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Mathematical Foundations Of Information Retrieval

Author : S. Dominich
ISBN : 0792368614
Genre : Computers
File Size : 45. 24 MB
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This book offers a comprehensive and consistent mathematical approach to information retrieval (IR) without which no implementation is possible, and sheds an entirely new light upon the structure of IR models. It contains the descriptions of all IR models in a unified formal style and language, along with examples for each, thus offering a comprehensive overview of them. The book also creates mathematical foundations and a consistent mathematical theory (including all mathematical results achieved so far) of IR as a stand-alone mathematical discipline, which thus can be read and taught independently. Also, the book contains all necessary mathematical knowledge on which IR relies, to help the reader avoid searching different sources. Audience: The book will be of interest to computer or information scientists, librarians, mathematicians, undergraduate students and researchers whose work involves information retrieval.

Mathematical Foundations Of Information Theory

Author : A. Ya. Khinchin
ISBN : 9780486318448
Genre : Mathematics
File Size : 73. 11 MB
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First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.

Mathematical Foundations Of Information Flow

Author : Samson Abramsky
ISBN : 9780821849231
Genre : Mathematics
File Size : 83. 21 MB
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This volume is based on the 2008 Clifford Lectures on Information Flow in Physics, Geometry and Logic and Computation, held March 12-15, 2008, at Tulane University in New Orleans, Louisiana. The varying perspectives of the researchers are evident in the topics represented in the volume, including mathematics, computer science, quantum physics and classical and quantum information. A number of the articles address fundamental questions in quantum information and related topics in quantum physics, using abstract categorical and domain-theoretic models for quantum physics to reason about such systems and to model spacetime. Readers can expect to gain added insight into the notion of information flow and how it can be understood in many settings. They also can learn about new approaches to modeling quantum mechanics that provide simpler and more accessible explanations of quantum phenomena, which don't require the arcane aspects of Hilbert spaces and the cumbersome notation of bras and kets.

Quantum Information Processing With Finite Resources

Author : Marco Tomamichel
ISBN : 3319218905
Genre : Science
File Size : 22. 68 MB
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This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.

Quantitative Graph Theory

Author : Matthias Dehmer
ISBN : 9781466584525
Genre : Computers
File Size : 81. 13 MB
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The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical technique

Mathematical Foundations Of Statistical Mechanics

Author : Aleksandr I?Akovlevich Khinchin
ISBN : 0486601471
Genre : Mathematics
File Size : 87. 50 MB
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Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.

Mathematical Foundations Of Complex Networked Information Systems

Author : P.R. Kumar
ISBN : 9783319169675
Genre : Mathematics
File Size : 37. 27 MB
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Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance. The book is self-contained, and requires only an undergraduate mathematical background.

Mathematical Foundations Of Statistical Mechanics

Author : A. Ya. Khinchin
ISBN : 9780486138732
Genre : Science
File Size : 41. 1 MB
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Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Reduction to the Problem of the Theory of Probability; and more.

Entropy And Information Theory

Author : Robert M. Gray
ISBN : 9781475739824
Genre : Computers
File Size : 36. 6 MB
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This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Much of the book is concerned with their properties, especially the long term asymptotic behavior of sample information and expected information. This is the only up-to-date treatment of traditional information theory emphasizing ergodic theory.

Mathematical Foundations Of Quantum Statistics

Author : Aleksandr Iakovlevich Khinchin
ISBN : 0486400255
Genre : Science
File Size : 24. 38 MB
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A coherent, well-organized look at the basis of quantum statistics’ computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, thermodynamics.

Information Theory And Statistics

Author : Solomon Kullback
ISBN : 9780486696843
Genre : Mathematics
File Size : 66. 67 MB
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Highly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.

Mathematical Foundations Of Game Theory

Author : Rida Laraki
ISBN : 9783030266462
Genre : Mathematics
File Size : 36. 82 MB
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This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text. Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text. Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability.

New Developments In Statistical Information Theory Based On Entropy And Divergence Measures

Author : Leandro Pardo
ISBN : 9783038979364
Genre : Social Science
File Size : 47. 88 MB
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This book presents new and original research in Statistical Information Theory, based on minimum divergence estimators and test statistics, from a theoretical and applied point of view, for different statistical problems with special emphasis on efficiency and robustness. Divergence statistics, based on maximum likelihood estimators, as well as Wald’s statistics, likelihood ratio statistics and Rao’s score statistics, share several optimum asymptotic properties, but are highly non-robust in cases of model misspecification under the presence of outlying observations. It is well-known that a small deviation from the underlying assumptions on the model can have drastic effect on the performance of these classical tests. Specifically, this book presents a robust version of the classical Wald statistical test, for testing simple and composite null hypotheses for general parametric models, based on minimum divergence estimators.

