Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
Abstract: Array technologies are now routinely applied to biomedical research, generating a significant amount of gene expression profile data from time course studies, dose-response studies, two-group comparison, clinical studies and synchronized experiments. How to extract relevant informaiton from such data sets presents an interesting challenge to data analysis. Currently, there are several heuristic approaches using, for example, visualization to inspect data or clustering analysis to group genes or cluster samples. While useful for exploratory purpose, these approaches can be subjective and have not taken full advantage of available information, such as external data about samples or about genes. For example, in time course studies, timing is essential, in clinical studies, clinical variables are integrated part of useful information, or in working on model organisms, candidate genes are often established from earlier works. Such data should be quite useful for hypothesis generation and testing. To utilize such information, we have developed a statistical framework, based upon a regression methodology, to focus on relationship of genomewide expression profiles with external data. Besides relying on a rich class of regression methods from statistical literature, this framework also acknowledges variations inherent to typical microarray experiments (namely, heterogeneity). In this talk, I will describe this framework, and will also illustrate this analytic approach through several examples. While this talk is tailored towards biomedical researches, I will also highlight some statistical challenges in modeling expression profile data.
*This seminar is funded by the Brown University Faculty Lectures as part of the Statistical Methodology for Genetics: Recent Advances lecture series.
Joint Seminar, Division of Engineering and The Center for Fluid Mechanics Seminar
Abstract: We consider two flows involving thin viscous films. As part of our introduction we provide a short overview of some common features of coating processes with thin films and then present research on two such problems. In the first example we investigate the influence of surfactants on a fiber coating process. The thin film thickness deposited on a fiber passed through a liquid bath is a non-monotonic function of speed and we further show that surfactants lead to some unanticipated variations in the film thickness at high surfactant loadings. Second, we consider flows of small droplets sliding along surfaces which lead to thin viscous films that exhibit corners.
Stochastic Systems Seminar
Brown Analysis Seminar
Special Lefschetz Center for Dynamical Systems Seminar
http://wwwrsphysse.anu.edu.au/nonlinear/ | |
Abstract: We discuss the properties of nonlinear photonic crystals including the nonlinearity-induced light localization and the formation of "discrete spatial optical solitons", and the bistable light transmission in straight waveguides and waveguide bends. With the help of the Green's function technique, we derive a discrete NLS-type model with long-range interaction that describes, with a good accuracy, many of the properties of the photonic-crystal circuits such as dispersion, defect states, bound modes in bends, resonant linear and nonlinear transmission, etc. The effective discrete equations may be considered as an analog of the Kirchhoff equations for the electronic circuits which are, however, more complicated and take into account the interference effects and diffraction in photonic crystals.
Applied Mathematics Colloquium
Abstract: In a number of physical and engineering systems, the result of basic modeling is a system of equations of non-hyperbolic type: these are equations whose linearizations are, in effect, meaningless vis a vis the character of the physical problem at hand. The user community has been uncertain about how to treat these models but there is a simple mathematical explanation: the models may be an incomplete (rather than incorrect) description of the physical phenomenon.
In this talk I will outline some models which arise in two-phase flow, and show how an analysis of the nonlinear nonhyperbolic operator can be undertaken using conservation law theory. A novel kind of weak solution -- a so-called singular shock -- appears in solving Riemann problems for this operator. Recent work by Michael Sever, which I will describe, sheds light on the nature of these singular shocks. Using these solutions, one can say that the models predict phenomena which are completely consistent with the physical considerations that went into their derivation.
Scientific Computing Seminar
Abstract: The scalar wave equation is separable in the prolate spheroidal coordinate system with solutions expressed in terms of angular and radial prolate spheroidal wavefunctions. In contrast to systems involving spherical and cylindrical geometry where the functions are well tabulated, the spheroidal wavefunctions have been tabulated over limited ranges of argument, degree, and order. New algorithms for calculating the prolate functions will be discussed that provide accurate values for the angular and radial functions over parameter ranges far wider than previously achievable. This is accomplished using novel techniques and expressions in regions where traditional approaches fail. The motivation for this research is based on developing a predictive capability for new sonar transducer arrays to be placed on doubly curved surfaces. An overview of the mathematical analysis and the use of the spheroidal wavefunctions in the prediction of the array performance will be covered.
PDE Seminar
Department of Mathematics Colloquium
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