Information Theory Combinatorics And Search Theory

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Information Theory, Combinatorics, and Search Theory

Author : Harout Aydinian
Publisher : Springer
ISBN 13 : 3642368999
Total Pages : 811 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Information Theory, Combinatorics, and Search Theory by : Harout Aydinian

Download or read book Information Theory, Combinatorics, and Search Theory written by Harout Aydinian and published by Springer. This book was released on 2013-03-09 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Rudolf Ahlswede, who passed away in December 2010. The Festschrift contains 36 thoroughly refereed research papers from a memorial symposium, which took place in July 2011. The four macro-topics of this workshop: theory of games and strategic planning; combinatorial group testing and database mining; computational biology and string matching; information coding and spreading and patrolling on networks; provide a comprehensive picture of the vision Rudolf Ahlswede put forward of a broad and systematic theory of search.

General Theory of Information Transfer and Combinatorics

Author : Rudolf Ahlswede
Publisher : Springer Science & Business Media
ISBN 13 : 3540462449
Total Pages : 1138 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis General Theory of Information Transfer and Combinatorics by : Rudolf Ahlswede

Download or read book General Theory of Information Transfer and Combinatorics written by Rudolf Ahlswede and published by Springer Science & Business Media. This book was released on 2006-12-14 with total page 1138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects 63 revised, full-papers contributed to a research project on the "General Theory of Information Transfer and Combinatorics" that was hosted from 2001-2004 at the Center for Interdisciplinary Research (ZIF) of Bielefeld University and several incorporated meetings. Topics covered include probabilistic models, cryptology, pseudo random sequences, quantum models, pattern discovery, language evolution, and network coding.

Information Theory

Author : Imre Csiszár
Publisher : Elsevier
ISBN 13 : 1483281574
Total Pages : 465 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Information Theory by : Imre Csiszár

Download or read book Information Theory written by Imre Csiszár and published by Elsevier. This book was released on 2014-07-10 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information Theory: Coding Theorems for Discrete Memoryless Systems presents mathematical models that involve independent random variables with finite range. This three-chapter text specifically describes the characteristic phenomena of information theory. Chapter 1 deals with information measures in simple coding problems, with emphasis on some formal properties of Shannon's information and the non-block source coding. Chapter 2 describes the properties and practical aspects of the two-terminal systems. This chapter also examines the noisy channel coding problem, the computation of channel capacity, and the arbitrarily varying channels. Chapter 3 looks into the theory and practicality of multi-terminal systems. This book is intended primarily for graduate students and research workers in mathematics, electrical engineering, and computer science.

Entropy, Search, Complexity

Author : Imre Csiszár
Publisher : Springer Science & Business Media
ISBN 13 : 3540327770
Total Pages : 262 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Entropy, Search, Complexity by : Imre Csiszár

Download or read book Entropy, Search, Complexity written by Imre Csiszár and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects survey papers in the fields of entropy, search and complexity, summarizing the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. The book will be useful to experienced researchers as well as young scientists and students both in mathematics and computer science.

Combinatorial Group Testing and Its Applications

Author : Dingzhu Du
Publisher : World Scientific
ISBN 13 : 9810241070
Total Pages : 337 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Combinatorial Group Testing and Its Applications by : Dingzhu Du

Download or read book Combinatorial Group Testing and Its Applications written by Dingzhu Du and published by World Scientific. This book was released on 2000 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group testing has been used in medical, chemical and electrical testing, coding, drug screening, pollution control, multiaccess channel management, and recently in data verification, clone library screening and AIDS testing. The mathematical model can be either combinatorial or probabilistic. This book summarizes all important results under the combinatorial model, and demonstrates their applications in real problems. Some other search problems, including the famous counterfeit-coins problem, are also studied in depth. There are two reasons for publishing a second edition of this book. The first is the usual need to update the text (after six years) and correct errors. The second -- and more important -- reason is to accommodate the recent sudden growth of interest in applying the idea of group testing to clone library screening. This development is much more than just a new application, since the new application brings with it new objectives which require a new twist of theory. It also embraces the growing importance of two topics: nonadaptive algorithms and error tolerance. Two new chapters, one on clone library screening and the other on error tolerance, have been added. Also included is a new chapter on counterfeit coins, the most famous search problem historically, which recently drew on an unexpected connection to some deep mathematical theory to yield new results. Finally, the chapters have been recognized into parts to provide focuses and perspectives.

Elements of Information Theory

Author : Thomas M. Cover
Publisher : John Wiley & Sons
ISBN 13 : 1118585771
Total Pages : 788 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Elements of Information Theory by : Thomas M. Cover

Download or read book Elements of Information Theory written by Thomas M. Cover and published by John Wiley & Sons. This book was released on 2012-11-28 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest edition of this classic is updated with new problem sets and material The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The Second Edition features: * Chapters reorganized to improve teaching * 200 new problems * New material on source coding, portfolio theory, and feedback capacity * Updated references Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.

