Convex Hypersurfaces and L p Estimates for Schrödinger Equations

This paper is concerned with Schrödinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the L p-L q estimate of solution operator in free case. This estimate, combining with the results of fractionally integrated groups, allows us to further obtain the L p estimate of solutions for the initial data belonging to a dense subset of L p in the case of integrable potentials

The impact of EV71 vaccination program on hand, foot and mouth disease in Zhejiang Province, China: A negative control study

Objective: To estimate the potential causal impact of Enterovirus A71 (EV71) vaccination program on the reduction of EV71-infected hand, foot, and mouth disease (HFMD) in Zhejiang Province. Methods: We utilized the longitudinal surveillance dataset of HFMD and EV71 vaccination in Zhejiang Province during 2010–2019. We estimated vaccine efficacy using a Bayesian structured time series (BSTS) model, and employed a negative control outcome (NCO) model to detect unmeasured confounding and reveal potential causal association. Results: We estimated that 20,132 EV71 cases (95% CI: 16,733, 23,532) were prevented by vaccination program during 2017–2019, corresponding to a reduction of 29% (95% CI: 24%, 34%). The effectiveness of vaccination increased annually, with reductions of 11% (95% CI: 6%, 16%) in 2017 and 66% (95% CI: 61%, 71%) in 2019. Children under 5 years old obtained greater benefits compared to those over 5 years. Cities with higher vaccination coverage experienced a sharper EV71 reduction compared to those with lower coverage. The NCO model detected no confounding factors in the association between vaccination and EV71 cases reduction. Conclusions: This study suggested a potential causal effect of the EV71 vaccination, highlighting the importance of achieving higher vaccine coverage to control the HFMD

The associations of glycosylated hemoglobin with grey matter volume and depression: Investigating mediating role of grey matter volume

Background: Depression has caused enormous health burden to human worldwide. Glycemia has been found as one important risk factor of depression. However, the biological mechanism underlying this relationship remained largely unknown. Methods: This analysis was derived from a cohort of 33,151 participants in the UK Biobank who provided brain magnetic resonance imaging data from 2014 to 2020. Participants were classified into diabetic, prediabetic and non-diabetic groups, as well as groups aged ≥60 years and <60 years. We assessed the associations between glycosylated hemoglobin (HbA1c), grey matter volume (GMV) in 117 brain regions, and depression based on the multivariable linear and logistic regression. We further investigated the mediation effect of GMV on the relationship between HbA1c and depression. Results: Higher HbA1c was found to be associated with reduced GMV and depression. Lower GMV was observed associated with depression. Moreover, the association was strongest in prediabetes compared to prediabetic and non-diabetic, and the association was greater in those aged ≥60 years. We further observed a significant mediation effect of GMV on the association between HbA1c and depression, and the proportions of the effect mediated by HbA1c-depression signatured regions was 7.29% (95% CI: 1.43%, 34.38%). Conclusions: This study suggests that HbA1c is associated with cerebral grey matter abnormality especially in participants aged ≥60 years. In the context of global aging, the unhealthy blood sugar can contribute to more severe brain damage for the population and effective control of blood sugar levels among the elderly can have a positive impact on brain health and potentially reduce the risk of developing depression