Cellular Automata and Groups

Author: Tullio Ceccherini-Silberstein,Michel Coornaert

Publisher: Springer Science & Business Media

ISBN: 9783642140341

Category: Computers

Page: 440

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Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.

Cellular Automata and Discrete Complex Systems

23rd IFIP WG 1.5 International Workshop, AUTOMATA 2017, Milan, Italy, June 7-9, 2017, Proceedings

Author: Alberto Dennunzio,Enrico Formenti,Luca Manzoni,Antonio E. Porreca

Publisher: Springer

ISBN: 3319586319

Category: Computers

Page: 201

View: 6103

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This volume constitutes the thoroughly refereed proceedings of the 23rd IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2017, held in Milan, Italy, in June 2017. The 14 full papers presented together with one full-length invited paper and 2 invited talk abstracts were carefully reviewed and selected from a total of 28 submissions. The papers feature research on correlated models of automata. The topics include aspects and features of such models: dynamics; topological, ergodic, and algebraic aspects; algorithmic and complexity issues; emergent properties; formal languages; symbolic dynamics; tilings; models of parallelism and distributed systems; timing schemes; synchronous versus asynchronous models; phenomenological descriptions; scientific modelling; practical applications.

Trends in Harmonic Analysis

Author: Massimo A. Picardello

Publisher: Springer Science & Business Media

ISBN: 8847028531

Category: Mathematics

Page: 448

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This book illustrates the wide range of research subjects developed by the Italian research group in harmonic analysis, originally started by Alessandro Figà-Talamanca, to whom it is dedicated in the occasion of his retirement. In particular, it outlines some of the impressive ramifications of the mathematical developments that began when Figà-Talamanca brought the study of harmonic analysis to Italy; the research group that he nurtured has now expanded to cover many areas. Therefore the book is addressed not only to experts in harmonic analysis, summability of Fourier series and singular integrals, but also in potential theory, symmetric spaces, analysis and partial differential equations on Riemannian manifolds, analysis on graphs, trees, buildings and discrete groups, Lie groups and Lie algebras, and even in far-reaching applications as for instance cellular automata and signal processing (low-discrepancy sampling, Gaussian noise).

Cellular Automata: Analysis and Applications

Author: Karl-Peter Hadeler,Johannes Müller

Publisher: Springer

ISBN: 3319530437

Category: Mathematics

Page: 467

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This book focuses on a coherent representation of the main approaches to analyze the dynamics of cellular automata. Cellular automata are an inevitable tool in mathematical modeling. In contrast to classical modeling approaches as partial differential equations, cellular automata are straightforward to simulate but hard to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction of cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of different topological concepts (Cantor, Besicovitch and Weyl topology). The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kůrka classification). These classifications suggest to cluster cellular automata, similar to the classification of partial differential equations in hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question, whether properties of cellular automata are decidable. Surjectivity, and injectivity are examined, and the seminal Garden of Eden theorems are discussed. The third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows to define self-similar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit). Pattern formation is related to linear cellular automata, to the Bar-Yam model for Turing pattern, and Greenberg-Hastings automata for excitable media. Also models for sandpiles, the dynamics of infectious diseases and evolution of predator-prey systems are discussed. Mathematicians find an overview about theory and tools for the analysis of cellular automata. The book contains an appendix introducing basic mathematical techniques and notations, such that also physicists, chemists and biologists interested in cellular automata beyond pure simulations will benefit.

Cellular Automata

11th International Conference on Cellular Automata for Research and Industry, ACRI 2014, Krakow, Poland, September 22-25, 2014, Proceedings

Author: Jaroslaw Was,Georgios Sirakoulis,Stefania Bandini

Publisher: Springer

ISBN: 3319115200

Category: Computers

Page: 713

View: 2271

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This book constitutes the proceedings of the 11th International Conference on Cellular Automata for Research and Industry, ACRI 2014, held in Krakow, Poland, in September 2014. The 67 full papers and 7 short papers presented in this volume were carefully reviewed and selected from 125 submissions. They are organized in topical sections named: theoretical results on cellular automata; cellular automata dynamics and synchronization; modeling and simulation with cellular automata; cellular automata-based hardware and computing; cryptography, networks and pattern recognition with cellular automata. The volume also contains contributions from ACRI 2014 workshops on crowds and cellular automata; asynchronous cellular automata; traffic and cellular automata; and agent-based simulation and cellular automata.

