Complex Systems Dynamics
An Introduction to Automata Networks
- 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 Interations
- 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 Probalistic 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
- 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