COVID-19 in the U.S. during pre-vaccination period: Shifting impact of sociodemographic factors and air pollution.

Pandemic "wave" usually refers to the rise and fall of the infections with time, however, for a large country, the variations due to geographical location could be considerable. In this work, we investigated COVID-19 infection and fatality across the U.S.

A Bayesian Model to Analyze the Association of Rheumatoid Arthritis With Risk Factors and Their Interactions.

Rheumatoid arthritis (RA) is a chronic autoimmune disorder that commonly manifests as destructive joint inflammation but also affects multiple other organ systems. The pathogenesis of RA is complex where a variety of factors including comorbidities, demographic, and socioeconomic variables are known to associate with RA and influence the progress of the disease. In this work, we used a Bayesian logistic regression model to quantitatively assess how these factors influence the risk of RA, individually and through their interactions.

Finite-time braiding exponents.

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors.

Applied Koopmanism.

A majority of methods from dynamical system analysis, especially those in applied settings, rely on Poincaré's geometric picture that focuses on "dynamics of states." While this picture has fueled our field for a century, it has shown difficulties in handling high-dimensional, ill-described, and uncertain systems, which are more and more common in engineered systems design and analysis of "big data" measurements. This overview article presents an alternative framework for dynamical systems, based on the "dynamics of observables" picture.