1. Automata Networks -- 1.1. Introduction -- 1.2. Definitions Regarding Automata Networks -- 1.3. Cellular Automata -- 1.4. Complexity Results for Automata Networks -- 1.5. Neural Networks -- 1.6. Examples of Automata Networks -- 2. Algebraic Invariants on Neural Networks -- 2.1. Introduction -- 2.2. K-Chains in 0-1 Periodic Sequences -- 2.3. Covariance in Time -- 2.4. Algebraic Invariants of Synchronous Iteration on Neural Networks -- 2.5. Algebraic Invariants of Sequential Iteration on Neural Networks -- 2.6. Block Sequential Iteration on Neural Networks -- 2.7. Iteration with Memory -- 2.8. Synchronous Iteration on Majority Networks -- 3. Lyapunov Functionals Associated to Neural Networks -- 3.1. Introduction -- 3.2. Synchronous Iteration -- 3.3. Sequential Iteration -- 3.4. Tie Rules for Neural Networks -- 3.5. Antisymmetrical Neural Networks -- 3.6. A Class of Symmetric Networks with Exponential Transient Length for Synchronous Iteration -- 3.7. Exponential Transient Classes for Sequential Iteration -- 4. Uniform One and Two Dimensional Neural Networks -- 4.1. Introduction -- 4.2. One-Dimensional Majority Automata -- 4.3. Two-Dimensional Majority Cellular Automata -- 4.4. Non-Symmetric One-Dimensional Bounded Neural Networks -- 4.5. Two-Dimensional Bounded Neural Networks -- 5. Continuous and Cyclically Monotone Networks -- 5.1. Introduction -- 5.2. Positive Networks -- 5.3. Multithreshold Networks -- 5.4. Approximation of Continuous Networks by Multithreshold Networks -- 5.5. Cyclically Monotone Networks -- 5.6. Positive Definite Interactions. The Maximization Problem -- 5.7. Sequential Iteration for Decreasing Real Functions and Optimization Problems -- 5.8. A Generalized Dynamics -- 5.9. Chain-Symmetric Matrices -- 6. Applications on Thermodynamic Limits on the Bethe Lattice -- 6.1. Introduction -- 6.2. The Bethe Lattice -- 6.3. The Hamiltonian -- 6.4. Thermodynamic Limits of Gibbs Ensembles -- 6.5. Evolution Equations -- 6.6. The One-Site Distribution of the Thermodynamic Limits -- 6.7. Distribution of the Thermodynamic Limits -- 6.8.Period ? 2 Limit Orbits of Some Non Linear Dynamics on $$ \mathbb{R}_{ + }̂{s} $$ -- 7. Potts Automata -- 7.1. The Potts Model -- 7.2. Generalized Potts Hamiltonians and Compatible Rules -- 7.3. The Complexity of Synchronous Iteration on Compatible Rules -- 7.4. Solvable Classes for the Synchronous Update -- References -- Author and Subject Index

1. Computer science
2. Computers
3. Computer science -- Mathematics
4. Statistical physics
5. Dynamical systems
6. Electrical engineering
7. Computer Science
8. Discrete Mathematics in Computer Science
9. Theory of Computation
10. Statistical Physics
11. Dynamical Systems and Complexity
12. Electrical Engineering