Table Of ContentSpringer Series in Synergetics
Editor: Hermann Haken
Synergetics, an interdisciplinary field of research, is concerned with the cooper
ation of individual parts of a system that produces macroscopic spatial, temporal
or functional structures. It deals with deterministic as well as stochastic processes.
1 Synergetics An Introduction 3rd Edition 21 Stochastic Phenomena and Chaotic Behaviour
By H. Haken in Complex Systems Editor: P. Schuster
2 Synergetics A Workshop 22 Synergetics - From Microscopic to Macroscopic
Editor: H. Haken Order Editor: E. Frehland
3 Synergetics Far from Equilibrium 23 Synergetics of the Brain
Editors: A. Pacault, C. Vidal Editors: E. Ba§ar, H. Flohr, H. Haken,
4 Structural Stability in Physics A.J. Mandell
Editors: W. Giittinger, H. Eikemeier 24 Chaos and Statistical Methods
5 Pattern Formation by Dynamic Systems and Editor: Y. Kuramoto
Pattern Recognition 25 Dynamics of Hierarchical Systems
Editor: H. Haken An Evolutionary Approach By J.S. Nicolis
6 Dynamics of Synergetic Systems 26 Self-Organization and Management of
Editor: H. Haken Social Systems
7 Problems of Biological Physics Editors: H. Ulrich, G.J. B. Probst
By L. A. Blumenfeld 27 Non-Equilibrium Dynamics in Chemical
8 Stochastic Nonlinear Systems Systems Editors: C. Vidal, A. Pacault
in Physics, Chemistry, and Biology 28 Self-Organization Autowaves and Structures
Editors: L. Arnold, R. Lefever Far from Equilibrium
Editor: V.1. Krinsky
9 Numerical Methods in the Study of Critical
Phenomena 29 Temporal Order
Editors: J. Della Dora, J. Demongeot, Editors: L. Rensing, N.!. Jaeger
B. Lacolle 30 Dynamical Problems in Soliton Systems
10 The Kinetic Theory of Electromagnetic Editor: S. Takeno
Processes By Yu.L. Klimontovich 31 Complex Systems - Operational Approaches
in Neurobiology, Physics, and Computers
11 Chaos and Order in Nature
Editor: H. Haken
Editor: H. Haken
32 Dimensions and Entropies in Chaotic Systems
12 Nonlinear Phenomena in Chemical Dynamics
Quantification of Complex Behavior
Editors: C. Vidal, A. Pacault
Editor: G. Mayer-Kress
13 Handbook of Stochastic Methods
33 Selforganization by Nonlinear Irreversible
for Physics, Chemistry, and the Natural Sciences
Processes
2nd Edition By C. W. Gardiner
Editors: W. Ebeling, H. Ulbricht
14 Concepts and Models of a Quantitative
34 Instabilities and Chaos in Quantum Optics
Sociology The Dynamics of Interacting
Editors: F. T. Arecchi, R. G. Harrison
Populations By W. Weidlich, G. Haag
35 Nonequilibrium Phase Transitions in
15 Noise-Induced Transitions Theory and
Semiconductors Self-Organization Induced by
Applications in Physics, Chemistry, and Biology
Generation and Recombination Processes
By W. Horsthemke, R. Lefever
By E. Scholl
16 Physics of Bioenergetic Processes 36 Temporal Disorder in Human
By L. A. Blumenfeld Oscillatory Systems
17 Evolution of Order and Chaos in Physics, Editors: L. Rensing, U. an der Heiden,
Chemistry, and Biology Editor H. Haken M.C. Mackey
18 The Fokker-Planck Equation 37 The Physics of Structure Formation
By H. Risken Theory and Simulation
19 Chemical Oscillations, Waves, and Turbnlence Editors: W. Giittinger and G. Dangelmayr
By Y. Kuramoto 38 Computational Systems - Natural and
20 Advanced Synergetics 2nd Edition Artificial
ByH. Haken Editor: H. Haken
Computational Systems
Natural and Artificial
Proceedings of the International Symposium
on Synergetics at SchloB Elmau, Bavaria
May 4-9, 1987
Editor: H. Haken
With 115 Figures
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo
Professor Dr. Dr. h.c. mult. Hermann Haken
Institut fUr Theoretische Physik, Universitat Stuttgart, Pfaffenwaldring 57/IV,
D-7000 Stuttgart 80, Fed. Rep. of Germany and
Center for Complex Systems, Florida Atlantic University,
Boca Raton, FL 33431, USA
ISBN -13: 978-3-642-73091-7 e-ISBN -13: 978-3-642-73089-4
DOl: 10.1007/978-3-642-73089-4
Library of Congress Cataloging-in-Publication Data. International Symposium on Synergetics (1987 : Schloss
Elmau, Bavaria) Computational systems-natural and artificial: proceedings of the International Symposium on
Synergetics at Schloss Elmau, Bavaria, May 4-9,19871 editor, H. Haken. (Springer series in synergetics ; v. 38)
Includes index. 1. System theory-Congresses. 2. Electronic data processing-Congresses. 3. Neural circuitry
Congresses. 1. Haken, H. II. Title. III. Series. Q295.1586 1987 003-dc 19 87-28854
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
specifically the rights of translation, reprinting, reuse of illustratio(ls, recitation, broadcasting, reproduction on
microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only
permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24,
1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German
Copyright Law.
