CUR Decompositions and Applications
DateTuesday, March 19, 2019 - 12:30pm
AbstractThis talk will focus on an interesting matrix decomposition (CUR) which decomposes a matrix by selecting representative columns and rows from it. We give several equivalent formulations of this decomposition, and discuss randomized column and row sampling procedures which guarantee a valid CUR decomposition of a matrix is attained with high probability. We also discuss some perturbation results for the decomposition and illustrate some connections with applications including motion segmentation and facial recognition, as well as other data applications requiring dimensionality reduction as a first step.
Detecting ancient epidemics in present human genomes
DateTuesday, March 19, 2019 - 4:00pm
AbstractModern humans migrated out of Africa about 60,000 years ago. As they started colonizing the new environments of Eurasia, they found that they were not the first humans to have ventured out of Africa. Neanderthals had preceded them and colonized the cold prehistoric Eurasia hundreds of thousands of years before. Modern humans and Neanderthals then not only came in contact with each other, but also interbred with each other. This interbreeding, however, hid an invisible poison: Neanderthal viruses that rapidly infected modern humans. At the same time however, Neanderthals gave us the antidote as a gift: genes from their genome that gave us resistance against their own viruses. Remarkably, these Neanderthal genes are still present is specific modern human populations to this day, and make it possible to identify which viruses Neanderthals infected modern humans with when they interbred. In other words, evolutionary genomicists have opened a new window on long-gone and forgotten epidemics.
A renewal reward approach for studying models of intracellular transport
DateThursday, March 21, 2019 - 12:30pm
AbstractMany biological agents transition between different biophysical states during movement. For example, proteins inside cells bind and unbind to and from cellular roads called microtubules, switching between bidirectional transport, diffusion, and stationary states. Since models of intracellular transport can be analytically intractable, asymptotic methods are useful in understanding effective cargo transport properties as well as their dependence on model parameters. We consider these models in the framework of renewal processes and derive the effective velocity and diffusivity of cargo at large time for a class of problems. We illustrate applications of the proposed method to macroscopic models of protein localization and microscopic models of cargo movement by teams of molecular motor proteins. We also show limitations of this approach in cases where the spatial dependence on microtubules is explicitly modeled. This is joint work with Scott McKinley, John Fricks, and Peter Kramer.
Partial Sample Average Approximation Method for Chance Constrained Programs
DateFriday, March 22, 2019 - 3:00pm
AbstractIn this talk, we present a new scheme of a sampling-based method, named Partial Sample Average Approximation (PSAA) method, to solve chance constrained programs. In contrast to Sample Average Approximation (SAA) which samples all of the random variables, PSAA only samples a portion of random variables by making use of the independence of some of the random variables for stepwise evaluation of the expectation. The main advantage of the proposed approach is that the PSAA approximation problem contains only continuous auxiliary variables, whilst the SAA reformulation contains binary ones. Moreover, we prove that the proposed approach has the same convergence properties as SAA. At the end, a numerical study on different applications shows the strengths of the proposed approach, in comparison with other popular approaches, such as SAA and scenario approach.