose of this study was to determine if actual RT applications in the 4th grade classrooms also possessed these seven conditions. Methods and how I carried out my study The research design The study question asked: “In what ways and to what extent is each RT application ideal-based? holistic? continuing? participative? very user-friendly? easy to adjust/improve? emancipatory?” Regarding the research design, one or two criteria were selected for each condition to count as evidence. The criteria are listed next to each condition in Figure 2 which uses the wheel as an illustrative metaphor. Evidence of the presence of the criteria was sought in the RT texts used (the Leader’s guide and five Basic readings), transcriptions of recordings of the RT sessions and revision sessions, and users’ views in interviews.
Figure 2. The seven conditions necessary in a systemic change effort is shown as a wheel
The people Four Los Angeles County 4th grade teachers with their classrooms participated in this study. Two of them were at a K-5 school in the South Bay, they had 11 and 27 years of teaching experience. Two of them were at a K-6 school in Santa Clarita. One had 4 years teaching experience, the other was a first year teacher. Two other people were involved in the study to assist in the research: an impartial non-user research assistant to help with the interviews and analyze data, and a recording technician.
The procedures Pre-Implementation focused on teacher concerns, authorization concerns, and on setting up the methods for data collection and recording. Preimplementation took very little actual time, and varied with each teacher. The pre-implementation period for Carol, two casual meetings over coffee and three visits to her school, spanned over 7 months: June 2000 to February 2001. For Linda, this period consisted of a few phone calls, two short meetings at her school and spanned over 4 months: (November 29, 2000-February, 2001). For Richard and Julie, this period was about a half hour of discussion. Implementation was focused on teacher’s concerns regarding instruction and student learning, as the data recording method had been arranged. The implementation period was 10 weeks (for a minimum of ten RT sessions) but lasted up to 15 weeks due to calendar conflicts – including Easter vacation, state testing, parent conferences, and a field trip. During implementation, we began with 5 RTs, the teacher and I taking turns leading. Then we had a revision session. We then held five more sessions, the teacher and students taking turns as leader. Post-implementation, marked by completion of the 10th RD (April 26 to May 30th) and had a double focus on data collecting and storage and developing other RTs for the users. Post-implementation questionnaire/interviews took place 2 weeks after the study for students and 2 to 5 weeks after the study for teachers.
Results Four conditions demonstrated to a significant extent The applications were found to be ideal-based, user-friendly, easy to adjust/improve, and emancipatory to a significant extent. The RT texts had many ideal-based words and phrases. Moreover, they contained no problembased words or phrases. Regarding the user-friendly condition, the RT applications were userfriendly in that they were user-ready for Phase 1 with these user-ready tools: the RT folder and student guides (both containing the Leader’s guide and
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readings), the room set up, a leader and reader checklist, and a Business Meeting Guide. The RT applications were user-friendly in that they were userready for the teachers and very engaging for the students. First, changes made in the RT texts during the study were few and they took little of the teachers’ time and energy. Second, the teachers’ views were that the RT was easy to adjust and improve during the study, and that the RT would be easy to adjust and improve for their future purposes, as their students developed throughout the year. Regarding the easy to adjust and improve condition, the RT texts that cue the RT were suitable as is. They were easy to adjust and improve when the change was simple: a change in a word in the RT texts. Teachers found them easy to adjust and improve and apply to their subject matter. They felt the RT would be easy to adjust and improve for their future lessons.
Three conditions demonstrated to some extent The applications were found to be holistic, continuing, and participatory to some extent. Regarding the holistic condition, the RT applications were holistic in that they were seen as suitable for K-12 students in many of their subject matters, especially language arts and social studies. In the South Bay, the two teachers’ involvement resulted in faculty RT demonstration. They felt strongly that the RT would be very suitable for faculty meetings, PTA and other adult and professional school groups. One teacher at the other school felt the RT would be suitable for all school groups too. But, she, along with the first year teacher felt that the RT would not be appealing to or suitable for the faculty meetings at their school. Regarding the continuing condition, the RT applications were continuing in that they were a regular part of the class and integrating well with much of the class subject matter. This was significant. However, the RT applications were continued after the study in only two or three of the four classrooms and only one teacher was certain to use it next year. Two think they will, one may use it in a modified form. Regarding the participatory condition, the RT applications were very participatory as students had equal time and opportunity as reader, speaker, and listener. They were not as participatory in the leader and co-planner roles. Only two students got to lead the RT which was disappointing to the students. However, students were pleased that they will all get to lead the RT, if it is started earlier in the year. Regarding the co-planner role, some students were very disappointed that they did not get to choose the topics and that the readings were not changed. However, in Richard’s class, a student actually initiated a change that was made which may have contributed to his students’ feelings of participation as co-planners.
In sum, the results of the study were that these hypotheses were supported adequately in this study, but more research and development is needed. Future studies proposed are: continuing RTs at these 4th grade sites, introducing new RTs at these school sites for interested educators, introducing RTs at new EAS sites; and more research on the seven conditions and their contribution to EAS change theory and practice. Other future studies and applications, are the continuing of the RTs at the yearly conferences at ISSS and ACC, and the introductions of RTs as opportunities arise. References Banathy, B.H. (1991), Systems Design of Education: A Journey to Create the Future, Educational Technology Publications, Englewood Cliffs, NJ. Banathy, B.H. (1992), A Systems View of Education: Concepts and Principles for Effective Practice, Educational Technology Publications, Englewood Cliffs, NJ. Banathy, B.H. (1996), Designing Social Systems in a Changing World: A Journey Toward a Creating Society, Plenum Press, NY. Bohm, D. (1996), On Dialogue, Routledge, NY. Bracey, G.W. (1992), “The condition of public education”, Phi Delta Kappan pp. 104-12. Carr, A. (1994), “Community participation in systemic educational change”, Educational Technology, Vol. 34 No. 1, pp. 43-50. Carr, A. (1998), “Good ideas to foment educational revolution: the role of systemic change in advancing situated learning, constructivism, and feminist pedagogy”, Educational Technology, Vol. 38 No. 1, pp. 5-15. Daniell, B. (1992), “Composing (as) power”, Paper Presented at the 43rd Annual Meeting of the Conference on College Composition and Communication, Cincinnati, OH, 19-21 March 1992. Daniell, B. (1994), “Composing (as) power”, College Composition and Communication, Vol. 45 No. 2, pp. 238-46. Erickson, D.A. (1989), “The communal ethos, privatization, and the dilemma of being public”, From the Campus: Perspectives of the School Reform Movement, Praeger, New York, pp. 136-53. Freire, P. (1970), The Pedagogy of the Oppressed, Continuum, New York. Fuhrman, S., Elmore, R. and Massell, D. (1993), School reform in the United States: putting it into context. Jacobsen, S. and Berne, R. (1993), Reforming education: the emerging systemic approach. Annual yearbook of the American Education Finance Association Corwin Press, Thousand Oaks, CA. Gabriele, S. (1996), “A systems analysis of ‘Twelve-Step’ meetings with a view to a theoretical and practical model for schools and classrooms”, Systems Research, Vol. 13 No. 2, pp. 109-26. Gabriele, S. (1997), “Boulding’s typology elaborated: a framework for understanding school and classroom systems”, Systems Practice, Vol. 10 No. 3, pp. 271-304. Gardner, H. (1991), The Unschooled Mind: How Children Think and How Schools Should Teach, Basic Books, New York. Goertz, M., Floden, P. and O’Day, J. (1996), Systemic Reform: Studies of Educational Reform, U. S. Department of Education.
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Goodman, K. (1986), What’s Whole in Whole Language? A Parent/Teacher Guide to Children’s Learning, Heinemann, Portsmouth, NH. Hough, P. (1992), “An investigation of critical self-reflective learning among members of Alcoholics anonymous”, Dissertation Abstracts International, 56-07A, 2529, UMI: Publications Number/Order Number AAI9539818. Jackson, M.C. (1992), Systems Methodology for the Management Sciences, Plenum Press, New York. Jackson, M.C. (2000), Systems Approaches to Management, Plenum Press, New York. Jenlink, P.M. (1995), Systemic Change: Touchstones for the Future School, Skylight Training and Publishing, Palatine, IL, Vol. 1. Johnson, D.W. (1975), Learning Together and Alone: Cooperative, Competitive and Individualistic Learning, Prentice Hall, Englewood Cliffs, NJ. Johnson, D.W. (1984), Circles of Learning: Cooperation in the Classroom, Association for Supervision and Curriculum Development, ASCD Publications, USA. Kemp, J. (1994), Designing Effective Instruction, Merrill MacMillan, NY. Lave, J. and Wenger, E. (1991), Situated Learning: Legitimate Peripheral Participation, Cambridge University Press, NY. Maeroff, G.I. (1986), “Withered hopes stillborn dreams: the dismal panorama of urban schools”, The Practice of Teaching, Teachers College Press, New York, p. 115. Makela, K., Arminen, I., Bloomfield, K., Eisenbach-Stagnl, I., Bergmark, K., Kurube, N., Mariolini, N., Olafsdottir, H., Peterson, J., Phillips, M., Rehm, J., Room, R., Rosenquist, P., Rosovsky, H., Stenius, K., Swiatkiewicz, B. and Zielinski, A. (1996), Alcoholics Anonymous as a Mutual-Help Movement: A Study in Eight Societies, University of Wisconsin Press, Madison, WI. Raywid, M. (1993), “Finding time for collaboration”, Educational Leadership, Vol. 51, pp. 30-4. Reed-Jones, S. (1992), “Faith in the reality of belonging: the story of Alonzo A”, Paper presented at the 43rd Annual Meeting of the Conference on College Composition and Communication, Cincinnati, OH, 19-21., March 1992. Reed-Jones, S. (1993), “Voice, text, and context: the social construction of an A.A. group (Alcoholics Anonymous)” Doctoral dissertation, University of Southern California, Dissertation Abstracts International, 56-07A, 2529. Rogers, D. (1989), “The professional bureaucracy”, in Ballantine, J.H. (Ed.), Schools and Society, Mayfield, Mountain View, CA, pp. 139-45. Rosenshine, B. (1986), “Synthesis of research on explicit teaching”, Educational Leadership, Vol. 43, pp. 60-9. Saettler, P. (1990), The Evolution of American Educational Technology, Libraries Unlimited, Inc., Englewood, CO. Seels, B. (1995), Instructional Design Fundamentals: A Reconsideration, Educational Technology Publications, Englewood Cliffs, NJ. Thomas, E. and the Newsweek Investigative team (October, 2001), The 10-year hunt for BinLaden: “the road to September 11”, Newsweek, pp. 38-49. Walker, Dean (1995), School Violence Prevention, ERIC Digest, N. p. 94. Whitford, B. and Jones, K. (2000), Accountability, Assessment, and Teacher Commitment: Lessons from Kentucky’s Reform Efforts. SUNY Series, Restructuring and School Change, State University of New York Press, State University Plaza, Albany, NY.
The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/0368-492X.htm
Epidemiologic modelling of HIV and CD4 cellular/molecular population dynamics
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T. Habtemariam, B. Tameru, D. Nganwa, L. Ayanwale and A. Ahmed Center for Computational Epidemiology, Bioinformatics and Risk Analysis (CCEBRA), College of Veterinary Medicine, Nursing and Allied Health, Tuskegee University, Tuskegee, USA
D. Oryang and H. AbdelRahman USDA/APHIS/PPD/RAS, Riverdale, MD, USA Keywords AIDS, Cybernetics, Computational model Abstract Computational models can facilitate the understanding of complex biomedical systems such as in HIV/AIDS. Untangling the dynamics between HIV and CD4+ cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we have developed a state transition systems dynamics and stochastic model that can be used to examine various alternatives for the control and treatment of HIV/AIDS. The specific objectives of our study were to use a cellular/molecular model to study optimal chemotherapies for reducing the HIV viral load and to use the model to study the pattern of mutant viral populations and resistance to drug therapies. The model considers major state variables (uninfected CD4+ lymphocytes, infected CD4+ cells, replicated virions) along with their respective state transition rates (viz. CD4+ replacement rate, infection rate, replication rate, depletion rate). The state transitions are represented by ordinary differential equations. The systems dynamics model was used for a variety of computational experimentations to evaluate HIV mutations, and to evaluate effective strategies in HIV drug therapy interventions.
Introduction In recent years, there has been a surge in molecular and cellular population studies of the Human Immunodeficiency Virus (HIV) and the Acquired Immunodeficiency Syndrome (AIDS) that continues to cause high morbidities and mortalities of humans across the globe (Anderson, 1993). Some of the focus of the research is targeted at unraveling the dynamic interactions between viral loads and CD4+ lymphocyte populations as well as in the evolution of viral phenotypes in HIV mutations. HIV/AIDS involves the interaction of cells of the body’s immune system and the HIV itself (Kirschner, 1996). These cells abound We are grateful for the support provided by the RCMI/NIH grant (5G12RR03059-12).
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mainly in the blood and the lymph, and are sometimes sequestrated in the lymphoreticular system (lymph nodes, thymus, tonsils, spleen, gut-associated lymphoid cells and macrophages). Not all cells of the immune system are involved. The most active cell type is the CD4+ cell (T4 or helper lymphocyte). The other cells play a secondary role; some act as antigen presenting cells especially the macrophages, though it is presently argued that there might be some active replication of HIV in these cell types. Mathematical and epidemiologic models of HIV/AIDS provide important insights in population dynamics through studies at the molecular and cellular levels as well as at the human population levels (Habtemariam et al., 1990, 1996; Ho et al., 1995; Perelson et al., 1996; Wei et al., 1995). Such research that exploits computational modelling falls in the emerging new area referred to as computational science that provides researchers a unique framework for advancing the understanding of science. In a comprehensive review in Science (vol. 256, April 1992), under the title “The Third Branch of Science Debuts”, (Poole, 1992) states: “Computer simulation has opened a new eye on the world, giving scientists in fields from biology to high energy physics a way to perform experiments that would be otherwise impossible”. This new science adds a third dimension to the traditional methods of theoretical and experimental approaches. One sub-component of this new science, which we have been developing and are applying it in this study, is that of computational epidemiology (Habtemariam et al., 1990). The understanding of the dynamics of CD4+ cells and HIV viral interactions has played a pivotal role in the development of HIV drugs. The development of a vaccine may also hinge on these same intricate studies. With the development of technology enabling quantification of HIV RNA in plasma, the dynamics of viral replication has been well described by Ho et al. (1995) and Wei et al. (1995). Such data provide opportunities for computational models that can be used for evaluation of chemotherapies as well as to evaluate avenues for development of vaccines that can outsmart the ongoing genetic mutations in HIV. The specific objectives of our study therefore were: a) to develop a computational model that represents cellular and molecular level dynamics of HIV and use the model to study optimal chemotherapies (nucleoside and non-nucleoside reverse transcriptase inhibitors and protease inhibitors) for reducing the HIV viral load; and b) to use the model to study the pattern of mutant viral populations and resistance to drug therapies. Although more is known about HIV than almost any other infectious agent, scientific questions remain unanswered that are critical to development of an HIV preventive vaccine as well as in the development of chemotherapies with lasting antiretroviral properties but with minimal side effects. Antigenic variation presents a considerable problem for vaccine development, as it will be essential to induce broadly cross-protective immunity against the diverging
strains as HIV spreads across the world. Several reports indicate that the long, clinically latent phase that characterizes HIV infection is not a period of viral inactivity, but an active process in which CD4+ cells are being infected and dying at a high rate and in large numbers. This results and leads to a simple steady-state model in which infection, cell death, and cell replacement are in balance, and imply that the unique feature of HIV is the extraordinarily large number of replication cycles that occur during infection of a single individual (Little et al. 1999). Chemotherapeutic development against HIV has come a long way and combination drug therapy involving different classes of drugs are now in common use. In multicombination therapies, reverse transcriptase inhibitors are used in conjunction with protease inhibitors and results from laboratory tests and tests in people show that certain protease inhibitors are many times more powerful than reverse transcriptase inhibitors greatly reducing the viral load sometimes up to 99.9 per cent (Saag et al., 1997). Mathematical modelling has been used to analyze HIV viral load after administration of a potent inhibitor of HIV-1 protease (Markowitz et al., 1995, Markowitz , 1996, Flexner, 1998). The findings on viral dynamics provide not only a kinetic picture of HIV1 pathogenesis, but also theoretical principles to guide the development of treatment strategies. Even with the advent of newer drugs, no amount of medical treatment has so far been able to prevent the eventual collapse of the immune system in people with advanced HIV infection or AIDS. The explanation for such a collapse of the immune complex is not well understood. One of the main reasons for this is our inadequate knowledge of the dynamics and interaction of the CD4+ lymphocytes with HIV, especially, in the presence of the different types of antiretroviral drugs that are presently available. Computational epidemiologic models of cellular and molecular level dynamics, if successfully developed, can be used to investigate these types of questions. Material and methods Epidemiologic modelling A systems analysis diagram that we developed to represent cellular/molecular model is presented in Figure 1. The classical epidemiologic triad of host/agent/environment interaction is described for the cellular/molecular level as follows. The host populations are CD4+ lymphocytes, the agent is HIV viral population and the environment is the cellular and intracellular/molecular ecosystem. The epidemiologic systems dynamics model of (CD4+ lymphocyte populations and HIV interactions) provides the framework to quantitatively describe the state transitions that occur in this disease complex. The major state variables for the model include: Uninfected CD4+ lymphocytes (immature CD4+ precursors and mature CD4+ lymphocytes), Infected CD4+ lymphocytes and HIV viral population. Uninfected (Healthy)
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Figure 1. An epidemiologic systems model of CD4+ and HIV population dynamics
CD4+ T-Lymphocytes develop from bone marrow stem cells (source), and their progenitors migrate to the thymus where they mature. The rate of T cell production by the thymus is greatest before puberty. The transition from stem cells to the CD4+ cells is represented by CD4+ replacement rate. The Uninfected CD4+ cells come in contact with the “initial infective dose of external virus population” (wild type virus) and become infected. The transition from Uninfected CD4+ cells to Infected CD4+ cells is represented by the “infection rate”. The uninfected CD4+ cells that contact the “initial infective dose of external virus population” and become infected are a critical component of the model. The last step leads to the “replication rate” that ends in the state variable “free virus population”. The “mature virions” represent the infectious stage of the replicated virus that leads to infection of “uninfected CD4+ cells”. A portion of the CD4+/HIV interaction leads to mutations, represented by the state variable “free mutant viral populations”. Portions of these return to cycle back and infect the “uninfected CD4+ cells” leading to further replication of the mutant subpopulation. The new state that represents infected CD4+ lymphocytes, referred to as “HIV infected CD4+ cell subpopulation”, is further subdivided into four substates: Productively infected, Latently infected, Defectively infected, and Chronically infected (Coffin, 1995).
Productively infected cells are those cells with the most rapid turnover, and proceed through a nonproducing phase followed by a producing phase and cell death.(Coffin, 1995). Latently infected cells have a nonproducing period that is substantially longer than for the productive infection cycle. Such cells would serve as a reservoir capable of maintaining the infection even in the presence of the most effective antiviral therapy (Coffin, 1995). Defectively Infected cells defects arise frequently as a consequence of errors during reverse transcription of wild-type genomes. A fraction of these will not produce virus, will not die prematurely and thus preserve the defective provirus. Chronically producing cells produce virus over an extended period of time, in contrast to the limited life span of productively infected cells (Coffin, 1995). The important rates in this systems dynamics model are: CD4+ replacement rate, CD4+ infection rate, CD4+ cells (infected and uninfected) depletion (death) rate, viral mutation rate, viral depletion (death) and clearance rates, and viral replication rates for mutated and wild type viral subpopulations. These rates lead to the respective “sinks” in the systems dynamics model. Other variables (auxiliary variables) may include antiretroviral immune response (cytotoxic T cells, antiretroviral antibodies) and suppressor T-Lymphocytes which inversely affect the replacement rate of CD4+ cells. Modelling the molecular (intracellular) level dynamics. In each of the four substates of the “ HIV infected CD4+ cell population”, viz. productively infected, latently infected, defectively infected, and chronically infected, molecular level interaction between HIV and CD4+ cells will continue to occur as part of the viral replication cycle. A sequence of events and molecular interactions and cytochemical kinetics are triggered when the HIV attaches to a CD4+ lymphocyte. The process includes: attachment and fusion; reverse transcription; integration; transcription; translation; and budding. Co-receptors are required for the process of HIV entry into target cells. CD4+ receptors are also present in at least trace amounts on every kind of cell infected by the HIV. Apparently the expression or encoding of only a very small amount of CD4+ is sufficient for infection by HIV. Macrophages are widely distributed throughout the body; they may play critical roles in persistence of HIV infection by providing reservoirs of chronically infected cells. An infected cell will remain infected and harbor the HIV provirus for the life of the cell. We incorporate the molecular level kinetics in the systems dynamics model shown in Figure 1. Modelling chemotherapeutic intervention. HIV virion production and clearance rates are directly affected by chemotherapies. HIV production in vivo occurs continuously at high rates (Ho et al., 1995; Wei et al., 1995). Viral decay is a composite of two separate effects: the clearance of free virions from plasma and the loss of virus-producing cells. Loss of infected cells could be the result of viral cytopathicity, immune elimination, or other processes such as
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apoptosis. Virion clearance could be the result of binding and entry into cells, immune elimination, or nonspecific removal by the reticuloendothelial system (Perelson et al., 1996). The systems dynamics model (Figure 1) and the equations derived thereof enabled us to examine the impact of chemotherapeutic interventions. Equations representing drug intake, clearance rates and drug concentrations are incorporated into the fully integrated epidemiologic model as discussed below.
The mathematical model Once the epidemiologic systems diagram was completed, parameter estimations and development of first order differential equations that realistically represent the systems dynamics followed. Each of the rates and auxiliary variables and other appropriate parameters were derived from preexisting data. In this model, we distinguish three types of variables: uninfected CD4+ cells Cu (t ) (not infected by HIV at time t ), two types of virus particles: wild type virus V (t ) and mutant virus Vm(t ), and two groups of infected CD4+ cells (virus reacts with uninfected cells to produce infected cells), cells infected by wild type virus and cells infected by mutant virus. Let us assume that uninfected cells are produced at a rate, l(t ), from a pool of precursor cells and that it has a natural death rate du. The wild type virus, V(t ), and mutant virus, Vm(t ), infect the CD4+ cells with rates b and bm respectively. We further divide each group of the infected CD4+ cells into four types of infected cells: CD(t )and CDm(t ) denote CD4+ cells Defectively(D) Infected by wild and mutant virus respectively, CL(t ) and CLm(t ) denote CD4+ cells Latently(L) Infected by wild and mutant virus respectively, CP(t ) and CPm(t ) denote CD4+ cells Productively(P) Infected by wild and mutant virus respectively, CC(t ) and CCm(t ) denote CD4+ cells Chronically (C) Infected by wild and mutant virus respectively, D(t ) denotes the drug concentration at time t, du the natural death rate of the uninfected cells. di’s denote the rates of loss of infected cell of type i, where i ¼ L; P, C, D,
m is the probability of mutation from wild type to resistant mutant virus,
gi’s denote the rate at which an HIV-infected CD4+ cell of type i release virus
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Thus, the kinetics of the uninfected CD4+ cells is given by: dC u ðtÞ ¼ lðtÞ 2 ½d u þ bV ðtÞ þ bm V m ðtÞC u ðtÞ dt
ð1Þ
Where lðtÞ ¼ ICðtÞ 2 ½k RNAcor =ðIC ð1=2Þ þ RNAcor Þ IC (t ) is the number of immature CD4+ cells RNAcor is the concentration of genomic RNA present in the viral core k is the product of reduction constant of immature cell and proportion of RNAcor to number of virions budding. IC(1/2) is half saturation constant of immature cell. And the reverse transcription can be given assuming Michaelis Menten kinetics (Reddy and Yin, 1999), d½RNAcor V m ½RNAcor ½dNTP · 2 kRNAcor ½RNAcor ¼2 dt K mðRNAcor Þ þ ½RNAcor K mðdNTPÞ þ ½dNTP where [RNAcor] is the concentration of genomic RNA present in the viral core and [dNTP] is the concentration of the dNTP pool of the host cell. K mðRNAcor Þ and Km(dNTP ) are the Michaelis constants for reverse transcriptase with the substrates RNAcor and the dNTP pool, respectively. kRNAcor is the degradation rate constant of the genomic RNA. Hence the dynamics of cell infection by wild type virus and wild type virion production are represented below. dC L ¼ aL V ðtÞC u ðtÞ 2 dL C L ðtÞ dt
ð2Þ
dC P ¼ aP V ðtÞC u ðtÞ 2 dP C P ðtÞ dt
ð3Þ
dC C ¼ aC V ðtÞC u ðtÞ 2 dC C C ðtÞ dt
ð4Þ
dC D ðtÞ ¼ aD V ðtÞC u ðtÞ 2 d D C D ðtÞ dt
ð5Þ
dV ðtÞ ¼ gL C L ðtÞ þ gP C P ðtÞ þ gC C C ðtÞ 2 ðu 2 wDðtÞÞV ðtÞ dt
ð6Þ
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Where ai ¼ pi bð1 2 mÞ for i ¼ L; P, C, D. The parameter pi describes the probability that upon infection a cell will enter type i and the parameter m is the probability of mutation from wild type to resistant mutant virus. D(t ) and w(t ) denote the drug concentration and drug inhibition factor respectively. Where wðtÞ ¼ 1 2 hðtÞ with h ¼ 1=ðDðtÞ þ D50 Þ and D50 is the dose required for 50 per cent effectiveness. The equation that describes the drug intake and clearance processes is defined as follows. dDðtÞ ¼ 2aDðtÞ þ gI ðtÞ dt
ð7Þ
where a is the drug clearance rate, g is the dosage, and I(t ) is an indicator function that has a value of 1 if the patient takes the drug at time t, 0 otherwise. A similar dynamics for mutant type cell infection and mutant type virion production can be given by: dC Lm ¼ pL bV ðtÞC u ðtÞ þ pLm bm V m ðtÞC u ðtÞ 2 d Lm C Lm ðtÞ dt
ð8Þ
dC Pm ¼ pP bV ðtÞC u ðtÞ þ pPm bm V m ðtÞC u ðtÞ 2 d Pm C Pm ðtÞ dt
ð9Þ
dC Cm ¼ pC bV ðtÞC u ðtÞ þ pCm bm V m ðtÞC u ðtÞ 2 dCm C Cm ðtÞ dt
ð10Þ
dC Dm ðtÞ ¼ pD bV ðtÞC u ðtÞ þ pDm bm V m ðtÞC u ðtÞ 2 d Dm C Dm ðtÞ dt
ð11Þ
dV m ðtÞ ¼ gLm C Lm ðtÞ þ gPm C Pm ðtÞ þ gCm C Cm ðtÞ 2 ðum þ lm DðtÞÞV m ðtÞ ð12Þ dt The equations presented above as well as other appropriately defined parameters were used to create the computational model which runs under STELLAw Research, version 4.02, modelling software (High Performance Systems). STELLA, an object-oriented compartmental modelling tool for the Power Mac, has previously been used to model and assess the risk factors for transmission of HIV infection and in the study of the epidemiology of HIV/AIDS (Habtemariam et al., 1996).
Simulation results and discussion Our simulation describes and quantitatively represents the cellular level dynamics between HIV virus and CD4+ lymphocytes. We rely on several assumptions and some of the parameter estimates that undoubtedly will improve over time. Of greater interest also is the intracellular dynamics that represent the molecular level dynamics and interactions between HIV and the biochemical and RNA kinetics. This area is quite critical and will be further examined in the future as additional data is generated. We do see the need for and importance of using computational models to represent complex biomedical systems that can best be studied cohesively and rationally using integrative systems dynamics modeling (Figures 2 and 3).
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Figure 2. (a) Computer simulation of the model for the CD4+ cell without drug intervention. (b) Computer simulation of the model for the HIV virus without drug intervention
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Figure 3. (a) Computer simulation of the model with drug intervention. (b) Computer simulation of the model for the virus without drug intervention
References Anderson, R.M. (1993), “AIDS: Trends, Predictions, Controversy”, Nature, Vol. 363, pp. 393-4. Coffin, J.M. (1995), “HIV population dynamics in vivo: Implications for genetic variation, pathogenesis and therapy”, Science, Vol. 267, pp. 483-9. Centers of Disease Control and Prevention (CDC) 2000. HIV/AIDS Surveillance Report Vol. 12 No. 2 Year End Edition (December). Flexner, C. (1998), “Drug therapy: HIV-protease inhibitors”, N Engl. J. Ed., Vol. 338, pp. 1281-92. Habtemariam, T., Oryang, D., Gabreab, F., Robnett, V. and Trammell, G. (1990), “Research in Computational Epidemiology”, Mathematical and Computer Modelling, Vol. 14, pp. 653-8. Habtemariam, T., Yu, P., Oryang, D., Nganwa, D., Obasa, M., Robnett, V. and Ayanwale, O. (1996), “Epidemiologic modeling using systems dynamic methods as applied to the AIDS epidemic in the USA”, J. of System Analysis, Modeling and Simulation, Vol. 23, pp. 265-74. Ho, D.D., Neumann, A.U., Perelson, A.S., Chen, W., Leonard, J.M. and Markowitz, M. (1995), “Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection”, Nature, Vol. 373, pp. 123-6.
Kirschner D. (1996), “Using mathematics to understand HIV immune dynamics”, AMS Notices, pp. 191-202. Little, S.J., McLen, A.R., Spine, C.A., Richman, D.D. and Havlir, D.V. (1999), “Viral dynamics of acute HIV-1 infection”, J. Exp. Med., Vol. 190, pp. 141-50. Markowitz, M. (1996), Protease Inhibitors: A New Family of Drugs for the Treatment of HIV Infection. International Association of physicians in AIDS Care (IAPAC), West Washington. Suite 2200. Chicago, EL 60606. Markowitz, M., Saag, M., Powderly, W.G., Hurley, A.M., Hsu, A., Valdes, J.M., Henry, D., Sattler, F., Marca, A.L., Leonard, J.M. and Ho, D.D. (1995), “A preliminary study of ritonavir, an inhibitor of HIV-1 protease, to treat HIV-1 infection”, N. Engl. J. Med., Vol. 333, pp. 1534-9. Perelson, A.S. and Nelson, P. (1999), “Mathematical analysis of HIV-1 dynamics in vivo”, SIAM Rev., Vol. 41, pp. 3-44. Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M. and Ho, D.D. (1996), “HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time”, Science, Vol. 271, pp. 1582-6. Poole, R. (1992), “The Third Branch of Science Debuts”, Science, Vol. 256. Reddy, B. and Yin, J. (1999), “Quantitative Intracellular Kinetics of HIV Type 1”, Aids Research and Human Retroviruses, Vol. 15 No. 3, pp. 273-83. Saag, M., Knowles, M., Chang, Y., Chapman, S. and Clendeninn, N.J. Viracept Cooperative Study Group. Durable effect of VIRACEPT (nelfinavir mesylate, NFV) in triple combination therapy. In: Program and Abstracts of the 37th Interscience Conference on Antimicrobial Agents and Chemotherapy. Toronto, 1997. Abstract I-101. 5. Wei, X., Ghosh, S.K., Taylor, M.E., Johnson, V.A., Emini, E.A., Deutsch, P., Lifson, J.D., Bonhoeffer, S., Nowak, M.A., Hahn, B.H., Saag, M.S. and Shaw, G.M. (1995), “Viral dynamics in human immunodeficiency virus type 1”, Nature, Vol. 373, pp. 117-22. Weiss, R.A. (1993), “How does HIV cause AIDS?”, Science, Vol. 260, pp. 1273-9.
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Application of systems analysis in modelling the risk of bovine spongiform encephalopathy (BSE) T. Habtemariam, B. Tameru, D. Nganwa, L. Ayanwale and A. Ahmed Center for Computational Epidemiology, Bioinformatics and Risk Analysis (CCEBRA), College of Veterinary Medicine, Nursing and Allied Health, Tuskegee University, Tuskegee, AL, USA
D. Oryang and H. AbdelRahman USDA/APHIS/PPD/RAS, Riverdale, MD, USA
G. Gray, J. Cohen and S. Kreindel Harvard Center for Risk Analysis, Harvard School of Public Health, Boston, MA, USA Keywords Cybernetics, Risk, Modelling, Bovine spongiform encephalopathy Abstract Bovine spongiform encephalopathy (BSE), widely known as “mad cow disease”, has virtually crippled the British livestock industry. Even though, no cases of BSE have been reported in the United States (US), a similar epidemic in the US would be catastrophic. The added concern for the risk of introduction of the human disease called variant Creutzfeldt-Jacob disease that has been linked to eating meat of BSE infected cattle compounds the risk of BSE. Systems dynamics models based on the underlying transmission pathways of BSE can help to anticipate the spread of this disease in different cattle populations and assist in the evaluation of potential risk mitigations for preventing its introduction or controlling its spread if it was introduced. With this in mind, an age and health status structured systems dynamics model was developed. By making assumptions and setting up feasible scenarios, the model can be used to examine potential prevalence and incidences rates of BSE; the effect of mitigations including changes in feeding habits or rendering processes and/or other policies and regulations designed to prevent the introduction of BSE. The systems dynamics simulation model enabled us to create virtual experiments whose real-world analogues would otherwise be expensive, dangerous, or even impossible to carryout.
Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1380-1390. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443581
Introduction The new landscape of the 21st century, while promising unparalleled advancements and growth, is fraught with a variety of hazards and risks. Risk We are grateful for grant support provided by the Harvard Center for Risk Analysis.
analysis (RA) and modelling provide powerful methodologies that can be used to assess and analyze the risks posed by diseases and pests of animals and plants. Based on sound, science-based RA, decision makers can devise policies and procedures that can minimize the risk of introduction and/or consequences that may arise from unwanted or unexpected introductions of diseases and pests. As multinational companies operate across borderless dimensions of the international market place, coupled with fast transportation systems, the risks of introduction and spread of emerging and re-emerging diseases and other risks continue to expand across the globe. At this point in time, it appears like the US food animal industry is being stalked by at least two potentially devastating emerging/re-emerging animal diseases from across the Atlantic Ocean (BSE Inquiry, 2000). One is a fast moving disease, commonly referred to as foot and mouth disease (FMD). The other one is a slower moving disease called bovine spongiform encephalopathy (BSE), also referred to as “mad cow disease”. BSE is a chronic, neurodegenerative disease affecting the brain, disrupting or destroying neurons in large numbers, which inevitably leads to the death of the infected animal. It belongs to the family of diseases known as the transmissible spongiform encephalopathies (TSE’s) (WHO, 2001; USDAAPHIS, 2000). These diseases are caused by a transmissible agent (prion), which is yet to be fully characterized. No cases of BSE have been reported in the USA, but if an epidemic occurred, it would be catastrophic to the livestock industry and to public health (CJD Surveillance Unit, 2001; Cousens et al., 1997). The most significant feature of BSE and other TSEs is the fact that they have a prolonged incubation period of months to years (Anderson et al., 1996). The most important transmission mechanism of BSE is through ruminant-toruminant feed. Other transmission pathways may include interspecies transmission, vertical or horizontal transmission, spontaneous transmission and other yet undefined mechanisms (Donnelly, 1998). The outbreak of BSE in Europe and Japan and other areas of the world highlight the importance of biosecurity for USA. Because of BSE, the loss of nearly 200,000 diseased cattle, followed by pre-emptive slaughter and destruction of nearly four and a half million asymptomatic cattle of more than 30 months of age, has crippled the British livestock industry (Donnelly et al., 1997, Ferguson et al., 1997). The drastic steps taken have also affected the tallow, gelatin, and pharmaceutical industries, all of which are used in formulations of bovine-derived products (Biopharm, 1997). Twelve other European countries and Japan have reported the presence of BSE. The economic devastation, its impact on public health, food safety and food security will be immense and the public will be greatly alarmed if this food animal disease was to enter the USA. On top of this, its potential as a bioterrorism agent cannot be ignored. Epidemiologic and mathematical models based on the underlying transmission mechanisms of
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BSE can help the scientific community to understand and anticipate the spread of this epidemic and to evaluate the potential effectiveness of different mitigations in managing the risks posed by the outbreak of BSE. Our objectives in this study were: (1) to first create a dynamic and stochastic RA model for BSE that will realistically simulate and predict the behaviour of the disease, and (2) using this dynamic RA model, to evaluate the behaviour of the disease over time and evaluate effective mitigations to manage risks posed by BSE. Our hypothesis was that a dynamic and stochastic RA model could be developed to assess the spread of BSE in cattle and vCJD in humans. The model can be used to examine the consequences of entry and enable the evaluation of mitigations that may be implemented to manage the risk of BSE. An important but critical consideration in our RA is that of modelling the dynamic properties of BSE risk. Basically, biologic risk such as in BSE is not static, it changes over time and place at different rates driven by the underlying epidemiologic factors and disease transmission pathways. Therefore, we saw the need to develop RA methodologies that are both dynamic and stochastic both in time and space to evaluate the risk profile of emerging/re-emerging diseases. In the case of BSE, computational epidemiologic and RA modelling will allow the examination of risk of introduction of variant Creutzfeldt-Jacob disease (vCJD) in humans. As of March 31, 2001, 100 people have been diagnosed with vCJD in Europe, but fortunately, there are no cases so far in the USA. Since vCJD in humans is suspected to be caused by the transmission of BSE from cattle through consumption of meats and animal products, we will be able to examine these risk pathways using a dynamic RA model. Material and methods Dynamic RA and modelling of BSE The systems dynamics model we developed for studying the risk of BSE is shown in Figure 1. The major components of the BSE modelling system are: (1) host populations (cattle, humans), and (2) the rendering and feed processing subsystem for the manufacture of meat and bone meal (MBM) used as protein supplement in the livestock industry. The external source for the introduction of BSE includes: (1) importation of BSE (or TSE) infected cattle, (2) imported MBM that may already contain the BSE infectious dose (ID50) and are imported and fed to cattle, and
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Figure 1. A systems analysis diagram showing the state transitions and rates of significance in assessing the risk of introduction of BSE
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(3) the possibility that other TSE agents may somehow be transformed and lead to the occurrence of BSE. Note that once BSE is introduced, it can cycle between the cattle population and the rendering and feed processing subsystems. This may occur when BSE infected cattle are slaughtered (or dead cattle) are sent to the rendering industry and are processed into MBM that can then be fed to other cattle. The “ruminant feed ban policy is designed in such a way that MBM from ruminant source (cattle, sheep, goats and other ruminants) is not allowed to be fed to ruminants (cattle, sheep and goats) but can be fed to non-ruminants (e.g. poultry and swine). In Figure 1, we can also evaluate the impact of risk mitigation policies and strategies such as the so-called “feed ban” in terms of reducing the risk of BSE introduction. Additionally, in certain cases, when BSE ID50s from infected cattle reach the human food chain, the consumption of such meats is assumed to cause vCJD. This component is of significant public health concern. In the cattle population subcomponent, which is of key interest in this model, the health states considered are “susceptible or healthy cattle” and “infected cattle”. The infected cattle state is further subdivided into “incubating, pre-clinical and clinical”. An incubating animal can stay as incubating for a minimum of 3 years and a maximum of 4 years, before moving to pre-clinical state. After about 4 months, the cattle subpopulation is moved to the next state referred to as “clinical” state. In the clinical state the cattle would either be detected or die on a farm. The time step in each health state except in the susceptible is taken to be 1 year, which can also be changed to a value smaller than 1 year. Epidemiologic and related risk data were obtained from Internet reported data on BSE by the Ministry of Agriculture, Fisheries and Foods (MAFF) of Great Britain (http://www.maff.gov.uk/ ) and The Office International Des Epizooties (http://www.oie.int/ ) and USDA. These sites are well maintained and the most recent data on BSE as well as other important diseases that affect the world economy and public health are posted regularly. These were supplemented by published literature data. We simulate and track infectivity via infectious oral dose (ID50). An ID50 is defined as the amount of infectious tissue that would on the average cause 50 per cent of exposed cattle to develop BSE (Gray et al., 2001). We track the population dynamics of animals, infectivity (ID50s) by apportioning the total host population into four classes. These classes are composed of the female cattle population which is divided into beef cattle and dairy cattle; the male cattle subpopulation which is divided into bulls and steers. We assume that all cattle are susceptible to infection and once infected, an animal harbors the disease for atleast 3 years prior to becoming pre-clinical. Once clinical, it is easy to detect infection and remove the animal from the rest of the population.
Dimensions of BSE model The cohorts of animals to be tracked are structured by animal use type. Animal use types include: .
dairy animals that produce milk, or
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beef animals that are raised for meat production.
Animal use type contributes towards the determination of: .
average amount of feed consumed,
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amount of MBM and bypass protein (BPP) in a unit of feed,
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the length of time the animals in the cohort live.
Animals in the system are removed due to slaughter (slaughter rate) or die off (death rate) while reproduction and import rates add to the population pool. Age is an important variable that contributes towards the determination of spontaneous infection rate and vertical transmission rate. The average amount of feed, and amount of MBM/BPP in a unit of feed, slaughter rates, reproduction rates, death rates also depend on the age variable. Disease status is another important factor because it contributes towards the determination of the amount of infectivity in the animal, and the likelihood of detecting infection.
Model input The model requires the following input: .
number of animals in each age group among beef and dairy calves, heifers, cows, steers and bulls for the first year of the simulation;
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birth rates, slaughter rates, death rates and spontaneous infection rates of the cattle population;
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amount of infectivity (measured in ID50s) per infected animal that goes to animal consumption in the form of MBM;
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amount of infectivity (measured in ID50s) per infected animal that goes to human consumption.
Most of the parameters for the model is provided from Harvard Center for RA; USDA and other published literature. Mathematical equations The following set of partial differential equations describes the dynamic behaviour of the systems between the BSE agent and the host population of cattle.
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›X 1 ð j; a; 0ÞðtÞ=›t þ ›X 1 ð j; a; 0ÞðtÞ=›a ¼ PRðX 1 ð j; a; 0ÞðtÞÞ 2 ½IRðX 1 ð j; a; tÞðtÞÞ þ RRðX 1 ð j; a; 0Þ ðtÞÞ* X 1 ð j; a; 0ÞðtÞ
ð1Þ
1386 ›X 2 ð j; a; tÞðtÞ=›t þ ›X 2 ð j; a; tÞðtÞ=›a þ ›X 2 ð j; a; tÞðtÞ=›t ¼ IRðX 1 ð j; a; tÞÞ þ ImpðX 2 ð j; a; tÞÞ 2 ½PRðX 2 ð j; a; tÞÞ þ RRðX 2 ð j; a; tÞÞ* X 2 ð j; a; tÞðtÞ ð2Þ
›X 3 ð j; a; tÞðtÞ=›t þ ›X 3 ð j; a; tÞðtÞ=›a þ ›X 3 ð j; a; tÞðtÞ=›t ¼ PRðX 2 ð j; a; tÞÞ þ ImpðX 3 ð j; a; tÞÞ 2 ½PRðX 3 ð j; a; tÞÞ þ RRðX 3 ð j; a; tÞÞ* X 3 ð j; a; tÞðtÞ ð3Þ
›X 4 ð j; a; tÞðtÞ=›t þ ›X 4 ð j; a; tÞðtÞ=›a þ ›X 4 ð j; a; tÞðtÞ=›t ¼ PRðX 3 ð j; a; tÞÞ þ ImpðX 4 ð j; a; tÞÞ 2 RRðX 4 ð j; a; tÞÞ* X 4 ð j; a; tÞðtÞ
ð4Þ
X i ð j; a; tÞð0Þ ¼ 0 for i ¼ 2; 3; 4 and for all age a and time since infection t. The time step in each health state except in the susceptible state will be computed at monthly intervals. In equations (1-4), at any time t the number of cattle in health status Xi ði ¼ 1; 2; 3; 4Þ of use type j ð j ¼ 1; 2; 3; 4Þ and age a infected for a time t is denoted by Xi( j,a,t )(t ), where X1 ¼ susceptible, X2 ¼ incubating, X3 ¼ pre-clinical, X4 ¼ clinical, j ¼ 1 is beef female cattle, j ¼ 2 is dairy female cattle, j ¼ 3 is bulls, j ¼ 4 is steers, a ¼ age of the animal where age 1 is calf and age 2 and 3 for beef and dairy females can be heifers,
t ¼ time since infection,
PR ¼ progression to the next disease status, RR ¼ removal rate,
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Imp ¼ importation rate, and IR ¼ infection rate. The earlier system of partial differential equations can be explained as follows: the number of susceptibles at a given point in time may change with age (›X1( j, a, t )(t )/›a ) and likewise the number at a given age may change over time (›X1( j, a, t )(t )/›t ), as susceptible are lost due to culling (that is, deaths not associated with infection and slaughter) at a rate RR(X1( j, a, 0)(t )), or as they are transferred to the infected but incubating class at a rate IR(X1( j, a, t )(t )). The infection rate in our model depends upon: .
the rate of spontaneous infection;
.
the rate of infection via feed; and
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the rate of vertical transmission.
Incubating individuals are either removed at a rate RR(X2( j, a, t )), or move to the pre-clinical class at a rate PR(X2( j, a, t )) and it increases due to importation [Imp(X3( j, a, t )(t ))]. The number of clinically infected animals of use type j and age a that have been infected for t years [X4( j, a, t )(t )] can decrease due to culling [RR(X4( j, a, t )(t ))]. The clinical cattle population state can increase by moving from the pre-clinical state entering into this clinical state with rate PR(X3( j, a, t )(t ) or due to importation [Imp(X4( j, a, t )(t ))]. Results and discussion An age, use type and health status structured systems dynamics model for BSE has been developed. This model assesses potential risk pathways for entry of TSE agents, including the BSE agent, into cattle and the food supply. The model then simulates how the BSE infectivity spreads in the population under study. STELLA (High Performance Systems, NH) software was used to create the systems analysis model. The STELLA software is an object-oriented programming vehicle that follows the systems dynamics methodology as developed by Jay Forrester (1968). The model provides results that consist of: .
number of BSE infected animals in each age group among beef and dairy calves, heifers, cows, steers and bulls for each year of the simulation;
.
amount of infectivity [measured in infectious dose (ID50s)] for each year;
.
prevalence and incidences of BSE;
.
the effect of changing feeding habits or rendering processes or MBM feeding bans on prevalence and incidence rates of BSE.
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Figure 2. (a) Prevalence of BSE from importing infected MBM containing 1 ID50; (b) Prevalence of BSE from importing infected MBM containing 100 ID50’s; (c) Prevalence of BSE from importing 1 infected (for 1 Year) dairy female; (d) Prevalence of BSE from importing 1000 infected (for 1 Year) dairy female
By assuming and setting up feasible scenarios, the model was used to examine potential future prevalence and incidences rates of BSE. The effect of mitigations including changes in feeding habits or rendering processes on prevalence and incidence rates of BSE were also examined. Note that we are including the new regulation of ruminant feedban in our simulations. Two simulation scenarios were conducted. Scenario #1: Assessing the risk of BSE if the ID50 is introduced via imported MBM of various weights. Scenario #2: Assessing the risk of BSE if the ID50 is introduced via imported cattle of various numbers. In each scenario the introduction of BSE leads to an epidemic that eventually dies out. The epidemic extends for a shorter period of time in bulls and steers, but extends for a much longer period in dairy (female) cattle. The policy of sustained mitigation efforts in dairy females is therefore advisable. In essence, a simulation model imitates (simulates) the behaviour of a complex system in some different medium – most commonly a computer – so that the behaviour of the model is conceptually similar to that of the real system. The behaviour of the model can be studied far more quickly, cheaply, and simply than that of the real system, and conclusions drawn from the model can be applied to real system. In conclusion, dynamic and quantitative risk assessment provides a method for measuring risk and providing decision makers with information that can be used to justify their decisions about plant and animal (and byproducts) import restrictions/allowances. In Figure 2(a), one ID50 is introduced into the livestock population. The consequence of this introduction was of no significance since the prevalence of BSE ( y-axis) was very low. When we increased the risk by 100 fold (100 ID50) the consequence of this introduction was also insignificant. We then examined the risk of BSE introduction via infected animals. In Figure 2(c), only one BSE infected animal is introduced into the livestock population. This also lead to an insignificant amount of BSE risk. When we increased the introduction of BSE infected animals to 1,000, this resulted in an epidemic and the risk became quite high. The prevalence increased to about 0.3 per cent in dairy and 0.7 per cent in bulls. This level of an epidemic in the livestock population will be of great concern since its impact can be quite devastating. References Anderson, R.M., Donnelly, C.A., Ferguson, N.M., Woolhouse, M.E., Watt, C.J., Udy, H.J., MaWhinney, S., Dunstan, S.P., Southwood, T.R., Wilesmith, J.W., Ryan, J.B., Hoinville, L.J., Hillerton, J.E., Austin, A.R. and Wells, G.A. (1996), “Transmission dynamics and epidemiology of BSE in British cattle”, Nature, Vol. 382, pp. 779-88.
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Biopharm (1997), “Assessment of the risk of bovine spongiform encephalopathy in pharmaceutical products”, http://www.biopharm.mag.com/resources/pharma0198.htm BSE Inquiry (2000), “Conclusions drawn from the scientific response to BSE”, http://www. bseinquiry.gov.uk/report/volume1/execsum2.htm CJD Surveillance Unit (2001), “Information on the new variant of CJD”, http://www.cjd.ed.ac.uk/ Cousens, S.N., Vynnycky, E., Zeidler, M., Will, R.G. and Smith, P.G. (1997), “Predicting the CJD epidemic in humans”, Nature, Vol. 385 No. 6613, pp. 197-8. Donnelly, C. (1998), “Maternal transmission of BSE: interpretation of the data on the offspring of BSE-affected pedigree suckler cows”, Veterinary Record, Vol. 142 No. 21, pp. 579-80. Donnelly, C.A., Ferguson, N.M., Ghani, A.C., Woolhouse, M.B.J., Watt, C.J. and Anderson, R.M. (1997), “The epidemiology of BSE in cattle herds in Great Britain. I. Epidemiological processes, demography of cattle and approaches to control by culling”, Philosophical Transactions of the Royal Society of London – Series B: Biological Sciences, Vol. 352 No. 1355, pp. 781-801. Ferguson, N.M., Donnelly, C.A., Woolhouse, M.E. and Anderson, R.M. (1997), “The epidemiology of BSE in cattle herds in Great Britain. II. Model construction and analysis of transmission dynamics”, Philosophical Transactions of the Royal Society of London – Series B: Biological Sciences, Vol. 352 No. 1355, pp. 803-38. Gray, G.M., Cohen, J.T., Duggar, K., Kreindel, S., Abdelrahman, H., HabteMariam, T., Oryang, D. and Tameru, B. “Evaluation of the potential for bovine spongiform encephalopathy in the United States”, USDA, http://www.aphis.usda.gov/oa/bse/ USDA-APHI, (2000), “Fact sheet: bovine spongiform encephalopathy”, http://www.aphis.usda. gov/oa/pubs/fsbse.pdf USDA-APHIS, (2000), “BSE Surveillance”, http://www.aphis.usda.gov/oa/bse/bsesurvey. html#charts USDA-FSIS, (1998), “Animal reporting system (ADRS) livestock slaughtered in USDA year 1998”, http://www.fsis.usda.gov/OPHS/adrsdata/1998adrs/98crm1.htm WHO, (2001), “Fact sheet: bovine spongiform encephalopathy”, http://www.who.int/inf-fs/en/ fact113.html
The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/0368-492X.htm
Tools for creation of multimodels Martin Hruby´, Radek Kocˇ´i, Petr Peringer and Zdena Ra´bova´ Department of Computer Science and Engineering, Brno University of Technology, Bozˇeteˇchova 2, Brno, Czech Republic
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Keywords Cybernetics, Simulation Abstract The process of creating complex models often requires different modelling methods and tools to be integrated. This paper provides a concise description of an object-oriented environment for creating composite models. The proposed approach is based on using simulation abstractions as basic model building blocks. The basic environment is built up of a Prolog interpreter, SIMLIB and object-oriented Petri nets.
1. Introduction In the process of modelling and simulation of complex systems there can be used various methods of model design and simulation experiment control. It turns out to be very important so that several different description methods and simulation tools could be combined in a single model. This leads to the use of the so-called multimodels. The most effective approach to creating such models is probably the use of object-oriented design and programming. In the following, we present an object-oriented framework for creating heterogeneous multimodels (Fishwick and Zeigler, 1992; Ra´bova´ and Peringer, 1998; Victor and Fishwick, 1995) based on several different paradigms and tools.
2. The methodology of model design The methodology of multimodel design we propose is based on the main principles of object orientation, which include encapsulation, abstraction, hierarchy, and modularity. Apart from that, we employ parallelism quite often. The other concepts, such as typing or persistence, can also be exploited, but they are not substantial. The most important concept we use is probably the concept of encapsulation. This concept allows for hiding implementation details of parts of models (submodels). It is then possible to easily change the underlying implementation of submodels without changing the other parts of the model This work has been done within the project CEZ:J22/98: 262200012 Research in Information and Control Systems and also supported by the Grant Agency of Czech Republic grants No. 102/01/1485 Environment for Development, Modelling, and Application of Heterogeneous Systems.
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provided that the interface of the submodel remains intact. The submodel provides its behavior and not the way this behavior is achieved. This is the main contribution of object-orientation for a simple and flexible model description. The mechanism of encapsulation can also be used to reflect the level of our knowledge. We can encapsulate some uncertain information if we cannot describe the corresponding phenomenon exactly. To describe the process of creating and simulating models we use the standard terms: .
A model defines the structure and functionality of a system.
.
An environment of a model is connected to the input/output interface of the model.
.
A simulator provides a background for an implementation of the behavior of a model and the environment surrounding it.
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An experiment controls the process of simulation over a model (including some initialization, observing states of the model, terminating the simulation, etc.).
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A computing environment is a tool for implementing a model and experiments over it. We use the underlying computing environment of a suitable programming language (for example Smalltalk, Prolog) implemented in some operating system.
To make the process of creating simulation models faster we propose using a predefined set of basic concepts directly implemented in the applied simulation system. These concepts (we call them “simulation abstractions”) provide basic blocks for building models together with methods suitable for using the blocks – they are “design patterns” (Gamma et al., 1995) developed for simulation purposes. The abstractions solve some well-defined and frequently encountered problems and thus make the process of model design easier. We have defined the following categories of simulation abstractions: .
model abstractions – abstractions for describing models
.
environmental abstractions – abstractions covering the simulator, model control, and I/O
.
abstractions for describing experiments – simulation control, model initialization, etc.
The set of basic simulation abstractions can be defined in various ways – it depends on the point of view and the level of our knowledge. Different areas of interest use different tools for describing the systems they are dealing with, however, it is possible to find some basic concepts which are common to all or at least most of the areas. Such concepts we use for a definition of the set of basic simulation abstractions.
It is obvious that every set of predefined abstractions will usually be incomplete – this naturally corresponds with the fact that the human knowledge of a given area is usually incomplete, as well. Because of this limitation, it is important to allow for adding new extensions to the basic set – the system of basic abstractions should be open. Easy extendibility is one of the main advantages of using object-oriented modelling and simulation tools. New modelling and simulation concepts and tools can be created in the way known from the area of software engineering. (1) Analysis of requirements to be met by a new tool and analysis of all the available existing tools. We should get all the available knowledge and prepare it to be used within the next steps of creating the new tool. (2) Design of the simulation system and the corresponding set of simulation abstractions. (3) Implementation in a chosen underlying programming language. (4) Testing the simulation system and verifying the basic abstractions. The architecture of models based on objects communicating via message sending allows us to combine different modelling paradigms and tools based on them. It is only required that these tools must somehow support the objectoriented style of communication via message sending. Thus it is possible to consider combining parts of models described by Smalltalk classes with parts of models described by fuzzy logic, object-oriented Prolog databases, or objectoriented Petri nets (OOPNs). In the following sections, we briefly describe several interesting paradigms and tools belonging to our framework for multimodelling.
3. SIMLIB Many simulation languages have been developed for the purpose of modelling and simulation, but only a few are widely used. These languages provide tools for an effective description of dynamic behavior and structure of model objects. This makes simulation model implementation and verification easier. But design, implementation, and maintenance of the simulation language compiler is difficult. When we need to do some changes in language specification or to add some functions, we must change the compiler of the language and the underlying library. The solution of these problems can be quite simple. We choose a general-purpose programming language, and we use it for modelling and simulation. Because of the aforementioned reasons, we decided to use C++ programming language and the principles of object-oriented programming (OOP). The model is a group of objects, which are linked together. Its structure can be modified according
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to the dynamic description of the relations between the system elements, which will lead to greater flexibility in model formulation. The description of models in C++ is not difficult if we use the subset of the language and predefined classes of objects. To simplify a model description we developed the simulation library (SIMLIB). This library contains: (1) functions for the simulation experiment control (2) standard classes for .
process and event description
.
discrete model objects (Queue, Facility, Store)
.
continuous blocks (Integrator, Relay, . . .)
.
objects for collection of statistical data
(3) standard functions (4) standard variables and objects (Time) (5) functions for output (6) pseudorandom number generators. The simulation experiment control is described in C++ main function. It is possible to proceed any number of simulation runs with any parameters. The general pattern of simulation experiment description is as follows: int main ( ) { , global_initialization . // experiment 1 Init( , start_time ., , end_time . ); , initialization_of_simulation_run1 . Run ( ); , outputs_after_run . // other experiments. . . , global_results_output . } Global initialization is a place for input and output files initialization, and any other initialization, which should be done once for all experiments. The standard function Init sets the time interval of simulation and initializes subsystem for simulation control. The Run function starts and executes a simulation experiment. After the end of the simulation it is possible to print
results or to do any other evaluation of experiment. The sequence of Init, initialization, Run, and results evaluation can be repeated. The main goal of simulation is to gain some information on the model. For this we need a means for collection of statistics and other information. The C++ language has – except for parallelism – all the features necessary for simulation models description. Discrete part of the model may be described by events or by processes. Blocks are used for continuous part description. It is possible to add the definition of the communication between the continuous and discrete parts of the model. To implement parallelism it is necessary to use the model behavior description either by events (which may not be interrupted) or by processes (which may be interrupted). The simulation library allows to unify the description of the behaviour of continuous and discrete system elements into a single class description. The implementation of combined models will resemble the structure of the real system.
4. Tools supporting a knowledge-based simulation An incomplete description, complexity, and variability are usual causes which can lead to using knowledge-based methods for describing models (Hruby´ et al., 2001). There are many similarities between knowledgeengineering and simulation modelling – the process of designing models and the process of creating knowledge-bases are similar. Simulating a model can then be viewed as an inference in a rule-based representation of a model. In the area of knowledge-based simulation, we can use a Prolog interpreter connected to other parts of model via TCP/IP sockets. Alternatively we can use C++ or Smalltalk extended with a class Prolog. This class allows a knowledge-based definition of a model. An object-oriented implementation of the Prolog interpreter as an instantiable class in Smalltalk or C++ giving us some benefits. (1) We can create several objects (instances of the class Prolog) and each can contain a different knowledge-base and solve different problems. (2) It is possible to call a C++ or Smalltalk code from within a Prolog instance and vice-versa. In a model, this mechanism can be used for scheduling and invoking simulation events. (3) Encapsulated Prolog objects can inherit databases on other encapsulated Prolog objects. This allows for a specialization of knowledge-based models implemented in Prolog. (4) Prolog objects further offer the possibility of creating self-modifying models.
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5. Using object-oriented petri nets The OOPN formalism (Cˇesˇka and Janousˇek, 1997) is characterized by a Smalltalk-based object orientation enriched by concurrency and polymorphic transition execution, which allow for message sending, waiting for and accepting responses, creating new objects, and performing primitive computations. OOPNs are especially suitable for modelling control structures which entail concurrency, nondeterminism, and conflicts. OOPNs can be processed in a special simulator based on Smalltalk or Prolog. Alternatively, OOPNs could be compiled into their Prolog representation and subsequently simulated in SIMLIB/C++ using its class Prolog (this solution is, however, hardly recommendable because of its poor performance). The interoperability between OOPNs and Prolog, as well as between OOPNs and Smalltalk, is possible due to the fact that OOPNs have communication mechanisms compatible both with Prolog predicate invocation, as well as with traditional object-oriented message sending. 6. Application – the expert simulator In this section, we attempt to show applicability of the SIMLIB, OOPNs and knowledge-based system represented by Prolog for modelling in a heterogenous environment. We have choosen an expert simulator, which has been proposed to serve as a common example of use of simulation methods, Petri nets and expert systems. The expert simulator allows a student to simulate an evolution of his/her study and as well as allows to select an optimal way to graduating by given criterias in relation to the student. The general structure of the expert simulator is shown in Figure 1. The three main parts of the expert simulator are distinguished below: (a) a model designed by means of the object-oriented Petri nets (OOPNs); (b) an expert system which provides controlling of the model and (c) a user interface.
Figure 1. Structure of the expert simulator
The model is simulated step by step, the expert system determines a transition which is fired in next step. It makes a decision by informations about a state of a simulation, a knowledge base and simulations from the student. The expert simulator has to satisfy some requirements: .
sufficiently precise simulation of the study evolution
.
interactive communication between the student and the simulator
.
prediction of supposed evolution of study in reference to given conditions
.
using a study model by means of OOPNs
Suppose the expert system is implemented in Prolog, the model of study is represented by OOPNs and the complete simulator is controlled by means of SIMLIB discrete processes. The expert system consists of a knowledge base, a control part and Prolog representation of the OOPNs model. OOPNs use a unification of arc expressions with marks of places as well as Prolog uses a unification to resolve desired goals. This feature facilitates an implementation of OOPNs in Prolog and allows a natural interconnection of OOPNs with the expert system. Now, we demonstrate how the places and transitions can be realized in Prolog. The place is a passive element of Petri nets, hence it can be represented by fact in Prolog. The transition is an active element, hence its representation is more complicated. There is an example how to represent the transition t in Prolog: firable(t, [X1, X2, . . ., Xn]):precondition, guard. fire(t, [X1, X2, . . ., Xn]):remove_marks, action, postcondition. The predicate firable investigates with the fireability of the transition t. The predicate fire executes the transition t. Both predicates realizes necessary actions to a simulation of OOPNs. There is an example how to define the simulation of OOPNs and the expert syste´m in next following predicates: simstep(ok):get_all_firable(List), List\ ¼ [ ], expert_selection(List,[Trans, Marks]),
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fire(Trans, Marks). simstep(blocked):write(‘Net is blocked’).
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Figure 2. An example of a method start
In each step, we have to get a list of firable transitions (a predicate get_all_firable ). The conditions of firability are consulted with the expert system, which determines a transition (a predicate expert_selection ). Then, this transition is fired by predicate fire. The OOPNs model defines a structure and actions of study. The exemplary model only consists of a class BcStudy, which represents B.Sc. study, for simplicity. A simulation starts by method start (Figure 2), which determines actions that the student has to perform. We can distinguish three actions of study: preliminate examination, study itself and final examination. The model implements second part of study by method study (Figure 3). The SIMLIB part of the expert simulator provides a run of the simulation, data acquisition etc. It allows the (quasi)parallel run of more simulations (by means of processes). Each simulation can be executed in different criterias and the evolution of the study. The process provides a communication with the expert system by means of an object derived from the SIMLIB class Prolog.
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Figure 3. An example of a method study
7. Conclusions Modelling and simulation of complex systems often requires different modelling paradigms and tools to be exploited at the same time. The principles of object-orientation allow us to propose a consistent framework for this kind of modelling leading to the so-called multimodels. Within the above proposed framework, we integrate Smalltalk-based classical simulation components, with fuzzy description, applying the knowledge-based approach, and using Petri nets. Within our future research, we would like to make our framework for creating multimodels even more consistent and would also like to increase its performance. We intend to exploit the interoperability features offered by the technologies like CORBA or HLA (HLA). It is also necessary to create and offer the modellers some higher-level and more comprehensive simulation abstractions based on the presented paradigms and tools.
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References Cˇesˇka, M. and Janousˇek, V. (1997), “A formal model for Object-Oriented Petri Nets modeling”, Advances in Systems Science and Applications, An Official Journal of the International Institute for General Systems Studies, Special Issue, pp. 119-24. Fishwick, P.A. and Zeigler, B.P. (1992), “A multimodel methodology for qualitative model engineering”, ACM Transactions on Modeling and Computer Simulation, Vol. 2 No. 1, pp. 52-81. Gamma, E., Helm, R., Johnson, R. and Vlissides, J. (1995), Design Patterns: Elements of Reusable Object-Oriented Software, Addison-Wesley. Hruby´, M., Peringer, P. and Ra´bova´, Z. (2001), “Knowledge-based simulator in object-oriented environment”, Proceedings of MOSIS 2001, MARQ Ostrava, Hradec nad Moravici´, s. 75-80, ISBN 80-214-1860-5 . High Level Architecture, a general purpose architecture for simulation reuse and interoperability, http://hla.dmso.mil/ Ra´bova´, Z. and Peringer, P. (1998), “Heterogeneous models”, Proceedings of ECI’98, SAV, Herlany, Slovak Republic. SIMLIB, http://www.fee.vutbr.cz/peringer/SIMLIB Victor, T. and Fishwick, P.A. (1995), “Hybrid heterogeneous hierarchical models for knowledgebased autonomous systems”, International Journal of Computer Simulation, Vol. 5 No. 3, pp. 209-27.
