| 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 | : David Ellerman |
| Publisher | : Springer Nature |
| Total Pages | : 121 |
| Release | : 2021-10-30 |
| Genre | : Philosophy |
| ISBN | : 3030865525 |
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.
| Author | : Amiel Feinstein |
| Publisher | : |
| Total Pages | : 160 |
| Release | : 1958 |
| Genre | : Information theory |
| ISBN | : |
| Author | : A. Ya. Khinchin |
| Publisher | : Courier Corporation |
| Total Pages | : 130 |
| Release | : 2013-04-09 |
| Genre | : Mathematics |
| ISBN | : 0486318443 |
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 | : George J. Klir |
| Publisher | : John Wiley & Sons |
| Total Pages | : 499 |
| Release | : 2005-11-22 |
| Genre | : Technology & Engineering |
| ISBN | : 0471755567 |
Deal with information and uncertainty properly and efficientlyusing tools emerging from generalized information theory Uncertainty and Information: Foundations of Generalized InformationTheory contains comprehensive and up-to-date coverage of resultsthat have emerged from a research program begun by the author inthe early 1990s under the name "generalized information theory"(GIT). This ongoing research program aims to develop a formalmathematical treatment of the interrelated concepts of uncertaintyand information in all their varieties. In GIT, as in classicalinformation theory, uncertainty (predictive, retrodictive,diagnostic, prescriptive, and the like) is viewed as amanifestation of information deficiency, while information isviewed as anything capable of reducing the uncertainty. A broadconceptual framework for GIT is obtained by expanding theformalized language of classical set theory to include moreexpressive formalized languages based on fuzzy sets of varioustypes, and by expanding classical theory of additive measures toinclude more expressive non-additive measures of varioustypes. This landmark book examines each of several theories for dealingwith particular types of uncertainty at the following fourlevels: * Mathematical formalization of the conceived type ofuncertainty * Calculus for manipulating this particular type ofuncertainty * Justifiable ways of measuring the amount of uncertainty in anysituation formalizable in the theory * Methodological aspects of the theory With extensive use of examples and illustrations to clarify complexmaterial and demonstrate practical applications, generoushistorical and bibliographical notes, end-of-chapter exercises totest readers' newfound knowledge, glossaries, and an Instructor'sManual, this is an excellent graduate-level textbook, as well as anoutstanding reference for researchers and practitioners who dealwith the various problems involving uncertainty and information. AnInstructor's Manual presenting detailed solutions to all theproblems in the book is available from the Wiley editorialdepartment.
| Author | : Roberto Togneri |
| Publisher | : CRC Press |
| Total Pages | : 385 |
| Release | : 2003-01-13 |
| Genre | : Computers |
| ISBN | : 0203998103 |
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
| Author | : Samson Abramsky |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 282 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821849239 |
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.
| Author | : Gregory J Chaitin |
| Publisher | : World Scientific |
| Total Pages | : 284 |
| Release | : 1987-12-18 |
| Genre | : Computers |
| ISBN | : 9814513733 |
The papers gathered in this book were published over a period of more than twenty years in widely scattered journals. They led to the discovery of randomness in arithmetic which was presented in the recently published monograph on “Algorithmic Information Theory” by the author. There the strongest possible version of Gödel's incompleteness theorem, using an information-theoretic approach based on the size of computer programs, was discussed. The present book is intended as a companion volume to the monograph and it will serve as a stimulus for work on complexity, randomness and unpredictability, in physics and biology as well as in metamathematics.
| Author | : Andrew Basden |
| Publisher | : Routledge |
| Total Pages | : 404 |
| Release | : 2017-10-24 |
| Genre | : Business & Economics |
| ISBN | : 131763330X |
Why does information technology disappoint or enslave us? Why do so many information systems projects collapse? How can we do better? There are many technical, social, economic and other aspects to consider. How do we ensure we take all these into account as we research ITC or employ them? ICT affects our lives and world more profoundly than ever before. How may we understand it? This book employs philosophy to lay foundations for understanding the complexity of ICT, in five areas: The nature of information and computers, and artificial intelligence; The use of ICT at work and home, for serious and less-serious use; The ICT features that annoy or delight us; Societal issues, such as surveillance, e-government, ICT in developing countries, climate change, what technological progress is and what is the role of ICT as a whole and of the information systems field; ICT development - including computer programming, knowledge engineering and project management. The ideas in this book emerge from five decades of experience of the author with ICT, across industry, the professions and academic life. Information systems researchers will enjoy this book because it offers them new ideas and fresh perspectives. On the 500th anniversary of the European Reformation, this book introduces and applies the Reformational Philosophy of mid-20th-century Dutch thinker, Herman Dooyeweerd, to contemporary challenges of the 21st century. Excitingly, this accessible philosophy is grounded in everyday experience and yields a rich seedbed of ideas, which researchers and practitioners can develop to their advantage.
