Lefschetz Center for Dynamical Systems Seminar
Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, Georgia | |
Abstract: Using two examples, the Kot-Shaffer growth-dispersal model for plants and the Kuramoto-Sivashinsky equation, I will describe a program designed to facilitate computer assisted proofs for infinite dimensional systems. The goal is to develop methods that are both computationally cheap and accurate. The techniques are based on algebraic topology and in particular the Conley index theory. We will finish with some open questions in computational geometry that are relevant to the development of algorithms for approximating the vector field.
Brown University Center for Statistical Sciences Seminar
Chairman, Department of Hygiene and Epidemiology, University of Ioannina School of Medicine | |
*Reception Following Seminar at 167 Angell Street., 2nd Floor Conference Room. |
Abstract: Over 2,000 meta-analyses have been performed in the last 20 years. These studies offer us a unique opportunity for addressing empirically problems that go beyond the definition of treatment effects and their heterogeneity for a specific single intervention. Several different meta-analyses may be analyzed together to gain insight into larger-scale problems pertaining to topics (medical research fields) rather than single interventions. We will discuss some of these potential ``meta-epidemiologic'' uses of meta-analyses. First, we will address the controversy of whether large-scale randomized designs yield similar answers as smaller-scale randomized trials using empirical data from various medical fields. Second, we will present recursive cumulative meta-analysis, a diagnostic for the evolution of effect sizes over time and for the assessment of the extent of anticipated future changes in the treatment effect for a given intervention, when seen in the context of previous experience for various interventions in the same field. Finally, we will discuss extrapolations of meta-epidemiologic approaches outside the domain of randomized trials, with emphasis on the comparison of randomized vs. observational designs across diverse medical topics.
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