In collaboration with Guilherme T. Goedert and Heber Mesa
Graduate Studies in Mathematics,Volume: 212
2021; Hardcover
MSC: Primary 34; Secondary 49; 65
Print ISBN: 978-1-4704-5114-1
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincare's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time?pure and applied alike?ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques.
The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman?Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincare?Hopf index theorem.
The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.
Undergraduate and graduate students interested in differential equations and dynamical systems.
Graduate Studies in Mathematics, Volume: 217
2021; 479 pp; Hardcover
MSC: Primary 53; 58; 22; Secondary 37
Print ISBN: 978-1-4704-6430-1
This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way.
?Alan Weinstein, University of California at Berkeley
This well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study.
?Eckhard Meinrenken, University of Toronto
Graduate students and researchers interested in Poisson geometry.
Paperback ISBN: 9780128158616
Imprint: Academic Press
Published Date: 1st November 2021
Page Count: 458
Statistical Modeling using Local Gaussian Approximation extends powerful characteristics of the Gaussian distribution - perhaps the most well-known and most used distribution in statistics - to a large class of non-Gaussian and nonlinear situations through local approximation. This extension enables the reader to follow new methods in assessing dependence and conditional dependence, in estimating probability and spectral density functions, and in discrimination. Three R-packages are integrated with the text, based on local Gaussian correlation, density and conditional density estimation, and local spectral analysis. The book is of particular relevance and interest to researchers in econometrics and financial econometrics.
Reviews local dependence modeling, with applications to time series and finance markets
Introduces new techniques for density estimation, conditional density estimation, and tests of conditional independence with applications in economics
Evaluates local spectral analysis, discovering hidden frequencies in extremes and hidden phase differences
Integrates textual content with three useful R packages
Readership
Graduate students and 1st year PhD students researching problems in econometrics, statistics, financial econometrics and related areas where it is important to model statistical dependence, do density and conditional density estimation, and seek for periodicities and cycles in data
Introduction
2. Parametric, nonparametric, locally parametric
3. Dependence
4. Local Gaussian correlation and dependence
5. Local Gaussian correlation and the copula
6. Applications in finance
7. Measuring dependence and testing for independence
8. Time series dependence and spectral analysis
9. Multivariate density estimation
10. Conditional density estimation
11. The local Gaussian partial correlation
12. Regression and conditional regression quantiles
13. A local Gaussian Fisher discriminant
No. of pages: 458
Language: English
Copyright: c Academic Press 2021
Published: 1st November 2021
Imprint: Academic Press
Paperback ISBN: 9780128158616
Dag Tjostheim
Dag Tjostheim is Emeritus Professor, Department of Mathematics, University of Bergen. He has a PhD in applied mathematics from Princeton University (1974). He has authored more than 120 papers in international journals. He is a member of the Norwegian Academy of Sciences and has received several prizes for his scientific work. His main interests are in econometrics, nonlinear time series, nonparametric methods, modeling of dependence, spatial variables and fishery statistics.
Hakon Otneim
Hakon Otneim is Assistant Professor at the Norwegian School of Economics. He has a PhD in statistics from the University of Bergen (2016), and he has published papers in international journals about multivariate density estimation and conditional density estimation. His research interests include development and application of non- and semi-parametric statistics, statistical programming and data visualization.
Bard Stove
Bard Stove is Professor of Statistics at the University of Bergen. He received his PhD degree in Statistics, 2005. He was Assistant Professor at the Norwegian School of Economics (2007-11), and worked as an Actuary in a consulting firm (2005-07). He has been working on the development of nonparametric models and application of such models to areas in finance and economics. He has published several research articles in such journals as Econometric Theory and Scandinavian Journal of Statistics.
Paperback ISBN: 9780128200988
Imprint: Academic Press
Published Date: 1st November 2021
Page Count: 800
Introduction to Robust Estimating and Hypothesis Testing, Fifth Edition is a useful ‘how-to’ on the application of robust methods utilizing easy-to-use software. This trusted resource provides an overview of modern robust methods, including improved techniques for dealing with outliers, skewed distribution curvature, and heteroscedasticity that can provide substantial gains in power. Coverage includes techniques for comparing groups and measuring effect size, current methods for comparing quantiles, and expanded regression methods for both parametric and nonparametric techniques. The practical importance of these varied methods is illustrated using data from real world studies. Over 1700 R functions are included to support comprehension and practice.
