On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2.

The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's infinitesimal generator (rate) matrix. Motivated by the derivative's extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a "blessing of dimensionality" result that is universal for a large class of rate matrices with random entries. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology.

Drowsiness detection from polysomnographic data using multivariate selfsimilarity and eigen-wavelet analysis.

Because drowsiness is a major cause in vehicle accidents, its automated detection is critical. Scale-free temporal dynamics is known to be typical of physiological and body rhythms. The present work quantifies the benefits of applying a recent and original multivariate selfsimilarity analysis to several modalities of polysomnographic measurements (heart rate, blood pressure, electroencephalogram and respiration), from the MIT-BIH Polysomnographic Database, to better classify drowsiness-related sleep stages. Clinical relevance- This study shows that probing jointly temporal dynamics amongst polysomnographic measurements, with a proposed original multivariate multiscale approach, yields a gain of above 5% in the Area-under-Curve quanti-fying drowsiness-related sleep stage classification performance compared to univariate analysis.

Fluid heterogeneity detection based on the asymptotic distribution of the time-averaged mean squared displacement in single particle tracking experiments.

A tracer particle is called anomalously diffusive if its mean squared displacement grows approximately as σ 2 t α as a function of time t for some constant σ 2, where the diffusion exponent satisfies α ≠ 1. In this article, we use recent results on the asymptotic distribution of the time-averaged mean squared displacement [20] to construct statistical tests for detecting physical heterogeneity in viscoelastic fluid samples starting from one or multiple observed anomalously diffusive paths. The methods are asymptotically valid for the range 0 < α < 3/2 and involve a mathematical characterization of time-averaged mean squared displacement bias and the effect of correlated disturbance errors. The assumptions on particle motion cover a broad family of fractional Gaussian processes, including fractional Brownian motion and many fractional instances of the generalized Langevin equation framework. We apply the proposed methods in experimental data from treated P. aeruginosa biofilms generated by the collaboration of the Hill and Schoenfisch Labs at UNC-Chapel Hill.