2003 XV, 536 p. 97 illus. Hardcover
0-387-95399-X
Applied statisticians in many fields must
frequently analyze time
to event data. While the statistical tools
presented in this book
are applicable to data from medicine, biology,
public health,
epidemiology, engineering, economics, and
demography, the focus
here is on applications of the techniques
to biology and medicine.
The analysis of survival experiments is complicated
by issues of
censoring, where an individual's life length
is known to occur
only in a certain period of time, and by
truncation, where
individuals enter the study only if they
survive a sufficient
length of time or individuals are included
in the study only if
the event has occurred by a given date. The
use of counting
process methodology has allowed for substantial
advances in the
statistical theory to account for censoring
and truncation in
survival experiments. This book makes these
complex methods more
accessible to applied researchers without
an advanced
mathematical background. The authors present
the essence of these
techniques, as well as classical techniques
not based on counting
processes, and apply them to data. Practical
suggestions for
implementing the various methods are set
off in a series of
Practical Notes at the end of each section.
Technical details of
the derivation of the techniques are sketched
in a series of
Technical Notes. This book will be useful
for investigators who
need to analyze censored or truncated life
time data, and as a
textbook for a graduate course in survival
analysis. The
prerequisite is a standard course in statistical
methodology.
Contents: Examples of Survival Data.- Basic
Quantities and Models.-
Censoring and Truncation.- Nonparametric
Estimation of Basic
Quantities for Right-Censored and Left-Truncated
Data.-
Estimation of Basic 1= Quantities for Other
Sampling Schemes.-
Topics in Univariate Estimation.- Hypothesis
Testing.-
Semiparametric Proportional Hazards Regression
with Fixed
Covariates.- Refinements of the Semiparametric
Proportional
Hazards Model.- Additive Hazards Regression
Models.- Regression
Diagnostics.- Inference for Parametric Regression
Models.-
Multivariate Survival Analysis.
Series: Statistics for Biology and Health.
2003 Approx. 560 p. 162 illus. Hardcover
0-387-00424-6
The appearance of Gruenbaum's book Convex
Polytopes in 1967 was a
moment of grace to geometers and combinatorialists.
The special
spirit of the book is very much alive even
in those chapters
where the book's immense influence made them
quickly obsolete.
Some other chapters promise beautiful unexplored
land for future
research. The appearance of the new edition
is going to be
another moment of grace. Kaibel, Klee and
Ziegler were able to
update the convex polytope saga in a clear,
accurate, lively, and
inspired way. --Gil Kalai, The Hebrew University
of Jerusalem The
original book of Gruenbaum has provided the
central reference for
work in this active area of mathematics for
the past 35 years...I
first consulted this book as a graduate student
in 1967; yet,
even today, I am surprised again and again
by what I find there.
It is an amazingly complete reference for
work on this subject up
to that time and continues to be a major
influence on research to
this day. --Louis J. Billera, Cornell University
The original
edition of Convex Polytopes inspired a whole
generation of
grateful workers in polytope theory. Without
it, it is doubtful
whether many of the subsequent advances in
the subject would have
been made. The many seeds it sowed have since
grown into healthy
trees, with vigorous branches and luxuriant
foliage. It is good
to see it in print once again. --Peter McMullen,
University
College London
Contents: * Preface * Notation and prerequisites
* Convex sets *
Polytopes * Examples * Fundamental properties
and constructions *
Polytopes with few vertices * Neighborly
polytopes * Euler's
relation * Analogues of Euler's relation
* Extremal problems
concerning numbers of faces * Properties
of boundary complexes *
k-Equivalence of polytopes * 3- Polytopes
* Angle-sums relations;
the Steiner point * Addition and decomposition
of polytopes (by G.C.
Shephard) * Diameters of Polytopes (by Victor
Klee) * Long paths
and cicuits on polytopes (by Victor Klee)
* Arrangements of
hyperplanes * Concluding remarks * Tables
* Addendum * Errata *
Bibliography * Index of terms * Index of
symbols
Series: Graduate Texts in Mathematics. Volume.
221
2003 Approx. 440 p. Hardcover
0-387-00151-4
This book introduces the notion of an E-semigroup,
a
generalization of the known concept of E_O-semigroup.
These
objects are families of endomorphisms of
a von Neumann algebra
satisfying certain natural algebraic and
continuity conditions.
This monograph will be of interest to graduate
students and
research mathematicians.
Contents: Preface * Dynamical Origins * Part
1: Index and
Perturbation Theory * E-semigroups * Continuous
Tensor Products *
Spectral C*-algebras * Part 2: Classification:
Type I Cases *
Path Spaces * Decomposable Product Systems
* Part 3:
Noncommutative Laplacians * CP-semigroups
* C*-Generators and
Dilation Theory * Index Theory for CP-Semigroups
* Bounded
Generators * Part 4: Causality and Dynamics
* Pure Perturbations
of CAR/CCR Flows * Interaction Theory * Part
5: Type III Examples
* Powers' Examples * Tsirelson-Vershik Product
Systems *
Bibliography * Index
Series: Springer Monographs in Mathematics.
2003 Approx. 575 p. 103 illus. Hardcover
0-387-95170-9
This is the first book that integrates useful
parametric and
nonparametric techniques with time series
modeling and
prediction, the two important goals of time
series analysis. A
distinct feature of this book is that it
applies many modern
nonparametric estimation and testing ideas
to time series
modeling and model identification, while
outlines many useful
ideas from more traditional time series analysis.
