Alexander Belyaev, Michael Garland (Editor)

Geometry Processing 2007

Summary

Research in the field of geometry processing is geared towards the creation of mathematical foundations and practical algorithms for the processing of complex geometric data sets, ranging from acquisition and editing to animation, transmission, and display. As such it draws on many disciplines spanning pure and applied mathematics, computer science, and engineering. Topics presented in this book include:

* Differential geometry

* Surface reconstruction

* Shape deformation

* Meshing and parameterization

* Modeling and registration

* Surface fairing and optimization

The fifth Eurographics Symposium on Geometry Processing was held July 4 - 6, 2007 in Barcelona, Spain.

Details

ISBN: 978-1-56881-365-3
Year: 2007
Format: Paperback
Pages: 250

Edited by: Joseph Stephen Verducci, Ohio State University, Columbus, OH, Xiaotong Shen, University of Minnesota, Minneapolis, MN, and John Lafferty, Carnegie Mellon University, Pittsburgh, PA

Prediction and Discovery

Contemporary Mathematics, Volume: 443
2007; 226 pp; softcover
ISBN-10: 0-8218-4195-5
ISBN-13: 978-0-8218-4195-2

Expected publication date is October 28, 2007.

These proceedings feature some of the latest important results about machine learning based on methods originated in Computer Science and Statistics. In addition to papers discussing theoretical analysis of the performance of procedures for classification and prediction, the papers in this book cover novel versions of Support Vector Machines (SVM), Principal Component methods, Lasso prediction models, and Boosting and Clustering. Also included are applications such as multi-level spatial models for diagnosis of eye disease, hyperclique methods for identifying protein interactions, robust SVM models for detection of fraudulent banking transactions, etc.

This book should be of interest to researchers who want to learn about the various new directions that the field is taking, to graduate students who want to find a useful and exciting topic for their research or learn the latest techniques for conducting comparative studies, and to engineers and scientists who want to see examples of how to modify the basic high-dimensional methods to apply to real world applications with special conditions and constraints.

Readership

Research mathematicians interested in machine learning.

Table of Contents

• J. S. Verducci and X. Shen -- Introduction
• J. Wang, X. Shen, and W. Pan -- On transductive support vector machines
• X. Deng, M. Yuan, and A. Sudjianto -- A note on robust kernel principal component analysis
• Y. Liu, H. H. Zhang, C. Park, and J. Ahn -- The L_q support vector machine
• Y. Wu and Y. Liu -- On multicategory truncated-hinge-loss support vector machines
• A. B. Owen -- A robust hybrid of lasso and ridge regression
• Y. Kim, Y. Kim, and J. Kim -- A gradient descent algorithm for LASSO
• B. Li and P. K. Goel -- Additive regression trees and smoothing splines-predictive modeling and interpretation in data mining
• E. P. Fokoue -- Estimation of atom prevalence for optimal prediction
• C. Rudin, R. E. Schapire, and I. Daubechies -- Precise statements of convergence for AdaBoost and arc-gv
• K. Marsolo, S. Parthasarathy, M. Twa, and M. Bullimore -- Ensemble-learning by model-based spatial averaging
• H. Zou, J. Zhu, S. Rosset, and T. Hastie -- Automatic bias correction methods in semi-supervised learning
• S. Wang and J. Zhu -- Variable selection for model-based high-dimensional clustering
• W. Pan and X. Shen -- Semi-supervised learning via constraints
• M. Steinbach, P - N. Tan, H. Xiong, and V. Kumar -- Objective measures for association pattern analysis

Edited by: Ezra Miller, University of Michigan, Ann Arbor, MI, Victor Reiner, University of Minnesota, Minneapolis, MN, and Bernd Sturmfels, University of California, Berkeley, CA

Geometric Combinatorics

IAS/Park City Mathematics Series, Volume: 13
2007; 691 pp; hardcover
ISBN-10: 0-8218-3736-2
ISBN-13: 978-0-8218-3736-8
Expected publication date is November 28, 2007.

Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. Perhaps the most familiar examples are polytopes and simplicial complexes, but the subject is much broader. This volume is a compilation of expository articles at the interface between combinatorics and geometry, based on a three-week program of lectures at the Institute for Advanced Study/Park City Math Institute (IAS/PCMI) summer program on Geometric Combinatorics. The topics covered include posets, graphs, hyperplane arrangements, discrete Morse theory, and more. These objects are considered from multiple perspectives, such as in enumerative or topological contexts, or in the presence of discrete or continuous group actions.

Most of the exposition is aimed at graduate students or researchers learning the material for the first time. Many of the articles include substantial numbers of exercises, and all include numerous examples. The reader is led quickly to the state of the art and current active research by worldwide authorities on their respective subjects.

Readership

Graduate students and research mathematicians interested in combinatorics; discrete methods in geometry and topology.

Table of Contents

What is geometric combinatorics?-An overview of the graduate summer school
Bibliography

• A. Barvinok, Lattice points, polyhedra, and complexity
• S. Fomin and N. Reading, Root systems and generalized associahedra
• R. Forman, Topics in combinatorial differential topology and geometry
• M. Haiman and A. Woo, Geometry of q and q,t-analogs in combinatorial enumeration
• D. N. Kozlov, Chromatic numbers, morphism complexes, and Stiefel-Whitney characteristic classes
• R. MacPherson, Equivariant invariants and linear geometry
• R. P. Stanley, An introduction to hyperplane arrangements
• M. L. Wachs, Poset topology: Tools and applications
• G. M. Ziegler, Convex polytopes: Extremal constructions and f-vector shapes

Gilles Royer, Universite d'Orleans, France

An Initiation to Logarithmic Sobolev Inequalities

SMF/AMS Texts and Monographs, Volume: 14
2007; 119 pp; softcover
ISBN-10: 0-8218-4401-6
ISBN-13: 978-0-8218-4401-4
Expected publication date is November 24, 2007.

