Center for Computational Molecular Biology Seminar
Abstract: Tiling DNA microarrays extend current microarray technology by probing the non-repeat portion of a genome at regular intervals in an unbiased fashion. A fundamental problem in the analysis of these data is the detection of genomic regions that are differently transcribed across multiple conditions. We propose a linear time algorithm based on segmentation techniques and linear modeling that can work at a user-selected false discovery rate. It also attains a four-fold sensitivity gain over the only competing algorithm when applied to a whole genome transcription data set spanning the embryonic development of Drosophila melanogaster.
Brown University Center for Statistical Sciences Seminar
Abstract: Recurrent events arise in many scientific areas: biomedical and public health; reliability and engineering; actuarial settings; economic, sociological, and political settings. In this talk, I will discuss issues of stochastic modeling of recurrent event data and the statistical inference concerning the parameters of such models. I will indicate unique and intrinsic features that lead to some difficulties with the handling of recurrent event data, specifically the impact of the sum-quota accrual scheme, which leads to both informative and dependent censoring. I will also discuss efficiency issues pertaining to the statistical inference of the model parameters. Some illustrations will be performed with biomedical data.
Abstract: Emission trading schemes are regulatory frameworks designed to reduce and control pollution levels by creating economic incentives for responsible emission sources. The talk is devoted to the mathematical analysis of the most important lesson learned from the first phase of the European experiment: the relations between carbon and electricity prices. We explain how the prices of goods and pollution permits come out of a competitive equilibrium model of the economy. We prove existence, and we characterize mathematically the price of a pollution permit in equilibrium, and we show that the prices of goods follow a classical merit order. In such an economy, pollution reduction is possible if the regulator can solve a complex (ill-posed) inverse problem. Using our model, we compare numerically, for a fixed emissions target, the social costs and the windfall profits for three different schemes: a plain tax, a cap-and-trade scheme as implemented by the European Union, and a new cap-and-trade scheme where pollution allowances are granted proportionally to production, and we show that the latter lowers the social costs and the windfall profits.
Department of Mathematics Colloquium
Scientific Computing Seminar
Abstract: The talk is about the approximation given by the original discontinuous Galerkin method for the transport-reaction equation in $d$ space dimensions. The approximation is optimal provided the meshes are suitably chosen: the $L^2$-norm of the error is of order $k+1$ when the method uses polynomials of degree $k$. These meshes are not necessarily conforming and do not satisfy any uniformity condition; they are only required to be made of simplexes each of which has a unique outflow face. We also find a new, element-by-element postprocessing of the derivative in the direction of the flow which superconverges with order $k+1$.
Abstract: We present recent results allowing us to estimate the time of existence of small data semilinear Klein-Gordon equations on Zoll manifolds (e.g. spheres of arbitrary dimension). The proof relies on the normal form method and on the specific distribution of the eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds.
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