Colloquia Fall 2008
The weekly "PinkSheet" seminar schedule is available here.
Our colloquium talks are held in Room G-5 Rolla Building. We begin with coffee and refreshments at 4:00 pm, followed by the hour-long lecture at 4:15 unless otherwise noted. The entire Missouri S&T community is warmly invited to attend. We especially encourage undergraduate students, graduate students, and faculty from other departments to attend.
Monday, August 25, 4:00 PM Note unusual day
Title: Periodical Cicadas
Abstract: In the US one finds 6(3) species of cicadas which have the longest known life cycle - 13 resp. 17 years. By means of a "realistic" model we describe this periodicity, the convergence and evolution of these insects.
Friday, September 12, 4:00 PM
Title: On the global asymptotic stability of planar dissipative maps
Abstract: We consider area-contracting maps in the plane, which are often called dissipative maps. If a smooth map has an asymptotically stable equilibrium point P, the area-contracting property seems necessary at least locally around P. Here we find sufficient conditions for global asymptotic stability of planar dissipative maps. Then, we apply this result to a 15 year old open problem about a second-order rational difference equation, posed by G. Ladas.
Friday, September 26, 4:00 PM
Title: Scattering theory for Jacobi operators with quasi-periodic background and applications to the Toda hierarchy
Abstract: Jacobi operators, which can be viewed as the discrete analogue of Sturm-Liouville operators, play a fundamental role in the investigation of completely integrable nonlinear lattices, in particular, the Toda lattice. We will develop scattering theory for Jacobi operators which are short range perturbations of (steplike) quasi-periodic finite-gap background operators via the Gel'fand-Levitan-Marchenko approach. Minimal scattering data which determine the perturbed operator uniquely will be presented. This will allow us to solve the associated initial value problem of the Toda hierarchy via the inverse scattering transform. This talk is based on joint work with Iryna Egorova (Kharkov) and Gerald Teschl (Vienna).
Friday, October 3, 4:00 PM
Title: Dimension Reduction Paradigms for Regression
Abstract: Dimension reduction for regression, represented primarily by principal components, is ubiquitous in the applied sciences. This is an old idea that has moved to a position of prominence in recent years because technological advances now allow scientists to routinely formulate regressions in which the number p of predictors is considerably larger than in the past. Although "large" p regressions are perhaps mainly responsible for renewed interest, dimension reduction methodology can be useful regardless of the size of p. Starting with a little history and a definition of "sufficient reductions", we will consider a variety of models for dimension reduction in regression. The models start from one in which maximum likelihood estimation produces principal components, step along a few incremental expansions, and end with forms that have the potential to improve on some standard methodology. This development provides remedies for two concerns that have dogged principal components in regression: principal components are typically computed from the predictors alone and then do not make apparent use of the response, and they are not equivariant under full rank linear transformation of the predictors.