Progress in Probability Vol.46

Bandt, C., University of Greifswald,Germany / Graf, S., University ofPassau, Germany
/ Z?hle, M.,University of Jena, Germany (Ed.)

Fractal Geometry andStochastics II

1999. Approx. 296 pages. Hardcover
ISBN 3-7643-6215-4
Due in December 1999

The combination of fractal geometry and stochastic methods can be used to
create convincing models in many different areas of science such as
biology, chemistry, computer science, mathematics and physics. The present
book deals with the mathematical theory needed for this purpose.

It contains contributions by outstanding mathematicians and is meant to highlight the
principal directions of research in the field. The contributors were the main speakers at
the conference "Fractal Geometry and Stochastics II" held at Greifswald/Koserow,Germany, in August 1998.

The book is addressed to mathematicians andscientists who are interested in any of the following topics:

fractal dimensions
fractal measures and multifractals
self-similar and self-affine fractals
random fractals
stable processes
ergodic theory and dynamical systems
harmonic analysis and stochastic processeson fractals

The readers will be introduced to the most recent results and problems on these subjects
and also be treated to an overview of their historical development. Both researchers and
graduate students will benefit from the clear expositions.


ISBN: 0123797772


Computer Vision and Applications, Concise Edition


Cover: CaseBound
Published: February 2000


GENERAL DESCRIPTION

Based on the highly successful 3-volume reference Handbook of Computer Vision and Applications, this concise edition covers in a single volume the entire spectrum of computer vision ranging form the imaging process to high-end algorithms and applications. This book consists of three parts, including an application gallery, and is
accompanied by an interactive CD-ROM.

KEY FEATURES

Bridges the gap between theory and practical applications Covers modern concepts in computer vision as well as modern developments in imaging sensor technology
Presents a unique interdisciplinary approach covering different areas of modern science
An accompanying CD-ROM provides full text with hyperlinks for quick searching and browsing along with reference material, interactive software components, code examples, image material, full color figures, and references to Internet sources.

CONTENTS:

Radiation and Illumination, Imaging Optics, Radiometry of Imaging, Solid-State Image Sensing, Geometric Calibration of Digital Imaging Systems, Three-Dimensional Imaging
Techniques, Representation of Multidimensional Signals, Neighborhood Operators, Motion, Three-Dimensional Imaging Algorithms, Design of Nonlinear Diffusion Filters,
Variational Methods for Adaptive Smoothing and Segmentation, Morphological Operators, Probabilistic Modeling in Computer Vision, Fuzzy Image Processing, Neural Net
Computing for Image Processing, Applications Gallery



ISBN: 0123042607

Language and the Brain


Author: GRODZINSKY

Cover: CaseBound
Published: January 2000

Representation and Processing

Edited by Yosef Grodzinsky Tel Aviv University, Israel Lew Shapiro San Diego State University, San Diego, California David Swinney University of California, San Diego, California

GENERAL DESCRIPTION

The study of language has increasingly become an area of interdisciplinary interest. Not only is it studied by speech specialists and linguists, but by psychologists and
neuroscientists as well, particularly in understanding how the brain processes meaning. This book is a comprehensive look at sentence processing as it pertains to the
brain, with contributions from individuals in a wide array of backgrounds, covering everything from language acquisition to lexical and syntactic processing, speech
pathology, memory, neuropsychology, and brain imaging.


Bohning; Dankmar

Computer Assisted Analysis of Mixtures

Description

Review recent developments in the area of computer assisted analysis of mixture distributions. Beside developments in theory and algorithms, Computer Assisted
Analysis of Mixtures focuses on developments in biometric applications, such as meta-analysis, disease mapping, fertility studies, estimation of prevalence under
clustering, and estimation of the distribution of survival time under interval-censoring.
The approach is nonparametric for the mixing distribution, including leaving the number of components of the mixing distribution unknown.

Audience

Pharmacology Statisticians / Epidemiologists /Social Scientists

Contents

Introduction
Population Heterogeneity
The Natural Genesis of Mixture Models
Some Examples
Parametric or Nonparametric Mixture Models
Classification Using Posterior Bayes
Connection to Empirical Bayes Estimation
Theory of Nonparametric Mixture Models
The Likelihood and its Properties
The Directional Derivative and the Gradient Function
The General Mixture Maximum Likelihood Theorem
Applications of the Theorem
Algorithms
Vertex Direction Method
Vertex Exchange Method
Step-Length Choices
C.A. MAN
The EM Algorithm for the Fixed Component Case
The Likelihood Ratio Test for the Number of Components
The Problem
Some Analytical Solutions
Simulation and Bootstrap Solutions
C.A.MAN-Application: Meta-Analysis
Conventional Approach
Heterogeneity
C.A.MAN Solution for Modeling Heterogeneity
Classification of Studies Using Posterior Bayes
Moment Estimators of the Variance of Mixing Distribution
The DerSimonian-Laird Estimator
The Bohning-Sarol Estimator
Estimation of Binomia- or Poisson Rate Under Heterogeneity
C.A. MAN-Application: Disease Mapping
Conventional Approach I: Mapping Percentiles
Conventional Approach II: Mapping P-Values
Estimating Map Heterogeneity
Classification Based on Posterior Bayes
Other C.A. MAN Applications
Fertility Studies
Modeling the Diagnostic Situation
Interval-Censored Survival Data