This will
enable readers to use modern data-analytic
techniques while
keeping in touch with traditional approaches,
and make the book
self-contained. Such a book will benefit
researchers and
practitioners in various fields such as econometricians,
meteorologists, biologists, among others
who wish to learn useful
time series methods within a short period
of time. The book also
intends to serve as a reference or text book
for graduate
students in statistics and econometrics.
Contents: Introduction.- Stationary Time
Series.- Smoothing in
Time Series.- ARMA Modeling and Forecasting.-
Parametric
Nonlinear Time Series Models.- Nonparametric
Models.- Hypothesis
Testing.- Continuous Time Models in Finance.-
Nonlinear
Prediction.
Series: Springer Series in Statistics.
2003 Approx. 480 p. 154 illus. Hardcover
0-387-95577-1
This book presents practical approaches for
the analysis of data
from gene expression microarrays. Each chapter
describes the
conceptual and methodological underpinning
for a statistical tool
and its implementation in software. Methods
cover all aspects of
statistical analysis of microarrays, from
annotation and
filtering to clustering and classification.
Chapters are written
by the developers of the software. All software
packages
described are free to academic users. The
book includes coverage
of various packages that are part of the
Bioconductor project and
several related R tools.
The materials presented cover a range of
software tools designed
for varied audiences. Some chapters describe
simple menu-driven
software in a user-friendly fashion, and
are designed to be
accessible to microarray data analysts without
formal
quantitative training. Most chapters are
directed at microarray
data analysts with master-level training
in computer science,
biostatistics or bioinformatics. A minority
of more advanced
chapters are intended for doctoral students
and researchers.
Contents: Introduction.- Visualization and
annotation of genomic
experiments.- Bioconductor R packages for
exploratory data
analysis and normalization of cDNA microarray
data.- An R package
for analyses of affymetrix oligonucleotide
arrays.- DNA-Chip
analyzer (d-Chip).- Expression Profiler.-
An S-Plus library for
the analysis of microarray data.- DRAGON
and DRAGON View: Methods
for the annotation, analysis, and visualization
of large-scale
gene expression data.- SNOMAD: User-friendly
web tools for the
standardization and normalization of microarry
data.- Microarray
analysis using the MicroArray Explorer.-
Parametric empirical
Bayes methods for microarrays.- SAM thresholding
and false
discovery rates for detecting differential
gene expression in DNA
microarrays.- Adaptive gene picking with
microarray data:
Detecting important low abundance signals.-MAANOVA:
A software
package for the analysis of spotted cDNA
microarray experiments.-
GeneClust.- POE Statistical Tools for molecular
profiling.-
Bayesian decomposition.- Cluster analysis
of gene expression
dynamics.- Relevance networks: A first step
towards finding
genetic regulatory networks within microarray
data.
Series: Statistics for Biology and Health.
2003 Approx. 330 p. 22 illus. Hardcover
0-387-00215-4
This book covers the main topics concerned
with interpolation and
approximation by polynomials. This subject
can be traced back to
the precalculus era but has enjoyed most
of its growth and
development since the end of the nineteenth
century and is still
a lively and flourishing part of mathematics.
In addition to
coverage of univariate interpolation and
approximation, the text
includes material on multivariate interpolation
and multivariate
numerical integration, a generalization of
the Bernstein
polynomials that has not previously appeared
in book form, and a
greater coverage of Peano kernel theory than
is found in most
textbooks. There are many worked examples
and each section ends
with a number of carefully selected problems
that extend the
student's understanding of the text. George
Phillips has lectured
and researched in mathematics at the University
of St. Andrews,
Scotland. His most recent book, Two Millenia
of Mathematics: From
Archimedes to Gauss (Springer 2000), received
enthusiastic
reviews in the USA, Britain and Canada. He
is well known for his
clarity of writing and his many contributions
as a researcher in
approximation theory.
Contents: * Preface * Univariate Interpolation
* Best
Approximation * Numerical Integration * Peano's
Theorem and
Applications * Multivariate Interpolation
* Splines * Bernstein
Polynomials * Properties of the q- integers
* References * Index
*
Series: CMS Books in Mathematics. Volume.
14
2003 Approx. 505 p. 49 illus. Hardcover
0-387-95535-6
The goal of this book is to explore some
of the connections
between control theory and geometric mechanics;
that is, control
theory is linked with a geometric view of
classical mechanics in
both its Lagrangian and Hamiltonian formulations
and in
particular with the theory of mechanical
systems subject to
motion constraints. The synthesis of the
topic is appropriate as
there is a particularly rich connection between
mechanics and
nonlinear control theory. The aim is to provide
a unified
treatment of nonlinear control theory and
constrained mechanical
systems that incorporates material that has
not yet made its way
into texts and monographs. This book is intended
for graduate
students who wish to learn this subject and
researchers in the
area who want to enhance their techniques.
Contents: Introduction.- Mathematical Preliminaries.-
Basic
Concepts in Mechanics.- An Introduction to
Geometric Control
Theory.- Nonholonomic Mechanics.- Controllability
and
Stabilizability for Mechanical and Nonholonomic
Systems.- Optimal
Control.- Energy Based Methods for Stability
of Nonholonomic
Systems.- Energy Based Methods for Stabilization
of Controlled
Lagrangian Systems.- Internet Supplementary
Materials.-
References.
Series: Interdisciplinary Applied Mathematics.
Volume. 24