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| Author | : Nathaniel F. G. Martin |
| Publisher | : Cambridge University Press |
| Total Pages | : 292 |
| Release | : 2011-06-02 |
| Genre | : Computers |
| ISBN | : 9780521177382 |
This excellent 1981 treatment of the mathematical theory of entropy gives an accessible exposition its application to other fields.
| Author | : Claude E Shannon |
| Publisher | : University of Illinois Press |
| Total Pages | : 141 |
| Release | : 1998-09-01 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 025209803X |
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.
| Author | : Tom Leinster |
| Publisher | : Cambridge University Press |
| Total Pages | : 457 |
| Release | : 2021-04-22 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 1108832709 |
Discover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.
| Author | : Robert M. Gray |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2013-03-14 |
| Genre | : Computers |
| ISBN | : 1475739826 |
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.
| Author | : Da-Quan Jiang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2004 |
| Genre | : Markov processes |
| ISBN | : 9783540206118 |
| Author | : Jan Kåhre |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 528 |
| Release | : 2002-06-30 |
| Genre | : Technology & Engineering |
| ISBN | : 9781402070648 |
The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon's noisy channel. The entropy in the 'classical information theory' is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron's law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making 'two plus two greater than four'. Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation.
| Author | : Aleksandr I?Akovlevich Khinchin |
| Publisher | : Courier Corporation |
| Total Pages | : 130 |
| Release | : 1957-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486604349 |
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.
| Author | : Tomasz Downarowicz |
| Publisher | : Cambridge University Press |
| Total Pages | : 405 |
| Release | : 2011-05-12 |
| Genre | : Mathematics |
| ISBN | : 1139500872 |
This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.
| Author | : Shu-Cherng Fang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 350 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 1461561310 |
Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization. The resulting entropy optimization models have proved their usefulness with successful applications in areas such as image reconstruction, pattern recognition, statistical inference, queuing theory, spectral analysis, statistical mechanics, transportation planning, urban and regional planning, input-output analysis, portfolio investment, information analysis, and linear and nonlinear programming. While entropy optimization has been used in different fields, a good number of applicable solution methods have been loosely constructed without sufficient mathematical treatment. A systematic presentation with proper mathematical treatment of this material is needed by practitioners and researchers alike in all application areas. The purpose of this book is to meet this need. Entropy Optimization and Mathematical Programming offers perspectives that meet the needs of diverse user communities so that the users can apply entropy optimization techniques with complete comfort and ease. With this consideration, the authors focus on the entropy optimization problems in finite dimensional Euclidean space such that only some basic familiarity with optimization is required of the reader.
| Author | : Mikhail V. Volkenstein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 214 |
| Release | : 2009-10-27 |
| Genre | : Science |
| ISBN | : 303460078X |
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.
