Cellular Automata and Cooperative Systems

✍ Scribed by Jean-Paul Allouche (auth.), Nino Boccara, Eric Goles, Servet Martinez, Pierre Picco (eds.)

• Publisher: Springer Netherlands
• Year: 1993
• Tongue: English
• Leaves: 544
• Series: NATO ASI Series 396
• Edition: 1
• Category: Library

✦ Synopsis

This book contains the lectures given at the NATO Advanced Study Institute on `Cellular Automata and Cooperative Systems', held at Les Houches, France, from June 22 to July 2, 1992.
The book contains contributions by mathematical and theoretical physicists and mathematicians working in the field of local interacting systems, cellular probabilistic automata, statistical physics, and complexity theory, as well as the applications of these fields.

✦ Table of Contents

Front Matter....Pages i-xvii
Complexity of Infinite Sequences and the Ising Transducer....Pages 1-9
Renormalization Group Analysis of Directed Models....Pages 11-17
Maximal Lyapunov Exponent for 1D Boolean Cellular Automata....Pages 19-28
Automata Network Epidemic Models....Pages 29-44
Structure Evolution of Neural Networks....Pages 45-54
Lower Bounds on the Memory Capacity of the Dilute Hopfield Model....Pages 55-66
Schrödinger Operators with Substitution Potentials....Pages 67-83
An Interplay Between Local and Global Dynamics in Biological Networks: The Case of Genetic Sequences....Pages 85-100
How to Fire Almost any Arbitrary Pattern on a Cellular Automaton....Pages 101-109
Dynamics of Random Neural Nets....Pages 111-120
A Matrix Method of Solving an Asymmetric Exclusion Model with Open Boundaries....Pages 121-133
A Formula of Full Semiinvariants....Pages 135-140
Non-Gibbsian States for Renormalization-Group Transformations and Beyond....Pages 141-152
Fluctuations in the Asymmetric Simple Exclusion Process....Pages 153-157
Analysis of a Network Model....Pages 159-172
Drift and Diffusion in Phase Space. An Application to Celestial Mechanics....Pages 173-189
Real Computation with Cellular Automata....Pages 191-202
Lyapunov Functionals Associated to Automata....Pages 203-210
Sand-Pile Dynamics in a One-Dimensional Bounded Lattice....Pages 211-225
Differential Inequalities for Potts and Random-Cluster Processes....Pages 227-236
Cryptography with Dynamical Systems....Pages 237-274
On Entropic Repulsion in Low Temperature Ising Models....Pages 275-287
The Distribution of Lyapunov Exponents for Large Random Matrices....Pages 289-298
Transience and Dislocations in One-Dimensional Cellular Automata....Pages 299-310
Properties of Limit Sets of Cellular Automata....Pages 311-321
Stochastic Equations on Random Trees....Pages 323-341
The Branching Diffusion, Stochastic Equations and Travelling Wave Solutions to the Equation of Kolmogorov — Petrovskii — Piskunov....Pages 343-366
Spin Models with Random Interactions: Some Rigorous Results....Pages 367-374
Low Temperature Phase Transitions on Quasiperiodic Lattices....Pages 375-386
Stability of Interfaces in Stochastic Media....Pages 387-394
Hydrodynamic Equation for Mean Zero Asymmetric Zero Range Processes....Pages 395-402
Clustering and Coexistence in Threshold Voter Models....Pages 403-410
Analytical Results for the Maximal Lyapunov Exponent....Pages 411-421
Some Remarks on Almost Gibbs States....Pages 423-432
Some Coded Systems that are not Unstable Limit Sets of Cellular Automata....Pages 433-449
Constructive Criteria for the Ergodicity of Interacting Particle Systems....Pages 451-461
Self-Similar Fractals can be Generated by Cellular Automata....Pages 463-471
Finite Volume Mixing Conditions for Lattice Spin Systems and Exponential Approach to Equilibrium of Glauber Dynamics....Pages 473-490
Quasi-Stationary Distributions for Birth-Death Chains. Convergence Radii and Yaglom Limit....Pages 491-505
Cooperative Phenomena in Swarms....Pages 507-518
Comparison of Semi-Oriented Bootstrap Percolation Models with Modified Bootstrap Percolation....Pages 519-523
Chaotic Size Dependence in Spin Glasses....Pages 525-529
On the Gibbs States for One-Dimensional Lattice Boson Systems with a Long-Range Interaction....Pages 531-538
Hydrodynamic Limits and Ergodicity for Hamiltonian System with Small Noise....Pages 539-542
Relaxation Times for Stochastic Ising Models in the Limit of Vanishing External Field at Fixed Low Temperatures....Pages 543-546

✦ Subjects

Physics, general;Discrete Mathematics in Computer Science;Theory of Computation;Statistical Physics, Dynamical Systems and Complexity