Series : Ergebnisse der Mathematik und ihrer Grenzgebiete. 3.
Folge / A Series of Modern Surveys in Mathematics , Vol. 48
2004, XVIII, 387 p. 25 illus., Hardcover
ISBN: 3-540-22533-1
About this book
This two volume work on Positivity in Algebraic Geometry contains
a contemporary account of a body of work in complex algebraic
geometry loosely centered around the theme of positivity. Topics
in Volume I include ample line bundles and linear series on a
projective variety, the classical theorems of Lefschetz and
Bertini and their modern outgrowths, vanishing theorems, and
local positivity. Volume II begins with a survey of positivity
for vector bundles, and moves on to a systematic development of
the theory of multiplier ideals and their applications. A good
deal of this material has not previously appeared in book form,
and substantial parts are worked out here in detail for the first
time. At least a third of the book is devoted to concrete
examples, applications, and pointers to further developments.
Volume I is more elementary than Volume II, and, for the most
part, it can be read without access to Volume II.
Table of contents
Series : Ergebnisse der Mathematik und ihrer Grenzgebiete. 3.
Folge / A Series of Modern Surveys in Mathematics , Vol. 49
2004, XVIII, 385 p. 20 illus., Hardcover
ISBN: 3-540-22534-X
About this book
This two volume work on Positivity in Algebraic Geometry contains
a contemporary account of a body of work in complex algebraic
geometry loosely centered around the theme of positivity. Topics
in Volume I include ample line bundles and linear series on a
projective variety, the classical theorems of Lefschetz and
Bertini and their modern outgrowths, vanishing theorems, and
local positivity. Volume II begins with a survey of positivity
for vector bundles, and moves on to a systematic development of
the theory of multiplier ideals and their applications. A good
deal of this material has not previously appeared in book form,
and substantial parts are worked out here in detail for the first
time. At least a third of the book is devoted to concrete
examples, applications, and pointers to further developments.
Whereas Volume I is more elementary, the present Volume II is
more at the research level and somewhat more specialized.
Table of contents
Series : Lecture Notes in Mathematics , Vol. 1851
2004, VIII, 273 p., Softcover
ISBN: 3-540-22572-2
About this book
Statistical learning theory is aimed at analyzing complex data
with necessarily approximate models. This book is intended for an
audience with a graduate background in probability theory and
statistics. It will be useful to any reader wondering why it may
be a good idea, to use as is often done in practice a notoriously
"wrong'' (i.e. over-simplified) model to predict, estimate
or classify. This point of view takes its roots in three fields:
information theory, statistical mechanics, and PAC-Bayesian
theorems. Results on the large deviations of trajectories of
Markov chains with rare transitions are also included. They are
meant to provide a better understanding of stochastic
optimization algorithms of common use in computing estimators.
The author focuses on non-asymptotic bounds of the statistical
risk, allowing one to choose adaptively between rich and
structured families of models and corresponding estimators. Two
mathematical objects pervade the book: entropy and Gibbs measures.
The goal is to show how to turn them into versatile and efficient
technical tools, that will stimulate further studies and results.
Table of contents
Series : Lecture Notes in Mathematics , Vol. 1852
2004, X, 134 p., Softcover
ISBN: 3-540-22603-6
About this book
This volume provides a self-contained introduction to some topics
in orbit equivalence theory, a branch of ergodic theory. The
first two chapters focus on hyperfiniteness and amenability.
Included here are proofs of Dye's theorem that probability
measure-preserving, ergodic actions of the integers are orbit
equivalent and of the theorem of Connes-Feldman-Weiss identifying
amenability and hyperfiniteness for non-singular equivalence
relations. The presentation here is often influenced by
descriptive set theory, and Borel and generic analogs of various
results are discussed. The final chapter is a detailed account of
Gaboriau's recent results on the theory of costs for equivalence
relations and groups and its applications to proving rigidity
theorems for actions of free groups.
Table of contents
Series : Ergebnisse der Mathematik und ihrer Grenzgebiete. 3.
Folge / A Series of Modern Surveys in Mathematics , Vol. 47
2004, XII, 483 p., Hardcover
ISBN: 3-540-22470-X
About this book
This Ergebnisse volume is aimed at a wide readership of
mathematicians and physicists, graduate students and
professionals. The main thrust of the book is to show how
algebraic geometry, Lie theory and Painleve analysis can be used
to explicitly solve integrable differential equations and
construct the algebraic tori on which they linearize; at the same
time, it is, for the student, a playing ground to applying
algebraic geometry and Lie theory. The book is meant to be
reasonably self-contained and presents numerous examples. The
latter appear throughout the text to illustrate the ideas, and
make up the core of the last part of the book. The first part of
the book contains the basic tools from Lie groups, algebraic and
differential geometry to understand the main topic.
