random graph dynamics cambridge series in statistical and probabilistic mathematics

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Random Graph Dynamics

Author : Rick Durrett
ISBN : 9781139460880
Genre : Mathematics
File Size : 34. 40 MB
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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.

Random Graphs And Complex Networks

Author : Remco van der Hofstad
ISBN : 9781316802311
Genre : Mathematics
File Size : 80. 56 MB
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This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.

Graph Theoretic Concepts In Computer Science

Author : Hans L. Bodlaender
ISBN : 9783319687056
Genre : Computers
File Size : 50. 84 MB
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This book constitutes the revised selected papers of the 43rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2017, held in Eindhoven, The Netherlands, in June 2017. The 31 full papers presented in this volume were carefully reviewed and selected from 71 submissions. They cover a wide range of areas, aiming at connecting theory and applications by demonstrating how graph-theoretic concepts can be applied in various areas of computer science. Another focus is on presenting recent results and on identifying and exploring promising directions of future research.

Mathematical Foundations Of Complex Networked Information Systems

Author : P.R. Kumar
ISBN : 9783319169675
Genre : Mathematics
File Size : 71. 90 MB
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Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance. The book is self-contained, and requires only an undergraduate mathematical background.

Random Networks

Author : Sreekalyani Shankar Bhamidi
ISBN : UCAL:C3481444
Genre :
File Size : 68. 5 MB
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American Book Publishing Record

Author :
ISBN : UOM:39015066180426
Genre : American literature
File Size : 22. 86 MB
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The Random Cluster Model

Author : Geoffrey R. Grimmett
ISBN : 9783540328919
Genre : Mathematics
File Size : 53. 48 MB
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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.

Groups Graphs And Random Walks

Author : Tullio Ceccherini-Silberstein
ISBN : 9781316604403
Genre : Mathematics
File Size : 58. 78 MB
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An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrdinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubtedly stem.

Amstat News

Author :
ISBN : UOM:39015072605929
Genre : Statistics
File Size : 76. 10 MB
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Probability Random Processes And Statistical Analysis

Author : Hisashi Kobayashi
ISBN : 9781139502610
Genre : Technology & Engineering
File Size : 85. 41 MB
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Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.

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