Information Theory

Author : Robert B. Ash
ISBN : 0486665216
Genre : Computers
File Size : 45. 13 MB
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Developed by Claude Shannon and Norbert Wiener in the late Forties, information theory, or statistical communication theory, deals with the theoretical underpinnings of a wide range of communication devices: radio, television, radar, computers, telegraphy, and more. This book is an excellent introduction to the mathematics underlying the theory. Designed for upper-level undergraduates and first-year graduate students, the book treats three major areas: analysis of channel models and proof of coding theorems (Chapters 3, 7 and 8); study of specific coding systems (Chapters 2, 4, and 5); and study of statistical properties of information sources (Chapter 6). Among the topics covered are noiseless coding, the discrete memoryless channel, error correcting codes, information sources, channels with memory and continuous channels. The author has tried to keep the prerequisites to a minimum. However, students should have a knowledge of basic probability theory. Some measure and Hilbert space theory is helpful as well for the last two sections of Chapter 8, which treat time-continuous channels. An appendix summarizes the Hilbert space background and the results from the theory of stochastic processes necessary for these sections. The appendix is not self-contained, but will serve to pinpoint some of the specific equipment needed for the analysis of time-continuous channels. In addition to historic notes at the end of each chapter indicating the origin of some of the results, the author has also included 60 problems, with detailed solutions, making the book especially valuable for independent study.

Foundations Of Information Theory

Author : Amiel Feinstein
ISBN : WISC:89037587300
Genre : Information theory
File Size : 37. 65 MB
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Information Theory

Author : Robert B. Ash
ISBN : 0486665216
Genre : Mathematics
File Size : 66. 71 MB
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Developed by Claude Shannon and Norbert Wiener in the late Forties, information theory, or statistical communication theory, deals with the theoretical underpinnings of a wide range of communication devices: radio, television, radar, computers, telegraphy, and more. This book is an excellent introduction to the mathematics underlying the theory. Designed for upper-level undergraduates and first-year graduate students, the book treats three major areas: analysis of channel models and proof of coding theorems (Chapters 3, 7 and 8); study of specific coding systems (Chapters 2, 4, and 5); and study of statistical properties of information sources (Chapter 6). Among the topics covered are noiseless coding, the discrete memoryless channel, error correcting codes, information sources, channels with memory and continuous channels. The author has tried to keep the prerequisites to a minimum. However, students should have a knowledge of basic probability theory. Some measure and Hilbert space theory is helpful as well for the last two sections of Chapter 8, which treat time-continuous channels. An appendix summarizes the Hilbert space background and the results from the theory of stochastic processes necessary for these sections. The appendix is not self-contained, but will serve to pinpoint some of the specific equipment needed for the analysis of time-continuous channels. In addition to historic notes at the end of each chapter indicating the origin of some of the results, the author has also included 60 problems, with detailed solutions, making the book especially valuable for independent study.

Mathematical Principles Of The Internet Volume 1

Author : Nirdosh Bhatnagar
ISBN : 9781351379144
Genre : Computers
File Size : 57. 4 MB
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This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.

Information Theory

Author : JV Stone
ISBN : 9780956372857
Genre : Business & Economics
File Size : 88. 6 MB
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Originally developed by Claude Shannon in the 1940s, information theory laid the foundations for the digital revolution, and is now an essential tool in telecommunications, genetics, linguistics, brain sciences, and deep space communication. In this richly illustrated book, accessible examples are used to introduce information theory in terms of everyday games like ‘20 questions’ before more advanced topics are explored. Online MatLab and Python computer programs provide hands-on experience of information theory in action, and PowerPoint slides give support for teaching. Written in an informal style, with a comprehensive glossary and tutorial appendices, this text is an ideal primer for novices who wish to learn the essential principles and applications of information theory.

An Introduction To Information Theory

Author : Fazlollah M. Reza
ISBN : 0486682102
Genre : Mathematics
File Size : 79. 8 MB
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Graduate-level study for engineering students presents elements of modern probability theory, elements of information theory with emphasis on its basic roots in probability theory and elements of coding theory. Emphasis is on such basic concepts as sets, sample space, random variables, information measure, and capacity. Many reference tables and extensive bibliography. 1961 edition.

Mathematical Principles Of The Internet Two Volume Set

Author : Nirdosh Bhatnagar
ISBN : 9781351379212
Genre : Computers
File Size : 32. 59 MB
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This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, these cover only a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.

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