Lefschetz Center for Dynamical Systems Seminar
University of Kansas, Lawrence, KS 66045 | |
and an Application | |
Abstract: In this talk, a geometric treatment of singularly perturbed systems with a certain type of turning points will be discussed. We will provide a result on the existence of semi-global invariant manifolds, which reveals a very crucial geometric structure of the system with the type of turning points. Incorporating the delay of stability loss associated with the turning points, we then establish some exchange lemmas to describe the behavior of invariant manifolds passing through the vicinity of the turning points.
We then illustrate an application to the study of wave fan profiles of some Riemann solutions of hyperbolic systems of conservation law in one space dimension.
Center for Fluid Mechanics Seminar
New Jersey Insititute of Technology, Newark, NJ | |
Abstract: The stratification process in a sedimenting suspension results in decay of velocity fluctuations. Obtaining a theoretical understanding of stratification through direct study of the exact dynamical equations for sedimentation would appear to have little possibility of success owing to large nonlinearities and the ill-posed nature of the problem. We present an analysis of the stratification process and the resulting decay of velocity fluctuations using approximate dynamics intended to capture the gross features of the exact dynamics without the overwhelming detail.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: How do you distinguish between metal, plastic, and paper from a photograph? If you know the amount of light incident on the surface from all directions, you could invert the computer graphics rendering process to determine reflectance properties such as shininess and gloss. If you don't know the illumination, on the other hand, the problem is underconstrained, because different combinations of illumination and reflectance can produce the same image. For example, a chrome sphere reflects the world around it, so if the illumination were just right, it could appear to be a ping-pong ball. Yet, in the real world, humans effortlessly recognize surfaces of different reflectance.
This talk will focus on a computer vision system to recognize surface reflectance properties from a single monochrome image under unknown illumination. Our reflectance estimation algorithm learns relationships between surface reflectance and certain statisitics computed from an observed image. This approach succeeds because the spatial structure of real-world illumination possesses a great deal of statistical regularity, akin to that described in the literature on natural image statistics. We have also conducted phychophysical experiments suggesting that the human visual system makes use of similar priors on illumination in recognizing surface reflectance properties.
This work involved collaborations with Ted Adelson, Alan Willsky, Roland Fleming, and Thomas Leung.
Brown Analysis Seminar
Scientific Computing Seminar
PDE Seminar
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