Part of London Mathematical Society Lecture Note Serie
Publication planned for: January 2018
availability: Not yet published - available from January 2018
format: Paperback
This volume presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Building on the foundations laid a quarter of a century ago in the volume Two-dimensional Homotopy and Combinatorial Group Theory (LMS 197), the editors here bring together much remarkable progress that has been obtained in the intervening years. And while the fundamental open questions, such as the Andrews?Curtis Conjecture and the Whitehead asphericity problem remain to be (fully) solved, this book will provide both students and experts with an overview of the state of the art and work in progress. Ample references are included to the LMS 197 volume, as well as a comprehensive bibliography bringing matters entirely up to date.
Provides an overview of the state of research in two-dimensional homotopy theory
Builds on the previous volume published in the same series in 1993
Includes an updated bibliography
Preface Wolfgang Metzler and Stephan Rosebrock
List of contributors
1. A survey of recent progress on some problems in 2-dimensional topology Jens Harlander and F. Rudolf Beyl
2. Further results concerning the Andrews?Curtis conjecture and its generalizations Cynthia Hog-Angeloni and Wolfgang Metzler
3. Aspects of TQFT and computational algebra Holger Kaden and Simon King
4. Labelled oriented trees and the Whitehead conjecture Stephan Rosebrock and Jens Harlander
5. 2-complexes and 3-manifolds Janina Glock, Cynthia Hog-Angeloni and Sergei Matveev
6. The relation gap problem Jens Harlander
7. On the relation gap problem for free products Cynthia Hog-Angeloni and Wolfgang Metzler
References
Index
Erratum.
Part of London Mathematical Society Lecture Note Series
Publication planned for: March 2018
availability: Not yet published - available from March 2018
format: Paperback
isbn: 9781108441988
Markov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject by first developing the theory of Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and graduates. The authors then introduce semi-Markov chains and hidden semi-Markov chains, before developing related estimation and filtering results. Genomics applications are modelled by discrete observations of these hidden semi-Markov chains. This book contains new results and previously unpublished material not available elsewhere. The approach is rigorous and focused on applications.
Presents the theory in a discrete time, finite state framework
Readily accessible to senior undergraduate and first-year graduate students
Contains a wealth of new and previously unpublished material
Preface
1. Observed Markov chains
2. Estimation of an observed Markov chain
3. Hidden Markov models
4. Filters and smoothers
5. The Viterbi algorithm
6. The EM algorithm
7. A new Markov chain model
8. Semi-Markov models
9. Hidden semi-Markov models
10. Filters for hidden semi-Markov models
Appendix A. Higher order chains
Appendix B. An example of a second order chain
Appendix C. A conditional Bayes theorem
Appendix D. On conditional expectations
Appendix E. Some molecular biology
Appendix F. Earlier applications of hidden Markov chain models
References
Index.
Part of London Mathematical Society Lecture Note Series
Publication planned for: April 2018
availability: Not yet published - available from April 2018
format: Paperback
isbn: 9781108413121
This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger?Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.
Presents the most recent activity in the field, helping the reader identify the current 'hotspots'
Provides a global view of the most important topics, made accessible through specific cases
Includes the necessary mathematical treatments to allow the reader to dive into the more specialised literature, using this book as a guide
Part of Cambridge Studies in Advanced Mathematics
Publication planned for: May 2018
availability: Not yet published - available from May 2018
format: Hardback
isbn: 9781108416764
Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson?Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom?Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson?Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathematical physicists, quantum field theorists, and probabilists, including graduate and advanced undergraduate students.
Introduces a new combinatorial calculus that provides an alternative to the usual Feynman diagram expansions
Provides detailed worked examples that demonstrate a broad range of applications
Offers a unified approach to combinatorial formulas for multiple stochastic integrals
Preface
Notation
1. Introduction to combinatorics
2. Probabilistic Moments and Cumulants
3. Quantum probability
4. Quantum fields
5. Combinatorial species
6. Combinatorial aspects of quantum fields: Feynman diagrams
7. Entropy, large deviations and legendre transforms
8. Introduction to Fock spaces
9. Operators and fields on the Boson Fock space
10. L2-representations of the Boson Fock space
11. Local fields on the Boson Fock space: free fields
12. Local fields on the Boson Fock space: interacting fields
13. Quantum stochastic calculus
14. Quantum stochastic limits
Bibliography
Index.
Series:De Gruyter Series in Nonlinear Analysis and Applications 23/2
Hardcover
To be published: February 2018
ISBN 978-3-11-053383-5
This second volume is related to asymptotics for partial differential equations.
Covers autoresonances, solitons, and nonlinear Cauchy problems for elliptic operators.
A fundamental study of asymptotics for nonlinear equations in two volumes.
This is the second volume of Nonlinear Equations with Small Parameter containing new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. They allow one to match asymptotics of various properties with each other in transition regions and to get unified formulas for connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena. These are beginnings of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering constructions and quantum systems. Apart from independent interest the approximate solutions serve as a foolproof basis for testing numerical algorithms. The second volume will be related to partial differential equations.
24.0 x 17.0 cm
Approx. xii, 390 pages 35 Fig.
Language: English
Type of Publication: Monograph
General Interest
Mathematics > Analysis
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