Search for: All records

Abstract Worldwide, governments imposed non-pharmaceutical interventions (NPIs) during the COVID-19 pandemic to contain the pandemic more effectively. We examined the effectiveness of individual NPIs in the United States during the first wave of the pandemic. Three types of analyses were performed. First, a prototypical Bayesian hierarchical model was employed to gauge the effectiveness of five NPIs and they are gathering restriction, restaurant capacity restriction, business closure, school closure, and stay-at-home order in the 42 states with over 100 deaths by the end of the wave. Second, we examined the effectiveness of the face mask mandate, the sixth and most controversial NPI by counterfactual modeling, which is a variant of the prototypical Bayesian hierarchical model allowing us to answer the question of what if the state had imposed the mandate or not. The third analysis used an advanced Bayesian hierarchical model to evaluate the effectiveness of all six NPIs in all 50 states and the District of Columbia, and thereby provide a full-scale estimation of the effectiveness of NPIs and the relative effectiveness of each NPI in the entire United States. Our results have enhanced the collective knowledge on the general effectiveness of NPIs in arresting the spread of COVID-19. 

IntroductionThe moment quantities associated with the nonlinear Schrödinger equation offer important insights into the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities are amenable to both analytical and numerical treatments. MethodsIn this paper, we present a data-driven approach associated with the “Sparse Identification of Nonlinear Dynamics” (SINDy) to capture the evolution behaviors of such moment quantities numerically. Results and DiscussionOur method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available. 

We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action. Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation. Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts.