Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
Epidemiology & Public Health, Yale University | |
Abstract: Extending the approach by Robins, Rotnizky and Zhao (JASA, 1995), we propose a class of inverse intensity of visit process weighted estimators for the parameters in marginal regression model of Liang and Zeger (Biometrics, 1986) for longitudinal response in the presence of general intermittent missing data. Asymptotic variance of the estimators are derived. These estimators can be used in studying the effect of treatments on the evolution of marginal mean of longitudinal response variable. The proposed model is easily extended to accommodate both intermittent missing data and dropouts simultaneously under the assumption of missing-at-random. The method is illustrated with simulations and a real data set (joint with Scharfstein).
Center for Fluid Mechanics Seminar
Department of Aerospace Engineering and Engineering Mechanics | |
Abstract: We have been involved with modeling near-continuum flows in which a detailed understanding of the complex physics is essential. When multiple species, radiation and particulate condensation are involved, it becomes difficult to even write down the Boltzmann equation to be solved. One then must resort to direct simulation of the intermolecular interactions.
Our most advanced models of the detailed physics of volcanic plumes on Jupiter's moon Io are presented. Two types of low density axisymmetric sulfur dioxide (SO2) plume flows are modeled using the direct simulation Monte Carlo method (DSMC). Thermal radiation from all three vibrational bands and overall rotational bands of SO2 molecules are examined. The radiation features are studied both by calculating infrared emission spectra along different lines-of-sight through the plume and the DSMC modeled emission images of the whole flow field. It is found that most of the radiation originates in the vicinity of the vent. A high resolution vent vicinity flow was obtained by multi-domain sequential calculation to better study the radiation signature. Two-phase (gas/dust) flows are briefly discussed. The simulation results are compared to the existing observation data. Other than the calculated general shape of the plumes, the calculated average SO2 column density over a Pele-type plume is in agreement with observations. The simulation results also show interesting gas-dynamic features such as the multi-bounce shock structure around Prometheus-type plumes and the frost depletion by plume scouring on the day-side of Io.
Stochastic Systems Seminar
Abstract: We discuss a probabilistic model arising in nonequilibrium statistical mechanics: a mechanical system coupled to several heat reservoirs at different temperatures. We discuss the ergodic properties of the model (existence of a stationary state, rate of convergence) and its physical properties (entropy production and its fluctuations). The main ingredient is the construction of Liapunov functions for the dynamics.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: We present a new adaptive mechanism for empirical ``on-line'' design of a vector quantizer codebook. The proposed scheme is based on the principle of ``natural type selection'' (NTS), presented in a recent work by Zamir and Rose. The NTS principle implies that backward adaptation, i.e., adaptation directed by the past reconstruction rather than by the uncoded source sequence, converges to an optimum rate-distortion codebook. We incorporate the NTS iteration step into a parametric encoder. We demonstrate that the codebook converges to an optimum rate-distortion solution within the associated parametric class. This new scheme does not suffer from the severe complexity at high dimensions of non-parametric solutions like the generalized Lloyd algorithm (GLA). Moreover, unlike existing parametric adaptive schemes (e.g., code-excited linear prediction (CELP)), this scheme is optimal even for low coding rates. [Joint work with Yuval Kochman.]
Brown Analysis Seminar
PDE Seminar
Department of Mathematics Colloquium
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