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Author: Brian Marcus
Publisher:
ISBN: 9781139092883
Category : Dynamics
Languages : en
Pages : 280
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Book Description
Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station Workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterizing the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is the problem of characterizing the mappings between dynamical systems which map Markov measures to Markov (or Gibbs) measures, and which allow for Markov lifts of Markov chains.
Author: Brian Marcus
Publisher:
ISBN: 9781139092883
Category : Dynamics
Languages : en
Pages : 280
Get Book
Book Description
Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station Workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterizing the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is the problem of characterizing the mappings between dynamical systems which map Markov measures to Markov (or Gibbs) measures, and which allow for Markov lifts of Markov chains.
Author: Brian Marcus
Publisher:
ISBN: 9781139090063
Category :
Languages : en
Pages :
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Book Description
Author: Brian Marcus
Publisher: Cambridge University Press
ISBN: 1139495747
Category : Mathematics
Languages : en
Pages : 279
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Book Description
This collection of research and survey papers sets out the theory of hidden Markov processes, in particular addressing a central problem of the subject: computation of the Shannon entropy rate of an HMP. Connections are drawn between approaches from various disciplines, whilst recent research results and open problems are described.
Author: Andrew M. Fraser
Publisher: SIAM
ISBN: 0898717744
Category : Mathematics
Languages : en
Pages : 142
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Book Description
This text provides an introduction to hidden Markov models (HMMs) for the dynamical systems community. It is a valuable text for third or fourth year undergraduates studying engineering, mathematics, or science that includes work in probability, linear algebra and differential equations. The book presents algorithms for using HMMs, and it explains the derivation of those algorithms. It presents Kalman filtering as the extension to a continuous state space of a basic HMM algorithm. The book concludes with an application to biomedical signals. This text is distinctive for providing essential introductory material as well as presenting enough of the theory behind the basic algorithms so that the reader can use it as a guide to developing their own variants.
Author: Douglas Lind
Publisher: Cambridge University Press
ISBN: 1108901964
Category : Mathematics
Languages : en
Pages : 572
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Book Description
Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C^*$-algebras. This Second Edition maintains the introductory character of the original 1995 edition as a general textbook on symbolic dynamics and its applications to coding. It is written at an elementary level and aimed at students, well-established researchers, and experts in mathematics, electrical engineering, and computer science. Topics are carefully developed and motivated with many illustrative examples. There are more than 500 exercises to test the reader's understanding. In addition to a chapter in the First Edition on advanced topics and a comprehensive bibliography, the Second Edition includes a detailed Addendum, with companion bibliography, describing major developments and new research directions since publication of the First Edition.
Author: Andreas Greven
Publisher: Princeton University Press
ISBN: 1400865220
Category : Mathematics
Languages : en
Pages : 376
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Book Description
The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding.
Author: Fred Diamond
Publisher: Cambridge University Press
ISBN: 1316062341
Category : Mathematics
Languages : en
Pages : 387
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Book Description
Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume two include curves and vector bundles in p-adic Hodge theory, associators, Shimura varieties, the birational section conjecture, and other topics of contemporary interest.
Author: Felix Fischer
Publisher: Cambridge University Press
ISBN: 1009490540
Category : Mathematics
Languages : en
Pages : 306
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Book Description
This volume contains nine survey articles by the invited speakers of the 30th British Combinatorial Conference, held at Queen Mary University of London in July 2024. Each article provides an overview of recent developments in a current hot research topic in combinatorics. Topics covered include: Latin squares, Erdős covering systems, finite field models, sublinear expanders, cluster expansion, the slice rank polynomial method, and oriented trees and paths in digraphs. The authors are among the world's foremost researchers on their respective topics but their surveys are accessible to nonspecialist readers: they are written clearly with little prior knowledge assumed and with pointers to the wider literature. Taken together these surveys give a snapshot of the research frontier in contemporary combinatorics, helping researchers and graduate students in mathematics and theoretical computer science to keep abreast of the latest developments in the field.
Author: James C. Robinson
Publisher: Cambridge University Press
ISBN: 1107554977
Category : Mathematics
Languages : en
Pages : 247
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Book Description
An accessible summary of a wide range of active research topics written by leaders in their field, including exciting new results.
Author: C. T. J. Dodson
Publisher: Cambridge University Press
ISBN: 1316601951
Category : Mathematics
Languages : en
Pages : 315
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Book Description
A new approach to studying Fréchet geometry using projective limits of geometrical objects modelled on Banach spaces.
