Series: Lecture Notes in Mathematics , Vol. 1913
2007, XVI, 524 p., 9 illus., Softcover
ISBN: 978-3-540-72469-8
Due: June 26, 2007
About this book
In this volume readers will find for the first time a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. Special emphasis is given to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. Ample background theory on symplectic reduction and cotangent bundle reduction in particular is provided. Novel features of the book are the inclusion of a systematic treatment of the cotangent bundle case, including the identification of cocycles with magnetic terms, as well as the general theory of singular reduction by stages.
Written for:
Researchers and graduate students
Table of contents
Series: Lecture Notes in Mathematics , Vol. 1917
2007, Approx. 130 p., Softcover
ISBN: 978-3-540-72689-0
Due: July 2007
About this book
The theory of random Schrodinger operators is devoted to the mathematical analysis of quantum mechanical Hamiltonians modeling disordered solids. Apart from its importance in physics, it is a multifaceted subject in its own right, drawing on ideas and methods from various mathematical disciplines like functional analysis, selfadjoint operators, PDE, stochastic processes and multiscale methods.
The present text describes in detail a quantity encoding spectral features of random operators: the integrated density of states or spectral distribution function. Various approaches to the construction of the integrated density of states and the proof of its regularity properties are presented.
The setting is general enough to apply to random operators on Riemannian manifolds with a discrete group action. References to and a discussion of other properties of the IDS are included, as are a variety of models beyond those treated in detail here.
Table of contents
Random Operators.- Existence of the Integrated Density of States.- Wegner Estimate.- Wegner's Original Idea. Rigorous Implementation.- Lipschitz Continuity of the IDS.- Appendix: Properties of the Spectral Shift Function.
Series: Springer Series in Statistics
2007, Approx. 365 p., Hardcover
ISBN: 978-0-387-71392-2
Due: August 2007
About this book
New topics featured that have not been discussed in other books: a unified framework of model for clustered, longitudinal, or vector outcomes based on dispersion models
A rigorous presentation of the theory of inference functions prior to the introduction to the marginal models
The means of quadratic inference function (QIF)
The theory of vector generalized linear models ? and more
This book presents some recent developments in correlated data analysis. It utilizes the class of dispersion models as marginal components in the formulation of joint models for correlated data. This enables the book to handle a broader range of data types than those analyzed by traditional generalized linear models. One example is correlated angular data.
This book provides a systematic treatment for the topic of estimating functions. Under this framework, both generalized estimating equations (GEE) and quadratic inference functions (QIF) are studied as special cases. In addition to marginal models and mixed-effects models, this book covers topics on joint regression analysis based on Gaussian copulas and generalized state space models for longitudinal data from long time series.
Various real-world data examples, numerical illustrations and software usage tips are presented throughout the book. This book has evolved from lecture notes on longitudinal data analysis, and may be considered suitable as a textbook for a graduate course on correlated data analysis. This book is inclined more towards technical details regarding the underlying theory and methodology used in software-based applications. Therefore, the book will serve as a useful reference for those who want theoretical explanations to puzzles arising from data analyses or deeper understanding of underlying theory related to analyses.
Peter Song is Professor of Statistics in the Department of Statistics and Actuarial Science at the University of Waterloo. Professor Song has published various papers on the theory and modeling of correlated data analysis. He has held a visiting position at the University of Michigan School of Public Health (Ann Arbor, Michigan).
Table of contents
Introduction and examples.- Dispersion models.- Inference functions.- Modeling correlated data.- Marginal generalized linear models.- Vector generalized linear models.- Mixed-effects models: likelihood-based inference.- Mixed-effects models: Bayesian inference.- Linear predictors.- Generalized state space models.- Generalized state space models for longitudinal binomial data.- Generalized state space models for longitudinal count data.- Missing data in longitudinal studies.
Series: Applied Mathematical Sciences , Vol. 162
2007, Approx. 325 p., 25 illus., Hardcover
ISBN: 978-0-387-71565-0
Due: August 2007
About this book
This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors.
The main approach is based on modern layer potential techniques. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics.
With its extensive list of references and open problems, the book should enhance accessibility to specialized literature and stimulate progress in the fields of impedance imaging and composite materials. Graduate students and researchers in applied mathematics will benefit from this book. Researchers in engineering and physics might also find this book helpful.