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Optimal control of variational inequalities
Optimal control and approximation of variational inequalities
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Hrubina Kamil Department of Informatics, Mathematics and Physics, University of Technology in Kosˇice with a seat in Presˇov, Presˇov, Slovak Republic
Jadlovska´ Anna Department of Cybernetics and Artificial Intelligence, Technical University of Kosˇice, Kosˇice, Slovak Republic Keywords Cybernetics, Control systems, Approximation concepts Abstract The paper deals with the problems of numerical approximation of the variational inequalities solution which occur in the optimal control problems. The Ky Fan-Sion theorem of the saddle point is used for the solution of variational inequalities. The theoretical results form the basis for the algorithms creation.
1. Introduction Problems of numerical methods algorithms creation of approximation of the variational inequalities solution which occur in the problems of optimal control in the field of physics and mechanics as well as errors estimation are still topical. The paper deals with stationary inequalities for the solution of which the theoretical results of the Ky Fan-Sion theorem of the saddle point are used. The main goal of the paper is to present the theoretical basis for the solution of defined variational inequalities. The paper was worked out as a part of solution of the scientific project “The Application of Logistics in the System of Manufacturing Control and Training”, number 1/7089/20. 2. The problems formulation Denotations of spaces, operators, . . . used in this paper is in accordance with the works of Ce´a (1971) and Lions (1968, 1972). Let V and H be the two Hilbert spaces on R and let us denote the norms as k·kV and k·kH and the corresponding scalar products as (.,.)V and (.,.)H. Let V , H ; injective representation from V to H be continuous and V be dense in H, i.e. there exists such a constant c, that jvj # ckvk:
ð1Þ
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We will identify the space H with its dual space. Let us denote by means of V the space dual to V0 . Then H can be identified with some subspace in V 0 : V , H , V0
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ð2Þ
where every space is dense in the following one with the continuous map. Let aðu; vÞ be a bilinear form on V, continuous and coercive, i.e. 2
aðu; vÞ $ akvk ;
a . 0;
;v[V
ð3Þ
Bilinear form a(u, v ) need not be symmetric. If V ¼ H ¼ V 0 are finitedimensional spaces, then aðu; vÞ ¼ ðAu; vÞ; where A is a matrix. The condition of coercive intensity in this case is equivalent to the inequality A þ A* $ 2aI ; where I is the unit matrix. Let L be a continuous linear form on V. According to equation (2) LðvÞ ¼ ð f ; vÞ;
f [ V0
ð4Þ
where we have denoted ( f, v ) the scalar product of the elements f [ V 0 and v [ V (which integrate with the dot product in H, when f [ H , i.e. ( f, v ) is the value of the functional f [ V 0 in the element v [ V ). Theorem 1. If the conditions (3) are satisfied, then for given f [ V 0 there exists the unique element y [ V , for which
aðy; cÞ ¼ ðf ; cÞ ;c [ V
ð5Þ
The equation (5) can be expressed in the following way: as the form v ! aðu; vÞ is linear and continuous on V we can write the following
aðu; vÞ ¼ ðAu; vÞ Au [ V 0
ð6Þ
A [ LðV ; V 0 Þ:
ð7Þ
that defines the operator
Thus, the equation (5) is equivalent to the equation A y¼f
ð8Þ
Now, we can formulate the first optimal control problem. Let us have the following: the space of controls U – the Hilbert space ðU ¼ V Þ and the representation B [ LðU ; V 0 Þ
ð9Þ
Let us consider the system (physical, electrical, mechanical, . . .), which is described by the well-known operator A [ LðV ; V 0 Þ:
For each control u [ U the state y of the system will be defined by the solution of the following equation A y ¼ f þ Bu;
y[V
It is evident that y depends on u, and hence denoted as y(u ). Thus, A yðuÞ ¼ f þ Bu;
yðuÞ [ V :
1403 ð10Þ
In addition, we consider the observation: zðuÞ ¼ C yðuÞ
ð11Þ
where C [ LðV ; H Þ; H is the Hilbert space. Finally, let us have positive definite Hermitean operator: N [ LðU ; U Þ; ðNu; uÞU $ vkuk2U ;
v . 0;
ð12Þ ;u [ U
Each control u [ U corresponds to the value of criterion function J ðuÞ ¼ kCyðuÞ 2 zd k2H þ ðNu; uÞU
ð13Þ
where zd is a given element of the space H. Let the set Up be convex and closed in U, (Up is a set of feasible controls). The optimal control problem consists in finding of such a control u [ U p that the criterion function will obtain the following value: J ðuÞ ¼ inf J ðvÞ v[U p
ð14Þ
under the condition of the equation (10) satisfaction. We are going to introduce the theorem which characterizes the optimal control and provides the functional equations and inequalities for the optimal control problem. From the work (Hrubina, 1992) it can be seen that these equations can be solved by iterative algorithms after their previous transformation. Before the theory of the state space application let us introduce once again the definition of the adjunct operators A*, B*, C* and LU. Let A* [ LðV ; V 0 Þ be the operator adjunct to A, let us define the adjunct state pðvÞ [ V ; which is the solution of the following equation: A* pðvÞ ¼ C* LðCyðvÞ 2 zd Þ
Optimal control of variational inequalities
ð15Þ
Let H 0 be the dual space to H and L ¼ LH be the canonical isomorphism from H on H 0 (we are dealing with the representation L : H ! H 0 where each
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element h [ H corresponds to the element Lh ¼ ðh; :ÞH [ H 0 , where (L, h, g ) is the value of the functional h in the element g, for ;h; g [ H ). Then, let B* [ LðV ; U 0 Þ be the operator adjunct to B, U 0 be the dual space for U and LU be the canonical isomorphism from U on U 0 . Theorem 2. Let the conditions (3) be satisfied and let the criterion function be expressed in the form (13). The satisfaction of the following equations and inequalities: A yðuÞ ¼ f þ Bu A* pðvÞ ¼ C* LðCyðvÞ 2 zd Þ; ðL21 u B* pðuÞ þ Nu; v 2 uÞU $ 0
ð16Þ
;v [ U p
is necessary and sufficient condition for the element u [ U p to be the optimal control. If the operator N satisfies the condition (12), then the optimal control is unique (i.e. the unique element u [ U p satisfies the equations (10), (15), and (16), (Hrubina, 1993a, b). The other problems of optimal control of the systems which deal with the inequalities are formulated in the works (Hrubina, 1993a, b, 1992). 3. Stationary variational inequalities We will consider the variational inequalities in the following two tasks: (1) to find such u [ K that
aðu; v 2 uÞ þ jðvÞ 2 jðuÞ $ ð f ; v 2 uÞ;
;v [ K
ð17Þ
;v [ K
ð18Þ
(2) to find such u [ K that
aðv; v 2 uÞ þ jðvÞ 2 jðuÞ $ ð f ; v 2 uÞ;
where aðu; v 2 uÞ is a bilinear form on V, continuous and coercive equation (3), j(v ), j(u ) are convex functions and K is a convex closed, nonvacuous space in V. Lemma 1. The tasks 1, 2 are equivalent: the solution of one task is the solution of the second task and vice versa. Lemma 2. If a(u, v ) is a bilinear form, coercive, so a(v, v ) is a convex function. Let us write Lðu; vÞ ¼ aðu; v 2 uÞ þ jðvÞ þ jðuÞ 2 ð f ; v 2 uÞ;
u [ K;
v[K
ð19Þ
We can show that L(u, v ) satisfies the assumptions of the Ky Fan-Sion theorem.
Optimal control of variational inequalities
Theorem 3. (Ky Fan-Sion). Suppose that the following is given: V and L two separate topological vector spaces, U compact and convex subset V, L L u ! Lðu; mÞ v ! Lðv; mÞ Statement
compact and convex subset L, such representation from U £ L to R that satisfies: concave and semi-continuous downwards representation ;v [ U convex and semi-continuous upwards representation ;m [ L: there exists such m, l [ U £ L that Lðu; mÞ # Lðu; lÞ # Lðv; lÞ;
;v; m [ L £ L
ð20Þ
If, in addition, we suppose that K is a constraint space, then the Theorem 3 guarantees the existence of the saddle point of the function L(u, v ) on K £ K: Let us define the next problems which are equivalent: Problem 3 (the saddle point problem) We have to find such ðu; vÞ [ K £ K that Lðu0 ; vÞ # Lðu; vÞ # Lðu; v0 Þ;
;ðu0 ; v0 Þ [ K £ K
ð21Þ
Problem 4 (the minimax problem) We have to find such a pair ðu; vÞ [ K £ K that Lðu0 ; vÞ ¼ min max Lðu0 ; v0 Þ Lðu; vÞ ¼ max 0 0 0 u [K
v [K u [K
ð22Þ
Problem 5 (the maximin problem) We have to find such ðu; vÞ [ K £ K that Lðu; v0 Þ ¼ max min Lðu0 ; v0 Þ Lðu; vÞ ¼ min 0 0 0 v [K
u [K v [K
ð23Þ
4. Algorithms According to (Alexejev et al. (1991), Ce´a (1971), Hrubina (2001), Hrubina et al. (1999), Obonˇa (1990), Za´da (1999) we can apply the procedure for the approximation of the solution in the space K or V, where K ¼ V ; forms a(u, v ), j(v ) and f. We will evidently apply the theorem for the convergence (weak, strong).
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The task is to find u [ K; K is closed convex space from the Hilbert space V, where
aðu; v 2 uÞ $ ðf ; v 2 uÞ;
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;v [ K
ð24Þ
where a(v, v2u ) is a continuous and coercive bilinear form which need not be symmetrical. 4.1 The Cauchy algorithm (1) The case without constraints ðK ¼ V Þ In order to find the solution we are going to create the sequence {un} where u0 is known, from the relationship unþ1 ¼ un 2 6LðAun 2 f Þ
ð25Þ
it follows unþ1 2 u ¼ un 2 u 2 6LAðun 2 uÞ Let us write 1n ¼ un 2 u:Then k1nþ1 k2 # k1n k2
ð1 2 2a6 þ M 2 r 2 Þ
ð26Þ
where a is the constant of coercive intensity, the convergence is guaranteed when the following condition is satisfied: 0,6,
2a : M
(2) The case with constraints ðK – V Þ PK will be called the operator of projection on K. We will define such a sequence {un} (u0 is given) that unþ1 ¼ P K ½un 2 6LðAun 2 f Þ
ð27Þ
We can obtain the relationship 2
kunþ1 2 un k # kP K ½un 2 6LðAn 2 f Þ 2 P K ½u 2 6LðAu 2 f Þ k
ð28Þ
where PK is the operator of contraction. 4.2 Algorithm for the solution of asymmetrical inequalities The task is to find such a solution u; u [ K; (K is convex, closed in the Hilbert space V ) that
aðu; v 2 uÞ $ ðf ; v 2 uÞ;
ð29Þ
where aðu; v 2 uÞ is a coercive, continuous form which need not be symmetrical. Let us introduce that the form a(u, v ) is continuous, and so the operator A [ LðV ; V 0 Þ can be assigned as
aðu; vÞ ¼ ðAu; vÞ
ð30Þ
Let L be the canonical isomorphism from V0 to V, then ðAu; vÞ ¼ ðLðAu; vÞÞ kLkLðV 0 ;V Þ ¼ kL21 kLðV ;V 0 Þ ¼ 1 The inequality (29) can be expressed as follows: ððLðAu 2 f Þ; v 2 uÞÞ $ 0;
;v [ K
If the operator A is symmetrical, the inequality (29) is equivalent minðAv; vÞ ¼ 2ðf ; vÞ
ð31Þ
v[K
Minimum u is characterized (A* is the adjunct operator to A ) by the inequality ððA þ A* Þu; v 2 uÞ $ 2ðf ; v 2 uÞ
;v [ K;
or it is equivalent to the inequality (if A is symmetrical) ðAu 2 f ; v 2 uÞ $ 0;
;v [ K
Finally, we can say that if A is not symmetrical, we can not consider the problem (equation 29) as the problem of the form minimization (equation 31), (Ce´a 1971; Lions 1968, 1972). 5. Conclusion The purpose of this paper is to define problems which contain variational inequalities. For these inequalities solution the theorems, which are considered to be the theoretical basis for numerical approximation algorithms creation, are presented in this paper. References Alexejev, A. et al. (1991), Matematicka´ teorie optima´lni´ch procesu˙, CˇSAV, Academia Praha. Butkovskij, A.G. (1975), Metody upravlenija sistemami s raspredelenymi parametrami, Nauka, Moskva. Ce´a, J. (1971), Optimisation, the´orie et algorithmes, Dunod, Paris. Ekeland, I. and Teman, K. (1976), Convex Analysis and Variational Problems, New York.
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Hrubina, K. (1992), “Optimal control problems for systems with distributed parameters and their solution using algorithms of numerical methods”, Elektrotech. cˇasopis, Vol. 6 No. 43, pp. 187-92. Hrubina, K. (1993a), “Solving optimal control problems for systems with distributed parameters by means of iterative algorithms of algebraic methods”, Kybernetika a informatika, Vol. 6 No. 1, pp. 48-64. Hrubina, K. (1993b), “Optimum control problems for systems with distributed parameters and their solution using the finite element method algorithm”, Elektrotechn. cˇasopis No. 1, pp. 11-20. Hrubina, K. et al. (1999), The Application of Informatics in the System of Manufacturing Control and Training, Informatech Ltd, TU Kosˇice-Presˇov, Project No. 1/4331/97, p. 298. Hrubina, K. (2001), “Algorithms of numerical methods and their application to the solution of optimizing problems”, Mathematical Modelling of Technical Processes, Informatech Ltd, Kosˇice, ISBN 80-88941-18-0 pp. 7-62. Jadlovska´, A. (2000), An Optimal Tracking Neuro-Controller for Nonlinear Dynamics Systems, ISBN 00-08-0435467 Elsevier Science, Pergamon, pp. 483-8. Lions, J.L. (1968), Controˆle optimal de syste´mes gouverne´s par des equations aux derives partielles, Dunod, Qauthier-Villars, Paris. Lions, J.L. (1972), “On the optimal control of distributed parameter systems”, in Balahrishnan, A. (Ed.), Techniques of Optimization, Academic Press. Obonˇa, J. (1990), Syste´my a syste´mova´ analy´za v praxi, 274 s. ISBN 80-05-00104-5, Alfa, Bratislava. Za´da, V. (1999), “O jedne´ univerza´lni´ metodeˇ optima´lni´ho rˇ´izeni´”, Cˇasopis Automatizace, 42, cˇ. 1, s. 18-25.
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Thorough numerical entropy analysis of some substitutive sequences by lumping
Numerical entropy analysis by lumping 1409
K. Karamanos Centre for Nonlinear Phenomena and Complex Systems, Universite´ Libre de Bruxelles, Boulevard du Triomphe, Brussels, Belgium
I. Kotsireas Department of Physics and Computing, Wilfrid Laurier University, Waterloo, Ontario, Canada Ontario Research Centre for Computer Algebra, University of Western Ontario, London, Ontario, Canada Keywords Cybernetics, Entropy, Analysis Abstract In this work we perform a detailed entropy analysis of some substitutive sequences using the technique of lumping. The basic novelty of the entropy analysis by lumping is that, unlike the Fourier transform or the conventional entropy analysis by gliding, it gives results that can be related to algorithmic aspects of the sequences and in particular with the important property of automaticity. All computations in this paper have been performed with TOOLS FOR SYMBOLIC DYNAMICS a Maple package developed by the authors.
Introduction Nature provides us with a wide variety of symbolic strings ranging from the sequences generated by the symbolic dynamics of nonlinear systems (Ebeling and Nicolis, 1991, 1992; Karamanos, 2000, 2001c; Karamanos and Nicolis, 1999; Nicolis, 1991, 1995; Nicolis and Gaspard, 1994) to the RNA and DNA sequences or the DLA patterns (Bai-Lin, 1994; Nicolis and Gaspard, 1994; Schro¨der, 1991). The study of a particular class of symbolic sequences coming from the world of Theoretical Computer Science, namely the substitutive sequences, The authors are indebted to Professors J.-P. Allouche and G. Nicolis for illuminating discussions and support. KK has been a NATO Fellow for the last three academic years and is currently a Van Buuren Foundation Fellow and a Petsalys-Lepage Foundation Fellow. IK would like to thank the Center of Nonlinear Phenomena and Complex Systems (CENOLI ) of ULB for the kind invitation to Brussels, as well as the Ontario Research Centre for Computer Algebra (ORCCA) for supporting this collaboration. The authors would also like to thank the Center of Symbolic Computation (CSO ) of the ULB, where a first version of the computational platform has been developed. This work has been supported in part by the Poˆles d’Attraction Interuniversitaires program of the Belgian Federal Office of Scientific, Technical and Cultural Affairs, the Ontario Research and Development Challenge Fund and the Natural Sciences and Engineering Research Council of Canada.
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has attracted considerable interest recently (Allouche, 1994, 2000; Allouche and Mende`s France, 1995; Allouche and Shallit, 1999; Cobham, 1972; Dokking, 1978; Ferenczi, 1995; Grassberger, 1986; Karamanos, 2001a, b; Queffe´lec, 1987, 1995; Schro¨der, 1991; Sloane, in preparation). A substitutive sequence oven a finite alphabet is defined by a set of substitutions, one for each letter, starting with one letter of the alphabet (Queffe´lec, 1987).
Discussion and analysis One very interesting class of substitutive sequences are the automatic sequences, more precisely the m-automatic sequences where m is an integer. A finite automaton with m-states can generate an m-automatic sequence. An important theorem stated by Cobham (1972) asserts that m-automatic sequences can be generated in an equivalent manner by a set of substitutions of length m, plus a letter-to-letter projection. Entropy-like quantities are a very useful took for the analysis of such sequences. Of special interest are the block entropies, extending Shannon’s classical definition of the entropy of a single state to the entropy of a succession of states (Karamanos and Nicolis, 1999; Khinchin, 1957; Nicolis and Gaspard, 1994). In particular, it has been shown that the scaling of the block entropies with length gives sometimes interesting information on the structure of the sequence (Ebeling and Nicolis, 1991, 1992; Karamanos, 2001b; Karamanos and Nicolis, 1999; Nicolis and Gaspard, 1994). Karamanos and Nicolis (1999) have examined how the estimation of the block entropies may actually depend on the method of reading, that is on the observer. This has immediate consequences on the “decoding” procedure, as different values of the block entropies mean different kinds and amounts of information extracted by the symbolic sequence. By using lumping, we have established a new decimation scheme for the symbolic dynamics of the Feigenbaum attractors of unimodal maps (Derrida et al., 1978; Metropolis, et al., 1973). The coarse-grained statistical properties of the attractors have been subsequently derived, with emphasis on the behavior of the block entropies. Lumping is the reading of the symbolic sequence by “taking portions”, as opposed to gliding where one has essentially a “moving frame”. Notice that gliding is the standard convention in the literature. Reading the symbolic sequence in a specific way is also called decimation of the sequence. The importance of the distinction between gliding and lumping codes in Genetics has been recognized very early by Crick et al. (1961) and also Lewin (1997) (called at that time overlapping an non-overlapping codes). As mentioned by Karamanos and Nicolis, (1999), the realization that the kind and the amount of information of a given symbolic sequence may depend on the way of reading brings symbolic dynamics closer to natural languages, in which the existence of distinct privileged words conveying a precise ‘meaning’ is crucial.
Moreover, Berthe´ (1994) has shown that the estimation of the (conditional) Numerical block entropies with the usual recipe of gliding cannot help us distinguish entropy analysis between sequences with different spectral properties and different levels of by lumping complexity. A similar situation arises in the quite different context of Supramolecular Chemistry, where certain inorganic molecules become capable of performing 1411 pattern recognition (Lehn, 1995). The inorganic “skeleton” of the macromolecule is then “read” by the molecules of its environment due to stereochemical interactions. This type of “reading” corresponds essentially to “lumping” as dealt with in the present paper. In the light of these results, we have tried to invent some criteria which could illuminate the structure of a symbolic sequence and give us some more specific information beyond the one provided by block entropies computed by gliding. In fact, we have derived an entropy criterion for the specific, yet quite important algorithmic property of automaticity of the sequence. We recall here the main result of the entropy analysis by lumping, see also Karamanos (2001a, b). Let m k be the length of a block encountered when lumping, H(m k) the associated block entropy. The following property then holds. If the symbolic sequence ðun Þn[N is m-automatic, then ’ ko [ {0; 1};
m [ N* ;
; k $ k0 :
H ðm ko Þ ¼ H ðm k Þ
ð1Þ
when lumping, starting from the beginning of the sequence. The meaning of the previous proposition is that for m-automatic sequences there is always an envelope in the diagram H(n )/n versus n, falling off exponentially as , m 2 k for blocks of length m k, k ¼ 1; 2; . . . For infinite ergodic strings, the conclusion does not depend on the starting point. Similar conclusions hold if instead of an one-to-one letter projection we have an one-tomany letters projection of constant length. In particular, we have the following result. If the symbolic sequence ðun Þn [ N is the image of the fixed point of a set of substitutions of length m by a projection of constant length m, then ’ ko [ {0; 1};
m [ N* ;
; k $ ko :
H ðm·m ko Þ ¼ H ðm·m k Þ
ð2Þ
when lumping, starting from the beginning of the sequence. Our propositions give an interesting diagnostic for automaticity. When one disposes of an unknown symbolic sequence and applies numerically the entropy analysis by lumping, then if the sequence does not obey such an invariance property predicted by the propositions, it is certainly non-automatic. In the opposite, if one observes the adequate invariance property, then the sequence is a candidate to be automatic. According to the propositions mentioned above it is interesting to study the evolution of H(n )/n as n increases, for an unknown symbolic sequence, in order to detect small-length automaticity. On the other hand, for a known
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symbolic sequence and in particular for a substitutive sequence, the abovestated propositions give only some invariance properties for some entropies, which is a partial result. One would need the complete diagram H(n )/n versus n for a better understanding of the behavior of the block entropies. These reasons led us to develop a Maple package called TOOLS FOR SYMBOLIC DYNAMICS . This package is intended to provide a set of tools to facilitate the analysis of the information content of symbolic sequences in order to: .
test theoretical predictions (especially the ones involving entropy-like quantities) up to a very high degree of accuracy,
.
perform efficiently different kinds of analyses to unknown sequences with the aim to discover potential patterns,
.
produce entropy graphs to help interpret the results.
A more detailed exposition of all the available features in TOOLS FOR SYMBOLIC is outside the scope of this extended abstract. The initial version of TOOLS FOR SYMBOLIC DYNAMICS has been written in Maple 5. Ports for both Maple 6 and 7 are currently available. The package may be used with both the text and the graphical interfaces of Maple. Using TOOLS FOR SYMBOLIC DYNAMICS we can perform entropy computations by lumping or gliding on known or unknown symbolic sequences over a finite alphabet with millions of terms, thus bypassing partially the well-known problem of combinatorial explosion (Ebeling and Nicolis, 1992). In this respect, the results presented here for substitutive sequences are a continuation of our recent papers (Karamanos, 2001a, b). The package TOOLS FOR SYMBOLIC DYNAMICS has indeed been tested in the analysis of various substitutive sequences (sequences generated by a set of substitution rules for each letter, over a finite alphabet) and the correctness of the relevant routines has been verified on large-scale computations. As a first test, we have examined by lumping the Feigenbaum symbolic sequence, much studied in the literature (Ebeling and Nicolis, 1992; Grassberger, 1986; Karamanos and Nicolis, 1999). This sequence can in an equivalent manner be generated by the Metropolis, Stein and Stein algorithm (Karamanos and Nicolis, 1999; Metropolis et al., 1973), or as the fixed point ðs F Þ1 ðRÞ of the set of substitutions of length 2: DYNAMICS
s F ðRÞ 2 RD; s F ðDÞ ¼ RR
ð3Þ
starting with R, or by a finite automation, (Karamanos, 2001a, b). According to our first proposition, for this sequence it holds H ð1Þ ¼ Hð2Þ ¼ . . . ¼ H ð2k Þ when lumping, and for any integer r,
ð4Þ
Hð2·rÞ ¼ H ðrÞ
ð5Þ
as shown by Karamanos and Nicolis (1999). The diagram H(n )/n versus n for this sequence as plotted with TOOLS FOR SYMBOLIC DYNAMICS is shown in Figure 1. It is also interesting to mention that for the special case of the Feigenbaum sequence, we have calculated theoretically (Karamanos and Nicolis, 1999), using a constructive step-by-step scheme the block entropies when lumping and related them to the block entropies when gliding. The results obtained with TOOLS FOR SYMBOLIC DYNAMICS for the wellstudied Feigenbaum sequence are quite impressive. One obtains in less than half an hour (30 min) a full entropy analysis until n ¼ 64 of the sequence for over two million terms (2,097,152), to be compared with an entropy analysis by lumping until n ¼ 32 for ten thousand terms (10,000) obtained by a more conventional program like ENTROPA in C++ (Basios, 1998).
Numerical entropy analysis by lumping 1413
Figure 1. Feigenbaum sequence
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Figure 2. Primitive and non-primitive chacon sequences
Moreover, it seems that the performances and limitations of our program compare well with other conventional methods of time series analysis. With TOOLS FOR SYMBOLIC DYNAMICS we also confirmed and deepened the understanding of a possibly new mathematical phenomenon associated with the entropy analysis of some “weakly mixing” ergodic sequences such as the primitive and the non-primitive Chacon sequence (see Figure 2 for the definitions) (Chacon, 1969; Ferenczi, 1995; Karamanos, 2001b; Queffe´lec, 1995; Sloane, in preparation). A similar phenomenon is observed for the AlloucheShallit sequence (see Figure 3 for the definition) (Shallit, 1996). Indeed, it seems that these sequences present a non-monotonic behaviour of the block entropies in an arithmetic progression of a certain number (this number being nine for the primitive and the non-primitive Chacon sequence, and eight for the Allouche-Shallit sequence). We hope that this is not a numerical artifact or an effect of bad statistics, but the real entropy behaviour of these sequences. In order to confirm this result, we undertook a large-scale computation to perform the entropy analysis of the non-primitive Chacon sequence for more than seven million (7,174,453) terms. This computation took almost 6 h. Clearly, more work is needed towards this direction. Moreover, it seems that the class of symbolic sequences for which the results for the block entropies when gliding and when lumping do not coincide contains not only the automatic sequences but also more general classes of sequences (as the non-primitive and the primitive Chacon sequences). A plausible conjecture first stated (Karamanos, 2001b) and tested further with TOOLS FOR SYMBOLIC DYNAMICS to a high degree of accuracy stipulates
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Figure 3. Allouche-Shallit sequence
that the block entropies when gliding establish an upper bound for the block entropies when lumping. To the author’s knowledge, the question of a functional relation between the block entropies when gliding and when lumping for an arbitrary sequence has not yet been addressed in the literature. It is clear that the entropy analysis by lumping of such a sequence with TOOLS FOR SYMBOLIC DYNAMICS can unveil substantial information on its algorithmic characteristics. References Allouche, J.-P. (1994), “On the complexity of infinite sequences”, Bull. Belg. Math. Soc., Vol. 1 No. 2, pp. 133-43. Allouche, J.-P. (2000), “Algebraic and analytic randomness”, in Planat, M. (Ed.), Noise, Oscillators and Algebraic Randomness, Lecture Note in Physics, Springer, 550, pp. 345-56. Allouche, J.-P. and Mende`s France M. (1995), “Automata and automatic sequences”, in Axel, F. and Gratias, D. (Eds), Beyond quasicrystals, Les Houches, Les E´ditions de Physique, and references therein Springer, pp. 293-367.
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Allouche, J.-P. and Shallit, J. (1999), “The ubiquitous Prouhet-Thue-Morse sequence”, Sequences and their Applications, Springer Ser. Discrete Math. Theor. Comput. Sci., Springer, London, pp. 1-16. Bai-Lin, H. (1994), Chaos, World Scientific, Singapore. Basios, V. (1998), ENTROPA program in C++, (c) Universite´ Libre de Bruxelles. Berthe´, V. (1994), “Conditional entropy of some automatic sequences”, J. Phys. A, Vol. 27, pp. 7993-8006, and references therein. Berthe´, V. (1995), “Entropy in deterministic and random systems”, in Axel, F. and Gratias, D. (Eds), Beyond quasicrystals, Les Houches, Les E´ditions de Physique, and references therein Springer, pp. 441-63. Burnows, B.L. and Sulston, K.W. (1991), “Measurement of disorder in nonperiodic sequences”, J. Phys. A, Vol. 24 No. 16, pp. 3979-87. Cassaigne, J. (1997), “Complexity and special factors”, Bull. Belg. Math. Soc., Vol. 4, pp. 67-88. Cobham, A. (1972), “Uniform tag sequences”, Math. Systems Theory, Vol. 6, pp. 164-92. Chacon, R.V. (1969), “Weakly mixing transformations which are not strongly mixing”, Proc. Amer. Math. Soc., Vol. 22, pp. 559-62. Crick, F.H.C., Barnett, L., Brenner, S. and Watts-Tobin, R.J. (1961), Nature, Vol. 192 (4809), p. 1227. Dokking, P.M. (1978), “The spectrum of dynamical systems arising from substitutions of constant length”, Zeit. Wahr., Vol. 41, p. 221. Derrida, B., Gervois, A. and Pomeau, Y. (1978), “Iteration of endomorphisms on the real axis and representation of numbers”, Ann. Inst. Henri Poincareˆ, Section A(N.S.), Vol. 29 No. 3, pp. 305-56. Ebeling, W. and Nicolis, G. (1991), Europhys. Lett., Vol. 14 No. 3, pp. 191-6. Ebeling, W. and Nicolis, G. (1992), “Word frequency and entropy of symbolic sequences: a dynamical perspective”, Chaos, Solitons and Fractals, Vol. 2 No. 6, pp. 635-50. Ferenczi, S. (1995), “Chacon transformations: combinatorics, geometric structure, relation with systems of complexity 2n+1”, Bull. Soc. Math. France, Vol. 123 No. 2, pp. 271-92. Grassberger, P. (1986), “Toward a quantitative theory of self-generated complexity”, Int. J. Theor. Phys., Vol. 25 No. 9, pp. 907-38. Karamanos, K. (2000), “From symbolic dynamics to a digital approach: chaos and transcendence”, in Planat, M. (Ed.), Noise, Oscillators and Algebraic Randomness, Lecture Note in Physics, Springer, 550, pp. 357-71. Karamanos, K. (2001a), “Entropy analysis of automatic sequences revisited: an entropy, diagnostic for automaticity”, in Dubois, D. (Ed.), Proceedings of Computing Anticipatory Systems 2000, CASY2000, AIP Conference Proceedings 573, pp. 278–284. Karamanos, K. (2001b), “Entropy analysis of substitutive sequences revisited”, J. Phys. A: Math. Gen., Vol. 34, pp. 1-11. Karamanos, K. (2001c), “From symbolic dynamics to a digital approach”, Int. J. Bif. Chaos, Vol. 11 No. 6, pp. 1683-94. Karamanos, K. and Nicolis, G. (1999), “Symbolic dynamics and entropy analysis of Feigenbaum limit sets”, Chaos, Solitons and Fractals, Vol. 10 No. 7, pp. 1135-50. Khinchin, A.I. (1957), Mathematical Foundations of Information Theory, Dover, New York. Lehn, J.M. (1995), Supramolecular Chemistry, VCH, Weinheim. Lewin, B. (1997), Genes, VI, Oxford University Press, New York.
Metropolis, N., Stein, M.L. and Stein, P.R. (1973), “On finite limit sets for transformations on the unit interval”, J. Comb. Theory Ser. A, Vol. 15, pp. 25-44. Nicolis, G. (1995), Introduction to Nonlinear Science, Cambridge University Press, Cambridge. Nicolis, G. and Gaspard, P. (1994), “Toward a probabilistic approach to complex systems”, Chaos, Solitons and Fractals, Vol. 4 No. 1, pp. 41-57. Nicolis, J.S. (1991), Chaos and Information Processing, World Scientific, Singapore. Queffe´lec, M. (1995), “Spectral study of automatic and substitutive sequences”, in Axel, F. and Gratias, D. (Eds), Beyond quasicrystals, Les Houches, Les E´ditions de Physique, and references therein Springer, pp. 369-414. Queffe´lec, M. (1987), “Substitution dynamical systems”, Spectral Analysis, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1294. Schro¨der, M. (1991), Fractals, Chaos, Power Laws, Freeman, New York. Shallit, J. (1996), “Automaticity. LV. Sequences, sets, and diversity”, J. The´or. Nombres Bordeaux, Vol. 8 No. 2, pp. 347-67. Sloane, N. The On-Line Encyclopedia of Integer Sequences, available electronically at http://www.research.att.com/njas/sequences/index.html
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The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/0368-492X.htm
Kybernetes 31,9/10
Mathematical bios Louis Kauffman
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Department of Mathematics, University of Illinois at Chicago, Chicago, IL, USA
Hector Sabelli Chicago Center for Creative Development, Chicago, IL, USA Keywords Chaos, Cybernetics Abstract In this paper we report on a mathematical pattern that we call bios, and its generation by recursions of bipolar feedback. Bios is a newly found form of organization, that resembles chaos in its aperiodic pattern and its extreme sensitivity to initial conditions, but has additional properties (diversification, novelty, nonrandom complexity, life-limited patterning, 1/f power spectrum) found in natural creative processes, and absent in chaos. The process equation At+1¼ At+gt sin(At) generates convergence to p, a cascade of bifurcations, chaos, bios and infinitation, as the value of the feedback gain gt increases. In the complex plane, series generated by orthogonal process equations display fractal organic patterns.
