An Introduction to Symbolic Dynamics and Coding

Author: Douglas Lind,Brian Marcus

Publisher: Cambridge University Press

ISBN: 9780521559003

Category: Mathematics

Page: 495

View: 3523

Symbolic dynamics is a rapidly growing area of dynamical systems. Although it originated as a method to study general dynamical systems, it has found significant uses in coding for data storage and transmission as well as in linear algebra. This book is the first general textbook on symbolic dynamics and its applications to coding. Mathematical prerequisites are relatively modest (mainly linear algebra at the undergraduate level) especially for the first half of the book. Topics are carefully developed and motivated with many examples, and there are over 500 exercises to test the reader's understanding. The last chapter contains a survey of more advanced topics, and a comprehensive bibliography is included. This book will serve as an introduction to symbolic dynamics for advanced undergraduate students in mathematics, engineering, and computer science.

Symbolic Dynamics and Its Applications

American Mathematical Society, Short Course, January 4-5, 2002, San Diego, California

Author: Susan G. Williams,American Mathematical Society. Short Course,American Mathematical Society,Short Course on Symbolic Dynamics and Its Applications

Publisher: American Mathematical Soc.

ISBN: 0821831577

Category: Mathematics

Page: 156

View: 6426

Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It contains introductory articles on the fundamental ideas of the field and on some of its applications.Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong shift equivalence theory. Contributors to the volume are experts in the field and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.

Different Aspects of Coding Theory

American Mathematical Society Short Course, January 2-3, 1995, San Francisco, California

Author: Robert Calderbank

Publisher: American Mathematical Soc.

ISBN: 0821803794

Category: Computers

Page: 239

View: 1510

This book connects coding theory with actual applications in consumer electronics and with other areas of mathematics. ""Different Aspects of Coding Theory"" covers in detail the mathematical foundations of digital data storage and makes connections to symbolic dynamics, linear systems, and finite automata. It also explores the use of algebraic geometry within coding theory and examines links with finite geometry, statistics, and theoretical computer science. This book features: a unique combination of mathematical theory and engineering practice; much diversity and variety among chapters, thus offering broad appeal; and, topics relevant to mathematicians, statisticians, engineers, and computer scientists. Contributions are by recognized scholars.

Encyclopedia of Nonlinear Science

Author: Alwyn Scott,Emeritus Professor of Mathematics Alwyn Scott

Publisher: Routledge

ISBN: 1135455589

Category: Reference

Page: 1104

View: 2096

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Formal Languages, Automata and Numeration Systems 1

Introduction to Combinatorics on Words

Author: Michel Rigo

Publisher: John Wiley & Sons

ISBN: 1119008220

Category: Computers

Page: 338

View: 1445

Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory.

Mathematics of Complexity and Dynamical Systems

Author: Robert A. Meyers

Publisher: Springer Science & Business Media

ISBN: 1461418054

Category: Mathematics

Page: 1858

View: 4145

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Computer Science -- Theory and Applications

7th International Computer Science Symposium in Russia, CSR 2012, Niszhny Novgorod, Russia, July 3-7, 2012, Proceedings

Author: Edward Hirsch,Juhani Karhumäki,Arto Lepistö,Michail Prilutskii

Publisher: Springer

ISBN: 364230642X

Category: Computers

Page: 327

View: 8957

This book constitutes the proceedings of the 7th International Computer Science Symposium in Russia, CSR 2012, held in Nizhny Novgorod in July 2012. The 28 full papers presented in this volume were carefully reviewed and selected from 66 submissions. CSR 2012 was one of the events of the Alan Turing Year 2012, the topics dealt with cover substantial parts of theoretical computer science and its applications.

Codes, Systems, and Graphical Models

Author: Brian Marcus,Joachim Rosenthal

Publisher: Springer Science & Business Media

ISBN: 1461301653

Category: Computers

Page: 513

View: 3979

Coding theory, system theory, and symbolic dynamics have much in common. A major new theme in this area of research is that of codes and systems based on graphical models. This volume contains survey and research articles from leading researchers at the interface of these subjects.

Struktur Und Interpretation Von Computerprogrammen/ Structure and Interpretation of Computer Programs

Eine Informatik-einfhrung/ a Computer Science Introduction

Author: Harold Abelson,Julie Sussman,Gerald Jay Sussman

Publisher: Springer

ISBN: 9783540423423

Category: Computers

Page: 682

View: 5956

Die Übersetzung der bewährten Einführung in die Informatik, entstanden am Massachusetts Institute of Technology (MIT), wird seit Jahren erfolgreich in der Lehre eingesetzt. Schritt für Schritt werden Konstruktion und Abstraktion von Daten und Prozeduren dargestellt. Von der Modularisierung bis zum Problemlösen mit Registermaschinen werden verschiedene Programmierparadigmen entwickelt und die effektive Handhabung von Komplexität gezeigt. Als Programmiersprache wird SCHEME verwendet, ein Dialekt von LISP. Alle Programme laufen in jeder dem IEEE-Standard entsprechenden SCHEME-Implementierung.

Unterdrückung und Befreiung

Herausgegeben von Peter Schreiner, Norbert Mette, Dirk Oesselmann, Dieter Kinkelbur in Kooperation mit Armin Bernhard

Author: Paulo Freire

Publisher: Waxmann Verlag

ISBN: 9783830968030

Category: Education

Page: 140

View: 4598

Diese Sammlung von Schriften aus der Zeit von 1970 bis 1990 des brasilianischen Pädagogen Paulo Freire (1921-1997) gibt einen Einblick in die Grundlagen und Prinzipien seiner Bildungsarbeit auf der Basis der Pädagogik der Befreiung. In den ausgewählten Texten werden nicht nur pädagogische Probleme und inhaltlich-methodische Fragen der Bildungsarbeit thematisiert. Sie enthalten ebenso Analysen und Bewertungen von Politik, Kultur, Religion, Ethik und Veränderungsmöglichkeiten von Gesellschaft - eine Erweiterung, die sich gegen eine Vorstellung wendet, Pädagogik sei von Gesellschaft und Politik losgelöst zu behandeln. Scharfsinnig hat Freire u.a. die verheerenden Folgen des Neoliberalismus für Individuum und Gesellschaft analysiert und zum widerständigen Denken und Handeln ermuntert. Eine Auswahl repräsentativer alter und neuer Texte von Paulo Freire: Wer sie zur Hand nimmt, entdeckt rasch, dass uns dieser brasilianische Pädagoge nicht nur für die Theorie und Praxis unserer Erziehungsarbeit, sondern für unser Überleben Entscheidendes zu sagen hat. Prof. Dr. Ulrich Becker, Universität Hannover

Topological and Symbolic Dynamics

Author: Petr Kůrka

Publisher: SMF

ISBN: 9782856291436

Category: Topological dynamics

Page: 315

View: 8212

"A dynamical system is a continuous self-map of a compact metric space. Topological dynamics studies the iterations of such a map, or equivalently the trajectories of points of the state space. The basic concepts of topological dynamics are: minimality, transitivity, recurrence, shadowing property, stability, equicontinuity, sensitivity, attractors and topological entropy. Symbolic dynamics studies dynamical systems whose state spaces are zero-dimensional and consist of sequences of symbols. The main classes of symbolic dynamical systems are: adding machines, subshifts of finite type, sofic subshifts, Sturman, substitutive and Toeplitz subshifts, and cellular automata."--BOOK JACKET.