Rice Fall 2006 Research Seminars in the Mathematical Sciences

The CAAM, MATH and STAT departments will offer 14 research seminars this semester.

These seminars bring

    Undergraduate, and 
    Graduate students
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 its intent.

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.

CAAM 499

MATH 499

STAT 499

Statistical Bioinformatics & Genetics: Applications in Cancer

Audience: Any undergraduate or graduate student interested in learning or wanting to participate in how statistics is applied in a biomedical setting.

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 participation.

Computational Mathematics of Curves and Surfaces

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 equations.

Introduction to P-Adic Numbers

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.

Edge Length Minimizing Polyhedra

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).

Decision Analysis

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.

Computational Finance: Co-volatility Across Markets

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.

Computational Finance: Dynamics of Electronic Markets

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, and simulation.

Continuum Mechanics and Inverse Scattering

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.

Computational Medical Image Processing

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

Geometric Computational Methods in PDE: Level Set Methods

Level set methods were introduced by Stanley Osher and James Sethian in computational 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)