Probability Seminar
Abstract: Consider the following model for a system of N weakly interacting particles: N stochastic differential equations (SDEs) with coefficients all of the same functional form describe the state evolution of the particles; particles interact through the empirical measure of their states at any given time. In the diffusion case, it is known that the sequence of empirical measures converges, as N tends to infinity, to the weak solution of an associated McKean-Vlasov equation and that it satisfies a large deviation principle. We will present the derivation of a Laplace principle equivalent to the large deviation principle, using the Ellis-Dupuis weak convergence approach. The proof, which avoids discretization arguments, is based on a representation theorem, weak convergence and ideas from stochastic optimal control. The method works under rather mild assumptions and also for models described by SDEs not of diffusion type; to illustrate this, we will present the case of SDE! s with delay.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract:
In this talk I will introduce dense scene alignment and how it can be applied to a number of computer vision problems varying from satellite image registration to object recognition and scene parsing. We propose SIFT flow that establishes dense, semantically meaningful correspondence between two images across scenes by matching pixel-wise SIFT features. Using SIFT flow, we develop a new framework for image parsing by transferring metadata information, such as annotation, motion and depth, from the images in a large database to an unknown query image. We demonstrate this framework using new applications such as predicting motion from a single image and motion synthesis via object transfer. Based on SIFT flow, we introduce a nonparametric scene parsing system using label transfer, with very promising experimental results suggesting that our system outperforms state-of-the-art techniques based on training classifiers.
[pizza will be provided]
Brown Special Analysis Seminar
Abstract: The product BMO space of Chang and Fefferman has received much attention in recent years in the work of Lacey, Muscalu, Petermichl, Pipher, Tao, Thiele, Treil, Wick, and others. In this talk, we identify its multplier algebra. The central tools are endpoint estimates for paraproducts and the connection between the dyadic and continuous version of product BMO, as recently found by Pipher, Ward, and Treil.
Center for Computational Molecular Biology Seminar Series
Hosted by: Daniel Weinreich Refreshments will be served at 3:45pm |
Abstract:
The 1000 genomes project aims to discover and characterize all common human genetic variation with a minor allele frequency (MAF) ≥ 0.5%. The pilot phase of the project was completed in June producing five terabases of Illumina/Solexa, SOLiD, and Roche/454 sequences in ~180 individuals sequenced to ~4x average depth genome-wide in three populations, 30-60x whole-genome sequence for two mother, father, daughter trios, and ~800 individuals with 50x+ coverage using hybrid capture in 1000 randomly-selected genes.
Here we describe the sequence calibration, realignment, and analysis tools we developed at the Broad to discover with high sensitivity and specificity single-nucleotide (SNPs) and short (< 20bp) insertion/ deletion (indels) polymorphisms in all three wings of the pilot phase of the 1000 genomes project. We assess our approach by comparing discovered variation among technologies, across pilot arms, to population genetic expectations and to complementary efforts from other groups participating the 1000 genomes project. Finally, we subject a randomly selected subset of SNP and indel calls to experimental validation to estimate project- wide specificity rates. We highlight best practices and lessons learned on the production and analysis of next-generation sequencer data.
Mathematics Colloquium
Abstract: How much symmetry can one expect in solutions of optimization problems (such as ground states for systems of interacting particles)? In this talk we'll look at several examples from mathematics and physics. In particular, I'll explain a phenomenon I find mysterious and bothersome: in certain very special cases, often related to exceptional mathematical structures, the pair correlation function unexpectedly encodes all relevant information, while in more general cases, even higher correlation functions seem surprisingly powerless.
Scientific Computing Seminar
PDE Seminar