Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds

In this paper we are concerned with the monodromy of Picard-Fuch differential equations associated with one-parameter families of Calabi-Yau threefolds. Our results show that in the hypergeometric cases the matrix representations of monodromy relative to the Frobenius bases can be expressed in terms of the geometric invariants of the underlying Calabi-Yau threefolds. This phenomenon is also verified numerically for other families of Calabi-Yau threefolds in the paper. Furthermore, we discover that under a suitable change of bases the monodromy groups are contained in certain congruence subgroups of Sp(4,Z) of finite index whose levels are related to the geometric invariants of the Calabi-Yau threefoldsComment: 32 pages References adde

Effects of After-School Programs on Student Cognitive and Non-Cognitive Abilities: A Meta-Analysis Based on 37 Experimental and Quasi-Experimental Studies

The after-school program is a crucial initiative for implementing the Double Reduction policy; however, prior research has not provided conclusive evidence on whether extended school hours contribute to students’ cognitive and non-cognitive development or on which types of after-school services are more beneficial for student development. This study analyzed 37 after-school programs from 18 publications using meta-analytic techniques, and the results indicated that participation in after-school programs had positive effects on student cognitive and non-cognitive development despite the small effect size (d = 0.327, p = 0.000). The decomposition of the effects of after-school programs revealed that they had modestly positive effects on academic achievement (d = 0.369) and social-emotional competence (d = 0.220). In addition, the analysis of moderating variables revealed that socioeconomic status, educational phase, number of after-school service days per week, sample size, and testing instrument all influenced the after-school program effects. This study concludes, based on the results of the meta-analysis, that there should be a balanced consideration of the development of student cognitive and non-cognitive abilities in planning after-school service, a substantial variety of activities in after-school programs, a flexible adoption of diverse after-school programs, and a reasonable participation frequency in after-school service

2022-1 The Role of Non-Pecuniary Considerations: Location Decisions of College Graduates from Low Income Backgrounds

We examine the initial post-college geographic location decisions of students from hometowns in the Appalachian region that often lack substantial high-skilled job opportunities, focusing on the role of non-pecuniary considerations. Novel survey questions allow us to measure the full non-pecuniary benfits of each relevant geographic location, in dollar equivalents. A new specification test is designed and implemented to provide evidence about the quality of these non-pecuniary measures. Supplementing perceived location choice probabilities and expectations about pecuniary factors with our new non-pecuniary measures allows a new approach for obtaining a comprehensive understanding of the importance of pecuniary and non-pecuniary factors for location decisions. We compare this approach to alternative expectations-based approaches. We also combine the non-pecuniary measures with realized location and earnings outcomes to characterize inequality in overall welfare

Regression-based heterogeneity analysis to identify overlapping subgroup structure in high-dimensional data

Heterogeneity is a hallmark of complex diseases. Regression-based heterogeneity analysis, which is directly concerned with outcome-feature relationships, has led to a deeper understanding of disease biology. Such an analysis identifies the underlying subgroup structure and estimates the subgroup-specific regression coefficients. However, most of the existing regression-based heterogeneity analyses can only address disjoint subgroups; that is, each sample is assigned to only one subgroup. In reality, some samples have multiple labels, for example, many genes have several biological functions, and some cells of pure cell types transition into other types over time, which suggest that their outcome-feature relationships (regression coefficients) can be a mixture of relationships in more than one subgroups, and as a result, the disjoint subgrouping results can be unsatisfactory. To this end, we develop a novel approach to regression-based heterogeneity analysis, which takes into account possible overlaps between subgroups and high data dimensions. A subgroup membership vector is introduced for each sample, which is combined with a loss function. Considering the lack of information arising from small sample sizes, an $l_2$ norm penalty is developed for each membership vector to encourage similarity in its elements. A sparse penalization is also applied for regularized estimation and feature selection. Extensive simulations demonstrate its superiority over direct competitors. The analysis of Cancer Cell Line Encyclopedia data and lung cancer data from The Cancer Genome Atlas shows that the proposed approach can identify an overlapping subgroup structure with favorable performance in prediction and stability.Comment: 33 pages, 16 figure

Impact of Pet Companionship on Student Development: A Meta-Analysis

Animal companionship has been found to have a positive influence on human well-being, and the presence of pets can have a subtle yet significant impact on the healthy development of students. Pet companionship takes various forms across different fields in China and other regions worldwide, and the impact of such companionship remains uncertain. Hence, it is imperative to investigate the impact of diverse forms of companionship and animals on multiple facets of student growth and development. This study employed meta-analysis methodologies to examine 47 effect sizes derived from 12 domestic and international studies on pet companionship. The aim was to investigate the overall trends of the influence of pet companionship on student development as well as the effects of diverse types of companionship and pets on different aspects of student development, including physical and mental health, social-emotional abilities, and academic performance. The objective was to enhance the exploration of approaches for maximizing the utilization of various forms of pet companionship. Furthermore, this research suggests a systematic and incremental approach to enhancing the function of pets within households, educational institutions, and medical facilities. Adequate content and organization are essential for scientific advancement and the development of students. In this particular context, it is possible to optimize the impact of pet companionship on the development of students

Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds

In this paper we are concerned with the monodromy of Picard-Fuchs differential equations associated with one-parameter families of Calabi-Yau threefolds. Our results show that in the hypergeometric cases the matrix representations of monodromy relative to the Frobenius bases can be expressed in terms of the geometric invariants of the underlying Calabi-Yau threefolds. This phenomenon is also verified numerically for other families of Calabi-Yau threefolds in the paper. Furthermore, we discover that under a suitable change of bases the monodromy groups are contained in certain congruence subgroups of Sp(4, ℤ) of finite index and whose levels are related to the geometric invariants of the Calabi-Yau threefolds. © Walter de Gruyter

Contextual Stochastic Bilevel Optimization

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This framework extends classical stochastic bilevel optimization when the lower-level decision maker responds optimally not only to the decision of the upper-level decision maker but also to some side information and when there are multiple or even infinite many followers. It captures important applications such as meta-learning, personalized federated learning, end-to-end learning, and Wasserstein distributionally robust optimization with side information (WDRO-SI). Due to the presence of contextual information, existing single-loop methods for classical stochastic bilevel optimization are unable to converge. To overcome this challenge, we introduce an efficient double-loop gradient method based on the Multilevel Monte-Carlo (MLMC) technique and establish its sample and computational complexities. When specialized to stochastic nonconvex optimization, our method matches existing lower bounds. For meta-learning, the complexity of our method does not depend on the number of tasks. Numerical experiments further validate our theoretical results.Comment: The paper is accepted by NeurIPS 202