2002. Approx. 735 pp. Hardcover
0-387-95440-6
Over the last ten years the introduction of computer intensive
statistical methods has opened new horizons concerning the
probability models that can be fitted to genetic data, the scale
of the problems that can be tackled and the nature of the
questions that can be posed. In particular, the application of
Bayesian and likelihood methods to statistical genetics has been
facilitated enormously by these methods. Techniques generally
referred to as Markov chain Monte Carlo (MCMC) have played a
major role in this process, stimulating synergies among
scientists in different fields, such as mathematicians,
probabilists, statisticians, computer scientists and statistical
geneticists. Specifically, the MCMC "revolution" has
made a deep impact in quantitative genetics. This can be seen,
for example, in the vast number of papers dealing with complex
hierarchical models and models for detection of genes affecting
quantitative or meristic traits in plants, animals and humans
that have been published recently.
This book, suitable for numerate biologists and for applied
statisticians, provides the foundations of likelihood, Bayesian
and MCMC methods in the context of genetic analysis of
quantitative traits. Most students in biology and agriculture
lack the formal background needed to learn these modern
biometrical techniques. Although a number of excellent texts in
these areas have become available in recent years, the basic
ideas and tools are typically described in a technically
demanding style, and have been written by and addressed to
professional statisticians. For this reason, considerable more
detail is offered than what may be warranted for a more
mathematically apt audience.
The book is divided into four parts. Part I gives a review of
probability and distribution theory. Parts II and III present
methods of inference and MCMC methods. Part IV discusses several
models that can be applied in quantitative genetics, primarily
from a bayesian perspective. An effort has been made to relate
biological to statistical parameters throughout, and examples are
used profusely to motivate the developments.
Contents: Probability and Random Variables.- Functions of Random
Variables.- An Introduction to Likelihood Inference.- Further
Topics in Likelihood Inference.- An Introduction to Bayesian
Inference.- Bayesian Analysis of Linear Models.- The Prior
Distribution and Bayesian Analysis.- Bayesian Assessment of
Hypotheses and Models.- Approximate Methods of Inference: The EM
Algorithm.- An Overview of Discrete Markov Chains.- Markov Chain
Monte Carlo.- Analysis of MCMC Samples.- Gaussian and Thick-tailed
Linear Models.- Analyses Involving Ordered Categorical Traits.-
Bayesian Analysis of Longitudinal Data.- Segregation and the QTL
Analysis.
Series: Statistics for Biology and Health.
2002. XI, 510 pp. Hardcover
3-540-43550-6
Graph algorithms is a well-established subject in mathematics and
computer science. Beyond classical application fields, like
approximation, combinatorial optimization, graphics, and
operations research, graph algorithms have recently attracted
increased attention from computational molecular biology and
computational chemistry. Centered around the fundamental issue of
graph isomorphism, this text goes beyond classical graph problems
of shortest paths, spanning trees, flows in networks, and
matchings in bipartite graphs. Advanced algorithmic results and
techniques of practical relevance are presented in a coherent and
consolidated way. This book introduces graph algorithms on an
intuitive basis followed by a detailed exposition in a literate
programming style, with correctness proofs as well as worst-case
analyses. Furthermore, full C++ implementations of all algorithms
presented are given using the LEDA library of efficient data
structures and algorithms. Numerous illustrations, examples, and
exercises, and a comprehensive bibliography support students and
professionals in using the book as a text and source of reference
Keywords: Graph algorithms, graph isomorphism, tree isomorphism,
computational biology, computational chemistry, literate
programming, computational graph theory, combinatorial
algorithms, algorithmic graph theory
Contents: Preface.- Part I. Introduction: 1. Introduction. 2.
Algorithmic Techniques.- Part II. Algorithms on Trees: 3. Tree
Traversal. 4. Tree Isomorphism.- Part III. Algorithms on Graphs:
5. Graph Traversal. 6. Clique, Independent Set, and Vertex Cover.
7. Graph Isomorphism; Appendices: A. An Overview of Leda. B.
Interactive Demonstration of Graph Algorithms. C. Program Modules.
- References.- Index.
2002. Approx. 515 pp. 144 figs. Hardcover
0-387-95457-0
S is a powerful environment for the statistical and graphical
analysis of data. It provides the tools to implement many
statistical ideas that have been made possible by the widespread
availability of workstations having good graphics and
computational capabilities. This book is a guide to using S
environments to perform statistical analyses and provides both an
introduction to the use of S and a course in modern statistical
methods. Implementations of S are available commercially in S-PLUS(R)
workstations and as the Open Source R for a wide range of
computer systems.
The aim of this book is to show how to use S as a powerful and
graphical data analysis system. Readers are assumed to have a
basic grounding in statistics, and so the book is intended for
would-be users of S-PLUS or R and both students and researchers
using statistics. Throughout, the emphasis is on presenting
practical problems and full analyses of real data sets. Many of
the methods discussed are state of the art approaches to topics
such as linear, nonlinear and smooth regression models, tree-based
methods, multivariate analysis, pattern recognition, survival
analysis, time series and spatial statistics. Throughout modern
techniques such as robust methods, non-parametric smoothing and
bootstrapping are used where appropriate.
This fourth edition is intended for users of S-PLUS 6.0 or R 1.5.0
or later. A substantial change from the third edition is updating
for the current versions of S-PLUS and adding coverage of R. The
introductory material has been rewritten to emphasis the import,
export and manipulation of data. Increased computational power
allows even more computer-intensive methods to be used, and
methods such as GLMMs, MARS, SOM and support vector machines are
considered.
