Titlebook: Probabilistic Cellular Automata; Theory, Applications Pierre-Yves Louis,Francesca R. Nardi Book 2018 Springer International Publishing AG 2

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An Example of Computation of the Density of Ones in Probabilistic Cellular Automata by Direct Recursionse words at the previous time step. One can then set up and solve a recursion for block probabilities. We demonstrate an example of such PCA, which can be viewed as a simple model of diffusion of information or spread of rumours. Expressions for the density of ones are obtained for this rule using the proposed method.

overwrought

Percolation Operators and Related Modelsused to model different biological phenomena. Specifically, we focused on models with absorbing states that, have spatially non-homogenous stationary states, or that have shown to be bi-stable. More generally, we aim to demonstrate the challenges associated with reconciling different mathematical descriptions of natural phenomena.

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Synchronization in Interacting Reinforced Stochastic ProcessesWe present a family of interacting stochastic processes introduced in [.] whose individual dynamics follow a reinforcement updating rule. This is a natural generalization of PCA dynamics on a continuous spin space. The interaction changes the long-time behavior of each process and the speed of evolution, producing a phenomenon of synchronization.

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CODA

https://doi.org/10.1007/978-3-319-65558-1high-dimensional interacting stochastic systems; dynamical systems; multiscale models; complex systems;