Probabilistic Cellular Automata: Theory, Applications and Future Perspectives

Description

This book explores Probabilistic Cellular Automata (PCA) from the perspectives of statistical mechanics, probability theory, computational biology and computer science. PCA are extensions of the well-known Cellular Automata models of complex systems, characterized by random updating rules. Thanks to their probabilistic component, PCA offer flexible computing tools for complex numerical constructions, and realistic simulation tools for phenomena driven by interactions among a large number of neighboring structures. PCA are currently being used in various fields, ranging from pure probability to the social sciences and including a wealth of scientific and technological applications. This situation has produced a highly diversified pool of theoreticians, developers and practitioners whose interaction is highly desirable but can be hampered by differences in jargon and focus. This book – just as the workshop on which it is based – is an attempt to overcome these difference and foster interest among newcomers and interaction between practitioners from different fields. It is not intended as a treatise, but rather as a gentle introduction to the role and relevance of PCA technology, illustrated with a number of applications in probability, statistical mechanics, computer science, the natural sciences and dynamical systems. As such, it will be of interest to students and non-specialists looking to enter the field and to explore its challenges and open issues. Front Matter ....Pages i-xviii Overview: PCA Models and Issues (Roberto Fernández, Pierre-Yves Louis, Francesca R. Nardi)....Pages 1-30 Probabilistic Cellular Automata in the Visual Arts (Roeland M. H. Merks)....Pages 31-34 Front Matter ....Pages 35-35 Basic Ideas to Approach Metastability in Probabilistic Cellular Automata (Emilio N. M. Cirillo, Francesca R. Nardi, Cristian Spitoni)....Pages 37-51 Strategic Interaction in Interacting Particle Systems (Paolo Dai Pra, Elena Sartori, Marco Tolotti)....Pages 53-67 Scaling and Inverse Scaling in Anisotropic Bootstrap Percolation (Aernout C. D. van Enter)....Pages 69-77 The Sandpile Cellular Automaton (Antal A. Járai)....Pages 79-88 Ising Model on the Torus and PCA Dynamics: Reversibility, Irreversibility, and Fast Tunneling (Carlo Lancia, Benedetto Scoppola)....Pages 89-104 Synchronization in Interacting Reinforced Stochastic Processes (Pierre-Yves Louis, Ida G. Minelli)....Pages 105-118 Nonequilibrium Physics Aspects of Probabilistic Cellular Automata (Christian Maes)....Pages 119-128 Front Matter ....Pages 129-129 An Example of Computation of the Density of Ones in Probabilistic Cellular Automata by Direct Recursion (Henryk Fukś)....Pages 131-144 Statistical Equilibrium in Deterministic Cellular Automata (Siamak Taati)....Pages 145-164 Epidemic Automaton and the Eden Model: Various Aspects of Robustness (Lucas Gerin)....Pages 165-178 Convergence Time of Probabilistic Cellular Automata on the Torus (Lorenzo Taggi)....Pages 179-196 Percolation Operators and Related Models (Piotr Słowiński)....Pages 197-214 Phase Transitions of Cellular Automata (Franco Bagnoli, Raúl Rechtman)....Pages 215-236 Front Matter ....Pages 237-237 A Trade-Off Between Simplicity and Robustness? Illustration on a Lattice-Gas Model of Swarming (Nazim Fatès, Vincent Chevrier, Olivier Bouré)....Pages 239-259 PCA Modelling of Multi-species Cell Clusters: Ganglion Development in the Gastrointestinal Nervous System (Kerry A. Landman, Donald F. Newgreen)....Pages 261-277 Cellular Potts Model: Applications to Vasculogenesis and Angiogenesis (Sonja E. M. Boas, Yi Jiang, Roeland M. H. Merks, Sotiris A. Prokopiou, Elisabeth G. Rens)....Pages 279-310 Cellular Potts Models for Interacting Cell Populations: Mathematical Foundation, Challenges, and Future Prospects (Anja Voss-Böhme)....Pages 311-325 Cellular Automata for Clouds and Convection (Daan Crommelin)....Pages 327-339 Back Matter ....Pages 341-344