Defining bios Bios is a pattern that we have discovered through examining both mathematical recursions (Kauffman and Sabelli, 1998) and biological, meteorological and economic data (Carlson-Sabelli et al., 1995; Sabelli, 2000; Sabelli and Kauffman, 1999; Sabelli et al., 1997). As natural creative processes, bios is nonstationary aperiodic series that displays: (1) diversification [increased variance with the duration of the sample (Sabelli and Abouzeid, in press)]; (2) novelty meaning less recurrent than its randomized copy (Figure 1) (Sabelli, 2001a, b); (3) nonrandom complexity (Sabelli, 2002); (4) episodic patterns with a beginning and end (“complexes”), in contrast to random, periodic or chaotic series that show uniform configuration over time; and (5) global sensitivity to initial conditions; chaos is only locally sensitive. The statistical distributions of biotic series are multimodal and asymmetric, in contrast to symmetric random, periodic and chaotic series. We regard Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1418-1428. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443626
Supported by Society for the Advancement of Clinical Philosophy. We are thankful to Drs. A. Sugerman, L. Carlson-Sabelli, M. Patel, J. Konecki and J. Sween for useful discussions of this research.
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Figure 1. Recurrence plots of biotic series (top) and of its shuffled copy (bottom). Note the time-limited patterns (complexes) in bios, and the increase in recurrences with shuffling (novelty)
asymmetry as an essential component of creativity, because cosmological evolution can be understood as a sequence of symmetry-breakings. Other noteworthy properties of bios are the 1/f power spectrum and the generation of Mandala patterns in complement plots (Figure 2). As chaos, bios is aperiodic, deterministic, and extremely sensitive to initial conditions. Chaos is bounded (Kaplan and Glass, 1995); bios may be bounded or not. Diversification, novelty, nonrandom complexity, and episodic patterning are measurable properties found in bios and in creative natural processes, but not observed in random, periodic, or chaotic series. In contrast to simpler chaos, bios is creative. We thus regard bios as an authentically new phenomenon rather than as a subtype of chaos. The exemplar of bios is heart rate variation, just as the exemplar of chaos is turbulence.
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Process equations Bios is generated by the recursion Atþ1 ¼ At þ g sinðAt Þ
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where At are real numbers. We call this equation the process equation (Kauffman and Sabelli, 1998). It models interactions that produce both positive (augmenting, synergistic) and negative (decreasing, antagonistic) change. Change is a function of the previous action, i.e. a feedback. The feedback is bipolar and diverse, spanning the range from plus to minus g through the continuity of the trigonometric function; g is the feedback gain. The circle map, widely discussed in the literature, computes the same recursion modulo p (Kaplan and Glass, 1995). The circle maps does not produce bios. Interesting variants are the process equation with delay Atþ1 ¼ At þ g sinðAt21 Þ that generates biotic series very close to those found in heartbeat data (Sabelli, 1999), and the kinetic process equation (Sabelli and Kauffman, 1999)
Figure 2. Complement plot. Top: Biotic series generated by process equation with delay Atþ1 ¼ At þ g sinðAt21 Þ; g ¼ 3; rounded to the nearest integer. Bottom: Complement plot generated by plotting the sine (y axis) and the cosine (x axis) of each term in a Cartesian plane and connecting successive term. The circular form imposed on the data reveals a surprising regularity that reminds us of Mandala archetypes. This pattern also appears in series of heartbeat intervals (Sabelli, 2000) but not in chaos
Atþ1 ¼ At þ gt sinðAt Þ in which the gain is a function of time. We usually take g t ¼ kt; where k is a small constant and t is the number of iterations. As the gain gt increases, the time series generates equilibrium, a cascade of bifurcations forming 2n periods, chaos, and bios, a sequence of increasing complexity and amplitude (Figure 3). For g , 2; the equation converges to an odd multiple of p (e.g. p for initial values between 0 and 2p). As the gain is increased the fixed point becomes unstable. At g $ 2; a bifurcation generates asymmetric opposites that diverge as the gain increases. Of course, it is the computational error in the computer that allows the bifurcation to begin. If the computer were mathematically perfect, then the process would remain at the fixed point! Following the initial bifurcation, there is shift in each branch of the series that looks as a bifurcation in which only one outcome is visible (unifurcation). The polarity of the unifurcation can be reversed by changing k, the rate of increase in gain. As g increases a cascade of period-doubling bifurcations generates 2N periods, followed by a transition to chaos, analogous to that in the logistic equation Atþ1 ¼ g At ð1 2 At Þ: Initially, the chaotic regime overlaps with period 2, at variance with the description of mutually exclusive basins of attraction. “Period 2 chaos” can also be readily demonstrated in the logistic equation, although we are not cognizant of previous reports. Remarkably, we can experimentally verify that the bifurcation sequence of the logistic equation occurs inside the time series of the process equation (Figure 4). In the process recursion, however, we have the abrupt expansions never seen in logistic chaos. Process chaos is interspersed with periodicities, among which
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Figure 3. Time series generated by the kinetic process equation. Note logarithmic scale
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Figure 4. Detail of process chaos, showing period 2 chaos in which each branch shows a logistic pattern that ends with the expansion of chaos that appears to continue the virtual branch of the unifurcation. There are periods 6 before and after this expansion. After the unification of chaos (end of period 2), there is a narrow period 3, and a prominent period 4
period 6 and period 4 are prominent. In contrast, period 3 is prominent in logistic chaos. The range of At increases throughout the chaotic phase, but it remains within the basin of attraction, and is always smaller than the range of differences between successive terms. When the range reaches 2p ðg # 4:604Þ; the time series expands both positively and negatively, generating aperiodic biotic patterns resembling those observed with cardiac data. The range of At becomes much larger than DAt. This disproportion between long duration change and moment-to-moment differences distinguishes bios from chaos. The transition from chaos to bios is best visualized in cobweb plots (Figure 5). Aperiodic bios is periodically interrupted by bioperiod 2 when the gain equals odd multiples of p (half rotation). From this new pair of opposites, a new biotic phase emerges. Chaos does not show periodic repetitions of period 2. Bioperiods differ from other periods in being sensitive to initial conditions. Aperiodic bios also is periodically interrupted by flights toward positive or negative infinity (infinitation) when the gain equals an even multiple of p (full rotation) and at few other critical values. As g increases further, new biotic series emerge, and further infinitations follow – a mathematical metaphor for death and renewal, essential features of living processes. This sequence from one initial state, successive bifurcations, and the generation of complex chaotic and biotic patterns resembles cosmological evolution and embryological development. This series illustrates the greater creativeness of bipolar interactions, both synergic and antagonistic, in comparison to simple positive or negative feedback. Process development is very flexible, allowing any initial value, and any value or sign for the g
Mathematical bios
1423 Figure 5. Cobweb plots during chaos (top) and bios (bottom). Each trajectory is generated with a constant g. The sinusoidal envelope in the cobweb plot portrays the generator of the aperiodic biotic process. The plot has a dotted wavy figure that is the graph of y ¼ fðxÞ ¼ x þ g sinðxÞ where x denotes the horizontal axis and y denotes the vertical axis. We draw lines from (x, x ) to (x, f(x)) and from (x, f(x )) to (f(x ), f(x )). The iterates of the function f(x ) appear as the off-diagonal points in the cobweb
parameter, and generates biotic patterns beyond chaos. Logistic development requires initial values between 0 and 1, and flights into infinity after chaos.
Sensitivity and reversibility Bios, bioperiods, and infinitations show global sensitivity to initial conditions, meaning that the entire series is displaced by a small change in initial value (Figure 6 top). In chaos, initial conditions change the trajectory but not the overall distribution of the data (Figure 6 bottom). Bios, bioperiods, and infinitations also show extreme sensitivity to changes in the rate k of change of the gain. If the gain first increases and then decreases, the time series evolves from an initial steady state to greater complexity, and then devolves back to simpler patterns (Figure 7). If the series evolves up to chaos, a subsequent decrease in the gain leads back to the initial steady state. In
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Figure 6. Global sensitivity to initial conditions in bios (top) and infinitation (middle). Local sensitivity in chaos (bottom)
contrast, if the series reaches the biotic regime, a subsequent decrease in gain does not lead back to the starting point. One is tempted to relate this mathematical irreversibility of bios, absent in chaos, to the irreversibility of physical processes.
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Figure 7. Time series computed with a positive increment in gain for 15,000 iterations and then a negative value for k
Differencing bios, integrating chaos The time series of differences between successive members is chaotic. Biotic patterns in natural processes will be mistakenly identified as chaotic when data are differenced prior to analysis. Integrating chaotic series (logistic chaos, process chaos, shift map, sine map, Rossler, Ikeda, and Henon attractors) does not generate bios. One may generate bios-like series by integrating the Lorenz attractor, the chaotic series generated by Atþ1 ¼ g sinðAt Þ or Atþ1 ¼ g cosðAt Þ; or other chaotic series after rescaling them to mean 0. Integrated chaos shows diversification and novelty, but do not show time-limited complexes characteristic of mathematical bios and of biological or economic data.
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Co-creating equations The process equation models Heraclitus’ notion that the interaction of opposites generates evolution (Sabelli and Kauffman, 1999). To study the phenomenon of co-creation (Sabelli, 2001a, b), we are exploring systems of two, three and many interacting process equations. We find that circles of equations enter into stable chaos, while cascades of equations generate progressively more complex patterns. The recursion shown in Figure 8 Atþ1 ¼ At þ Bt cosðAt Þ Btþ1 ¼ Bt þ At sinðBt Þ is a self-contained two dimensional process consisting in two interlocked process equations where the gain of each equation is the output of the other equation. This mutuality gives rise to a very beautiful attractor (Sabelli, 1999). In the co-creating equations Atþ1 ¼ At þ g Bt sinðBt Þ Btþ1 ¼ Bt þ h At cosðAt Þ the gain and feedback of each recursion comes from the other one. For specific values as shown in Figure 9, we get a most extraordinary development of an organic-like pattern that displays fractal repetition at successive levels of magnification. In summary, biotic and organic patterns can be generated by simple equations that model bipolar and diverse opposition, suggesting how synergic and conflictual interactions in nature may contribute to creative evolution.
Figure 8. The Sabelli attractor (see text)
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Figure 9. The generation of organic forms by the interaction of two process equations. X axis: Atþ1 ¼ At þ 0:1 Bt sinðBt Þ: Y axis: Btþ1 ¼ Bt þ 0:01 At cosðAt Þ: Initial values A1 ¼ 6:3734761; B1 ¼ 0:001: The progressive development of complex pattern with iteration is presented in the sequence of XY graphs A, B, C, and D. Note how each larger pattern contains and repeats at a larger scale the previous ones (fractality)
References Carlson-Sabelli, L., Sabelli, H., Patel, M., Messer, J., Zbilut, J., Sugerman, A., Walthall, K., Tom, C. and Zdanovics, O. (1995), “Electropsychocardiography. Illustrating the application of process methods and chaos theory to the comprehensive evaluation of coronary patients”, Complexity and Chaos in Nursing, Vol. 2, pp. 16-24.
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Kaplan, D. and Glass, L. (1995), Understanding Nonlinear Dynamics, Springer-Verlag, New York. Kauffman, L. and Sabelli, H. (1998), “The process equation”, Cybernetics and Systems, Vol. 29, pp. 345-62. Sabelli, H. (1999), “Action creates bios”, in Ferrer, L. (Ed.), Proceedings of the 4th Systems Science European Congress, pp. 103-12. Sabelli, H. (2000), “Complement plots: analyzing opposites reveals Mandala-like patterns in human heartbeats”, International Journal of General Systems, Vol. 29, pp. 799-830. Sabelli, H. (2001a), “Novelty, a measure of creative organization in natural and mathematical time series”, Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 5, pp. 89-113. Sabelli, H. (2001b), “The co-creation hypothesis”, in Ragsdell, G. and Wilby, J. (Eds), Understanding Complexity, Kluwer Academics/Plenum Publishers, London. Sabelli, H. (2002), “Arrangement, a measure of nonrandom complexity”, J. Applied Systems Studies (in press). Sabelli, H. and Kauffman, L. (1999), “The process equation: formulating and testing the process theory of systems”, Cybernetics and Systems, Vol. 30, pp. 261-94. Sabelli, H., Carlson-Sabelli, L., Patel, M. and Sugerman, A. (1997), “Dynamics and psychodynamics. Process foundations of psychology”, J. Mind and Behavior, Vol. 18, pp. 305-34.
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On the reachable robustness limits for time delay control systems
Robustness limits for control systems 1429
L. Keviczky and Cs. Ba´nya´sz Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Kende u, Hungary Keywords Cybernetics, Control systems Abstract The paper presents a new decomposition method to handle optimal control design for two-degree of freedom time delay control systems. In this approach exact relationships between the actuator, process and design parameters and also robustness measures are developed. The ultimate robustness limit of any control can be explicitly calculated by this approach.
Introduction A generic two-degree of freedom (G2DF ) system (Keviczky, 1995) was introduced by the authors, which was successfully applied for several linear and nonlinear control (NG2DF ) problems (Haber and Keviczky, 1999). The G2DF system is based on the Youla-parametrization providing all realizable stabilizing regulators (ARS ) for open-loop stable plants and on a special structure, which is a certain extension of the well known IMC approach. A G2DF control system is shown in Figure 1, where yr, u, y and w are the reference, process input, output and disturbance signals, respectively. The optimal ARS regulator (Maciejowski, 1989) of the G2DF scheme (Keviczky and Ba´nya´sz, 1999) is given by P w Gw S 21 P wKw Qo þ Ro ¼ ¼ ¼ 1 2 P w K w S 1 2 Qo S 1 2 P w Gw S 2 z 2d
ð1Þ
Qo ¼ Qw ¼ P w K w ¼ P w Gw S 21 þ
ð2Þ
where
is the associated Y-parameter (Maciejowski 1989). Furthermore 21 21 Qr ¼ P r K r ¼ P r Gr S 21 þ . . .; . . .K w ¼ Gw S þ . . .; . . .K r ¼ Gr S þ
assuming that the process is factorable as This work was supported by the Hungarian NSF (OTKA).
ð3Þ Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1429-1441. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443635
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S ¼ S þ S 2 ¼ S þ S 2 z 2d
ð4Þ
where S+ means the inverse stable (IS ) and S2 the inverse unstable (IU ) factors, respectively. z 2 d corresponds to the discrete time delay, which is the integer multiple of the sampling time. It is interesting to see how the transfer characteristics of this system looks like: y ¼ P r K r S yr 2 ð1 2 P w K w SÞw ¼ P r Gr S 2 z 2d yr 2 ð1 2 P w Gw S 2 z 2d Þw ¼ yt þ yd
ð5Þ
where yt is the tracking (servo) and yd is the regulating (or disturbance rejection) independent behaviors of the closed-loop response, respectively. Here Pr and Pw are assumed to be stable and proper transfer functions, that are partly capable to place desired poles in the servo and the regulatory transfer functions. Furthermore, they are usually referred as reference signal and output disturbance predictors. They can even be called as reference models, so reasonably P r ðv ¼ 0Þ ¼ 1 and P w ðv ¼ 0Þ ¼ 1 are selected. The ultimate optimal goal of any control system could be to exactly follow a prescribed external (usually a unit step) excitation by the (step) response of the closed-loop system. Using the G2DF system we were required to follow the transients prescribed by Pr and Pw (more exactly ð1 2 P w Þ), i.e. the ideal overall transfer function of the G2DF control system would be y o ¼ P r yr 2 ð1 2 P w Þw ¼ yot þ yod
ð6Þ
Equation (5) shows that we can not reach these ideal tracking yot ¼ P r yr and regulatory behaviors yod ¼ ð1 2 P w Þw, because of the uncompensable timedelay and the so-called invariant zeros in the IU factor S2 . The reachable best transient is given by P r Gr S 2 z 2d and ð1 2 P w Gw S 2 z 2d Þ respectively, where Gr and Gw can optimally attenuate the influence of S2 (Unfortunately S2 and z 2 d do not depend on the control design and can only slightly be influenced via the proper selection of the sampling time. These factors are basic behaviors of the process, so they can be considerably changed only via certain technological changes.). Express the deviation between the ideal y o and the best reachable (realizable and optimal) closed-loop (given by equation (5)) as:
Figure 1. The generic 2DF (G2DF ) control system
Robustness limits for control systems
Dy ¼ y o 2 y ¼ P r ð1 2 K r SÞyr þ P w ð1 2 K w SÞw ¼ P r ð1 2 Gr S 2 z 2d Þyr þ P w ð1 2 Gw S 2 z 2d Þyr ¼ 1w yr þ 1w w ¼ Dyot þ Dyod
ð7Þ
So the deviation transfer functions from the ideal ones for both the tracking Dyot and the regulatory properties Dyod have the same structure: P x ð1 2 Gx S 2 z 2d Þjx¼r;w : This deviation form is excellent for (sometimes called model matching) optimization of the generic scheme as it was shown by Keviczky and Ba´nya´sz (1999). An interesting result was (Keviczky and Ba´nya´sz, 1999) that the optimization of the G2DF scheme can be performed in H2 and H1 norm spaces by the proper selection of the serial Kr and embedded Kw filters (compensators). Observe that in these optimizations both Kr and Kw use full cancellation of the IS factor of the process and the originally quite sophisticated optimization could be reduced to the optimal computation of the Gr and Gw filters (Keviczky and Ba´nya´sz, 1999). If Gr and Gw are optimally selected, then Ro in equation (1) denotes the optimal ARS regulator (The reasonable factorization of S means that the IU factor S2 is monic. So if the optimal Gw is also monic, then a unity gain selection for Pw – which was assumed above – provides that Ro is integrating, so has a pole at 1. The same considerations can be derived for Gr and Pr.). Do not forget that the optimal ARS regulator Ro is introduced for discrete-time systems, when the above cancellation process does not result in a nonrealizable order condition; so it is not so restrictive, than in the equivalent continuous case. However, in some special cases even the continuous version is applicable, as it will be shown later. A decomposition approach for controller design The control error transfer functions of the G2DF system are given by e ¼ ð1 2 P r Gr S 2 z 2d Þyr 2 ð1 2 P w Gw S 2 z 2d Þw ¼ E r yr þ E w w ¼ E r yr þ Ew ¼ er þ ew
ð8Þ
where the control tracking performance can be best evaluated from the deviation Dyor E r ¼ 1 2 P r Gr S 2 z 2d ¼ 1 2 P r þ P r 2 P r Gr S 2 z 2d ¼ ð1 2 P r Þ þ P r ð1 2 Gr S 2 z 2d Þ ¼ 1or þ 1r
ð9Þ
Here the first term characterizes the design performance: how close Pr is to the ideal unity and the second term characterizes the performance degradation
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caused by the invariant factors of the process, i.e. how close PrGrS2 z 2 d is to Pr. The form of equation (9) is a reasonable decomposition of the general controller design paradigm. A corresponding cost function can be constructed by using the triangle inequality and applying an appropriate norm J rcontrol # J rdesign þ J rdegradation ¼ k1 2 P r k þ kP r 2 P r Gr S 2 z 2d k
ð10Þ
The same observations can be made for the tracking errors, too. Formally both terms in equation (8) are the same, however, the control sensitivity function is the second one E ¼ E w ¼ 1 2 P w Gw S 2 z 2d
ð11Þ
which does not equal to the sensitivity function 1w ¼ P w ð1 2 Gw S 2 z 2d Þ
ð12Þ
in equation (7) generating the regulatory model matching error Dyot : A short analysis shows that E ¼ E w ¼ 1 2 P w Gw S 2 z 2d ¼ 1 2 P w þ P w 2 P r Gr S 2 z 2d ¼ ð1 2 P w Þ þ P w ð1 2 Gw S 2 z 2d Þ ¼ 1ow þ 1w
ð13Þ
Similar cost function can be constructed for the regulatory performance, too. w w 2d k Jw control # J design þ J degradation ¼ k1 2 P w k þ kP w 2 P w Gw S 2 z
ð14Þ
Summarizing the above results: the control error (resulting either from tracking or from disturbance rejection) is the sum of a design error and a reference model performance degradation error, so the overall control performance is the sum of the design and degradation performances. The authors believe that the relatively easy and reasonably optimal solution of a generally very sophisticated control problem strongly depends on the proper decomposition of the original paradigm. These decompositions would correspond to a natural control engineering practice, too, where the best reachable design goal and the way how to obtain it appear in a generally iterative sequential procedure. A large percentage of papers suggesting optimal controller design do not follow the above decomposition possibility. Most of them introduce only an optimization technique. Some, who are familiar with the practical needs, apply further special detuning methods to increase the robustness of the solution or reduce the control action. The basic theoretical optimal design methods usually result in too sensitive controllers and assume no amplitude constraints for the control action signal. However, in the control engineering practice one should always assume a nonlinear limiter, corresponding to a real actuator. In many cases the optimal regulator obtained by sophisticated theoretical methods
generates too big control actions (amplitude changes at the output of the Robustness regulator). These big changes mostly cannot, of course, “go through” the limits for control amplitude (sometimes rate) constrained real actuator. Therefore industrial systems control experts used to laugh at the optimal regulators of theorists because they state that the resulting transient rather depends on the practical limits than on the optimality of the design algorithm. 1433 This is the case for almost all dead-beat, pole-cancellation and H2 optimal regulators, except if this input action is not penalized in the control criterion, which reduces this effect. Therefore the energy of the plant input is generally included in the control cost function at the LQG and model-predictive controls. In this way it is generally possible to reduce the variation of the regulator output considerably. Input penalization is always a possible way of detuning. Optimization and detuning is also a certain decomposition approach. However, it is not a simple procedure to find the proper weighting (penalizing) factors and filters in the criterion and there is no easy way to calculate the obtained bandwidth for the closed-loop system. The practice is usually based on a “trial and check” method. The recent advanced methodology tries to fulfill both performance and robustness requirements via special compromising loopshaping techniques. These techniques can also be considered to a certain decomposition methodology. New relationships for robustness measures In our recent research application, projects and studies we stick on the above decomposition, which considers the optimal design and optimal performance degradation to be the two major steps in equation (14). For the minimization of the second terms wide class of solutions exist depending on the applied norm, process and some existing constraints if the process parameters are known. If these parameters are not available, then an iterative combined ID and control technique or its adaptive version can be used. The recent advanced methods try to use the available or assumed plant uncertainties in the optimization. Relatively much less papers deal with the optimization of the first term. The simple formal description of this paradigm is opt r P r ¼ arg minð J design Þ ¼ arg mink1 2 P r k ð15Þ Pr Pr u[U
P opt w
w ¼ arg minð J design Þ Pw
u[U
u[U
¼ arg mink1 2 P w k Pw
u[U
where U is the (mostly amplitude: U : juj # 1) constrained input signal domain. A nonlinear limiter representing a real actuator is always an important source of considerable performance degradation comparing to the original linear optimal system design. The general solution of this paradigm is a certain
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rescaling of the nonlinear practical system to achieve a linear operational domain. The performance degradation caused by the limiting actuator and by the necessary rescaling is calculable and known, if we use a reference model redesign technique to fulfill the amplitude constraints requirements and to solve the paradigm (Keviczky and Ba´nya´sz, 1997). Using the iterative reference model redesign technique the fastest reference model (so the highest closed-loop bandwidth) can be found reachable within the linear operational range. The situation is more complex, because changing the reference model also change the robustness margins of the closed-loop. It would be desirable to know how the limiting robustness measure depends on the limiting reference model. In the sequel, this relationship will be investigated. In our analysis the continuous time equivalent of the G2DF will be used, where the following simple assumptions are used: 1 1 Pw ¼ ; S ¼ S þ e 2st ¼ ð16Þ e 2st 1 þ sT w 1 þ sT So the IS process is a first order time delay lag and the reference model is a first order lag. The continuous-time optimal ARS regulator based on equation (1) is now 1 1 1 þ sT Ro ¼ ðP w S 21 ð17Þ þ Þ¼ 1 2 P w e 2st 1 2 e 2st =ð1 þ sT w Þ 1 þ T w which can be easily realized, e.g. by a simple closed-loop according to Figure 2. Note that Ro has a pole at s ¼ 0; so it is an integrating regulator. It is easy to compute that the open-loop transfer function for the G2DF system is: P w e 2st Y ¼ Ro S ¼ ð18Þ 1 2 P w e 2st So the crossover frequency vc can be obtained from the condition jY j ¼ 1, i.e. when jP w e 2st j ¼ j1 2 P w e 2st j
ð19Þ
For the ideal no delay case this condition means that jP w j ¼ j1 2 P w j
Figure 2. The simple realization of the optimal continuoustime ARS regulator
ð20Þ
This equation gives a very simple geometrical tool to determine the crossover Robustness frequency vc, demonstrated in Figure 3. This method gives vc by the limits for control intersection of Pw( jv ) and the vertical line drawn at the point ð0:5 þ 0jÞ; where systems jP w ð jvc Þj equals the distance from the point ð1 þ 0j Þ; i.e. j1 2 P w ðjvc Þj: This method can also be applied to determine the distorted crossover frequency vc0 for the uncompensable process time delay e 2 st using P w ðjvÞe 2jvt : 1435 The corresponding sensitivity function equation (11) of the G2DF system is E ¼ 1 2 P w e 2st ¼ 1 2
1 1 þ sT w 2 e 2st e 2st ¼ 1 þ sT w 1 þ sT w
ð21Þ
The kEk1 of the sensitivity function can also be determined graphically from Figure 3, which is the farthest distance of P w ð jvÞe 2jvt from the point ð1 þ 0 jÞ: Let us denote the well-known robustness measure: the distance between the point ð21 þ 0 jÞ and any Y( jv ) point of the Nyquist curve of the open-loop frequency characteristics by r
r ¼ rðv; RÞ ¼ j1 þ RSj ¼
1 jEðv; RÞj
ð22Þ
Because r changes by v and the shape of r(v ) is difficult to characterize by one scalar indicator, therefore the real stability/robustness measure is 1 rm ¼ rmin ðRÞ ¼ minj rðv; RÞj ¼ minj1 þ RSj ¼ ð23Þ v v kEk1 which is the distance between the point ð21 þ 0jÞ and the closest point of Y( jv ) and the reciprocal value of the norm kEk1 : (Note that in the most general case of jY ðv ¼ 1Þj ¼ 0 this measure falls into the range 0 # rm # 1
Figure 3. The demonstration of the change of the crossover frequency vc to vc0 for the uncompensable process time delay e 2 st
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Figure 4. The reachable robustness measure rm ¼ rmin and a practical upper bound
for stable closed-loops.) It can be well seen in Figure 3 that real part of P w ðjvÞe 2jvt at first the intersection with the real axis at v¯ can be used as a lower limit for kEk1 ; so its reciprocal value is an appropriate upper limit for rm 1 rm # ð24Þ 1 2 Re P w ð jvÞe 2j vt One can see from Figure 3 that rm depends only on our design goal (Tw) and on the process behavior time delay (t ), more exactly on their relative value x ¼ T w =t. Unfortunately, there is no simple analytical solution to obtain the relationship rm ðxÞ (and r¯m(x )), only a numerical procedure can be applied following the graphical interpretation for kEk1 in Figure 3. The rm(x ) and r¯m(x ) curves obtained by MATLAB numerical calculations are plotted in Figure 4. The interpretation of rm(x ) is very important, because this curve gives the theoretically best reachable robustness measure with any controller for an arbitrary IS time-delay plant. This measure is rm ð0Þ ¼ 0:5 for cases when the P w reference model requires a very fast transient response from the time-delay process and the measure is rm ð1Þ ¼ 1; if the time-delay is negligible comparing to the time-delay of Pw. A typical time-response of a PID regulator for a square-wave input excitation is shown in Figure 5 for continuous-time case. Here the steady-state value Du þ ð1Þ ¼ 2Du 2 ð1Þ is the virtual gain of the regulation between the excitation and the control action. The ratio of the initial peak Du +(0) to the change 2Du þ ð1Þ in the steady-state value
þ Du þ ð0Þ Du þ ð0Þ uþ 1 max ð0Þ þ Du ð1Þ ¼ ¼ ¼ ps ¼ þ 2 þ þ a Du ð1Þ 2 Du ð1Þ 2Du ð1Þ 2Du ð1Þ
Robustness ð25Þ limits for control systems
is sometimes called the power-surplus or the virtual differential effect of the regulator. Its reverse a gives the ratio of the time lag and the differential time of a D-effect ðsT D =ð1 þ saT D ÞÞ: It is easy to see from the form of Ro in our first order example that the initial peak for a unit step excitation is Ro ðv ¼ 1Þ ¼ T=T w , so the power surplus is ps ¼ T=T w
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ð26Þ
which comes from a simple physical interpretation: we should like to speed up the closed-loop from the original open-loop bandwidth v b;o ¼ 1=T to the desired closed-loop reference bandwidth v b;c ¼ 1=T w , therefore ps is their ratio ps ¼ v b;c =v b;o ¼ T=T w
ð27Þ
Introducing an auxiliary variable y ¼ T w =T it is possible to draw a complex four quadrant figure representing the relationships between rm, x, y and ps parameterized by the ratio T=t as shown by Figure 6. In a practical application the bottom two quadrants are not necessary, these stand here only for explanation. The numerically computed exact values are plotted in Figure 7. 1 is to use Figure 7 to determine the necessary The first possibility W power surplus ps to a required design goal x ¼ T w =t for a given process
Figure 5. A typical time-response of a PID regulator for a square-wave reference signal excitation in a closed-loop
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Figure 6. Complex relationships between rm, x, y and ps parameterized by the ratio T=t
2 is when the technically characterized by T=t: The other possibility W allowable maximum power surplus ps is given and one can determine the fastest possible reference model xmin and the corresponding worst (smallest) minimal robustness measure r˘min. These two design problems are represented in Figure 8. It is also possible that r˘min is given and we need the corresponding xmin and ps.
Example Assume a first order time delay plant as S¼
e 25s ; 1 þ 5s
Sþ ¼
1 ; 1 þ 5s
where T=t ¼ 1 and use the design goals
e 2st ¼ e 25s
ð28Þ
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Figure 7. Dependence of rm from x, ps and T=t
Figure 8. Two possible design problems
Pr ¼
1 1þs
e s
Pw ¼
1 1 þ 2:5s
ð29Þ
So in this case x ¼ T w =t ¼ 0:5: In Figure 7 ps ¼ 2 and rm ¼ 0:56 correspond to these process and design parameters. Therefore if we need higher robustness value rm it can only be reached by applying a slower reference model Pw. Figure 9 shows the unit step responses of Pr, Pw and S+, respectively.
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Figure 9. Unit step responses of Pr, Pw and S+
Figure 10. Model tracking (Pr) and disturbance rejection (Pw) properties of the G2DF scheme by y(t )
Figure 11. The output of the regulator u(t ) with ps and ps0
Assume a unit-step reference signal excitation yr ¼ 1ðt 2 5Þ and also a step output disturbance w ¼ 0:5 £ 1ðt 2 25Þ at the G2DF closed-loop (here 1(t ) is the classical unit-step signal, i.e. 1ðtÞ ¼ 1 for t $ 0 and 1ðtÞ ¼ 0 for t , 0). Figure 10 shows the output response y(t ) of the closed-loop for the yr(t ) and w(t ) excitations. The output of the regulator is shown in Figure 11, where it is easy to see that ps ¼ 2 (0.5ps is shown in the figure, because the amplitude of w(t ) was 0.5 !!!). Do not miss ps with the power surplus p0s ¼ 5 necessary to Pr, which does not depend on the closed-loop properties directly and is independent of ps.
