Fernholz, E.R., INTECH, Princeton, NJ, USA
Stochastic Portfolio Theory
2002. XIV, 177 pp. 38 figs. Hardcover
0-387-95405-8
Stochastic portfolio theory is a mathematical
methodology for
constructing stock portfolios and for analyzing
the effects
induced on the behavior of these portfolios
by changes in the
distribution of capital in the market.
Stochastic portfolio theory has both theoretical
and practical
applications: as a theoretical tool it can
be used to construct
examples of theoretical portfolios with specified
characteristics
and to determine the distributional component
of portfolio return.
On a practical level, stochastic portfolio
theory has been the
basis for strategies used for over a decade
by the institutional
equity manager INTECH, where the author has
served as chief
investment officer.
This book is an introduction to stochastic
portfolio theory for
investment professionals and for students
of mathematical finance.
Each chapter includes a number of problems
of varying levels of
difficulty and a brief summary of the principal
results of the
chapter, without proofs.
Contents: Stochastic Portfolio Theory.- Stock
Market Diversity.-
Portfolio Generating Functions.- Functions
of Ranked Market
Weights.- Stable Model for the Distribution
of Capital.- Behavior
of Functionally Generated Portfolios.- Applications
of Stochastic
Portfolio Theory.
Series: Applications of Mathematics. VOL.
48
Bialynicki-Birula, A., University of Warsaw, Poland; Carrell, J., The University
of British Columbia, Vancouver, BC, Canada;
McGovern, W.M., University of Washington,
Seattle, WA, USA
Algebraic Quotients. Torus Actions and Cohomology.
The Adjoint Representation and the Adjoint
Action
2002. V, 242 pp. Hardcover
3-540-43211-6
This is the second volume of the new subseries
"Invariant
Theory and Algebraic Transformation Groups".
The aim of the
survey by A. Bialynicki-Birula is to present
the main trends and
achievements of research in the theory of
quotients by actions of
algebraic groups. This theory contains geometric
invariant theory
with various applications to problems of
moduli theory. The
contribution by J. Carrell treats the subject
of torus actions on
algebraic varieties, giving a detailed exposition
of many of the
cohomological results one obtains from having
a torus action with
fixed points. Many examples, such as toric
varieties and flag
varieties, are discussed in detail. W.M.
McGovern studies the
actions of a semisimple Lie or algebraic
group on its Lie algebra
via the adjoint action and on itself via
conjugation. His
contribution focuses primarily on nilpotent
orbits that have
found the widest application to representation
theory in the last
thirty-five years.
Keywords: invariants, quotients, adjoint
representation,
transformation group
Series: Encyclopaedia of Mathematical Sciences.
VOL. 131
Castillo-Chavez, C., Cornell University,
Ithaca, NY, USA; Blower, S., UCLA School of
Medicine, Los Angeles, CA, USA; Driessche,
P.vande, University of Victoria, BC, Canada;
Kirschner, D., University of Michigan Medical
Scholl, Ann Arbor, MI,
Mathematical Approaches for Emerging and
Reemerging Infectious Diseases Part I: An Introduction to Models, Methods,
and Theory
2002. Approx. 390 pp. Hardcover
0-387-95354-X
This book grew out of the discussions and
presentations that
began during the Workshop on Emerging and
Reemerging Diseases (May
17-21, 1999) sponsored by the Institute for
Mathematics and its
Application (IMA) at the University of Minnesota
with the support
of NIH and NSF. The workshop started with
a two-day tutorial
session directed at ecologists, epidemiologists,
immunologists,
mathematicians, and scientists interested
in the study of disease
dynamics. The core of this first volume,
Volume 125, covers
tutorial and research contributions on the
use of dynamical
systems (deterministic discrete, delay, PDEs,
and ODEs models)
and stochastic models in disease dynamics.
The volume includes
the study of cancer, HIV, pertussis, and
tuberculosis.
Beginning graduate students in applied mathematics,
scientists in
the natural, social, or health sciences or
mathematicians who
want to enter the fields of mathematical
and theoretical
epidemiology will find this book useful.
Contents: From the contents: New directions
in the mathematics of
infectious disease.- Fred Brauer: The man
and his mathematics.-
Kenneth L. Cooke: Researcher, educator par
excellance.- Basic
ideas of mathematical epidemiology.- Extensions
of the basic
models.- New vaccination strategies for pertussis.-
Time delay in
epidemic models.- Nonlocal response in a
simple epidemiological
model.- Discrete-time S-I-S models with simple
and complex
population dynamics.- Intraspecific competition,
dispersal, and
disease dynamics in discrete-time patchy
environments.- The
impact of long-range dispersal on the rate
of spread in
population and epidemic models.- Endemicity,
persistence, and
quasi-stationarity.- On the computation of
Ro and its role in
global stability.- Nonlinear mating models
for populations with
discrete generations.- Center manifolds and
normal forms in
epidemic models.- Remarks on modeling host-viral
dynamics and
treatment.- A multiple compartment model
for the evolution of HIV-1
after highly active antiretroviral therapy.-
Modeling cancer as
an infectious disease.- Frequency dependent
risk of infection and
the spread of infectious diseases.- Long-term
dynamics and
emergence of tuberculosis.
Series: The IMA Volumes in Mathematics and
its Applications. VOL.
125
Castillo-Chavez, C., Cornell University,
Ithaca, NY, USA; Blower, S., UCLA School of
Medicine, Los Angeles, CA, USA; Driessche,
P.vande, University of Victoria, BC, Canada
(Eds.)
