## Neural and Automata Networks: Dynamical Behavior and Applications"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 is divergent; therefore we may be smse'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'!ltre of this series. |

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### Contents

Introduction | 1 |

for Synchronous Iteration | 88 |

Continuous and Cyclically Monotone Networks | 137 |

Copyright | |

3 other sections not shown

### Other editions - View all

Neural and Automata Networks: Dynamical Behavior and Applications E. Goles,Servet Martínez Limited preview - 2013 |

Neural and Automata Networks: Dynamical Behavior and Applications E. Goles,Servet Martínez No preview available - 2011 |

### Common terms and phrases

Applications associated assume Automata Networks automaton behaviour belongs block bound called cells Cellular Automata Chapter Complex computing condition configuration connections consider constructed contained continuous converges convex cycle deduce defined definition denote developed dynamics equality equation equivalent evolution examples exists fact Figure finite fixed points give given Goles graph Hence holds implies instance interactions introduce invariant lattice Lemma limit Lyapunov functional Majority Math maximal means neighbourhood Neural Networks Note obtain one-dimensional orbits otherwise particular partition period physics positive problem Proof Proposition prove Recall relation respectively rule satisfies sequential iteration sequential updating simulate space steps strictly suppose symmetric matrix synchronous iteration Systems Theorem theory threshold transient length Turing Machine Universal values vector weighted write