Gibbs Measures In Biology And Physics The Potts Model

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Gibbs Measures In Biology And Physics: The Potts Model

Author : Utkir A Rozikov
Publisher : World Scientific
ISBN 13 : 9811251258
Total Pages : 367 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Gibbs Measures In Biology And Physics: The Potts Model by : Utkir A Rozikov

Download or read book Gibbs Measures In Biology And Physics: The Potts Model written by Utkir A Rozikov and published by World Scientific. This book was released on 2022-07-28 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.

Gibbs Measures on Cayley Trees

Author : Utkir A Rozikov
Publisher : World Scientific
ISBN 13 : 9814513393
Total Pages : 404 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Gibbs Measures on Cayley Trees by : Utkir A Rozikov

Download or read book Gibbs Measures on Cayley Trees written by Utkir A Rozikov and published by World Scientific. This book was released on 2013-07-11 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present systematically all known mathematical results on Gibbs measures on Cayley trees (Bethe lattices). The Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Moreover, the Gibbs measure is the unique measure that maximizes the entropy for a given expected energy. The method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees, and nonlinear analysis. This book discusses all the mentioned methods, which were developed recently. Contents:Group Representation of the Cayley TreeIsing Model on the Cayley TreeIsing Type Models with Competing InteractionsInformation Flow on TreesThe Potts ModelThe Solid-on-Solid ModelModels with Hard ConstraintsPotts Model with Countable Set of Spin ValuesModels with Uncountable Set of Spin ValuesContour Arguments on Cayley TreesOther Models Readership: Researchers in mathematical physics, statistical physics, probability and measure theory. Keywords:Cayley Tree;Configuration;Hamiltonian;Temperature;Gibbs MeasureKey Features:The book is for graduate, post-graduate students and researchers. This is the first book concerning Gibbs measures on Cayley treesIt can be used to teach special courses like “Gibbs measures on countable graphs”, “Models of statistical physics”, “Phase transitions and thermodynamics” and many related coursesReviews: “The extensive commentaries and references which follow are as valuable as the mathematical text. At the end of each chapter, the author gives extensive commentaries and a list of references to the literature, including very recent ones. The reader may find useful and insightful open problems concluding the end of each chapter. The book is written from the mathematician's point of view and its addressees are professionals in statistical mechanics and mathematical physics.” Zentralblatt MATH

Gibbs Measures on Cayley Trees

Author : Utkir A. Rozikov
Publisher : World Scientific
ISBN 13 : 9814513385
Total Pages : 404 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Gibbs Measures on Cayley Trees by : Utkir A. Rozikov

Download or read book Gibbs Measures on Cayley Trees written by Utkir A. Rozikov and published by World Scientific. This book was released on 2013 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Moreover, the Gibbs measure is the unique measure that maximizes the entropy for a given expected energy. The method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees, and nonlinear analysis. This book discusses all the mentioned methods, which were developed recently.

Graphs, Morphisms, and Statistical Physics

Author : Jaroslav Nešetřil
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871058
Total Pages : 220 pages
Book Rating : 4.8/5 (71 download)

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Book Synopsis Graphs, Morphisms, and Statistical Physics by : Jaroslav Nešetřil

Download or read book Graphs, Morphisms, and Statistical Physics written by Jaroslav Nešetřil and published by American Mathematical Soc.. This book was released on with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intersection of combinatorics and statistical physics has experienced great activity in recent years. This flurry of activity has been fertilized by an exchange not only of techniques, but also of objectives. Computer scientists interested in approximation algorithms have helped statistical physicists and discrete mathematicians overcome language problems. They have found a wealth of common ground in probabilistic combinatorics. Close connections between percolation and random graphs, graph morphisms and hard-constraint models, and slow mixing and phase transition have led to new results and perspectives. These connections can help in understanding typical behavior of combinatorial phenomena such as graph coloring and homomorphisms. Inspired by issues and intriguing new questions surrounding the interplay of combinatorics and statistical physics, a DIMACS/DIMATIA workshop was held at Rutgers University. These proceedings are the outgrowth of that meeting. This volume is intended for graduate students and research mathematicians interested in probabilistic graph theory and its applications.

Phase Transitions: Mathematics, Physics, Biology... - Proceedings Of The Conference

Author : Roman Kotecky
Publisher : World Scientific
ISBN 13 : 981455264X
Total Pages : 274 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Phase Transitions: Mathematics, Physics, Biology... - Proceedings Of The Conference by : Roman Kotecky

Download or read book Phase Transitions: Mathematics, Physics, Biology... - Proceedings Of The Conference written by Roman Kotecky and published by World Scientific. This book was released on 1993-11-19 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the theory of phase transitions and its interdisciplinary aspects. More specifically, the idea is to discuss the notion of the Gibbs state and its use (and limitations) in different applications.

Spatial and Temporal Mixing of Gibbs Measures

Author : Allan Murray Sly
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.:/5 (35 download)

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Book Synopsis Spatial and Temporal Mixing of Gibbs Measures by : Allan Murray Sly

Download or read book Spatial and Temporal Mixing of Gibbs Measures written by Allan Murray Sly and published by . This book was released on 2009 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Probability on Graphs

Author : Geoffrey Grimmett
Publisher : Cambridge University Press
ISBN 13 : 1108542999
Total Pages : 279 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Probability on Graphs by : Geoffrey Grimmett

Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

P-adic Analysis and Mathematical Physics

Author : Vasili? Sergeevich Vladimirov
Publisher : World Scientific
ISBN 13 : 9789810208806
Total Pages : 350 pages
Book Rating : 4.2/5 (88 download)

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Book Synopsis P-adic Analysis and Mathematical Physics by : Vasili? Sergeevich Vladimirov

Download or read book P-adic Analysis and Mathematical Physics written by Vasili? Sergeevich Vladimirov and published by World Scientific. This book was released on 1994 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.

