Download or read book Entropy and Information Theory written by Robert M. Gray and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Entropy and Information written by Mikhail V. Volkenstein and published by Springer Science & Business Media. This book was released on 2009-10-27 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is just...entropy, he said, thinking that this explained everything, and he repeated the strange word a few times. 1 ? Karel Capek , “Krakatit” This “strange word” denotes one of the most basic quantities of the physics of heat phenomena, that is, of thermodynamics. Although the concept of entropy did indeed originate in thermodynamics, it later became clear that it was a more universal concept, of fundamental signi?cance for chemistry and biology, as well as physics. Although the concept of energy is usually considered more important and easier to grasp, it turns out, as we shall see, that the idea of entropy is just as substantial—and moreover not all that complicated. We can compute or measure the quantity of energy contained in this sheet of paper, and the same is true of its entropy. Furthermore, entropy has remarkable properties. Our galaxy, the solar system, and the biosphere all take their being from entropy, as a result of its transferenceto the surrounding medium. Thereis a surprisingconnectionbetween entropyandinformation,thatis,thetotalintelligencecommunicatedbyamessage. All of this is expounded in the present book, thereby conveying informationto the readeranddecreasinghis entropy;butitis uptothe readertodecidehowvaluable this information might be.
Download or read book New Foundations for Information Theory written by David Ellerman and published by Springer Nature. This book was released on 2021-10-30 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory) and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement. Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory.
Download or read book An Introduction to Transfer Entropy written by Terry Bossomaier and published by Springer. This book was released on 2016-11-15 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers a relatively new metric in complex systems, transfer entropy, derived from a series of measurements, usually a time series. After a qualitative introduction and a chapter that explains the key ideas from statistics required to understand the text, the authors then present information theory and transfer entropy in depth. A key feature of the approach is the authors' work to show the relationship between information flow and complexity. The later chapters demonstrate information transfer in canonical systems, and applications, for example in neuroscience and in finance. The book will be of value to advanced undergraduate and graduate students and researchers in the areas of computer science, neuroscience, physics, and engineering.
Download or read book The Biggest Ideas in the Universe written by Sean Carroll and published by Penguin. This book was released on 2022-09-20 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: INSTANT NEW YORK TIMES BESTSELLER “Most appealing... technical accuracy and lightness of tone... Impeccable.”—Wall Street Journal “A porthole into another world.”—Scientific American “Brings science dissemination to a new level.”—Science The most trusted explainer of the most mind-boggling concepts pulls back the veil of mystery that has too long cloaked the most valuable building blocks of modern science. Sean Carroll, with his genius for making complex notions entertaining, presents in his uniquely lucid voice the fundamental ideas informing the modern physics of reality. Physics offers deep insights into the workings of the universe but those insights come in the form of equations that often look like gobbledygook. Sean Carroll shows that they are really like meaningful poems that can help us fly over sierras to discover a miraculous multidimensional landscape alive with radiant giants, warped space-time, and bewilderingly powerful forces. High school calculus is itself a centuries-old marvel as worthy of our gaze as the Mona Lisa. And it may come as a surprise the extent to which all our most cutting-edge ideas about black holes are built on the math calculus enables. No one else could so smoothly guide readers toward grasping the very equation Einstein used to describe his theory of general relativity. In the tradition of the legendary Richard Feynman lectures presented sixty years ago, this book is an inspiring, dazzling introduction to a way of seeing that will resonate across cultural and generational boundaries for many years to come.
Download or read book Entropy and Diversity written by Tom Leinster and published by Cambridge University Press. This book was released on 2021-04-22 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.
Download or read book Grammatical Man written by Jeremy Campbell and published by . This book was released on 1984 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Entropy and Information written by Paralternativecelsus and published by Strategic Book Publishing. This book was released on 2012-10 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entropy and Information is a science/philosophical book. The author considers the function Entropy as the tool of the Second Law of Thermodynamics, subsequently applicable to link different areas. Entropy and Information: Unveiling the Mysterious Stuff Permeating the Universe is both holistic and interdisciplinary. I think it brings a new scope on how to face reality. It starts with basic concepts for a rationale on Entropy. Entropy is placed in context with Information Theory, a great milestone contributed by Shannon in 1948. Basically, Entropy gives us estimation on how elements or constituents interrelate in systems, the author says. As principles, entropy and information intimately deal with the human mind. Thus they are paramount in evolution, stupidity, memetics, societies and cultures. The final parts of the book are reflections and criticisms of so-called modern medicine, particularly for its uncouth business orientation. This book fills a gap in interdisciplinary science and is sure to be highly valued by a vast array of readers. Entropy, an old and poorly understood natural function, can be applied to many dimensional scenarios and areas of knowledge.About the Author: Paralternativecelus is an M.D. and a freelance philosopher interested in the process of knowledge and diagnosis. He is constantly challenging the status quo of medicine. For him, medicine is far from being a science, as some people may contrarily believe. Physical principles must be incorporated into health for breakthroughs to happen. Publisher's website: http: //sbpra.com/Paralternativecelsu
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.
