Download or read book Connectivity Properties of the Random cluster Model written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Random Cluster Model written by Geoffrey R. Grimmett and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
Download or read book Mathematical Statistical Physics written by and published by Elsevier. This book was released on 2006-06-27 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians. - Introduction to a field of math with many interdisciplinary connections in physics, biology, and computer science - Roadmap to the next decade of mathematical statistical mechanics - Volume for reference years to come
Download or read book Random Graphs Phase Transitions and the Gaussian Free Field written by Martin T. Barlow and published by Springer Nature. This book was released on 2019-12-03 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2017 PIMS-CRM Summer School in Probability was held at the Pacific Institute for the Mathematical Sciences (PIMS) at the University of British Columbia in Vancouver, Canada, during June 5-30, 2017. It had 125 participants from 20 different countries, and featured two main courses, three mini-courses, and twenty-nine lectures. The lecture notes contained in this volume provide introductory accounts of three of the most active and fascinating areas of research in modern probability theory, especially designed for graduate students entering research: Scaling limits of random trees and random graphs (Christina Goldschmidt) Lectures on the Ising and Potts models on the hypercubic lattice (Hugo Duminil-Copin) Extrema of the two-dimensional discrete Gaussian free field (Marek Biskup) Each of these contributions provides a thorough introduction that will be of value to beginners and experts alike.
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.
Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2017 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Download or read book Probability and Statistical Physics in St Petersburg written by V. Sidoravicius and published by American Mathematical Soc.. This book was released on 2016-04-28 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.
Download or read book Advanced Wireless Communications and Internet written by Savo G. Glisic and published by John Wiley & Sons. This book was released on 2011-05-03 with total page 1025 pages. Available in PDF, EPUB and Kindle. Book excerpt: ADVANCED WIRELESS COMMUNICATIONS AND INTERNET THIRD EDITION ADVANCED WIRELESS COMMUNICATIONS AND INTERNET Future Evolving Technologies The new edition of Advanced Wireless Communications: 4G Cognitive and Cooperative Broadband Technology, 2nd Edition, including the latest developments In the evolution of wireless communications, the dominant challenges are in the areas of networking and their integration with the Future Internet. Even the classical concept of cellular networks is changing and new technologies are evolving to replace it. To reflect these new trends, Advanced Wireless Communications & INTERNET builds upon the previous volumes, enhancing the existing chapters, and including a number of new topics. Systematically guiding readers from the fundamentals through to advanced areas, each chapter begins with an introductory explanation of the basic problems and solutions followed with an analytical treatment in greater detail. The most important aspects of new emerging technologies in wireless communications are comprehensively covered including: next generation Internet; cloud computing and network virtualization; economics of utility computing and wireless grids and clouds. This gives readers an essential understanding of the overall environment in which future wireless networks will be operating. Furthermore, a number of methodologies for maintaining the network connectivity, by using tools ranging from genetic algorithms to stochastic geometry and random graphs theory, and a discussion on percolation and connectivity, are also offered. The book includes a chapter on network formation games, covering the general models, knowledge based network formation games, and coalition games in wireless ad hoc networks. Illustrates points throughout using real-life case studies drawn from the author’s extensive international experience in the field of telecommunications Fully updated to include the latest developments, key topics covered include: advanced routing and network coding; network stability control; relay-assisted Wireless Networks; multicommodity flow optimization problems, flow optimization in heterogeneous networks, and dynamic resource allocation in computing clouds Methodically guides readers through each topic from basic to advanced areas Focuses on system elements that provide adaptability and re-configurability, and discusses how these features can improve wireless communications system performance Enjoyed this book? Why not tell others about it and write a review on your favourite online bookseller.
Download or read book Handbook of the Tutte Polynomial and Related Topics written by Joanna A. Ellis-Monaghan and published by CRC Press. This book was released on 2022-07-06 with total page 805 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials. Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial’s many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial. Features Written in an accessible style for non-experts, yet extensive enough for experts Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations
Download or read book Selected Works of Oded Schramm written by Itai Benjamini and published by Springer Science & Business Media. This book was released on 2011-08-12 with total page 1199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of the late Oded Schramm (1961-2008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensitivity, Random Walks and Graph Limits, Percolation, and finally Schramm-Loewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects.
