Title: Traditional Applied Math, and then, Working with High Dimensional Biological Data
I will give an overview of my interests in two parts. The first part will be on passive tracer problems – with the goal of finding formulas of descriptive statistics (mean, variance, skewness) for a solute distribution advected by a smooth flow in a tube with arbitrary cross-section. We found explicit formulas which predict these statistics relying ultimately only on the cross-section of the tube, and see agreement with numerical simulation as well as experiment. Some partial derivatives and pretty pictures from simulations will be shown.
In the second part, I’ll talk about my projects outside of partial differential equations. The main thrust of my (pre-pandemic) postdoctoral project was applying math and machine learning approaches to identify biomarkers predictive of pre-symptomatic infection in “omics” data sets from human challenge studies of influenza-like illnesses. I’ll define the jargon, and talk about our successes* in answering a few questions:
Given a collection of blood samples from study participants, can one identify (classify) a new blood sample as coming from a “shedder” (one who may be expected to be contagious) in the first 24 hours after exposure?
Given a collection of granular blood samples from study participants over the first week of infection, and given a blood sample from someone already known to be infected, can one predict how long it has been since the exposure event?