On The Random Cluster Model
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The Random Cluster Model
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Author : Geoffrey R. Grimmett
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-13
The Random Cluster Model written by Geoffrey R. Grimmett and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-13 with Mathematics categories.
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.
On The Random Cluster Model
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Author : Cornelis Marius Fortuin
language : en
Publisher:
Release Date : 1971
On The Random Cluster Model written by Cornelis Marius Fortuin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
The Random Cluster Model
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Author : Geoffrey R. Grimmett
language : en
Publisher: Springer
Release Date : 2009-09-02
The Random Cluster Model written by Geoffrey R. Grimmett and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Mathematics categories.
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.
The Random Cluster Model
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Author : Geoffrey Grimmett
language : en
Publisher: Springer Verlag
Release Date : 2006-01-01
The Random Cluster Model written by Geoffrey Grimmett and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Mathematics categories.
The random-cluster model has emerged in recent years 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. This systematic study includes accounts of the subcritical and supercritical phases, together with clear statements of important open problems. There is an extensive treatment of the first-order (discontinuous) phase transition, as well as a chapter devoted to applications of the random-cluster method to other models of statistical physics.
Random Graphs And Complex Networks
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Author : Remco van der Hofstad
language : en
Publisher: Cambridge University Press
Release Date : 2017
Random Graphs And Complex Networks written by Remco van der Hofstad and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Computers categories.
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Phylogeny
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Author : Mike Steel
language : en
Publisher: SIAM
Release Date : 2016-09-29
Phylogeny written by Mike Steel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-29 with Science categories.
Phylogenetics is a topical and growing area of research. Phylogenies (phylogenetic trees and networks) allow biologists to study and graph evolutionary relationships between different species. These are also used to investigate other evolutionary processes?for example, how languages developed or how different strains of a virus (such as HIV or influenza) are related to each other.? This self-contained book addresses the underlying mathematical theory behind the reconstruction and analysis of phylogenies. The theory is grounded in classical concepts from discrete mathematics and probability theory as well as techniques from other branches of mathematics (algebra, topology, differential equations). The biological relevance of the results is highlighted throughout. The author supplies proofs of key classical theorems and includes results not covered in existing books, emphasizes relevant mathematical results derived over the past 20 years, and provides numerous exercises, examples, and figures.?
Statistical Methods In Psychiatry And Related Fields
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Author : Ralitza Gueorguieva
language : en
Publisher: CRC Press
Release Date : 2017-11-20
Statistical Methods In Psychiatry And Related Fields written by Ralitza Gueorguieva and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-20 with Mathematics categories.
Data collected in psychiatry and related fields are complex because outcomes are rarely directly observed, there are multiple correlated repeated measures within individuals, there is natural heterogeneity in treatment responses and in other characteristics in the populations. Simple statistical methods do not work well with such data. More advanced statistical methods capture the data complexity better, but are difficult to apply appropriately and correctly by investigators who do not have advanced training in statistics. This book presents, at a non-technical level, several approaches for the analysis of correlated data: mixed models for continuous and categorical outcomes, nonparametric methods for repeated measures and growth mixture models for heterogeneous trajectories over time. Separate chapters are devoted to techniques for multiple comparison correction, analysis in the presence of missing data, adjustment for covariates, assessment of mediator and moderator effects, study design and sample size considerations. The focus is on the assumptions of each method, applicability and interpretation rather than on technical details. Features Provides an overview of intermediate to advanced statistical methods applied to psychiatry. Takes a non-technical approach with mathematical details kept to a minimum. Includes lots of detailed examples from published studies in psychiatry and related fields. Software programs, data sets and output are available on a supplementary website. The intended audience are applied researchers with minimal knowledge of statistics, although the book could also benefit collaborating statisticians. The book, together with the online materials, is a valuable resource aimed at promoting the use of appropriate statistical methods for the analysis of repeated measures data. Ralitza Gueorguieva is a Senior Research Scientist at the Department of Biostatistics, Yale School of Public Health. She has more than 20 years experience in statistical methodology development and collaborations with psychiatrists and other researchers, and is the author of over 130 peer-reviewed publications.
Random Graphs Phase Transitions And The Gaussian Free Field
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Author : Martin T. Barlow
language : en
Publisher: Springer Nature
Release Date : 2019-12-03
Random Graphs Phase Transitions And The Gaussian Free Field written by Martin T. Barlow and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-03 with Mathematics categories.
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.
Probability On Discrete Structures
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Author : Harry Kesten
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Probability On Discrete Structures written by Harry Kesten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.
Handbook Of The Tutte Polynomial And Related Topics
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Author : Joanna A. Ellis-Monaghan
language : en
Publisher: CRC Press
Release Date : 2022-07-06
Handbook Of The Tutte Polynomial And Related Topics written by Joanna A. Ellis-Monaghan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-06 with Computers categories.
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