Aspects Of Kolmogorov Complexity The Physics Of Information
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Aspects Of Kolmogorov Complexity The Physics Of Information
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Author : Bradley S. Tice
language : en
Publisher: CRC Press
Release Date : 2022-09-01
Aspects Of Kolmogorov Complexity The Physics Of Information written by Bradley S. Tice and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Science categories.
The research presented in Aspects of Kolmogorov Complexity addresses the fundamental standard of defining randomness as measured by a Martin-Lof level of randomness as found in random sequential binary strings. A classical study of statistics that addresses both a fundamental standard of statistics as well as an applied measure for statistical communication theory. The research points to compression levels in a random state that are greater than is found in current literature. A historical overview of the field of Kolmogorov Complexity and Algorithmic Information Theory, a subfield of Information Theory, is given as well as examples using a radix 3, radix 4, and radix 5 base numbers for both random and non-random sequential strings. The text also examines monochromatic and chromatic symbols and both theoretical and applied aspects of data compression as they relate to the transmission and storage of information. The appendix contains papers on the subject given at conferences and the references are current.ContentsTechnical topics addressed in Aspects of Kolmogorov Complexity include:• Statistical Communication Theory• Algorithmic Information Theory• Kolmogorov Complexity• Martin-Lof Randomness• Compression, Transmission and Storage of Information
An Introduction To Kolmogorov Complexity And Its Applications
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Author : Ming Li
language : en
Publisher: Springer
Release Date : 2019-06-11
An Introduction To Kolmogorov Complexity And Its Applications written by Ming Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Mathematics categories.
This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features. This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the Gács-Kučera theorem, the Day-Gács theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lovász local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution. Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface. As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science.
A Level Of Martin Lof Randomness
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Author : Bradley S. Tice
language : en
Publisher: CRC Press
Release Date : 2012-10-09
A Level Of Martin Lof Randomness written by Bradley S. Tice and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-09 with Mathematics categories.
This work addresses the notion of compression ratios greater than what has been known for random sequential strings in binary and larger radix-based systems as applied to those traditionally found in Kolmogorov complexity. A culmination of the author's decade-long research that began with his discovery of a compressible random sequential string, th
The Kolmogorov Legacy In Physics
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Author : Angelo Vulpiani
language : en
Publisher: Springer
Release Date : 2003-12-08
The Kolmogorov Legacy In Physics written by Angelo Vulpiani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-08 with Science categories.
The present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance.
Elements Of Information Theory
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Author : Thomas M. Cover
language : en
Publisher: John Wiley & Sons
Release Date : 2012-11-28
Elements Of Information Theory written by Thomas M. Cover and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-28 with Computers categories.
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.
Physics Of Complex Systems
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Author : Dragutin Mihailović
language : en
Publisher: CRC Press
Release Date : 2023-09-01
Physics Of Complex Systems written by Dragutin Mihailović and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-01 with Science categories.
This book analyses the physics of complex systems to elaborate the problems encountered in teaching and research. Inspired by the of Kurt Gödel (including his incompleteness theorems) it considers the concept of time, the idea of models and the concept of complexity before trying to assess the state of physics in general. Using both general and practical examples, the idea of information is discussed, emphasizing its physical interpretation, debates ideas in depth using examples and evidence to provide detailed considerations on the topics. Based on the authors’ own research on these topics, this book puts forward the idea that the application of information measures can provide new results in the study of complex systems. Helpful for those already familiar with the concepts who wish to deepen their critical understanding, Physics of Complex Systems will be extremely valuable both for people that are already involved in complex systems and also readers beginning their journey into the subject. This work will encourage readers to follow and continue these ideas, enabling them to investigate the various topics further.
The Physics Of The Law Legal Systems Through The Prism Of Complexity Science
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Author : Pierpaolo Vivo
language : en
Publisher: Frontiers Media SA
Release Date : 2022-05-05
The Physics Of The Law Legal Systems Through The Prism Of Complexity Science written by Pierpaolo Vivo and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-05 with Science categories.
Descriptional Complexity Of Formal Systems
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Author : Martin Kutrib
language : en
Publisher: Springer
Release Date : 2012-07-09
Descriptional Complexity Of Formal Systems written by Martin Kutrib and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-09 with Computers categories.
This book constitutes the refereed proceedings of the 14th International Workshop of Descriptional Complexity of Formal Systems 2012, held in Braga, Portugal, in July 2012. The 20 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 33 submissions. The topics covered are automata, grammars, languages and related systems, various measures and modes of operations (e.g., determinism and nondeterminism); trade-offs between computational models and/or operations; succinctness of description of (finite) objects; state explosion-like phenomena; circuit complexity of Boolean functions and related measures; resource-bounded or structure-bounded environments; frontiers between decidability and undecidability; universality and reversibility; structural complexity; formal systems for applications (e.g., software reliability, software and hardware testing, modeling of natural languages); nature-motivated (bio-inspired) architectures and unconventional models of computing; Kolmogorov complexity.
Computation Physics And Beyond
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Author : Michael J. Dinneen
language : en
Publisher: Springer
Release Date : 2012-02-15
Computation Physics And Beyond written by Michael J. Dinneen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-15 with Computers categories.
This Festschrift volume has been published in honor of Cristian Calude on the occasion of his 60th birthday and contains contributions from invited speakers and regular papers presented at the International Workshop on Theoretical Computer Science, WTCS 2012, held in Auckland, New Zealand, in February 2012. Cristian Calude has made a significant contribution to research in computer science theory. Along with early work by Chaitin, Kučera, Kurtz, Solovay, and Terwijn his papers published in the mid-1990s jointly with Khoussainov, Hertling, and Wang laid the foundation for the development of modern theory of algorithmic randomness. His work was essential for establishing the leading role of New Zealand in this area. The research interests of Cristian Calude are reflected in the topics covered by the 32 papers included in this book, namely: algorithmic information theory, algorithms, automata and formal languages, computing and natural sciences, computability and applications, logic and applications, philosophy of computation, physics and computation, and unconventional models of computation. They have been organized into four parts. The first part consists of papers discussing his life achievements. This is followed by papers in the three general areas of complexity, computability, and randomness; physics, philosophy (and logic), and computation; and algorithms, automata, and formal models (including unconventional computing).
Statistical Mechanics And The Physics Of Many Particle Model Systems
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Author : Alexander Leonidovich Kuzemsky
language : en
Publisher: World Scientific
Release Date : 2017-02-24
Statistical Mechanics And The Physics Of Many Particle Model Systems written by Alexander Leonidovich Kuzemsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-24 with Science categories.
The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models.This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography.The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.