2013 268 pages
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
978-1-46-656023-9
23rd July 2013.
Written by a prominent statistician and author, the first edition of this bestseller broke new ground in the then emerging subject of spatial statistics with its coverage of spatial point patterns. Retaining all the material from the second edition and adding substantial new material, Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, Third Edition presents models and statistical methods for analyzing spatially referenced point process data.
Reflected in the title, this third edition now covers spatio-temporal point patterns. It explores the methodological developments from the last decade along with diverse applications that use spatio-temporally indexed data. Practical examples illustrate how the methods are applied to analyze spatial data in the life sciences.
This edition also incorporates the use of R through several packages dedicated to the analysis of spatial point process data. Sample R code and data sets are available on the authorfs website.
2014 - 700 pages
Hardback:
978-1-48-223078-9
26th June 2014
This book covers many important classes of difference equations, including general, linear, first, second, and Nth order, along with nonlinear equations, partial difference equations, functional equations, and Nth order equations having constant coefficients. It presents a wide range of techniques for calculating exact and approximate solutions. Numerous worked examples illustrate the use of the methodologies. This edition includes new chapters on advanced topics, such as asymptotic behavior of solutions and functional equations, as well as problems that have appeared in the recent mathematical literature.
The Difference Calculus. First-Order Difference Equations. Linear Difference Equations. Linear Difference Equations with Constant Coefficients. Linear Partial Difference Equations. Nonlinear Difference Equations. Advanced Topics. Miscellaneous Topics and Worked Problems. Appendix. Notes and References. Bibliography. Index.
Published: 30 August 2013
Backward Simulation Methods for Monte Carlo Statistical Inference presents and discusses various backward simulation methods for Monte Carlo statistical inference. The focus is on SMC-based backward simulators, which are useful for inference in analytically intractable models, such as nonlinear and/or non-Gaussian SSMs, but also in more general latent variable models.
Keywords
Bayesian learning | Markov chain Monte Carlo | Nonlinear signal processing
Particle smoothing, Sequential Monte Carlo
1. Introduction
2. Monte Carlo Preliminaries
3. Backward Simulation for State-Space Models
4. Backward Simulation for General Sequential Models
5. Backward Simulation in Particle MCMC
6. Discussion
Acknowledgments
Notations and Acronyms
References
The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra g* of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac*Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra.
The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras * such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations * simplify and clarify the constructions of the first edition of the book.
This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory.
*Definition of Positive-Energy Representations of Vir
*Complete Reducibility of the Oscillator Representations of Vir
*Lie Algebras of Infinite Matrices
*Boson*Fermion Correspondence
*Schur Polynomials
*N-Soliton Solutions
*The Kac Determinant Formula
*Nonabelian Generalization of Virasoro Operators: The Sugawara Construction
*The Weyl*Kac Character Formula and Jacobi*Riemann Theta Functions
*Completion of the Proof of the Kac Determinant Formula
*Lambda*Bracket of Local Formal Distributions
*Completion of U, Restricted Representations and Quantum Fields
*Non-Commutative Wick Formula
*Conformal Weights
*Definition of a Vertex Algebra
*Definition of a Representation of a Vertex Algebra
*and other lectures
Readership: Mathematicians studying representation theory and theoretical physicists.
252pp Aug 2013
ISBN: 978-981-4522-18-2 (hardcover)
.ISBN: 978-981-4522-19-9 (softcover)
About This Book This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values.
*Scientific Background:
*On Functions with Values in Metric Spaces: Basic Notions, Approximation Operators
*On Sets: Sets, Set Operations and Parametrizations
*On Set-Valued Functions (SVFs): Representations and Regularity
*Approximation of SVFs:
*Methods Based on Canonical Representations
*Methods Based on Minkowski Convex Combinations
*Methods Based on the Metric Average
*Methods Based on Metric Linear Combinations
*Methods Based on Metric Selections
*Approximation of SVFs with Images in R:
*Regularity of the Boundaries of the Graph
*Multisegmental and Topological Representations
*Methods Based on Topological Representation
Readership: Researchers and graduate students in the fields of approximation theory, set-valued analysis, dynamical systems, control and game theory, optimization and geometric modeling.
200pp Aug 2014
ISBN: 978-1-78326-302-8
Hardcover
London Mathematical Society Student Texts, vol.80
available from November 2013
Hardback isbn: 9781107047211
Paperback isbn: 9781107685314
This book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function fields, along with an explanation of the connections with Nevanlinna theory and non-commutative geometry. The connection with non-commutative geometry is given special attention, with a complete determination of the Weil terms in the explicit formula for the point counting function as a trace of a shift operator on the additive space, and a discussion of how to obtain the explicit formula from the action of the idele class group on the space of adele classes. The exposition is accessible at the graduate level and above, and provides a wealth of motivation for further research in this area.
A graduate-level introduction to an active area of research at the intersection of number theory and non-commutative geometry Describes how ideas from non-commutative geometry could be used to attack the famous Riemann Hypothesis The book provides a basis for further research
List of illustrations
Preface
Introduction
1. Valuations
2. The local theory
3. The zeta function
4. Weil positivity
5. The Frobenius flow
6. Shift operators
7. Epilogue
References
Notation
Index.
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