Entropy and Information Theory

Entropy and Information Theory PDF

Author: Robert M. Gray

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 346

ISBN-13: 1475739826

DOWNLOAD EBOOK →

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.

New Foundations for Information Theory

New Foundations for Information Theory PDF

Author: David Ellerman

Publisher: Springer Nature

Published: 2021-10-30

Total Pages: 121

ISBN-13: 3030865525

DOWNLOAD EBOOK →

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.

Entropy and Information

Entropy and Information PDF

Author: Mikhail V. Volkenstein

Publisher: Springer Science & Business Media

Published: 2009-10-27

Total Pages: 214

ISBN-13: 303460078X

DOWNLOAD EBOOK →

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.

An Introduction to Transfer Entropy

An Introduction to Transfer Entropy PDF

Author: Terry Bossomaier

Publisher: Springer

Published: 2016-11-15

Total Pages: 210

ISBN-13: 3319432222

DOWNLOAD EBOOK →

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.

Entropy and Information

Entropy and Information PDF

Author: Paralternativecelsus

Publisher: Strategic Book Publishing

Published: 2012-10

Total Pages: 348

ISBN-13: 9781618971982

DOWNLOAD EBOOK →

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

Entropy and Diversity

Entropy and Diversity PDF

Author: Tom Leinster

Publisher: Cambridge University Press

Published: 2021-04-22

Total Pages: 457

ISBN-13: 1108832709

DOWNLOAD EBOOK →

Discover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.

Information, Entropy, Life, and the Universe

Information, Entropy, Life, and the Universe PDF

Author: Arieh Ben-Naim

Publisher: World Scientific Publishing Company

Published: 2015

Total Pages: 0

ISBN-13: 9789814651677

DOWNLOAD EBOOK →

Entropy is commonly interpreted as a measure of disorder. This interpretation has caused a great amount of "disorder" in the literature.This book explains what information theory is and how it is related to thermodynamic entropy. Then it 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.

Information, Entropy, and Progress

Information, Entropy, and Progress PDF

Author: Robert U. Ayres

Publisher: Springer Science & Business Media

Published: 1997-05-08

Total Pages: 324

ISBN-13: 9780883189115

DOWNLOAD EBOOK →

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.

Information Theory, Inference and Learning Algorithms

Information Theory, Inference and Learning Algorithms PDF

Author: David J. C. MacKay

Publisher: Cambridge University Press

Published: 2003-09-25

Total Pages: 694

ISBN-13: 9780521642989

DOWNLOAD EBOOK →

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.

The Biggest Ideas in the Universe

The Biggest Ideas in the Universe PDF

Author: Sean Carroll

Publisher: Penguin

Published: 2022-09-20

Total Pages: 305

ISBN-13: 0593186583

DOWNLOAD EBOOK →

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.