Lefschetz Center for Dynamical Systems Seminar
Abstract: We investigate the dynamical system governing travelling wave solutions of a perturbed Boussinesq system. In contrast to classical dynamical system theory, the current system possesses a variety of weak, non-analytic solitary wave solutions that coexist in the neighborhood of the same equilibrium points and are the limits of homoclinic, or heteroclinic orbits. This phenomenon is closely related to the nonlinear dispersion in the original physical problem. In this talk, we shall analyze the nonlinear effect on the existence of non-smooth travelling waves and their singularity formation in the dynamical system.
Brown University, Joint Materials/Solid Mechanics Seminar Series
Center for Statistical Sciences Seminar
Candidate for Assistant/Associate Professor, Department of Community Health | |
Abstract: The use of the correlation coefficient for testing bivariate independence, although most common, has serious limitations. In this talk I will discuss Hoeffding's (1948) test of bivariate independence, and its asymptotic equivalent due to Blum, Kiefer and Rosenblatt (1961), which are well known to be consistent against all dependence alternatives. Specifically, I will describe the status of their null distribution, offer some convenient approximations and compare their power using a variety of copulas, including those due to Morgenstern, Gumbel, Plackett, Marshall and Olkin, Raftery, Clayton, and Frank. I will also show how the tests of bivariate independence can be used for constructing simple goodness-of-fit tests.
Brown University Center for Statistical Sciences Seminar
Candidate for Assistant Professor, Community Health | |
Please Note Late Notice Special Seminar |
Abstract: In an observational study, the experimenters do not have explicit control over the assignment of subjects to treatment. Because of the lack of randomization, the differences between the outcomes in treated and control groups could reflect either effects caused by treatment, inherent pretreatment differences, or both.
Matching is one of the several plausible methods in observational study to adjust for the bias introduced by observed covariates. When there are many covariates, propensity score matching turns out to be very effective and efficient. The matching method I will introduce, multivariate matching with doses of treatment, differs from the traditional treatment-control matching in three ways: First, pairs must not only balance covariates, but also must differ markedly in dose. Secondly, any two subjects may be paired, so that the matching is non-bipartite, and a new algorithm is required. Finally, a propensity score with doses must be used in place of the conventional propensity score. I will illustrate multivariate matching with doses using pilot data from a media campaign against drug abuse.
Brown University Department of Mathematics Analysis Seminar
Special Brown University, Division of Applied Mathematics Seminar
Abstract One of the most common ways to cluster data is to model it as a mixture of Gaussians. This is the most well-weathered statistical model of clustered data, and has been the subject of close study for well over a century. However, the only algorithms known for this clustering task have been heuristics with rather weak performance guarantees.
I shall describe an efficient, provably correct algorithm which learns an important class of mixtures of Gaussians from arbitrarily high-dimensional data. It recovers the centers of the Gaussian clusters to within the precision specified by the user, in time which scales linearly in the dimension of the data and polynomially in the number of Gaussians.
The algorithm depends crucially upon an understanding of the geometric structure of high-dimensional Gaussian clusters, and upon a particular projection technique which reduces the dimension of the data while at the same time provably enhancing useful aspects of this structure.
Scientific Computing Seminar
College of William and Mary, Virginia | |
Abstract: This talk consists of three parts. In the first part of the talk we will describe the parallel mesh generation problem and we present a brief overview of current state-of-the art parallel tetrahedral and triangulation mesh generation methods. In the second part of the talk we will present a parallel programming environment we developed to ease the task of implementing parallel adaptive applications like mesh generation. Using this software we developed four different parallel tetrahedral mesh generation methods based on: (1) Domain Decomposition, (2) Speculative execution (3) Constrained Delaunay Triangulation, and (4) Domain Decoupling. In the third part, after we describe these methods we will present performance data which point to future research directions and open problems in parallel mesh generation.
Center for Statistical Sciences Seminar
Department of Community Health, Purdue University, Department of Statistics | |
Abstract In order to understand the role of microorganisms in an environment, the identification and characterization of the relevant microbial community is necessary. Characteristic profiles of microbial communities are obtained by denaturing gradient gel electrophoresis (DGGE) of polymerase chain reaction (PCR) amplified 16S rDNA from soil extracted DNA. These characteristic profiles, commonly called community DNA fingerprints, can be represented in the form of high-dimensional binary vectors. The corresponding statistical problem of modeling and variable selection for high-dimensional multivariate binary data can be addressed from both a frequentist and a Bayesian perspective. Permutation-based approaches are employed to select variables which vary significantly with respect to a treatment effect and the properties of these methods are explored via simulation. Bayesian methods for model selection were also employed using an Empirical Bayes model for multivariate binary response data, but these results will only be discussed as time permits. In conclusion, an application of the proposed methodology is presented in the context of a controlled agricultural experiment.
PDE Seminar
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