Part of London Mathematical Society Lecture Note Series
Publication planned for: January 2016
format: Paperback
isbn: 9781107529007
The ICM 2010 satellite conference 'Geometry, Topology and Dynamics in Negative Curvature' afforded an excellent opportunity to discuss various aspects of this fascinating interdisciplinary subject in which methods and techniques from geometry, topology, and dynamics often interact in novel and interesting ways. Containing ten survey articles written by some of the leading experts in the field, this proceedings volume provides an overview of important recent developments relating to negative curvature. Topics covered include homogeneous dynamics, harmonic manifolds, the Atiyah Conjecture, counting circles and arcs, and hyperbolic buildings. Each author pays particular attention to the expository aspects, making the book particularly useful for graduate students and mathematicians interested in transitioning from other areas via the common theme of negative curvature.
Preface C. S. Aravinda, F. T. Farrell and J.-F. Lafont
1. Gap distributions and homogeneous dynamics Jayadev S. Athreya
2. Topology of open nonpositively curved manifolds Igor Belegradek
3. Cohomologie et actions isometriques propres sur les espaces Lp Marc Bourdon
4. Compact Clifford?Klein forms ? geometry, topology and dynamics David Constantine
5. A survey on noncompact harmonic and asymptotically harmonic manifolds Gerhard Knieper
6. The Atiyah conjecture Peter A. Linnell
7. Cannon?Thurston maps for surface groups ? an exposition of amalgamation geometry and split geometry Mahan Mj
8. Counting visible circles on the sphere and Kleinian groups Hee Oh and Nimish Shah
9. Counting arcs in negative curvature Jouni Parkkonen and Frederic Paulin
10. Lattices in hyperbolic buildings Anne Thomas.
Part of Encyclopedia of Mathematics and its Applications
Publication planned for: January 2016
format: Hardback
isbn: 9781107077027
Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms.
List of contributors
Preface
Acknowledgments
1. Preliminaries V. Berthe and M. Rigo
2. Expansions in non-integer bases M. de Vries and V. Komornik
3. Medieties, end-first algorithms, and the case of Rosen continued fractions B. Rittaud
4. Repetitions in words N. Rampersad and J. Shallit
5. Text redundancies G. Badkobeh, M. Crochemore, C. S. Iliopoulos and M. Kubica
6. Similarity relations on words V. Halava, T. Harju and T. Karki
7. Synchronised automata M.-P. Beal and D. Perrin
8. Cellular automata, tilings and (un)computability J. Kari
9. Multidimensional shifts of finite type and sofic shifts M. Hochman
10. Linearly recursive sequences and Dynkin diagrams C. Reutenauer
11. Pseudo-randomness of a random Kronecker sequence. An instance of dynamical analysis E. Cesaratto and B. Vallee
Notation index
General index.
Part of Cambridge Studies in Advanced Mathematics
Publication planned for: February 2016
format: Hardback
isbn: 9781107128446
Aimed at graduate students and researchers, this fascinating text provides a comprehensive study of the Erdos-Ko-Rado Theorem, with a focus on algebraic methods. The authors begin by discussing well-known proofs of the EKR bound for intersecting families. The natural generalization of the EKR Theorem holds for many different objects that have a notion of intersection, and the bulk of this book focuses on algebraic proofs that can be applied to these different objects. The authors introduce tools commonly used in algebraic graph theory and show how these can be used to prove versions of the EKR Theorem. Topics include association schemes, strongly regular graphs, the Johnson scheme, the Hamming scheme and the Grassmann scheme. Readers can expand their understanding at every step with the 170 end-of-chapter exercises. The final chapter discusses in detail 15 open problems, each of which would make an interesting research project.
Preface
1. The Erdos-Ko-Rado Theorem
2. Bounds on cocliques
3. Association schemes
4. Distance-regular graphs
5. Strongly regular graphs
6. The Johnson scheme
7. Polytopes
8. The exact bound
9. The Grassmann scheme
10. The Hamming scheme
11. Representation theory
12. Representations of symmetric group
13. Orbitals
14. Permutations
15. Partitions
16. Open problems
Glossary of symbols
Glossary of operations and relations
References
Index.
ISBN: 978-1-118-63432-5
608 pages
October 2015
A modern and accessible guide to the analysis of introductory time series data
Featuring an organized and self-contained guide, Time Series Analysis provides a broad introduction to the most fundamental methodologies and techniques of time series analysis. The book focuses on the treatment of univariate time series by illustrating a number of well-known models such as ARMA and ARIMA.
