Lefschetz Center for Dynamical Systems Seminar
Abstract: We present a mathematical theory of time-reversal experiments. In such experiments a signal is emitted by a localized source, propagated through a medium and recorded on a small array of receivers-transducers. The signal is re-emitted into the medium reversed in time, that is, the part of the signal recorded first is re-emitted last and vice versa. The re- propagated signal approximately refocuses back on the original source. This is somewhat surprising since the recording array has a small finite size. It is also observed that refocusing is significantly better in a random medium. We will give an explanation for refocusing and explain why random media are good for refocusing, as are ergodic billiards.
This is a joint work with Guillaume Bal.
Brown University Joint Solid Mechanics/Materials Science Seminar Series
Abstract: A three-dimensional finite element micro-mechanical model has been developed to predict the elastic-plastic behaviour of unidirectional metal matrix composites (MMCs). The model consists of a unit cell, representing a quarter fibre surrounded by matrix as a repeating element in a square array of fibres. Boundary conditions have been developed to allow the simultaneous application of axial shear, normal and transverse loading and thermal residual stress. The model includes the important effects of debonding of the interface between fibre and matrix, friction between fibre and matrix and the presence of thermal residual stress. The results of the model have been compared with experimental stress-strain data for a SiC/Ti composite system loaded at various off-axis angles between 0^{o} and 90^{o}. There is good agreement between the model and experiment for Young's Modulus, elastic limit and ultimate strength.
Brown University Center for Statistical Sciences Seminar
Abstract: Even in the absence of unmeasured confounding factors of model misspecification, standard methods for estimating the causal effect of time-varying treatments on survival are biased when (i) there exists a time-dependent risk factor for survival that also predicts subsequent treatment, and (ii) past treatment history predicts subsequent risk factor level. In contrast, methods based on either structural nested models (SNMs) or marginal structural models (MSMs) can provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent. The parameters of SNMs are estimated using g-estimation and those of MSMs are estimated using inverse-probability- of-treatment weighting. We use a structural nested failure time model and a marginal structural Cox proportional hazards model to estimate the causal effect of potent antiretroviral therapy on the survival of HIV-infected patients in two prospective studies, and compare our results to the possibly biased estimate from a standard time-dependent Cox Model. The causal mortality hazard ratio from the MSM is 0.58 (95% confidence interval: 0.38, 0.87) compared to 0.70 (95% confidence interval: 0.48, 1.09) from a standard time-dependent Cox model. We then compare the effect estimates and the relative efficiency of MSMs and SNMs through simulations.
*This is joint work with Stephen Cole, Anthony Philippakis, and James Robins.
*Refreshments will be available at the seminar.
Stochastic Systems Seminar
Abstract: Consider optimizing a linear function over a polymatroid with side constraints, a problem that often arises in dynamic scheduling of multiclass queues (e.g., Klimov's model) with additional performance constraints. We develop an $O(n^3)$ algorithm that solves the problem to optimality. The algorithm has a simple and intuitive "grouping" structure. We also establish connections to other basic combinatorial optimization problems, such as set selection and submodular function minimization. (Based on joint work with Yingdong Lu of IBM Research.)
Brown Analysis Seminar
PDE Seminar
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