The mathematics of the wearable revolution

Daniel Forger (May 5, 2020)

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Abstract

Millions of Americans track their steps, heart rate, and other physiological signals through wearables. The scale of this data is unprecedented; I will describe several of our ongoing studies each of which collects wearable and mobile data from thousands of users, even in > 100 countries. This data is so noisy that it often seems unusable. It is in desperate need of new mathematical techniques to extract key signals that can be used in the (ode) mathematical modeling typically done in mathematical biology. I will describe several techniques we have developed to analyze this data and simulate models including gap orthogonalized least squares, a new ansatz for coupled oscillators which is similar to the popular ansatz by Ott and Antonsen, but which gives better fits to biological data and a new level-set Kalman Filter that can be used to simulate population densities. I will also describe how these methods can be used to understand the impact of social distancing and COVID lockdowns on circadian timekeeping and sleep.