Hardcover. 204 pages.
ISBN: 978-1-57146-146-9
To be published: November 2010
Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2009 at Harvard University.
Survey on the fundamental lemma
Ngo Bao Chau
The Arf-Kervaire problem in algebraic topology: an introduction
Michael A. Hill, Michael J. Hopkins, and Douglas C. Ravenel
Phase transitions, minimal surfaces, and a conjecture of de Giorgi
O. Savin
Recent developments in mathematical quantum chaos
Steve Zelditch
Hardcover. 680 pages.
ISBN: 978-1-57146-200-8
To be published: 12 November 2010
Nonconvex analysis is a rapidly developing, multi-disciplinary field of research, comprehending theoretical analysis in mathematical modelling of natural systems, bifurcation and chaos in dynamical systems, finite deformation theory, nonlinear partial differential equations, global optimization, calculus of variation, numerical methods, and scientific computations. The field of nonconvex analysis has undergone considerable development in a remarkably short time -- with extensive applications to theoretical physics, material science, modern mechanics, complex systems, and scientific computations.
The present volume, Handbook of Nonconvex Analysis and Applications, consists of thirteen chapters written by notable experts in the field, addressing essential recent developments in nonconvex analysis and its applications, and keeping a balance between major areas of theory, methods, and applications. Each chapter provides an illuminating exposition of state-of-the-art approaches to a specific topic, with discussions of the central contributions, and pointers to some basic references. A variety of topics regarding nonconvex analysis and its applications are discussed: nonconvex variational principles; comparison principles; nonlinear eigenvalue problems; critical point theory; boundary value problems; topological methods, including Morse theory; nonlinear elliptic equations; evolution problems; difference equations; inequality problems; geometric properties of functions and spaces; and applications in mechanics.
This Handbook will serve as a much-needed reference work for the dynamic and ever-growing field of nonconvex analysis and its applications.
Nonlinear difference equations through variational methods
Gabriele Bonanno and Pasquale Candito
Sub-supersolution method for multi-valued elliptic and evolution problems
Siegfried Carl and Dumitru Motreanu
Prox-regular sets and applications
Giovanni Colombo and Lionel Thibault
Multiplicity of solutions for nonlinear elliptic equations with combined nonlinearities
Leszek Gasinski and Nikolaos S. Papageorgiou
Study of some semilinear elliptic problems on Rn via variational methods
Alexandru Kristaly and Nikolaos S. Papageorgiou
Equations and inequalities in Orlicz-Sobolev spaces: Selected topics
Vy Khoi Le and Klaus Schmitt
Non-smooth critical point theory
Roberto Livrea and Salvatore Angelo Marano
Evolution hemivariational inequalities with applications
Stanislaw Migorski
Morse theory and applications to variational problems
Kanishka Perera
Quasiconvex optimization and its applications
Enkhbat Rentsen
Nonlinear eigenvalue problems
Biagio Ricceri
The method of Nehari manifold
Andrzej Szulkin and Tobias Weth
Solutions for elliptic problems with precise sign information
Zhitao Zhang
ISBN: 978-0-471-69274-4
Hardcover
624 pages
January 2011
Despite the flurry of relatively recent research activity in spatio-temporal statistics, there are no books on spatio-temporal statistical modeling that consider the modern hierarchal perspective. The state of the literature is similar to the spatial statistics literature in the late 1980's before the introduction of Cressie's STATISTICS FOR SPATIAL DATA. The authors' goal is to present an overview of traditional spatio-temporal modeling approaches as well as the modern hierarchal perspective.
ISBN: 978-0-470-54280-4
Hardcover
448 pages
March 2011
This book provides a comprehensive overview of the entire edit and imputation process for detecting and correcting errors in survey research. The authors begin with an introduction to the problem of errors and missing values in survey data and then go on to explore the methods for correcting systematic errors, identifying random errors, and error localization in numerical and categorical data. Next, an intricate discussion of selective editing outlines various mechanisms for identifying the appropriate resources for treating data errors. A basic framework for imputation is provided in the next chapter with a breakdown of key methods and models along with a comparison of imputation with the weighting approach to correct missing values. The remaining chapters delve into more advanced topics in imputation methodology as well as new developments on imputation under edit constraints and benchmarking. Each chapter organizes the presented information in uniform components, with an introduction, outline of key theory and formulae, illustration of algorithms, a concise summary of key points, and a reference section listing additional resources on the topic. This presentation solidifies the book’s goal of serving as a practical, one-stop reference on data editing and imputation.
ISBN: 978-0-470-38555-5
Hardcover
320 pages
February 2011
This new edition continues to provide a contemporary look at the nature of GLM (general linear model) analyses, describing how to implement such analyses throughout the experiment design process, from data examination to the testing of hypotheses. The book begins with a brief history of the separate development of ANOVA and regression analyses, and then goes on to demonstrate how both analyses are incorporated into the understanding of general linear models (GLM). The chapters that follow are clearly organized by the nature of the experimental design and its analyses, detailing conventional statistical concepts of ANOVA and ANOVA and interpreting them in GLM terms. The book proceeds to cover the main single- and multi-factor designs as they relate to ANOVA and ANCOVA. All chapters have been revised, as each area of coverage now concludes with discussion of tests of main effects and type 1 error issues. Furthermore, a new chapter on hierarchical models introduces the use of this technique to methods in experimental psychology. Additional topics that have been expanded upon and added include: different approaches to carrying out the simple effect analyses and pairwise comparisons (particularly with regard to related and repeated measure analyses), the power of the different approaches to the different effect analyses, optimal experimental designs, a review of Wilcox’s arguments, normality violations and their consequence for experimental analyses, and the issue of inflated Type 1 error due to multiple hypotheses testing.
September 2010
6 x 9, 344 pp., 33 illus.
(PAPER)
ISBN-13:
978-0-262-51473-6
In Discovering Complexity, William Bechtel and Robert Richardson examine two heuristics that guided the development of mechanistic models in the life sciences: decomposition and localization. Drawing on historical cases from disciplines including cell biology, cognitive neuroscience, and genetics, they identify a number of "choice points" that life scientists confront in developing mechanistic explanations and show how different choices result in divergent explanatory models. Describing decomposition as the attempt to differentiate functional and structural components of a system and localization as the assignment of responsibility for specific functions to specific structures, Bechtel and Richardson examine the usefulness of these heuristics as well as their fallibility?the sometimes false assumption underlying them that nature is significantly decomposable and hierarchically organized.
When Discovering Complexity was originally published in 1993, few philosophers of science perceived the centrality of seeking mechanisms to explain phenomena in biology, relying instead on the model of nomological explanation advanced by the logical positivists (a model Bechtel and Richardson found to be utterly inapplicable to the examples from the life sciences in their study). Since then, mechanism and mechanistic explanation have become widely discussed. In a substantive new introduction to this MIT Press edition of their book, Bechtel and Richardson examine both philosophical and scientific developments in research on mechanistic models since 1993.
William Bechtel is Professor of Philosophy at the University of California, San Diego, and a Fellow of the American Association for the Advancement of Science. He is the author of Mental Mechanisms: Philosophical Perspectives on Cognitive Neuroscience and other books.
Robert C. Richardson is Charles Phelps Taft Professor of Philosophy and a University Distinguished Research Professor at the University of Cincinnati, and a Fellow of the American Association for the Advancement of Science. He is the author of Evolutionary Psychology as Maladapted Psychology (MIT Press, 2007).