Features the significant contributions of many leading statisticians and data
scientists to contemporary health sciences
Includes a comprehensive review of statistical methods and new approaches
in health research to guide the reader in learning efficiently
Covers new developments in EHR data analysis, clinical trials, FDR, big
network analytics, applications in GWAS, graphical modeling in genomic
studies, survival analysis, and functional data analysis
Offers innovative statistical procedures, computer program, new data sets,
and novel applications in modern health research
This book brings together the voices of leading experts in the frontiers of biostatistics,
biomedicine, and the health sciences to discuss the statistical procedures, useful methods, and
novel applications in biostatistics research. It also includes discussions of potential future
directions of biomedicine and new statistical developments for health research, with the intent
of stimulating research and fostering the interactions of scholars across health research
related disciplines. Topics covered include: Health data analysis and applications to EHR data
Clinical trials, FDR, and applications in health science Big network analytics and its applications
in GWAS Survival analysis and functional data analysis Graphical modelling in genomic studies
The book will be valuable to data scientists and statisticians who are working in biomedicine
and health, other practitioners in the health sciences, and graduate students and researchers in
biostatistics and health.
Due 2021-07-30
1st ed. 2021, VIII, 392 p. 82 illus.
Hardcover
ISBN 978-3-030-72436-8
Product category : Contributed volume
Series : Emerging Topics in Statistics and Biostatistics
Statistics : Statistics for Life Sciences, Medicine, Health Sciences
Highlights the key points of the theory before discussing various properties
and structures that a model category may have
Boasts over 200 pages of examples of model categories in algebra and
topology, and everything in between, ranging over 12 themes
Features a table of curiosities highlighting a range of, sometimes unexpected,
phenomena that occur when working with model categories
This book outlines a vast array of techniques and methods regarding model categories, without
focussingon the intricacies of the proofs. Quillen model categories are a fundamental tool for
the understanding of homotopy theory. While many introductions to model categories fall back
on the same handful of canonical examples, the present book highlights a large, self-contained
collection of other examples which appear throughout the literature. In particular, it collects a
highly scattered literature into a single volume. The book is aimed at anyone who uses, or is
interested in using, model categories to study homotopy theory. It is written in such a way that
it can be used as a reference guide for those who are already experts in the field. However, it
can also be used as an introduction to the theory for novices.
Due 2021-08-19
1st ed. 2021, XI, 330 p. 2 illus.
Hardcover
ISBN 978-3-030-75034-3
Product category : Handbook
Series : Algebra and Applications
Mathematics : Category Theory, Homological Algebra
Connects a mathematical principle used in quantum mechanics to the study
of steady state solutions in galactic dynamics
Presents a novel result in great detail
Includes appendices that cover necessary background material
This monograph develops an innovative approach that utilizes the Birman-Schwinger principle
from quantum mechanics to investigate stability properties of steady state solutions in galactic
dynamics. The opening chapters lay the framework for the main result through detailed
treatments of nonrelativistic galactic dynamics and the Vlasov-Poisson system, the Antonov
stability estimate, and the period function $T_1$. Then, as the main application, the BirmanSchwinger
type principle is used to characterize in which cases the gbest constanth in the
Antonov stability estimate is attained. The final two chapters consider the relation to the GuoLin
operator and invariance properties for the Vlasov-Poisson system, respectively. Several
appendices are also included that cover necessary background material, such as spherically
symmetric models, action-angle variables, relevant function spaces and operators, and some
aspects of Kato-Rellich perturbation theory. A Birman-Schwinger Principle in Galactic Dynamics
will be of interest to researchers in galactic dynamics, kinetic theory, and various aspects of
quantum mechanics, as well as those in related areas of mathematical physics and applied
mathematics.
Due 2021-07-29
1st ed. 2021, X, 175 p. 2 illus.
Hardcover
ISBN 978-3-030-75185-2
Product category : Monograph
Series : Progress in Mathematical Physics
Mathematics : Mathematical Physics
The mathematical models are motivated by practical applications
Contains a complete mathematical theory of fractional differential equations
Suitable as a postgraduate-level textbook in applied and computational
mathematics
Includes an up-to-date extensive list of references
Provides many examples and exercises
This graduate textbook provides a self-contained introduction to modern mathematical theory
on fractional differential equations. It addresses both ordinary and partial differential equations
with a focus on detailed solution theory, especially regularity theory under realistic
assumptions on the problem data. The text includes an extensive bibliography, applicationdriven
modeling, extensive exercises, and graphic illustrations throughout to complement its
comprehensive presentation of the field. It is recommended for graduate students and
researchers in applied and computational mathematics, particularly applied analysis, numerical
analysis and inverse problems.
