Probabilistic Cellular Automata : Theory, Applications and Future Perspectives (Emergence, Complexity and Computation)

Louis, Pierre-Yves (EDT)/ Nardi, Francesca R. (EDT)

Springer Nature Switzerland AG（2019/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 344 p.
• 商品コード 9783030097424

Full 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.

Contents

Preface.- Acknowledgements.- 1 Overview: PCA models and issues.- 2 Probabilistic Cellular Automata in Art.- Part I Probability and statistical mechanics.- 3 Basic ideas to approach metastability in Probabilistic Cellular Automata.- 4 Strategic Interaction in Interacting Particle Systems.- 5 Scaling and inverse scaling in anisotropic bootstrap percolation.- 6 The sandpile cellular automaton.- 7 Ising Model on the Torus and PCA Dynamics: reversibility, irreversibility, and fast tunneling.- 8 Synchronization in Interacting Reinforced Stochastic Processes.- 9 Nonequilibrium physics aspects of Probabilistic Cellular Automata.- Part II Computer science and discrete dynamical systems.- 10 An example of computation of the density of ones in Probabilistic Cellular Automata by direct recursion.- 11 Statistical equilibrium in deterministic Cellular Automata.- 12 Epidemic automaton and the Eden model: various aspects of robustness.- 13 Convergence time of Probabilistic Cellular Automata on the torus.- 14 Percolation operators and related models.- 15 Phase transitions of Cellular Automata.-  Part III Applications to natural sciences and computational (cell) biology.- 16 A trade-off between simplicity and robustness? Illustration on a lattice-gas model of swarming.- 17 PCA modelling of multi-species cell clusters: ganglion development in the gastrointestinal nervous system.- 18 Cellular Potts model: applications to vasculogenesis and angiogenesis.- 19 Cellular Potts Models for interacting cell populations: mathematical foundation, challenges and future prospects.- 20 Cellular Automata for clouds and convection.- Participants of the 2013 Eindhoven meeting.