2003 Vol. A: XXXVIII, 648 S. Vol B: XXXIV, 570 S. Vol. XXXIV,
664 S. (3 volume-set, not available separately). Hardcover
3-540-44389-4
This book offers an in-depth overview of polyhedral methods and
efficient algorithms in combinatorial optimization.These methods
form a broad, coherent and powerful kernel in combinatorial
optimization, with strong links to discrete mathematics,
mathematical programming and computer science. In eight parts,
various areas are treated, each starting with an elementary
introduction to the area, with short, elegant proofs of the
principal results, and each evolving to the more advanced methods
and results, with full proofs of some of the deepest theorems in
the area. Over 4000 references to further research are given, and
historical surveys on the basic subjects are presented.
Keywords: combinatorial optimization, graph theory, integer
programming, polyhedral combinatorics, polynomial-time algorithms
Contents: Introduction.- Paths and Flows.- Bipartite Matching and
Covering.- Nonbipartite Matching and Covering.- Matroids and
Submodular Functions.- Trees, Branchings, and Connectors.-
Cliques, Stable Sets and Colouring.- Multiflows and Disjoint
Paths.- Hypergraphs.- Survey of Problems, Questions and
Conjectures.- References.- Name Index.- Subject Index.
Series: Algorithms and Combinatorics. Volume. 24
2003 XVIII, 523 pp. Hardcover
3-540-44236-7
Lattices are discrete subgroups of maximal rank in a Euclidean
space. To each such geometrical object, we can attach a canonical
sphere packing which, assuming some regularity, has a density.
The question of estimating the highest possible density of a
sphere packing in a given dimension is a fascinating and
difficult problem: the answer is known only up to dimension 3.
This book thus discusses a beautiful and central problem in
mathematics, which involves geometry, number theory, coding
theory and group theory, centering on the study of extreme
lattices, i.e. those on which the density attains a local
maximum, and on the so-called perfection property.
Written by a leader in the field, it is closely related to,
though disjoint in content from, the classic book by J.H. Conway
and N.J.A. Sloane, Sphere Packings, Lattices and Groups,
published in the same series as vol. 290.
Every chapter except the first and the last contains numerous
exercises. For simplicity those chapters involving heavy
computational methods contain only few exercises. It includes
appendices on Semi-Simple Algebras and Quaternions and Strongly
Perfect Lattices.
Keywords: Euclidean lattices, sphere packings, perfect lattices,
eutactic lattices, number theory
Contents: General Properties of Lattices.- Geometric Inequalities.-
Perfection and Eutaxy.- Root Lattices.- Lattices Related to Root
Lattices.- Low-Dimensional Perfect Lattices.- The Voronoi
Algorithm.- Hermitian Lattices.- The Configurations of Minimal
Vectors.- Extremal Properties of Families of Lattices.- Group
Actions.- Cross-Sections.- Extensions of the Voronoi Algorithm.-
Numerical Data.- Appendix 1: Semi-Simple Algebras and Quaternions.-
Appendix 2: Strongly Perfect Lattices.
Series: Grundlehren der mathematischen Wissenschaften. Volume.
327
2003 Approx. 370 p. Hardcover
0-387-95556-9
During the last decades, there has been an explosion in
computation and information technology. This development comes
with an expansion of complex observational studies and clinical
trials in a variety of fields such as medicine, biology,
epidemiology, sociology, and economics among many others, which
involve collection of large amounts of data on subjects or
organisms over time. The goal of such studies can be formulated
as estimation of a finite dimensional parameter of the population
distribution corresponding to the observed time- dependent
process. Such estimation problems arise in survival analysis,
causal inference and regression analysis. This book provides a
fundamental statistical framework for the analysis of complex
longitudinal data. It provides the first comprehensive
description of optimal estimation techniques based on time-dependent
data structures subject to informative censoring and treatment
assignment in so called semiparametric models. Semiparametric
models are particularly attractive since they allow the presence
of large unmodeled nuisance parameters. These techniques include
estimation of regression parameters in the familiar (multivariate)
generalized linear regression and multiplicative intensity models.
They go beyond standard statistical approaches by incorporating
all the observed data to allow for informative censoring, to
obtain maximal efficiency, and by developing estimators of causal
effects. It can be used to teach masters and Ph.D. students in
biostatistics and statistics and is suitable for researchers in
statistics with a strong interest in the analysis of complex
longitudinal data.
Contents: Introduction.- General Methodology.- Monotone Censored
Data.- Cross
Sectional Data and Right Censored Data Combined.- Multivariate
Right
Censored Multivariate Data.- Unified Approach for Causal
Inference and
Censored Data.