© Springer-Verlag Berlin Heidelberg 1987
Softcoverreprint of the hardcover 1st edition 1987
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific
statement, that such names are exempt from the relevant protective laws and regulations and therefore free for
general use.
2153/3150-543210
Preface
This book contains the invited papers presented at an international sympo
sium held at Schloss Elmau, Bavaria (FRG), May 4-9, 1987. Leading experts
from neurobiology, medicine, physics, and the computer sciences joined to
gether to present and discuss their most recent results. A particular example
of the natural computational systems discussed is the visual system of man
and animals. A bridge between neural networks and physical systems is
provided by spin glass models of neural networks, which were also treated.
Concrete realizations of new kinds of devices in microelectronics were among
the further topics, as were general problems on the calculation of chaotic
orbits. In this way these proceedings present a number of quite recent ap
proaches to problems which are of great current interest in fields concerned
with computational systems.
Bringing together scientists from neurobiology, physics, and the computer
sciences has been one of the main aims of the synergetics enterprise, and in
particular of its international symposia, from the very beginning. For exam
ple, its first meeting held in 1972 at Schloss Elmau included, among others,
papers by R. Landauer and J.W.F. Woo on cooperative phenomena in data
processing, by W. Reichardt on mechanisms of pattern recognition by the
visual system of insects, by B. Julesz on stereoscopic depth perception, and
by H.R. Wilson on cooperative phenomena in a homogeneous cortical tissue
model. Whole meetings and the corresponding proceedings were devoted to
these problems, e.g. "Pattern Formation and Pattern Recognition" (Springer
Ser. in Synergetics, Vol. 5), where papers by K.S. Fu on syntactic pattern
recognition and by T. Kohonen on associative memory are included. The
proceedings on "Synergetics of the Brain" (Springer Ser. in Synergetics,
Vol. 23), edited by Basar, Flohr, Haken and Mandell, contains papers by von
der Malsburg, Bienenstock, Kohonen, Grossberg, Carpenter, Huberman and
others on neural nets. The proceedings on "Complex Systems, Operational
Approaches in Neurobiology, Physics and Computers" (Springer Ser. in Syn
ergetics, Vol. 31) covers similar topics.
In a number of recent publications on the rapidly developing fields of
neural computers and all-optical computers, the opinion was expressed that
it is becoming more and more necessary to bring together neurobiologists,
physicists, computer scientists and scientists from other branches of science.
I am delighted that this type of meeting, which I initiated 15 years ago, has
led to this kind of cross-fertilization and is now bearing fruit. I do hope that
v
these proceedings in their turn will help to deepen our understanding of the
complex processes of pattern recognition in natural systems and to pave the
way for the construction of entirely new types of computers.
The organisation of these types of meetings in the frame of synergetics
would not have been possible without the continued and generous support
of the Volkswagenwerk Foundation. Their efforts are particularly remarkable
because we are living in a time where, in general, support seems to be given
by most agencies only to projects which are on highly specialized topics. Last
but not least I wish to express my cordial thanks to Mrs. Ursula Funke who
organized this meeting, as all the previous ones, perfectly.
