Series: Springer Monographs in Mathematics
1st Edition., 2011, V, 315 p. 30 illus. With online files/update., Hardcover
ISBN: 978-4-431-53912-4
Due: January 13, 2011
This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy holonomic system of linear difference equations with respect to the exponents. These are basically deduced from Grothendieck-Delignefs rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhofffs classical theory on analytic difference equations on the other.
1 Introduction: the Euler-Gauss Hypergeometric Function.- 2 Representation of Complex Integrals and Twisted de Rham Cohomologies.- 3 Hypergeometric functions over Grassmannians.- 4 Holonomic Difference Equations and Asymptotic Expansion References Index.
Series: Springer Texts in Statistics
1st Edition., 2011, XX, 638 p., Hardcover
ISBN: 978-1-4419-7786-1
Due: December 29, 2010
Examples using financial markets and economic data illustrate important concepts
R Labs with real-data exercises give students practice in data analysis
Integration of graphical and analytic methods for model selection and model checking quantify
Helps mitigate risks due to modeling errors and uncertainty
Financial engineers have access to enormous quantities of data but need powerful methods for extracting quantitative information, particularly about volatility and risks. Key features of this textbook are: illustration of concepts with financial markets and economic data, R Labs with real-data exercises, and integration of graphical and analytic methods for modeling and diagnosing modeling errors. Despite some overlap with the author's undergraduate textbook Statistics and Finance: An Introduction, this book differs from that earlier volume in several important aspects: it is graduate-level; computations and graphics are done in R; and many advanced topics are covered, for example, multivariate distributions, copulas, Bayesian computations, VaR and expected shortfall, and cointegration. The prerequisites are basic statistics and probability, matrices and linear algebra, and calculus. Some exposure to finance is helpful.
David Ruppert is Andrew Schultz, Jr., Professor of Engineering and Professor of Statistical Science, School of Operations Research and Information Engineering, Cornell University, where he teaches statistics and financial engineering and is a member of the Program in Financial Engineering. His research areas include asymptotic theory, semiparametric regression, functional data analysis, biostatistics, model calibration, measurement error, and astrostatistics. Professor Ruppert received his PhD in Statistics at Michigan State University. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics and won the Wilcoxon prize. He is Editor of the Electronic Journal of Statistics, former Editor of the Institute of Mathematical Statistics's Lecture Notes--Monographs Series, and former Associate Editor of several major statistics journals. Professor Ruppert has published over 100 scientific papers and four books: Transformation and Weighting in Regression, Measurement Error in Nonlinear Models, Semiparametric Regression, and Statistics and Finance: An Introduction.
Introduction.- Returns.- Fixed income securities.- Exploratory data analysis.- Modeling univariate distributions.- Resampling.- Multivariate statistical models.- Copulas.- Time series models: basics.- Time series models: further topics.- Portfolio theory.- Regression: basics.- Regression: troubleshooting.- Regression: advanced topics.- Cointegration.- The capital asset pricing model.- Factor models and principal components.- GARCH models.- Risk management.- Bayesian data analysis and MCMC.- Nonparametric regression and splines.
Series: Advanced Courses in Mathematics - CRM Barcelona
1st Edition., 2011, X, 186 p., Softcover
ISBN: 978-3-0348-0051-8
Due: December 2010
This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods.
Moerdijkfs lectures offer a detailed introduction to dendroidal sets, which were introduced by himself and Weiss as a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it also reveals new phenomena. For example, dendroidal sets admit a closed symmetric monoidal structure related to the Boardman?Vogt tensor product of operads. The lecture notes start with the combinatorics of trees and culminate with a suitable model structure on the category of dendroidal sets. Important concepts are illustrated with pictures and examples.
The lecture series by Toen presents derived algebraic geometry. While classical algebraic geometry studies functors from the category of commutative rings to the category of sets, derived algebraic geometry is concerned with functors from simplicial commutative rings (to allow derived tensor products) to simplicial sets (to allow derived quotients). The central objects are derived (higher) stacks, which are functors satisfying a certain up-to-homotopy descent condition. These lectures provide a concise and focused introduction to this vast subject, glossing over many of the technicalities that make the subjectfs research literature so overwhelming.
