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.

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