Georgia Institute of Technology College of Sciences

How advances in science are made, and how they may come to benefit mankind at large are complex issues. The discoveries that most infuence the way we think about nature seldom can be anticipated, and frequently the applications for new technologies developed to probe a specific characteristic of nature are also seldom clear, even to the inventors of these technologies. One thing is most clear: seldom do individuals make such advances alone. Rather, they result from the progress of the scientific community, asking questions, developing new technologies to answer those questions, and sharing their results and their ideas with others. However, there are indeed research strategies that can substantially increase the probability of one's making a discovery, and the speaker will illustrate some of these strategies in the context of a number of well known discoveries, including the work he did as a graduate student, for which he shared the Nobel Prize for Physics in 1996.

The goal in matrix recovery problems is to estimate an unknown rank-r matrix S of size m based on a set of n observations. It is easy to see that even in the case where the observations are not contaminated with noise, there exist low rank matrices that cannot be recovered based on n observations unless n is very large. In order to deal with these cases, Candes and Tao introduced the called low-coherence assumptions and a parameter \nu measuring how low-coherent the objective matrix S is. Using the low-coherence assumptions, Gross proved that S can be recovered with high probability if n>O(\nu r m \log^2(m)) by an estimator based on nuclear norm penalization. Let's consider the generalization of the matrix recovery problem where the matrix S is not only low-rank but also "smooth" with respect to the geometry given by a graph G. In this 40 minutes long talk, the speaker will present an approximation error bound for a proposed estimator in this generalization of the matrix recovery problem.

A discussion of the paper "Beyond energy minimization: approaches to the kinetic folding of RNA'' by Flamm and Hofacker (2008).

A discussion of the paper "Using Motion Planning to Study RNA Folding Kinetics" by Tang et al (J Comp Biol, 2005).