Department of Mathematics

The Florida State University

This Week in Mathematics

17-21 January 2000

Monday: 17 January 2000

Tuesday: 18 January 2000

Structural Biology/Biochemistry Seminar

Gregg Fields, Florida Atlantic University

Engineering Synthetic Proteins to Probe Tumor Cell Invasion Mechanisms

The metastatic process involves a coordinated series of tumor cell behaviors, including adhesion to and migration on extracellular matrix components and invasion of the basement membrane. Such interactions may be mediated by a great variety of cell surface biomolecules, including integrins and proteoglycans. The importance of three-dimensional interactions between these receptors with their respective ligands have been not been extensively explored. We have developed two novel strategies for creating cellular recognition sites incorporating distinct molecular architecture that more closely approximate the structure of ligands within their native proteins. Our initial studies have focused on collagen-like triple-helical structures. The first strategy utilizes a template-based approach, while the second uses the alignment of amphiphilic compounds at the lipid-solvent interface to facilitate peptide structure initiation and propagation. The resultant structures have been characterized by CD and NMR spectroscopies and found to be thermally stable over physiological temperature ranges. The synthetic triple-helical proteins were used in solution as well as attached to various substrata to determine the importance of ligand conformation in modulating cellular function. The effects of ligand three-dimensional structure on possible signal transduction pathways induced by integrin binding have been specifically evaluated. Overall, we have found that (i) a model of an isolated sequence from type IV collagen can induce integrin-mediated signal transduction in melanoma cells and (ii) ligand conformation (secondary, tertiary, and/or quarternary structure) can directly influence several integrin-mediated signal transduction events. The effects of ligand conformation suggest that a "collagen structural modulation" mechanism may exist for tumor cell invasion, whereby triple-helical collagen promotes cell binding and induction of signal transduction, subsequently leading to collagen dissolution by proteases, decreased signal transduction, and enhanced tumor cell motility.

No Algebraic Schemes Seminar, 2:00 p.m., 104 Love Building

Applied Topology Seminar, 3:35 p.m., 104 Love Building

De Witt Sumners, Javier Arsuaga and Mariel Vazquez, Florida State University

A Report on the LJIS San Diego Meeting: Quantitative Challenges in the Post-Genomic Sequence Era

Wednesday: 19 January 2000

No Graduate Student Seminar, 1:15 p.m., 204B Love Building

No (Real) Analysis Seminar, 2:30 p.m., 201 Love Building

No Complex/Symbolic Seminar, 3:35 p.m., 102 Love Building

Joint Applied Mathematics & Scientific Computing Seminar, 3:25 p.m., 104 Love Building

David Kopriva, Florida State University

Spectral Element Solution of Maxwell's Equations

Thursday: 20 January 2000

No Algebraic Curves Seminar, 2:00 p.m., 104 Love Building

No QUANTUM! Seminar, 3:35 p.m., 104 Love Building

Friday: 21 January 2000

No Colloquium Coffee, 3:00 p.m., 204 Love Building
No Colloquium, 3:30 p.m., 101 Love Building

Coming Attractions

Structural Biology/Biochemistry Seminar

Stephanie Dillon/Bruce Baumann, Florida State University

Student Seminar

Algebraic Schemes Seminar, 2:00 p.m., 104 Love Building

Paolo Aluffi, Florida State University

Hilbert Schemes, I

Financial Mathematics Seminar, 4:00 p.m., SCRI

Dennis Ridley, Florida A & M University & SCRI

Univariate Moving Window SpectralTime Series Analysis & Forecasting Theory & Application To Quarterly Cash Flows

Theory: The univariate moving window spectral (MWS) method of time series analysis and forecasting is a frequency domain method that will reduce bias in estimating the parameters of a time series model when the time series contains periodic components. Based on spectral analysis, the approach provides a more direct estimation of cyclical components in times series, and therefore a better model than might be arrived at by time domain methods. The theory of the MWS method will be presented.
      Application: Financial theory suggests that discounted future operating cash flows (CF) is the basis for firm stock price evaluation. Aggregate CF contains a wide variety of discontinuities, variability, seasonality, cycles and trends, hitherto unexplained by time series models. Application of the MWS method to quarterly CF time series analysis, statistical auditing & control, and forecasting will be demonstrated using the computer program FOURCAST.

Wednesday: 26 January 2000

Graduate Student Seminar, 1:15 p.m., 204B Love Building

Brian Felkel, Florida State University

[ topic to be announced ]

No (Real) Analysis Seminar, 2:30 p.m., 201 Love Building

Thursday: 27 January 2000

Algebraic Curves Seminar, 2:00 p.m., 104 Love Building

Paolo Aluffi, Florida State University

Riemann-Roch

QUANTUM! Seminar, 3:35 p.m., 104 Love Building

Phil Bowers, Florida State University

Commutation Relations

Friday: 28 January 2000

Colloquium Coffee, 3:00 p.m., 204 Love Building
Colloquium, 3:30 p.m., 101 Love Building

Edward Qian, Vice-President, Putnam Investments

On Conditional Distribution and Portfolio Optimization

Diversification is one of the central themes in modern portfolio theory. Yet, mean-variance optimization, which plays a fundamental role in the theory, often gives rise to portfolios that are overwhelmingly concentrated in just a few assets. The reason for this is that mean-variance optimization is notoriously sensitive to its inputs, which are expected returns and covariance matrix.
      The Black-Litterman method was developed to alleviate the input sensitivity problem. It combines the market equilibrium expected returns, which are obtained by solving an inverse problem, with conditional distribution theory, which adjusts the mean vector to reflect an investor's personal forecast of a few expected returns. In this talk, we outline the background and approach behind their method. We then present a new unified method that extends the results by Black-Litterman. The motivation for the method is to obtain conditional mean vector as well as conditional covariance matrix given an investor's view, which embraces forecasts not only of expected returns but also of volatilities and correlations. Our method is based on a simple application of conditional distribution but it does not requires a Bayesian approach as in the Black-Litterman method. Finally, we discuss its application to asset allocation problems and certain risk management issues.

Seminars and colloquia at "that other" university [a.k.a. the University of Florida]

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This document is maintained by Melissa Elaine Smith / smith@math.fsu.edu