Hardback (ISBN-13: 9780521899048)
Paperback (ISBN-13: 9780521727884)
65 line diagrams 3 tables 240 exercises 65 figures 105 worked examples
Page extent: 250 pages
Size: 246 x 189 mm
This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to most exercises available online for instructors.
* Integrated approach to probability and information suitable for pure or applied students * Illustrates a wide range of applications in science and mathematics * Modern, rigorous approach that needs only a background in basic calculus
Contents
Preface to the first edition; Preface to the second edition; 1. Introduction; 2. Combinatorics; 3. Sets and measures; 4. Probability; 5. Discrete random variables; 6. Information and entropy; 7. Communication; 8. Random variables with probability density functions; 9. Random vectors; 10. Markov chains and their entropy; Exploring further; Appendix 1. Proof by mathematical induction; Appendix 2. Lagrange multipliers; Appendix 3. Integration of exp (-*x2); Appendix 4. Table of probabilities associated with the standard normal distribution; Appendix 5. A rapid review of Matrix algebra; Selected solutions; Index.
Series: Publications of the Newton Institute (No. 11)
Paperback (ISBN-13: 9780521055383)
25 line diagrams
Page extent: 455 pages
Size: 228 x 152 mm
Weight: 0.684 kg
Certain nonlinear optimization problems arising in such disparate areas as the theory of computation, pure and applied probability and mathematical physics, can be solved by linear methods, provided one replaces the usual number system with one in which addition satisfies the idempotent law. This systematic study of the subject has emerged, triggered in part by a workshop organized by Hewlett-Packard’s Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together many leading researchers in the area. This volume is a record of that workshop, but it also includes other invited contributions, a broad Introduction to Idempotency, written specially for the book, and a bibliography of the subject. In sum, the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.
* Brings together for the first time contributions from the main research groups in the area * Theoretical contributions as well as applications to practical problems * Specially written introduction to both the subject and the individual papers
Contents
Foreword; Preface; List of participants; 1. An introduction to idempotency Jeremy Gunawardena; 2. Tropical semirings Jean-Eric Pin; 3. Some automata-theoretic aspects of min-max-plus semirings Daniel Krob; 4. The finite power property for rational sets of a free group Flavio d’Alessandro and Jacques Sakarovitch; 5. The topological approach to the limitedness problem on distance automata Hing Leung; 6. Types and dynamics in partially additive categories Gianfranco Mascari and Marco Pedicini; 7. Task resource models and (max,+) automata Stephane Gaubert and Jean Mairesse; 8. Algebraic system analysis of timed Petri nets Guy Cohen, Stephane Gaubert and Jean-Pierre Quadrat; 9. Ergodic theorems for stochastic operators and discrete event networks Francois Baccelli and Jean Mairesse; 10. Computational issues in recursive stochastic systems Bruno Gaujal and Alain Jean-Marie; 11. Periodic points of nonexpansive maps Roger D. Nussbaum; 12. A system-theoretic approach for discrete-event control of manufacturing systems Ayla Gurel, Octavian C. Pastravanu and Frank L. Lewis; 13. Idempotent structures in the supervisory control of discrete event systems Darren D. Cofer and Vijay K. Garg; 14. Maxpolynomials and discrete-event dynamic systems Raymond A. Cunninghame-Green; 15. The Stochastic HJB equation and WKB method Vassili N. Kolokoltsov; 16. The Lagrange problem from the point of view of idempotent analysis Serguei Samborskii; 17. A new differential equation for the dynamics of the Pareto sets Vassili N. Kolokoltsov and Victor P. Maslov; 18. Duality between probability and optimization Marianne Akian, Jean-Pierre Quadrat and Michel Viot; 19. Maslov optimization theory: topological aspects Pierre Del Moral; 20. Random particle methods in (max,+) optimization problems Pierre Del Moral and Gerard Salut; 21. The geometry of finite dimensional pseudomodules Edouard Wagneur; 22. A general linear max-plus solution technique Elizabeth A. Walkup and Gaetano Borriello; 23. Axiomatics of thermodynamics and idempotent analysis Victor P. Maslov; 24. The correspondence principle for idempotent calculus and some computer applications Grigori L. Litvinov and Victor P. Maslov.
