Gradient map of isoparametric polynomial and its application to Ginzburg-Landau system

In this note, we study properties of the gradient map of the isoparametric polynomial. For a given isoparametric hypersurface in sphere, we calculate explicitly the gradient map of its isoparametric polynomial which turns out many interesting phenomenons and applications. We find that it should map not only the focal submanifolds to focal submanifolds, isoparametric hypersurfaces to isoparametric hypersurfaces, but also map isoparametric hypersurfaces to focal submanifolds. In particular, it turns out to be a homogeneous polynomial automorphism on certain isoparametric hypersurface. As an immediate consequence, we get the Brouwer degree of the gradient map which was firstly obtained by Peng and Tang with moving frame method. Following Farina's construction, another immediate consequence is a counter example of the Br\'ezis question about the symmetry for the Ginzburg-Landau system in dimension 6, which gives a partial answer toward the Open problem 2 raised by Farina.Comment: 10 page

遺伝的アルゴリズムを導入した誤差逆伝播法によるニューラルネットワークを用いた夏季の屋外空間における平均放射温度の長期予測

要約のみTohoku University持田灯課

Schoen-Yau-Gromov-Lawson theory and isoparametric foliations

Motivated by the celebrated Schoen-Yau-Gromov-Lawson surgery theory on metrics of positive scalar curvature, we construct a double manifold associated with a minimal isoparametric hypersurface in the unit sphere. The resulting double manifold carries a metric of positive scalar curvature and an isoparametric foliation as well. To investigate the topology of the double manifolds, we use K-theory and the representation of the Clifford algebra for the FKM-type, and determine completely the isotropy subgroups of singular orbits for homogeneous case.Comment: 24 pages, to appear in Communications in Analysis and Geometr

Preliminary study to explore gene-PM2.5 interactive effects on respiratory system in traffic policemen

Objectives: Traffic-related particulate matter (PM) is one of the major sources of air pollution in metropolitan areas. This study is to observe the interactive effects of gene and fine particles (particles smaller than 2.5 μm – PM2.5) on the respiratory system and explore the mechanisms linking PM2.5 and pulmonary injury. Material and Methods: The participants include 110 traffic policemen and 101 common populations in Shanghai, China. Continuous 24 h individual-level PM2.5 is detected and the pulmonary function, high-sensitivity C-reactive protein (hs-CRP), Clara cell protein 16 (CC16) and the polymorphism in CXCL3, NME7 and C5 genes are determined. The multiple linear regression method is used to analyze the association between PM2.5 and health effects. Meanwhile, the interactive effects of gene and PM2.5 on lung function are analyzed. Results: The individual PM2.5 exposure for traffic policemen was higher than that in the common population whereas the forced expiratory volume in 1 s (FEV1), the ratio of FEV1 to forced vital capacity (FEV1/FVC) and lymphocytes are lower. In contrast, the hs-CRP level is higher. In the adjusted analysis, PM2.5 exposure was associated with the decrease in lymphocytes and the increase in hs-CRP. The allele frequencies for NME7 and C5 have significant differences between FEV1/FVC ≤ 70% and FEV1/FVC > 70% participants. The results didn’t find the interaction effects of gene and PM2.5 on FEV1/FVC in all the 3 genes. Conclusions: The results indicated that traffic exposure to high levels of PM2.5 was associated with systemic inflammatory response and respiratory injury. Traffic policemen represent a high risk group suffering from the respiratory injury

The role of Th17 cells and regulatory T cells in Coxsackievirus B3-induced myocarditis

AbstractIL-17-producing (Th17) and regulatory T (Treg) cells have been well established in the pathogenesis of many inflammatory diseases. To assess whether Th17 and Treg were altered in acute virus-induced myocarditis (AVMC) mice, we assessed Th17/Treg functions on different levels in AVMC. It was shown that the expression of splenic Th17 cells and Th17-related cytokines (IL-17A, IL-21) markedly increased. Interestingly, the expression of splenic Treg cells and Treg-related cytokines (TGF-β, IL-10) also significantly increased. Using neutralization of IL-17 in the AVMC, we found that Treg cells roughly decreased compared with isotype control mice. However, T cells and perforin dramatically increased, followed by a marked reduction in CVB3 replication. The results suggested that Th17 cells possibly contributed to viral replication through the action of Treg cells in mediating T cells and perforin response in AVMC

Advances in research on autophagy mechanisms in resistance to endometrial cancer treatment

Administering medication is a crucial strategy in improving the prognosis for advanced endometrial cancer. However, the rise of drug resistance often leads to the resurgence of cancer or less-than-ideal treatment outcomes. Prior studies have shown that autophagy plays a dual role in the development and progression of endometrial cancer, closely associated with drug resistance. As a result, concentrating on autophagy and its combination with medical treatments might be a novel approach to improve the prognosis for endometrial cancer. This study explores the impact of autophagy on drug resistance in endometrial cancer, investigates its core mechanisms, and scrutinizes relevant treatments aimed at autophagy, aiming to illuminate the issue of treatment resistance in advanced endometrial cancer

Operation and evaluation of digitalized retail electricity markets under low-carbon transition: recent advances and challenges

With the growth of electricity consumers purchasing green energy and the development of digital energy trading platforms, the role of digitalized retail electricity markets in the low-carbon transition of electric energy systems is becoming increasingly crucial. In this circumstance, the research work on retail electricity markets needs to be further analyzed and expanded, which would facilitate the efficient decision-making of both market players and policymakers. First, this paper introduces the latest developments in the retail electricity market under low-carbon energy transition and analyzes the limitations of the existing research works. Second, from three aspects of power trading strategy, retail pricing methodology, and market risk management, it provides an overview of the existing operation and mechanism design strategies of the retail electricity market; then, it provides a systematic introduction to the evaluation system and monitoring methodology of electricity markets, which is not sufficient for the current digitalized retail electricity markets. Finally, the issues regarding operation evaluation and platform optimization of the current digitalized retail electricity market are summarized, and the research topics worth further investigations are recommended

A bilateral inequality on a nonnegative bounded random sequence

A bilateral inequality on the Borel-Cantelli lemma in [Xie, Y.Q., 2008. A bilateral inequality on the Borel-Cantelli lemma. Statist. Probab. Lett. 78, 2052-2057] is improved and extended to the case of a bounded nonnegative sequence of random variables.