Brown Analysis Seminar
Brown University Center for Statistical Sciences Seminar
Refreshments beginning at 3:15pm |
Abstract: In longitudinal clinical trials, when outcome variables at later time points are only defined for patients who survive to those times, the evaluation of the causal effect of treatment is complicated. In this presentation, we describe an approach that can be used to obtain the causal effect of three treatment arms with ordinal outcomes in the presence of death using a principal stratification approach. We introduce a set of flexible assumptions to identify the causal effect and implement a sensitivity analysis for non-identifiable assumptions which we parameterize parsimoniously. Methods are illustrated on quality of life data from a recent colorectal cancer clinical trial. Joint work with Keunbaik Lee (LSU) and Dan Sargent (Mayo Clinic).
Center for Fluid Mechanics Seminar
Abstract: In this talk, the effects of fluid elasticity on the dynamics of filament thinning and drop breakup processes are investigated in a cross-slot microchannel. Elasticity effects are examined using dilute aqueous polymeric solutions of molecular weight (MW) ranging from 1.5 x 103 to 1.8 x 107. Results for polymeric fluids are compared to those for a viscous Newtonian fluid. The shearing or continuous phase that induces breakup is mineral oil. All fluids possess similar shearviscosity (~0.2 Pa s) so that the viscosity ratio between the oil and aqueous phases is close to unity. Measurements of filament thickness as a function of time show different thinning behavior for the different aqueous fluids. For Newtonian fluids, the thinning process shows a single exponential decay of the filament thickness. For low MW fluids (103, 104, and 105), the thinning process also shows a single exponential decay, but with a decay rate that is slower than for the Newtonian fluid. The decay time increases with polymer MW. For high MW (106 and 107) fluids, the initial exponential decay crosses over to a second exponential decay in which elastic stresses are important. We show that the decay rate of the filament thickness in this exponential decay regime can be used to measure the steady extensional viscosity of the fluids. At late times, all fluids cross over to an algebraic decay which is driven mainly by surface tension.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract:
In the past few years there has been a growing interest, in diverse scientific communities, in endowing "shape spaces" with Riemannian metrics, so to be able to measure similarities between shapes and perform statistical analysis on data sets (e.g. for object recognition, target detection and tracking, classification, and automated medical diagnostics). The geometry of such spaces has started to emerge only very recently; in this talk we will explore the sectional curvature for the Riemannian manifold of landmark points (which is one of the simplest, in that it is finite-dimensional) and discuss its effects on applications.
[pizza will be provided]
Boston University/Brown University PDE Seminar
Abstract: I will talk about generalized traveling waves for scalar reaction diffusion equations in an inhomogeneous environment. As the name suggests, these solutions generalize the traditional notion of a traveling wave, although the wave profile is not fixed and the wave speed may not be well-defined. These solutions are stable attractors. If the environment has a certain statistical structure, then the asymptotic wave speed is well-defined, and the interface moves like a Brownian motion with positive drift.
Boston University/Brown University PDE Seminar
Abstract: Burgers vortices are explicit solutions of the three-dimensional Navier-Stokes equations which are often used to model the vortex filaments observed in turbulent flows. Despite obvious limitations, this model describes in a correct way the fundamental mechanisms which are responsible for the persistence of coherent structures in three-dimensional turbulence. In this perspective, an important problem is to determine the stability of Burgers vortices with respect to perturbations in the largest possible class. This question has been open for almost three decades, and rigorous answers have been obtained so far for small Reynolds numbers only, or in the particular case of two-dimensional perturbations. In this talk, I shall show how a detailed analysis of the linearized operator allows to prove the stability of Burgers vortices with respect to three-dimensional perturbations, for any given value of the circulation number. This is a joint work with Yasunori Maekawa (Kobe University).
Scientific Computing Seminar
Abstract: In this talk we consider a stochastic Darcy's pressure equation with random permeability and random right-hand side forcing term. I will discuss an infinity-dimensional Petrov-Galerkin framework to accommodate the lack of ellipticity and singular forcing terms. The framework unify both representations of permeability stochastic fields based on KL or on convolution kernels. We present continuous and discrete inf-sup conditions, well-posedness, a priori error estimations and numerical experiments.
PDE Seminar
Graduate Student Pizza Seminar
Abstract: Compressed or Compressive sensing is concerned with e?cient and robust sparse signal recovery. The idea is as follows. Suppose we have a signal x of length N, where N is very large. We say that x is S sparse if it only has S nonzero values. Now, we want to recover x, but all we observe or measure are its discrete Fourier coefficients. Of course, if we were to measure all N discrete Fourier coefficients, we can recover the signal exactly. But, is there another way to measure far less and still obtain exact signal recovery? We will see that indeed we can, and, in fact, we only need to take measurements on the order of S log N. Furthermore, via l_1 minimization, we can obtain exact signal recovery. If time permits, we will also explore applications and computational techniques.
Probability Seminar
Abstract: We derive some sufficient conditions for testing the extinction a.s.,non-extinction with positive probability, explosion and non-explosion of time-nonhomogeneous Markov chains with a countable state space. The method of Lyapunov functions is used for this purpose. Several theorems concerned with such sufficient conditions are proven for a general class of time-nonhomogeneous Markov chains. Then they are applied to some problems in the time-nonhomogeneous birth-death processes and branching Markov processes. It is joint work with P.L.Chow.