Conclusions Robustness The full cross relationships of the most important actuator, process parameters limits for control and robustness measures are presented, according to the decomposition systems approach discussed previously. The developed plots are very important, because they give the ultimate control limits reachable by any regulator. The assumed plant was a simple first order time delay lag and the question arises 1441 what can we say for higher order and nonminimum phase plants. In case of a higher order plant one can always use the dominant time constant as T in these investigations. All further lag term (higher order denominator in S ) makes the situation worst lowering the rm(x ) curve (decreasing the robustness of the closed-loop). The influence of minimum phase lead terms (higher order numerator in S ) improves the situation by increasing the rm(x ) curve. The influence of IU nonminimum phase lead terms (higher order unstable numerator in S ) have the same effects as further lags in the denominator of S. This is how the limiting character of the above results should be interpreted. References Haber, R. and Keviczky, L. (1999), Nonlinear System Identification – Input-Output Modeling Approach, Kluwer Academic Publishers. Keviczky, L. (1995), “Combined identification and control: another way (Invited plenary paper)”, 5th IFAC Symposium on Adaptive Control and Signal Processing, ACASP’95, Budapest, H, pp. 13-30. Keviczky, L. and Ba´nya´sz, Cs. (1997), “An iterative redesign technique of reference models: how to reach the maximal bandwidth?”, 11th IFAC Symposium on System Identification SYSID’97, Fukuoka, Japan, pp. 619-24. Keviczky, L. and Ba´nya´sz, Cs. (1999), “Optimality of two-degree of freedom controllers in H2and H1-norm space, their robustness and minimal sensitivity”, 14th IFAC World Congress, Beijing, PRC, Vol. F, pp. 331-6. Maciejowski, J.M. (1989), Multivariable Feedback Design, Addison Wesley.
The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/0368-492X.htm
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“Physics” approach to general systems theory J. Korn Visiting Fellow, London School of Economics, UK Keywords Cybernetics, General living systems theory Abstract A number of empirical statements intended to capture features of “systems” considered to be pervasive, is given. A symbolism based on processed natural language is outlined. The symbolism can be used for analysis of scenarios with predominantly qualitative properties i.e. human activity situations. It is capable of carrying the appropriate mathematics and uncertainties associated with operation of human and other types of components, is based on a kind of predicate logic and exhibits changes of states in time. The approach has led to a definition of information and product and systems design.
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Introduction A very general view of the world is to see it in terms of parts or objects any of which is selected by someone who is interested. An object can be in a stationary state or undergoing change, a dynamic state or event. A number of interrelated/interacting states and events is referred to as a situation or scenario. A state is a conjunction of properties as defined in physics (Rogers and Mayhew, 1957) but used extensively in natural language in much the same sense. They emerge out of the infinite number available for description depending on the interest of the party viewing the state or the event (Korn, 2000). We speak of physical properties which are directly observable by the senses, or through instruments, and mental and abstract properties which are not accessible to observation (Korn, 2001). The human intellect has been interested for a long time in describing states and their changes and in predicting future events using some kind of symbolism. Assignment of properties to objects and the arrangement of either or both in an inferential mechanism constitutes a means of prediction, guessing is another. Heated entrails of an animal, logic, mathematics or linguistic modelling using processed natural language are all symbolic means of description and prediction (Korn, 1994 2001b; Quirk and Greenbaum, 1973). Conventional science has focused on situations and scenarios which can be described in terms of quantifiable properties. Such descriptions are possible in natural, technical and selected instances of human activity situations. Conventional science is good at: creating relations of properties assigned to a phenomenon, perceiving far reaching general features embodied in explanatory hypotheses and inventing predictive, theoretical structures expressed in mathematical symbolism. It is, however, poor in creating dynamic theories of interacting objects especially in the multidisciplinary field. It cannot cope with
purposive or control activity (Lanczos, 1970; Korn, 1995; Dorf, 1986) and is unsuitable for handling situations with predominantly qualitative properties i.e. living and especially human activities. Conventional science provides knowledge base for conventional engineering and aids it in element/component design (Korn, 1996). Early workers when perceived and were confronted with the immense variety, diversity and pervasive nature of “systems” proposed and later attempted a general systems theory along mathematical lines (Bertalanffy von, 1950; Klir, 1969). They rejected the application of conventional science to the “systems phenomenon” in its entirety which perhaps with hindsight was a mistake, and embarked on a variety of developments such as soft systems method, various methodologies, ill defined diagrams etc. (Checkland, 1981; Jackson, 2000). Approaches to the essentially unique systems phenomenon emphasise the differences in particular manifestations of “systems” in diverse fields, social, technical etc. rather than to work towards integration through perceiving the underlying generalities. Current work attempts to develop an empirical theory consisting of a number of general statements and a symbolism. This notion, by no means new, is described more fully as follows: (1) Observation driven generalisations regarded as pervasive throughout the immense variety of manifestations of systems, are asserted. The generalisations concern precise notions of property, objects and interactions expressed as physical power or influence carrying specific form of energy or information respectively (Korn, 2000; 2001a, b). These are seen as the constituents of situations, or scenarios, with human, living, natural and/or technical components. (2) A symbolism for an inferential structure called linguistic modelling is developed from natural language and aspects of predicate logic. The symbolism is capable of handling objects with qualitative as well as quantitative properties and uncertainties associated with behaviour of living, human and other objects affecting the outcomes of a situation. (3) Emphasis is shifted from current preoccupation with “systems” to “states” as conjunctions of properties produced by a system, situation or scenario by chance or in accordance with purpose. Such a shift is desirable since it is the arrangement of states expressed as “properties” which is of primary interest in analysis and design. A system/situation/scenario/organisation can then be seen as the mechanism for creating a particular arrangement. This paper outlines linguistic modelling as a possible approach to the development of a general systems theory.
Approach to general systems theory 1443
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An outline of linguistic modelling A theory of change is developed consisting of empirical content and symbolism which has already resulted in a concept of information and a representation of information systems (Korn, 2001a). Empirical content (1) The concept of property is defined in physics as a means of description of initial and final states of a changing object which are independent of the path of reaching the latter from the former (Rogers and Mayhew, 1957). We use the concept in natural language extensively in much the same sense although linguistic analysis and a number of assumptions are required to make it explicit (Korn, 2000, 2001b). There are concrete properties such as: geometric, material, numerical and energetic open to perception. Abstract properties are the result of denotation arrived at through inference. For example, from the geometric and material properties of the skin on the face of a person we can conclude whether he/she is young/old, happy and so on. The introduction of abstract properties increases the expressive power of language by avoiding the need for repeated recital of conjunctions of concrete properties. We note that a branch of conventional science such as mechanics, is based on a closed set of physical properties selected from geometric, material, numerical and energetic and organised into relations, theories. An approach to engineering systems uses a classification of properties (Korn, 1995). Because of the immense variety of a chosen set of properties which can enter into a description of a situation, we can only suggest schemes enabling identification of properties rather than properties themselves. In natural language properties are used to qualify other linguistic constituents in a variety of ways (Quirk and Greenbaum, 1973). (2) No change of state expressed as property is possible by itself either by chance or in accordance with purpose. From these two statements we can derive a number of others. (a) An empirical object or a chosen part of the world is seen as a conjunction of an infinite number of properties. A theoretical object is a particular case of a few explicitly stated properties which are situation-dependent and emerge as an object progresses from one situation to the next or changes its properties in the same situation (Korn, 2000). A theoretical object, or just object, is a theoretical construct. We take an interest in and express a view of an object using properties captured by the subject-predicate construction. This notion is used
Approach to general systems (b) Interaction is a means to accomplish a change of state expressed as theory to define the concept of information in terms of quantity and meaning (Korn, 2001a).
properties. Physical power carrying the appropriate kind of energy attached to a medium, is a form of interaction as defined in physics used to accomplish changes in physical properties. Influence carrying the appropriate information through a medium, is another form of interaction with, theoretically, zero physical power used for accomplishing mental properties (Korn, 2000, 2001a, b). Interaction itself can be described in terms of objects and properties (Korn, 2000). A verb such as ‘dig’ can be used for symbolising power-like interaction. Another verb, for example, ‘to notify’ can have a subjectpredicate form attached to it as a subordinate clause and as such it can carry information to represent influence-like interaction (Korn, 2001a). The sentence ‘The bank notified the customer that he/she exceeded the credit limit’ represents influence carrying information. Verbs like the ones just mentioned can be used to generate ‘situation logic’. Information can be used to create ‘thinking logic’. (c) Chance has a number of manifestations such as an event seen as accident or a probable event. The notion of purpose is incorporated in a ‘purposive system’(Korn, 2000, 1995; Dorf, 1986; Korn, 2001a). It can change one property at a time since only two properties can be compared, the one to be changed with that which is desired. (d) Energy is conserved in a closed situation, information can be created or destroyed. Energy is described by a positive definite function in the mathematical sense. Information is expressed, perhaps most frequently, in linguistic terms, it is either present or absent. There is no negative information. (e) Mutually interacting objects are bounded by objects with properties which are regarded constant or can be varied at will. Such objects constitute the environment and are identified in linguistic modelling by having only one incoming or outgoing, continuous directed lines. Interacting and environmental objects constitute a situation/scenario. The sense organs and instruments, the extension of the former, are used to maintain an interface between a living thing or an organisation and its environment. A sense organ is of delicate construction so as to minimise its energy consumption. When this consumption is assumed to be zero, the sense organ carries influence.
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(f) Situations/scenarios create outcomes expressed as physical or mental properties. A situation exist or brought into existence for this purpose. A scenario can have: power interactions only which create physical properties;
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influence interaction only which create mental properties; influence and power interactions interfaced by amplifiers which create physical properties by exercising ‘skilled power’ like drilling a hole to specification or any everyday activity like cutting a slice of bread, all involving activities of purposive systems.
Symbolism We are concerned mostly with scenarios which involve activities by living, in particular human, entities. In such scenarios the properties of interest carried by objects are qualitative rather than quantitative. Thus, mathematics although may be used where quantitative work is appropriate, is not a suitable symbolism. Natural language is but it cannot be used directly as it has complexities, ambiguities, metaphors, idioms etc. Linguistic modelling converts a story of declarative sentences in natural language into another formal symbolism which can then be manipulated to exhibit explicitly the outcomes of a scenario. The symbolism carries objects and their properties which affect the outcomes and takes into account uncertainties associated with activities of living entities. The stages of LM are depicted in Figure 1 and its details are illustrated by an example. LM begins with a story or narrative describing a situation followed by linguistic analysis with two assumptions (Korn, 2000, 2001a): (1) any complex linguistic pattern can be converted into a combination of simple sentences with a single stative or dynamic verb; (2) in the course of linguistic analysis the meaning of the original story or narrative remains invariant to an acceptable degree. The function of linguistic analysis is as follows. (1) To identify sentences which contribute to the structure of a situation, or scenario, i.e. those used for modelling, and those carrying information captured in subordinate clauses attached to special verbs (Korn, 2001a). In other words, to identify verbs which represent power/energy or influence/information interactions. The latter type of verbs may be divided into groups expressing: perception (see, hear, sense, . . .), mental processes or storage (consider, think, believe, remember, . . .), transmission (describe, say, indicate, shout, announce, detect, . . .) and
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Figure 1. Stages of linguistic modelling of situations
commitment (offer, request, assess, . . .), all capable of carrying information. (2) To reduce linguistic complexities into combinations of simple, one- and two-place sentences with dynamic verbs called “basic constituents”. (3) To identify within each simple sentence the nouns and a verb which form a context-free sentence together with the noun initiating activity and those which are affected (Korn, 2000, 2001a, b; Quirk and Greenbaum, 1973). (4) To identify the qualifiers, or properties, of nouns and verb as adjectival and adverbial phrases in a basic constituent. Without qualifiers a sentence of nouns, verb and functional words although meaningful, is not anchored in the space of meaning. Qualifiers make a sentence situation-dependent (Korn, 2001a).
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Linguistic analysis has made explicit the dynamic verbs which attract one or two nouns in context-free sentences, together with their qualifiers. These are the basic constituents of which a complete scenario is constructed as a semantic diagram. We assume that “a dynamic verb refers to causation”. This assumption implies the following. (1) The interaction represented by a dynamic verb is related to the relevant, contingent properties of an object initiating interaction. The relation is causal to driving (dp) properties supplemented by enabling, facilitating/hindering (ip) properties, (2) The change of property of an affected object or change of state leading to an “acquired property” (ap) driven by the interaction, is causally related to the interaction (in) itself supplemented by enabling, facilitating/hindering (ep) properties of the object, (3) A property once acquired (ap) can function as a driving property “dp”, can support an interaction as an “ip” or the change of property of another object as “ep”, in the course of propagation of change of state as a scenario unfolds. In addition we introduce the notion of calculating property (cp) to qualify causation which performs comparison, decision or calculations as required in a situation with purposive activities. The implications thus formed lead to expressing a one- or two-place basic constituent as a pair of logical conditionals. For instance, the sentence “As part of his duty with care about the job (dp) and with good eye sight (ip), the postman sorts (in) according to code (adverbial phrase) properly addressed (ep) letters” can be formulated as follows. “IF (it is part of his duty and with care about the job) AND (he has good eye sight) THEN the postman sorts letters (according to code)”. “IF the postman sorts letters (according to code) AND the letters are (properly addressed) THEN the letters become sorted (ap)”. The result of the “postman’s” action in the above example is a change of physical property of the “letters”, referred to as outcome. Exercising his skilled power, the “postman” converted letters from unsorted into sorted, he has created order out of chaos. However, the conditionals at this stage contain no indication of uncertainty, the outcome is inevitable. Symbols are assigned to qualifiers according to their function/meaning leading to a pair of logic statements as in the “postman” example. We demonstrate this by the simple scenario based on the following story. “As the tree was close to the house, the gardener who was also a tree surgeon, cut down the apple tree in 10 min with a wide bladed axe. Seeing that the job was completed, the boss boisterous by nature shouted loudly to the attentive gardener that his offer for the job was £5. The gardener, an educated man and in need of money, reluctantly considered that the offer was acceptable”.
Approach to general systems Adjectival qualifiers with grading theory dp(1,1) – gardener knew that tree was close to house (very, notvery, far)
Following the procedure in Figure 1 we arrive at Figure 2 from which:
ip(1,1) – gardener was tree surgeon (good, poor) ip(1,5) – gardener was educated (well, poorly), sensitive (very, just), proud (very, just)
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ep(1,5) – gardener was in need of money (very much, not much) ep(1,1) – gardener was attentive (very, not) ep(2,2) – tree was apple dp(4,4) – boss seeing that the job was finished ip(4,4) – boss was boisterous (very, not) Interactions with adverbial qualifiers in(1,2) – cutdown
: time(less than), how(with axe)
in(4,1) – shouted
: how(loud), info(his offer)
in(5,5) – considered
: how(reluct), info(offer)
Logic sequences/topology of scenario Causal chains: 1 ¼ 3; 2; 1 and 2 ¼ 6; 5; 1; 4
Figure 2. Semantic diagram of gardener/boss scenario
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For causal chain 1. 1/1 dp(1,1) ^ ip(1,1) ! in(1,2) 1/2 in(1,2) ^ ep(2,2) ! ap(3,3) For causal chain 2.
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2/1 dp(4,4) ^ ip(4,4) ! in(4,1) 2/2 in(4,1) ^ ep(1,1) ! ap(5,5) 2/3 ip(1,5) ^ ap(5,5) ! in(5,5) 2/4 in(5,5) ^ ep(1,5) ^ ap(5,5) ! ap(6,6) Logic sequences with graded adjectives/data for certainty factors (cf) (Durkin, 1994) 1/1 dp(tree,1,1,(close(very,90/.9,not very,80/.7,far,60/.4))) ^ ip(gard,1,1,(treesur(good,90/.8,poor,60/.4)))(.) ! (..)in(cut,gard,1,tree,2,(time(less than), how(with axe)))(. . .)and so on for all terms in the causal chains. The logic sequences give cf of all possible states. In order to find out which properties with which grades produce a particular outcome, we need to trace a particular sequence leading to a cf. of a specific outcome. For example, in the second causal chain. From 2/1: if “boss seeing that job was finished” and “boss was very boisterous” then “boss shouted loudly to gardener with offer” with cf. ¼ 0.9 i.e. almost certain From 2/2: if “boss shouted loudly to gardener with offer” and “gardener was very attentive” then “gardener was aware of loud shouting with offer” with cf. =0.8 i.e. nearly certain and so on.
Conclusions The idea suggested here is to shift attention initially from the notion of “system” to that of change of state and its description in terms of physical or mental properties whereby bringing the treatment of “soft” problems closer to that in physics. Such changes are brought about by interacting objects including environmental objects forming a whole and are considered necessary for the change. This idea appears to be pervasive throughout experience. In this paper we have described briefly how this idea can be translated into theoretical terms by formulating notions thought to be basic and general guiding the symbolism. The symbolism based on processed natural language and a form of predicate logic, models changes in time together with the objects and their properties thought to be contributing to changes. Uncertainties
associated with human and other activities are taken into account (Durkin, 1994; Korn, 2000, 2001a, b). The method is rooted in accepted branches of knowledge and uses well defined concepts yet handles “soft” situations. However, it still lacks larger scale, more realistic applications and software back up. References Bertalanffy von, L. (1950), “An outline of general systems theory”, The British J. for the Philosophy of Science, Vol. 1 No. 2. Checkland, P. (1981), Systems Thinking Systems Practice, Wiley, Chichester. Dorf, R.C. (1986), Modern Control Systems, Addison-Wesley, Reading, USA. Durkin, J. (1994), Expert Systems, Macmillan, NY. Jackson, M.C. (2000), Systems Approaches to Management, Plenum Publishers, NY. Klir, G.J. (1969), An Approach to General Systems Theory, van Nostrand, NY. Korn, J. (1994), “Fundamental problems in engineering degree courses”, European J. of Engineering Education, Vol. 19 No. 2. Korn, J. (1995), “Theory of spontaneous processes”, Structural Eng. Review, Vol. 7 No. 1. Korn, J. (1996), “Domain-independent design theory”, J. Engineering Design, Vol. 7 No. 3. Korn, J. (2000), “Possibility of general systems theory”, 44th Annual Meeting ISSS, 16-22 July, Toronto, Canada. Korn, J. (2001a), “Design and delivery of information”, European J. of Information Systems, Vol. 10 No. 1. Korn, J. (2001b). “Linguistic modelling of information and information systems”, 6th Annual Conference of UKAIS, 18-20 April, Portsmouth, UK. Lanczos, C. (1970), The Variational Principles of Mechanics, University of Toronto Press, Canada. Quirk, R. and Greenbaum, S. (1973), A University Grammar in English, Longman, London. Rogers, G.F.C. and Mayhew, Y.R. (1957), Engineering Thermodynamics, Longman, London.
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The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/0368-492X.htm
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A systems approach to self-organization in the dreaming brain Stanley Krippner Saybrook Graduate School, San Francisco, CA, USA
Allan Combs University of North Carolina, Asheville, One University Heights, Asheville, NC, USA Keywords Cybernetics, Brain, Self-development Abstract This systems model of dreaming consciousness examines the self-organizing properties of the sleeping brain, offering a step towards reconciling brain-based and content-based attempts to understand the nature of dreaming. The brain can be understood as a complex self-organizing system that, in dreaming, responds to subtle influences such as residual feelings and memories. The hyper-responsiveness of the brain during dreaming is viewed in terms of the tendency of complex chaotic-like systems to respond to small variations in initial conditions and to the amplification of subtle emotional and cognitive signals through the mechanism of stochastic resonance, all in combination with psychophysiological changes in the brain during both slow wave and rapid eye movement (REM) dreaming. These changes include the active inhibition of extroceptive stimulation and, especially in REM sleep, alterations in the brain’s dominant neuromodulatory systems, bombardment of the visual cortex with bursts of PGO activity, increases in limbic system activity, and a reduction of activity in the prefrontal regions.
Introduction There are many theoretical approaches to the process of dreaming. These have emphasized the cognitive aspects of dreaming (Foulkes, 1985, 1999), the psychophysiological processes underlying dreaming (Hobson and McCarley, 1977; Hobson et al., 2000), and the neurological substrate of dreaming combined with psychoanalytical considerations (Solms, 1997; Ullman, 1999). There are also connectionist (Hartmann, 1999) and neural network (Crick and Michison, 1986) models for understanding the dreaming brain. We have attempted to combine the psychophysiological approach with the connectionist and neural network models, leading to considerations about the cognitive structure of dreams. Our model views the dreaming brain in terms of dynamical neurological processes that are most accurately described as chaotic (Arden, 1996; Screenivason et al., 1999). Kybernetes, Vol. 31 No. 9/10, 2002, pp. 1452-1462. q MCB UP Limited, 0368-492X DOI 10.1108/03684920210443653
Dreaming in REM sleep Much of the research on the dreaming brain pertains specifically to rapid eye movement (REM) sleep, in part because of the misconception that dreams occur
only in this state, and, more properly, because awakenings from REM sleep are more likely to be associated with dream recall. The reason why dreams occur more frequently during REM sleep is not well understood, but it is evident that during the REM state the brain is especially disposed to dreaming. The brain actively inhibits extroceptive sensory input during REM sleep, and also blocks motor output from the higher centers of the brain. Only those motor commands that are sent to the extremities, that is, to the fingers and toes, ordinarily get through, as do those sent to the eyes. The presence of REMs is highly correlated with bursts (or “waves”) of large and seemingly randomly timed “spikes” of neuronal activity which originate in the pons of the lower brainstem and travel upward to the lateral geniculate bodies, from where they proceed on to the primary visual cortex. These pontine-geniculate-occipital (PGO) waves play an important role in the widely respected activation-synthesis hypothesis, originally proposed by Allan Hobson and his research group (Hobson and McCarley, 1977). It stated that the arrival of this irregular PGO activity at the occipital lobe serves as a powerful unstructured stimulus in which the sleeping brain seeks meaning, finding it in the creation of the images that we experience as dreams. Since its original publication, Hobson’s model has undergone a series of revisions (Hobson et al., 1998). The model has retained its original form while honing its physiological accuracy and expanding its reach toward a general theory of conscious states and the brain. Hobson’s model is abbreviated as AIM, referring to the activation level of the brain in wakefulness, REM, and NREM sleep, the source of the information that the brain processes (external or internal), and the chemical modulation (aminergic or cholinergic) of the brain. Hobson’s model has in its favor that the timing of PGO waves is irregular, and globally (though not precisely) correlated with REM activity. It also helps to put into perspective, the fact that animals compensate for lost PGO activity to a greater degree than they do for lost REM time. At least one “primitive” mammal, the echidna (spiny anteater), exhibits periods of PGO activity in the brainstem during sleep while showing no REM whatsoever. The AIM model is not, however, without difficulties. From a physiological point of view, it elevates diffuse cortical stimulation from the brainstem to the status of optical sensory input (Vogel, 1978). This inconsistency is especially problematic if Foulkes’ (1999) contention turns out to be true that infants – who exhibit a great deal of REM sleep – in fact hardly dream at all [but see Hobson et al., (2000)], for a considered counter-argument). From the psychological point of view, Hobson’s approach puts dream activity under the control of seemingly random PGO bombardment arising from the oldest and lowest levels of the brain. However, Hobson has not pursued a relentless reductionism. He and his colleague David Kahn have published an exploration of the idea that dream experiences are in part a product of self-organizing tendencies in the brain
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during REM sleep (Kahn and Hobson, 1993). This paper moved beyond the notion of dreams as random brain events, but did not yet articulate the actual formative processes that might underlie dreaming. Recently, we have worked with Kahn to develop a more detailed understanding of the brain’s dream process, one that spans the traditional chasm between the neurobiology of dreaming and the study of the content of dreams (Kahn et al., 1998).
The self-organizing brain in REM dreaming Our basic proposal is that the dreaming brain “relaxes” into natural patterns of self-organized activity that often reflect the residual moods, stresses, and concerns of waking life. To understand this, recall that during dreaming, the brain is immersed in something like a sensory isolation tank and cut off from the influences of external sensory input. In this situation, patterns of brain activity can relax into forms that are dependent primarily upon internal conditions. Consider, for instance, what happens when sand is dropped onto a vibrating surface like a drumhead or orchestral symbol. It dances about forming complex patterns characteristic of the physical dynamics of the vibrating surface beneath. Such patterns have been used to study the resonance properties of instruments such as violins. In chaos theory, the pattern created by the vibrating sand is termed an attractor, because it is the configuration towards which the system of the sand on the vibrating surface is naturally drawn. Attractors can also be seen in fluid systems, such as the complex patterns of ripples that appear in water flowing over and around stones in a stream. One can disrupt such a pattern by dipping a hand into the water and disrupting the current, but unless the rocks themselves are moved the pattern will quickly reestablish itself. The idea here is that the complex electrochemical activity of the brain during dream sleep likewise finds its own inherent configurations. In our view, the patterns of activity unfolding over time in the dreaming brain are experienced as the narratives that play themselves out in dreams (Combs and Krippner, 1998; Krippner and Combs, 2000). We suggest that while the conditions under which these patterns unfold are different than in the waking state, the fundamental principles that underlie their creation are the same. A beginning has been made in working out these conditions for cognitive systems (Hardy, 1998; Port and van Gelder, 1995), for algorithmic systems (Goertzel, 1994), and in terms of the phenomenology of the mind (Combs, 1996; Combs and Krippner, 1998). The basic idea in each case concerns complex chaotic systems that contain multiple processes that interact with each other to create new processes. These in turn interact, and so on. Out of this complex soup of interactions emerge more or less stable configurations of processes that
evolve in time. There is considerable evidence to suggest that many brain processes might be understood in terms of such dynamics (Basar, 1990; Freeman and Barrie, 1994; Halaz, 1995). Returning to the role played by PGO activity in the dreaming brain during REM sleep, we suggest that this activity sets the cortical system into motion and keeps it there. PGO discharges carry with them waves of powerful cholinergic stimulation to the cortex, keeping the brain on the move, and shaking it down again and again, towards relaxed configurations. In line with this way of thinking, Mamelak and Hobson (1989) have suggested that PGO stimulation is tied to the high rate of narrative or plot shifts experienced during REM dreaming. Such shifts are significantly more frequent in REM dreaming than during dreaming reported from slow wave sleep, and may be essential to the “bizarreness” of REM dreams. One of the major contributions of Hobson and his group was the discovery that during REM sleep the brain shifts away from the widespread inhibition that characterizes waking activity because of the dominance of aminergic neurochemicals (serotonin and norepinepherine). With the onset of sleep the brain comes under the influence of the cholinergic neurochemical acetylcholine, which predisposes it to easy activation (Hobson, 1988, 1994). In other words, activity in the dreaming brain during REM sleep is less viscous and more mercurial than in the waking brain, allowing it to move easily into residual patterns left by moods and concerns of waking life. Such fluidity would also enlarge the attractors through which brain activity flows, effectively allowing easier connections to be made between feelings, memories, and the products of the imagination, which is to say that dream experience is open to greater novelty than is wakefulness. A similar idea is suggested by Hartmann (1999), who notes that during dreaming the neural networks that comprise the working circuitry of the brain seem less constrained by daytime reality and more open to novel connections. The extent of agreement between Hartmann’s approach and our own is witnessed by the fact that the formal analysis of activity patterns in complex neural networks such as those found in the brain are often carried out in terms of attractors. Studies of brain activity during REM sleep It turns out that one important aspect of REM sleep is a significant reduction in the activation of the prefrontal cortex (Maquet et al., 1996). This region of the brain is important for a number of higher mental abilities on which we rely during wakefulness. These include working memory, the ability to keep important facts in mind while carrying out a task. With a reduced working memory during dreaming it is not surprising that we find the abrupt transitions in plot and location less surprising during dreaming than we would in waking life. The idea of a state-specific amnesia for working memory during
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REM sleep is further supported by Hobson (1988) who notes that such amnesia is facilitated by a reduction of aminergic modulation in the brain by 50 per cent in NREM sleep and nearly 100 per cent in REM sleep. The prefrontal cortex also plays an important role in making plans for the future. People with damage to this area often seem listless and without direction, in part because they do not think about what lies ahead. Likewise, the dreamer thinks little about the future, and simply goes along with the dream narrative without question (Hall and Van de Castle, 1966). In this vein, there seems a significant attenuation of attention during dreaming, as well as a loss of self-reflection (Blagrove, 1996). In waking life the prefrontal lobe may also play an important role in maintaining a sense of self-identity, and particularly an ability for self-reflection. With these abilities “off-line” during dreaming (Blagrove, 1996) the dreamer has little ability to reflect on the situation, or even notice the strangeness of events experienced. The recorded images of the sleeping brain during REM show that in contrast to the prefrontal cortex, portions of the limbic system are highly active during REM sleep (Maquet et al., 1996). These structures are associated with emotion, which makes perfect sense given the fact that dreams are high in emotional content. The limbic system is far from well understood, however, research continues to disclose new aspects of its operations. Anderson (1998) has explored the idea that the right and left amygdaloid complexes of the limbic system are key structures for cataloging emotional memories. Therefore, PGO activity shared between them in REM sleep helps balance the activation of such memories to keep the brain from getting stuck in particular attractor patterns such as depression or anxiety. Images of the sleeping brain during REM sleep show increased activity in the anterior cingulate cortex and the right parietal lobe, both associated with the regulation of attention. Contrary to what would be expected from the original activation-synthesis hypothesis, there actually seems to be a lowered level of activity in the primary visual cortex of the occipital lobe compared to that seen during waking visual activity, but relatively robust activation of the adjacent (parastriate) regions. According to some researchers (Crick and Koch, 1995) the latter are involved in the processing of visual images and are essential to the conscious experience of vision. In fact, Hobson et al. (2000) have expanded their model to include the importance of activity in the parastriate area in dream imagery. REM and SWS dreaming Some accounting must be made of the fact that dream reports are often obtained following awakenings from NREM, or slow wave sleep (SWS). Though the likelihood of obtaining dream reports is lower for SWS than REM sleep, such reports are associated with all stages of SWS. On the average they indicate less vividness and clarity of imagery and fewer plot shift than REM
associated reports, but the differences are usually small and not always reliable. Tracy and Tracy (1974), for example, reported dreams of high vividness from both light (stage 2) and deep (stage 4) SWS, casting doubt on the commonly held assumption that REM dreams are vivid because cortical activation is high during REM sleep. However, Hobson and his colleagues (Hobson et al., 2000) as well as Nielsen (1999) undertook extensive re-analyses of REM and NREM dream studies reported throughout the literature, leading them to reaffirm the importance of differences in dream content between these two types of sleep. Therefore, the issue of differences between REM and NREM dreaming is not settled. It would appear to us, however, that differences do exist and that they are important. This means that, on average, the characteristics of NREM dreams are somewhere between those of REM dreams and ordinary waking consciousness. Such a view still leaves unanswered the question why NREM dreams occur in the first place. The simplest answer would seem to be that NREM sleep is sufficiently similar to REM sleep to support dreaming, albeit dreaming that is more like waking mentation than is REM dreaming. This idea is consistent with the observation that a significant predictor of vividness is simply the level of energy metabolism in the cortex (Antrobus, 1991). Beyond this, it seems likely that the process of dream production is not centered in the brainstem, but in the forebrain. Solms (1997) has made such a suggestion, arguing that dreaming and REM sleep are distinct in terms of the brain processes that underlie them. He supports this contention with clinical studies that show no loss of dreaming following deep brainstem lesions (but see Hobson et al., 2000), while dreaming is lost after certain cortical lesions even when brainstem initiated REM sleep is not disturbed. In a similar vein, Foulkes (1999) argues that dreaming is characterized by high level cognitive processes and self-awareness. He maintains that this explains why dreams are rarely reported by infants or young children, though Hobson (1994) believes this to be an artifact of REM state amnesia. The factors that could facilitate dreaming during SWS include a relaxation of waking constraints on cortical activity brought about during sleep by isolation from outside stimulation, the cessation of ordinary rational thought, and the sleep-associated neurochemical changes mentioned earlier. Such factors also include the presence of residual feelings and concerns from waking life. All this must be animated by chaotic-like perturbation that allows cortical circuits to “relax” into the inherently comfortable but ever-changing attractor patterns that underlie the dream experience. Finally, some minimum level of arousal is necessary to sustain consciousness. It would seem from Tracy and Tracy’s (1974) findings that this minimum level is lower than commonly thought. We further note that during SWS higher brain functions are evidently isolated from external sensory input to a greater degree than is usually
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appreciated. This is evidenced, for example, by the general failure of sleeplearning studies to obtain positive results, even when using highly sensitive verbal priming techniques during light SWS. From this it would seem that the brain in SWS is sufficiently isolated from environmental stimulation to allow independent internal activities (Antrobus, 1990). In this connection, let us also bear in mind that chaotic-like activity is inherent in cortical processes in general, even during deep SWS (Roschke and Aldenhoff, 1992). This being the case, it would seem that the cortex is primed to flow from attractor to attractor even when not in REM sleep, though not as vigorously as when stimulated by PGO bombardment. Hobson’s (1994) finding of neurochemical differences in the brain between REM, SWS, and wakefulness, suggests a greater elasticity in the REM dreaming than the waking brain, with SWS falling in between, as is consistent with dream content reports. It is not surprising, however, that REM dreams evidence greater emotional intensity than do those associated with SWS (Foulkes, 1992). All and all, it would seem that essentially the same dream facilitating factors are at play in SWS as in REM sleep. Nevertheless, the presence of PGO stimulation in the latter, along with greater limbic system involvement, as well as differences in neurochemical modulation and decreased frontal lobe activity, render the REM sleeping brain more favorable for dreaming. Dream content and sensitivity to subtle influences There are two important aspects of the behavior of complex systems such as the human brain during sleep that can make such systems sensitive to subtle influences. First, systems that reside in chaotic or near-chaotic states are subject to the butterfly effect (Kellert, 1993; Peak, 1994); very small alterations in the present state of a system can lead to surprisingly large variations in its future states. There seems little doubt that the human brain with its many chaotic and chaotic-like patterns of activity, is subject to the butterfly effect. Second, and more important, under certain circumstances the introduction of noise into such a system (chaotic or not) can cause the system to respond to signals too small to ordinarily be effected by them. Termed stochastic resonance, this seemingly paradoxical effect has been demonstrated in electronic circuits as well as in nerve cells (Moss and Wiesenfeld, 1995). It results from the fact that the presence of noise, or vibration, keeps the system in motion and following the signal, rather than allowing it to become stuck. This is an active instance of the relaxing of a system that is exposed to vibration, as described earlier. For instance, objects on a vibrating tabletop are sometimes seen to “walk” about, especially if the table is not level. In fact, they are following the line of least resistance down the slope of the surface, ordinarily not available to them because of friction with the top of the table. Here, we might imagine that the arrival of PGO waves has a similar effect on the higher
cortical regions of the brain during REM sleep, causing activity there to “slide” in the direction of least resistance. In the dreaming brain, isolated from daytime sensory bombardment and detached by neuromodulatory amnesia from those experiences that immediately precede sleep, chaotic dynamics like the butterfly effect and stochastic resonance cause the brain to become especially responsive to subtle influences such as faint residual memories or emotional residues. Given a dreaming brain that is amnesiac for short-term pre-sleep events, and at the same time responsive to subtle influences such as emotions and memories, it is not surprising that dream content frequently includes fragments of old memories and once-familiar feelings from the past (Hall and Van de Castle, 1966). In such a hyper-sensitive system other influences might occasionally be felt as well. For example, Smith (1986) found among cardiac patients that the number of death references in men’s dreams, and separation references in women’s dreams, correlate with poor clinical outcomes, an effect that seemed independent of patients’ attitudes about the severity of their condition. These findings suggest the presence of a subtle biological influence on dreaming. Others have reported anomalous influences on dreams (Krippner, 1991). It is not our intention to evaluate these or other claims of seemingly unusual influences in dreams. Rather, we offer the thesis that the dreaming brain is a delicately poised system, responsive to the slightest perturbation, and thus reflective of even the subtlest aspects of human experience.