ISBN: 1584881798
Publication Date: 11/24/99

 


Ivanoff; B G / Merzbach; Ely

Set Indexed Martingales

Description

Set Indexed Martingales offers a unique, comprehensive development of a general theory of martingales indexed by a family of sets. The authors establish-for the first time-an appropriate framework that provides a suitable structure for a theory of martingales with enough generality to include many interesting examples.
Developed from first principles, the theory brings together the theories of martingales with a directed index set and set-indexed stochastic processes. Part One presents several classical concepts extended to this setting, including: stopping, predictability, Doob-Meyer decompositions, martingale characterizations of the set-indexed Poisson process, and Brownian motion. Part Two addresses convergence of sequences of set-indexed processes and introduces functional convergence for processes whose sample paths live in a Skorokhod-type space and semi-functional convergence for processes whose sample paths may be badly behaved. Completely self-contained, the theoretical aspects of this work are rich and promising. With its many important applications-especially in the theory of spatial
statistics and in stochastic geometry- Set Indexed Martingales will undoubtedly generate great interest and inspire further research and development of the theory and applications.

Contents

Introduction
General Theory
Generalities. Predictability. Martingales. Decompositions and Quadratic Variation
Martingale Characterizations. Generalizations of Martingales
Weak Convergence.
Weak Convergence of Set-Indexed Processes
Limit Theorems for Point Processes
Martingale Central Limit Theorems
References
Index.

Features

+ Offers a unique, self-contained development of the theory of set-indexed martingales
+ Leads readers from first principles to fundamental results and through to applications
+ Includes numerous examples throughout the book to illustrate theoretical concepts
+ Contains an extensive bibliography-to date, the most comprehensive bibliography of the subject available

ISBN: 1584880821
Publication Date: 10/27/99

 


Leonard; Tom

A Course in Categorical Data Analysis

Description

Categorical data-comprising counts of individuals, objects, or entities in different categories-emerge frequently from many areas of study, including medicine, sociology, geology, and education. They provide important statistical information that can lead to real-life conclusions and the discovery of fresh knowledge.
Therefore, the ability to manipulate, understand, and interpret categorical data becomes of interest-if not essential-to professionals and students in a broad range ofdisciplines.
Although t-tests, linear regression, and analysis of variance are useful, valid methods for analysis of measurement data, categorical data requires a different methodology and techniques typically not encountered in introductory statistics courses. Developed from long experience in teaching categorical analysis to a multidisciplinary mix of undergraduate and graduate students, A Course in Categorical Data Analysis presents the easiest, most straightforward ways of extracting real-life conclusions from contingency tables. The author uses a Fisherian approach to categorical data analysis and incorporates numerous examples and real data sets. Although he offers S-PLUS routines through the Internet, readers do not need full knowledge of a statistical software package.
In this unique text, the author chooses methods and an approach that nurtures intuitive thinking. He trains his readers to focus not on finding a model that fits the data, but on using different models that may lead to meaningful conclusions. The book offers some simple, innovative techniques not highighted in other texts that
help make the book accessible to a broad, interdisciplinary audience.
A Course in Categorical Data Analysis enables readers to quickly use its offering of tools for drawing scientific, medical, or real-life conclusions from categorical data sets.

Audience

Professionals and students in Mathematics, Statistics, Social Sciences, Economics, Medicine, Business, and Actuarial Science Researchers in these and other areas, including education, psychology, and biology

