Special Stochastic Systems Seminar
Abstract: We consider the following question. Given a finite set A, what is the smallest number of spheres (of some fixed radius) needed to cover A^n (almost) completely? More generally, given a ``mass'' function M on A, what is the minimal mass M^n(B) of subsets B of A^n such that the spheres centered at the points of B (almost) cover A^n? Distance is measured by a coordinate-wise metric, almost-covering is with respect to a product measure on A^n, and n is typically large.
In the first part of this talk we will present a precise answer to the above question, and show that it implies various results as corollaries, including Shannon's data compression theorem, Stein's lemma (hypothesis testing), and new converses to some important concentration-of-measure inequalities. In the second part we will discuss data compression in more detail, describing recent work on the fundamental limits of how well data can be compressed in practice. Here, most of the emphasis will be placed in refining and even avoiding asymptotics as much as possible.
Lefschetz Center for Dynamical Systems Seminar
Brown University Joint Applied Mathematics and Material Science Seminar
Abstract: Chemical vapor infiltration (CVI) is emerging as a technology for fabricating fiber-reinforced composite materials. The technique utilizes the chemical vapor deposition process in which a precursor gas stream reacts on the internal surfaces of a porous body at elevated temperatures to deposit matrix material. The method allows high temperature phases to be produced at temperatures well below their melting point and with minimal stress so as to preserve the often less tolerant reinforcement. The interrelated thermal, mass transport, and kinetic processes have been modeled to allow for optimization of infiltration and, most recently, prototypical silicon carbide matrix heat exchanger tubes have been prepared. The CVI process has also been used to produce carbon composite proton exchange membrane fuel cell bipolar plates for automotive propulsion applications.
Research sponsored by the U. S. Department of Energy, Office of Fossil Energy, Advanced Research and Technology Development Materials Program and Energy Efficiency and Renewable Energy, Office of Transportation Technology, under contract DE-AC05-96OR22464 with Lockheed Martin Energy Research Corporation.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Stochastic Systems Seminar
Abstract: Many classical nonparametric methods misbehave when the regression surface is not smooth, that is when it displays some kind of spatial inhomogeneities. For instance, images of natural scenes exhibit rapid changes of light-intensity -- edges -- and, therefore, classical methods are not well suited for their analysis.
This talk examines the estimation of such discontinuous objects from both a theoretical and a practical viewpoint. On the one hand, optimal decision theoretic results will be presented for some models of images with edges; on the other hand, simple and concrete procedures which nearly achieve the best estimation bounds will be introduced. These procedures are based on newly developed tools like {\em ridgelets} and their derivatives: e.g., {\em curvelets}. Several numerical examples will illustrate the power of these new ideas.
Scientific Computing Seminar
Abstract: We describe a framework for doing parallel adaptive computation for finite element and finite volume schemes. The parallel data management system is capable of handling high-order techniques and heterogeneous computing environments. We present an application involving the solution of compressible flow problems using the discontinuous Galerkin method. Error estimation procedures involve superconvergence at the Radau points. These are shown to produce asymptotically correct error estimates. Results are presented for several problems.
Special Joint - Brown Applied Mathematics Pattern Theory and Vision Seminar and Department of Neuroscience
Abstract: I will be talking about coding properties of stochastic networks from the information-theoretic stand-point. In particular, I will be discussing how the accuracy of population coding is affected by: (i) correlations between neurons, (ii) internal noise, and (iii) short-term synaptic dynamics (plasticity). Understanding of how these factors influence the coding is important for getting insights about general issue of information processing in neural networks. I will show that: (i) only stimulus-driven temporal correlations between neurons improve the accuracy of coding, (ii) for subthreshold inputs some finite noise is required for optimal coding, (iii) short- term synaptic plasticity can improve significantly the coding accuracy for excitatory networks.
PDE Seminar
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