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Title Probabilistic cellular automata : theory, applications and future perspectives / Pierre-Yves Louis, Francesca R. Nardi, editors
Published Cham, Switzerland : Springer, 2018

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Description 1 online resource (xviii, 344 pages) : illustrations (some color)
Series Emergence, complexity and computation, 2194-7287 ; volume 27
Emergence, complexity and computation ; 27. 2194-7287
Contents Intro; Editorial Board; Preface; Acknowledgements; Contents; Editors, Associate Editors and Contributors; 1 Overview: PCA Models and Issues; 1.1 Introduction; 1.2 Phenomena Addressed by PCA Modeling; 1.2.1 Metastability and Traps; 1.2.2 Epidemics and Extinction; 1.2.3 Wildfire and Percolation Phenomena; 1.3 The Multiple Faces of the PCA Paradigm; 1.3.1 Mathematical Issues; 1.3.2 Computational Issues; 1.3.3 Applications of PCA; 1.4 Future Perspectives; 1.5 Structure of the Book; References; 2 Probabilistic Cellular Automata in the Visual Arts; References
Part I Probability and Statistical Mechanics3 Basic Ideas to Approach Metastability in Probabilistic Cellular Automata; 3.1 Introduction; 3.2 Reversible Probabilistic Cellular Automata; 3.3 The Tuned Cross PCA; 3.4 Main Ingredients for Metastability; 3.5 Metastable Behavior of the Tuned Cross PCA; References; 4 Strategic Interaction in Interacting Particle Systems; 4.1 Introduction; 4.2 Strategic and Non-strategic Interaction; 4.2.1 An Equivalent Optimization Problem; 4.2.2 Strategic Interaction; 4.2.3 Trend-Driven Dynamics; 4.3 A Linear, Mean-Field Model; 4.3.1 The Non-strategic Case
4.3.2 The Strategic Case: The Utility with No Trend4.3.3 The Strategic Case: The Utility with Trend; 4.4 Conclusion; References; 5 Scaling and Inverse Scaling in Anisotropic Bootstrap Percolation; 5.1 Bootstrap Percolation Models; 5.2 A Tractable Example: The (1,2)-Model; 5.3 Inversion; 5.4 Generalisations: Related Models, Higher Dimensions and Other Graphs; References; 6 The Sandpile Cellular Automaton; 6.1 Introduction; 6.2 Definition, Examples and Some Remarks; 6.3 Key Properties; 6.3.1 The Least Action Principle; 6.3.2 Recurrent Sandpiles, Group Structure, Dhar's Formula
6.3.3 Bijection with Spanning Trees6.3.4 Some Computable Quantities; 6.4 Challenges; References; 7 Ising Model on the Torus and PCA Dynamics: Reversibility, Irreversibility, and Fast Tunneling; 7.1 Introduction; 7.2 Reversible and Irreversible PCA on 2D Torus; 7.2.1 Parallel Implementation of the Dynamics; 7.2.2 Stationary Measure of the Dynamics; 7.3 Gibbsian Regime of the Stationary Measure and Fast Mixing; 7.4 Numerical Experiments in the Non-Gibbsian Regime; References; 8 Synchronization in Interacting Reinforced Stochastic Processes; 8.1 A Natural Generalization of PCA Dynamics
8.2 Introduction to the Main Concepts8.2.1 What Is Synchronization?; 8.2.2 A Basic Model of Self-reinforcement: Classical Pólya urn; 8.2.3 Two Examples of Generalized Pólya urns; 8.3 Interacting Urns and Synchronization; 8.3.1 Mean Field Interacting Pólya urns; 8.3.2 First Remarks; 8.3.3 Simulations; 8.4 Main Results; 8.5 Sketch of Synchronization's Proof; 8.6 Related Models of Interacting Urns; 8.6.1 Forced Pólya urn Model; 8.6.2 Urns with a ̀̀Preferred'' Color; 8.6.3 A Simple Finite Range Interacting Case; 8.7 Open Questions; References
Summary 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
Notes Online resource; title from PDF title page (SpringerLink, viewed February 28, 2018)
Subject Cellular automata.
Cybernetics & systems theory.
Maths for scientists.
Probability & statistics.
Biology, life sciences.
Maths for computer scientists.
COMPUTERS -- General.
Cellular automata
Form Electronic book
Author Louis, Pierre-Yves, editor
Nardi, Francesca R., editor
ISBN 9783319655581
3319655582