Contents

S-PLUS Routines
Sampling Distributions
Experimental Design for a Population Proportion
Further Properties of the Binomial Distribution
Estimation, Inference, and Hypothesis Testing for the Binomial Distribution
The Poisson Distributions: Its Characterizations and Properties
Estimation, Inference, and Hypothesis Testing for the Poisson Distribution
The Multinomial distribution
Sir Ronald Fisher's Conditioning Result
More general Sampling Models
Generalizing the Binomial Distribution
The Discrete Exponential Facility of Distribution
Generalizing the Multinomial Distribution
Two by Two Contingency Tables
Conditional Probability and Independence
Independence of Rows and columns
Investigating Independence, Give Observational Data
Edwards' Theorem
Log Contrasts and the Multinomial Distribution
The Log Measure of Association Test (Single Multinomial Model)
The Product Binomial
The Independent Poisson Model
Fisher's Exact Test
Power Properties of our Test Procedures
Simpson's Paradox and 23 Tables
Probability Theory
The Cornish Pixie: Irish Leprechaun Example
Interpretation of Simpson's Paradox
The Three-Directional Approach
Measure of Association Analysis for 23 Tables
Medical Example
The Madison Drug Alcohol Abuse Study
Experimental Design and Data Collection
Sensitivity and Specificity
Analysis of Results
Goodman's Full Rank Interaction Analyzed for Two Way Tables
Introductory Example
Methodological Development
Numerical Example
Methodological Developments
Business School Example
Methodological Developments
Advertising Example
Testing for Equality of Unconditional Cell Probabilities of Several r x s Tables
Analysis of Berkeley Admissions Data
Further Data Sets
Further Examples
Further Examples and Extensions
A Three-Way Table-Hypertension Obesity, and Alcohol Consumption
The Bristol Cervical Smear Data
Higher Grade Results for Eight Moray Secondary Schools
Further Data Sets
Conditional Independence Models for Two-Way Tables
Fixed Zeros and Missing Observations
Conditional Independence in Incomplete Tables
Perfectly Fitting Further Cells
Conditional Independence in Complete Tables
Further Data
Logistic Regression
Review of General Methodology
Analyzing Your Data Using S-PLUS
Analysis of Mice Exposure Data
Generalized Linear Models
A Generalized Linear Model for Poisson Data
A Generalized Linear Model for Point Processes
Analysis Using Splus
Extending Generalized Linear Models for Poisson Counts
Further Topics
Logistic Discrimination Analysis
Medical Examples
Three-Way Contingency Tables

Features

+ Details the most useful methods for extracting information and drawing meaningful conclusions from categorical data
+ Uses a direct approach from a Fisherian viewpoint
+ Encourages intuitive thinking
+ Includes simple, innovative methods not highlighted in other texts

ISBN: 1584881801
Publication Date: 11/24/99


Dafermos, C., Brown University, Providence, RI, USA

Hyberbolic Conservation Laws in Continuum Physics

2000. XVI, 443 pp. 38 figs.
3-540-64914-X

This masterly exposition of the mathematical theory of hyperbolic system laws brings out the intimate connection
with continuum thermodynamics, emphasizing issues in which the analysis may reveal something about the physics
and, in return, the underlying physical structure may direct and drive the analysis. The reader should have a
certain mathematical sophistication and be familiar with (at least) the rudiments of the qualitative theory of partial
differential equations, whereas the required notions from continuum physics are introduced from scratch. The
target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of
conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum
mechanics; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d)
analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws.

Keywords: hyperbolic conservation laws partial differential equations Thermodynamics Entropy .

Series: Grundlehren der mathematischen Wissenschaften.BD. 325


Dautray, R., Paris, France,
Lions, J.-L., College de France, Paris, France

Mathematical Analysis and Numerical Methods for Science and Technology
Volume 2: Functional and Variational Methods

ペーパー版 出来

1st. ed. 1988. 2nd printing 2000. XV, 589 pp. 20 figs.
3-540-66098-4

These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists
and both distinguished international figures - compile the mathematical knowledge required by researchers in
mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical
and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der
mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date
publication presenting the mathematical tools needed in applications of mathematics in directly implementable
form. The advent of large computers has in the meantime revolutionised methods of computation and made this
gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in
physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model
here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in
time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time
to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of
using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical
and industrial activity has been affected by these developments. Modeling by distributed systems now also
supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and
mechanics and is finding increasing use in the life sciences.

Contents: Functional Transformations.- Sobolev Spaces.- Linear Differential Operators.- Operators in Banach
Spaces and in Hilbert Spaces.- Linear Variational Problems.- Regularity.- Appendix: "Distributions".-
Bibliography.- Table of Notations.- Index.


Joyner, D., Annapolis, MD, USA (Ed.)

Coding Theory and Cryptography

From Enigma and Geheimschreiber to Quantum Theory

2000. VII, 256 pp. 39 figs.
3-540-66336-3

These are the proceedings of the Conference on Coding Theory, Cryptography, and Number Theory held at the
U.S. Naval Academy during October 25-26, 1998. This book concerns elementary and advanced aspects of
coding theory and cryptography. The coding theory contributions deal mostly with algebraic coding theory. Some
of these papers are expository, whereas others are the result of original research. The emphasis is on geometric
Goppa codes, but there is also a paper on codes arising from combinatorial constructions. There are both,
historical and mathematical papers on cryptography. Several of the contributions on cryptography describe the
work done by the British and their allies during World War II to crack the German and Japanese ciphers. Some
mathematical aspects of the Enigma rotor machine and more recent research on quantum cryptography are
described. Moreover, there are two papers concerned with the RSA cryptosystem and related number-theoretic
issues.