This book provides an introduction to logarithmic Sobolev inequalities with some important applications to mathematical statistical physics. Royer begins by gathering and reviewing the necessary background material on selfadjoint operators, semigroups, Kolmogorov diffusion processes, solutions of stochastic differential equations, and certain other related topics. There then is a chapter on log Sobolev inequalities with an application to a strong ergodicity theorem for Kolmogorov diffusion processes. The remaining two chapters consider the general setting for Gibbs measures including existence and uniqueness issues, the Ising model with real spins and the application of log Sobolev inequalities to show the stabilization of the Glauber-Langevin dynamic stochastic models for the Ising model with real spins. The exercises and complements extend the material in the main text to related areas such as Markov chains.

Readership

Advanced graduate students and researchers interested in mathematical statistical physics.

Table of Contents

• Self-adjoint operators
• Semi-groups
• Logarithmic Sobolev inequalities
• Gibbs measures
• Stabilization of the Langevin dynamic
• Appendix A
• Bibliography

Rolf Nevanlinna and Veikko Paatero

Introduction to Complex Analysis: Second Edition

AMS Chelsea Publishing
1969; 350 pp; hardcover
ISBN-10: 0-8218-4399-0
ISBN-13: 978-0-8218-4399-4
Expected publication date is November 10, 2007.

It really is a gem, both in terms of its table of contents and the level of discussion. The exercises also look very good.
--Clifford Earle, Cornell University

This book has a soul and has passion.
--William Abikoff, University of Connecticut

This classic book gives an excellent presentation of topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem. The two quotes above confirm that the book can be successfully used as a text for a class or for self-study.

Readership

Undergraduate and graduate students interested in complex analysis.

Table of Contents

• The concept of an analytic function
• General properties of rational functions
• Linear transformations
• Mapping by rational functions of second order
• The exponential function and its inverse. The general power
• The trigonometric functions
• Infinite series with complex terms
• Integration in the complex domain. Cauchy's theorem
• Cauchy's integral formula and its applications
• The residue theorem and its applications
• Harmonic functions
• Analytic continuation
• Entire functions
• Periodic functions
• The Euler Gamma-function
• The Riemann zeta-function
• The theory of conformal mapping
• Index

Edited by: Yi-Zhi Huang, Rutgers University, Piscataway, NJ,
and Kailash C Misra, North Carolina State University, Raleigh, NC

Lie Algebras, Vertex Operator Algebras and Their Applications

Contemporary Mathematics, Volume: 442
2007; 474 pp; softcover
ISBN-10: 0-8218-3986-1
ISBN-13: 978-0-8218-3986-7
Expected publication date is November 1, 2007.

The articles in this book are based on talks given at the international conference "Lie algebras, vertex operator algebras and their applications", in honor of James Lepowsky and Robert Wilson on their sixtieth birthdays, held in May of 2005 at North Carolina State University. Some of the papers in this volume give inspiring expositions on the development and status of their respective research areas. Others outline and explore the challenges as well as the future directions of research for the twenty-first century. The focus of the papers in this volume is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.

This book is useful for graduate students and researchers in mathematics and mathematical physics who want to be introduced to different areas of current research or explore the frontiers of research in the areas mentioned above.

Readership

Graduate students and research mathematicians interested in lie algebras, their representations, and generalizations.

Table of Contents

• Lie algebras and related topics
• K. Baur and N. Wallach -- A class of gradings of simple Lie algebras
• S. Berman and J. Morita -- Conjugacy results for the Lie algebra mathfrak{sl}_2 over an algebra which is a UFD
• V. Chari and A. Moura -- Kirillov-Reshetikhin modules associated to G_2
• R. Farnsteiner -- Support spaces and Auslander-Reiten components
• J. Feldvoss -- On the cohomology of modular Lie algebras
• H. Garland -- Eisenstein series on loop groups: Maass-Selberg relations 4
• A. Hoshino -- Generalized Littlewood-Richardson rule for exceptional Lie algebras E_6 and F_4
• D. Nacin -- An introduction to Q_n and its graph related quotients
• T. Nakashima -- Affine geometric crystal of type G^{(1)}_2
• F. F. Nichita and D. Parashar -- New constructions of Yang-Baxter systems
• V. Retakh, S. Serconek, and R. L. Wilson -- Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials
• A. Savage -- Geometric and combinatorial realizations of crystals of enveloping algebras
• H. Strade -- Lie algebras of small dimension Vertex (operator) algebras and related topics
• I. I. Anguelova -- Symmetric polynomials and H_D-quantum vertex algebras
• M. J. Bergvelt -- H_T-vertex algebras
• C. Calinescu -- On intertwining operators and recursions
• C. Dong and C. Jiang -- Representations of vertex operator algebras
• J. Fuchs -- On non-semisimple fusion rules and tensor categories
• K. Hubbard -- The duality between vertex operator algebras and coalgebras, modules and comodules
• J. Lepowsky -- Some developments in vertex operator algebra theory, old and new
• H. Li -- Twisted modules and quasi-modules for vertex operator algebras
• G. Mason and M. P. Tuite -- Chiral algebras and partition functions
• A. Milas -- Modular forms and almost linear dependence of graded dimensions
• M. Primc -- (k,r)-Admissible configurations and intertwining operators
• Z. Qin and W. Wang -- Hilbert schemes of points on the minimal resolution and soliton equations
• C. Schweigert, J. Fuchs, and I. Runkel -- Twining characters and Picard groups in rational conformal field theory