Cellular Automata and Discrete Complex Systems

22nd IFIP WG 1.5 International Workshop, AUTOMATA 2016, Zurich, Switzerland, June 15-17, 2016, Proceedings

Author: Matthew Cook,Turlough Neary

Publisher: Springer

ISBN: 3319393006

Category: Computers

Page: 199

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This volume constitutes the thoroughly refereed proceedings of the 22nd IFIP WG 1.5International Workshop on Cellular Automata and Discrete ComplexSystems, AUTOMATA 2016, held in Zurich, Switzerland, in June 2016. This volume contains 3 invited talks in full-paper length and 12 regularpapers, which were carefully reviewed and selected from a total of 23submissions. The papers feature research on all fundamental aspects of cellular automata and related discrete complex systems and deal with the following topics: dynamical, topological, ergodic and algebraic aspects; algorithmic and complexity issues; emergent properties; formal language processing; symbolic dynamics; models of parallelism and distributed systems; timing schemes; phenomenological descriptions; scientific modeling; and practical applications.

Cellular Automata and Discrete Complex Systems

21st IFIP WG 1.5 International Workshop, AUTOMATA 2015, Turku, Finland, June 8-10, 2015. Proceedings

Author: Jarkko Kari

Publisher: Springer

ISBN: 366247221X

Category: Computers

Page: 263

View: 4344

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This volume constitutes the thoroughly refereed proceedings of the 21st International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2015, held in Turku, Finland, in June 2015. This volume contains 4 invited talks in full-paper length and 15 regular papers, which were carefully reviewed and selected from a total of 33 submissions. Topics of interest include, the following aspects and features of such systems: dynamical, topological, ergodic and algebraic aspects; algorithmic and complexity issues; emergent properties; formal language processing aspects; symbolic dynamics; models of parallelism and distributed systems; timing schemes; phenomenological descriptions; scientific modeling; and practical applications.

Cellular Automata

12th International Conference on Cellular Automata for Research and Industry, ACRI 2016, Fez, Morocco, September 5-8, 2016. Proceedings

Author: Samira El Yacoubi,Jarosław Wąs,Stefania Bandini

Publisher: Springer

ISBN: 3319443658

Category: Computers

Page: 468

View: 6106

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This book constitutes the proceedings of the 12th International Conference on Cellular Automata for Research and Industry, ACRI 2016, held in Fez, Morocco, in September 2014. The 45 full papers and 4 invited talks presented in this volume were carefully reviewed and selected from 59 submissions. This volume contains invited contributions and accepted papers from the main track and from the three organized workshops. The first part is organized according to three topics: (1) Cellular Automata Theory and Implementation (2) Cellular Automata Dynamics and Synchronization, (3) Asynchronous Cellular Automata and Asynchronous Discrete Models - ACA. The second part of the volume contains three topics: (4) Modelling and Sim-ulation with Cellular Automata (5) Crowds, Traffic and Cellular Automata –CT&CA (6) Agent-Based Simulation and Cellular Automata – ABS&CA.

