A New Kind of Graded Lie Algebra and Parastatistical Supersymmetry

In this paper the usual $Z_2$ graded Lie algebra is generalized to a new form, which may be called $Z_{2,2}$ graded Lie algebra. It is shown that there exists close connections between the $Z_{2,2}$ graded Lie algebra and parastatistics, so the $Z_{2,2}$ can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems

Learn to Generate Time Series Conditioned Graphs with Generative Adversarial Nets

Deep learning based approaches have been utilized to model and generate graphs subjected to different distributions recently. However, they are typically unsupervised learning based and unconditioned generative models or simply conditioned on the graph-level contexts, which are not associated with rich semantic node-level contexts. Differently, in this paper, we are interested in a novel problem named Time Series Conditioned Graph Generation: given an input multivariate time series, we aim to infer a target relation graph modeling the underlying interrelationships between time series with each node corresponding to each time series. For example, we can study the interrelationships between genes in a gene regulatory network of a certain disease conditioned on their gene expression data recorded as time series. To achieve this, we propose a novel Time Series conditioned Graph Generation-Generative Adversarial Networks (TSGG-GAN) to handle challenges of rich node-level context structures conditioning and measuring similarities directly between graphs and time series. Extensive experiments on synthetic and real-word gene regulatory networks datasets demonstrate the effectiveness and generalizability of the proposed TSGG-GAN

Dermatophagoides farinae microRNAs released to external environments via exosomes regulate inflammation-related gene expression in human bronchial epithelial cells

BackgroundDermatophagoides farinae (DFA) is an important species of house dust mites (HDMs) that causes allergic diseases. Previous studies have focused on allergens with protein components to explain the allergic effect of HDMs; however, there is little knowledge on the role of microRNAs (miRNAs) in the allergic effect of HDMs. This study aimed to unravel the new mechanism of dust mite sensitization from the perspective of cross-species transport of extracellular vesicles-encapsulated miRNAs from HDMs.MethodsSmall RNA (sRNA) sequencing was performed to detect miRNAs expression profiles from DFA, DFA-derived exosomes and DFA culture supernatants. A quantitative fluorescent real-time PCR (qPCR) assay was used to detect miRNAs expression in dust specimens. BEAS-2B cells endocytosed exosomes were modeled in vitro to detect miRNAs from DFA and the expression of related inflammatory factors. Representative dfa-miR-276-3p and dfa-novel-miR2 were transfected into BEAS-2B cells, and then differentially expressed genes (DEGs) were analyzed by RNA sequencing. Protein-protein interaction (PPI) network analysis and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway and Gene Ontology (GO) terms enrichment analyses were performed on the first 300 nodes of DEGs.ResultssRNA sequencing identified 42 conserved miRNAs and 66 novel miRNAs in DFA, DFA-derived exosomes, and DFA culture supernatants. A homology analysis was performed on the top 18 conserved miRNAs with high expression levels. The presence of dust mites and miRNAs from HDMs in living environment were also validated. Following uptake of DFA-derived exosomes by BEAS-2B cells, exosomes transported miRNAs from DFA to target cells and produced pro-inflammatory effects in corresponding cells. RNA sequencing identified DEGs in dfa-miR-276-3p and dfa-novel-miR2 transfected BEAS-2B cells. GO and KEGG enrichment analyses revealed the role of exosomes with cross-species transporting of DFA miRNAs in inflammatory signaling pathways, such as JAK-STAT signaling pathway, PI3K/AKT signaling pathway and IL-6-mediated signaling pathway.ConclusionOur findings demonstrate the miRNAs expression profiles in DFA for the first time. The DFA miRNAs are delivered into living environments via exosomes, and engulfed by human bronchial epithelial cells, and cross-species regulation may contribute to inflammation-related processes

Uniformly asymptotic normality of the regression weighted estimator for negatively associated samples

In this paper, we discuss the uniformly asymptotic normality of the weighted function estimate of the fixed design regression model for negatively associated samples. We give the rates of uniform asymptotic normality. The rate is near n-1/4 when the third moment is finite.Fixed design regression Weighted estimate Asymptotic normality Negatively associated

Moment inequalities for sums of products of independent random variables

In this paper, we extend the Rosenthal-type moment inequalities for sums of products of independent random variables to a general case. The inequalities improve the corresponding ones in Gadidov [1998. Strong law of large numbers for multilinear forms. Ann. Probab. 26(2), 902-923].Sums of products Rosenthal type Moment inequality

On the Exponential Inequality for Weighted Sums of a Class of Linearly Negative Quadrant Dependent Random Variables

The exponential inequality for weighted sums of a class of linearly negative quadrant dependent random variables is established, which extends and improves the corresponding ones obtained by Ko et al. (2007) and Jabbari et al. (2009). In addition, we also give the relevant precise asymptotics

A general method to the strong law of large numbers and its applications,”

Abstract A general method to prove the strong law of large numbers is given by using the maximal tail probability. As a result the convergence rate of S n =n for both positively associated sequences and negatively associated sequences is n À1=2 ðlog nÞ 1=2 ðlog log nÞ d=2 for any d41. This result closes to the optimal achievable convergence rate under independent random variables, and improves the rate