Brown University Center for Statistical Sciences Seminar
Professor Department of Epidemiology and Biostatistics | |
Abstract: In the `alternating sequence design' used to compare the success rates with assisted reproductive technologies, women or couples are randomized to receive either the standard or experimental treatment in the first cycle, and -- if they do not become pregnant---crossed between standard and experimental treatments after each successive cycle. Norman and Daya (Fertility and Sterility, 2000) have shown that, in the presence of heterogeneity of fertility, and an effective treatment, the overall efficacy of the experimental treatment is overestimated by this design. They advised that in order to achieve an accurate estimate, the trial should be run for at least three cycles and all data from even-numbered cycles be excluded from the analysis, which should then be restricted only to odd-numbered cycles. In this talk, I describe several approaches, of varying complexity, that can make use of the data from all cycles to produce estimates that are unbiased and more precise. Some of the methods use the aggregated data from each cycle, while the others use the couple-cycle as the unit of analysis. The methods are also applicable to the `constant sequence' design, where naive methods that do not take account of the heterogeneity produce underestimates of treatment efficacy.
This is joint work with Robert Platt, Marie-H\'el\`ene Mayrand and Nandini Dendukuri
*Coffee and donuts will be served.
Brown Analysis Seminar
Scientific Computing Seminar
Institute for Applied Mathemaics and Numerical Analysis (Inst. E 115), Vienna, Austria | |
in Computational Microstructures | |
Abstract: Nonconvex minimisation problems are encountered in many applications such as phase transitions in solids (1) or liquids but also in optimal design tasks (2) or micromagnetism (3). In contrast to rubber-type elastic materials and many other variational problems in continuum mechanics, the minimal energy may be not attained. In the sense of (Sobolev) functions, the non-rank-one convex minimization problem (M) is ill-posed: As illustrated in the introduction of FERM, the gradients of infimising sequences are enforced to develop finer and finer oscillations called microstructures. Some macroscopic or effective quantities, however, are well- posed and the target of an efficient numerical treatment.
The presentation proposes adaptive mesh-refining algorithms for the finite element method for the effective equations ($R$), i.e. the macroscopic problem obtained from relaxation theory. For some class of convexified model problems, a~priori and a~posteriori error control is available with a reliability-efficiency gap. Nevertheless, convergence of some adaptive finite element schemes is guaranteed. Applications involve model situations for (1), (2), and (3) where the relaxation is provided by a simple convexification.
PDE Seminar
Abstract: The interface between a heavy fluid resting above a light fluid is unstable to small perturbations. Conventional wisdom has been that instability implies unpredictability. This is in sharp contrast with robust evidence (experimental and numerical) of simple dynamical scaling laws in these flows, and a long tradition in engineering of simple models for bulk transport that sometimes work remarkably well.
I will describe rigorous results (coarsening rates, sharp transport estimates) on the evolution of a labyrinthine network of "fingers" in miscible flows in a porous medium. If time permits, I will also describe ongoing work on flows with inertia (Rayleigh-Taylor flows). The tools are simple ideas from the theory of conservation laws, calculus of variations and nonlinear waves.
This is work with Felix Otto (Bonn).
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