Conclusion Bringing the earlier ideas together, the intent of this paper is to take a credible first step toward a reconciliation of brain-based (“process”) and content-based (“interpretative” or meaning oriented) approaches to understanding dreaming. Our discussion is based on the premise that the dreaming brain is a complex self-organizing system. Such systems can exhibit multifaceted adaptive properties that are, broadly speaking, “cognitive” in nature (Varela et al., 1991). These arise through the interactions of their constitutive processes (Combs, 1996; Combs and Krippner, 1998; Goertzel, 1994). In the case of the dreaming brain, these processes represent emotional, sensory, mnemonic, and other aspects of brain activity. Their ongoing readout into consciousness is the narrative experience of the dream. We are not suggesting that a sufficient knowledge of such processes and their interactions would yield an explanation of the meaning of a particular dream in an individual’s conscious experience, or in the context of his or her life – at least not in the foreseeable future. Even if the regularities that underlie the neurological events of dreaming become well understood, they may still look quite different than those that best characterize the experiential aspects of dreaming (Haskell, 1986), which in turn set the stage for a dream’s meaning in
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the context of an individual’s life. Finding the precise relationships that connect the neurological to the experiential levels of dreaming is future work for cognitive neuropsychology. Our aim here is to lay a foundation for this work by making explicit some of the important ways in which the dreaming brain engages in complex self-organizing processes. Far from being random, they are more than adequate in their regularity and complexity to support, at the level of consciousness, the experiential dream narratives that are the basis of interpretative approaches to dreaming. References Anderson, C.M. (1998), “Ibogaine therapy in chemical dependency and posttraumatic stress disorder: a hypothesis involving the fractal nature of fetal REM sleep and interhemispheric reintegration”, Multidisciplinary Association for Psychedelic Studies, Vol. 8, pp. 5-14. Antrobus, J.S. (1991), “Dreaming: cognitive processes during cortical activation and high afferent thresholds”, Psychological Review, Vol. 98, pp. 96-121. Antrobus, J.S., Hartwig, P., Rosa, D., Reisel, R. and Fein, G. (1987), “Brightness and clarity of REM and NREM imagery: photo response scale”, Sleep Research, Vol. 16, p. 240. Arden, J.B. (1996), Consciousness, Dreams, and Self: A Transdisciplinary Approach, Psychosocial Press, Madison, CT. Arkin, A.M., Antrobus, J.S. and Ellman, S.J. (1978), The Mind in Sleep: Psychology and Psychophysiology, Lawrence Erlbaum, Hillsdale, New Jersey. Blagrove, M. (1996), “Problems with the cognitive psychological modeling of dreaming”, Journal of Mind and Behavior, Vol. 17, pp. 99-134. Combs, A. (1996), The Radiance of Being: Complexity, Chaos, and the Evolution of Consciousness, Paragon House, St Paul, Minnesota. Combs, A. and Krippner, S. (1998), “Dream sleep and waking reality: a dynamical view of two states of consciousness”, in Hameroff, S., Kaszniak, A.W. and Scott, A.C. (Eds), Toward a Science of Consciousness: The Second Tucson Discussions and Debates, MIT Press, Cambridge, MA, pp. 478-93. Crick, F. and Koch, C. (1995), “Are we aware of neural activity in primary visual cortex?”, Nature, Vol. 375, pp. 121-3. Crick, F. and Michison, G. (1986), “REM sleep and neural nets”, Journal of Mind and Behavior, Vol. 7, pp. 229-50. Foulkes, D. (1985), Dreaming: A Cognitive-Psychological Analysis, Harvard University Press, Cambridge, Massachusetts. Foulkes, D. (1999), Children’s Dreaming and the Development of Consciousness, Harvard University Press, Cambridge, Massachusetts. Freeman, W.J. and Barrie, J.M. (1994), “Chaotic oscillations and the genesis of meaning in cerebral cortex”, in Buza´ke, G., Llina´s, R., Singer, W., Berthoz, A. and Christen, Y. (Eds),Temporal coding in the brain, Springer-Verlag, New York, pp. 13-38. Goertzel, B. (1994), Chaotic Logic, Plenum, New York. Halaz, M.F. (1995), “Nonlinear dynamics in behavioral systems”, American Psychologist, Vol. 50, pp. 109-405. Hall, C.S. and Van de Castle, R.L. (1966), The Content Analysis of Dreams, Appletion-CenturyCrofts, New York.
Hardy, C. (1998), Networks of Meaning: The Bridge Between Mind and Matter, Greenwood Publishing, Westport, CT.
Dreaming brain
Hartmann, E. (1999), Dreams and Nightmares: The New Theory on the Origin and Meaning of Dreams, Plenum Press, New York. Haskell, R.E. (1986), “Cognitive psychology and dream research: historical, conceptual, and epistemological considerations”, Journal of Mind and Behavior, Vol. 7, pp. 131-60. Hobson, J.A. (1988), The Dreaming Brain, Basic Books, New York. Hobson, J.A. (1994), The Chemistry of Consciousness: How the Brain Changes its Mind, Little Brown, New York. Hobson, J.A. and McCarley, R.W. (1977), “The brain as a dream-state generator: an activationsynthesis hypothesis of the dream process”, American Journal of Psychiatry, Vol. 134, pp. 1335-68. Hobson, J.A., Pace-Schott, E.F. and Stickgold, R. (2000), “Dreaming and the brain: toward a cognitive neuroscience of conscious states”, Behavioral and Brain Sciences, Vol. 23, pp. 793-1121. Hobson, J.A., Pace-Schott, E.F., Stickgold, R. and Kahn, D. (1998), “To dream or not to dream? Relevant data from new neuroimaging and electrophysiological studies”, Current Opinion in Neurobiology, Vol. 8, pp. 239-44. Kahn, D., Combs, A. and Krippner, S. (1998), “The dreaming brain as a self-organizing system”, in Consciousness Research Abstracts: Toward a Science of Consciousness; Tucson III, Imprint Academic, Thorverton, UK, p. 94. Kahn, D. and Hobson, J.A. (1993), “Self-organization theory of dreaming”, Dreaming, Vol. 3, pp. 151-78. Kahn, D., Pace-Schott, E. and Hobson, J. (1997), “Consciousness in the waking brain: the roles of neuronal oscillation and neuromodulation in determining similarities and differences”, Neuroscience, Vol. 78, pp. 13-38. Kampis, G. (1991), Self-modifying Systems in Biology and Cognitive Science, Pergamon, New York. Kellert, S.H. (1993), In the Wake of Chaos: Unpredictable Order in Dynamical Systems, University of Chicago Press, Chicago. Krippner, S. (1991), “An experimental approach to the anomalous dream”, in Gackenbach, J. and Sheikh, A.A. (Eds), Dream Images: A Call to Mental Arms, Baywood Publishing, Amityville, New York, pp. 31-54. Krippner, S. and Combs, A. (2000), “Self-organization in the dreaming brain”, Journal of Mind and Behavior, Vol. 21, pp. 399-412. Mamelak, A.N. and Hobson, J.A. (1989), “Dream bizarreness as the cognitive correlate of altered neuronal behavior in REM sleep”, Journal of Cognitive Neuroscience, Vol. 1, pp. 201-22. Maquet, P., Peters, J.M., Aerts, J., Delfiore, G., Degueldre, C., Luxen, A. and Franck, G. (1996), “Functional neuroanatomy of human rapid-eye-movement sleep and dreaming”, Nature, Vol. 383, pp. 163-6. Nielsen, T.A. (1999), “Mentation During Sleep: the NREM/REM distinction”, in Lydic, R. and Baghdoyan, H.A. (Eds), Handbook of Behavioral State Control: Molecular and Cellular Mechanisms, CRC Press, Boca Raton, Florida, pp. 101-28. Peak, D. (1994), Chaos Under Control: The Art and Science of Complexity, W.H. Freeman, New York.
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Port, R.F. and van Gelder, T. (1995), Mind as Motion: Explorations in the Dynamics of Cognition, MIT Press, Cambridge, MA. Roschke, J. and Aldenhoff, J.B. (1992), “A nonlinear approach to brain function: deterministic chaos and sleep EEG”, Sleep, Vol. 15, pp. 95-101. Russell, C., Bruck, D. and Coleman, G. (1997), “Induction of visual imagery during SWS”, Sleep, Vol. 20, pp. 948-56. Screenivason, R., Pradhan, N. and Rapp, P. (Eds), (1999), Nonlinear Dynamics and Brain Functioning, Nova Science, Huntington, New York. Smith, R.C. (1986), “Evaluating dream function: emphasizing the study of patients with organic disease”, Journal of Mind and Behavior, Vol. 7, pp. 397-410. Solms, M. (1997), The Neuropsychology of Dreams: A Clinico-Anatomical Study, Lawrence Erlbaum, Mahwah, NJ. Tracy, R.L. and Tracy, L.N. (1974), “Reports of mental activity from sleep stages 2 and 4”, Perceptual and Motor Skills, Vol. 38, pp. 647-8. Ullman, M. (1999), “Dreaming consciousness and quantum concepts: suggestive correlations”, Journal of Scientific Exploration, Vol. 13, pp. 91-112. Varela, F.J., Thompson, E. and Rosch, E. (1991), The Embodied Mind: Cognitive Science and Human Experience, MIT Press, Cambridge, MA. Vogel, G.W. (1978), “An alternative view of the neurobiology of dreaming”, American Journal of Psychiatry, Vol. 135, pp. 1531-5.
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Asymptotic models and methods in complex systems dynamics (General approach)
Asymptotic models and methods 1463
Lyudmila K. Kuzmina Kazan Aviation Institute, Adamuck, Kazan-15, Russian Federation Keywords Cybernetics, Stability, Modelling Abstract The paper is concerned with the different aspects of mathematical modelling and analysis in dynamics of complex non-linear systems, that are generated by applied problems of engineering practice. Main aims are the problems of optimal (in some sense) mechanicalmathematical modelling and the regular schemes of decomposition. The critical step in the use of mathematics for solving complex engineering problems is the building of a suitable mathematical model, that, generally speaking, is the result of combining the mathematical formalized procedures as well as heuristic (non-formalized) manners (conjunction of rigorous science and free art). This work advocates a novel approach to the building process of mathematical models, presenting an overview of concepts and techniques needed for modelling, via comprehension of modelling problem as singularly perturbed one. Here uniform methodology, based on methods of Lyapunov theory, Perturbations theory [Asymptotic method in theory of non-linear oscillations (1963)] in accordance with Stability postulate and Singularity postulate is developed. This asymptotic approach (called – LPSS approach) allows to elaborate the general conception of the modelling; to determine the conditions of qualitative equivalence between full model and simplified model. As applications, the different examples of concrete physical nature are considered.
1. Introduction The generalization of reduction principle, that is well-known in stability theory (Lyapunov, 1956), is a very important goal for engineering practice, with applications in framework of computational techniques to modelling, control and automation. Under the designing of any real object in engineering practice various aspects arise from first stages. In the conditions of hard standards upon precision in dynamics problems, it is necessary to take into consideration the most varied factors, that, on the one hand, allow to obtain the detailized, good valid, adequate model; and, on the other hand, introduce vagueness into dynamic model of object. As a rule, original technical object (IO) and initial mathematical model (IMM) is a non-linear, multi-connective, high-dimensional one. Besides, such mathematical model is extremely complex for investigation by analytical and computer-analytical manners. Therefore, in an early step of designing system there arises a necessity to reduce the initial full model (FM) to Author is grateful to Russian Foundation of Fundamental Investigations for the support in this work.
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a simpler one, but with keeping acceptability. So, the complexity is leading to the necessity of the simplification of original FM, with the separation of the system parameters on the substantial and non-substantial ones, with the revealing of main degrees of system freedom, with the subsequent transition to the shortened model (SM); and central problem in any analysis of complex systems is a problem of modelling-reduction. IO ! FM ! SM But in applied works the SM is obtained “on intuition”, without rigorous mathematical analysis of influence of rejected members on dynamic properties. The correctness problem and qualitative equivalence are not discussed. The criterion of validity of this SM on “intuitive level” is experienced. It is obviously, the initial (true) system is the “thing in itself”, that is impossible to be obtained in the process of practical modelling. We should be contented with partial descriptions, that are significant ones in framework of concrete applied problems. For the same system several models may be needed that will be suitable for different regimes. IO ! FM ! SM1
!
SM2
SM3 . . . !
For example, for gyrostabilization system (GSS) that is modelled by Lagrange’s equations in generalized form, IMM is presented as shown (Kuzmina, 1997): d ›T ›R dqM ¼ q_ M þ þ G_qM ¼ Q 0M þ QME þ Q 00M ; dt dt ›q_ M ›q_ M
ð1Þ
d ›T ›R þ ¼ Q 0E þ QEM þ Q 00E dt ›q_ E ›q_ M It is FM, that is electromechanical system (EMS) of ð2n þ uÞ order, with k ¼ n þ u freedom degree; qM is n – vector of Lagrange’s generalized coordinates; qE is u – vector of Maxwell generalized coordinates. In engineering practice, for such FM the SMs of less order are used (Andronov et al., 1959; Kuzmina, 1997; Merkin, 1956):
ð2Þ
These models are introduced on intuitive level as some idealized models, and there is no rigorous substantiation of these models’ legitimacy in applied investigations. Besides, the idealization is understood (Andronov et al., 1959; Chetayev, 1957; Kuzmina, 1997; Merkin, 1956) as selecting main factors and rejecting minor properties, attributes of process under study (in conditions of problem statement). And on this base the forming minimal equations is carried out [minimal model on Moiseev (1981, 1987)]. Here there are important questions: .
how to determine what is substantial, and what is non-substantial;
.
how to select essential attributes from non-essential ones;
.
how to substantiate mathematical decomposition case (SM1 type in equation (2)), that gives minimal SM.
At present, there are no regular efficient algorithms, that allows us to select substantial factors (variables, freedom degrees, etc.) on early step. Also, it is not discussed, how to interpret the idealized model, used in engineering practice. In general, idealized model is only formalized construction, mathematical abstraction, that does not describe the motion of some real object (Campbell, 1980; Merkin, 1956; Siljak, 1991), and it is necessary for the special analysis of validity. In this work a regular algorithm for the effective mechanical-mathematical models is built; the simple schemes of engineering level for decomposition of full systems and dynamical properties are worked out. Besides proposed approach reduces the size of initial problem, thus making the problem computationally tractable. This approach enables us to obtain the simplified models, presenting interest for applications, with rigorous substantiation of their acceptability. In the applications to mechanics (for mechanical systems (MSs) with gyroscopes; for EMSs; for robotics systems, etc.) the obtained results enable to construct the shortened-design models (known and new) by strict method, with the substantiation of their correctness in the dynamical analysis and synthesis. The interpretation of these models leads to new approximate theories in applications of engineering practice. It allows us to optimize the modelling process, to cut down the engineering design time. 2. Initial background Our task is solving the principal problems: .
modelling problems [how to construct the simplified model (SM) in a rigorous mathematical way];
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acceptability problems (when to reduce the investigation of FM to the SM);
.
estimation problems (how to determine the domains of admissible parameters).
Note that for rigorous mathematical statements and rigorous solutions for concrete dynamic properties and concrete cases of SM there are in works of many authors, beginning from early classical works of Lyapunov (in stability theory); Andronov (in oscillations theory); Meerov and Feldbaum (in control theory); Gradstein and Tikhonov (in differential equations theory); Merkin (in gyroscopes theory); etc. There are different approaches, manners, methods for various statements of reduction problem. So, it is necessary to work out the general approach and the rigorous solution for fundamental modelling problem; to elaborate the engineering methods for our principal problems (Kuzmina, 1997; Moiseev, 1987). As initial assumptions, we take the stability postulate (Chetayev, 1936) and the singularity postulate (Kuzmina, 1986, 1997). Besides any object is treated as one of singularly perturbed class, for that IMM always may be represented in standard form as singularly perturbed system (SPS); required transformation of variables always may be constructed. SM is treated as an asymptotic model of the s-level on small parameter m (Kuzmina, 1997), that corresponds to approximate shortened systems (SSs). Constructing this SM is realized by elaborated method, that gives the regular algorithm (simple scheme) of engineering level:
m:
IO ! IMM ! SPS ! SS ! SM ð3Þ ðq; q † Þ
ðyÞ
ðyÞ
ðq; q † Þ
(q, q †) is vector of original phase variables; y is vector of new variables, with what IMM is led to the standard form of system with the non-regular members: SPS
M ðmÞ
dy ¼ Y ðt; m; yÞ dt
ð4Þ
With reference to requirement of mechanics we assume here that m . 0 is a small dimensionless parameter; y is the vector of state variables, connected with the original phase variables (generalized coordinates) by corresponding transformation; M(m ) is matrix, for that the elements are the functions, containing m parameter in different powers (generally speaking, non-integer ones), m ai ; 0 # ai # r; Y(t, m, y ) is non-linear vector function, that is holomorphic one on the set of all variables, including m.
As SS for equation (4) we introduce the SS of s-level (s-system) (Kuzmina, 1994, 1998): SS
M s ðmÞ
dy ¼ Y s ðt; m; yÞ dt
ð5Þ
System (5) is an approximate one, in what the members with m ai are kept only for ai # s; and s , r is concrete, chosen in advance, number. Notice: we use, as generating system, this SPS (5). Such non-traditional approach is very perspective for the above formulated problems in mechanics. Many familiar SM, widely used in applications (see Section 1) are non-limit models, and the technique of limiting transition does not give the possibility to obtain these models through rigorous mathematical ways; it also does not allow us to investigate specific critical cases, characteristic for such systems. It is necessary that new approaches are developed here. In addition, we obtain the possibility to introduce the sequence of different simplified systems, in accordance with the introducing hierarchy of variables on small parameter m
m
ðSS0 Þm ; ðSS1 Þm ; ðSS2 Þm ; . . .
ð6Þ
Besides, returning to old variables (q, q †), we obtain the simplified models
m
ðSM0 Þm ; ðSM1 Þm ; ðSM2 Þm ; . . .
Asymptotic models and methods
ð7Þ
Solving the important problem of the constructing comparison systems and comparison models is an effectual method. Such a manner permits to detour many features in the singular systems theory and to solve the main problems: the building of correct simplified systems in a strict mathematical way; the substantiation of acceptability for these SS; the estimation of the errors. For the determination of correctness conditions, we use the ideology of stability theory. Following the ideas of Chetayev, in accordance with the methods of Lyapunov, we solve here the several dynamic problems (of stability, of proximity, of optimality, of quickoperativeness, etc. both in non-critical and in critical cases; for simple and for multiple roots, etc.) as singular problems (Kuzmina, 1991). 3. Some theoretical and applied aspects Here, the uniform method is elaborated. It is based on Lyapunov’s stability theory methods, on Chetayev’s stability postulate and on singularity postulate. Regular technique is developed, that gives the constructive tools for solving our problem (modelling-reduction), because it may be covered by modification of stability problems in Lyapunov’s sense.
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For example, in the extension of classical statements of stability problems, the other problems were stated and solved (that have close connection with modelling-reduction problem in context of SPS theory): .
problem of (A, l )-estimation for approximate solution of differential equations system (Chetayev);
.
problem of set-stability (S.V. Zubov);
.
problem of (l, l, t0, T )-estimation for approximate solution (Chetayev);
.
problem of proximity between solutions of full system and approximate system (Gradstein);
.
problem of quasi-stability (Persidskiy);
.
problem of stability with parametric perturbations (Kuzmin, regular case; Kuzmina, non-regular case);
.
problem of (1, d, m*, g )-estimation (Kuzmina).
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Besides goal is the development of manners, approaches for process modelling; but non-elaboration of mathematical methods for solving complex differential equations. First stage (methodology and tools). Main statements: initial object is treated as system of singularly perturbed class; IMM is represented in standard form of singular equations system; besides shortened model is treated as asymptotic model, that is corresponding s-approximation (approximate, singularly perturbed s-system). Second stage (shortened models’/legitimacy). Basic points: shortened model is treated as some idealized model (Chetayev, 1957; Kuzmina, 1997); acceptability problem is comprehended as stability problem in extended sense (singularly perturbed problem). Solving problem is separated into several steps, for concrete dynamic singularly perturbed problems: stability, set stability, optimality, maximal stability degree, etc.). Third stage (estimations of parameters domains, permitting introduced reduction). Here also methods of stability theory is used as a powerful tool for development of regular technology in solving these problems (estimations). We considered the different mechanical objects, using unified approach, as objects of singularly perturbed class. Proposed, elaborated approach corroborated the universality of it: for all investigated systems we constructed the corresponding transformation of variables, that is bringing the IMM of type (1) (accepted in framework of traditional Newton’s model) to the standard form of equation (4); we obtained the simplified models, using the scheme (3), as comparison models, that are correct in dynamic problems; we determined the conditions of their acceptability.
These results are received for: .
MSs with non-rigid elements;
.
gyroscopic systems (GSs) with fast gyroscopes and small gyroscopes;
.
EMSs with small-inertia electrical circuits;
.
systems of gyrostabilization (modelled as EMS) with quick-response follow subsystems, fast gyroscopes in control subsystems, and big stabilized mass;
.
robotic systems with fast-response drives; with non-absolute rigidity of elements;
.
MS with big friction;
.
point mass dynamics, etc.
Also in this work the singularly perturbed problems of stability are considered for special cases, unsolved in perturbation theory. The proximity problems between the solutions of IMM and SM are solved on infinite time interval; the results are obtained, generalizing the ones of L. Fletto, N. Levinson for Lagrange’s models of MSs. 4. Conclusion We obtained new interesting results for general modelling theory. From mathematical view point – it is elaborated asymptotic approach, combining Lyapunov’s theory methods and perturbations theory methods, that allows us to investigate dynamic complex system by computer-analytical way, because it is effectively reducing the complexity. From philosophical point – this approach allows us to comprehend the essence of idealization problem (here, there is another, more correct, statement: that should be kept in shortened model, if some real property is interesting for system behaviour). From gnosiological point – the substantiation of legitimacy of approximate models (theories) in mechanics (that are different from Newton’s model) is obtained. These results are perspective both for the perturbations theory (the singular problems in specific cases are solved) and for applications in mechanics (the problems of mathematical modelling in oscillation theory; in systems theory with fast rotors, with non-rigid elements, with quick-responsive drives, with big friction, etc. are discussed). Here we obtain the way to investigate a compound system by analytical, computer-analytical methods; to introduce the reduction of original model with the division of variables on different frequency groups. New approximate models are constructed as comparison models; interesting physical interpretation is revealed for these formalized mathematical “constructions”, including the ones known in mechanics
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precessional model, Aristotel’s model, etc. Also some general aspects of modelling, concerned with Newton’s model in mechanics, are ones at issue in work (with accepted points, within the scope of stability postulate and singularity postulate). This research is corroborating, that LPSS-approach, founded on Lyapunov’s methods, is a worthwhile, constructive, mathematical tool in complex systems dynamics, with good perspectives. References Andronov, A.A., Vitt, A.A. and Khaikin, S.E. (1959), Oscillations Theory, St. publish, Moscow. Bogolyubov, N.N. and Mitropolsky, Yu.A. (1963), Asymptotic Methods in Theory of Non-linear Oscillations, St. publish, Moscow. Campbell, S.L. (1980), Singular Systems of Differential Equations, Pitman Publishing, NY. Chetayev, N.G. (1936), Proceedings of Kazan Aviation Institute, Vol. 5, pp. 3-8. Chetayev, N.G. (1957), Appl. Math. Mech., Vol. 21 No. 3, pp. 419-21. Kuzmina, L.K. (1986), Proceedings, VIth Union Congress of Theor. And Appl. Mechanics, Tashkent, p. 398. Kuzmina, L.K. (1991), Appl. Math. Mech., Vol. 55 No. 4, pp. 594-601. Kuzmina, L.K. (1994), Advances in Model and Analysis, ASME Press, Vol. 44, No. 4 pp. 56-64. Kuzmina, L.K. (1997), Syst. Anal. Model. Simul., Vol. 29, pp. 105-18. Kuzmina, L.K. (1998), Asymptotic Approach to the General Problem of Modelling, IEEE-SMC’98, San Diego, Vol. 4. Lyapunov, A.M. General Problem of Motion Stability, Moscow, USSR AS, Coll. of papers, Vol. 2 No. 7, p. 263. Merkin, D.R. (1956), Gyroscopic Systems, St. publish, Moscow. Moiseev, N.N. (1981), Mathematical Problems of Systemic Analysis, St. publish, Moscow. Moiseev, N.N. (1987), Development Algorithms, St. publish, Moscow. Siljak, D.D. (1991), Decentralized Control of Complex Systems, Academic Press, Inc., NY.
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Relonics: balascopy-based systems-specific technology Vadim I. Kvitash Department of General Internal Medicine, School of Medicine, University of California at San Francisco and Personal Health Response, Inc., San Francisco, CA, USA
Balascopy-based systems-specific technology 1471
Keywords Cybernetics, Control, Coordination Abstract Relonics is a systems-specific technology based on a complete scientific theory of control, regulation and coordination in super-complex systems which allows generation of a new class of relational systemic information currently not available from any existing technologies.
Introduction We are still living in the shadow of the great Ludwig von Bertalanffy and continue to ruminate on his profound insights. New theories often do not live up to their initial promises, especially when they work their way toward pragmatic applications. This is what also happens to the General Systems Theory. General Systems Theory did not progress to the level of a complete scientific theory for significant reasons: lack of operationally defined systemsspecific methodologies, practical useful tools (Nagel, 1961) and above all, the power to predict systems complex behavior (Loeb, 1916). To overcome these limitations, Relonics was developed, tested and verified (Kvitash, 1993, 1994, 2001). Relonics is a systems-specific technology and complete scientific General Systems Theory derived from Balascopy-based triple black-box axiomatic theory of control, regulation and coordination in super-complex systems which contain ten axioms of existence, functioning and purpose:. Axiom 1. There are different types of systems-specific relationships. Axiom 2. There are three black-box type sub-systems: for control, for regulation, and for coordination. Axiom 3. There are systems-specific internal logic, systems-specific metrics and structural signaling. Axiom 4. Control governs both regulation and coordination.
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Axiom 5. Regulation is responsible for quantitative and directional changes which can be measured by available artificial metrics external to the systems itself. Axiom 6. Coordination is responsible for relational and qualitative changes within the systems which cannot be measured due to lack of natural metrics internal to the systems itself. Axiom 7. Functions of Regulation and Coordination are mutually independent. Axiom 8. The purpose of control is to maintain systems syntegrity. Axiom 9. The purpose of regulation is to maintain systems sequential adaptation. Axiom 10. The purpose of coordination is to maintain systems constant optimality. Balascopy is an applied methodology and pragmatic tool for mining and simultaneous mapping of quantitative, qualitative, relational and directional information in multi-parametric systems. Balascopy scale is a natural systemic, quantitative scale between empirical minimal and maximal extremes, scored from 0 to 100 in natural systems equivalent units (Kvitash, 1983, 1985). Super-complex systems are defined as a natural or human-made systems, global behavior of which cannot be predicted or sufficiently understood. From Axiom 7 it follows that malfunctioning regulation can coexist with normal coordination. Malfunctioning coordination can co-exist with normal regulation. Also, both regulation and coordination can be malfunctioning at the same time. Together, they represent regulation-coordination duality. Regulation (R) and Coordination (C) also possess a normal-abnormal duality: nR-aR, nC-aC. The double duality of Regulation-Coordination and normalabnormal has a significant role in achieving syntegrity and maintaining unity and systems wholeness and is expressed as: (nRnC) – optimal systems functioning (aRnC) – adaptive systems changes (nRaC) – hidden systems malfunctions (aRaC) – overt systems failures This construct provides an effective practical tool for discrimination of adaptive and non-adaptive systemic changes (Souroujon and Kvitash, 2001).
Systems relational universals Balascopy-based It is generally accepted that relationships are the essential features of any systems-specific systems. However, the word “relationships” is overloaded with a variety of technology completely different meanings. To avoid the danger of confusion of adding new meaning to an old word (Clark and Gerrig, 1983), systems relationships are termed as relons and reloms. 1473 Relons are defined as normal, functional, symmetrical or balanced binary relationships which do not contribute to systems malfunction or failure. They exist as two different types: normal and adaptive. Reloms are defined as abnormal, dysfunctional, asymmetrical, imbalanced or dysbalanced binary relationships which directly contribute to systems malfunction, insufficiency or failure. They exist as five different types: inversion, simple inversion, integration, inverted integration, disintegration, inverted disintegration (Kvitash, 2001). Inversion is a relationship amongst system components when their mutual position on the balascopy scale is inverted and their numerical values are either normal or abnormal. Simple Inversion is relationships among system components when their mutual position on the balascopy scale is inverted but their numerical values are still within established normal ranges of functioning. Integration is relationships among system components when their mutual position on the balascopy scale is abnormally close to each other. Inverted Integration is relationships among system components when their mutual position on the balascopy scale is abnormally close to each other, and at the same time is inverted. Disintegration is relationships among system components when their mutual position on the balascopy scale is abnormally far away from each other. Inverted Disintegration is relationships among system components when their mutual position on the balascopy scale is abnormally far away from each other and at the same time is inverted. In Relonics, multiple binary relationships among elements, parts, subsystems or processes are precisely identified, computed and subsequently mapped as primary, secondary and tertiary meta-networks. Primary meta-networks Primary meta-networks are the simplest structures, irreducible to other structures without losing basic structural characteristics. (Table I). Secondary meta networks Secondary meta-networks are any combination of the same types of primary meta-networks. (Table II).