Download or read book Information Theoretic Learning written by Jose C. Principe and published by Springer Science & Business Media. This book was released on 2010-04-06 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first cohesive treatment of ITL algorithms to adapt linear or nonlinear learning machines both in supervised and unsupervised paradigms. It compares the performance of ITL algorithms with the second order counterparts in many applications.
Download or read book The Mathematical Theory of Communication written by Claude E Shannon and published by University of Illinois Press. This book was released on 1998-09-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
Download or read book Statistical Data Analysis and Entropy written by Nobuoki Eshima and published by Springer Nature. This book was released on 2020-01-21 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reconsiders statistical methods from the point of view of entropy, and introduces entropy-based approaches for data analysis. Further, it interprets basic statistical methods, such as the chi-square statistic, t-statistic, F-statistic and the maximum likelihood estimation in the context of entropy. In terms of categorical data analysis, the book discusses the entropy correlation coefficient (ECC) and the entropy coefficient of determination (ECD) for measuring association and/or predictive powers in association models, and generalized linear models (GLMs). Through association and GLM frameworks, it also describes ECC and ECD in correlation and regression analyses for continuous random variables. In multivariate statistical analysis, canonical correlation analysis, T2-statistic, and discriminant analysis are discussed in terms of entropy. Moreover, the book explores the efficiency of test procedures in statistical tests of hypotheses using entropy. Lastly, it presents an entropy-based path analysis for structural GLMs, which is applied in factor analysis and latent structure models. Entropy is an important concept for dealing with the uncertainty of systems of random variables and can be applied in statistical methodologies. This book motivates readers, especially young researchers, to address the challenge of new approaches to statistical data analysis and behavior-metric studies.
Download or read book Maxwell s Demon written by Harvey S. Leff and published by Princeton University Press. This book was released on 2014-07-14 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: About 120 years ago, James Clerk Maxwell introduced his now legendary hypothetical "demon" as a challenge to the integrity of the second law of thermodynamics. Fascination with the demon persisted throughout the development of statistical and quantum physics, information theory, and computer science--and linkages have been established between Maxwell's demon and each of these disciplines. The demon's seductive quality makes it appealing to physical scientists, engineers, computer scientists, biologists, psychologists, and historians and philosophers of science. Until now its important source material has been scattered throughout diverse journals. This book brings under one cover twenty-five reprints, including seminal works by Maxwell and William Thomson; historical reviews by Martin Klein, Edward Daub, and Peter Heimann; information theoretic contributions by Leo Szilard, Leon Brillouin, Dennis Gabor, and Jerome Rothstein; and innovations by Rolf Landauer and Charles Bennett illustrating linkages with the limits of computation. An introductory chapter summarizes the demon's life, from Maxwell's illustration of the second law's statistical nature to the most recent "exorcism" of the demon based on a need periodically to erase its memory. An annotated chronological bibliography is included. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Information Entropy Life and the Universe written by Arieh Ben-Naim and published by World Scientific Publishing Company Incorporated. This book was released on 2015 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to explain in simple language what we know and what we do not know about information and entropy -- two of the most frequently discussed topics in recent literature -- and whether they are relevant to life and the entire universe. Entropy is commonly interpreted as a measure of disorder. This interpretation has caused a great amount of "disorder" in the literature. One of the aims of this book is to put some "order" in this "disorder." The book explains with minimum amount of mathematics what information theory is and how it is related to thermodynamic entropy. Then it critically examines the application of these concepts to the question of "What is life?" and whether or not they can be applied to the entire universe.
Download or read book Information Entropy and Progress written by Robert U. Ayres and published by Springer Science & Business Media. This book was released on 1997-05-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Market: Those in economics, especially thermodynamics, statistical mechanics, cybernetics, information theory, resource use, and evolutionary economic behavior. This book presents an innovative and challenging look at evolution on several scales, from the earth and its geology and chemistry to living organisms to social and economic systems. Applying the principles of thermodynamics and the concepts of information gathering and self- organization, the author characterizes the direction of evolution in each case as an accumulation of "distinguishability" information--a type of universal knowledge.
Download or read book Mathematical Theory of Entropy written by Nathaniel F. G. Martin and published by Cambridge University Press. This book was released on 2011-06-02 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent 1981 treatment of the mathematical theory of entropy gives an accessible exposition its application to other fields.