Series: Encyclopedia of Mathematics and its Applications (No. 70)
Paperback (ISBN-13: 9780521054317)
11 line diagrams 11 tables
Page extent: 563 pages
Size: 234 x 156 mm
Weight: 0.786 kg
Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey’s theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra.
* Deals in a unique way with harmonic and functional analysis * Contains a long list of problems which may serve as a starting point for research * Can be used as an advanced text
Contents
Preface; Introduction; Preliminaries; 1. Ideal norms and operator ideals; 2. Ideal norms associated with matrices; 3. Ideal norms associated with orthonormal systems; 4. Rademacher and Gauss ideal norms; 5. Trigonometric ideal norms; 6. Walsh ideal norms; 7. Haar ideal norms; 8. Unconditionality; 9. Miscellaneous; Summaries; List of symbols; Bibliography; Index.
Paperback (ISBN-13: 9780521057936)
Page extent: 328 pages
Size: 228 x 152 mm
Weight: 0.542 kg
This is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory. The book covers all the basic material - propositional languages, semantics and correspondence results, proof systems and completeness results - as well as some topics not usually covered in a modal logic course. It is written from a mathematical standpoint. To help the reader, the material is covered in short chapters, each concentrating on one topic. These are arranged into five parts, each with a common theme. An important feature of the book is the many exercises and an extensive set of solutions is provided.
Contents
Introduction; Acknowledgements; Part I. Preliminaries: 1. Survey of propositional logic; 2. The modal language; Part II. Transition Structures and Semantics: 3. Labelled transition structures; 4. Valuation and satisfaction; 5. Correspondence theory; 6. The general confluence result; Part III. Proof Theory and Completeness: 7. Some consequence relations; 8. Standard formal systems; 9. The general completeness result; 10. Kripke-completeness; Part IV. Model Constructions: 11. Bismulations; 12. Filtrations; 13. The finite model property; Part V. More Advanced Material: 14. SLL logic; 15. Lob logic; 16. Canonicity without the fmp; 17. Transition structures aren't enough; Part VI. Two Appendices: Bibliography.
Hardback (ISBN-13: 9780521852296)
150 line diagrams 185 exercises
Page extent: 560 pages
Size: 247 x 174 mm
Having trouble deciding which coding scheme to employ, how to design a new scheme, or how to improve an existing system* This summary of the state-of-the-art in iterative coding makes this decision more straightforward. With emphasis on the underlying theory, techniques to analyse and design practical iterative coding systems are presented. Using Gallager’s original ensemble of LDPC codes, the basic concepts are extended for several general codes, including the practically important class of turbo codes. The simplicity of the binary erasure channel is exploited to develop analytical techniques and intuition, which are then applied to general channel models. A chapter on factor graphs helps to unify the important topics of information theory, coding and communication theory. Covering the most recent advances, this text is ideal for graduate students in electrical engineering and computer science, and practitioners. Additional resources, including instructor’s solutions and figures, available online: www.cambridge.org/9780521852296.
* Helps you to decide which coding scheme to employ, how to design a new scheme and how to improve an existing system * Emphasis is on the underlying theory so that the reader develops an intuitive understanding * Provides a comprehensive description of turbo codes and iterative codes (including LDPC codes) over the binary erasure channel
Contents
Preface; 1. Introduction; 2. Factor graphs; 3. Binary erasure channel; 4. Binary memoryless symmetric channels; 5. General channels ; 6. Convolutional codes and turbo codes; 7. General ensembles; 8. Expander codes and the flipping algorithm; Appendices: A. Encoding low-density parity-check codes; B. Efficient implementation of density evolution; C. Concentration inequalities; D. Formal power sums.