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Tertiary meta-networks Tertiary meta-networks are any combination of not the same types of primary meta-networks. (Table III) Systems functions are usually globally described in terms of balance or out of balance. In both cases, balance and out of balance are used in a metaphorical sense implying mostly mechanical analogy. In a systems sense, “out of balance” actually consists of two distinct types – Systems Imbalance and Systems Dysbalance. Systems Imbalances are abnormal relationships between two systems components or systems processes. Systems Dysbalance is a complex, multiple, abnormal relationship among three or more systems components or systems processes. Application of Relonics for evaluation of complexity of biochemical processes constantly going on in the human body in health and disease revealed extreme structural diversity of metabolic reloms. For pragmatic purposes, structures of human metabolic reloms are represented as primary, secondary, tertiary biochemical meta-networks and categorized by ten levels of their severity as seen in different diseases (Figures 1-10).
Table I.
Linear Single Chains Non-linear Fans Loops Webs
Table II.
Fan and Fan Loop and Loop Web and Web Fan and Fan and Fan Loop and Loop and Loop Web and Web and Web
(F-F) (L-L) (W-W) (F-F-F) (L-L-L) (W-W-W)
Table III.
Fan and Loop Chain and Loop Single and Loop Fan and Loop and Web Chain and Loop and Web Chain and Loop and Web and Fan
(F-L) (C-L) (S-L) (F-L-W) (C-L-W) (C-L-W-F)
(S) (C) (F) (L) (W)
Empirical study of the seven types of relational invariants – normal relons (N.), Balascopy-based adaptive relons (A.), disintegrated reloms (D.), integrated reloms (I.), inverted systems-specific reloms (Ni), inverted disintegrated reloms (Di), inverted integrated reloms (Ii) – technology reveals a highly complex systemic changes in biochemical processes at different pathological conditions in the human body and shows that the spread
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Key: (Biochemical variables legend: ALB – albumin, CAL – calcium, PHO – phosphorus, SGO – SGOT (AST), GLU - glucose, ALK – alkaline phosphotase, LDH, T.B – total bilirubin, BUN, UR – uric acid, CHO – cholesterol, T.P – total protein. This key applies to Figures 2 – 10 also.)
Figure 1. Level 1. Single biochemical imbalances: Any of the six types of biochemical imbalances can exist only between any of two variables
Figure 2. Level 2. Linear biochemical dysbalances: Any of the six types of biochemical dysbalances can exist in a linear sequence involving three or more variables
Figure 3. Level 3. Fan metanetworks of biochemical dysbalances: Any of the six types of biochemical dysbalances can exist structurally as a fan involving four or more variables
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of imbalances through the metabolic systems as well as their dynamical changes from one type of relons or reloms to another type are neither random nor chaotic but homogenetic. Their transformations can go only through a strict hierarchy of three connected directional pathways: one linear pathway and two non-linear circular pathways. Linear pathway: [D. $ N. $ I. $ Ii $ Ni $ Di.] Non-linear circular pathways:[N. $ A. $ I. $ N.]; [N. $ A. $ D. $ N.] The identification of three distinct directional pathways provides a tool for deeper understanding of systems dynamics, precise assessment of type, extent
Figure 4. Level 4. Loop metanetworks of biochemical dysbalances: Any of the six types of biochemical dysbalances can exist structurally as a loop involving three or more variables
Figure 5. Level 5. Web metanetworks of biochemical dysbalances: Any of the six types of biochemical dysbalances can exist structurally as a web involving four or more variables
Figure 6. Level 6. Secondary metanetworks of biochemical dysbalances: Any of the six types of biochemical dysbalances can exist as a secondary network involving only two structures from the same level
and severity of systems dysfunctions. Tracking directional pathways also Balascopy-based provides significant information which can be used for accurate prediction and systems-specific monitoring of systems dynamics (Lozitsky and Kvitash, 2001). technology Clinical usefulness of developed tools were successfully verified in Ischemic Heart Diseases (Kvitash et al., 1986; Kvitash, 2001, 2002), Pulmonary Function Testing (Fallat and Kvitash, 1985), Allergy (Kvitash 1477 et al., 1994), HIV-related diseases (Schmidt and Kvitash, 1987; Schmidt et al., 1993) and Geriatrics (Mahler et al., 1993). These tools identified previously unknown patterns of metabolic networks in 66 diseases (Kvitash and Kaufman, 1985; Kvitash, 1999, 2001, 2002) and discovered a novel class of knowledge – detectable immuno-metabolic pathology (Schmidt et al., 1985; Kvitash et al., 1986). Presented technology demonstrated its usefulness in the following: (1) Mining new class of systems-specific relational information which is not available from any existing modalities. (2) Effectively communicating results in clear, understandable and precisely measurable ways.
Figure 7. Level 7. Secondary metanetworks of biochemical dysbalances: Any of the six types of biochemical dysbalances can exist as a secondary network involving three or more structures combined from Level 3 with Level 3, or Level 4 with Level 4, or Level 5 with Level 5
Figure 8. Level 8. Tertiary metanetworks of biochemical dysbalances: Any of the six types of biochemical dysbalances can exist as a tertiary network involving any two structures combined from different levels
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(3) Simultaneously evaluating relational quantitative, qualitative and directional feature of natural and human-made systems in syntegrated 66-D multiple-dimensional ways. (4) Transforming numerical data points into useful coherent relational patterns of 66-D networks.
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(5) Accelerating human heuristic abilities and enhancing creativity. (6) Pushing the limits of human perception, cognition and communication. (7) Facilitating accurate and reliable medical diagnosis, effective treatment decisions and disease management. (8) Early recognition of diseases. (9) To discover new clinical entities, and identifying new subtypes of known diseases, and diagnostic pattern cognition/recognition. (10) Allows critical enhancement in human potential to benefit from the complexities which exist in natural and human-made systems.
Figure 9. Level 9. Tertiary metanetworks of biochemical dysbalances: Any of the six types of biochemical dysbalances can exist as a tertiary network involving any three structures combined from different levels
Figure 10. Level 10. Tertiary metanetworks of biochemical dysbalances: Any of the six types of biochemical dysbalances can exist as a tertiary network involving three or more structures combined from different levels.
References Clark, H.H. and Gerrig, R.J. (1983), “Understanding old words with new meanings”, Journal of Verbal Learning and Verbal Behavior, Vol. 22, pp. 591-608. Fallat, R.J. and Kvitash, V.I. (1985), “Computerized pulmo-balascopy”, AAMSI CONGRESS 85, Proceedings of the Congress on Medical Informatics, San Francisco, CA, pp. 372-4. Kvitash, V.I. (1983), “Balascopy as a tool for heuristic diagnosis”, AAMSI Congress 83, Proceedings of the Congress on Medical Informatics, San Francisco, CA, pp. 121-5. Kvitash, V.I. (1985), “Balascopy: method for detecting and rapidly evaluating multiple imbalances within multi-parametric systems”, U.S. Patent No. 4,527,240. Kvitash, V.I. (1993), “Balascopy-based cognitive tools for dynamical systems analysis”, Conversation on the Future of International Society for the Systems Sciences, Strategic Planning Conference, 3-5 October, Asilomar Conference Center, Pacific Grove, CA, p. 44. Kvitash, V.I. (1994), “Balascopy-based systems science technology: from theoretical foundations to pragmatic cognitive tools. Workshop/Tutorial. New systems thinking and action for a new century”, Proceedings of the 38th Annual Meeting of International Society for the Systems Sciences, Asilomar Conference Center, Pacific Grove, CA, 14-19 June, Vol. 2, pp. 1613-4. Kvitash, V.I. (1999a), “Sic Transit Gloria numeri: methodology and practical tools for mining diagnostic information from useless and seemingly normal data”, Emerging Statistical Issues in Public Health for the 21st Century, 7th Biennial CDC and ATSDR Symposium on Statistical Methods, 27-29 January, Atlanta, Georgia, p. 96. Kvitash, V.I. (1999b), “Balascopy-based general systems technology: theory, methodology and practical tools”, The 43rd Annual Conference of the International Society for the Systems Sciences, 27 June - 2 July, Asilomar, CA, pp. 244-5. Kvitash, V.I. (2001a) “Balascopy-based systems modeling categorically predicts heart attack outcome”, 45th Meeting of the International Society for the Systems Sciences, Asilomar, CA, 8-13 June, pp. 189-91. Kvitash, V.I. (2001b), “Relons and reloms: the living systems relational universals”, 45th Meeting of the International Society for the Systems Sciences, Asilomar, CA, 8-13 June, pp. 192-3. Kvitash, V.I. (2002a), “Categorical prediction of acute chest pain outcome by relonics”. This issue. Kvitash, V.I. (2002b), The cruel blow to the biomedical paradigm not based on systems sciences and cybernetics. This issue. Kvitash, V.I. (2002c), “Specific relonic patterns from non-specific or useless laboratory data”. Part II - Vol. 32 Nos 5/6, 2003. Kvitash, V.I. and Kaufman, H.S. (1985), “Computerized medical balascopy”, AAMSI Congress 83, Proceedings of the Congress on Medical Informatics, San Francisco, CA, pp. 365-69. Kvitash, V.I., Erdberg, P. and Gaines R. (1994), “Kvitash-Erdberg-Gaines syndrome in atopic females: red wine-induced headache, low total ige, chronic tiredness, personality disorders, drugs and animal hypersensitivity”, XV International Congress of Allergology and Clinical Immunology, Annual Meeting of the European Academy of Allergology and Clinical Immunology, 26 June-1 July, Stockholm, Sweden, p. 178. Kvitash, V.I., Kaufman, H.S. and Elevitch F. R. (1986), “Balascopic patterns of early multiple metabolic abnormalities in patients with acute coronary heart disease”, Proceedings of AAMSI Congress 1986. Computer Applications in Medicine and Health Care, Anaheim, CA, pp. 303-4. Kvitash, V.I., Schmidt, R.M. and Kaufman, H.S. (1986), “Nutrition-immunity-disease continuum: novel technology for detection, quantification and representation”, Proceedings of
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International Symposium, Nutritional Regulation of Immunity and Infection, Toronto, Canada. Loeb, J. (1916), The Organism as a Whole, G. P. Putnam’s Sons, New York and London. Lozitsky, V.P. and Kvitash, V.I. (2001), “Tracking directional pathways of systems imbalances”, 45th Meeting of the International Society for the Systems Sciences, Asilomar, CA, 8-13 June, pp. 226-7. Mahler, E.M., Schmidt, R.M. and Kvitash, V.I. (1993), “An artificial intelligence system to predict progression of immune dysfunction in healthy older patients”, Journal of Medical Systems, Vol. 17, pp. 173-81. Nagel, E. (1961), The Structure of Science. Problems in the Logic of Scientific Explanation, Harcourt, Brace and World, Inc., New York and Burlingame. Schmidt, R.M. and Kvitash, V.I. (1987), “Behavioral, immunological and biochemical patterns in ARC and AIDS”, III International Conference on AIDS, 1-5 June, Washington, DC, p. 95. Schmidt, R.M., Kvitash, V.I. and Kaufman, H.S. (1985), “Immuno-deficiency: abnormal immunometabolic networks in ARC and AIDS” 7th European Immunology Meeting, Jerusalem, Israel, 1-13 September, p. 26. Schmidt, R.M., Mahler, E.M. and Kvitash, V.I. (1993), “Metabolic cofactors associated with progression to Kaposi’s Sarcoma or PCP with initial diagnosis of AIDS”, Abstracts of IXth International Conference on AIDS and IVth STD World Congress, 6-11 June, Berlin, Vol. 2, p. 288. Souroujon, S. and Kvitash, V.I (2001), “Hierarchial Taxonomy of Living Systems Duality”, 45th Meeting of the International Society for the Systems Sciences, Asilomar, CA, 8-13 June, pp. 297-8.
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The cruel blow to the biomedical paradigm not based on systems sciences and cybernetics
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Vadim I. Kvitash Department of General Internal Medicine, School of Medicine, University of California at San Francisco and Personal Health Response, Inc., San Francisco, CA, USA Keywords Cybernetics, Biomedical Abstract Systems-Specific Technology can detect, identify, evaluate and represent previously unknown patterns of multi-dimensional networks which underline clinically significant metabolic disorders not identifiable by currently available diagnostic modalities.
Introduction and discussion Systems-Specific Technology can detect, identify, evaluate and represent previously unknown patterns of multi-dimensional networks which underline clinically significant metabolic disorders not identifiable by currently available diagnostic modalities. “Everything is perfectly normal” are probably the most dangerous words which a chronic symptomatic patient can hear from a physician. In such situations, both feel uneasy and the patient often leaves with a sense of disappointment and sometimes even in anger which can damage the patientphysician therapeutic relationship. However, such words are not a result of bad intentions or subconscious hostility toward difficult patients. Neither is it a sign of neglect or professional incompetency. Rather, they are reflections of negative sides of the Biomedical Paradigm which is still missing the opportunity offered by Systems Sciences and Cybernetics. To illustrate how current sophisticated diagnostic technology can be deceptive despite an evidence of immediately obvious gross abnormalities, I would like to demonstrate a case of unusual pattern of morbid obesity involving primarily the buttocks and thighs which hang over normal size knees (Turner, 1986). Just by looking at Figures 1 and 2, one is sure that this woman is definitely not healthy and any physician will immediately think of hypertension, diabetes, thyroid and adrenal pathology.
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Figure 1.
However, this was not the case. Her blood pressure was normal. Her tests for thyroid function, cortisol suppression and diabetes were all normal as well. Her basic metabolic profile was also within reference ranges except for borderline LDH elevation of 310: albumin 4.0, calcium 8.6, phosphorus 3.7, AST (SGOT) 32, glucose 118, alkaline phosphatase 108, total bilirubin 0.5, BUN 15, uric acid 8.4, cholesterol 225, total protein 7.5. Why did our sophisticated diagnostic technology fail in detecting the underlying metabolic pathology which should clearly exist in this case? What was overlooked? The answer is obvious. Biochemical data points do not provide relational information of how different metabolic functions are coordinated and how they perform together as an integrated team. To demonstrate the power of Systems Sciences and Cybernetics approach, the above biochemical results were analyzed by Systems-Specific Technology: Balascopy (version KAMM-12 ) which allowed simultaneous assessment of quantitative + qualitative + relational + directional systemic features of human metabolism (Kvitash, 1983, 1985, 1999; Kvitash and Kaufman, 1985).
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Figure 2.
Figure 3. Ideal network of metabolic relons
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Figure 4. Relons in unusual obesity case
Figure 5. Reloms in unusual obesity case
Presented below is a network of 66 normal systemic relationships – relons (Kvitash, 2001, 2002) which exists among 12 biochemical variables. This complex network reflects a perfect balance among biochemical variables (Figures 3 – 5). From the above graph, we can see that in this case of morbid obesity, among 11 completely normal biochemical variables, only 62 per cent of normal
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Figure 6.
metabolic relationships (41 relons) are still functioning as an organized and well-coordinated system. Also, from that graph it is easy to see which relons are lost. For example, ALB-TP, ALB-UR and so on up to 23 other relons. Therefore, between albumin and total protein, albumin and uric acid now exist other relationships – abnormal systemic relationships, or reloms (6) which are graphically presented below.
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This graph shows a structure of 25 reloms participating in an overall network of metabolic disorder which exists among 12 biochemical variables. Structure and complexity of reloms has a special diagnostic meaning. Reloms have been classified into 6 distinct types of Meta-Networks of Biochemical Imbalances: Type 1 (Inversion), Type 2, (Simple Inversion), Type 3 (Integration), Type 4 (Inverted Integration), Type 5 (Disintegration), Type 6 (Inverted Disintegration) and are presented. (Figure 6) On Meta-Networks of Biochemical Imbalances for that morbidly obese case, we can see that Balascopy (version KAMM-12 ) for the first time identifies previously unknown eight deep structures of systemic metabolic pathology. Types 1, 2, 3, 4 and 5 of Relational Biochemical Abnormalities. Two single reloms of Types 1 and 4, two linear reloms of Types 1 and 2 and four non-linear complex reloms network of Types 1, 2, 3 and 5. As this case shows, Systems Specific Technology can detect, identify, evaluate and represent previously unknown abnormalities which we believe are the reason for significant metabolic disorders underlying this unusual case of morbid obesity with otherwise normal diagnostic work-up. References Kvitash, V.I. (1983), “Balascopy as a tool for heuristic diagnosis”, AAMSI Congress 83, Proceedings of the Congress on Medical Informatics, San Francisco, CA, pp. 121-5. Kvitash, V.I. (1985), “Balascopy: method for detecting and rapidly evaluating multiple imbalances within multi-parametric systems”, U.S. Patent No. 4,527,240. Kvitash, V.I. (1999), “Sic transit Gloria numeri: methodology and tool for mining information from useless numerical data”, Emerging Statistical Issues in Public Health for the 21st Century. 7th Biennial Centers for Disease Control Symposium on Statistical Methods, 27–29 January, Atlanta, Georgia, p. 96. Kvitash, V.I. (2001), “Relons and reloms: the living systems relational universals”, 45th Meeting of The International Society for the Systems Sciences, Asilomar, 8-13 June, CA, pp. 192-3. Kvitash, V.I. (2002), “Relonics: Balascopy-Based Systems-Specific Technology”. This issue. Kvitash, V.I. and Kaufman, H.S. (1985), “Computerized medical balascopy”, AAMSI Congress 83, Proceedings of the Congress on Medical Informatics, San Francisco, CA, pp. 365-9. Turner, R.C. (1986), “An unusual obesity”, Consultant, p. 147.
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Categorical prediction of acute chest pain outcome by relonics Vadim I. Kvitash Department of General Internal Medicine, School of Medicine, University of California at San Francisco and Personal Health Response, Inc., San Francisco, CA, USA
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Keywords Cybernetics, Biomedical Abstract Relonics, for the first time, identifies previously unknown multi-dimensional patterns of biochemical meta-networks which can serve as specific and sensitive systemic markers for categorical prediction of acute chest pain outcome in individual patients at the time of admission in Intensive Care Unit.
Introduction and discussion Relonics, for the first time, identifies previously unknown multi-dimensional patterns of biochemical meta-networks which can serve as specific and sensitive systemic markers for categorical prediction of acute chest pain outcome in individual patients at the time of admission in Intensive Care Unit. To be useful, prognostic indicators must be highly specific, sufficiently sensitive, minimally intrusive and reasonably expensive. (Goldstein and Holmboe, 1999). According to the American Heart Association statistics, in 1997 alone $10.8 billion was spent for the treatment of coronary heart disease (http://www.americanheart). However, $600 million of that enormous cost proved to be unnecessary: in 85 per cent patients hospitalized with acute chest pain, diagnosis of Acute Myocardial Infarction (AMI) was not confirmed (Ornato, 1999) because of lack of reliable prognostic indicators which could be used prior to hospital admission. Categorical prediction is operationally defined as prognostic assessment of outcome for individual patient using three mutually exclusive categories: (1) definitive non-fatal outcome; (2) definitive fatal outcome; or (3) uncertain outcome (Kvitash, 2001a, b). For the development of prediction patterns for categorical assessment of outcome from patients with acute chest pain, quantitative information from 12 biochemical tests routinely used in clinical medicine for evaluation of metabolic processes in the human body were obtained for initial data base: albumin, calcium, phosphorus, ASL (SGOT), glucose, alkaline phosphatase, LDH, total
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bilirubin, BUN, uric acid, cholesterol, and total protein in 82 consecutive patients were admitted to ICU with acute chest pain to rule out AMI. In 38 patients, diagnosis of AMI was ruled out and in 44 patients, diagnosis of AMI was confirmed. Thirty patients with AMI survived their catastrophic cardiac event and did not develop recurrent myocardial infarctions during the next 24 months of follow-up. Fourteen patients with confirmed AMI died within 48 h from the onset of acute chest pain. For 82 patients admitted to the ICU, routine biochemical tests were performed on admission. Patients were stratified by actual outcome into four clearly distinct groups: (1) AMI with positive non-fatal outcome (Figure 1); (2) AMI with fatal outcome (Figure 2); (3) severe angina (Figure 3); (4) non-angina/non-AMI (Figure 4). Statistical analysis using two-tailed Student’s t-test with significance level of P , 0:05 demonstrated that routine biochemical variables by itself or in any combinations are absolutely useless for predicting outcome in patients with acute chest pain. The same useless numerical data points were reanalyzed by Relonics (Kvitash, 2002) based on Balascopy – Systems-Specific Technology for multidimensional simultaneous assessment of relational quantitative, qualitative, and directional changes (Kvitash, 1983, 1985, 1999, 2001a, b; Kvitash and Kaufman, 1985). Then information from available initial biochemical data points was processed for relonic pattern mining and pattern cognition. Results are presented in the following pages as biochemical meta-networks. Statistical evaluation of overall Relonics performance in categorical prediction of outcome of acute chest pain demonstrated 92.9 per cent sensitivity, 93.3 per cent specificity, 86.7 per cent accuracy for positive prediction, 96.6 per cent accuracy for negative prediction, 6.7 per cent false positive ratio, 7.1 per cent false negative ratio and 93.2 per cent accuracy in identification of patients with acute chest pain who do not need to be admitted into the ICU. In conclusion, practical application of Relonics for categorical individual prediction of acute chest pain outcome demonstrated the following significant advantages. (1) Relonics, for the first time, provided accurate and reliable identification of patients with acute chest pain, therefore averting costly, unnecessary admittance into the ICU. (2) Relonics, for the first time, reliably identified previously unknown and even unsuspected highly ordered patterns of biochemical meta-networks
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Figure 1.
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Figure 2.
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Figure 3.
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Figure 4.
strongly associated with different outcomes in patients with acute chest pain. (3) Biochemical meta-networks can serve as reliable markers for definitive, categorical and individual prediction of acute chest pain outcome. (4) Practical application of Relonics does not require employment of additional and expensive laboratory tests. It utilizes a battery of routine laboratory tests readily available in medical facilities. (5) Application of Relonics demonstrated the validity of Systems Sciences and Cybernetics approach in the resolution of current critical issues in clinical medicine. References American Heart Association. http://www.americanheart.org/statistics/coronary.html Goldstein, R.E. and Holmboe, E.S. (1999), “Prognostic indicators for coronary artery disease”, JAMA, Vol. 281, pp. 565-6. Kvitash, V.I. (1983), “Balascopy as a tool for heuristic diagnosis”, AAMSI Congress 83, Proceedings of the Congress on Medical Informatics, San Francisco, CA, pp. 121-5. Kvitash, V.I. (1985), “Balascopy: method for detecting and rapidly evaluating multiple imbalances within multi-parametric systems”, U.S. Patent No. 4,527,240. Kvitash, V.I. (1999), “Sic transit gloria numeri: methodology and tool for mining information from useless numerical data”, Emerging Statistical Issues in Public Health for the 21st Century. 7th Biennial Centers for Disease Control Symposium on Statistical Methods, Atlanta, Georgia, 27-29 January, p. 96. Kvitash, V.I. (2001a), “Balascopy-based systems modeling categorically predicts heart attack outcome”, 45th Meeting of The International Society for the Systems Sciences, Asilomar, CA, 8-13 June, pp. 189-91. Kvitash, V.I. (2001b), “Relons and reloms: the living systems relational universals”, 45th Meeting of The International Society for the Systems Sciences, Asilomar, CA, 8-13 June, pp. 192-3. Kvitash, V.I. (2002), “Relonics: balascopy-based systems-specific technology”. This issue. Kvitash, V.I. and Kaufman, H.S. (1985), “Computerized medical balascopy”, AAMSI Congress 83, Proceedings of the Congress on Medical Informatics, San Francisco, CA, pp. 365-9. Ornato, J.P. (1999), “Enhanced chest pain evaluation: successful approaches at three centers”, Journal of Critical Illnesses, Vol. 14, pp. 161-5.
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Note from the publisher Looking forward – Kybernetes in 2003 In 2002 Kybernetes continued to develop its reputation at the world’s most authoritative voice on issues relating to cybernetics and systems. As well as regular features such as technical reviews, Internet commentaries, communications and forum contributions and book reviews and reports, the journal continued to publish leading research articles as well as its unique ‘‘Contemporary Systems and Cybernetics’’ section. Additionally, the journal published special issues on Charles Muses, the respected cybernetician and mathematician, Contemporary Cybernetic and Systemic Researches, and of course the current issue centred around papers given at this year’s World Organisation of Systems and Cybernetics Congress. Published in two special double issues. Part II is to be published in Volume 32, No 5/6, 2003. In 2003, we can expect special issues on: . Artificial Life, . Reconstructability Analysis, . New theories about space-time, . Grey systems theory, methodology and applications. These issues will be prepared by the editorial team with the backing of distinguished Guest Editors.
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The Kybernetes Research Award As the official journal of the World Organisation of Systems and Cybernetics (WOSC), Kybernetes was once again delighted to present its Research Award at the WOSC 12th Triannual Congress, held in Pittsburgh, PA. The award, judged by Professor Robert Vallee and Dr. Alex Andrew, was presented to M. Nemiche and Raphael Pla-Lopez of Universitat de Valencia for their paper ‘‘A Learning Model for the Dual Evolution of Human Social Behaviours’’. Three Highly Commended awards were also presented to: . Gary Shaffer of Southern Louisiana University for his paper ‘‘Simulating ecosystem dynamics by isolating events comprised of only a few variables: needs for K-systems granulation methodology’’. . Sifeng Liu, Yi Lin, Yaoguo Dang and Bingjun Li for their paper ‘‘The technical change and the funds for science and technology’’. . Willard Fey and Ann Lam for their paper ‘‘The bridge to humanity’s future’’. Emerald was pleased to support this initiative.
Kybernetes – usage in 2002 Electronic usage of Kybernetes has continued to increase in 2002, with an average of between 3,000 and 4,000 articles being downloaded every month. Over 8,000 article downloads were achieved in March alone. The benefits of having an electronic archive are clear to see when we look at the top ten most accessed articles so far this year. As we can see below, content from the 1997 volume continues to be accessed regularly alongside more recent content: Top ten most accessed articles for 2002 (1) ‘‘Organisations, complexity, and viable knowledge management’’ VMaurice Yolles Volume 29 Number 9 (2) ‘‘Systemic thinking as the philosophical foundation for knowledge management and organizational learning’’ Jon-Arild Johanessen, Johan Olaisen and Bjørn Olsen Volume 28 Number 1 (3) ‘‘Some complementary concepts of communication theory’’ Lars Skyttner Volume 27 Number 2 (4) ‘‘Expert systems: an integral part of knowledge management’’ Jay Liebowitz Volume 27 Number 2 (5) ‘‘Styles of learning and approaches to studying in higher education’’ Noel Entwistle Volume 30 Number 5 (6) ‘‘What have we learnt about student learning? A review of the research on study approach and style’’ Stella Tickle Volume 30 Number 7 (7) ‘‘Organisations as social systems: the search for a systemic theory of organisational innovation processes’’ Jon-Arild Johannessen Volume 27 Number 4
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(8) ‘‘A look at why information systems fail’’ Jay Liebowitz Volume 28 Number 1 (9) ‘‘The viable system model and knowledge management’’ Allena Leonard Volume 29 Number 5 (10) ‘‘Intelligent agent behavior based on organizational image theory’’ David G Schwartz and Dov Te’eni Volume 30 Number 2 Do not forget to use your electronic entitlement as a subscriber to this journal – tell us about the articles you like, and subjects you would be interested to see covered in the journal. For more information, contact Managing Editor, Vicky Williams at
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Index to Kybernetes, Volume 31, 2002 Authors ABBAOUI, K., see NGARHASTA, N. ABDELRAHMAN, H., see HABTEMARIAM, T. ABDELRAHMAN, H., see HABTEMARIAM, T. ADAMATZKY, A. and HOLLAND, O., Reaction-diffusion and ant-based load balancing of communication networks, No. 5, pp. 667-681. ADAMATZKY, A., see TARAKANOV, A. AHMED, A., see HABTEMARIAM, T. AHMED, A., see HABTEMARIAM, T. ANDREW, A.M., Unfinished business, No. 7-8, pp. 1014-1020. ANNA, J., see KAMIL, H. ˜ , P., MOLINA, R., PUJOL, M. and RIZO, R., A cybernetic approach to ARQUES, P., COMPAN the multiscale minimization of energy function: Grey level image segmentation, No. 3-4, pp. 596-610. AYANWALE, L., see HABTEMARIAM, T. AYANWALE, L., see HABTEMARIAM, T. BACKLUND, A., The concept of complexity in organisations and information systems, No. 1, pp. 30-43. BADIE, K., Creative idea generation via interpretative approach to analogical reasoning, No. 9-10, pp. 1210-1219. ´ NYA ´ SZ, Cs., and KEVICZKY, L., CLCR optimal input design for IS and IU plant, No. 9-10, BA pp. 1220-1235. ´ NYA ´ SZ, Cs., see KEVICZKY, L. BA
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BEER, S., What is cybernetics? No. 2, pp. 209-219. ´ N, F., see CASTILLO, M. BELTRA BENABIDALLAH, A., CHERRUAULT, Y. and MORA, G., Approximation of multiple integrals by length of -dense curves, No. 7-8, pp. 1133-1150. BENABIDALLAH, A., CHERRUAULT, Y. and TOURBIER, Y., Approximation of several variables functions by products or sums of one variable functions, No. 5, pp. 701-714. BOUNIAS, M., Universe as a self-observable, self-ethical, life-embedding mathematical system, No. 9-10, pp. 1236-1248. BROEKSTRA, G., A synergetics approach to disruptive innovation, No. 9-10, pp. 1249-1249. BUBNICKI, Z., Uncertain variables and their applications for control systems, No. 9-10, pp. 1260-1273. CˇAPKOVICˇ, F., Control synthesis of a class of DEDS, No. 9-10, pp. 1274-1281. CARLSON-SABELLI, L., see SABELLI, H. ´ N, F., Incentives: mechanisms for the consistency of CASTILLO, M., DUQUE, G. and BELTRA the Colombian educational system, No. 9-10, pp. 1282-1288. CˇESˇKA, M., JANOUSEK, V. and VOJNAR, T., Modelling, prototyping, and verifying concurrent and distributed applications using object-oriented petri nets, No. 9-10, pp. 1289-1299. CHEN, Y.-Q., see LI, Z.
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CHERRUAULT, Y., see BENABIDALLAH, A. CHERRUAULT, Y., see BENABIDALLAH, A. CHERRUAULT, Y., see INC, M. CHERRUAULT, Y., see KHELIFA, S. CHERRUAULT, Y., see KHELIFA, S.
