Abstract: Reverse engineering whole-genome networks from large-scale gene expression measurements and analyzing them to extract biologically valid hypotheses are important challenges in systems biology. While simpler models easily scale to large number of genes and gene expression datasets, more accurate models are compute intensive limiting their scale of applicability. In this talk, I will present our research on the development of parallel mutual information and Bayesian network based structure learning methods to eliminate such bottlenecks and facilitate learning of genome-scale networks. Such networks can be used as a guide to predicting gene function and extracting context-specific subnetworks.

Abstract: The mathematical connections between graph theory and linear algebra are intimate and well known. The computational links between the two fields are also deep, extending from basic data structures to fundamental decompositions to the design of efficient algorithms. During the first 50 years of this computational relationship, graphs served numerical linear algebra by enabling efficient sparse matrix computation. Recently, matrix computation has been returning the favor. I will talk about the past and present of the relationship in both directions, and speculate a bit on its future.

Abstract: Graph theoretic optimization problems that have been dormant for fifty years are now seeing new and exciting algorithms. These advances have been made possible by Spectral Graph Theory, the interplay between linear algebra and combinatorial graph theory. One application of this interplay is a nearly linear time solver for Symmetric Diagonally Dominant systems (SDD). This seemingly restrictive class of linear systems has received substantial interest in the last fifteen years, and there is an ever growing list of problems that are amenable to SDD solvers, including image segmentation, image denoising, finding solutions to elliptic equations, computing maximum flow in a graph, and graph sparsification. All these examples can be viewed as special cases of convex optimization problems on graphs.