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Since stochastic approximation (SA) based algorithms are easy to implement and need less memory, they are very popular in distributed stochastic optimization problems. Many works have focused on the consistency of the objective values and the iterates returned by the SA based algorithms. It is of fundamental interest to know how to quantify the uncertainty associated with SA solutions via the confidence regions of a prescribed level of significance for the true solution. In this paper, we discuss the framework of constructing the asymptotic confidence regions of the optimal solution to distributed stochastic optimization problem with a focus on the distributed stochastic gradient tracking method. To attain this goal, we first present the asymptotic normality of Polyak–Ruppert averaged distributed stochastic gradient tracking method. We then estimate the corresponding covariance matrix through online estimators. Finally, we provide a practical procedure to build the asymptotic confidence regions for the optimal solution. Numerical tests are also conducted to show the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

Lung cancer is characterized by high-risk and high mortality, among which non-small cell lung cancer (NSCLC) conquers a dominant position. Previous studies have reported that corylin has anti-inflammatory, anti-oxidant, and anti-tumor effects; however, its role in NSCLC cells remains unclear. Corylin inhibits the progression of NSCLC cells. A lentivector NF-κB luciferase reporter was constructed by molecular cloning. Corylin was screened and identified as an NF-κB pathway inhibitor by luciferase reporter assay. Corylin inhibited the expression of NF-κB downstream genes, which was detected by qRT-PCR. The effect of corylin on NSCLC cells was detected by colony formation assay, cell apoptosis, cell proliferation, in vitro invasion, and cell scratch assay. Corylin inhibited p65 nuclear translocation and was detected by molecular docking, immunofluorescence assay, and Western blot analysis. We constructed a lentiviral expression vector, containing an NF-κB luciferase reporter and established a stable A549 cell line for its expression. Using this cell line, corylin was screened and identified as an NF-κB pathway inhibitor. It was found that corylin inhibited the expression of NF-κB downstream genes and inhibited the proliferation and migration of NSCLC cells. Meanwhile, it was also found that corylin significantly reversed the increased proliferation of NSCLC cell lines induced by p65 overexpression. Molecular docking analysis showed that corylin could bind to p65 by hydrogen bonding. Further study showed that corylin inhibited the NF-κB signaling pathway by blocking p65 nuclear translocation. Our study screened and identified corylin as an NF-κB inhibitor and elucidated the molecular mechanism by which corylin inhibits the growth of NSCLC cells. The present study provides a novel strategy for improving the prognosis and treatment of NSCLC patients. [ABSTRACT FROM AUTHOR]

Abstract Polyamide membranes based on trimesoyl chloride (TMC) have captured the majority of the market share for desalination in water treatment. The TMC based membrane is prone to form calcium bridges with the organic foulants due to the relatively strong deprotonation ability of the benzoic acid generated from the incomplete reaction of the acyl chloride monomers. The foulants are thus rapidly deposited on the surface of the TMC based membrane, which results in the deterioration of water production and decrease of membrane lifespan. Herein, we have fabricated a polyamide membrane based on novel trimesoyl-[4,4-dimethyl-5(4H)-azlactone] (TMDMA) monomer instead of TMC monomer. Since the carboxylic groups of the prepared TMDMA polyamide nanofilm are not directly connected to the phenyl ring, the acidity coefficient (p K a ) value is higher and, consequently, deprotonation ability is expected to be weaker. To confirm this theory, we have conducted the fouling experiment on TMDMA based membrane using alginate as a model foulant and compared that with TMC based polyamide membranes. A lower flux decline (33%) and higher cleaning efficiency (90.72%) are observed for the TMDMA polyamide membrane, while the flux decline and cleaning efficiency for the TMC based polyamide membrane are 52% and 49.52% respectively. Furthermore, the average Ca2+ density of the TMDMA polyamide membrane surface before and after cleaning are 81.52 mg m−2 and 21.61 mg m−2 respectively, which are lower than that of the TMC based polyamide membrane surface. Thus, it is clearly showing that the surface of the TMDMA polyamide membrane is not prone to form calcium bridges with foulants due to the weaker complexation between Ca2+ and the carboxylic acid groups. Graphical abstract Image 1 Highlights • Novel non-trimesoyl chloride based polyamide were fabricated by interfacial polymerization. • The novel membrane showed lower flux decline and higher cleaning efficiency than that of TMC based polyamide membranes. • Significantly reduced Ca2+ deposition density was observed on the surface of the novel membrane. [ABSTRACT FROM AUTHOR]