Georgia Institute of Technology College of Sciences

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.

Let $\M$ be a smooth connected manifold endowed with a smooth measure $\mu$ and a smooth locally subelliptic diffusion operator $L$ which is symmetric with respect to $\mu$. We assume that $L$ satisfies a generalized curvature dimension inequality as introduced by Baudoin-Garofalo \cite{BG1}. Our goal is to discuss functional inequalities for $\mu$ like the Poincar\'e inequality, the log-Sobolev inequality or the Gaussian logarithmic isoperimetric inequality.

Implicit solvent models are important components of modern biomolecular simulation methodology due to their efficiency and dramatic reduction of dimensionality. However, such models are often constructed in an ad hoc manner with an arbitrary decomposition and specification of the polar and nonpolar components. In this talk, I will review current implicit solvent models and suggest a new free energy functional which combines both polar and nonpolar solvation terms in a common self-consistent framework. Upon variation, this new free energy functional yields the traditional Poisson-Boltzmann equation as well as a new geometric flow equation. These equations are being used to calculate the solvation energies of small polar molecules to assess the performance of this new methodology. Optimization of this solvation model has revealed strong correlation between pressure and surface tension contributions to the nonpolar solvation contributions and suggests new ways in which to parameterize these models. **Please note nonstandard time and room.**

Pardon the inconvenience. We plan to reschedule later...