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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 Here
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:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Time-delayed actions appear as an essential component of numerous systems especially in evolution processes, natural phenomena, and particular technical applications and are associated with the existence of a memory. Under common conditions, external forces or state dependent parameters modify the length of the delay with time. Consequently, an altered dynamical behavior emerges, whose characterization is compulsory for a deeper understanding of these processes. In this thesis, the well-investigated class of time-homogeneous finite-state Markov processes is utilized to establish a variation of memory length by combining a first-order Markov chain with a memoryless Markov chain of order zero. The fluctuations induce a non-stationary process, which is accomplished for two special cases: a periodic and a random selection of the available Markov chains. For both cases, the Kolmogorov-Sinai entropy as a characteristic property is deduced analytically and compared to numerical approximations to the entropy rate of related symbolic dynamics. The convergences of per-symbol and conditional entropies are examined in order to recognize their behavior when identifying unknown processes. Additionally, the connection from Markov processes with varying memory length to hidden Markov models is illustrated enabling further analysis. Hence, the Kolmogorov-Sinai entropy of hidden Markov chains is calculated by means of Blackwell's entropy rate involving Blackwell's measure. These results are used to verify the previous computations.
Author: Katy Marchand
Publisher:
ISBN:
Category :
Languages : en
Pages : 148
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Book Description
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: 131658934X
Category : Mathematics
Languages : en
Pages : 247
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Book Description
The rigorous mathematical theory of the Navier–Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier–Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier–Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.
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.
Author: Yann Ollivier
Publisher: Cambridge University Press
ISBN: 1139993623
Category : Mathematics
Languages : en
Pages : 317
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Book Description
The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.
