Progress in Probability Vol.46
Bandt, C., University of Greifswald,Germany / Graf, S.,
University ofPassau, Germany
/ Z?hle, M.,University of Jena, Germany (Ed.)
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.
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
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.
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
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
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
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
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.)
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.