Mathematical Approaches for Emerging and
Reemerging Infectious Diseases Part II: Models, Methods, and Theory
2002. Approx. 390 pp. Hardcover
0-387-95355-8
This book grew out of the discussions and
presentations that
began during the Workshop on Emerging and
Reemerging Diseases (May
17-21, 1999) sponsored by the Institute for
Mathematics and its
Application (IMA) at the University of Minnesota
with the support
of NIH and NSF. The workshop started with
a two-day tutorial
session directed at ecologists, epidemiologists,
immunologists,
mathematicians, and scientists interested
in the study of disease
dynamics. The core of this second volume,
Volume 126, covers
research contributions on the use of dynamical
systems (deterministic
discrete, delay, PDEs, and ODEs models) and
stochastic models in
disease dynamics. Contributions motivated
by the study of
diseases like influenza, HIV, tuberculosis,
and macroparasitic
like schistosomiasis are also included.
This second volume requires additional mathematical
sophistication, and graduate students in
applied mathematics,
scientists in the natural, social, and health
sciences, or
mathematicians who want to enter the field
of mathematical and
theoretical epidemiology will find it useful.
The collection of
contributors includes many who have been
in the forefront of the
development of the subject.
Contents: From the contents: Maximal prevalence
and the basic
reproduction number in simple epidemics.-
The transition through
stages with arbitrary length distributions,
and applications in
epidemics.- Measles outbreaks are not chaotic.-
Epidemics among a
population of households.- Infection transmission
dynamics and
vaccination program effectiveness as a function
of vaccine
effects in individuals.- The influence of
different forms of
cross-protective immunity on the population
dynamics of
antigenetically diverse pathogens.- Dynamics
of multiple strains
of infectious agents coupled by cross-immunity.-
Virulence
evolution in macro-parasites.- Mathematical
models for
schistosomiasis with delays and multiple
definitive hosts.-
Infectious disease models with chronological
age structure and
epidemiological age structure.- Effects of
genetic heterogeneity
on HIV transmission in homosexual populations.-
Age-structured
core group model and its impact on STD dynamics.-
Global dynamics
of tuberculosis models with density dependent
demography.- Global
stability in some SEIR epidemic models.
Series: The IMA Volumes in Mathematics and
its Applications. VOL.
126
Chu, C.-H., University of London, UK;
Lau, A.T.-M., University of Alberta, Edmonton,
AB, Canada
Harmonic Functions on Groups and Fourier
Algebras
2002. VII, 100 pp. Softcover
3-540-43595-6
This research monograph introduces some new
aspects to the theory
of harmonic functions and related topics.
The authors study the
analytic algebraic structures of the space
of bounded harmonic
functions on locally compact groups and its
non-commutative
analogue, the space of harmonic functionals
on Fourier algebras.
Both spaces are shown to be the range of
a contractive projection
on a von Neumann algebra and therefore admit
Jordan algebraic
structures. This provides a natural setting
to apply recent
results from non-associative analysis, semigroups
and Fourier
algebras. Topics discussed include Poisson
representations,
Poisson spaces, quotients of Fourier algebras
and the Murray-von
Neumann classification of harmonic functionals.
Keywords: Harmonic function . Locally compact
group . Jordan
algebra . Fourier algebra . Semigroup . Mathematics
subject
classification ( 2000 ): 43A05, 43A20, 43A35
,31C05, 45E10, 22D25,
46L70, 32M15 .
Series: Lecture Notes in Mathematics. VOL.
1782
Aguilar, M.A., Universidad Nacional Autonoma de Mexico, DF, Mexico; Gitler, S., University
of Rochester, NY, USA; Prieto, C., Universidad
Nacional Autonoma de Mexico, DF, Mexico
Algebraic Topology from a Homotopical Viewpoint
2002. Approx. 595 pp. 37 figs. Hardcover
0-387-95450-3
The purpose of this book is to introduce
algebraic topology using
the novel approach of homotopy theory, an
approach with clear
applications in algebraic geometry as understood
by Lawson and
Voevodsky. This method allows the authors
to cover the material
more efficiently than the more common method
using homological
algebra. The basic concepts of homotopy theory,
such as
fibrations and cofibrations, are used to
construct singular
homology and cohomology, as well as K-theory.
Throughout the text
many other fundamental concepts are introduced,
including the
construction of the characteristic classes
of vector bundles.
Although functors appear constantly throughout
the text, no
knowledge about category theory is expected
from the reader. This
book is intended for advanced undergraduates
and graduate
students with a basic knowledge of point
set topology as well as
group theory and can be used in a two semester
course.
Marcelo Aguilar and Carlos Prieto are Professors
at the Instituto
de Matemticas, Universidad Nacional Autonoma
de Mexico, and
Samuel Gitler is a member of El Colegio Nacional
and professor at
the Centro de Investigacion y Estudios Avanzados
del IPN.
Keywords: Algebraic topology
Contents: Introduction.- Basic Concepts and
Notation.- Function
Spaces.- Connectedness and Algebraic Invariants.-
Homotopy Groups.-
Homotopy Extension and Lifting Properties.-
CW-Complexes Homology.-
Homotopy Properties of CW-Complexes.- Cohomology
Groups and
Related Topics.- Vector Bundles.- K-Theory.-
Adams Operations and
Applications.- Relations Between Cohomology
and Vector Bundles.-
Cohomology Theories and Brown Representability.-
Appendix A:
Proof of the Dold-Thom Theorem.- Appendix
B: Proof of the Bott
Periodicity Theorem.- References.- Index.-
Glossary.
Series: Universitext.