Dirichlet's and Thomson's principles for non-selfadjoint elliptic operators with application to non-reversible metastable diffusion processes

We present two variational formulae for the capacity in the context of non-selfadjoint elliptic operators. The minimizers of these variational problems are expressed as solutions of boundary-value elliptic equations. We use these principles to provide a sharp estimate for the transition times between two different wells for non-reversible diffusion processes. This estimate permits to describe the metastable behavior of the system

Of mice and men: Sparse statistical modeling in cardiovascular genomics

In high-throughput genomics, large-scale designed experiments are becoming common, and analysis approaches based on highly multivariate regression and anova concepts are key tools. Shrinkage models of one form or another can provide comprehensive approaches to the problems of simultaneous inference that involve implicit multiple comparisons over the many, many parameters representing effects of design factors and covariates. We use such approaches here in a study of cardiovascular genomics. The primary experimental context concerns a carefully designed, and rich, gene expression study focused on gene-environment interactions, with the goals of identifying genes implicated in connection with disease states and known risk factors, and in generating expression signatures as proxies for such risk factors. A coupled exploratory analysis investigates cross-species extrapolation of gene expression signatures--how these mouse-model signatures translate to humans. The latter involves exploration of sparse latent factor analysis of human observational data and of how it relates to projected risk signatures derived in the animal models. The study also highlights a range of applied statistical and genomic data analysis issues, including model specification, computational questions and model-based correction of experimental artifacts in DNA microarray data.Comment: Published at http://dx.doi.org/10.1214/07-AOAS110 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A New Statistic for Analyzing Baryon Acoustic Oscillations

We introduce a new statistic omega_l for measuring and analyzing large-scale structure and particularly the baryon acoustic oscillations. omega_l is a band-filtered, configuration space statistic that is easily implemented and has advantages over the traditional power spectrum and correlation function estimators. Unlike these estimators, omega_l can localize most of the acoustic information into a single dip at the acoustic scale while also avoiding sensitivity to the poorly constrained large scale power (i.e., the integral constraint) through the use of a localized and compensated filter. It is also sensitive to anisotropic clustering through pair counting and does not require any binning. We measure the shift in the acoustic peak due to nonlinear effects using the monopole omega_0 derived from subsampled dark matter catalogues as well as from mock galaxy catalogues created via halo occupation distribution (HOD) modeling. All of these are drawn from 44 realizations of 1024^3 particle dark matter simulations in a 1h^{-1}Gpc box at z=1. We compare these shifts with those obtained from the power spectrum and conclude that the results agree. This indicates that any distance measurements obtained from omega_0 and P(k) will be consistent with each other. We also show that it is possible to extract the same amount of acoustic information using either omega_0 or P(k) from equal volume surveys.Comment: 12 pages, 7 figures. ApJ accepted. Edit: Now updated with final accepted versio