Providing contemporary coverage, the book features several useful and newly-developed techniques such as weak and strong dependence, Bayesian methods, non-Gaussian data, local stationarity, missing values and outliers, and threshold models. Time Series Analysis includes practical applications of time series methods throughout, as well as:
Real-world examples and exercise sets that allow readers to practice the presented methods and techniques
Numerous detailed analyses of computational aspects related to the implementation of methodologies including algorithm efficiency, arithmetic complexity, and process time
End-of-chapter proposed problems and bibliographical notes to deepen readers’ knowledge of the presented material
Appendices that contain details on fundamental concepts and select solutions of the problems implemented throughout
A companion website with additional data files and computer codes
Time Series Analysis is an excellent textbook for undergraduate and beginning graduate-level courses in time series as well as a supplement for students in advanced statistics, mathematics, economics, finance, engineering, and physics. The book is also a useful reference for researchers and practitioners in time series analysis, econometrics, and finance.
Preface xiii
Acknowledgments xvii
Acronyms xix
1 Introduction 1
1.1 Time Series Data 2
1.2 Random Variables and Statistical Modeling 16
1.3 Discrete-Time Models 22
1.4 Serial Dependence 22
1.5 Nonstationarity 25
1.6 Whiteness Testing 32
1.7 Parametric and Nonparametric Modeling 36
1.8 Forecasting 38
1.9 Time Series Modeling 38
1.10 Bibliographic Notes 39
Problems 39
and more
ISBN: 978-1-119-02266-4
352 pages
November 2015
Geometry of Convex Sets begins with basic definitions of the linear concepts of addition and scalar multiplication and then defines the notion of convexity for subsets of n-dimensional space. Many properties of convex sets can be discovered using just the linear structure. However, for more interesting results, it is necessary to discuss the notion of distance about open sets, closed sets, bounded sets, and compact sets. The book illustrates the interplay between these linear and topological concepts, which makes the notion of convexity so appealing.
Thoroughly class-tested, the book discusses topology and convexity in the context of normed linear spaces, specifically with a norm topology on an n-dimensional space. Geometry of Convex Sets also features:
An introduction to n-dimensional geometry including points; lines; vectors; distance; norms; inner products; orthogonality; convexity; hyperplanes; and linear functionals
An introduction to n-dimensional norm topology including interior points and open sets; accumulation points and closed sets; boundary points and closed sets; compact subsets of n-dimensional space; completeness of n-dimensional space; sequences; equivalent norms; distance between sets; and support hyperplanes
Basic properties of convex sets; convex hulls; interior and closure of convex sets; closed convex hulls; accessibility lemma; regularity of convex sets; affine hulls; flats or affine subspaces; affine basis theorem; separation theorems; extreme points of convex sets; supporting hyperplanes and extreme points; existence of extreme points; Krein-Milman theorem; polyhedral sets and polytopes; and Birkhoff’’s theorem on doubly stochastic matrices
Discussions on Helly’s theorem; the Art Gallery theorem; Vincensini’s problem; Hadwiger’s theorems; theorems of Radon and Caratheodory; Kirchberger’s theorem; Helly-type theorems for circles; covering problems; piercing problems; sets of constant width; Reuleaux triangles; Barbier’s theorem; and Borsuk’s problem
Geometry of Convex Sets is a useful textbook for upper-undergraduate level courses in geometry of convex sets and is essential for graduate level courses in convex analysis. An excellent reference for academics and readers interested in learning the various applications of higher geometry, the book is also appropriate for teachers who would like to convey a better understanding and appreciation of the field to students.
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ISBN: 978-1-118-74224-2
320 pages
January 2016
This Second Edition features a unique overview that melds the concepts of conditional probability and stochastic processes into real-life applications. By combining the applied aspects of randomization in clinical trials with a nonparametric approach to inference, the book has become a 'must have' for biostatisticians and pharmaceutical industry statisticians. The book also focuses on the linear rank test under a randomization model, with added discussion on likelihood-based inference as it relates to sufficiency and ancillarity.Developments in stochastic processes and applied probability are presented where appropriate and includes response-adaptive randomization, Bayesian designs, CARA randomization, and covariate-adaptive randomization in theory and practice. Additional coverage of "randomization in practice", such as cluster randomization, new developments in restricted randomization, and increased discussions on philosophical issues in randomization, have also been included. This new edition also has an increased focus on computation of randomized tests rather than the asymptotic theory of randomized tests. Chapter coverage includes: randomization and the clinical trial; issues in the design of clinical trials; restrited randomization; balancing on covariates; accidental bias; selection bias; randomization as a basis for inference; inference for stratified, blocked, and covariate-adjusted analysesl randomization in practice; cluster randomization; response-adaptive randomization; response-adaptive randomization in practice; inference for response-adaptive and covariate-adaptive randomization; and covariate-adjusted response-adaptive randomization.