Exploring RANDOMNESS, Gregory J. Chaitin

Автор: Cristian S. Calude
Название: Information and Randomness
ISBN: 3642077935 ISBN-13(EAN): 9783642077937
Издательство: Springer
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Описание: The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob- lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom- pleteness". The really comprehensive new bibliography makes the book very valuable for a researcher. The new results about the characterization of computably enumerable random reals, as well as the fascinating Omega Numbers, should contribute much to the value of the book as a textbook. The author has been directly involved in these results that have appeared in the prestigious journals Nature, New Scientist and Pour la Science.

Автор: V. I. Ivanenko
Название: Decision Systems and Nonstochastic Randomness
ISBN: 144195547X ISBN-13(EAN): 9781441955470
Издательство: Springer
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Цена: 18366 р.
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Описание: This book presents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models.

Автор: Itai Benjamini
Название: Coarse Geometry and Randomness
ISBN: 3319025759 ISBN-13(EAN): 9783319025759
Издательство: Springer
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Цена: 5356 р.
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Описание:

Isoperimetry and expansions in graphs.- Several metric notions.- The hyperbolic plane and hyperbolic graphs.- More on the structure of vertex transitive graphs.- Percolation on graphs.- Local limits of graphs.- Random planar geometry.- Growth and isoperimetric profile of planar graphs.- Critical percolation on non-amenable groups.- Uniqueness of the infinite percolation cluster.- Percolation perturbations.- Percolation on expanders.- Harmonic functions on graphs.- Nonamenable Liouville graphs.

Автор: Dieter van Melkebeek
Название: Randomness and Completeness in Computational Complexity
ISBN: 3540414924 ISBN-13(EAN): 9783540414926
Издательство: Springer
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Цена: 10713 р.
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Описание: This text, based on the author`s competition-winning PhD thesis, studies central issues in computational complexity: the relative power of time, space, and randomness in computing and verification. He presents approaches based on such concepts as density, redundancy, and frequency of occurrence.

Автор: Alejandro Maass; Servet Mart?nez; Jaime San Mart?n
Название: Dynamics and Randomness
ISBN: 1402005911 ISBN-13(EAN): 9781402005916
Издательство: Springer
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Цена: 21428 р.
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Описание: Contains the lectures given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile, on December 2000. This volume is useful for those working in probability theory, stochastic processes, information theory, coding theory, statistical physics, and thermodynamics.

Автор: Rodney G. Downey; Denis R. Hirschfeldt
Название: Algorithmic Randomness and Complexity
ISBN: 1493938207 ISBN-13(EAN): 9781493938209
Издательство: Springer
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Цена: 15305 р.
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Описание: Exploring the theory of computability and complexity over the real numbers, this book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists working in diverse fields concerned with theoretical computer science.

Автор: V. I. Ivanenko
Название: Decision Systems and Nonstochastic Randomness
ISBN: 1489984968 ISBN-13(EAN): 9781489984968
Издательство: Springer
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Цена: 18366 р.
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Описание: This book presents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models.

Автор: Igor I. Gorban
Название: Randomness and Hyper-randomness
ISBN: 3319607790 ISBN-13(EAN): 9783319607795
Издательство: Springer
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Цена: 21428 р.
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Описание: The monograph compares two approaches that describe the statistical stability phenomenon - one proposed by the probability theory that ignores violations of statistical stability and another proposed by the theory of hyper-random phenomena that takes these violations into account.

Автор: Jaroslaw Strzalko; Juliusz Grabski; Przemyslaw Per
Название: Dynamics of Gambling: Origins of Randomness in Mechanical Systems
ISBN: 3642039596 ISBN-13(EAN): 9783642039591
Издательство: Springer
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Цена: 12244 р.
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Описание: Not only does this monograph provide a general analysis of random effects in mechanical (engineering) systems, but it addresses deep questions concerning the nature of randomness, and gives potentially useful tips for gamblers and the gaming industry.

Автор: Jaroslaw Strzalko; Juliusz Grabski; Przemyslaw Per
Название: Dynamics of Gambling: Origins of Randomness in Mechanical Systems
ISBN: 3642261949 ISBN-13(EAN): 9783642261947
Издательство: Springer
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Цена: 12873 р.
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Описание: Not only does this monograph provide a general analysis of random effects in mechanical (engineering) systems, but it addresses deep questions concerning the nature of randomness, and gives potentially useful tips for gamblers and the gaming industry.

Автор: Khrennikov Andrei
Название: Probability And Randomness: Quantum Versus Classical
ISBN: 1783267968 ISBN-13(EAN): 9781783267965
Издательство: World Scientific Publishing
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Цена: 16817 р.
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Описание:

Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Probability and Randomness: Quantum versus Classical rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level.