Includes the latest developments in robust regression
Provides many new, improved and accessible R functions
Offers comprehensive coverage of ANOVA and ANCOVA methods
Advanced UG / graduate students in mathematics and applied courses; Researchers/Professionals; Robust Statistics, Robust Methods in Statistics
1. Introduction
2. A Foundation for Robust Methods
3. Estimating Measures of Location and Scale
4. Confidence Intervals in the One-Sample Case
5. Comparing Two Groups
6. Some Multivariate Methods
7. One-Way and Higher Designs for Independent Groups
8. Comparing Multiple Dependent Groups
9. Correlation and Tests of Independence
10. Robust Regression
11. More Regression Methods
12. ANCOVA
No. of pages: 800
Language: English
Copyright: c Academic Press 2021
Published: 1st November 2021
Imprint: Academic Press
Paperback ISBN: 9780128200988
Rand Wilcox
Rand R. Wilcox has a Ph.D. in psychometrics, and is a professor of psychology at the University of Southern California. Wilcox's main research interests are statistical methods, particularly robust methods for comparing groups and studying associations. He also collaborates with researchers in occupational therapy, gerontology, biology, education and psychology. Wilcox is an internationally recognized expert in the field of Applied Statistics and has concentrated much of his research in the area of ANOVA and Regression. Wilcox is the author of 12 books on statistics and has published many papers on robust methods. He is currently an Associate Editor for four statistics journals and has served on many editorial boards. He has given numerous invited talks and workshops on robust methods.
IRMA Lectures in Mathematics and Theoretical Physics Vol. 33
ISBN print 978-3-98547-001-3, ISBN online 978-3-98547-501-8
DOI 10.4171/IRMA/33
July 2021, 698 pages, hardcover, 16.5 x 23.5 cm.
The present volume consists of a collection of essays dedicated to Vladimir Turaev.
The essays cover the large spectrum of topics in which Turaev has been interested, including knot and link invariants, quantum representations, TQFTs, state sum constructions, geometric structures on knot complements, Kleinian groups, geometric group theory and its relationship with 3-manifolds, mapping class groups, operads, mathematical physics, Grothendieck’s program, the philosophy of mathematics, and several other topics.
At the same time, this volume will give an overview of topics that are at the forefront of current research in topology and geometry. Some of the essays are research articles and contain new results, sometimes answering questions that were raised by Turaev. The rest of the essays are surveys that will introduce the reader to some key ideas in the field.
Keywords: higher linking numbers for links in the 3-sphere, intersection of loops on surfaces, Turaev cobracket, Poincare complexes, Poincare duality, spin structures in 3-manifolds, explicit constructions of cocycles, Turaev surface, Turaev volume, skein module, quantum invariants of knots, links and 3-manifolds, 6j-symbols; Turaev?Viro invariant, Reshetikhin?Turaev invariant, TQFT, HQFT, Gauss words and links, enumeration problems in topology and group theory, generalizations of the Thurston norm, knotoids, knots, links, braids, intersections and self-intersections of loops on surfaces, cobrackets, combinatorial group theory, metric geometry, phylogenetics
EMS Textbooks in Mathematics
ISBN print 978-3-98547-010-5, ISBN online 978-3-98547-510-0
DOI 10.4171/ETB/22
August 2021, 144 pages, hardcover, 16.5 x 23.5 cm.
This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject.
The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto’s calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given.
The book is suitable for a course at the graduate level, and also includes an appendix with a series of exercises along with their solutions.
Keywords: optimal transport, Wasserstein distance, duality, gradient flows, measure theory, displacement convexity
EMS Series of Lectures in Mathematics
ISBN print 978-3-98547-008-2, ISBN online 978-3-98547-508-7
DOI 10.4171/ELM/33
August 2021, 128 pages, softcover, 17 x 24 cm.
This book presents an introduction to orthogonal polynomials, with an algebraic flavor, based on linear functionals defining the orthogonality and the Jacobi matrices associated with them. Basic properties of their zeros as well as quadrature rules are discussed. A key point is the analysis of those functionals satisfying Pearson equations (semiclassical case) and the hierarchy based on their class.
The book's structure reflects the fact that its content is based on a set of lectures delivered by one of the authors at the first Orthonet Summer School in Seville, Spain in 2016. The presentation of the material is self-contained and will be valuable to students and researchers interested in a novel approach to the study of orthogonal polynomials, focusing on their analytic properties.
Keywords: linear functionals, orthogonal polynomials, Jacobi matrices, zeros of orthogonal polynomials, Gauss quadrature formulas, spectral transformations, matrix factorization, semiclassical linear functionals, Askey scheme