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＜電子ブック＞
Theory of Information and its Value / by Ruslan L. Stratonovich ; edited by Roman V. Belavkin, Panos M. Pardalos, Jose C. Principe

版	1st ed. 2020.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2020
本文言語	英語
大きさ	XXII, 419 p. 33 illus., 4 illus. in color : online resource
著者標目	*Stratonovich, Ruslan L author Belavkin, Roman V editor Pardalos, Panos M editor Principe, Jose C editor SpringerLink (Online service)
件　名	LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Data structures (Computer science) LCSH:Information theory LCSH:Mathematical physics LCSH:Spintronics LCSH:Mathematical optimization FREE:Mathematical Applications in Computer Science FREE:Data Structures and Information Theory FREE:Theoretical, Mathematical and Computational Physics FREE:Spintronics FREE:Optimization
一般注記	Foreword -- Preface -- 1 Definition of information and entropy in the absence of noise- 2 Encoding of discrete information in the absence of noise and penalties -- 3 Encoding in the presence of penalties. The first variational problem- 4 The first asymptotic theorem and relative results -- 5 Computation of entropy for special cases. Entropy of stochastic processes -- 6 Information in the presence of noise. The Shannon's amount of information -- 7 Message transmission in the presence of noise. The second asymptotic theorem and its various formulations -- 8 Channel capacity. Important particular cases of channels -- 9 Definition of the value of information -- 10 The value of Shannon information for the most important Bayesian systems -- 11 Asymptotical results related to the value of information. The Third asymptotic theorem -- 12 Information theory and the second law of thermodynamics -- Appendix Some matrix (operator) identities -- Index. This English version of Ruslan L. Stratonovich’s Theory of Information (1975) builds on theory and provides methods, techniques, and concepts toward utilizing critical applications. Unifying theories of information, optimization, and statistical physics, the value of information theory has gained recognition in data science, machine learning, and artificial intelligence. With the emergence of a data-driven economy, progress in machine learning, artificial intelligence algorithms, and increased computational resources, the need for comprehending information is essential. This book is even more relevant today than when it was first published in 1975. It extends the classic work of R.L. Stratonovich, one of the original developers of the symmetrized version of stochastic calculus and filtering theory, to name just two topics. Each chapter begins with basic, fundamental ideas, supported by clear examples; the material then advances to great detail and depth. The reader is not required to be familiar with the more difficult and specific material. Rather, the treasure trove of examples of stochastic processes and problems makes this book accessible to a wide readership of researchers, postgraduates, and undergraduate students in mathematics, engineering, physics and computer science who are specializing in information theory, data analysis, or machine learning HTTP:URL=https://doi.org/10.1007/978-3-030-22833-0

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