Table of contents
Series : Springer Proceedings in Physics , Vol. 95
2004, IX, 255 p. 110 illus., Hardcover
ISBN: 3-540-20021-5
About this book
This status report features the most recent developments in the
field, spanning a wide range of topical areas in the computer
simulation of condensed matter/materials physics. Highlights of
this volume include various aspects of non-equilibrium
statistical mechanics, studies of properties of real materials
using both classical model simulations and electronic structure
calculations, and the use of computer simulation in teaching.
Table of contents
Introduction.- Fast Coarsening and Steady States in a Low-Dimensional
Driven System.- A Nonequilibrium Lattice Gas of Two-species:
Monte Carlo Investigations. - Stochastic Growth in a Small World.-
Flicker Noise in a Model of Coevolving Biological Populations.-
Physical and Computational Aspects of Density Functional Spin
Dynamics.- Multi-hole Tunneling between Charge Domains in Doped
Antiferromagnets.- Decoherence in Quantum Spin Systems.- Finite
Temperature Simulation Based on Lanczos Algorithm for Low-Dimensional
Quantum Systems.- Quantum Phase Transitions of Quasi-One-Dimensional
Heisenberg Antiferromagnets.- Quantum Computing Simulation using
the Auxiliary Field Decomposition.- Quenched Disorder
Distributions in Three-Dimensional Diluted Ferromagnets.- Weak
Universality of Spin Glasses in Three Dimensions.- Critical
Exponents of the Two Dimensional Melting.- Numerical Study of
Critical Exponents for Kosterlitz-Thouless Transition Systems.-
Critical Wetting and Interface Localization: Delocalization
Transition in a Double Wedge.- Effect of Packing Parameter on
Amphiphilic Self-Assembly.- The Droplet Evaporation/Condensation
Transition in a Finite Volume.- Configurational Bias Monte Carlo
Applied to Lipid Membranes in the Semi-grand Ensemble to Speed Up
Mixing.- Folding Polymer Chains.- Polymer Collapse in High
Dimensions: Monte Carlo Simulation of Lattice Models.- Computer
Simulation of Polymers: Physics and Methods from Specific to
Universal.- Using Simulations to Teach Statistical Physics.-
Visualization of Melting Simulations.- Network Algorithms and
Critical Manifolds in Disordered Systems.- Random Graphs as
Building Blocks for a Network Model.- Adaptive Integration Method.-
Generalized Probability-Changing Algorithm.- Lattice
Instabilities of Perovskite Oxides from First Principles.- Monte
Carlo Simulations of Metal Monoatomic Layers.- Molecular Dynamics
Simulation of Nanoindentation.
Series : Probability and its Applications
2004, Approx. 250 p. 16 illus., Hardcover
ISBN: 1-85233-868-7
About this book
A problem of broad interest - the estimation of the spectral gap
for matrices or differential operators (Markov chains or
diffusions) - is covered in this book. In particular, it studies
a subset of the general problem, taking some approaches that
have, up till now, only appeared largely in the Chinese
literature. Eigenvalues, Inequalities and Ergodic Theory serves
as an introduction to this developing field, and provides an
overview of the methods used in an accessible and concise manner.
Each chapter starts with a summary and, in order to appeal to non-specialists,
ideas are introduced through simple examples rather than
technical proofs. In the latter chapters readers are introduced
to problems and application areas, including stochastic models of
economy. Intended for researchers, graduates and postgraduates in
probability theory, Markov processes, mathematical physics and
spectrum theory, this book will be a welcome introduction to a
growing area of research.
Table of contents
Preface.- An Overview of the Book.- Optimal Markovian Couplings.-
New Variational Formulas for the First Eigenvalue.- Generalized
Cheeger's Method.- Ten Explicit Criteria in Dimension One.-
Poincare-type Inequalities in Dimension One.- Functional
Inequalities.- A Diagram of Nine Types of Ergodicity.- Reaction-Diffusion
Processes.- Stochastic Models of Economic Optimization.- Appendix
A: Some Elementary Lemmas.- Appendix B: Examples of Ising Model
on Two-Four Sites.- References.- Author Index.- Subject Index.