Brown University Center for Statistical Sciences Seminar
Harvard School of Public Health | |
Association Tests: A Powerful New Testing Strategy | |
1st Floor Conference Room |
Abstract: For genetic association studies with multiple phenotypes, we propose a new strategy for multiple testing with family-based association tests (FBATs). The strategy increases the power by using all available family data and by reducing the number of hypotheses tested, while being robust against population admixture and stratification. Using conditional power calculations, the approach screens all possible null-hypotheses without biasing the nominal significance level and identifies the subset of phenotypes which has optimal power when tested for association either by univariate or by multivariate FBATs. An application of our strategy to an asthma study shows the practical relevance of the proposed methodology. In simulation studies, we compare our testing strategy with standard methodology for family-studies. Further, the proposed principle of using all data without biasing the nominal significance in an analysis prior to the computation of the test statisic has broad and powerful applications in many areas of family-based association studies.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: Imaging of objects under variable lighting directions is an important and frequent practice in computer vision and image-based rendering. We introduce an approach that significantly improves the quality of such images, practically at no cost.
Traditional methods for acquiring images under variable illumination directions use only a single light source per acquired image. In contrast, our approach is based on a multiplexing principle, in which multiple light sources illuminate the object simultaneously from different directions. Thus, the object irradiance is much higher. The acquired images are then computationally demultiplexed.
We give the optimal code by which the illumination should be multiplexed to obtain the highest quality output. We then demonstrate its utility in experiments using high directional resolution lighting. The mathematical principle behind this approach is useful in other domains of imaging, unrelated to the regime of illumination.
** Joint work with Shree Nayar and Peter Belhumeur**
Scientific Computing Seminar
Department of Mathematics, Raleigh, NC 27695 | |
Theory and Numerics | |
Abstract: We endow the nonlinear degenerate parabolic equation used to describe propagation of thermal waves in plasma or in a porous medium, with a mechanism for flux saturation intended to correct the nonphysical gradient-flux relations at high gradients. We study the model both analytically and numerically, and discover that in certain cases the motion of the front is controlled by the saturation mechanism and instead of the typical infinite gradients resulting from the linear flux-gradients relations we obtain a sharp, shock-like front, typically associated with nonlinear hyperbolic phenomena. We prove that if the initial support is compact, independently of the smoothness of the initial datum inside the support, a sharp front discontinuity forms in a finite time, and until then the front does not expand.
Being able to resolve the discontinuities accurately is crucial for a faithful description of the ensuing patterns. Hence, we propose a new numerical method capable to resolve almost perfectly the discontinuous solutions, and thus allows us to follow numerically the evolution of the patterns. The new method is a generalization of the diffusion-velocity particle method [2]. To prevent the clustering of particles at discontinuities we employ a special procedure which merges clustered particles into a new particle located in the center of mass of the removed particles. The smearing of discontinuities is avoided by using smooth mollifiers with variable size supports as approximations to a delta-function.
This is the joint work with A. Kurganov and P. Rosenau.
PDE Seminar
Abstract: The endeavor to understand how fluid dynamical equations can be derived from kinetic theory goes back to the founding works of Maxwell and Boltzmann. Most of these derivations have been well understood at several formal levels for some time, and yet their full mathematical justifications are still missing. This talk will introduce this general problem and survey recent works in which the acoustic, the incompressible Stokes, and the incompressible Navier-Stokes limits have been globally establish for the classical Boltzmann equation considered over periodic spatial domains of dimension two or more.
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