On enforcing non-negativity in polynomial approximations in high dimensions

Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range, due to constraints posed by the underlying physical problems. Efficient numerical methods are thus needed to enforce such conditions. In this paper, we discuss effective numerical algorithms for polynomial approximation under non-negativity constraints. We first formulate the constrained optimization problem, its primal and dual forms, and then discuss efficient first-order convex optimization methods, with a particular focus on high dimensional problems. Numerical examples are provided, for up to $200$ dimensions, to demonstrate the effectiveness and scalability of the methods

慢型克山病与扩张型心肌病患者抗氧化能力对比研究

Objective: To compare the serum levels of selenium, selenoprotein and malondialdehyde about Keshan disease (KSD) and dilated cardiomyopathy (DCM) patients and to investigate the relationship between the antioxidant capacity and myocardial injury. Methods: 26 KSD patients, 18 DCM patients, 24 healthy people in KSD areas and 22 healthy people in non-KSD areas were selected by all-round physical examination and electrocardiography. Blood samples were collected by informing consent and volunteering. The serum selenium was determined by using 2,3 - two amino-naphthalene fluorescence method. The serum selenoprotein and malondialdehyde were measured by using biotin double-antibody sandwich method of enzyme linked immunosorbent assay (ELISA) (according to kit instructions). Results: There were no statistical differences about the distribution of the gender and age in every subjects’ groups (P＞0.05). The levels of serum selenium and selenoprotein in Keshan disease group and dilated cardiomyopathy group were significantly lower than those of healthy group whether in KSD areas or in non- KSD areas , and the serum malondialdehyde were higher than those in healthy controls. There were no statistical significance about the concentrations of serum selenium, selenoprotein and malondialdehyde between Keshan disease group and dilated cardiomyopathy group, KSD areas’ control group and non- KSD areas’ control group. Conclusion: The myocardial injury of KSD patients and dilated cardiomyopathy patients may be associated with the decrease of antioxidant ability because of the lower selenium levels.目的  对比研究慢型克山病与扩张型心肌病患者体内血清硒、硒蛋白和丙二醛浓度，探讨抗氧化能力与心肌损伤的关系。方法  选择慢型克山病患者26例，扩张型心肌病患者18例，同时在克山病病区选取24名经过全面查体和心电图描记无异常的健康人作为病区健康对照组，在非克山病区选择22名健康人作为非病区健康对照组。在知情同意、患者自愿情况下采集受检者血样，检测克山病患者、扩心病患者、病区健康人及非病区健康人的血清硒、硒蛋白水平及丙二醛浓度。血清硒含量测定采用2,3-二氨基萘荧光法；血清硒蛋白和丙二醛浓度测定采用生物素双抗体夹心酶联免疫吸附法（ELISA）（按试剂盒说明操作）。结果  各组调查对象性别及年龄分布均无统计学差异（P＞0.05）；克山病组和扩张型心肌病组血清硒、硒蛋白水平均明显低于病区健康对照组与非病区健康对照组，血清丙二醛浓度均高于病区健康对照组及非病区健康对照组；克山病组与扩张型心肌病组，病区健康对照组与非病区健康对照组血清硒、硒蛋白水平以及丙二醛浓度差异均无显著性。结论  慢型克山病和扩张型心肌病患者心肌损伤都可能与低硒导致的抗氧化能力降低有关

Analysis of ground state in random bipartite matching

Bipartite matching problems emerge in many human social phenomena. In this paper, we study the ground state of the Gale–Shapley model, which is the most popular bipartite matching model. We apply the Kuhn–Munkres algorithm to compute the numerical ground state of the model. For the first time, we obtain the number of blocking pairs which is a measure of the system instability. We also show that the number of blocking pairs formed by each person follows a geometric distribution. Furthermore, we study how the connectivity in the bipartite matching problems influences the instability of the ground state

Genetic Basis and Expression Pattern Indicate the Biocontrol Potential and Soil Adaption of Lysobacter capsici CK09

Lysobacter species have attracted increasing attention in recent years due to their capacities to produce diverse secondary metabolites against phytopathogens. In this research, we analyzed the genomic and transcriptomic patterns of Lysobacter capsici CK09. Our data showed that L. capsici CK09 harbored various contact-independent biocontrol traits, such as fungal cell wall lytic enzymes and HSAF/WAP-8294A2 biosynthesis, as well as several contact-dependent machineries, including type 2/4/6 secretion systems. Additionally, a variety of hydrolytic enzymes, particularly extracellular enzymes, were found in the L. capsici CK09 genome and predicted to improve its adaption in soil. Furthermore, several systems, including type 4 pili, type 3 secretion system and polysaccharide biosynthesis, can provide a selective advantage to L. capsici CK09, enabling the species to live on the surface in soil. The expression of these genes was then confirmed via transcriptomic analysis, indicating the activities of these genes. Collectively, our research provides a comprehensive understanding of the biocontrol potential and soil adaption of L. capsici CK09 and implies the potential of this strain for application in the future