The mathematics of the wearables with applications to circadian rhythms and sleep
Millions of individuals track their steps, heart rate, and other physiological signals through wearables. This data scale is unprecedented; I will describe several of our apps and 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 and in desperate need of new mathematical techniques to extract key signals 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. My focus applications will be determining the phase of circadian rhythms, the scoring of sleep and the detection of COVID with wearables.