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Author :
Publisher :
ISBN 13 :
Total Pages : 652 pages
Book Rating : 4.:/5 (133 download)
Download or read book Numbers, Information, and Complexity written by and published by . This book was released on 2000 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Burgin Mark
Publisher : World Scientific
ISBN 13 : 9813109041
Total Pages : 412 pages
Book Rating : 4.8/5 (131 download)
Download or read book Information And Complexity written by Burgin Mark and published by World Scientific. This book was released on 2016-11-28 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of papers of experts in the fields of information and complexity. Information is a basic structure of the world, while complexity is a fundamental property of systems and processes. There are intrinsic relations between information and complexity. The research in information theory, the theory of complexity and their interrelations is very active. The book will expand knowledge on information, complexity and their relations representing the most recent and advanced studies and achievements in this area. The goal of the book is to present the topic from different perspectives — mathematical, informational, philosophical, methodological, etc.
Author : J. F. Traub
Publisher : Cambridge University Press
ISBN 13 : 9780521485067
Total Pages : 152 pages
Book Rating : 4.4/5 (85 download)
Download or read book Complexity and Information written by J. F. Traub and published by Cambridge University Press. This book was released on 1998-12-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.
Author : Jorma Rissanen
Publisher : Springer Science & Business Media
ISBN 13 : 0387688129
Total Pages : 145 pages
Book Rating : 4.3/5 (876 download)
Download or read book Information and Complexity in Statistical Modeling written by Jorma Rissanen and published by Springer Science & Business Media. This book was released on 2007-12-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.
Author : Lenore Blum
Publisher : Springer Science & Business Media
ISBN 13 : 1461207010
Total Pages : 456 pages
Book Rating : 4.4/5 (612 download)
Download or read book Complexity and Real Computation written by Lenore Blum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.
Author : Wolfgang Arendt
Publisher : John Wiley & Sons
ISBN 13 : 3527628037
Total Pages : 502 pages
Book Rating : 4.5/5 (276 download)
Download or read book Mathematical Analysis of Evolution, Information, and Complexity written by Wolfgang Arendt and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.
Author : Thomas Moscibroda
Publisher : Springer
ISBN 13 : 3319035789
Total Pages : 362 pages
Book Rating : 4.3/5 (19 download)
Download or read book Structural Information and Communication Complexity written by Thomas Moscibroda and published by Springer. This book was released on 2013-11-09 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 20th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2013, held in Ischia, Italy, in July 2013. The 28 revised full papers presented were carefully reviewed and selected from 67 submissions. SIROCCO is devoted to the study of communication and knowledge in distributed systems. Special emphasis is given to innovative approaches and fundamental understanding, in addition to efforts to optimize current designs. The typical areas include distributed computing, communication networks, game theory, parallel computing, social networks, mobile computing (including autonomous robots), peer to peer systems, communication complexity, fault tolerant graph theories and randomized/probabilistic issues in networks.
Author : Mitra Basu
Publisher : Springer Science & Business Media
ISBN 13 : 1846281725
Total Pages : 309 pages
Book Rating : 4.8/5 (462 download)
Download or read book Data Complexity in Pattern Recognition written by Mitra Basu and published by Springer Science & Business Media. This book was released on 2006-12-22 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic pattern recognition has uses in science and engineering, social sciences and finance. This book examines data complexity and its role in shaping theory and techniques across many disciplines, probing strengths and deficiencies of current classification techniques, and the algorithms that drive them. The book offers guidance on choosing pattern recognition classification techniques, and helps the reader set expectations for classification performance.
Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.5/5 (214 download)
Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author : Fred J. Hickernell
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110635461
Total Pages : 158 pages
Book Rating : 4.1/5 (16 download)
Download or read book Multivariate Algorithms and Information-Based Complexity written by Fred J. Hickernell and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.
