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State and local governments imposed social distancing measures in March and April 2020 to contain the spread of the novel coronavirus disease (COVID-19). These measures included bans on large social gatherings; school closures; closures of entertainment venues, gyms, bars, and restaurant dining areas; and shelter-in-place orders. We evaluated the impact of these measures on the growth rate of confirmed COVID-19 cases across US counties between March 1, 2020, and April 27, 2020. An event study design allowed each policy's impact on COVID-19 case growth to evolve over time. Adoption of government-imposed social distancing measures reduced the daily growth rate of confirmed COVID-19 cases by 5.4 percentage points after one to five days, 6.8 percentage points after six to ten days, 8.2 percentage points after eleven to fifteen days, and 9.1 percentage points after sixteen to twenty days. Holding the amount of voluntary social distancing constant, these results imply that there would have been ten times greater spread of COVID-19 by April 27 without shelter-in-place orders (ten million cases) and more than thirty-five times greater spread without any of the four measures (thirty-five million cases). Our article illustrates the potential danger of exponential spread in the absence of interventions, providing information relevant to strategies for restarting economic activity.

Tensor Krylov subspace methods are popular technologies for solving Sylvester tensor equations, among which the GMRES method based on tensor format (GMRES_BTF) and the FOM method based on tensor format (FOM_BTF) are two commonly used ones. Both of them rely on the Arnoldi process based on tensor format (Arnoldi_BTF) to construct orthonormal bases for tensor Krylov subspace. However, the computational costs and storage requirements of the tensor Krylov subspace methods will increase tremendously as the Arnoldi_BTF process proceeds. Restarting is an efficient way to deal with this problem. To the best of our knowledge, there are few efficient restarting strategies for tensor Krylov subspace methods. In order to fill-in this gap, we apply the deflated restarting strategy to the GMRES_BTF and FOM_BTF methods, and propose two deflated restating methods for solving Sylvester tensor equations. The key is that the two proposed methods retain some useful information in the harmonic Ritz tensors or Ritz tensors obtained from the previous tensor Krylov subspace, respectively. Numerical experiments on both artificial and real data sets demonstrate the superiority of the proposed methods over many state-of-the-art methods for Sylvester tensor equations.

For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generalized minimal residual method (GMRES). We propose a flexible variant of GMRES with the randomized Gram-Schmidt–based Arnoldi iteration to produce a set of basis vectors of the Krylov subspace. Even though the Krylov basis is no longer l 2 orthonormal, its random projection onto the low dimensional space achieves l 2 orthogonality. As a result, the numerical stability is observed which turns out to be independent of the dimension of the problem even in extreme scale problems. On the other hand, as the harmonic Ritz values are commonly used in GMRES with deflated restarting to improve convergence, we consider another deflation strategy, for instance disregarding the singular vectors associated with the smallest singular values. We thus introduce a new algorithm of the randomized flexible GMRES with singular value decomposition (SVD)–based deflated restarting. At the end, we carry out numerical experiments in the context of compressible turbulent flow simulations. Our proposed approach exhibits a quite competitive numerical behaviour to existing methods while reducing computational costs.

Stateless ordered restart-delete automata (stl-ORD-automata) are studied. These are obtained from the stateless ordered restarting automata (stl-ORWW-automata) by introducing an additional restart-delete operation, which, based on the surrounding context, deletes a single letter. While the stl-ORWW-automata accept the regular languages, we show that the swift stl-ORD-automata yield a characterization for the class of context-free languages. Here a stl-ORD-automaton is called swift if it can move its window to any position after performing a restart. We also study the descriptional complexity of swift stl-ORD-automata and relate them to limited context restarting automata.

When using the Arnoldi method for approximating $f(A){\\mathbf b}$, the action of a matrix function on a vector, the maximum number of iterations that can be performed is often limited by the storage requirements of the full Arnoldi basis. As a remedy, different restarting algorithms have been proposed in the literature, none of which has been universally applicable, efficient, and stable at the same time. We utilize an integral representation for the error of the iterates in the Arnoldi method which then allows us to develop an efficient quadrature-based restarting algorithm suitable for a large class of functions, including the so-called Stieltjes functions and the exponential function. Our method is applicable for functions of Hermitian and non-Hermitian matrices, requires no a priori spectral information, and runs with essentially constant computational work per restart cycle. We comment on the relation of this new restarting approach to other existing algorithms and illustrate its efficiency and numerical stability by various numerical experiments. [PUBLICATION ABSTRACT]

Abstract The laying accuracy of the automated fiber placement (AFP) machine determines the actual laying position of the prepreg tow, which directly affects the mechanical properties of the composite component after curing. The laying accuracy is affected by the coupling of multiple factors such as the spatial movement of the AFP machine, the delivery of the tow, and the coordinated movement of the AFP machine and the tow. Aiming at the problem that the friction conveying accuracy of the tow is difficult to guarantee, the transport model of the tow in the restarting stage is established, and the restarting accuracy of the tow is improved by optimizing the clamping scheme. A timing-based execution method of the restarting and cutting instructions is proposed to meet the process requirements of high placement speed and high coordination precision of the AFP process. Finally, the laying experiments are carried out on a special mold, and the start and end points of the tows can meet the requirements of laying accuracy.