Both sets of lectures assume a working knowledge of model categories in the sense of Quillen. For Toenfs lectures, some background in algebraic geometry is also necessary.
Part I: Lectures on Dendroidal Sets 1. Operads 2. Trees as operads 3. Dendroidal sets 4. Tensor product of dendroidal sets 5. A Reedy model structure on dendroidal spaces 6. The Boardman-Vogt resolution and homotopy coherent nerve 7. Inner Kan complexes and normal dendroidal sets 8. Model structures on dendroidal sets Part II: Simplicial Presheaves and Derived Algebraic Geometry 1. Motivation and objectives 2. Simplicial presheaves as stacks 3. Algebraic stacks 4. Simplicial commutative algebras 5. Derived stacks and derived algebraic stacks 6. Examples of derived algebraic stacks.
Series: Applied Mathematical Sciences, Vol. 175
1st Edition., 2011, 171 p. 38 illus., 12 in color., Hardcover
ISBN: 978-3-642-16728-7
Due: January 2011
Complex optimization problems abound in the real world. In the face of these challenges, established methods often fall short of providing solutions. However, eexactf and eheuristicf techniques are dramatically enhancing our ability to solve significant practical problems in the world of optimization. They are changing the landscape in the field, broadening the frontiers of the possible, and allowing us to engage effectively with a whole new range of challenges. This monograph sets out state-of-the-art optimization methods for tackling the elinear ordering problemf (LOP). Whereas important applications in business, engineering and economics lie beyond the reach of methodologies that have been the focus of academic research for three decades, the fresh approaches set out in this volume provide practical solutions to the LOP. The focus on the LOP does not limit the monographfs scope and applicability, however. The exact and heuristic techniques outlined in these pages can be put to use in any number of combinatorial optimization problems. While the authors employ the LOP to illustrate cutting-edge optimization technologies, the book is also a tutorial on how to design effective and successful implementations of exact and heuristic procedures alike. The information in these pages provides readers with a toolkit that can be employed in a variety of settings. As a result, the book will be of great interest to researchers and practitioners in a number of fields, including computer science, mathematics, operations research, management science, industrial engineering, and economics. It is also suitable for use as a textbook on issues of practical optimization in a masters course, or as a reference book for engineering optimization algorithms. The authors have sought to make the book accessible to as wide an audience as possible by providing the reader with basic definitions and concepts in optimization. In addition, the numerous tutorials aid speedy assimilation, while the coverage given to the next generation of Flash software prepares readers for future developments.
1 Introduction.- 2 Heuristic Methods.- 3 Meta-Heuristics.- 4 Branch-and-Bound.- 5 Branch-and-Cut.- 6 The Linear Ordering Polytope.- 7 Further Aspects.- References.- Index.
Series: Operator Theory: Advances and Applications, Vol. 215
1st Edition., 2011, 290 p., Hardcover
ISBN: 978-3-0348-0071-6
Due: March 31, 2011
The extrapolation theorem of Rubio de Francia is one of the deepest results in the study of weighted norm inequalities in harmonic analysis. This book provides a comprehensive treatment of extrapolation theory. Starting from an extremely clear and simple proof of the classical result of Rubio de Francia, we show how the key ideas can be used to extend the theory to a number of contexts. Our treatment generalizes and unifies all existing results in one-weight extrapolation theory. In the two-weight case we systematically develop a new approach to extrapolation and factorization that is closely tied to existing theory of two-weight norm inequalities. We give a large number of applications that include both new results and new techniques that can be applied in other settings.
Preface.- Preliminaries.- Part I. One-Weight Extrapolation.- Chapter 1. Introduction to Norm Inequalities and Extrapolation.- Chapter 2. The Essential Theorem.- Chapter 3. Extrapolation for Muckenhoupt Bases.- Chapter 4. Extrapolation on Function Spaces.- Part II. Two-Weight Factorization and Extrapolation.- Chapter 5. Preliminary Results.- Chapter 6. Two-Weight Factorization.- Chapter 7. Two-Weight Extrapolation.- Chapter 8. Endpoint and A1 Extrapolation.- Chapter 9. Applications of Two-Weight Extrapolation.- Chapter 10. Further Applications of Two-Weight Extrapolation.- Appendix A. The Calderon-Zygmund Decomposition.- Bibliography.- Index.