1498
CHERRUAULT, Y., see NGARHASTA, N. CHONG-FENG, W., see YI-RONG, Y. CHORAYAN, O.G. and CHORAYAN, G.O., Fuzzy algorithms of the problem solving, No. 9-10, pp. 1300-1305. CHORAYAN, G.O., see CHORAYAN, O.G. CHOUDHURY, M.A. and KORVIN, G., Simulation versus optimization in knowledge-induced fields, No. 1, pp. 44-60. COHEN, J., see HABTEMARIAM, T. COMBS, A., see KRIPPNER, S. ˜ , P., see ARQUES, P. COMPAN COURANT, M. and PEUTREC, S.L., Towards autonomous application interfaces, No. 9-10, pp. 1306-1312. DAN, F., see KE, Z. DOMEK, S., see SKOCZOWSKI, S. DUARTE-MERMOUD, M.A. and IGNACIO CHANG, J., Robust controller design based on model reference approach, No. 1, pp. 76-95. DUQUE, G., see CASTILLO, M. ESPINOSA, A. and JACKSON, M.C. A systemic look at educational development programs: a recent Colombian experience, No. 9-10, pp. 1324-1335. FAN, Y., see WEI, Y. FENG, L.(X)., see HONG-YI, Y. FEY, W.R. and LAM, A.C.W. The bridge to humanity’s future two perspectives on text of a multimedia address, No. 9-10, pp. 1336-1349. FIDELMAN, U., Temporal and simultaneous processing in the brain: a possible cellular basis of cognition, No. 3-4, pp. 432-484. FRANK, M., What is ‘‘engineering systems thinking’’?, No. 9-10, pp. 1350-1360. GABRIELE, S.F., The ‘‘Roundtable’’ for school learning and planning groups: planting a seed for systemic renewal, No. 9-10, pp. 1361-1368. GAUR, S.K., see SATSANGI, P.S. GEYER F., The march of self-reference, No. 7-8, pp. 1021-1042. C´IROVIC´, G. and CEKIC´, Z., Case-based reasoning model applied as a decision support for construction projects, No. 6, pp. 896-910. GRAY, G., see HABTEMARIAM, T. GUO, D., see WU, X
HABTEMARIAM, T., TAMERU, B., NGANWA, D., AYANWALE, L., AHMED, A., ORYANG, D. and ABDELRAHMAN, H., Epidemiologic modelling of HIV and CD4 cellular/ molecular population dynamics, No. 9-10, pp. 1369-1379. HABTEMARIAM, T., TAMERU, B., NGANWA, D., AYANWALE, L., AHMED, A., ORYANG, D., ABDELRAHMAN, H., GRAY, G., COHEN, J. and KREINDEL, S., Application of systems analysis in modelling the risk of bovine spongiform encephalopathy (BSE), No. 9-10, pp. 1380-1390. HANULIAK, I., On the analysis and modelling of computer communication systems, No. 5, pp. 715-730. HOLLAND, O., see ADAMATZKY, A. HONG-YI, Y., FENG, L.(X). and RAN, Y., Pansystems, Guankong technology and information quantization, (to be published in Part II Volume 32, No 5/6, 2003). ´ BOVA ´ , Z., Tools for creating of multimodels, HRUBY´, M., KOCˇ´I, R., PERINGER, P. and RA No. 9-10, pp. 1391-1400. HUBEY, H.M., Evolution of intelligence: direct modeling of temporal effects of environment on a global absolute scale vs statistics, No. 3-4, pp. 361-431. IGNACIO CHANG, J., see DUARTE-MERMOUD, M.A. INC, M. and CHERRUAULT, Y., A new approach to solve a diffusion-convection problem, No. 3-4, pp. 536-549. JACKSON, M.C., see ESPINOSA, A. JAIN, D.K., see SATSANGI, P.S. JANOUSEK, V., see CˇESˇKA, M. JIANGLING, Z., see KE, Z. JOHANNESSEN, J.-A., OLAISEN, J. and OLSEN, B., Aspects of a systemic philosophy of knowledge: from social facts to data, information and knowledge, No. 7-8, pp. 1099-1120. JUMARIE, G., Scaling observation with complex-valued coefficients: some remarks and prospects, No. 5, pp. 682-700. JUMARIE, G., Would dynamic systems involving human factors be necessarily of fractal nature?, No. 7-8, pp. 1050-1058. KAMIL, H. and ANNA, J., Optimal control and approximation of variational inequalities, No. 9-10, pp. 1401-1408. KARAMANOS, K. and KOTSIREAS, I., Thorough numerical entropy analysis of some substitutive sequences by lumping, No. 9-10, pp. 1409-1417. KAUFFMAN, L. and SABELLI, H., Mathematical bios, No. 9-10, pp. 1418-1428. KE, Z., JIANGLING, Z. and DAN, F., Data self-create in data storage system, (to be published in Part II Volume 32, No 5/6, 2003). ´ NYA ´ SZ, Cs., On the reachable robustness limits for time delay control KEVICZKY, L. and BA systems, No. 9-10, pp. 1429-1441. ´ NYA ´ SZ, Cs. KEVICZKY, L., see BA KHELIFA, S. and CHERRUAULT, Y., Approximation of the solution for a class of first order p.d.e. by Adomian method, No. 3-4, pp. 577-595. KHELIFA, S. and CHERRUAULT, Y., Biomedical and biocybernetics applications: the decomposition method for solving first order partial differential equations, No. 6, pp. 844-871.
Index
1499
Kybernetes 31,9/10
KHOUKHI, A., Dynamic modelling and optimal time-energy off-line programming of mobile robots: a cybernetic problem, No. 5, pp. 731-765. KHOUKHI, A., Prototyped genetic search: a cybernetical approach to job-shop scheduling problems, No. 1, pp. 96-114. KOCˇ´I, R., see HRUBY´, M. KONECKI, J., see SABELLI, H.
1500
KORN, J., ‘‘Physics’’ approach to general systems theory, No. 9-10, pp. 1442-1451. KORVIN, G., see CHOUDHURY, M.A. KOTSIREAS, I., see KARAMANOS, K. KREINDEL, S., see HABTEMARIAM, T. KRIPPNER, S. and COMBS, A., A systems approach to self-organization in the dreaming brain, No. 9-10, pp. 1452-1462. KRISHNANKUTTY, K.V., see SUBRAMONIAM, S. KUZMINA, L.K., Asymptotic models and methods in complex systems dynamics (General approach), No. 9-10, pp. 1463-1470. KVITASH, V.I., Relonics: balascopy-based systems-specific technology, No. 9-10, pp. 1471-1480. KVITASH, V.I., The cruel blow to the biomedical paradigm not based on systems sciences and cybernetics, No. 9-10, pp. 1481-1486. KVITASH, V.I., Categorical prediction of acute chest pain outcome by relonics, No. 9-10, pp. 1487-1493. KVITASH, V.I., Specific relonic patterns from non-specific or useless data, No. 9-10, pp. 1494-1515. LAM, A.C.W., see FEY, W.R. LEE, E.T., Line-oriented two-dimensional parallel computer languages, No. 6, pp. 872-883. LI, X., see LI, Z. LI, Y., see LI, Z. LI, Z., CHEN, Y.-Q., LI, Y., LI, X. and LIN, Y., Raster space with relativity, (to be published in Part II Volume 32, No 5/6, 2003). LIN, Y., see ZHILIN, LI. LIU, G., Normal sum decomposition of general systems, (to be published in Part II Volume 32, No 5/6, 2003). LIU, G., Supporting sets for general systems, No. 2, pp. 246-254. LLERAS, E., Communities of learning: a case in local development, (to be published in Part II Volume 32, No 5/6, 2003). LLORET-CLIMENT, M., Direct and indirect causality in living systems, No. 3-4, pp. 485-495. MACKIN, K.J. and TAZAKI, E., Multiagent communication combining genetic programming and pheromone communication, No. 6, pp. 827-843. MARTINEZ, M.E., A biocultural model of aging, (to be published in Part II Volume 32, No 5/6, 2003). MEJI´A, D.A., Can the system idea help promote critical thinking and intellectual autonomy in pedagogy?, No. 9-10, pp. 1313-1323. MISHRA, D.S., see SATSANGI, P.S.
MOLINA, R., see ARQUES, P. MORA, G., see BENABIDALLAH, A. MUSE`S, C., Recollections of Norbert Wiener, Warren McCulloch and Stafford Beer, No. 7-8, pp. 1005-1009. MUSE`S, C., Simplifying complexity: the greatest present challenge to management and government, No. 7-8, pp. 962-988. MUSE`S, C., The unique reach of cybernetics in our fin-de-sie`cle, No. 7-8, pp. 989-1004. NAGIB, J., see SABELLI, H. NECHVAL, K.N., NECHVAL, N.A. and VASERMANIS, E.K., Adaptive dual control in one biomedical problem, (to be published in Part II Volume 32, No 5/6, 2003). NECHVAL, K.N., see NECHVAL, N.A. NECHVAL, K.N., see VASERMANIS, E.K. NECHVAL, N.A., NECHVAL, K.N. and VASERMANIS, E.K., Effective state estimation of stochastic systems, (to be published in Part II Volume 32, No 5/6, 2003). NECHVAL, N.A., see NECHVAL, K.N. NECHVAL, N.A., see VASERMANIS, E.K. NEMICHE, M. and PLA-LOPEZ, R., A learning model for the dual evolution of human social behaviors, (to be published in Part II Volume 32, No 5/6, 2003). NEGOITA, C.V., Postmodernism, cybernetics and fuzzy set theory, No. 7-8, pp. 1043-1049. NGANWA, D., see HABTEMARIAM, T. NGANWA, D., see HABTEMARIAM, T. NGARHASTA, N., SOME, B., ABBAOUI, K. and CHERRUAULT, Y., New numerical study of Adomian method applied to a diffusion model, No. 1, pp. 61-75. OLAISEN, J., see JOHANNESSEN, J.-A. OLSEN, B., see JOHANNESSEN, J.-A. ORYANG, D., see HABTEMARIAM, T. ORYANG, D., see HABTEMARIAM, T. ¨ STERMARK, R., Designing a superstructure for parametric search for optimal search spaces O in non-trivial optimization problems, No. 2, pp. 255-281. PAN, J., see WU, X., PATEL, M., see SABELLI, H. PATEL, M. and SABELLI, H. Autocorrelation and frequency analysis differentiate cardiac and economic bios from 1/f noise, (to be published in Part II Volume 32, No 5/6, 2003). PERINGER, P., see HRUBY´, M. PETKOV, D., see PETKOVA, O. PETKOVA, O. and PETKOV, D., A holistic approach towards the validation and legitimisation of information systems, (to be published in Part II Volume 32, No 5/6, 2003). PEUTREC, S.L., see COURANT, M. PIETRUSEWICZ, K., see SKOCZOWSKI, S.
Index
1501
Kybernetes 31,9/10
PLA-LOPEZ, R., see NEMICHE, M. PUJOL, M., see ARQUES, P. RADICE, G., Development of an autonomous spacecraft for planetary exploration, (to be published in Part II Volume 32, No 5/6, 2003).
1502
RAN, Y., see HONG-YI, Y. ´ BOVA ´ , Z., see HRUBY´, M. RA RIZO, R., see ARQUES, P. ROSE, J.N., ‘‘How much cybernetics can you handle?’’, (to be published in Part II Volume 32, No 5/6, 2003). ROVENTA, E. and SPIRCU, T., Using Be´zier curves in approximate reasoning, No. 7-8, pp. 1121-1132. RUDIN, D.O., Axiomatic combinatorial world theory with emergent intelligence: simplifying understanding and professionalizing general education, (to be published in Part II Volume 32, No 5/6, 2003). RUGHOOPUTH, H.C.S. and RUGHOOPUTH, S.D.D.V., Neural network process vision systems for flotation process, No. 3-4, pp. 529-535. RUGHOOPUTH, S.D.D.V., see RUGHOOPUTH, H.C.S. SABELLI, H., Mathematical development: a theory of natural creation, (to be published in Part II Volume 32, No 5/6, 2003). SABELLI, H., PATEL, M., CARLSON-SABELLI, L., KONECKI, J., NAGIB, J. and SUGERMAN, A., Aging and social systems, (to be published in Part II Volume 32, No 5/6, 2003). SABELLI, H. and SUGERMAN, A., Life-long creation in the prevention of premature aging, (to be published in Part II Volume 32, No 5/6, 2003). SABELLI, H., see KAUFFMAN, L. SABELLI, H., see PATEL, M. SABELLI, H., see SUGERMAN, A. SANTOLI, S., Inside communication in nanostructured evolutionary automata nanophysics and an information concept for viable technologies, (to be published in Part II Volume 32, No 5/6, 2003). SASTRE-VAZQUEZ, P., see USO´-DOME`NECH, J.L. SATSANGI, P.S., MISHRA, D.S., GAUR, S.K., SINGH, B.K. and JAIN, D.K., System dynamics modelling, simulation and optimization of integrated urban systems: a soft computing approach, (to be published in Part II Volume 32, No 5/6, 2003). SINGH, B.K., see SATSANGI, P.S. SKOCZOWSKI, S., DOMEK, S. and PIETRUSEWICZ, K., Model following PID control system, (to be published in Part II Volume 32, No 5/6, 2003). SKYTTNER, L., Monitoring and early warning systems – a design for human survival, No. 2, pp. 220-245. SOME, B., see NGARHASTA, N. SPIRCU, T., see ROVENTA E. STEFANUK, V.L. and ZHOZHIKASHVILI, A.V., Productions and rules in artificial intelligence, No. 6, pp. 817-826.
SUBRAMONIAM, S. and KRISHNANKUTTY, K.V., An expert system for the selection of strategic planning technique, No. 3-4, pp. 550-560.
Index
SUGERMAN, A. and SABELLI, H., Novelty, diversification and nonrandom complexity define creative processes, (to be published in Part II Volume 32, No 5/6, 2003). SUGERMAN, A., see SABELLI, H. SUGERMAN, A., see SABELLI, H. SUSHIL Physical system theory: fundamentals, recent developments and relationships with system dynamics, No. 3-4, pp. 496-528. TAMERU, B., see HABTEMARIAM, T. TAMERU, B., see HABTEMARIAM, T. TAO, L., On the criterion of optimal product structure in the micro-economic system (enterprise) and adjustment of product structure, (to be published in Part II Volume 32, No 5/6, 2003). TARAKANOV, A. and ADAMATZKY, A., Virtual clothing in hybrid cellular automata, No. 7-8, pp. 1059-1072. TAZAKI, E., see MACKIN K.J. TOURBIER, Y., see BENABIDALLAH, A. TSAGANEA, D., Entropic properties of international systems, No. 7-8, pp. 1073-1098. USO´-DOME`NECH, J.L. and SASTRE-VAZQUEZ, P., Semantics of L(MT): a language for ecological modelling, No. 3-4, pp. 561-576. VALENTINO, C.C. Smarter computer intrusion detection utilizing decision modeling, (to be published in Part II Volume 32, No 5/6, 2003). VALLE`E, R., On Charles Muse`s, No. 7-8, p. 1013. VALLE´E, R., Cybernetics and systems, from past to future, (to be published in Part II Volume 32, No 5/6, 2003). VASERMANIS, E.K., NECHVAL, K.N. and NECHVAL, N.A., Statistical validation of simulation models of observable systems, (to be published in Part II Volume 32, No 5/6, 2003). VASERMANIS, E.K., see NECHVAL, K.N. VASERMANIS, E.K., see NECHVAL, N.A. VOJNAR, T., see CˇESˇKA, M. WEI, Y., ZHANG, L. and FAN, Y., Swarm based study on spatial-temporal emergence in flood, (to be published in Part II Volume 32, No 5/6, 2003). WOOD, J., Towards a cybernetics of value, presence, and anticipation, (to be published in Part II Volume 32, No 5/6, 2003). WU, X., see WU, X., WU, X., GUO, D., PAN, J. and WU, X., Pansystems mathematics: an analysis of panweighted field-network, (to be published in Part II Volume 32, No 5/6, 2003). YI, L., see YI-RONG, Y. YI-RONG, Y., CHONG-FENG, W. and YI, L. On stochastic optimal control for stock price volatility, (to be published in Part II Volume 32, No 5/6, 2003). ZEEBERG, B., Randomization and eventual reordering: a number theoretical approach, (to be published in Part II Volume 32, No 5/6, 2003).
1503
Kybernetes 31,9/10
ZHANG, L., see WEI, Y. ZHOZHIKASHVILI, A.V., see STEFANUK, V.L. Titles A biocultural model of aging, MARTINEZ, M.E., (to be published in Part II Volume 32, No 5/6, 2003).
1504
A cybernetic approach to the multiscale minimization of energy function: Grey level image segmentation, ARQUES, P., COMPAN˜, P., MOLINA, R., PUJOL, M. and RIZO, R., No. 3-4, pp. 596-610. A holistic approach towards the validation and legitimisation of information systems, PETKOVA, O. and PETKOV, D., (to be published in Part II Volume 32, No 5/6, 2003). A learning model for the dual evolution of human social behaviors, NEMICHE M. and PLA-LOPEZ, R., (to be published in Part II Volume 32, No 5/6, 2003). A new approach to solve a diffusion-convection problem, INC, M. and CHERRUAULT, Y., No. 3-4, pp. 536-549. A synergetics approach to disruptive innovation, BROEKSTRA, G., No. 9-10, pp. 1249-1249. A systemic look at educational development programs: two perspectives on a recent Colombian experience, ESPINOSA, A. and JACKSON, M.C., No. 9-10, pp. 1324-1335. A systems approach to self-organization in the dreaming brain, KRIPPNER, S. and COMBS, A., (to be published in Part II Volume 32, No 5/6, 2003). Adaptive dual control in one biomedical problem, NECHVAL, K.N., NECHVAL, N.A. and VASERMANIS, E.K., (to be published in Part II Volume 32, No 5/6, 2003). Aging and social systems, SABELLI, H., PATEL, M., CARLSON-SABELLI, L., KONECKI, J., NAGIB J., and SUGERMAN, A., (to be published in Part II Volume 32, No 5/6, 2003). An expert system for the selection of strategic planning technique, SUBRAMONIAM, S. and KRISHNANKUTTY, K.V., No. 3-4, pp. 550-560. Application of systems analysis in modelling the risk of bovine spongiform encephalopathy (BSE), HABTEMARIAM, T., TAMERU, B., NGANWA, D., AYANWALE, L., AHMED, A., ORYANG, D., ABDELRAHMAN, H., GRAY, G., COHEN, J. and KREINDEL, S., No. 9-10, pp. 1380-1390. Approximation of multiple integrals by length of -dense curves, BENABIDALLAH, A., CHERRUAULT Y. and MORA G., No. 7-8, pp. 1133-1150. Approximation of several variables functions by products or sums of one variable functions, BENABIDALLAH, A., CHERRUAULT, Y. and TOURBIER, Y., No. 5, pp. 701-714. Approximation of the solution for a class of first order p.d.e. by Adomian method, KHELIFA, S. and CHERRUAULT, Y., No. 3-4, pp. 577-595. Aspects of a systemic philosophy of knowledge: from social facts to data, information and knowledge, JOHANNESSEN, J.-A., OLAISEN, J. and OLSEN, B., No. 7-8, pp. 1099-1120. Asymptotic models and methods in complex systems dynamics (General approach), KUZMINA, L., No. 9-10, pp. 1463-1470. Autocorrelation and frequency analysis differentiate cardiac and economic bios from 1/f noise, PATEL, M. and SABELLI, H., (to be published in Part II Volume 32, No 5/6, 2003). Axiomatic combinatorial world theory with emergent intelligence: simplifying understanding and professionalizing general education, RUDIN, D.O. , (to be published in Part II Volume 32, No 5/6, 2003).
Biomedical and biocybernetics applications: the decomposition method for solving first order partial differential equations, KHELIFA, S. and CHERRUAULT, Y., No. 6, pp. 844-871.
Index
Can the system idea help promote critical thinking and intellectual autonomy in pedagogy?, MEJI´A, D.A., No. 9-10, pp. 1313-1323. Categorical prediction of acute chest pain outcome by relonics, KVITASH, V.I., No. 9-10, pp. 1487-1493. ´ NYA ´ SZ, Cs. and KEVICZKY, L., CLCR optimal input design for IS and IU plants, BA No. 9-10, pp. 1220-1235. Communities of learning: a case in local development, LLERAS, E., (to be published in Part II Volume 32, No 5/6, 2003). Control synthesis of a class of DEDS, CˇAPKOVICˇ, F., No. 9-10, pp. 1274-1281. Creative idea generation via interpretative approach to analogical reasoning, BADIE, K., No. 9-10, pp. 1210-1219. Cybernetics and systems, from past to future, VALLE´E, R., (to be published in Part II Volume 32, No 5/6, 2003). Data self-create in data storage system, KE, Z., JIANGLING, Z. and DAN, F., No. 9-10, pp. 1805-1809. Designing a superstructure for parametric search for optimal search spaces in non-trivial optimization problems, O¨STERMARK, R., No. 2, pp. 255-281. Development of an autonomous spacecraft for planetary exploration, RADICE, G., (to be published in Part II Volume 32, No 5/6, 2003). Direct and indirect causality in living systems, LLORET-CLIMENT, M., No. 3-4, pp. 485-495. Dynamic modelling and optimal time-energy off-line programming of mobile robots: a cybernetic problem, KHOUKHI, A., No. 5, pp. 731-765. Effective state estimation of stochastic systems, NECHVAL, N.A., NECHVAL, K.N., and VASERMANIS, E.K., (to be published in Part II Volume 32, No 5/6, 2003). Entropic properties of international systems, TSAGANEA, D., No. 7-8, pp. 1073-1098. Epidemiologic modelling of HIV and CD4 cellular/molecular population dynamics, HABTEMARIAM, T., TAMERU, B., NGANWA, D., AYANWALE, L., AHMED, A., ORYANG, D. and ABDELRAHMAN, H., No. 9-10, pp. 1369-1379. Evolution of intelligence: direct modeling of temporal effects of environment on a global absolute scale vs statistics, HUBEY, H.M., No. 2, pp. 361-431. Fuzzy algorithms of the problem solving, CHORAYAN, O.G. and CHORAYAN, G.O., No. 9-10, pp. 1300-1305. ‘‘How much cybernetics can you handle?’’, ROSE, J.N., (to be published in Part II Volume 32, No 5/6, 2003). Incentives: mechanisms for the consistency of the Colombian educational system, ´ N, F., No. 9-10, pp. 1282-1288. CASTILLO, M., DUQUE, G. and BELTRA Inside communication in nanostructured evolutionary automata nanophysics and an information concept for viable technologies, SANTOLI, S., (to be published in Part II Volume 32, No 5/6, 2003). Life-long creation in the prevention of premature aging, SABELLI, H. and SUGERMAN, A., (to be published in Part II Volume 32, No 5/6, 2003). Line-oriented two-dimensional parallel computer languages, LEE, E.T., No. 6, pp. 872-883. Mathematical bios, KAUFFMAN, L. and SABELLI, H., No. 9-10, pp. 1418-1428.
1505
Kybernetes 31,9/10
Mathematical development: a theory of natural creation, SABELLI, H., (to be published in Part II Volume 32, No 5/6, 2003). Model following PID control system, SKOCZOWSKI, S., DOMEK S. and PIETRUSEWICZ, K., (to be published in Part II Volume 32, No 5/6, 2003). Modelling, prototyping, and verifying concurrent and distributed applications using objectoriented petri nets, CˇESˇKA, M., JANOUSˇEK V. and VOJNAR, T., No. 9-10, pp. 1289-1299.
1506
Monitoring and early warning systems – a design for human survival, SKYTTNER, L., No. 2, pp. 220-245. Multiagent communication combining genetic programming and pheromone communication, MACKIN, K.J. and TAZAKI, E., No. 6, pp. 827-843. Neural network process vision systems for flotation process, RUGHOOPUTH, H.C.S. and RUGHOOPUTH, S.D.D.V., No. 3-4, pp. 529-535. New numerical study of Adomian method applied to a diffusion model, NGARHASTA, N., SOME, B., ABBAOUI, K. and CHERRUAULT, Y., No. 1, pp. 61-75. Normal sum decomposition of general systems, LIU, G., (to be published in Part II Volume 32, No 5/6, 2003). Novelty, diversification and nonrandom complexity define creative processes, SUGERMAN, A. and SABELLI, H., (to be published in Part II Volume 32, No 5/6, 2003). On Charles Muse`s, VALLE`E, R., No. 7-8, pp. 1013. On stochastic optimal control for stock price volatility, YI-RONG, Y., CHONG-FENG, W. and YI, L., (to be published in Part II Volume 32, No 5/6, 2003). On the analysis and modelling of computer communication systems, HANULIAK, I., No. 5, pp. 752-730. On the criterion of optimal product structure in the micro-economic system (enterprise) and adjustment of product structure, TAO, L., (to be published in Part II Volume 32, No 5/6, 2003). On the reachable robustness limits for time delay control systems, KEVICZKY L. and ´ NYA ´ SZ, CS., No. 9-10, pp. 1429-1441. BA Optimal control and approximation of variational inequalities, KAMIL, H. and ANNA, J. , No. 9-10, pp. 1401-1408. Pansystems mathematics: an analysis of panweighted field-network, WU, X., GUO, D., PAN, J. and WU, X., (to be published in Part II Volume 32, No 5/6, 2003). Pansystems, Guankong technology and information quantization, HONG-YI, Y., FENG, L.(X). and RAN, Y., (to be published in Part II Volume 32, No 5/6, 2003). Physical system theory: fundamentals, recent developments and relationships with system dynamics, SUSHIL, No. 3-4, pp. 496-528. ‘‘Physics’’ approach to general systems theory, KORN, J., No. 9-10, pp. 1442-1451. Postmodernism, cybernetics and fuzzy set theory, NEGOITA, C.V., No. 7-8, pp. 1043-1049. Productions and rules in artificial intelligence, STEFANUK, V.L. and ZHOZHIKASHVILI, A.V., No. 6, pp. 817-826. Prototyped genetic search: a cybernetical approach to job-shop scheduling problems, KHOUKHI, A., No. 1, pp. 96-114.
Randomization and eventual reordering: a number theoretical approach, ZEEBERG, B., (to be published in Part II Volume 32, No 5/6, 2003).
Index
Raster space with relativity, LI, Z., CHEN, Y.-Q., LI, Y., LI, X. and LIN, Y., (to be published in Part II Volume 32, No 5/6, 2003). Reaction-diffusion and ant-based load balancing of communication networks, ADAMATZKY, A. and HOLLAND, O., No. 5, pp. 667-681. Recollections of Norbert Wiener, Warren McCulloch and Stafford Beer, MUSE`S C., No. 7-8, pp. 1005-1020. Relonics: balascopy-based systems-specific technology, KVITASH, V.I., No. 9-10, pp. 1471-1480. Robust controller design based on model reference approach, DUARTE-MERMOUD, M.A. and IGNACIO CHNAG J., No. 1, pp. 76-95. Scaling observation with complex-valued coefficients: some remarks and prospects, JUMARIE G., No. 5, pp. 682-700. Semantics of L(MT): a language for ecological modelling, USO´-DOME`NECH, J.L. and SASTRE-VAZQUEZ, P., No. 3-4, pp. 561-576. Simplifying complexity: the greatest person challenge to management and government, MUSE`S, C., No. 7-8, pp. 962-988. Simulation versus optimization in knowledge-induced fields, CHOUDHURY, M.A. and KORVIN, G., No. 1, pp. 44-60. Smarter computer intrusion detection utilizing decision modeling, VALENTINO, C.C., (to be published in Part II Volume 32, No 5/6, 2003). Specific relonic patterns from non-specific or useless data, KVITASH, V.I., No. 9-10, pp. 1494-1515. Statistical validation of simulation models of observable systems, VASERMANIS, E.K., NECHVAL, K.N. and NECHVAL, N.A., (to be published in Part II Volume 32, No 5/6, 2003). Supporting sets for general systems, LIU, G., No. 2, pp. 246-254. Swarm based study on spatial-temporal emergence in flood, WEI, Y., ZHANG, L. and FAN, Y., (to be published in Part II Volume 32, No 5/6, 2003). System dynamics modelling, simulation and optimization of integrated urban systems: a soft computing approach, SATSANGI, P.S., MISHRA, D.S., GAUR, S.K., SINGH, B.K. and JAIN, D.K., (to be published in Part II Volume 32, No 5/6, 2003). Temporal and simultaneous processing in the brain: a possible cellular basis of cognition, FIDELMAN, U., No. 2, pp. 432-484. The ‘‘Roundtable’’ for school learning and planning groups: planting a seed for systemic renewal, GABRIELE, S.F., No. 9-10, pp. 1361-1368. The bridge to humanity’s future text of a multimedia address, FEY, W.R. and LAM, A.C.W., No. 9-10, pp. 1336-1349. The concept of complexity in organisations and information systems, BACKLUND, A., No. 1, pp. 30-43. The cruel blow to the biomedical paradigm not based on systems sciences and cybernetics, KVITASH, V.I., No. 9-10, pp. 1481-1486. The march of self-reference, GEYER, F., No. 7-8, pp. 1021-1042. The unique reach of cybernetics in our fin-de-sie`cle, MUSE`S, C., No. 7-8, pp. 989-1004.
1507
Kybernetes 31,9/10
Thorough numerical entropy analysis of some substitutive sequences by lumping, KARAMANOS, K. and KOTSIREAS, I., No. 9-10, pp. 1409-1417. ´ BOVA ´ , Z., Tools for creating of multimodels, HRUBY´, M., KOCˇ´I, R., PERINGER, P. and RA No. 9-10, pp. 1391-1400. Towards a cybernetics of value, presence, and anticipation, WOOD, J., (to be published in Part II Volume 32, No 5/6, 2003).
1508
Towards autonomous application interfaces, COURANT, M. and PEUTREC, S.L., No. 9-10, pp. 1306-1312. Uncertain variables and their applications for control systems, BUBNICKI, Z., No. 9-10, pp. 1260-1273. Unfinish business, ANDREW, A.M., No. 7-8, pp. 1014-1017. Universe as a self-observable, self-ethical, life-embedding mathematical system, BOUNIAS, M., No. 9-10, pp. 1236-1248. Using Be´zier curves in approximate reasoning, ROVENTA, E. and SPIRCU, T., No. 7-8, pp. 1121-1132. Virtual clothing in hybrid cellular automata, TARAKANOV, A. and ADAMATZKY, A., No. 7-8, pp. 1059-1072. What is ‘‘engineering systems thinking?’’, FRANK, M., No. 9-10, pp. 1350-1360. What is cybernetics?, BEER, S., No. 2, pp. 209-219. Would dynamic systems involving human factors be necessarily of fractal nature?, JUMARIE, G., No. 7-8, pp. 1050-1058. Book reviews (C.J.H. Mann) RYABININ, I.A., Reliability and Safety of Structure-Complex Systems, No. 1, pp. 143-155. LEWIS, R., Modelling Control Systems using IEC 61499: Applying function blocks to distributed systems, No. 2, pp. 317-326. OMICINI, A., ZAMBONELLI, F., KLUSCH, M. and TOLKSDORF, R. (Eds) Coordination of Internet Agents: Models, Technologies, and Applications No. 3/4, pp. 619-626. FAUGERAS, O., and LUONG, Q.-T., with contributions from PAPADOPOULO, T., The Geometry of Multiple Images: The Laws That Govern the Formation of Multiple Images of a Scene and Some of Their Applications No. 5, pp. 777-782. REITER, R., Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems, No. 6, pp. 924-932. Book reports (C.J.H. Mann) JACKSON, M.C., Systems approaches to management, No. 1, pp. 156-158. RASKIN, J., The Human Interface – New Directions for Designing Interactive Systems, No. 2, pp. 327-329. BEKAKOS, M.P., Highly Parallel Computations: Algorithms and Applications, No. 3/4, pp. 627-631. ANTHONY, M., Artificial Neural Networks: A useful book in this field which uses mathematics linking combinatorics is: Discrete Mathematics of Neural Networks, No. 5, pp. 783-785. CROSS, V.V. and SUDKAMP, T.A., Similarity and Compatibility in Fuzzy Set Theory – Assessment and Applications, No. 6, pp. 933-936.
Communications and forum GUANGCHENG, X., Abstract neural automata: variability of structure, thought and Riemannian volume, No. 1, pp. 130-139.
Index
ANDREW, A.M., Faith, physics and biology, No. 1, pp. 140-142. BOUDERAH, B. and MEKIAS, H., A cybernetic approach to the problem of cusp free-surface flow caused by a line sink on a sloping bottom, No. 2, pp. 305-316. C´IROVIC´, G. and CEKIC´, Z., Case-based reasoning model applied as a decision support for construction projects, No. 6, pp. 896-910. OH, S.-K. and PEDRYCZ, W., The design of hybrid fuzzy controllers based on genetic algorithms and estimation techniques, No. 6, pp. 911-917. Contemporary systems and cybernetics (Rudall B.H) The viable system model (VSM) in management, Biocybernetics, Reliability and safety of systems, Communications revolution, New products and systems, Cybernetics and robotics, Thought-controlled computer, No. 1, pp. 9-23. Future trends in cyberneticsl; Imaging processing; Telemedicine revolutionary procedure; Information systems; Cybernetics and robotics; New research activities, No. 2, pp. 192-204. Biocybernetics, Software innovations, Interdisciplinary initiatives, Tissue engineering, Management cybernetics, Creative cognition, Distribution of information, World robotics, No. 5, pp. 652-664. Biocybernetics, Brain scanners and emotions, Wearable computers, Decision support systems, Mind machines, Innovations, Automation and cybernetics, No. 6, pp. 800-812. Internet commentary ANDREW, A.M., No. 1, pp. 24-29; No. 2, pp. 205-208; No. 3/4, pp. 615-618; No. 6, pp. 813-816; No. 7/8, pp. 1151-1154. Short papers PUJOL, F.A., CHAMIZO, J.M.G., FUSTER, A., PUJOL, M. and RIZO, R., Use of mathematical morphology in real-time path planning, No. 1, pp. 115-123. CHERRUAULT, Y., MORA, G., TOURBIER, Y., A new method for calculating multiple integrals, No. 1, pp. 124-129. ANDREW, A.M., Homogenising Simpson’s rule, No. 2, pp. 282-291. MORA, G., CHERRUAULT, Y., BENABIDALLAH, A. and TOURBIER Y., Approximating multiple integrals via -dense curves, No. 2, pp. 292-304. CHERRUAULT, Y., INC, M. and ABBAOUI K., On the solution of the nonlinear Korteweg-de Vries equation by the decomposition method, No. 5, pp. 766-772. CHRYSOS, M., SANCHEZ, F. and CHERRUAULT, Y., Improvement of convergence of Adomian’s method using Pade´ approximants, No. 6, pp. 884-895. Software review (A. Adamatzky) CKS: Chemical Kinetics Simulator, No. 1, pp. 159-166. StarLogo, No. 2, pp. 330-335. ISAAC, No. 3/4, pp. 632-638.
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