Solving Large-Scale Computational Problems Using Insights from Statistical Physics PDF Download
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Languages : en
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Book Description
Many challenging problems in computer science and related fields can be formulated as constraint satisfaction problems. Such problems consist of a set of discrete variables and a set of constraints between those variables, and represent a general class of so-called NP-complete problems. The goal is to find a value assignment to the variables that satisfies all constraints, generally requiring a search through and exponentially large space of variable-value assignments. Models for disordered systems, as studied in statistical physics, can provide important new insights into the nature of constraint satisfaction problems. Recently, work in this area has resulted in the discovery of a new method for solving such problems, called the survey propagation (SP) method. With SP, we can solve problems with millions of variables and constraints, an improvement of two orders of magnitude over previous methods.
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Publisher:
ISBN:
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Languages : en
Pages :
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Book Description
Many challenging problems in computer science and related fields can be formulated as constraint satisfaction problems. Such problems consist of a set of discrete variables and a set of constraints between those variables, and represent a general class of so-called NP-complete problems. The goal is to find a value assignment to the variables that satisfies all constraints, generally requiring a search through and exponentially large space of variable-value assignments. Models for disordered systems, as studied in statistical physics, can provide important new insights into the nature of constraint satisfaction problems. Recently, work in this area has resulted in the discovery of a new method for solving such problems, called the survey propagation (SP) method. With SP, we can solve problems with millions of variables and constraints, an improvement of two orders of magnitude over previous methods.
Author: K.-H. Hoffmann
Publisher: Springer Science & Business Media
ISBN: 3662048043
Category : Science
Languages : en
Pages : 312
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Book Description
In recent years statistical physics has made significant progress as a result of advances in numerical techniques. While good textbooks exist on the general aspects of statistical physics, the numerical methods and the new developments based on large-scale computing are not usually adequately presented. In this book 16 experts describe the application of methods of statistical physics to various areas in physics such as disordered materials, quasicrystals, semiconductors, and also to other areas beyond physics, such as financial markets, game theory, evolution, and traffic planning, in which statistical physics has recently become significant. In this way the universality of the underlying concepts and methods such as fractals, random matrix theory, time series, neural networks, evolutionary algorithms, becomes clear. The topics are covered by introductory, tutorial presentations.
Author: K. -H Hoffmann
Publisher:
ISBN: 9783662048054
Category :
Languages : en
Pages : 320
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Book Description
Author: Gandhimohan M Viswanathan
Publisher: World Scientific
ISBN: 9814590150
Category : Science
Languages : en
Pages : 346
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Book Description
Statistical Physics (SP) has followed an unusual evolutionary path in science. Originally aiming to provide a fundamental basis for another important branch of Physics, namely Thermodynamics, SP gradually became an independent field of research in its own right. But despite more than a century of steady progress, there are still plenty of challenges and open questions in the SP realm.In fact, the area is still rapidly evolving, in contrast to other branches of science, which already have well defined scopes and borderlines of applicability. This difference is due to the steadily expanding number of applications, as well as ongoing improvements and revisions of concepts and methods in SP. Such particular aspects of SP lend further significance and timeliness to this book about perspectives and trends within the field.Here, the aim is to present the state-of-the-art vision of expert researchers who study SP and Complex Systems. Although a comprehensive treatment is well beyond what can be treated in a single volume, the book provides a snapshot of the field today, as well as a glimpse of where the field may be heading during the next decade.The book is aimed at graduate and advanced undergraduate physics students, as well as researchers who work with SP, Complex Systems, Computational Physics, Biological Physics and related topics. It addresses questions such as: What insights can be gained from recent advances in the study of traditional problems in SP? How can SP help us understand problems that arise in the biological sciences and in the study of complex systems? How can new problems be formulated using the ‘language’ of SP? In this way, it attempts to document partial progress in answering these and related questions.The book also commemorates the occasion of the 70th anniversary in 2011 of two important physicists and friends who dedicated their lives to the understanding of nature in general and to the development of Statistical Physics and the science of Complexity in particular: Liacir Lucena and H Eugene Stanley.
Author: National Research Council
Publisher: National Academies Press
ISBN: 0309287812
Category : Mathematics
Languages : en
Pages : 191
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Book Description
Data mining of massive data sets is transforming the way we think about crisis response, marketing, entertainment, cybersecurity and national intelligence. Collections of documents, images, videos, and networks are being thought of not merely as bit strings to be stored, indexed, and retrieved, but as potential sources of discovery and knowledge, requiring sophisticated analysis techniques that go far beyond classical indexing and keyword counting, aiming to find relational and semantic interpretations of the phenomena underlying the data. Frontiers in Massive Data Analysis examines the frontier of analyzing massive amounts of data, whether in a static database or streaming through a system. Data at that scale-terabytes and petabytes-is increasingly common in science (e.g., particle physics, remote sensing, genomics), Internet commerce, business analytics, national security, communications, and elsewhere. The tools that work to infer knowledge from data at smaller scales do not necessarily work, or work well, at such massive scale. New tools, skills, and approaches are necessary, and this report identifies many of them, plus promising research directions to explore. Frontiers in Massive Data Analysis discusses pitfalls in trying to infer knowledge from massive data, and it characterizes seven major classes of computation that are common in the analysis of massive data. Overall, this report illustrates the cross-disciplinary knowledge-from computer science, statistics, machine learning, and application disciplines-that must be brought to bear to make useful inferences from massive data.