Combinatorial Methods and Models

Author : Rudolf Ahlswede
Publisher : Springer
ISBN 13 : 3319531395
Total Pages : 395 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Combinatorial Methods and Models by : Rudolf Ahlswede

Download or read book Combinatorial Methods and Models written by Rudolf Ahlswede and published by Springer. This book was released on 2017-06-30 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth volume of Rudolf Ahlswede’s lectures on Information Theory is focused on Combinatorics. Ahlswede was originally motivated to study combinatorial aspects of Information Theory via zero-error codes: in this case the structure of the coding problems usually drastically changes from probabilistic to combinatorial. The best example is Shannon’s zero error capacity, where independent sets in graphs have to be examined. The extension to multiple access channels leads to the Zarankiewicz problem. A code can be regarded combinatorially as a hypergraph; and many coding theorems can be obtained by appropriate colourings or coverings of the underlying hypergraphs. Several such colouring and covering techniques and their applications are introduced in this book. Furthermore, codes produced by permutations and one of Ahlswede’s favourite research fields -- extremal problems in Combinatorics -- are presented. Whereas the first part of the book concentrates on combinatorial methods in order to analyse classical codes as prefix codes or codes in the Hamming metric, the second is devoted to combinatorial models in Information Theory. Here the code concept already relies on a rather combinatorial structure, as in several concrete models of multiple access channels or more refined distortions. An analytical tool coming into play, especially during the analysis of perfect codes, is the use of orthogonal polynomials. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.

Analytic Combinatorics

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Combinatorics and Graph Theory

Author : John Harris
Publisher : Springer Science & Business Media
ISBN 13 : 0387797114
Total Pages : 392 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Combinatorics and Graph Theory by : John Harris

Download or read book Combinatorics and Graph Theory written by John Harris and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Information, Physics, and Computation

Author : Marc Mézard
Publisher : Oxford University Press
ISBN 13 : 019857083X
Total Pages : 584 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Information, Physics, and Computation by : Marc Mézard

Download or read book Information, Physics, and Computation written by Marc Mézard and published by Oxford University Press. This book was released on 2009-01-22 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

Principles and Practice of Information Theory

Author : Richard E. Blahut
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 480 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Principles and Practice of Information Theory by : Richard E. Blahut

Download or read book Principles and Practice of Information Theory written by Richard E. Blahut and published by Addison Wesley Publishing Company. This book was released on 1987 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinatorial Set Theory

Author : Lorenz J. Halbeisen
Publisher : Springer
ISBN 13 : 3319602314
Total Pages : 586 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Combinatorial Set Theory by : Lorenz J. Halbeisen

Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer. This book was released on 2017-12-20 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.

Information and Coding Theory

Author : Gareth A. Jones
Publisher : Springer Science & Business Media
ISBN 13 : 1447103610
Total Pages : 217 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Information and Coding Theory by : Gareth A. Jones

Download or read book Information and Coding Theory written by Gareth A. Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an elementary introduction to information and coding theory. The first part focuses on information theory, covering uniquely decodable and instantaneous codes, Huffman coding, entropy, information channels, and Shannon’s Fundamental Theorem. In the second part, linear algebra is used to construct examples of such codes, such as the Hamming, Hadamard, Golay and Reed-Muller codes. Contains proofs, worked examples, and exercises.

Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

Author : Mauro Di Nasso
Publisher : Springer
ISBN 13 : 3030179567
Total Pages : 206 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by : Mauro Di Nasso

Download or read book Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory written by Mauro Di Nasso and published by Springer. This book was released on 2019-05-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.

Information Theory, Inference and Learning Algorithms

Author : David J. C. MacKay
Publisher : Cambridge University Press
ISBN 13 : 9780521642989
Total Pages : 694 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Information Theory, Inference and Learning Algorithms by : David J. C. MacKay

Download or read book Information Theory, Inference and Learning Algorithms written by David J. C. MacKay and published by Cambridge University Press. This book was released on 2003-09-25 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.

Combinatorics and Random Matrix Theory

Author : Jinho Baik
Publisher : American Mathematical Soc.
ISBN 13 : 0821848410
Total Pages : 478 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Combinatorics and Random Matrix Theory by : Jinho Baik

Download or read book Combinatorics and Random Matrix Theory written by Jinho Baik and published by American Mathematical Soc.. This book was released on 2016-06-22 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.

Fundamentals of Information Theory and Coding Design

Author : Roberto Togneri
Publisher : CRC Press
ISBN 13 : 0203998103
Total Pages : 385 pages
Book Rating : 4.2/5 (39 download)

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Book Synopsis Fundamentals of Information Theory and Coding Design by : Roberto Togneri

Download or read book Fundamentals of Information Theory and Coding Design written by Roberto Togneri and published by CRC Press. This book was released on 2003-01-13 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Books on information theory and coding have proliferated over the last few years, but few succeed in covering the fundamentals without losing students in mathematical abstraction. Even fewer build the essential theoretical framework when presenting algorithms and implementation details of modern coding systems. Without abandoning the theoret