A Statistical Mechanical Interpretation of Algorithmic Information Theory

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Publisher : Springer Nature
ISBN 13 : 9811507392
Total Pages : 136 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis A Statistical Mechanical Interpretation of Algorithmic Information Theory by : Kohtaro Tadaki

Download or read book A Statistical Mechanical Interpretation of Algorithmic Information Theory written by Kohtaro Tadaki and published by Springer Nature. This book was released on 2019-11-11 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first one that provides a solid bridge between algorithmic information theory and statistical mechanics. Algorithmic information theory (AIT) is a theory of program size and recently is also known as algorithmic randomness. AIT provides a framework for characterizing the notion of randomness for an individual object and for studying it closely and comprehensively. In this book, a statistical mechanical interpretation of AIT is introduced while explaining the basic notions and results of AIT to the reader who has an acquaintance with an elementary theory of computation. A simplification of the setting of AIT is the noiseless source coding in information theory. First, in the book, a statistical mechanical interpretation of the noiseless source coding scheme is introduced. It can be seen that the notions in statistical mechanics such as entropy, temperature, and thermal equilibrium are translated into the context of noiseless source coding in a natural manner. Then, the framework of AIT is introduced. On this basis, the introduction of a statistical mechanical interpretation of AIT is begun. Namely, the notion of thermodynamic quantities, such as free energy, energy, and entropy, is introduced into AIT. In the interpretation, the temperature is shown to be equal to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate measured by means of program-size complexity. Additionally, it is demonstrated that this situation holds for the temperature itself as a thermodynamic quantity. That is, for each of all the thermodynamic quantities above, the computability of its value at temperature T gives a sufficient condition for T to be a fixed point on partial randomness. In this groundbreaking book, the current status of the interpretation from both mathematical and physical points of view is reported. For example, a total statistical mechanical interpretation of AIT that actualizes a perfect correspondence to normal statistical mechanics can be developed by identifying a microcanonical ensemble in the framework of AIT. As a result, the statistical mechanical meaning of the thermodynamic quantities of AIT is clarified. In the book, the close relationship of the interpretation to Landauer's principle is pointed out.

A Statistical Mechanical Interpretation of Algorithmic Information Theory III

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Publisher :
ISBN 13 :
Total Pages : 6 pages
Book Rating : 4.:/5 (428 download)

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Book Synopsis A Statistical Mechanical Interpretation of Algorithmic Information Theory III by :

Download or read book A Statistical Mechanical Interpretation of Algorithmic Information Theory III written by and published by . This book was released on 2009 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Unconventional Computation and Natural Computation

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Publisher : Springer
ISBN 13 : 3319081233
Total Pages : 418 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Unconventional Computation and Natural Computation by : Oscar H. Ibarra

Download or read book Unconventional Computation and Natural Computation written by Oscar H. Ibarra and published by Springer. This book was released on 2014-07-08 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Unconventional Computation and Natural Computation, UCNC 2014, held in London, ON, Canada, in July 2014. The 31 revised full papers were carefully reviewed and selected from 79 submissions. The papers cover a wide range of topics including among others molecular, quantum, optical and chaos computing as well as neural computation, evolutionary computation, swarm intelligence and computational neuroscience.

A Computable Universe

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Publisher : World Scientific
ISBN 13 : 9814374296
Total Pages : 855 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis A Computable Universe by : Hector Zenil

Download or read book A Computable Universe written by Hector Zenil and published by World Scientific. This book was released on 2013 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? and How does nature compute?

Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions

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Publisher : Springer Science & Business Media
ISBN 13 : 3034803567
Total Pages : 246 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions by : Lev A. Sakhnovich

Download or read book Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions written by Lev A. Sakhnovich and published by Springer Science & Business Media. This book was released on 2012-07-18 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions.