Table of contents
Introduction.- Layer Potentials and Transmission Problems.- Uniqueness for Inverse Conductivity Problems.- Generalized Isotropic and Anisotropic Polarization Tensors.- Full Asymptotic Formula for the Potentials.- Near-Boundary Conductivity Inclusions.- Impedance Imaging of Conductivity Inclusions.- Effective Properties of Electrical Composites.- Transmission Problem for Elastostatics.- Elastic Moment Tensor.- Full Asymptotic Expansion of the Displacement Field.- Imaging of Elastic Inclusions.- Effective Properties of Elastic Composites.- Appendices.- References.- Index
Series: CMS Books in Mathematics
2007, Approx. 510 p., 15 illus., Hardcover
ISBN: 978-0-387-72125-5
Due: September 2007
About this book
Contains recent advances and results in number theory
Collects papers never before published in book form
Explains the Riemann Hypothesis to someone without a background in complex analysis
Collecting papers never before published in book form, this volume presents an analysis of the Riemann Hypothesis as well as connected problems. It also supplies a generous helping of the body of theory developed towards the problem’s solution. In addition, the work contains recent advances and results in number theory. Almost all the material here is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics, as the book explains the Riemann Hypothesis in terms suitable for someone without a background in complex analysis.
The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the “expert witnesses” whose insight into this field is both invaluable and irreplaceable.
Table of contents
Why This Book.- Analytic Preliminaries.- Extensions of the Riemann Hypothesis.- Equivalent Statements.- Empirical Evidence.- Assuming the Riemann Hypothesis.- Failed Attempts at Proof.- Opinions and Quotations.- Appendix A: Formulae.- Appendix B: Algorithms for Calculating \zeta (s).- Appendix C: Timeline.- Appendix D: Original Papers.- References.- Index.-
Series: Springer Series in Statistics
2007, Approx. 320 p., Hardcover
ISBN: 978-0-387-71886-6
Due: October 2007
About this book
With the development of modeling techniques, it has been required to construct model selection criteria, relaxing the assumptions imposed AIC and BIC.
The Akaike information criterion (AIC) derived as an estimator of the Kullback-Leibler information discrepancy provides a useful tool for evaluating statistical models, and numerous successful applications of the AIC have been reported in various fields of natural sciences, social sciences and engineering.
One of the main objectives of this book is to provide comprehensive explanations of the concepts and derivations of the AIC and related criteria, including Schwarz’s Bayesian information criterion (BIC), together with a wide range of practical examples of model selection and evaluation criteria. A secondary objective is to provide a theoretical basis for the analysis and extension of information criteria via a statistical functional approach. A generalized information criterion (GIC) and a bootstrap information criterion are presented, which provide unified tools for modeling and model evaluation for a diverse range of models, including various types of nonlinear models and model estimation procedures such as robust estimation, the maximum penalized likelihood method and a Bayesian approach.
Sadanori Konishi is Professor of Faculty of Mathematics at Kyushu University. His primary research interests are in multivariate analysis, statistical learning, pattern recognition and nonlinear statistical modeling. He is the editor of the Bulletin of Informatics and Cybernetics and is co-author of several Japanese books. He was awarded the Japan Statistical Society Prize in 2004 and is a Fellow of the American Statistical Association.
Genshiro Kitagawa is Director-General of the Institute of Statistical Mathematics and Professor of Statistical Science at the Graduate University for Advanced Study. His primary interests are in time series analysis, non-Gaussian nonlinear filtering and statistical modeling. He is the executive editor of the Annals of the Institute of Statistical Mathematics, co-author of Smoothing Priors Analysis of Time Series, Akaike Information Criterion Statistics, and several Japanese books. He was awarded the Japan Statistical Society Prize in 1997 and Ishikawa Prize in 1999, and is a Fellow of the American Statistical Association.
Table of contents
Concept of statistical modeling.- Statistical models.- Information criterion.- Statistical modeling by AIC.- Generalized information criterion GIC.- Statistical modeling by GIC.- Theoretical development and asymptotic properties of the GIC.- Bootstrap information criterion.- Bayesian information criteria.- Various model evaluation criteria.