Geometric Group Theory

An Introduction

Author: Clara Löh

Publisher: Springer

ISBN: 3319722549

Category: Mathematics

Page: 389

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Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Cellular Automata in Image Processing and Geometry

Author: Paul Rosin,Andrew Adamatzky,Xianfang Sun

Publisher: Springer

ISBN: 3319064312

Category: Computers

Page: 304

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The book presents findings, views and ideas on what exact problems of image processing, pattern recognition and generation can be efficiently solved by cellular automata architectures. This volume provides a convenient collection in this area, in which publications are otherwise widely scattered throughout the literature. The topics covered include image compression and resizing; skeletonization, erosion and dilation; convex hull computation, edge detection and segmentation; forgery detection and content based retrieval; and pattern generation. The book advances the theory of image processing, pattern recognition and generation as well as the design of efficient algorithms and hardware for parallel image processing and analysis. It is aimed at computer scientists, software programmers, electronic engineers, mathematicians and physicists, and at everyone who studies or develops cellular automaton algorithms and tools for image processing and analysis, or develops novel architectures and implementations of massive parallel computing devices. The book will provide attractive reading for a general audience because it has do-it-yourself appeal: all the computer experiments presented within it can be implemented with minimal knowledge of programming. The simplicity yet substantial functionality of the cellular automaton approach, and the transparency of the algorithms proposed, makes the text ideal supplementary reading for courses on image processing, parallel computing, automata theory and applications.

Classical Potential Theory

Author: David H. Armitage,Stephen J. Gardiner

Publisher: Springer Science & Business Media

ISBN: 1447102339

Category: Mathematics

Page: 333

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A long-awaited, updated introductory text by the world leaders in potential theory. This essential reference work covers all aspects of this major field of mathematical research, from basic theory and exercises to more advanced topological ideas. The largely self-contained presentation makes it basically accessible to graduate students.

Applications of Automata Theory and Algebra

Via the Mathematical Theory of Complexity to Biology, Physics, Psychology, Philosophy, and Games

Author: John L. Rhodes,Chrystopher L. Nehaniv

Publisher: World Scientific

ISBN: 9812836969

Category: Mathematics

Page: 274

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This book was originally written in 1969 by Berkeley mathematician John Rhodes. It is the founding work in what is now called algebraic engineering, an emerging field created by using the unifying scheme of finite state machine models and their complexity to tie together many fields: finite group theory, semigroup theory, automata and sequential machine theory, finite phase space physics, metabolic and evolutionary biology, epistemology, mathematical theory of psychoanalysis, philosophy, and game theory. The author thus introduced a completely original algebraic approach to complexity and the understanding of finite systems. The unpublished manuscript, often referred to as "The Wild Book," became an underground classic, continually requested in manuscript form, and read by many leading researchers in mathematics, complex systems, artificial intelligence, and systems biology. Yet it has never been available in print until now. This first published edition has been edited and updated by Chrystopher Nehaniv for the 21st century. Its novel and rigorous development of the mathematical theory of complexity via algebraic automata theory reveals deep and unexpected connections between algebra (semigroups) and areas of science and engineering. Co-founded by John Rhodes and Kenneth Krohn in 1962, algebraic automata theory has grown into a vibrant area of research, including the complexity of automata, and semigroups and machines from an algebraic viewpoint, and which also touches on infinite groups, and other areas of algebra. This book sets the stage for the application of algebraic automata theory to areas outside mathematics. The material and references have been brought up to date bythe editor as much as possible, yet the book retains its distinct character and the bold yet rigorous style of the author. Included are treatments of topics such as models of time as algebra via semigroup theory; evolution-complexity relations applicable to both ontogeny and evolution; an approach to classification of biological reactions and pathways; the relationships among coordinate systems, symmetry, and conservation principles in physics; discussion of "punctuated equilibrium" (prior to Stephen Jay Gould); games; and applications to psychology, psychoanalysis, epistemology, and the purpose of life. The approach and contents will be of interest to a variety of researchers and students in algebra as well as to the diverse, growing areas of applications of algebra in science and engineering. Moreover, many parts of the book will be intelligible to non-mathematicians, including students and experts from diverse backgrounds.

Combinatorics of Coxeter Groups

Author: Anders Bjorner,Francesco Brenti

Publisher: Springer Science & Business Media

ISBN: 3540275967

Category: Mathematics

Page: 366

View: 8165

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Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups

Automata, Languages and Programming

29th International Colloquium, ICALP 2002, Malaga, Spain, July 8-13, 2002. Proceedings

Author: Peter Widmayer,Francisco Triguero,Rafael Morales,Matthew Hennessy,Stephan Eidenbenz,Ricardo Conejo

Publisher: Springer

ISBN: 3540454659

Category: Computers

Page: 1072

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Topological Dimension and Dynamical Systems

Author: Michel Coornaert

Publisher: Springer

ISBN: 3319197940

Category: Mathematics

Page: 233

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Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner’s characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active areas of current research in mathematics and mathematical physics, the prerequisites needed for reading it remain modest; essentially some familiarities with undergraduate point-set topology and, in order to access the final two chapters, some acquaintance with basic notions in group theory. Topological Dimension and Dynamical Systems is intended for graduate students, as well as researchers interested in topology and dynamical systems. Some of the topics treated in the book directly lead to research areas that remain to be explored.

Non-Equilibrium Social Science and Policy

Introduction and Essays on New and Changing Paradigms in Socio-Economic Thinking

Author: Jeffrey Johnson,Andrzej Nowak,Paul Ormerod,Bridget Rosewell,Yi-Cheng Zhang

Publisher: Springer

ISBN: 3319424246

Category: Science

Page: 232

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The overall aim of this book, an outcome of the European FP7 FET Open NESS project, is to contribute to the ongoing effort to put the quantitative social sciences on a proper footing for the 21st century. A key focus is economics, and its implications on policy making, where the still dominant traditional approach increasingly struggles to capture the economic realities we observe in the world today - with vested interests getting too often in the way of real advances. Insights into behavioral economics and modern computing techniques have made possible both the integration of larger information sets and the exploration of disequilibrium behavior. The domain-based chapters of this work illustrate how economic theory is the only branch of social sciences which still holds to its old paradigm of an equilibrium science - an assumption that has already been relaxed in all related fields of research in the light of recent advances in complex and dynamical systems theory and related data mining. The other chapters give various takes on policy and decision making in this context. Written in nontechnical style throughout, with a mix of tutorial and essay-like contributions, this book will benefit all researchers, scientists, professionals and practitioners interested in learning about the 'thinking in complexity' to understand how socio-economic systems really work.

Lattice-Gas Cellular Automata and Lattice Boltzmann Models

An Introduction

Author: Dieter A. Wolf-Gladrow

Publisher: Springer

ISBN: 3540465863

Category: Mathematics

Page: 314

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Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

Mathematics and Computing

ICMC, Haldia, India, January 2015

Author: Ram N. Mohapatra,Dipanwita Roy Chowdhury,Debasis Giri

Publisher: Springer

ISBN: 8132224523

Category: Mathematics

Page: 493

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This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. This is the second conference on mathematics and computing organized at Haldia Institute of Technology, India. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computing are of vital importance to a broad range of communities, including mathematicians and computing professionals across different educational levels and disciplines. In current research, modeling and simulation, making decisions under uncertainty and pattern recognition have become very common. Professionals across different educational levels and disciplines need exposure to advances in mathematics and computing. In this context, this book presents research papers on applicable areas of current interest. It also includes papers in which experts summarize research findings, such as signal processing and analysis and low-rank-matrix approximation for solving large systems, which will emerge as powerful tools for further research. These new advances and cutting-edge research in the fields of mathematics and their applications to computing are of paramount importance for young researchers.

Hypergeometric Orthogonal Polynomials and Their q-Analogues

Author: Roelof Koekoek,Peter A. Lesky,René F. Swarttouw

Publisher: Springer Science & Business Media

ISBN: 9783642050145

Category: Mathematics

Page: 578

View: 5429

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The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969–1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).

The Cellular Automaton Interpretation of Quantum Mechanics

Author: Gerard 't Hooft

Publisher: Springer

ISBN: 331941285X

Category: Science

Page: 298

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This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.