Aspects of Kolmogorov Complexity the Physics of Information

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Publisher : CRC Press
ISBN 13 : 1000797155
Total Pages : 98 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Aspects of Kolmogorov Complexity the Physics of Information by : Bradley S. Tice

Download or read book Aspects of Kolmogorov Complexity the Physics of Information written by Bradley S. Tice and published by CRC Press. This book was released on 2022-09-01 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Logical Foundations of Computer Science

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Publisher : Springer
ISBN 13 : 3540926879
Total Pages : 478 pages
Book Rating : 4.5/5 (49 download)

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Book Synopsis Logical Foundations of Computer Science by : Sergei Artemov

Download or read book Logical Foundations of Computer Science written by Sergei Artemov and published by Springer. This book was released on 2009-02-11 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2009, held in Deerfield Beach, Florida, USA in January 2008. The volume presents 31 revised refereed papers carefully selected by the program committee. All current aspects of logic in computer science are addressed, including constructive mathematics and type theory, logical foundations of programming, logical aspects of computational complexity, logic programming and constraints, automated deduction and interactive theorem proving, logical methods in protocol and program verification and in program specification and extraction, domain theory logics, logical foundations of database theory, equational logic and term rewriting, lambda and combinatory calculi, categorical logic and topological semantics, linear logic, epistemic and temporal logics, intelligent and multiple agent system logics, logics of proof and justification, nonmonotonic reasoning, logic in game theory and social software, logic of hybrid systems, distributed system logics, system design logics, as well as other logics in computer science.

Undecidability, Uncomputability, and Unpredictability

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Publisher : Springer Nature
ISBN 13 : 3030703541
Total Pages : 181 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Undecidability, Uncomputability, and Unpredictability by : Anthony Aguirre

Download or read book Undecidability, Uncomputability, and Unpredictability written by Anthony Aguirre and published by Springer Nature. This book was released on 2021-08-20 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.​

Mathematical Foundations of Computer Science 2009

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Publisher : Springer
ISBN 13 : 3642038166
Total Pages : 773 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Mathematical Foundations of Computer Science 2009 by : Rastislav Královic

Download or read book Mathematical Foundations of Computer Science 2009 written by Rastislav Královic and published by Springer. This book was released on 2009-08-19 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science, MFCS 2009, held in Novy Smokovec, High Tatras, Slovakia, in August 2009. The 56 revised full papers presented together with 7 invited lectures were carefully reviewed and selected from 148 submissions. All current aspects in theoretical computer science and its mathematical foundations are addressed, including algorithmic game theory, algorithmic tearning theory, algorithms and data structures, automata, grammars and formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, cryptography and security, databases and knowledge-based systems, formal specifications and program development, foundations of computing, logic in computer science, mobile computing, models of computation, networks, parallel and distributed computing, quantum computing, semantics and verification of programs, theoretical issues in artificial intelligence.

Deep Learning

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Publisher : Elsevier
ISBN 13 : 0443184313
Total Pages : 270 pages
Book Rating : 4.4/5 (431 download)

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Book Synopsis Deep Learning by :

Download or read book Deep Learning written by and published by Elsevier. This book was released on 2023-02-28 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep Learning, Volume 48 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Generative Adversarial Networks for Biometric Synthesis, Data Science and Pattern Recognition, Facial Data Analysis, Deep Learning in Electronics, Pattern Recognition, Computer Vision and Image Processing, Mechanical Systems, Crop Technology and Weather, Manipulating Faces for Identity Theft via Morphing and Deepfake, Biomedical Engineering, and more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Includes the latest information on Deep Learning

Computation, Physics and Beyond

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Publisher : Springer Science & Business Media
ISBN 13 : 3642276539
Total Pages : 436 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Computation, Physics and Beyond by : Michael J. Dinneen

Download or read book Computation, Physics and Beyond written by Michael J. Dinneen and published by Springer Science & Business Media. This book was released on 2012-01-17 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Unconventional Computation

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Publisher : Springer
ISBN 13 : 3642135234
Total Pages : 207 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Unconventional Computation by : Christian S. Calude