Statistical Mechanics

Author : James Sethna
Publisher : OUP Oxford
ISBN 13 : 0191566217
Total Pages : 374 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Statistical Mechanics by : James Sethna

Download or read book Statistical Mechanics written by James Sethna and published by OUP Oxford. This book was released on 2006-04-07 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.

Algebraic Statistics for Computational Biology

Author : L. Pachter
Publisher : Cambridge University Press
ISBN 13 : 9780521857000
Total Pages : 440 pages
Book Rating : 4.8/5 (57 download)

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Book Synopsis Algebraic Statistics for Computational Biology by : L. Pachter

Download or read book Algebraic Statistics for Computational Biology written by L. Pachter and published by Cambridge University Press. This book was released on 2005-08-22 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.

Equilibrium Statistical Physics (2nd Edition)

Author : Michael Plischke
Publisher : World Scientific Publishing Company
ISBN 13 : 9813104716
Total Pages : 537 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Equilibrium Statistical Physics (2nd Edition) by : Michael Plischke

Download or read book Equilibrium Statistical Physics (2nd Edition) written by Michael Plischke and published by World Scientific Publishing Company. This book was released on 1994-12-14 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newer Edition Available: Equilibrium Statistical Physics (3rd Edition)This revised and expanded edition of one of the important textbook in statistical physics, is a graduate level text suitable for students in physics, chemistry, and materials science.After a short review of basic concepts, the authors begin the discussion on strongly interacting condensed matter systems with a thorough treatment of mean field and Landau theories of phase transitions. Many examples are worked out in considerable detail. Classical liquids are treated next. Along with traditional approaches to the subject such as the virial expansion and integral equations, newer theories such as perturbation theory and density functional theories are introduced.The modern theory of phase transitions occupies a central place in this book. The development is along historical lines, beginning with the Onsager solution of the two-dimensional Ising model, series expansions, scaling theory, finite-size scaling, and the universality hypothesis. A separate chapter is devoted to the renormalization group approach to critical phenomena. The development of the basic tools is completed in a new chapter on computer simulations in which both Monte Carlo and molecular dynamics techniques are introduced.The remainder of the book is concerned with a discussion of some of the more important modern problems in condensed matter theory. A chapter on quantum fluids deals with Bose condensation, superfluidity, and the BCS and Landau-Ginzburg theories of superconductivity. A new chapter on polymers and membranes contains a discussion of the Gaussian and Flory models of dilute polymer mixtures, the connection of polymer theory to critical phenomena, a discussion of dense polymer mixtures and an introduction to the physical properties of solid and fluid membranes. A chapter on linear response includes the Kubo formalism, the fluctuation-dissipation theorem, Onsager relations and the Boltzmann equation. The last chapter is devoted to disordered materials.Each chapter contains a substantial number of exercises. A manual with a complete set of solutions to these problems is available under separate cover.

Physics Briefs

Author :
Publisher :
ISBN 13 :
Total Pages : 1118 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Physics Briefs by :

Download or read book Physics Briefs written by and published by . This book was released on 1994 with total page 1118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Statistical Physics

Author : Lucas Böttcher
Publisher : Cambridge University Press
ISBN 13 : 9781108841429
Total Pages : 275 pages
Book Rating : 4.8/5 (414 download)

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Book Synopsis Computational Statistical Physics by : Lucas Böttcher

Download or read book Computational Statistical Physics written by Lucas Böttcher and published by Cambridge University Press. This book was released on 2021-08-26 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Graphical Models, Exponential Families, and Variational Inference

Author : Martin J. Wainwright
Publisher : Now Publishers Inc
ISBN 13 : 1601981848
Total Pages : 324 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Graphical Models, Exponential Families, and Variational Inference by : Martin J. Wainwright

Download or read book Graphical Models, Exponential Families, and Variational Inference written by Martin J. Wainwright and published by Now Publishers Inc. This book was released on 2008 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of this paper is a general set of variational principles for the problems of computing marginal probabilities and modes, applicable to multivariate statistical models in the exponential family.

A Guide to Monte Carlo Simulations in Statistical Physics

Author : David P. Landau
Publisher : Cambridge University Press
ISBN 13 : 9780521653664
Total Pages : 402 pages
Book Rating : 4.6/5 (536 download)

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Book Synopsis A Guide to Monte Carlo Simulations in Statistical Physics by : David P. Landau

Download or read book A Guide to Monte Carlo Simulations in Statistical Physics written by David P. Landau and published by Cambridge University Press. This book was released on 2000-08-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, as well as in related fields, such as polymer science and lattice gauge theory. The authors give a succinct overview of simple sampling methods and develop the importance sampling method. In addition they introduce quantum Monte Carlo methods, aspects of simulations of growth phenomena and other systems far from equilibrium, and the Monte Carlo Renormalization Group approach to critical phenomena. The book includes many applications, examples, and current references, and exercises to help the reader.

Random Graph Dynamics

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 1139460889
Total Pages : 203 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Random Graph Dynamics by : Rick Durrett

Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-05-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.