Cellular Automata and Cooperative Systems, 1993 Nato Science Series C: Series, Vol. 396

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.

Complexity of Infinite Sequences and the Ising Transducer.- Renormalization Group Analysis of Directed Models.- Maximal Lyapunov Exponent for 1D Boolean Cellular Automata.- Automata Network Epidemic Models.- Structure Evolution of Neural Networks.- Lower Bounds on the Memory Capacity of the Dilute Hopfield Model.- Schrödinger Operators with Substitution Potentials.- An Interplay Between Local and Global Dynamics in Biological Networks: the Case of Genetic Sequences.- How to Fire almost any Arbitrary Pattern on a Cellular Automaton.- Dynamics of Random Neural Nets.- A Matrix Method of Solving an Asymmetric Exclusion Model with Open Boundaries.- A Formula of full Semiinvariants.- Non-Gibbsian States for Renormalization-Group Transformations and Beyond.- Fluctuations in the Asymmetric Simple Exclusion Process.- Analysis of a Network Model.- Drift and Diffusion in Phase Space. An Application to Celestial Mechanics.- Real Computation with Cellular Automata.- Lyapunov Functionals Associated to Automata.- Sand-Pile Dynamics in a One-Dimensional Bounded Lattice.- Differential Inequalities for Potts and Random-Cluster Processes.- Cryptography with Dynamical Systems.- On Entropic Repulsion in Low Temperature Ising Models.- The Distribution of Lyapunov Exponents for Large Random Matrices.- Transience and Dislocations in One-Dimensional Cellular Automata.- Properties of Limit Sets of Cellular Automata.- Stochastic Equations on Random Trees.- The Branching Diffusion, Stochastic Equations and Travelling Wave Solutions to the Equation of Kolmogorov — Petrovskii — Piskunov.- Spin Models with Random Interactions: Some Rigorous Results.- Low Temperature Phase Transitions on Quasiperiodic Lattices.- Stability of Interfaces in Stochastic Media.- Hydrodynamic Equation for Mean ZeroAsymmetric Zero Range Processes.- Clustering and Coexistence in Threshold Voter Models.- Analytical Results for the Maximal Lyapunov Exponent.- Some Remarks on Almost Gibbs States.- Some Coded Systems that are Not Unstable Limit Sets of Cellular Automata.- Constructive Criteria for the Ergodicity of Interacting Particle Systems.- Self-Similar Fractals Can be Generated by Cellular Automata.- Finite Volume Mixing Conditions for Lattice Spin Systems and Exponential Approach to Equilibrium of Glauber Dynamics.- Quasi-Stationary Distributions for Birth-Death Chains. Convergence Radii and Yaglom Limit.- Cooperative Phenomena in Swarms.- Comparison of Semi-Oriented Bootstrap Percolation Models with Modified Bootstrap Percolation.- Chaotic Size Dependence in Spin Glasses.- On the Gibbs States for One-Dimensional Lattice Boson Systems with a Long-Range Interaction.- Hydrodynamic Limits and Ergodicity for Hamiltonian System with Small Noise.- Relaxation Times for Stochastic Ising Models in the Limit of Vanishing External Field at Fixed Low Temperatures.