Stuttgart, June 1987 R. Raken
VI
Contents
Part I Introduction
Synergetic Computers for Pattern Recognition and Associative
Memory. By H. Haken (With 18 Figures) ................... 2
Part II Natural Computational Systems
The Representation of Space-Time in the Human Visual System
By J.J. Koenderink and A.J. van Doorn .................... 24
Neuronal Mechanisms of the First, Second, and Third Order
Contrast in the Visual System. E. Peterh ans , and R. von der Heydt
(With 8 Figures) ...................................... 35
A Model of Figure/Ground Separation Based on Correlated Neural
Activity in the Visual System
By H.J. Reitbock, R. Eckhorn, and M. Pabst (With 8 Figures) .... 44
Self-organization of the Visual Information Channel and Solitons
By R.S. Ingarden (With 3 Figures) ........................ 55
Human Brain EEG Fields: Micro-states and Their Functional
Significance
By D. Lehmann, D. Brandeis, H. Ozaki, and 1. Pal (With 2 Figures) 65
Spatio-Temporal Analysis of Multi-channel Alpha EEG Map Series
By A. Fuchs, R. Friedrich, H. Haken, and D. Lehmann
(With 11 Figures) ..................................... 74
Part III Pattern Analysis and Pattern Formation
Singular System Analysis of Time Series Data
By E.R. Pike (With 5 Figures) ........................... 86
Geometrical Principles of Pattern Formation and Pattern Recognition
By W. Giittinger, P. Haug, and D. Lang (With 16 Figures) ....... 97
VII
Part IV Spin Glass Models and Neural Networks
Dynamics of Spin Glasses and Related Models of Neural Networks
By H. Horner (With 7 Figures) ........................... 118
Mean-Field Theory of Spin Glasses and Neural Networks with Finite
Coordination Number. By 1. Kanter (With 2 Figures) .......... 133
Neural Networks for Associative Memory Design
By L. Personnaz, 1. Guyon, and G. Dreyfus (With 6 Figures) 142
Part V Physical Devices
Towards the Quantum Computer: Information Processing with Single
Electrons. By G. Mahler and K. Obermayer (With 8 Figures) 154
Chaos and Pulsating Instabilities in Lasers
By R.G. Harrison, J.V. Moloney, and J.S. Uppal (With 6 Figures) 166
Part VI General Computational Processes
Systems with Statistically Coupled Processors
By V. Cerny (With 10 Figures) ........................... 178
Chaotic Dynamical Systems as Machines. By J.L. McCauley. . . . .. 188
Digital and Analog Approach to Intermittencies and l/f Noise in
a Nonlinear Helmholtz Oscillator. By M.A. Rubio, M. de la Torre,
J.C. Antoranz, and M.G. Velarde (With 5 Figures) ............. 196
Part VII Robotics
Towards Automatic Error Correction in Robots: Inferring the Task
from the Program. By V. Caglioti and M. Somalvico ........... 204
Index of Contributors. . . . . . . . . . . . . . . . . . . . . . . . . . .. 215
VIII
Part I
Introduction
Synergetic Computers for Pattern Recognition
and Associative Memory
H. Haken
Institut fiir Theoretische Physik und Synergetik, Universitat Stuttgart,
Pfaffenwaldring 57, D-7000 Stuttgart 80, Fed. Rep. of Germany
1. What these Proceedings are About
The purpose of my contribution is twofold: In this part I wish to present a brief
preview on the contents of this volume and how its individual contributions are
connected with each other. Then in the main part I wish to present my own model on
the synergetic computer which allows for pattern recognition and associative
memory. As I mentioned in the preface, it has been the goal of synergetics from
the very beginning to bring scientists from neurobiology, physics, chemistry,
computers, and other fields together and to provide a forum for interdisciplinary
discussions. One of the main subj ects of synergetics has been the relationship
between pattern formation and pattern recognition. This tradition is followed up
in the present proceedings where the first chapter deals with natural
computational systems. Here we shall deal with the visual system (Koenderingk et
al.), and (Baumgaertner et al.). (Here and in the following the quoted names refer
to those authors who presented the paper.) It is wellknown from the cognitive
sciences that we may complement an incomplete image, for instance by inserting
automatically contour lines which are not present at all, but which are for
instance indicated only by pieces of their ends. In the experiments by
Baumgaertner et al. it is shown that under the above-mentioned circumstances quite
evidently neurons start to fire which have been quiescent otherwise. Thus by means
of the property of the total network of the visual cortex, there is a material
substrate for this complementation effect. I do not doubt that these findings are
of great importance for the construction of neural computers. An important problem
in this context is figure / ground discrimination, on which a model is developed
by Reitboeck et al. An abstract mathematical approach employing a variational
approach is presented by Ingarden.
Macroscopic pattern formation in neural systems seems to occur in the E.E.G.
patterns and two contributions (Lehmann et al. and Fuchs et al.) are devoted to
this kind of phenomena. While the biological significance of E.E.G. pattern seems
not yet clear at the present moment, we can analyse these formations as that of
macroscopic complex systems in analogy to many other processes going on in other
synergetic systems when selforganisation starts.
The line of thought how to analyse complex patterns, in particular those occurring
in time series, is then carried on in the contribution by Pike, where he presents
a rather general formalism. The paper by Guettinger et al. elucidates pattern
formation and pattern recognition again from a rather general point of view. We
then proceed to physical realizations of abstract models on pattern recognition,
where models of spin glasses representing neural nets are an important
intermediate step. After the seminal paper of J. Hopfield a number of physicists
who are experts in spin glasses and statistical physics have studied such spin
glass models in great detail. Recent results are presented by Horner and Kanter in
these proceedings. Possible realizations of associative memory designs are
discussed by Dreyfus et al. At least at this point the reader of these proceedings
may get a feeling which seized all participants of this symposium, namely how
fruitful and fascinating an interdisciplinary discussion ranging from basic
problems to applications can be.
2
