Cellular Automata, Dynamical Systems and Neural Networks by François Blanchard (auth.), Eric Goles, Servet Martínez

By François Blanchard (auth.), Eric Goles, Servet Martínez (eds.)

This publication comprises the classes given on the 3rd college on Statistical Physics and Cooperative platforms held at Santiago, Chile, from 14th to 18th December 1992. the most proposal of this periodic university used to be to collect scientists paintings­ with fresh traits in Statistical Physics. extra accurately ing on topics comparable similar with non linear phenomena, dynamical structures, ergodic conception, mobile au­ tomata, symbolic dynamics, huge deviation idea and neural networks. Scientists operating in those topics come from a number of components: arithmetic, biology, physics, laptop technology, electric engineering and synthetic intelligence. lately, a crucial cross-fertilization has taken position in regards to the aforesaid medical and technological disciplines, with the intention to provide a brand new method of the learn whose universal center is still in statistical physics. every one contribution is dedicated to 1 or extra of the former topics. mostly they're dependent as surveys, proposing even as an unique perspective in regards to the subject and exhibiting ordinarily new effects. The expository textual content of Fran

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Kuulasmaa (1982), Kuulasmaa and Zachary (1984), and Cox and Durrett (1988). 28 germ meets an infected individual or goes to an empty site, nothing happens. After an individual has been removed his site remains empty for ever. The infectives have all the same emission rate and identical lifetime distribution. All these different versions of the spatial general epidemic model still neglect the motion of the individuals. The influence of this factor on the spread of the epidemic is one of the main concerns of this series of lectures.

005. This value for /3(0) is the same as for directed percolation (Bease 1977). This result is in favor of a universal critical behavior for one-dimensional cellular automata with one absorbing state (Kinzell983), the universality class being characterized by the space dimensionality and the dependence of the mean-field map for small densities (Bidaux et all989). The extinction method being rather time consuming, it has been used only for m = 0 to check the precision of the other method. 02. 9.

Hm logm log (f3(m)- f3(0)) . 05. it is very important to determine (J(m) with a sufficient precision, that is, the percolation threshold Pc( m) has to be measured with great precision. 46 (b) (a) 'I 'I 'I ? 001 f I! 11. Pc (a) and (3 (b) as functions of m. Nonlocal site-exchange. 12. Spatio-temporal pattern for p close to to Pc(m) for long-range moves. 1, p = 068. 47 3. 1. VARIOUS MODELS We will essentially consider epidemic models and occasionally predator-prey models. , those individuals who are not infected but who are capable of contracting the disease and become infective.

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