Lefschetz Center for Dynamical Systems Seminar
Abstract: The Discrete Nonlinear Schr{\"o}dinger equation (DNLS) has been recognized as a model of relevance in nonlinear optics, Bose-Einstein condensation or the local denaturation of DNA. In this talk we present the basic features of its solitary wave solutions in 1+1 and 2+1 dimensions and describe their stability and dynamical properties, using analytical and numerical methods. Some interesting implications for applications and connections to recent experiments will also be briefly discussed.
Brown University Center for Statistical Sciences Seminar
Abstract: Advancing medical technologies provide promising means for better detection of disease. Before these advances become standard, they must undergo rigorous evaluation to assess how well they diagnose diseased and non-diseased states. With continuous test results, the Receiver-Operating Characteristic (ROC) curve provides a visual description of inherent test accuracy. The area under the ROC curve (AUC) and the partial AUC give two summary indices of test accuracy. Careful evaluation of a new technology must examine the dependence of accuracy measures on covariate information. Such data may be used, for example, to identify populations in which a test is more (or less) accurate.
In this talk, I develop regression models for AUCs and partial AUCs and propose a semi-parametric method of estimation which can be implemented using standard binary regression algorithms. Partial AUC regression models are more complicated than AUC models because partial AUCs depend on quantiles, and quantile regression methods may be required. In the no-covariate case, the estimating function for the AUC gives the Mann-Whitney U-statistic, while for the partial AUC a new, non-parametric estimator results. The estimating function depends on cross-correlated binary random variables, hence asymptotic distribution theory is non-standard. Simulation results show that the method performs well. Application of the method to evaluate a technology for diagnosing hearing impairment illustrates its usefulness.
An important undercurrent of this work is the premise that modeling the summary measure directly, as opposed to modeling the test result and then evaluating its diagnostic ability, is more scientifically robust. Three general approaches to regression modeling in this setting have been proposed: 1) model the test result and then obtain the induced measures of accuracy, 2) model the ROC curve directly, 3) model the summary measure directly. I will discuss the issues in evaluating which approach is best and present simulation results.
Center for Fluid Mechanics Seminar
Abstract: When bubbles are continuously released from a point source at the bottom of a fluid layer initially at rest, a plume is produced. Collective effects induced by the bubbles are modelled by the simulation of the Navier-Stokes equations forced by a spatio-temporal distribution of momentum (two-way coupling simulations with bubbles represented by points force). A detailed analysis of the plume transition is proposed. Behavior of bubble plumes is clearily more unstable than its thermal analog in air.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: Quantum information sources can be represented by systems of interacting particles or spins where a state of the system is described by the density matrix of a Gibbs ensemble. A natural conjecture is that the information rate of a quantum information source is equal to the von Neuman entropy per particle (or a unit volume). In the talk I'll give known results (old and new) on this conjecture and discuss open questions. No preliminary knowledge of information theory (classical or quantum) will be required.
Special Stochastic Systems Seminar
Please Note Special Room For This Week Only |
Abstract: We consider stochastic approximation (SA) algorithms with reflection terms constraining the iterates $\theta_n$ to polytopes $H$. In particular, we consider the rate of convergence for such algorithms for cases where the SA limit point $\bar{\theta}$ lies on the boundary of $H$. In previous work (apart from large deviation approaches), only $\bar{\theta}$ interior to $H$ were considered. In these cases, typically one forms the normalized iterates $U_n = (\theta_n - \bar\theta)/ \sqrt{\epsilon_n}$ ($\epsilon_n$ is the SA step-size) and then applies weak convergence methods to the interpolated processes formed from normalized iterates, obtaining a limit process $U(\cdot)$. The varience of the stationary distribution of $U(\cdot)$ measures the rate of convergence.
We take a similar approach, but a complicating feature in our case, compared to when $\bar{\theta}$ is interior to $H$, is dealing with the reflection term which remains in the limit processes $U(\cdot)$. We will show that the limit processes are stochastic differential equations with reflection (SDER). A large effort along the way to show this is proving tightness of the normalized iterates. We will also mention some very preliminary numerical results and a possible direction for characterizing the stationary distribution of the limiting SDERs.
Brown University, Joint Mechanics/Materials Seminar
Sponsored by the General Motors Collaborative Research Lab
Sandia National Las, Albuquerque, NM | |
Abstract: The crystal plasticity model phenomenology partitions permanent material deformation among predetermined shear planes and directions in a crystalline material. Thus, crystal orientation and material hardening along the predefined shear systems evolve within a material element during a deformation simulation. To develop a methodology that performs relevant micromechanical deformation simulations of polycrystalline materials, a finite element model based on the crystal plasticity framework has been implemented into JAS-3D, a quasistatic, nonlinear code developed at Sandia National Laboratories. The model has successfully performed simulations of realistic 3-D polycrystalline FCC microstructures composed of as many as 200 grains with approximately 200 elements per grain. Through the crystal plasticity phenomenology, the finite element simulations generate local crystal orientation and shear system strength information, and predict intragranular deformation evolution of material microstructure. Although evidence strongly suggests that the fundamental phenomenology is sound, issues such as incorporating a length scale, the influence of mesh refinement, and appropriate experimental validation brings into question the predictive capability of polycrystal plasticity finite element simulations composed of several hundred elements per grain. Results will be presented to highlight these issues, address possible avenues of additional research and emphasize successes using this predictive capability. These studies include comparison of predicted polycrystalline yield surface results using isotropic and a commonly employed latent (anisotropic) shear system deformation evolution, the influence of mesh refinement, using SEM generated electron backscattered Kikuchi pattern (EPKP) data to compare with simulated results, and employing a method that more accurately captures the influence of grain boundaries within the simulations.
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.
PDE Seminar
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