Author: Werner Krauth
Publisher: OUP Oxford
ISBN: 9780198515357
Category : Computers
Languages : en
Pages : 356
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Book Description
This book discusses the computational approach in modern statistical physics, adopting simple language and an attractive format of many illustrations, tables and printed algorithms. The discussion of key subjects in classical and quantum statistical physics will appeal to students, teachers and researchers in physics and related sciences. The focus is on orientation with implementation details kept to a minimum. - ;This book discusses the computational approach in modern statistical physics in a clear and accessible way and demonstrates its close relation to other approaches in theoretical physics. Individual chapters focus on subjects as diverse as the hard sphere liquid, classical spin models, single quantum particles and Bose-Einstein condensation. Contained within the chapters are in-depth discussions of algorithms, ranging from basic enumeration methods to modern Monte Carlo techniques. The emphasis is on orientation, with discussion of implementation details kept to a minimum. Illustrations, tables and concise printed algorithms convey key information, making the material very accessible. The book is completely self-contained and graphs and tables can readily be reproduced, requiring minimal computer code. Most sections begin at an elementary level and lead on to the rich and difficult problems of contemporary computational and statistical physics. The book will be of interest to a wide range of students, teachers and researchers in physics and the neighbouring sciences. An accompanying CD allows incorporation of the book's content (illustrations, tables, schematic programs) into the reader's own presentations. - ;'This book is the best one I have reviewed all year.' Alan Hinchliffe, Physical Sciences Educational Reviews -
Author: Lucas Böttcher
Publisher: Cambridge University Press
ISBN: 1108896650
Category : Science
Languages : en
Pages : 274
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Book Description
Providing a detailed and pedagogical account of the rapidly-growing field of computational statistical physics, this book covers both the theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational applications such as percolation, random walks, magnetic systems, machine learning dynamics, and spreading processes on complex networks. A detailed discussion of molecular dynamics simulations is also included, a topic of great importance in biophysics and physical chemistry. The accessible and self-contained approach adopted by the authors makes this book suitable for teaching courses at graduate level, and numerous worked examples and end of chapter problems allow students to test their progress and understanding.
Author: Luc T. Wille
Publisher: Springer Science & Business Media
ISBN: 3662089688
Category : Science
Languages : en
Pages : 369
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Book Description
This book provides a unique insight into the latest breakthroughs in a consistent manner, at a level accessible to undergraduates, yet with enough attention to the theory and computation to satisfy the professional researcher Statistical physics addresses the study and understanding of systems with many degrees of freedom. As such it has a rich and varied history, with applications to thermodynamics, magnetic phase transitions, and order/disorder transformations, to name just a few. However, the tools of statistical physics can be profitably used to investigate any system with a large number of components. Thus, recent years have seen these methods applied in many unexpected directions, three of which are the main focus of this volume. These applications have been remarkably successful and have enriched the financial, biological, and engineering literature. Although reported in the physics literature, the results tend to be scattered and the underlying unity of the field overlooked.
Author: George H. Weiss
Publisher: SIAM
ISBN: 1611971551
Category : Science
Languages : en
Pages : 266
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Book Description
This collection of independent articles describes some mathematical problems recently developed in statistical physics and theoretical chemistry. The book introduces and reviews current research on such topics as nonlinear systems and colored noise, stochastic resonance, percolation, the trapping problem in the theory of random walks, and diffusive models for chemical kinetics. Some of these topics have never before been presented in expository book form. Applied mathematicians will be introduced to some contemporary problems in statistical physics. In addition, a number of unsolved problems currently attracting intensive research efforts are described, and some of the techniques used in this research are outlined, along with principal results and outstanding questions. A wide spectrum of mathematical techniques is covered, but the main emphasis is on introducing the mathematician to different research areas with open and interesting problems. This is an ideal starting point for the mathematician with an elementary acquaintance with the methodology of statistical physics. The material is meant to be introductory and terms are carefully defined. Many topics that require further study are introduced, providing new research ideas for the applied mathematician or thesis problems for the graduate student.
Author: Andrea Gabrielli
Publisher: Springer Science & Business Media
ISBN: 3540269991
Category : Science
Languages : en
Pages : 420
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Book Description
This book has its roots in a series of collaborations in the last decade at the interface between statistical physics and cosmology. The speci?c problem which initiated this research was the study of the clustering properties of galaxies as revealed by large redshift surveys, a context in which concepts of modern statistical physics (e. g. scale-invariance, fractality. . ) ?nd ready application. In recent years we have considerably broadened the range of problems in cosmology which we have addressed, treating in particular more theoretical issues about the statistical properties of standard cosmological models. What is common to all this research, however, is that it is informed by a perspective and methodology which is that of statistical physics. We can say that, beyond its speci?c scienti?c content, this book has an underlying thesis: such interdisciplinary research is an exciting playground for statistical physics, and one which can bring new and useful insights into cosmology. The book does not represent a ?nal point, but in our view, a marker in the development of this kind of research, which we believe can go very much further in the future. Indeed as we complete this book, new developments - which unfortunately we have not been able to include here - have been made on some of the themes described here. Our focus in this book is on the problem of structure in cosmology.