Author : Ming Li
Publisher : Springer Science & Business Media
ISBN 13 : 1475726066
Total Pages : 655 pages
Book Rating : 4.4/5 (757 download)
Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Author : Bradley S. Tice
Publisher : River Publishers
ISBN 13 : 8792329268
Total Pages : 175 pages
Book Rating : 4.7/5 (923 download)
Download or read book Aspects of Kolmogorov Complexity the Physics of Information written by Bradley S. Tice and published by River Publishers. This book was released on 2009-08 with total page 175 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. It offers 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 what is found in current literature. A historical overview of the field of Kolmogorov Complexity and Algorithmic Information Theory, a subfield of Information Theory, is provided 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 read at conferences on the subject and current references. Technical 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
Author : Tomasz Jurdziński
Publisher : Springer Nature
ISBN 13 : 3030795276
Total Pages : 389 pages
Book Rating : 4.0/5 (37 download)
Download or read book Structural Information and Communication Complexity written by Tomasz Jurdziński and published by Springer Nature. This book was released on 2021-06-19 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed conference proceedings of the 28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021, held in Wrocław, Poland, in June 2021. Due to COVID-19, the conference will be held online. The 20 full papers presented in this book were carefully reviewed and selected from 48 submissions. The papers are solicited from all areas of study of local structural knowledge and global communication and computational complexities. Among the typical areas are distributed computing, communication networks, game theory, parallel computing, social networks, mobile computing
Author : Cristian Calude
Publisher : World Scientific
ISBN 13 : 9812770828
Total Pages : 466 pages
Book Rating : 4.8/5 (127 download)
Download or read book Randomness and Complexity written by Cristian Calude and published by World Scientific. This book was released on 2007 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.
Author : Stefan C. Müller
Publisher : Springer
ISBN 13 : 3319643347
Total Pages : 421 pages
Book Rating : 4.3/5 (196 download)
Download or read book Complexity and Synergetics written by Stefan C. Müller and published by Springer. This book was released on 2017-11-16 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: All of us are confronted with complex phenomena occurring in daily life and in the living and inanimate nature surrounding us. Our scientific curiosity strives to unravel the mechanisms at work to create such complexity. Among various approaches to solve this problem, the field of synergetics, developed by Hermann Haken, has proven very successful as a general and interdisciplinary concept for describing and explaining complex phenomena that appear in systems under non-equilibrium conditions. These comprise dynamical states in evolving systems, spatial structure-forming processes, synchronization of states and regulatory mechanisms, and many other examples. The encompassing concepts have been applied to many disciplines, like physics, chemistry, biology, and beyond those also from synergetics to information theory, brain science, economics, and others. Starting from basic methods of complexity research and synergetics, this volume contains thirty contributions on complex systems that exhibit spontaneous pattern formation far from thermal equilibrium. Written by international experts and young researchers assembled under one roof, this volume reflects state of the art research from a variety of scientific fields and disciplines where complexity theory and synergetics are important or even indispensable tools today and in the future.
Author : Ivo D. Dinov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110697823
Total Pages : 489 pages
Book Rating : 4.1/5 (16 download)
Download or read book Data Science written by Ivo D. Dinov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-12-06 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated. Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive. The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the "problems of time". The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework. The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public.
Author : Cristian S. Calude
Publisher : World Scientific
ISBN 13 : 9812770836
Total Pages : 466 pages
Book Rating : 4.8/5 (127 download)
Download or read book Randomness and Complexity written by Cristian S. Calude and published by World Scientific. This book was released on 2007 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin''s 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays. Sample Chapter(s). Chapter 1: On Random and Hard-to-Describe Numbers (902 KB). Contents: On Random and Hard-to-Describe Numbers (C H Bennett); The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law (P C W Davies); What is a Computation? (M Davis); A Berry-Type Paradox (G Lolli); The Secret Number. An Exposition of Chaitin''s Theory (G Rozenberg & A Salomaa); Omega and the Time Evolution of the n-Body Problem (K Svozil); God''s Number: Where Can We Find the Secret of the Universe? In a Single Number! (M Chown); Omega Numbers (J-P Delahaye); Some Modern Perspectives on the Quest for Ultimate Knowledge (S Wolfram); An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding (D Zeilberger); and other papers. Readership: Computer scientists and philosophers, both in academia and industry.
