Neural and Automata Networks

Inhaltsverzeichnis

• 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.