Effect of Mitigation Measures on the Spreading of COVID-19 in Hard-Hit States

State government-mandated social distancing measures have helped to slow down the growth of the COVID-19 pandemic in the United States. Current predictive models of the development of COVID-19, especially after mitigation efforts, are largely based on extrapolating the data from other countries. Since most states enforced stay-at-home orders towards the end of March, their effect should be reflected in the death and infection counts at the end of April. Using the data available until April 25th, we investigate the change in the infection rate due to the mitigation efforts, and project death and infection counts until September, 2020, for some of the most heavily impacted states: New York, New Jersey, Michigan, Massachusetts, Illinois and Louisiana. We find that with the current mitigation efforts five of those six states reduce their reproduction number to a value less than one, stopping the exponential growth of the pandemic. We also projected different scenarios after the mitigation is relaxed. Analysis for other states can be found at https://covid19projection.org/.Comment: 8 pages, 6 figures, 2 table

Identifying structural changes with unsupervised machine learning methods

Unsupervised machine learning methods are used to identify structural changes using the melting point transition in classical molecular dynamics simulations as an example application of the approach. Dimensionality reduction and clustering methods are applied to instantaneous radial distributions of atomic configurations from classical molecular dynamics simulations of metallic systems over a large temperature range. Principal component analysis is used to dramatically reduce the dimensionality of the feature space across the samples using an orthogonal linear transformation that preserves the statistical variance of the data under the condition that the new feature space is linearly independent. From there, k-means clustering is used to partition the samples into solid and liquid phases through a criterion motivated by the geometry of the reduced feature space of the samples, allowing for an estimation of the melting point transition. This pattern criterion is conceptually similar to how humans interpret the data but with far greater throughput, as the shapes of the radial distributions are different for each phase and easily distinguishable by humans. The transition temperature estimates derived from this machine learning approach produce comparable results to other methods on similarly small system sizes. These results show that machine learning approaches can be applied to structural changes in physical systems

The flexural mechanics of creased thin strips

© 2019 Many structures in Nature and Engineering are dominated by the influence of folds. A very narrow fold is a crease, which may be treated with infinitesimal width for a relatively simple geometry; commensurately, it operates as a singular hinge line with torsional elastic properties. However, real creases have a finite width and thus continuous structural properties. We therefore consider the influence of the crease geometry on the large-displacement flexural behaviour of a thin creased strip. First, we model the crease as a shallow cylindrical segment connected to initially flat side panels. We develop a theoretical model of their coupled flexural behaviour and, by adjusting the relative panel size, we capture responses from a nearly singular crease up to a full tape-spring. Precise experiments show good agreement compared to predictions.Cambridge Home and European Scholarship Schem

Deep learning on the 2-dimensional Ising model to extract the crossover region with a variational autoencoder

The 2-dimensional Ising model on a square lattice is investigated with a variational autoencoder in the non-vanishing field case for the purpose of extracting the crossover region between the ferromagnetic and paramagnetic phases. The encoded latent variable space is found to provide suitable metrics for tracking the order and disorder in the Ising configurations that extends to the extraction of a crossover region in a way that is consistent with expectations. The extracted results achieve an exceptional prediction for the critical point as well as agreement with previously published results on the configurational magnetizations of the model. The performance of this method provides encouragement for the use of machine learning to extract meaningful structural information from complex physical systems where little a priori data is available