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Probabilistic Cellular Automata

Part of the Emergence, Complexity and Computation Book Series (volume 27)

Editors: Louis, Pierre-Yves; Nardi, Francesca R.

DOI: 10.1007/978-3-319-65558-1

ISBN: 978-3-319-65556-7

Publisher: Springer International Publishing - Springer Journals

Feb 22, 2018

11 - 20 of 20 Chapters

LitStream

Statistical Equilibrium in Deterministic Cellular Automata

Taati, Siamak

Pages: 145 –164

[Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal disorder. This chapter is an exposition of this phenomenon and...
LitStream

Epidemic Automaton and the Eden Model: Various Aspects of Robustness

Gerin, Lucas

Pages: 165 –178

[The two-dimensional probabilistic cellular automaton Epidemic models the spread of an epidemic without recovering on graph. We discuss some well-known and less well-known properties of Epidemic on a finite grid and its analogous on the infinite square lattice: the Eden model. This survey is...
LitStream

Convergence Time of Probabilistic Cellular Automata on the Torus

Taggi, Lorenzo

Pages: 179 –196

[Many probabilistic cellular automata (PCA) exhibit a transition from an ergodic to a non-ergodic regime. Namely, if the free parameter is above a certain critical threshold, the process converges to a state that does not depend on the initial state (ergodicity), whereas if the free parameter is...
LitStream

Percolation Operators and Related Models

Słowiński, Piotr

Pages: 197 –214

[Here we review the theory and methods of the two basic stochastic models with absorbing states: percolation operators and contact processes. We explore connections between them by studying discrete-time approximations of a continuous-time contact processes. In particular, we look at the...
LitStream

Phase Transitions of Cellular Automata

Bagnoli, Franco; Rechtman, Raúl

Pages: 215 –236

[We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of the Monte Carlo approach for a discrete system. We then formulate the cellular automaton problem using simple models and illustrate different types of possible phase transitions:...
LitStream

A Trade-Off Between Simplicity and Robustness? Illustration on a Lattice-Gas Model of Swarming

Fatès, Nazim; Chevrier, Vincent; Bouré, Olivier

Pages: 239 –259

[We re-examine a cellular automaton model of swarm formation. The local rule is stochastic and defined simply as a force that aligns particles with their neighbours. This lattice-gas cellular automaton was proposed by Deutsch to mimic the self-organisation process observed in various natural...
LitStream

PCA Modelling of Multi-species Cell Clusters: Ganglion Development in the Gastrointestinal Nervous System

Landman, Kerry A.; Newgreen, Donald F.

Pages: 261 –277

[A defining characteristic of the enteric nervous system (ENS) is mesoscale patterned entities called ganglia. Ganglia are clusters of neurons with associated enteric neural crest (ENC) cells, which form in the simultaneously growing gut wall. At first, the precursor ENC cells proliferate and...
LitStream

Cellular Potts Model: Applications to Vasculogenesis and Angiogenesis

Boas, Sonja E. M.; Jiang, Yi; Merks, Roeland M. H.; Prokopiou, Sotiris A.; Rens, Elisabeth G.

Pages: 279 –310

[The cellular Potts model (CPM, a.k.a. Glazier–Graner–Hogeweg or GGH model) is a somewhat liberal extension of probabilistic cellular automata. The model is derived from the Ising and Potts models and represents biological cells as domains of CA-sites of the same state. A Hamiltonian energy is...
LitStream

Cellular Potts Models for Interacting Cell Populations: Mathematical Foundation, Challenges, and Future Prospects

Voss-Böhme, Anja

Pages: 311 –325

[Cellular Potts models (CPMs) are extensions of asynchronous probabilistic cellular automata (PCA) developed specifically to model interacting cell populations. They constitute a modeling framework for the field of cell and tissue biology that is particularly useful when the details of...
LitStream

Cellular Automata for Clouds and Convection

Crommelin, Daan

Pages: 327 –339

[Numerical models of the global atmosphere have spatial resolutions that are much too coarse to resolve clouds and convection processes explicitly. Because these processes play an important role in the atmosphere and climate system, they are included in numerical models by means of simplified...

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