The Variational Implicit Solvent Model (VISM) is a theoretical and computational framework for studying bimolecular systems with complex topology. Central in VISM is an effective free-energy of all possible interfaces separating solutes (e.g., proteins) from solvent (e.g., water). Such a functional can be minimized numerically by a level-set method to determine the stable equilibrium conformations and solvation free energies. In this talk we introduce two numerical methods related to VISM. The first one is the Compact Coupling Interface Method (CCIM), which is a finite difference method for elliptic interface problems with accurate gradient approximation. The second one is the Binary Level Set-VISM, which is coupled with the Monte Carlo method to simulate the binding of biomolecules.

Please join the Division of Physical Sciences for a virtual public lecture presented by the 2019-20 Lattimer Fellows: Rommie Amaro (Chemistry and Biochemistry), Suckjoon Jun (Physics), and Bo Li (Mathematics).
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The George W. and Carol A. Lattimer Faculty Research Fellowship seeks to stimulate thought about avenues of productive scientific exploration that may result from unique fusions and collaborations and promotes cross-collateral work between scientists and non-scientists at UC San Diego.
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Learn more about this opportunity and hear from past fellows about their research made possible through this fellowship.

We give an overview of dimensionality reduction methods, or sketching, for a number of problems in optimization, first surveying work using these methods for classical problems, which gives near optimal algorithms for regression, low rank approximation, and natural variants. We then survey recent work applying sketching to column subset selection, kernel methods, sublinear algorithms for structured matrices, tensors, trace estimation, and so on. The focus in the talk will be on fast algorithms.