Download or read book Unconventional Computation written by Christian S. Calude and published by Springer. This book was released on 2010-06-26 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 9th International Conference on Unconventional Computation, UC 2010, was organized under the auspices of EATCS and Academia Europaea, by the University of Tokyo (Tokyo, Japan), and the Center for Discrete Mathematics and Theoretical Computer Science (Auckland, New Zealand). It was held in Tokyoduring June 21–25,2010(seehttp://arn.local.frs.riken.jp/UC10/). The venue was the Sanjo (Hilltop) Conference Hall at Hongo Campus of the University of Tokyo. Hongo Campus was formerly the residence of the Maeda family, one of the richest feudal lords in the Edo period of Japan. The Japanese garden in the residence is partially preserved, including the pond and the hill on which the conference hall is located. Within walking distance from Hongo Campus are Ueno park with many museums, the Akihabara area, which is now the center of Japanesepop culture, and the Korakuenamusement park/baseball stadium. The International Conference on Unconventional Computation (UC) series (seehttp://www.cs.auckland.ac.nz/CDMTCS/conferences/uc/)isdevotedto all aspects of unconventional computation — theory as well as experiments and applications. Typical, but not exclusive, topics are: natural computing including quantum, cellular, molecular, membrane, neural, and evolutionary computing, as well as chaos and dynamical system-based computing, and various proposals for computational mechanisms that go beyond the Turing model.

Statistical Physics and Information Theory

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Publisher : Now Publishers Inc
ISBN 13 : 1601984065
Total Pages : 224 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Statistical Physics and Information Theory by : Neri Merhav

Download or read book Statistical Physics and Information Theory written by Neri Merhav and published by Now Publishers Inc. This book was released on 2010 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on lecture notes of a graduate course, which focuses on the relations between information theory and statistical physics. The course was delivered at the Technion during the Spring of 2010 for the first time, and its target audience consists of EE graduate students in the area of communications and information theory, as well as graduate students in Physics who have basic background in information theory. Strong emphasis is given to the analogy and parallelism between information theory and statistical physics, as well as to the insights, the analysis tools and techniques that can be borrowed from statistical physics and 'imported' to certain problem areas in information theory. This is a research trend that has been very active in the last few decades, and the hope is that by exposing the students to the meeting points between these two disciplines, their background and perspective may be expanded and enhanced. This monograph is substantially revised and expanded relative to an earlier version posted in arXiv (1006.1565v1 cs.iT]).

Artificial Intelligence Tools

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Publisher : CRC Press
ISBN 13 : 1498760198
Total Pages : 475 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Artificial Intelligence Tools by : Diego Galar Pascual

Download or read book Artificial Intelligence Tools written by Diego Galar Pascual and published by CRC Press. This book was released on 2015-04-22 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artificial Intelligence Tools: Decision Support Systems in Condition Monitoring and Diagnosis discusses various white- and black-box approaches to fault diagnosis in condition monitoring (CM). This indispensable resource:Addresses nearest-neighbor-based, clustering-based, statistical, and information theory-based techniquesConsiders the merits of e

From Statistical Physics to Statistical Inference and Back

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Publisher : Springer
ISBN 13 :
Total Pages : 372 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis From Statistical Physics to Statistical Inference and Back by : P. Grassberger

Download or read book From Statistical Physics to Statistical Inference and Back written by P. Grassberger and published by Springer. This book was released on 1994-03-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Cargèse (Corsica), France, August 31--September 12, 1992

Elements of Information Theory

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Publisher : John Wiley & Sons
ISBN 13 : 1118585771
Total Pages : 788 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Elements of Information Theory by : Thomas M. Cover

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.

Reachability Problems

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Publisher : Springer Science & Business Media
ISBN 13 : 3642044190
Total Pages : 243 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Reachability Problems by : Igor Potapov

Download or read book Reachability Problems written by Igor Potapov and published by Springer Science & Business Media. This book was released on 2009-09-07 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the research papers presented at the 3rd International Workshop, RP 2009 held in Palaiseau, France, September 23-25, 2009. The 20 full papers of this workshop reflect reachability problems that appear in algebraic structures, computational models, hybrid systems and verification. Reachability is a fundamental problem in the context of many models and abstractions which are describing various computational processes. Topics of interest include reachability problems in infinite state systems, rewriting systems, dynamical and hybrid systems, reachability problems in logic and verification, reachability analysis in different computational models, counter, timed, cellular, communicating automata, Petri-Nets, computational aspects of algebraic structures and predictability in iterative maps and new computational paradigms.