Finite Markov Chains and Algorithmic Applications
Finite Markov Chains and Algorithmic Applications

Author: Olle Häggström

Publisher: Cambridge University Press

Published: 2002-05-30

Total Pages: 132

ISBN-13: 9780521890014

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Based on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.

Algorithms for Random Generation and Counting: A Markov Chain Approach
Algorithms for Random Generation and Counting: A Markov Chain Approach

Author: A. Sinclair

Publisher: Springer Science & Business Media

Published: 1993-02

Total Pages: 161

ISBN-13: 0817636587

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This monograph is a slightly revised version of my PhD thesis [86], com pleted in the Department of Computer Science at the University of Edin burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.

Markov Chains: Models, Algorithms and Applications
Markov Chains: Models, Algorithms and Applications

Author: Wai-Ki Ching

Publisher: Springer Science & Business Media

Published: 2006-06-05

Total Pages: 212

ISBN-13: 038729337X

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Markov chains are a particularly powerful and widely used tool for analyzing a variety of stochastic (probabilistic) systems over time. This monograph will present a series of Markov models, starting from the basic models and then building up to higher-order models. Included in the higher-order discussions are multivariate models, higher-order multivariate models, and higher-order hidden models. In each case, the focus is on the important kinds of applications that can be made with the class of models being considered in the current chapter. Special attention is given to numerical algorithms that can efficiently solve the models. Therefore, Markov Chains: Models, Algorithms and Applications outlines recent developments of Markov chain models for modeling queueing sequences, Internet, re-manufacturing systems, reverse logistics, inventory systems, bio-informatics, DNA sequences, genetic networks, data mining, and many other practical systems.

Probabilistic Methods for Algorithmic Discrete Mathematics
Probabilistic Methods for Algorithmic Discrete Mathematics

Author: Michel Habib

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 342

ISBN-13: 3662127881

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Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.

Handbook of Research on Applied AI for International Business and Marketing Applications
Handbook of Research on Applied AI for International Business and Marketing Applications

Author: Christiansen, Bryan

Publisher: IGI Global

Published: 2020-09-25

Total Pages: 702

ISBN-13: 1799850781

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Artificial intelligence (AI) describes machines/computers that mimic cognitive functions that humans associate with other human minds, such as learning and problem solving. As businesses have evolved to include more automation of processes, it has become more vital to understand AI and its various applications. Additionally, it is important for workers in the marketing industry to understand how to coincide with and utilize these techniques to enhance and make their work more efficient. The Handbook of Research on Applied AI for International Business and Marketing Applications is a critical scholarly publication that provides comprehensive research on artificial intelligence applications within the context of international business. Highlighting a wide range of topics such as diversification, risk management, and artificial intelligence, this book is ideal for marketers, business professionals, academicians, practitioners, researchers, and students.

Markov Chain Monte Carlo
Markov Chain Monte Carlo

Author: W. S. Kendall

Publisher: World Scientific

Published: 2005

Total Pages: 239

ISBN-13: 9812700919

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Markov Chain Monte Carlo (MCMC) originated in statistical physics, but has spilled over into various application areas, leading to a corresponding variety of techniques and methods. That variety stimulates new ideas and developments from many different places, and there is much to be gained from cross-fertilization. This book presents five expository essays by leaders in the field, drawing from perspectives in physics, statistics and genetics, and showing how different aspects of MCMC come to the fore in different contexts. The essays derive from tutorial lectures at an interdisciplinary program at the Institute for Mathematical Sciences, Singapore, which exploited the exciting ways in which MCMC spreads across different disciplines.

Markov Chains and Mixing Times
Markov Chains and Mixing Times

Author: David A. Levin

Publisher: American Mathematical Soc.

Published: 2017-10-31

Total Pages: 465

ISBN-13: 1470429624

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This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines. The central tools for estimating convergence times, including coupling, strong stationary times, and spectral methods, are developed. The authors discuss many examples, including card shuffling and the Ising model, from statistical mechanics, and present the connection of random walks to electrical networks and apply it to estimate hitting and cover times. The first edition has been used in courses in mathematics and computer science departments of numerous universities. The second edition features three new chapters (on monotone chains, the exclusion process, and stationary times) and also includes smaller additions and corrections throughout. Updated notes at the end of each chapter inform the reader of recent research developments.

Algorithms and Computation
Algorithms and Computation

Author: Toshihide Ibaraki

Publisher: Springer Science & Business Media

Published: 2003-12-03

Total Pages: 764

ISBN-13: 3540206957

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This book constitutes the refereed proceedings of the 14th International Symposium on Algorithms and Computation, ISAAC 2003, held in Kyoto, Japan, in December 2003. The 73 revised full papers presented were carefully reviewed and selected from 207 submissions. The papers are organized in topical sections on computational geometry, graph and combinatorial algorithms, computational complexity, quantum computing, combinatorial optimization, scheduling, computational biology, distributed and parallel algorithms, data structures, combinatorial and network optimization, computational complexity and cryptography, game theory and randomized algorithms, and algebraic and arithmetic computation.

Markov Chains
Markov Chains

Author: Pierre Bremaud

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 456

ISBN-13: 1475731248

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Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.