Complex Systems Dynamics

By Gérard Weisbuch

	Inside this Book Back of Book Info Table of Contents Series SFI Studies in the Sciences of Complexity Pub. Date 1991 Publisher Addison Wesley Longman Order Info 0-201-62732-9 $46.21 (paper)

Table of Contents

Foreword
L. M. Simmons, Jr.

Foreword
Christof Koch

Preface

1 Introduction

1-1 Disordered Systems

1-2 Origins

1-3 Toward a Technology

2 Definitions

2-1 Automata

2-1-1 Classical Definition

2-1-2 Simplified Definition

2-1-3 Examples

2-1-4 Automata and Differential Equations

2-2 Automata Networks

2-2-1 Structural Properties

2-2-2 Dynamical Properties

2-2-3 A Simple Case: The "Crabs"

3 Cellular Automata

3-1 Definitions

3-2 One-Dimensional Cellular Automata with Three Inputs

3-3 One-Dimensional Cellular Automata with Two Inputs

References

4 Two-Dimensional Cellular Automata

4-1 Counters and Growth

4-2 Window Automata and Dendritic Growth

4-3 Conway's "Game of Life"

4-4 Models of Lattice Gas Dynamics

4-4-1 Principles

4-4-2 Numerical Simulations

4-4-3 Perspectives

References

5 The Hopfield Model

5-1 Definition of the Network

5-2 Energy and Fixed Points

5-3 The Hebb Rule

5-4 Simulation Results

5-5 The Signal-to-Noise-Ratio Method

5-5-1 The Fundamental Rule

5-5-2 The Invariance of the References

5-5-3 Scaling Law

5-5-4 Attraction of the References

5-6 The Hopfield Network as a Model of a Cognitive System

References

6 Beyond the Hopfield Model

6-1 Increasing the Capacity

6-1-1 The Perceptron Algorithm

6-1-2 Algebraic Methods

6-1-3 Changing the Connectivity

6-2 Avoiding Catastrophe: The Palimpsests

6-3 Asymmetrical Networks and Dilution

6-4 Sequences

6-5 Temporary Conclusion

References

7 Hidden Units

Classifications

7-1 The Perceptron

Linear Classifiers

The Convergence Theorem

A Simple Counter-Example

Hidden Units

Some History: The Perceptron Debate

7-2 Layered Networks

7-2-1 Structure

7-2-2 Back-Propagation

7-2-3 A Typical Application: NETalk

Conclusions

References

8 Statistical Physics

8-1 The Fundamental Quantities: Energy and Temperature

8-1-1 Energy and Symmetry of Interactions

8-1-2 Temperature and Probabilities

8-2 Probabilistic Automata and Monte Carlo Dynamics

8-3 The Ising Model

8-3-1 Ferromagnetism

8-3-2 Generalizations

8-3-3 The Frustration

8-4 Formal Probabilistic Neurons

8-5 Spin Glasses

References

9 Simulated Annealing

The Assignment Problem

Thermal Annealing

9-1 Simulated Annealing

9-1-1 The Traveling Salesman Problem

9-1-2 The Partition Problem

9-2 Image Processing

9-2-1 Definitions and Cellular Methods

9-2-2 Probabilistic Processing

References

10 Random Boolean Networks

10-1 In Search of Genetic Properties

10-2 Scaling Laws for Periods

The Case of Complete Connectivity

10-3 Cellular Networks with Random Functions

10-3-1 Functional Structuring

10-3-2 The Plateaus

10-3-3 Forcing Structures

10-3-4 The Phase Transition

10-3-5 Percolation

10-3-6 The "Magnetization"

10-4 The Distance Method

Diluted Networks

10-5 Conclusions

10-6 Application of the Distance Method to Spin Glasses

References

11 Genotypes and Phenotypes

11-1 Cell Differentiation

11-2 The Origin of Life

11-3 The Evolution of Species

11-3-1 Population Dynamics

11-3-2 Solution of the System of Differential Equations by the Perturbation Method

References

12 Conclusions

12-1 On the Proper Use of the Networks

12-1-1 Scope of the Models

12-1-2 Conditions of Applicability of the Algorithms

12-2 The State of the Art and Future Perspectives

12-2-1 Computer Science Problems

12-2-2 Specialized Machines

12-3 Bibliography

Books

Conference Proceedings

Journals

Appendix: Algorithms

Coding

Configurations

Boolean Functions

Definition of the Network

The Initial Conditions

Iterations

Determining the Iteration Graph

The Statistical Approach

Cellular Automata and Boundary Problems

The Gradient Descent Method

Index