Series: Springer Series in Statistics.
2003 Approx. 295 p. 95 illus. Softcover
0-387-95585-2
Discrete mathematics is quickly becoming one of the most
important areas of mathematical research, with applications to
cryptography, linear programming, coding theory and the theory of
computing. This book is aimed at undergraduate mathematics and
computer science students interested in developing a feeling for
what mathematics is all about, where mathematics can be helpful,
and what kinds of questions mathematicians work on. The authors
discuss a number of selected results and methods of discrete
mathematics, mostly from the areas of combinatorics and graph
theory, with a little number theory, probability, and
combinatorial geometry. Wherever possible, the authors use proofs
and problem solving to help students understand the solutions to
problems. In addition, there are numerous examples, figures and
exercises spread throughout the book.
Laszlo Lovasz is a Senior Researcher in the Theory Group at
Microsoft Corporation. He is a recipient of the 1999 Wolf Prize
and the Godel Prize for the top paper in Computer Science. Jozsef
Pelikan is Professor of Mathematics in the Department of Algebra
and Number Theory at Eotvos Lorand University, Hungary. In 2002,
he was elected Chairman of the Advisory Board of the
International Mathematical Olympiad. Katalin Vesztergombi is
Senior Lecturer in the Department of Mathematics at the
University of Washington.
Contents: Preface.- Let us count!- Combinatorial tools.- Binomial
Coefficients and Pascal's Triangle.- Fibonacci numbers.-
Combinatorial probability.- Integers, divisors, and primes.-
Graphs.- Trees.- Finding the optimum.- Matchings in graphs.-
Combinatorics in geometry.- Euler's formula.- Coloring maps and
graphs.- Finite geometries, codes, Latin squares, and other
pretty creatures.- A glimpse of complexity and cryptography.-
Answers to exercises.
Series: Undergraduate Texts in Mathematics.
2003 Approx. 720 pp. Hardcover
0-387-95548-8
This book is a systematic presentation of the theory of Hankel
operators. It covers the many different areas of Hankel operators
and presents a broad range of applications, such as approximation
theory, prediction theory, and control theory. The author has
gathered the various aspects of Hankel operators and presents
their applications to other parts of analysis. This book contains
numerous recent results which have never before appeared in book
form. The author has created a useful reference tool by pulling
this material together and unifying it with a consistent
notation, in some cases even simplifying the original proofs of
theorems. Hankel Operators and their Applications will be used by
graduate students as well as by experts in analysis and operator
theory and will become the standard reference on Hankel operators.
Vladimir Peller is Professor of Mathematics at Michigan State
University. He is a leading researcher in the field of Hankel
operators and he has written over 50 papers on operator theory
and functional analysis.
Contents: An Introduction to Hankel Operators.- Vectorial Hankel
Operators.- Toeplitz Operators.- Singular Values of Hankel
Operators.- Parametrization of Solutions of the Nehari Problem.-
Hankel Operators and Schatten-von Neumann Classes.- Best
Approximation by Analytic and Meromorphic Functions.- An
Introduction to Gaussian Spaces.- 1= Regularity Conditions for
Stationary Processes.- Spectral Properties of Hankel Operators.-
Hankel Operators in Control Theory.- The Inverse Spectral Problem
for Self-Adjoint Hankel Operators.- Wiener-Hopf Factorizations
and the Recovery Problem.- Analytic Approximation of Matrix
Functions.- Hankel Operators and Similarity to a Contraction.-
Appendix I.- Appendix II.- References.- Author Index.- Subject
Index.
Series: Springer Monographs in Mathematics.
2nd ed. 2003 Approx. 360 p. 65 illus. Hardcover
0-387-95410-4
This book provides a well-written and clear introduction to the
main topics of modern numerical analysis - sequence of linear
equations, error analysis, least squares, nonlinear systems,
symmetric eigenvalue problems, three-term recursions,
interpolation and approximation, large systems and numerical
integrations. It contains a large number of examples and
exercises and many figures. This text is suitable for courses in
numerical analysis and can also form the basis for a numerical
linear algebra course.
Contents: Linear Equations.- Error Analysis.- Linear Least
Squares.- Nonlinear
Equations and Least Squares.- Symmetric Eigenvalue Problems.-
Three-
Term Recursions.- Interpolation and Approximation.- Large
Symmetric
Systems and Eigenvalue Problems.- Definite Integrals.
