Brown University Center for Statistical Sciences Seminar
Abstract: Variance-component linkage analysis is a powerful and flexible tool for detecting genes that influence complex quantitative traits. However, the variance-component method makes the crucial assumption that the trait of interest follows a multivariate normal distribution within a family. Variance-component linkage analysis of non-normal data may lead to biased parameter estimates and elevated type I error rates. Therefore, the application of the traditional variance-component method to binary data (e.g. presence/absence of disease), censored normal data, or other non-normal trait data will be difficult. Therefore, I show how one can extend the traditional variance- component method to accommodate non-normal data using generalized linear mixed-model theory. I illustrate the utility of this new variance-component method by application to both simulated binary and censored normal data. I will also employ the method to analyze censored normal data from the Finland-United States Investigation of Non-Insulin-Dependent Diabetes Mellitus Genetics (FUSION) study. Extension of the method to accommodate non-random sampling schemes will also be discussed.
Lefschetz Center for Dynamical Systems Seminar
Brown University Dissertation Defense
Brown University Dissertation Defense
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: Inpainting is the art of modifying an image in a form that is not detectable to an ordinary observer. The applications of this are numerous, from special effects in movies to wireless image transmission. In this talk we will describe novel algorithms for image (and surface) inpainting that we have been developing in the last few years. The algorithms are based on partial differential equation such as those used to model fluid dynamics. We will mention the connections of our algorithms with biological processes.
Special Stochastic Systems Seminar
Abstract: The past few years have seen a substantial progress in the mathematical theory of utility maximization in incomplete semimartingale financial market models. Convex duality, coupled with the proper functional-analytic setup, has proven to be a versatile and sucessful method for attacking these non-Markovian problems.
In my talk I will present a short survey of the recent results and show how to optimize your utility of consumption when you are facing not only an undiversifiable uncertainty in the market movements, but also a stochastic "speed of time".
Distinguished Lectures in Mathematics
Brown University Graduate School Dissertation Defense
Scientific Computing Seminar
Abstract: In this talk, we will review various splitting schemes for solving time dependent Navier-Stokes equations. These schemes share the same advantage that one only needs to solve a sequence of decoupled Poisson-type equations at each time step and have been widely used in practice due to their efficiency and simplicity. However, since the splitting involves non-commutative operators, how to design accurate and stable splitting schemes, is a very subtle issue. We will present error estimates for two class of splitting schemes, namely pressure-correction and velocity-correction schemes and show that they all suffer from an irreducible splitting error for the pressure and vorticity. We will then present a new class of truly consistent splitting schemes.
Finally, we will discuss the influence of open boundary conditions on the accuracy of the splitting schemes.
Distinguished Lectures in Mathematics
Distinguished Lectures in Mathematics
<--- 2003 Index