Due 2021-08-02
1st ed. 2021, XII, 357 p. 32 illus., 6 illus. in color.
Hardcover
ISBN 978-3-030-76042-7
Product category : Graduate/advanced undergraduate textbook
Series : Applied Mathematical Sciences
Mathematics : Analysis
Synthesizes research from the past 40 years on rational sphere maps
Explores connections with other areas of mathematics, such as combinatorics,
optimization, and number theory
Includes several computational examples worked out in detail
This monograph systematically explores the theory of rational maps between spheres in
complex Euclidean spaces and its connections to other areas of mathematics. Synthesizing
research from the last forty years, the author aims for accessibility by balancing abstract
concepts with concrete examples. Numerous computations are worked out in detail, and more
than 100 optional exercises are provided throughout for readers wishing to better understand
challenging material. The text begins by presenting core concepts in complex analysis and a
wide variety of results about rational sphere maps. The subsequent chapters discuss
combinatorial and optimization results about monomial sphere maps, groups associated with
rational sphere maps, relevant complex and CR geometry, and some geometric properties of
rational sphere maps. Fifteen open problems appear in the final chapter, with references
provided to appropriate parts of the text. These problems will encourage readers to apply the
material to future research. Rational Sphere Maps will be of interest to researchers and
graduate students studying several complex variables and CR geometry. Mathematicians from
other areas, such as number theory, optimization, and combinatorics, will also find the material
appealing.
Due 2021-08-10
1st ed. 2021, X, 191 p.
Hardcover
ISBN 978-3-030-75808-0
Product category : Monograph
Series : Progress in Mathematics
Mathematics : Several Complex Variables and Analytic Spaces
Presents the latest results on inference in multivariate, multilinear and mixed
linear models
Features review contributions by experts in the field
Provides an extensive bibliography of related publications
This book presents the latest findings on statistical inference in multivariate, multilinear and
mixed linear models, providing a holistic presentation of the subject. It contains pioneering and
carefully selected review contributions by experts in the field and guides the reader through
topics related to estimation and testing of multivariate and mixed linear model parameters.
Starting with the theory of multivariate distributions, covering identification and testing of
covariance structures and means under various multivariate models, it goes on to discuss
estimation in mixed linear models and their transformations. The results presented originate
from the work of the research group Multivariate and Mixed Linear Models and their meetings
held at the Mathematical Research and Conference Center in Bdlewo, Poland, over the last 10
years. Featuring an extensive bibliography of related publications, the book is intended for PhD
students and researchers in modern statistical science who are interested in multivariate and
mixed linear models
Due 2021-09-02
1st ed. 2021, XVIII, 358 p. 47 illus., 30 illus. in color.
Hardcover
ISBN 978-3-030-75493-8
Product category : Contributed volume
Series : Contributions to Statistics
Statistics : Statistical Theory and Methods
https://doi.org/10.1142/12135 | October 2021
Pages: 370
ISBN: 978-981-123-134-6 (hardcover)
The book introduces classical inequalities in vector and functional spaces with applications to probability. It develops new analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales, to transformed Brownian motions and diffusions, to Markov and point processes, renewal, branching and shock processes.
In this third edition, the inequalities for martingales are presented in two chapters for discrete and time-continuous local martingales with new results for the bound of the norms of a martingale by the norms of the predictable processes of its quadratic variations, for the norms of their supremum and their p-variations. More inequalities are also covered for the tail probabilities of Gaussian processes and for spatial processes.
This book is well-suited for undergraduate and graduate students as well as researchers in theoretical and applied mathematics.
Preliminaries
Inequalities for Means and Integrals
Analytic Inequalities
Inequalities for Discrete Martingales
Inequalities for Time-Continuous Martingales
Stochastic Calculus
Functional Inequalities
Markov Processes
Inequalities for Processes
Inequalities in Complex Spaces
Appendix
Advanced undergraduate and graduate students as well as researchers in probability and integration theory. The book may be used for courses in analysis and integration theory for undergraduate students, and stochastic processes for graduate students.