Cellular Automata and Cooperative Systems

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