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Neural and Automata Networks : Dynamical Behavior and Applications / by Eric Goles, Servet Martínez.

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"Et moi ..., si j'avait Sll comment en revenir. One sennce mathematics has rendered the human race. It has put common sense back je n'y serais point alle.' Jules Verne whe", it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Golès, E.
Other Authors: Martínez, Servet
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands, 1990.
Series:Mathematics and its applications (Kluwer Academic Publishers) ; v. 58.
Subjects:
Computer science.
Information theory.
Computational complexity.
Computer engineering.
Table of Contents:
  • 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.

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