Paradigms of Combinatorial Optimization. Problems and New Approaches

A gentle introduction to the geometry of convex sets in n-dimensional space Geometry of Convex Sets begins with basic definitions of the concepts of vector 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 introduce the notion of distance in order to discuss 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 interesting. 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 Coverage of 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 of 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 convex geometry, the book is also appropriate for teachers who would like to convey a better understanding and appreciation of the field to students. I. E. Leonard, PhD, was a contract lecturer in the Department of Mathematical and Statistical Sciences at the University of Alberta. The author of over 15 peer-reviewed journal articles, he is a technical editor for the Canadian Applied Mathematical Quarterly journal. J. E. Lewis, PhD, is Professor Emeritus in the Department of Mathematical Sciences at the University of Alberta. He was the recipient of the Faculty of Science Award for Excellence in Teaching in 2004 as well as the PIMS Education Prize in 2002.

Praise for the First Edition “…extremely well written…a comprehensive and up-to-date overview of this important field.” – Journal of Environmental Quality Exploration and Analysis of DNA Microarray and Other High-Dimensional Data, Second Edition provides comprehensive coverage of recent advancements in microarray data analysis. A cutting-edge guide, the Second Edition demonstrates various methodologies for analyzing data in biomedical research and offers an overview of the modern techniques used in microarray technology to study patterns of gene activity. The new edition answers the need for an efficient outline of all phases of this revolutionary analytical technique, from preprocessing to the analysis stage. Utilizing research and experience from highly-qualified authors in fields of data analysis, Exploration and Analysis of DNA Microarray and Other High-Dimensional Data, Second Edition features: A new chapter on the interpretation of findings that includes a discussion of signatures and material on gene set analysis, including network analysis New topics of coverage including ABC clustering, biclustering, partial least squares, penalized methods, ensemble methods, and enriched ensemble methods Updated exercises to deepen knowledge of the presented material and provide readers with resources for further study The book is an ideal reference for scientists in biomedical and genomics research fields who analyze DNA microarrays and protein array data, as well as statisticians and bioinformatics practitioners. Exploration and Analysis of DNA Microarray and Other High-Dimensional Data, Second Edition is also a useful text for graduate-level courses on statistics, computational biology, and bioinformatics.

This book is a new edition of a title originally published in1992. No other book has been published that treats inverse spectral and inverse scattering results by using the so called Poisson summation formula and the related study of singularities. This book presents these in a closed and comprehensive form, and the exposition is based on a combination of different tools and results from dynamical systems, microlocal analysis, spectral and scattering theory. The content of the first edition is still relevant, however the new edition will include several new results established after 1992; new text will comprise about a third of the content of the new edition. The main chapters in the first edition in combination with the new chapters will provide a better and more comprehensive presentation of importance for the applications inverse results. These results are obtained by modern mathematical techniques which will be presented together in order to give the readers the opportunity to completely understand them. Moreover, some basic generic properties established by the authors after the publication of the first edition establishing the wide range of applicability of the Poison relation will be presented for first time in the new edition of the book.

Praise for the First Edition “…this book is quite inspiring, giving many practical ideas for survey research, especially for designing better questionnaires.” —International Statistical Review Reflecting modern developments in the field of survey research, the Second Edition of Design, Evaluation, and Analysis of Questionnaires for Survey Research continues to provide cutting-edge analysis of the important decisions researchers make throughout the survey design process. The new edition covers the essential methodologies and statistical tools utilized to create reliable and accurate survey questionnaires, which unveils the relationship between individual question characteristics and overall question quality. Since the First Edition, the computer program Survey Quality Prediction (SQP) has been updated to include new predictions of the quality of survey questions on the basis of analyses of Multi-Trait Multi-Method experiments. The improved program contains over 60,000 questions, with translations in most European languages. Featuring an expanded explanation of the usage and limitations of SQP 2.0, the Second Edition also includes: • New practice problems to provide readers with real-world experience in survey research and questionnaire design • A comprehensive outline of the steps for creating and testing survey questionnaires • Contemporary examples that demonstrate the many pitfalls of questionnaire design and ways to avoid similar decisions Design, Evaluation, and Analysis of Questionnaires for Survey Research, Second Edition is an excellent textbook for upper-undergraduate and graduate-level courses in methodology and research questionnaire planning, as well as an ideal resource for social scientists or survey researchers needing to design, evaluate, and analyze questionnaires. Design, Evaluation, and Analysis of Questionnaires for Survey Research, Second Edition is an excellent textbook for upper-undergraduate and graduate-level courses in methodology and research questionnaire planning, as well as an ideal resource for social scientists or survey researchers needing to design, evaluate, and analyze questionnaires.Reflecting modern developments in the field of survey research, the Second Edition ofDesign, Evaluation, and Analysis of Questionnaires for Survey Research continues toprovide cutting-edge analysis of the important decisions researchers make throughout thesurvey design process.The new edition covers the essential methodologies and statistical tools utilized to createreliable and accurate survey questionnaires, which unveils the relationship between individualquestion characteristics and overall question quality. Since the First Edition, the computerprogram Survey Quality Prediction (SQP) has

The application of Bayesian Networks (BN) or Dynamic Bayesian Networks (DBN) in dependability and risk analysis is a recent development. A large number of scientific publications show the interest in the applications of BN in this field. Unfortunately, this modeling formalism is not fully accepted in the industry. The questions facing today's engineers are focused on the validity of BN models and the resulting estimates. Indeed, a BN model is not based on a specific semantic in dependability but offers a general formalism for modeling problems under uncertainty. This book explains the principles of knowledge structuration to ensure a valid BN and DBN model and illustrate the flexibility and efficiency of these representations in dependability, risk analysis and control of multi-state systems and dynamic systems. Across five chapters, the authors present several modeling methods and industrial applications are referenced for illustration in real industrial contexts.