Graduate Student Seminar
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When/Where:Every Tuesday, 12:30 pm in Fine Hall 224
Next Time (April 22):
Speaker: Gorkem Ozkaya
Subject: Lifting Scheme for Construction of Second Generation Wavelets
Wavelet transforms are important tools for signal analysis, enabling efficient representations with a large number of zero coefficients. Typical wavelet bases are composed of dyadic translates and dilates of a single function, called as the mother wavelet. These are called first generation wavelets. These types of constructions are not possible when the domain of the signals we are interested are irregular. In a more general setting, wavelets are not necessarily translates and dilates of a single function; but they still share many of the important properties of first generation wavelets. These are referred to as second generation wavelets. We will talk about construction of second generation wavelets on convoluted domains using the lifting scheme, which is a simple and efficient technique.
Coming Soon (Apr 29):
Speaker:Benjamin Sonday
Subject: TBA
Schedule for Spring 2007/2008:
Date Speaker Title of the talk Location 26 Feb 2008 Linda Hung Orbital-Free Density Functional Theory Fine Hall 224 4 Mar 2008 Filip Matejka Rational Inattention: Discrete and Rigid Pricing Fine Hall 224 11 Mar 2008 Mike Sekora Extremum-Preserving Limiters Fine Hall 224 25 Mar 2008 Chenwei Zhu Random Measurements in Sparse Recovery, methods and algorithms Fine Hall 224 1 Apr 2008 TBA TBA Fine Hall 224 8 Apr 2008 Dacheng Xiu Statistical Inference for Stochastic Volatility Models with High Frequency Data Fine Hall 224 15 Apr 2008 Manny Lazar Not Your Grandmother's Old-fashioned Beer Bubbles: The Evolution of Cellular Structures via Mean Curvature Motion: Theory and Applications to Materials Science Fine Hall 224 22 Apr 2008 Gorkem Ozkaya Lifting Scheme for Construction of Second Generation Wavelets Fine Hall 224 29 Apr 2008 Benjamin Sonday TBA Fine Hall 224
Previous Abstracts
Gorkem Ozkaya: Lifting Scheme for Construction of Second Generation Wavelets (Apr 22 2008)
Wavelet transforms are important tools for signal analysis, enabling efficient representations with a large number of zero coefficients. Typical wavelet bases are composed of dyadic translates and dilates of a single function, called as the mother wavelet. These are called first generation wavelets. These types of constructions are not possible when the domain of the signals we are interested are irregular. In a more general setting, wavelets are not necessarily translates and dilates of a single function; but they still share many of the important properties of first generation wavelets. These are referred to as second generation wavelets. We will talk about construction of second generation wavelets on convoluted domains using the lifting scheme, which is a simple and efficient technique.
Emanuel Lazar:Not Your Grandmother's Old-fashioned Beer Bubbles: The Evolution of Cellular Structures via Mean Curvature Motion: Theory and Applications to Materials Science (Apr 15 2008)
Cellular structures abound not only in biological and life-science contexts, but also in Tiger Wood's titanium clubs and in the foam on top of your Monday-night Yuengling (10pm, Fine 221). Material scientists spend much time studying how these structures evolve in order to better understand their mechanical properties, which in turn allow engineers to manufacture better golf clubs and allow companies like Budweiser and Corona to manufacture better beers. You'll be surprised to learn how much mathematical beauty is involved in describing these structures and their evolution.
Dacheng Xiu: Statistical Inference for Stochastic Volatility Models with High Frequency Data
This paper proposes a consistent, most efficient, and robust parametric estimator of integrated volatility with high frequency data in the presence of market microstructure noise. A variety of Monte Carlo simulations and empirical studies with real data are performed to verify the estimation results.
Chenwei Zhu: Random Measurements in Sparse Recovery, methods and algorithms (25 Mar 2008)
Suppose one is given a small number of (possibly noisy) linear measurements of a signal. If the number of measurements is less than the number of degrees of freedom of the signal, then one of course cannot reconstruct the signal from the measurements in general. But if one makes the additional hypothesis that the signal is sparse, or at least compressible, then it does become possible to recover the signal accurately, stably, and quickly, --from random measurements. Our approach is through a regularized minimization. I will briefly explain this method and related algorithms.
Mike Sekora: "Extremum-Preserving Limiters" (11 Mar 2008)
Limiters are nonlinear hybridization techniques that are used to preserve positivity and monotonicity when numerically solving hyperbolic conservation laws such as the Euler equations in fluid dynamics. Unfortunately, the original limiting methods used in MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) and PPM (Piecewise Parabolic Method) suffer from the truncation error being 1st order accurate at all extrema despite the overall accuracy of the higher-order method. To remedy this problem, higher-order extensions such as the WENO (Weighted Essentially Non-Oscillatory) Method were developed which relied on elaborate analytic and/or geometric constructions. In revisiting the limiter problem, Colella and Sekora derived a new family of limiting techniques that ensure higher-order spatial accuracy while maintaining simplicity such that the extremum-preserving limiters directly plug into any algorithm which uses conventional limiting techniques. The Colella-Sekora limiters are based on constraining interpolated values at extrema (and only at extrema) and using nonlinear combinations of various difference approximations of the second derivatives.
Filip Matejka: "Rational Inattention: Discrete and Rigid Pricing" (4 Mar 2008)
Prices do not always respond to shocks in input cost or even to shocks in demand for a product. Moreover, when they do respond, they tend to switch back and forth between a few values only. We will discuss how this phenomenon can be explained when agents (sellers and consumers) are assumed to have limited information capacity.
Linda Hung: "Orbital-Free Density Functional Theory" (28 Feb 2008)
Computational methods are increasingly important for studying materials. First-principles methods, such as density functional theory (DFT), model a material at the subatomic scale. While these methods are accurate, typical simulations can only model materials up to the nanometer scale. Unfortunately, material properties such as strength or plasticity often depend on the material?s configuration up to the micro- or macroscale. My talk will be about pushing the limits of a first principles method: orbital-free density functional theory (OFDFT).
OFDFT is the least expensive of all first principles electronic structure methods for materials, scaling nearly linearly with the size of the system (O(NlogN)). (In comparison, Kohn-Sham density functional theory (DFT) scales as O(N^3 ).) The efficient scaling occurs because OFDFT describes a system?s electronic structure solely by the electron density. I will provide an overview of OFDFT, addressing its abilities and shortcomings. I will also talk about some numerical methods (e.g. particle-mesh Ewald) used in our implementation of the theory. Finally, I will give some results from test systems of fcc aluminum.
Last updated: 28 Feburary 2008
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