Rice Fall 2006 Research Seminars in the Mathematical Sciences
The CAAM, MATH and STAT departments will offer 14 research seminars this
These seminars bring
together around a research topic of common interest.
Each ensemble is
referred to as a PFUG, pronounced fugue:
a composition in which a subject is announced by one voice and then
developed contrapuntally by each of usually two or three other voices.
In the following three sections,
STAT, MATH and
CAAM, we list
The name of the PFUG
The contact person with email address
The time and place of the PFUG's first meeting
and in some cases we link to a PFUG page or a short description of
Each seminar is offered for variable credit, and a number of the them
have spawned a 699 appendage. Query the PFUG contact person for details.
Audience: Any undergraduate or graduate student interested in learning
or wanting to participate in how statistics is applied in a biomedical
Courses: The courses, Stat 499 and 699, will introduce students to
basic genetics, cancer biology, biotechnology in cancer research,
and statistical methods applied to ongoing research problems with
Baylor College of Medicine and MD Anderson collaborators. The
format of the course will be a research style seminar in which the
first half of the term will be devoted to the biological background
and the second half to research presentations by group members.
Course credit is variable from 1-3 hours depending on level of
Matthias Heinkenschloss (faculty)
Dmitriy Leykekhman (post doc)
We study mathematical tools for the representation
and manipulation of curves and surfaces with
applications in CAD (computer aided design),
shape optimization, and solution of partial differential
Real and p-adic numbers are tools for analyzing
limits and convergence of sequences of rational numbers.
While real numbers are associated with the development of
calculus and analysis, p-adic numbers are primarily used
in number theory and algebra. This seminar will focus
on various representations of p-adic numbers and solutions
of polynomial equations with p-adic coefficients.
This PFUG focuses on Melzak's problem (also known as the "Waste
Container Problem"): finding a polyhedral region which minimizing total
edge length for a given volume. We will be cotinuing our work from the
summer analyzing restricted versions of this problem and studying this
problem from the point of view of moduli spaces (a way of mathematically
describing possible configurations and symmetries of polyhedra).
Formal decision analysis is becoming increasingly used in
medicine, business, and engineering. It involves the use of quantitative
tools to analyze the uncertainty and tradeoffs in making decisions.
Primarily, we will explore problems in experimental design and which
involves a variety of issues including Bayesian design techniques,
cost-effectiveness analysis, and optimization. Participants will learn
about a particular subject area where the methodology is applied, as well
as some of the mathematical tools. In addition, there are many
opportunities for undergraduate participation since many of the
mathematical tools are from undergraduate level courses.
We are developing new statistical tools targeting the
estimation of the correlation between financial data streams that are
observed on different time scales. Better understanding of correlation (or
covalatility) leads to proper diversification of an investment portfolio.
The efforts this past summer focused on estimation the correlation between
stocks and bonds. This fall we will focus on energy futures.
With the advancement of computer aided trading, markets
become increasingly sensitive to timing at a very fine granularity. The
goal of this PFUG is to understand and quantify the exposure of both,
traders (short term) as well as an electronic market place (long term) in
terms of returns from financial investment and market stability.
Our premise states that an informational advantage is in fact always a
temporal advantage. Eventually, information becomes available to anyone;
having it firs, however, creates an advantage. With electronic
communication becoming prevalent, information flows quicker and is more
readily available. Few models are known to explicitly incorporate
information. During this semester we focus on trading models, reviewing
existing ones and building appropriate ones, which allow us to study
temporal aspects of trading with a view on one-sided information. We will
study models from the point of view of analysis, estimation, prediction,
Inverse scattering is the art of extracting information about
mechanical or electrical structures from waves scattered from them. This
project begins with the fundamental continuum physics of waves and the
scattering process, works through the mathematical analysis of these
phenomena, and arrives at an understanding of contemporary data processing
methods, sufficiently powerful to suggest innovations and improvements. A
natural "Houston" focus is reflection seismology, the most important
method of petroleum exploration, an inverse scattering technology with
lots of local expertise and resources.
499 (section 6) - Additional topics and in-depth exploration of the issues
addressed in CAAM 436. Will likely start with an overview of the elastic
string, of possible interest to those drawn to the
Physics of Strings PFUG, then introduction to viscoacoustics and
viscoelasticity, along with extended discussion of CAAM 436 topics.
Possible additional topics are TBD according to the taste of the
participants; possibilities include the theory of elastic shells,
thermoelasticity, reacting flows, and magnetohydrodynamics.
699 (6) - Seminar on mathematics of reflection seismology. Will work
through and expand on the notes "Mathematical Foundations of Reflection
Seismology" available on the TRIP page.
We study mathematical and computational problems arising from image
processing in medical and other applications.
Faculty: Profs. Wotao Yin and Yin Zhang
Collaborator: Prof. Thomas Guerrero, M.D. Anderson
Postdoc fellow: Dr. Elaine Hale
Level set methods were introduced by Stanley Osher and James Sethian in
mathematics in the early nineties. They in turn inspired research in
pure and applied mathematics, engineering and computer science. The
topics covered including the relations between PDE, computations, and
applications will be broad enough to involve many participants from a
variety of backgrounds.
Postdoc fellow: Rolf Ryham (Math)
Faculty: Robert Hardt (Math) and Steve Cox (CAAM)