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Author : Ingo Althofer,Ning Cai,Gunter Dueck
Publisher : Unknown
Page : 676 pages
File Size : 53,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475760493
Author : J. F. Traub,Arthur G. Werschulz
Publisher : Cambridge University Press
Page : 152 pages
File Size : 43,6 Mb
Release : 1998-12-10
Category : Computers
ISBN : 0521485061
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 : Fred J. Hickernell,Peter Kritzer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 158 pages
File Size : 49,9 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783110635461
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 : Burgin Mark,Calude Cristian S
Publisher : World Scientific
Page : 412 pages
File Size : 43,5 Mb
Release : 2016-11-28
Category : Language Arts & Disciplines
ISBN : 9789813109049
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 : A. Blaquiere,S. Diner,G. Lochak
Publisher : Springer
Page : 356 pages
File Size : 43,9 Mb
Release : 2014-05-04
Category : Science
ISBN : 9783709129715
Author : Jorma Rissanen
Publisher : Springer Science & Business Media
Page : 145 pages
File Size : 54,9 Mb
Release : 2007-12-15
Category : Mathematics
ISBN : 9780387688121
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 : Magnús M. Halldórsson
Publisher : Springer
Page : 372 pages
File Size : 47,7 Mb
Release : 2014-07-16
Category : Computers
ISBN : 9783319096209
This book constitutes the refereed proceedings of the 21st International Colloquium on Structural Information and Communication Complexity, SIROCCO 2014, held in Takayama, Japan, in July 2014. The 24 full papers presented together with 5 invited talks were carefully reviewed and selected from 51 submissions. The focus of the colloquium is on following subjects Shared Memory and Multiparty Communication, Network Optimization, CONGEST Algorithms and Lower Bounds, Wireless networks, Aggregation and Creation Games in Networks, Patrolling and Barrier Coverage, Exploration, Rendevous and Mobile Agents.
Author : Lenore Blum,Felipe Cucker,Michael Shub,Steve Smale
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461207016
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 : IOS Press
Publisher : IOS Press
Page : 440 pages
File Size : 40,6 Mb
Release : 2008-04-28
Category : Political Science
ISBN : 9781607503217
The fundamental concept developed in this book is that in order to achieve security in a complex world, it is essential to ensure that we have sufficient variety available to cope with complexity and its potential dangers. The book develops many facets of this idea, covering all major contemporary world issues, including energy, food and environmental security, climate change, economic transitions, and the role of technology. Encompassing a uniquely diverse collection of viewpoints, this book achieves a highly original contribution to the debate about where our civilization is heading. Airy speculation is however eschewed: arguments are developed on the basis of solid evidence available to all. This book by no means attempts to have the last word: it invites response and debate. Above all, it contributes to deepening understanding of what it means to be human in the face of our ever-growing knowledge about the universe and its nature. And, the ideas developed lead to some surprisingly definite conclusions about the policies to be promulgated in the future.
Author : Ming Li,Paul Vitanyi
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 40,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475726060
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 : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 45,7 Mb
Release : 2009-04-20
Category : Computers
ISBN : 9780521424264
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author : E. Börger
Publisher : Elsevier
Page : 591 pages
File Size : 51,9 Mb
Release : 1989-07-01
Category : Mathematics
ISBN : 008088704X
The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems. The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory. It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions.
Author : D.G. Bonchev,D.H. Rouvray
Publisher : CRC Press
Page : 226 pages
File Size : 51,5 Mb
Release : 2003-01-23
Category : Science
ISBN : 041528791X
This volume covers the rapidly developing field of complexity studies with the underlying theme that complexity is to be found everywhere. The volume discusses many chemical applications and offers a comprehensive coverage of complexity and the ways in which it may be measured, complexity indices, complexity measures based on Shannon's information theory, and thermodynamic complexity. Complexity: Introduction and Fundamentals provides a valuable source of reference for graduates and researchers for mathematical chemistry.
Author : Marcello Pelillo,Irene Poli,Andrea Roli,Roberto Serra,Debora Slanzi,Marco Villani
Publisher : Springer
Page : 323 pages
File Size : 51,9 Mb
Release : 2018-04-02
Category : Computers
ISBN : 9783319786582
This book constitutes the revised selected papers of the 12th Italian Workshop on Advances in Artificial Life, Evolutionary Computation, WIVACE 2017, held in Venice, Italy, in September 2017.The 23 full papers presented were thoroughly reviewed and selected from 33 submissions. They cover the following topics: physical-chemical phenomena; biological systems; economy and society; complexity; optimization.
Author : Cristian S. Calude,Gregory J. Chaitin
Publisher : World Scientific
Page : 466 pages
File Size : 55,7 Mb
Release : 2007
Category : Computers
ISBN : 9789812770837
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.