Download or read book Soft Computing Applications in Sensor Networks written by Sankar K. Pal and published by CRC Press. This book was released on 2016-10-03 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses tutorials and new material to describe the basic concepts of soft-computing which potentially can be used in real-life sensor network applications. It is organized in a manner that exemplifies the use of an assortment of soft-computing applications for solving different problems in sensor networking. Written by worldwide experts, the chapters provide a balanced mixture of different problems concerning channel access, routing, coverage, localization, lifetime maximization and target tracking using emerging soft-computing applications.
Download or read book Rigidity Theory and Applications written by M.F. Thorpe and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although rigidity has been studied since the time of Lagrange (1788) and Maxwell (1864), it is only in the last twenty-five years that it has begun to find applications in the basic sciences. The modern era starts with Laman (1970), who made the subject rigorous in two dimensions, followed by the development of computer algorithms that can test over a million sites in seconds and find the rigid regions, and the associated pivots, leading to many applications. This workshop was organized to bring together leading researchers studying the underlying theory, and to explore the various areas of science where applications of these ideas are being implemented.
Download or read book Modeling and Analysis of Bio molecular Networks written by Jinhu Lü and published by Springer Nature. This book was released on 2020-12-06 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses a number of questions from the perspective of complex systems: How can we quantitatively understand the life phenomena? How can we model life systems as complex bio-molecular networks? Are there any methods to clarify the relationships among the structures, dynamics and functions of bio-molecular networks? How can we statistically analyse large-scale bio-molecular networks? Focusing on the modeling and analysis of bio-molecular networks, the book presents various sophisticated mathematical and statistical approaches. The life system can be described using various levels of bio-molecular networks, including gene regulatory networks, and protein-protein interaction networks. It first provides an overview of approaches to reconstruct various bio-molecular networks, and then discusses the modeling and dynamical analysis of simple genetic circuits, coupled genetic circuits, middle-sized and large-scale biological networks, clarifying the relationships between the structures, dynamics and functions of the networks covered. In the context of large-scale bio-molecular networks, it introduces a number of statistical methods for exploring important bioinformatics applications, including the identification of significant bio-molecules for network medicine and genetic engineering. Lastly, the book describes various state-of-art statistical methods for analysing omics data generated by high-throughput sequencing. This book is a valuable resource for readers interested in applying systems biology, dynamical systems or complex networks to explore the truth of nature.
Download or read book Bacterial Conversations written by Ian Joint and published by . This book was released on 2007 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamical Processes on Complex Networks written by Alain Barrat and published by Cambridge University Press. This book was released on 2008-10-23 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The availability of large data sets has allowed researchers to uncover complex properties such as large-scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-experts in the subject.
Download or read book The Random Cluster Model on the Tree written by Sam Finch and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fortuin-Kasteleyn random cluster model was adapted to the tree by Häggström [38] who considered a Gibbs specification corresponding to "wired boundary conditions" on the tree. Grimmett and Janson [36] generalized this idea by considering boundary conditions defined by equivalence relations on the set of rays of the tree. In this thesis we continue this project by defining a new object, a "random connection;" a type of random equivalence relation that allows us to redefine what is meant by a cluster of edges on the tree. Our definition is general enough to include Grimmett and Janson's boundary conditions. The random connection approach allows us to reconnect the random cluster model on the tree with Bernoulli bond percolation and we define two critical probabilities for bond percolation on a tree associated with each random connection that allow us to identify three behavioral phases of the associated random cluster model. We consider some examples of random connections defined by equivalence relations, including the "open" boundary conditions described in [36] where we are able to describe the behaviour of the random cluster model exactly and "Mandelbrot" bondary conditions described by a map from the boundary of a tree to the unit square that defines fractal percolation. In addition we adapt work of Zachary [66] to the wired random cluster model on a tree so as to prove a conjecture of Häggström concerning uniqueness of the Gibbs measure for large bond strengths.
Download or read book Dynamics of Complex Interconnected Systems Networks and Bioprocesses written by Arne T. Skjeltorp and published by Springer Science & Business Media. This book was released on 2006-12-22 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews the synergism between various fields of research that are confronted with networks, such as genetic and metabolic networks, social networks, the Internet and ecological systems. In many cases, the interacting networks manifest so-called emergent properties that are not possessed by any of the individual components. Knowledge gained from the study of complex non-biological systems can be applied to the intricate braided relationships that govern cellular functions.
