Special Scientific Computing Seminar
Abstract: I will discuss a series of practical wave-making numerical experiments, including the generation of KdV solitons. It then will discuss the generation of "bubble solitons", which are steady state solutions to the Kadomtsev Petviashvili equation.
Nonlinear Waves Seminar
Lefschetz Center for Dynamical Systems Seminar
Abstract: We study the splitting of separatrices in a class of near-integrable real-analytic Hamiltonian systems. Our method is based upon a single application of a version of KAM-type proof, global in nature, which unlike the traditional approach, avoids the application of Moser lemma, providing instead at once two symplectic charts valid globally in the vicinity of perturbed stable and unstable separatrices. We show that all the information about the splitting can be extracted from the construction of such a pair of coordinate systems. Robust as it is, the KAM-type construction allows to study the splitting of separatrices in a variety of models, which earlier have been restricted solely to a pendulum coupled with rotators. In particular, it extends itself to the case of heteroclinic connections.
Brown University Center for Statistical Sciences Seminar
Sponsored by: The Bruce M. Bigelow Class of 1955 Lecture Series, The Charles K. Colver Lectureships and Publication Fund and the Department of Diagnostic Imaging at Brown University and Rhode Island Hospital/Lifespan
A Lecture Series on Methodologic Challenges in Health Care and Policy Research
Abstract: In an observational study, treatments are not randomly assigned to experimental subjects, so treated and control subjects may differ prior to treatment in ways that matter for the outcomes under study. Even when treated and control subjects are matched on recorded covariates, they may nonetheless differ in ways that have not been recorded. A sensitivity analysis asks how hidden biases of various magnitudes might alter the conclusions of a study. Two simple examples of sensitivity analysis will be presented, one from epidemiology and one from economics. In the economics example, the sensitivity of an instrumental variable estimator will also be examined.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: The problem of visual search is formulated as Bayesian inference, with the set of problem instances drawn from a Bayesian Ensemble. In particular, we address the problem of detecting visual contours in noise/clutter by optimizing a global criterion which combines local intensity and geometry information. We specialize to the specific task of tracking a contour -- such as a road in an aerial image. We determine order parameters, which depend on statistical properties of the target and domain, that characterize the difficulty of the task independently of the algorithm employed to detect the target. For the road tracking problem, we show that there is a phase transition at a critical value of the order parameter -- above this phase transition it is impossible to detect the target by any algorithm. In addition, we derive closely related order parameters which determine the mean computational complexity of search. Although the worst-case complexity of tracking a road of length N is exponential in N, we present an A* search strategy with expected time complexity linear in N (as long as the road is detectable).
We also consider the case where there is a low-level generic model and a more specific high-level model of the target. We demonstrate that in certain regimes (of the order parameters) both models are effective at detecting the target. However, at a critical value of the order parameters there is a phase transition and it becomes effectively impossible to detect the target unless high-level target specific knowledge is used. At another phase transition, the target will become undetectable by any model. These phase transitions determine different regimes within which different search strategies will be effective. These results have implications for bottom-up and top-down theories of vision.
Brown Analysis Seminar
Department of Mathematics Colloquium
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