An arc-search interior-point method is a type of interior-point method that approximates the central path by an ellipsoidal arc, and it can often reduce the number of iterations. In this work, to further reduce the number of iterations and the computation time for solving linear programming problems, we propose two arc-search interior-point methods using Nesterov’s restarting strategy which is a well-known method to accelerate the gradient method with a momentum term. The first one generates a sequence of iterations in the neighborhood, and we prove that the proposed method converges to an optimal solution and that it is a polynomial-time method. The second one incorporates the concept of the Mehrotra-type interior-point method to improve numerical performance. The numerical experiments demonstrate that the second one reduced the number of iterations and the computational time compared to existing interior-point methods due to the momentum term.

The popularity of running continues to increase, which means that the incidence of running-related injuries will probably also continue to increase. Little is known about risk factors for running injuries and whether they are sex-specific. The aim of this study was to review information about risk factors and sex-specific differences for running-induced injuries in adults. The databases PubMed, EMBASE, CINAHL and Psych-INFO were searched for relevant articles. Longitudinal cohort studies with a minimal follow-up of 1 month that investigated the association between risk factors (personal factors, running/training factors and/or health and lifestyle factors) and the occurrence of lower limb injuries in runners were included. Two reviewers' independently selected relevant articles from those identified by the systematic search and assessed the risk of bias of the included studies. The strength of the evidence was determined using a best-evidence rating system. Sex differences in risk were determined by calculating the sex ratio for risk factors (the risk factor for women divided by the risk factor for men). Of 400 articles retrieved, 15 longitudinal studies were included, of which 11 were considered high-quality studies and 4 moderate-quality studies. Overall, women were at lower risk than men for sustaining running-related injuries. Strong and moderate evidence was found that a history of previous injury and of having used orthotics/inserts was associated with an increased risk of running injuries. Age, previous sports activity, running on a concrete surface, participating in a marathon, weekly running distance (30-39 miles) and wearing running shoes for 4 to 6 months were associated with a greater risk of injury in women than in men. A history of previous injuries, having a running experience of 0-2 years, restarting running, weekly running distance (20-29 miles) and having a running distance of more than 40 miles per week were associated with a greater risk of running-related injury in men than in women. Previous injury and use of orthotic/inserts are risk factors for running injuries. There appeared to be differences in the risk profile of men and women, but as few studies presented results for men and women separately, the results should be interpreted with caution. Further research should attempt to minimize methodological bias by paying attention to recall bias for running injuries, follow-up time, and the participation rate of the identified target group.

We propose new restarting strategies for the accelerated coordinate descent method. Our main contribution is to show that for a well chosen sequence of restarting times, the restarted method has a nearly geometric rate of convergence. A major feature of the method is that it can take profit of the local quadratic error bound of the objective function without knowing the actual value of the error bound. We also show that under the more restrictive assumption that the objective function is strongly convex, any fixed restart period leads to a geometric rate of convergence. Finally, we illustrate the properties of the algorithm on a regularized logistic regression problem and on a Lasso problem.

[...]the notebook is made available, along with its data (Rule 8), in a manner encouraging public exploration and contribution (Rules 9–10). https://doi.org/10.1371/journal.pcbi.1007007.g001 Rule 1: Document the process, not just the results Computational notebooks’ interactivity makes it quick and easy to try out and compare different approaches or parameters—so quick and easy that we often fail to document those interactive investigations at the time we perform them. [...]the advice long provided regarding paper lab scientific notebooks becomes even more critical: make sure to document all your explorations, even (or perhaps especially) those that led to dead ends. Version control systems compare differences in these JSON files, not differences in the user-friendly notebook graphical user interface (GUI). Because of this, reported differences between versions of a given notebook are usually difficult for users to find and understand because they are expressed as changes in the abstruse JSON metadata for the notebook. Perform preparatory steps, like data cleaning, directly in the notebook and avoid manual interventions. Because notebooks’ interactivity make them vulnerable to accidental overwriting or deletion of critical steps by the user, if your analysis runs quickly, make a habit of regularly restarting your kernel and rerunning all cells to make sure you did not accidentally delete a step while cleaning your notebook (and if you did, retrieve the code for it from version control).