Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order

We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the $k$th eigenvalue in terms of the lower eigenvalues independently of the particular geometry of the domain.Comment: 24 page

Inverse probability weighting for covariate adjustment in randomized studies

Covariate adjustment in randomized clinical trials has the potential benefit of precision gain. It also has the potential pitfall of reduced objectivity as it opens the possibility of selecting a 'favorable' model that yields strong treatment benefit estimate. Although there is a large volume of statistical literature targeting on the first aspect, realistic solutions to enforce objective inference and improve precision are rare. As a typical randomized trial needs to accommodate many implementation issues beyond statistical considerations, maintaining the objectivity is at least as important as precision gain if not more, particularly from the perspective of the regulatory agencies. In this article, we propose a two-stage estimation procedure based on inverse probability weighting to achieve better precision without compromising objectivity. The procedure is designed in a way such that the covariate adjustment is performed before seeing the outcome, effectively reducing the possibility of selecting a 'favorable' model that yields a strong intervention effect. Both theoretical and numerical properties of the estimation procedure are presented. Application of the proposed method to a real data example is presented

Estimation of treatment effect in a subpopulation: An empirical Bayes approach

It is well recognized that the benefit of a medical intervention may not be distributed evenly in the target population due to patient heterogeneity, and conclusions based on conventional randomized clinical trials may not apply to every person. Given the increasing cost of randomized trials and difficulties in recruiting patients, there is a strong need to develop analytical approaches to estimate treatment effect in subpopulations. In particular, due to limited sample size for subpopulations and the need for multiple comparisons, standard analysis tends to yield wide confidence intervals of the treatment effect that are often noninformative. We propose an empirical Bayes approach to combine both information embedded in a target subpopulation and information from other subjects to construct confidence intervals of the treatment effect. The method is appealing in its simplicity and tangibility in characterizing the uncertainty about the true treatment effect. Simulation studies and a real data analysis are presented

College English Teaching Under Web-based Context and Autonomous Learning

Abstract Web-based English learning is a complicated systematic engineering. At present, universities and colleges are generally short of web-based teaching resources. Under such circumstances, the paper probes into the possibility and maneuverability of web-based English learning implementation, and discusses the appropriate combination of classroom English teaching and webbased English teaching so as to establish web-based teaching environment, highlight shared web-based English learning, and realize students’ blended learning and individuation learning. It is a brand-new and eternal research subject of web-based English learning to make full use of network resources, cultivate students’ autonomous learning abilities and improve teaching quality and students’ learning efficiency. Key words: College English; Teaching pattern; Webbased teaching; Autonomous learning; Learning strategies Résumé L’apprentissage de l’angalis sur le Web est un processus compliquée et systématique. A l'heure actuelle, les universités et les instituts supérieurs sont généralement à court de ressources pédagogiques sur Internet. Dans de telles circonstances, la presse fait débat sur la possibilité et la maniabilité de la mise en oeuvre de l’apprentissage de l’anglais basée sur le Web , sur la combinaison appropriée de l'enseignement en classe et sur le Web afin d'établir les conditions d'enseignement en ligne et sur comment souligner l’apprentissage de l’anglais partagé et de détecter l’apprentissage mixte et l'apprentissage d'individuation des étudiants. Cultiver les capacité d’autonomie des étudiants en améliorant la qualité pédagogique et l”efficacité d’apprentissge des étudiants: faire pleinement usages des ressources du réseau au sujet de l’apprentissage de l’anglais basé sur le web, ce qui représente un sujet neuf et un recherche éternel. Mots-clés: Anglais de l’enseignement supérieur; Modèle de l'enseignement; Enseignement en ligne; Apprentissage autonome; Stratégies d'apprentissag

W-MAE: Pre-trained weather model with masked autoencoder for multi-variable weather forecasting

Weather forecasting is a long-standing computational challenge with direct societal and economic impacts. This task involves a large amount of continuous data collection and exhibits rich spatiotemporal dependencies over long periods, making it highly suitable for deep learning models. In this paper, we apply pre-training techniques to weather forecasting and propose W-MAE, a Weather model with Masked AutoEncoder pre-training for multi-variable weather forecasting. W-MAE is pre-trained in a self-supervised manner to reconstruct spatial correlations within meteorological variables. On the temporal scale, we fine-tune the pre-trained W-MAE to predict the future states of meteorological variables, thereby modeling the temporal dependencies present in weather data. We pre-train W-MAE using the fifth-generation ECMWF Reanalysis (ERA5) data, with samples selected every six hours and using only two years of data. Under the same training data conditions, we compare W-MAE with FourCastNet, and W-MAE outperforms FourCastNet in precipitation forecasting. In the setting where the training data is far less than that of FourCastNet, our model still performs much better in precipitation prediction (0.80 vs. 0.98). Additionally, experiments show that our model has a stable and significant advantage in short-to-medium-range forecasting (i.e., forecasting time ranges from 6 hours to one week), and the longer the prediction time, the more evident the performance advantage of W-MAE, further proving its robustness