Memoires de la Societe Mathematique de France Volume: 161
2019; 100 pp; Softcover
MSC: Primary 52; 53; 39; 47;
Print ISBN: 978-2-85629-905-0
The authors consider smooth isotropic immersions from the 2-dimensional torus into R2n, for n?2. When n=2 the image of such map is an immersed Lagrangian torus of R4. The authors prove that such isotropic immersions can be approximated by arbitrarily C0-close piecewise linear isotropic maps. If n?3 the piecewise linear isotropic maps can be chosen so that they are piecewise linear isotropic immersions as well.
The proofs are obtained using analogies with an infinite dimensional moment map geometry due to Donaldson. As a byproduct of these considerations, the authors introduce a numerical flow in finite dimension, whose limits provide, from an experimental perspective, many examples of piecewise linear Lagrangian tori in R4. The DMMF program, which is freely available, is based on the Euler method and shows the evolution equation of discrete surfaces in real time, as a movie.
Graduate students and research mathematicians.
Memoires de la Societe Mathematique de France Volume: 162
2019; 140 pp; Softcover
MSC: Primary 32; 58;
Print ISBN: 978-2-85629-908-1
Among the transversally elliptic operators initiated by Atiyah and Singer, Kohn's □b operator on CR manifolds with S1 action is a natural one of geometric significance for complex analysts.
The authors' first main result establishes an asymptotic expansion for the heat kernel of such an operator with values in its Fourier components, which involves a contribution in terms of a distance function from lower dimensional strata of the S1-action. The second main result computes a local index density, in terms of tangential characteristic forms, on such manifolds as Sasakian manifolds (of interest in string theory), by showing that certain non-trivial contributions from strata in the heat kernel expansion will eventually cancel out by applying Getzler's rescaling technique to off-diagonal estimates. This leads to a local result which can be thought of as a type of local index theorem on these CR manifolds.
The authors give examples of these CR manifolds, some of which arise from Brieskorn manifolds. Moreover, in some cases, the authors reinterpret Kawasaki's Hirzebruch-Riemann-Roch formula for a complex orbifold equipped with an orbifold holomorphic line bundle as an index theorem obtained by a single integral over a smooth CR manifold. They achieve this without the use of equivariant cohomology methods.
Graduate students and research mathematicians.
Published: 7 January 2020
Publisher: International Press of Boston, Inc.
Paperback
94 pages
This is the fourteenth issue (Vol. 7, No. 2, December 2019) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization.
Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education.
Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.
Published: 7 January 2020
Publisher: International Press of Boston, Inc.
Paperback
306 pages
This volume represents contributions from two conferences held in 2013. The first was a workshop at the Tsinghua Sanya International Mathematics Forum (Hainan, China) centered around three topics close to Wilfried Schmid’s recent research interests: mixed Hodge modules, the unitary dual of real reductive Lie groups, and Voronoi summation formulas for automorphic forms. The second conference, entitled Representation Theory, Automorphic Forms, and Complex Geometry, was hosted by Harvard University in honor of Prof. Schmid’s 70th birthday.
ISBN: 978-1-118-59461-2
November 2019 880 Pages
Advanced Statistics with Applications in R fills the gap between several excellent theoretical statistics textbooks and many applied statistics books where teaching reduces to using existing packages. This book looks at what is under the hood. Many statistics issues including the recent crisis with p-value are caused by misunderstanding of statistical concepts due to poor theoretical background of practitioners and applied statisticians. This book is the product of a forty-year experience in teaching of probability and statistics and their applications for solving real-life problems.
There are more than 442 examples in the book: basically every probability or statistics concept is illustrated with an example accompanied with an R code. Many examples, such as Who said π? What team is better? The fall of the Roman empire, James Bond chase problem, Black Friday shopping, Free fall equation: Aristotle or Galilei, and many others are intriguing. These examples cover biostatistics, finance, physics and engineering, text and image analysis, epidemiology, spatial statistics, sociology, etc.
Advanced Statistics with Applications in R teaches students to use theory for solving real-life problems through computations: there are about 500 R codes and 100 datasets. These data can be freely downloaded from the author's website dartmouth.edu/~eugened.
This book is suitable as a text for senior undergraduate students with major in statistics or data science or graduate students. Many researchers who apply statistics on the regular basis find explanation of many fundamental concepts from the theoretical perspective illustrated by concrete real-world applications.
ISBN: 978-1-119-54993-2 May 2020 368 Pages
Hardcover
This book provides a user-friendly and practical guide on R, with emphasis on covering a broader range of statistical methods than previous books on R. This is a “how to” book and will be of use to undergraduates and graduate students along with researchers and professionals who require a quick go-to source to help them perform essential statistical analyses and data management tasks in R. The book only assumes minimal prior knowledge of statistics, providing readers with the tools they need right now to help them understand and interpret their data analyses. This book covers univariate, bivariate, and multivariate statistical methods, as well as some nonparametric tests. It provides students with a hands-on easy-to-read manual on the wealth of applied statistics and essential R computing that they will need for their theses, dissertations, and research publications. A strength of this book is its scope of coverage of univariate through to multivariate procedures, w...
Preface
Chapter 1 Introduction to Applied Statistics
Chapter 2 Introduction to R and Computational Statistics
Chapter 3 Exploring Data with R: Essential Graphics and Visualization
Chapter 4 Means, Correlations, Counts: Drawing Inferences Using Easy-to-Implement Statistical Tests
Chapter 5 Power Analysis and Sample Size Estimation Using R
Chapter 6 Analysis of Variance: Fixed Effects, Random Effects, Mixed Models and Repeated Measures
Chapter 7 Simple and Multiple Linear Regression
Chapter 8 Logistic Regression and the Generalized Linear Model
Chapter 9 Multivariate Analysis of Variance (MANOVA) and Discriminant Analysis
Chapter 10 Principal Components Analysis
Chapter 11 Exploratory Factor Analysis
Chapter 12 Cluster Analysis
Chapter 13 Nonparametric Tests
Index