This article examines the relationship between parental networks and parental school involvement during the elementary school years. Using a large, nationally representative data set of elementary school students—the Early Childhood Longitudinal Study–Kindergarten Cohort—and contextual data from the 2000 U.S. Census, our multilevel analysis shows that higher levels of parental networks in first grade are associated with higher levels of parental school involvement in third grade after controlling for individual- and school-level characteristics. Parental networks are positively related to school involvement activities in formal organizations that consist of parents, teachers, and school staff, including participating in parent–teacher organizations and volunteering at school. Furthermore, the positive effects of parental networks on parental school involvement is stronger for families whose children attend schools in disadvantaged neighborhoods. This suggests that well-connected parental networks can serve as a buffer against school neighborhood disadvantages in encouraging parents to be actively involved in schools.

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The reaction-diffusion system is naturally used in chemistry to represent substances reacting and diffusing over the spatial domain. Its solution illustrates the underlying process of a chemical reaction and displays diverse spatial patterns of the substances. Numerical methods like finite element method (FEM) are widely used to derive the approximate solution for the reaction-diffusion system. However, these methods require long computation time and huge computation resources when the system becomes complex. In this paper, we study the physics of a two-dimensional one-component reaction-diffusion system by using machine learning. An encoder-decoder based convolutional neural network (CNN) is designed and trained to directly predict the concentration distribution, bypassing the expensive FEM calculation process. Different simulation parameters, boundary conditions, geometry configurations and time are considered as the input features of the proposed learning model. In particular, the trained CNN model manages to learn the time-dependent behaviour of the reactiondiffusion system through the input time feature. Thus, the model is capable of providing concentration prediction at certain time directly with high test accuracy (mean relative error <3.04%) and 300 times faster than the traditional FEM. Our CNN-based learning model provides a rapid and accurate tool for predicting the concentration distribution of the reaction-diffusion system.

Previous analyses of large national datasets have tended to report a negative relationship between parental homework help and student achievement. Yet these studies have not examined heterogeneity in this relationship based on the propensity for a parent to provide homework help. By using a propensity score–based approach, this study investigates the relationship between daily parental homework help in first grade and student achievement in third grade with nationally representative data from the Early Childhood Longitudinal Study–Kindergarten Class. Results indicated that low prior achievement, socioeconomic disadvantage, and minority status were associated with a high propensity to provide daily homework help. Daily parental homework help was also associated with improved achievement for children whose parents had a high propensity to provide daily homework help. These patterns suggest that complex factors induce daily parental homework help and that these factors are related to heterogeneity in the relationship between daily parental homework help and achievement.

The governmental responses to coronavirus disease 2019 (COVID-19) pandemic, including the approach, interventions, and their associated effectiveness, vary across social, cultural, political, and institutional contexts. In China, the Wuhan lockdown significantly reduced the transmission of COVID-19 throughout the country. Chinese central and local governments' responses to disease containment and mitigation were uniform in policymaking but implemented differently across local governing contexts. This study examines the variation in the effects of human mobility restrictions on inter-provincial migration flow during the COVID-19 outbreak in China. The results show that mobility restrictions reduced the inter-provincial in-migration flow by 63%, and the out-migration flow by 62% from late January to early May in 2020, but the effects varied significantly across provinces. Further, the negative effects of mobility restrictions on province's outflow migration were greater in provinces where local governments had higher levels of social media involvement, greater public security spending, and longer duration of first-level response to public health emergencies. The finding provides important insights for understanding China's local governmental responses to mobility restrictions and their effects on the spread of COVID-19. The coronavirus disease 2019 (COVID-19) emerged in Wuhan, Hubei Province, China, in early December of 2019, and rapidly evolved into a global pandemic. In China, a range of interventions were implemented to CONTACT Zhen Liu