Contents: Introduction.- Data Manipulation.- The S Language.-
Graphics.- Univariate Statistics.- Linear Statistical Models.-
Generalized Linear Models.- Non-linear and Smooth Regression.-
Tree-based Methods.- Random and Mixed Effects.- Exploratory
Multivariate Analysis.- Classification.- Survival Analysis.- Time
Series Analysis.- Spatial Statistics.- Optimization.
Series: Statistics and Computing.
2002. Approx. 200 pp. Hardcover
0-387-95460-0
In this book, Denis Serre begins by providing a clean and concise
introduction to the basic theory of matrices. He then goes on to
give many interesting applications of matrices to different
aspects of mathematics and also other areas of science and
engineering. The book mixes together algebra, analysis,
complexity theory and numerical analysis. As such, this book will
provide many scientists, not just mathematicians, with a useful
and reliable reference. It is intended for advanced undergraduate
and graduate students with either applied or theoretical goals.
This book is based on a course given by the author at the Ecole
Normale Superieure de Lyon.
Denis Serre is Professor of Mathematics at Ecole Normale
Superieure de Lyon and a former member of the Institut
Universaire de France. He is a member of numerous editorial
boards and the author of Systems of Conservation Laws (Cambridge
University Press 2000). The present book is a translation of the
original French edition, Les Matrices: Theorie et Pratique,
published by Dunod (2001).
Contents: Elementary Theory.- Square Matrices.- Matrices with
Real or Complex Entries.- Norms.- Non-negative Matrices.-
Matrices with Entries in a Principal Domain.- Jordan's Reduction.-
Exponential of a Matrix, Polar Decomposition and Classical Groups.-
Matrix Factorizations.- Iterative Methods for Linear Problems.-
Approximation of Eigenvalues.- Bibliography.- Index.- List of
Symbols.
Series: Graduate Texts in Mathematics. VOL. 216
2002. VI, 357 pp. 172 figs. Softcover
3-540-43498-4
Geometry, this very ancient field of study of mathematics,
frequently remains too little familiar to students. Michele
Audin, professor at the University of Strasbourg, has written a
book allowing them to remedy this situation and, starting from
linear algebra, extend their knowledge of affine, Euclidean and
projective geometry, conic sections and quadrics, curves and
surfaces.
It includes many nice theorems like the nine-point circle,
Feuerbach's theorem, and so on. Everything is presented clearly
and rigourously. Each property is proved, examples and exercises
illustrate the course content perfectly. Precise hints for most
of the exercises are provided at the end of the book. This very
comprehensive text is addressed to students at upper
undergraduate and Master's level to discover geometry and deepen
their knowledge and understanding.
Keywords: Euclidean geometry, projective geometry, conics,
quadrics, differential geometry 51XX, 53XX
Contents: Introduction.- Affine geometry.- Euclidean geometry,
generalities.- Euclidean geometry in the plane.- Euclidean
geometry in space.- Projective geometry.- Conics and quadrics.-
Curves, envelopes, evolutes.- Surfaces in the dimension-3 space.-
A few hints and solutions to exercises.- Bibliography.- Index
Series: Universitext.
2002. Approx. 340 pp. 2 figs. Hardcover
0-387-98760-6
This book is a modern introduction to model theory which stresses
applications to algebra throughout the text. The first half of
the book includes classical material on model construction
techniques, type spaces, prime models, saturated models,
countable models, and indiscernibles and their applications. The
author also includes an introduction to stability theory
beginning with Morley's Categoricity Theorem and concentrating on
omega-stable theories. One significant aspect of this text is the
inclusion of chapters on important topics not covered in other
introductory texts, such as omega-stable groups and the geometry
of strongly minimal sets. The author then goes on to illustrate
how these ingredients are used in Hrushovski's applications to
diophantine geometry.
David Marker is Professor of Mathematics at the University of
Illinois at Chicago. His main area of research involves
mathematical logic and model theory, and their applications to
algebra and geometry. This book was developed from a series of
lectures given by the author at the Mathematical Sciences
Research Institute in 1998.
Contents: Part A: Structures and Theories. Basics. Algebraic
Examples.- Part B: Realizing and Omitting types. Indiscernibles.-
Part C: Categoricity. Omega-stable groups. Geometry of Strongly
Minimal Sets.- Appendices.
Series: Graduate Texts in Mathematics. VOL. 217
2002. XXVI, 838 pp. Hardcover
3-540-43416-X
The target audience of this book is students and researchers in
computational sciences who need to develop computer codes for
solving partial differential equations. The exposition is focused
on numerics and software related to mathematical models in solid
and fluid mechanics. The book teaches finite element methods, and
basic finite difference methods from a computational point of
view. The main emphasis regards development of flexible computer
programs, using the numerical library Diffpack. The application
of Diffpack is explained in detail for problems including model
equations in applied mathematics, heat transfer, elasticity, and
viscous fluid flow. Diffpack is a modern software development
environment based on C++ and object-oriented programming. All the
program examples, as well as a test version of Diffpack, are
available for free over the Internet. The second edition contains
several new applications and projects, improved explanations,
correction of errors, and is up to date with Diffpack version 4.0.
Keywords: Diffpack, partial differential equations, computation,
programming
Series: Texts in Computational Science and Engineering. VOL. 1