Mosco convergence of SLLN for triangular arrays of rowwise independent random sets

2013 ◽  
Vol 83 (4) ◽  
pp. 1117-1126 ◽  
Author(s):  
Nguyen Van Quang ◽  
Duong Xuan Giap
Keyword(s):  
Mosco Convergence ◽  
Random Sets ◽  
Triangular Arrays ◽  
Rowwise Independent

Depth and outliers for samples of sets and random sets distributions

2021 ◽  
Author(s):  
Ignacio Cascos ◽  
Qiyu Li ◽  
Ilya Molchanov
Keyword(s):  
Random Sets

scholarly journals Scott functions, their representations on domains, and applications to random sets

2021 ◽  
Vol 498 (2) ◽  
pp. 124976
Author(s):  
Motoya Machida ◽  
Alexander Y. Shibakov
Keyword(s):  
Random Sets

scholarly journals Multiple Alu exonization in 3’UTR of a primate specific isoform of CYP20A1 creates a potential miRNA sponge

2020 ◽  
Author(s):  
Aniket Bhattacharya ◽  
Vineet Jha ◽  
Khushboo Singhal ◽  
Mahar Fatima ◽  
Dayanidhi Singh ◽  
...  
Keyword(s):  
Heat Shock ◽  
Cortical Neurons ◽  
Regulatory Networks ◽  
Large Scale ◽  
Neuronal Development ◽  
Random Sets ◽  
Rna Seq ◽  
Orphan Gene ◽  
Mirna Sponge ◽  
Human Neurons

Abstract Alu repeats contribute to phylogenetic novelties in conserved regulatory networks in primates. Our study highlights how exonized Alus could nucleate large-scale mRNA-miRNA interactions. Using a functional genomics approach, we characterize a transcript isoform of an orphan gene, CYP20A1 (CYP20A1_Alu-LT) that has exonization of 23 Alus in its 3’UTR. CYP20A1_Alu-LT, confirmed by 3’RACE, is an outlier in length (9 kb 3’UTR) and widely expressed. Using publically available datasets, we demonstrate its expression in higher primates and presence in single nucleus RNA-seq of 15928 human cortical neurons. miRanda predicts ∼4700 miRNA recognition elements (MREs) for ∼1000 miRNAs, primarily originated within these 3’UTR-Alus. CYP20A1_Alu-LT could be a potential multi-miRNA sponge as it harbors ≥10 MREs for 140 miRNAs and has cytosolic localization. We further tested whether expression of CYP20A1_Alu-LT correlates with mRNAs harboring similar MRE targets. RNA-seq with conjoint miRNA-seq analysis was done in primary human neurons where we observed CYP20A1_Alu-LT to be downregulated during heat shock response and upregulated in HIV1-Tat treatment. 380 genes were positively correlated with its expression (significantly downregulated in heat shock and upregulated in Tat) and they harbored MREs for nine expressed miRNAs which were also enriched in CYP20A1_Alu-LT. MREs were significantly enriched in these 380 genes compared to random sets of differentially expressed genes (p = 8.134e-12). Gene ontology suggested involvement of these genes in neuronal development and hemostasis pathways thus proposing a novel component of Alu-miRNA mediated transcriptional modulation that could govern specific physiological outcomes in higher primates.

Random sets and Markov fields

1987 ◽  
pp. 339-344
Keyword(s):  
Random Sets ◽  
Markov Fields

A novel underwater sonar image enhancement algorithm based on approximation spaces of random sets

2021 ◽  
Author(s):  
Pengfei Shi ◽  
Liang Lu ◽  
Xinnan Fan ◽  
Yuanxue Xin ◽  
Jianjun Ni
Keyword(s):  
Image Enhancement ◽  
Random Sets ◽  
Approximation Spaces ◽  
Sonar Image ◽  
Enhancement Algorithm

scholarly journals Complete convergence for sums of arrays of random elements

2000 ◽  
Vol 23 (11) ◽  
pp. 789-794 ◽  
Author(s):  
Soo Hak Sung
Keyword(s):  
Complete Convergence ◽  
Moment Conditions ◽  
Random Elements ◽  
Rowwise Independent

Let{Xni}be an array of rowwise independentB-valued random elements and{an}constants such that0<an↑∞. Under some moment conditions for the array, it is shown that∑i=1nXni/anconverges to0completely if and only if∑i=1nXni/anconverges to0in probability.

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