Series: Texts in Applied Mathematics. Volume. 43
2003 Approx, 330 p. 68 illus. Hardcover
0-387-95547-X
More mathematicians have been taking part in the development of
digital image processing as a science and the contributions are
reflected in the increasingly important role modeling has played
solving complex problems. This book is mostly concerned with
energy-based models. Through concrete image analysis problems,
the author develops consistent modeling, a know-how generally
hidden in the proposed solutions. The book is divided into three
main parts. The first two parts describe the materials necessary
to the models expressed in the third part. These materials
include splines (variational approach, regression spline, spline
in high dimension), and random fields (Markovian field,
parametric estimation, stochastic and deterministic optimization,
continuous Gaussian field). Most of these models come from
industrial projects in which the author was involved in robot
vision and radiography: tracking 3D lines, radiographic image
processing, 3D reconstruction and tomography, matching,
deformation learning. Numerous graphical illustrations accompany
the text showing the performance of the proposed models. This
book will be useful to researchers and graduate students in
applied mathematics, computer vision, and physics.
Contents: Introduction.- Non-Parametric Spline Models.-
Parametric Spline Models.-
Auto-Associative Models.- Fundamental Aspects.- Bayesian
Estimation.-
Simulation and Optimization.- Parameter Estimation.- Model-Building.-
Degradation in Imaging.- Detection of Filamentary Entities.-
Reconstruction and Projections.- Matching.- References.
Series: Applied Mathematical Sciences. Volume. 155
2003 Approx. 435 p. Hardcover
3-540-44171-9
This self-contained book by a leading topologist is devoted to
algorithmic low-dimensional topology, a branch of mathematics
that has recently been undergoing an intense development. The
book contains plenty of important fundamental material, which is
carefully presented. The book also contains some of the author's
own original contributions. For the first time ever, it gives a
full exposition of the complexity theory of 3-manifolds and a
complete proof of the solution of the homeomorphism problem for
Haken manifolds. The subject of the book is the topology of bare
3-manifolds, without geometric structures, which became
incorporated into 3-dimensional topology by the work of Thurston.
This non-geometric part of low-dimensional topology is presented
by Matveev in a truly geometric way. Although the author
emphasizes the algorithmic side of the subject, the book presents
also the background non-algorithmic contents of the subject. The
style of the book is very lively, with a lot of useful pictures,
making the book enjoyable for those who like visual topology. The
writing is clear and the proofs are careful and detailed. This
book fills a gap in the exisiting literature and will become a
standard reference for this aspect of 3-dimensional topology both
for graduate students and researchers.
Keywords: 3-manifold, algorithmic recognition, special spine,
sufficiently large manifold
Contents: 1. Simple and special polyhedra 1.1. Spines of 3-manifolds
1.2 Elementary moves on special spines 1.3 Special polyhedra
which are not spines 2. Complexity theory of 3-manifolds 2.1.
What is a complexity of a 3-manifold? 2.2 Properties of the
complexity 2.3 Closed manifolds of small complexity 3. The Turaev-Viro
invariants 3.1 The Turaev-Viro invariants 3.2 3-Manifolds having
the same Turaev-Viro invariants 4. Haken theory of normal
surfaces 4.1 Basic notion and Hakens scheme 4.2 Theory of normal
curves 4.3 Normal surfaces in triangulated 3-manifolds 4.4
Examples of algorithms based on Hakens theory 4.5 Normal surfaces
in handle decompositions 5. Algorithmic recognition of the 3-sphere
5.1 Thin position of links 5.2 Almost normal surfaces and the
Rubinstein theorem 5.3 The algorithm 6. Classification of Haken 3-manifolds
6.1 Introduction 6.2 Theorem of Waldhausen 6.3 Simple skeletons
and hierarchies 6.4 Jaco-Shalen-Johannson decomposition 6.5 The
proof of the algorithmic classification theorem 7. Computer
recognition of 3-manifolds 7.1 Simplifying moves on spines 7.2
Experimental results and conjectures 7.3 An efficient partial
recognition algorithm 8. Computer calculation of the degree of
maps between 3-manifolds 8.1 A conjecture of C. Legrand and H.
Zieschang 8.2 Boundary cycles of Seifert 3-manifolds 8.3
Algorithm for calculating the degree 8.4 Computer implementation
and results 9. Appendix 9.1 Tables of 3-manifolds up to
complexity 6 9.2 Turaev-Viro invariants of manifolds up to
complexity 6 9.3 Minimal spines of manifolds up to complexity 6 9.4
Sporadic 3-manifolds of complexity 7.
Series: Algorithms and Computation in Mathematics. Volume. 9