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

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 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.

Asymptotic properties of stereological estimators of volume fraction for stationary random sets

1982 ◽  
Vol 19 (1) ◽  
pp. 111-126 ◽  
Author(s):  
Shigeru Mase
Keyword(s):  
Volume Fraction ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Parametric Estimation ◽  
Random Sets ◽  
Stationary Time Series ◽  
Boolean Models ◽  
Window Functions ◽  
Spectral Density Functions ◽  
Point Estimators

We shall discuss asymptotic properties of stereological estimators of volume (area) fraction for stationary random sets (in the sense of Matheron) under natural and general assumptions. Results obtained are strong consistency, asymptotic normality, and asymptotic unbiasedness and consistency of asymptotic variance estimators. The method is analogous to the non-parametric estimation of spectral density functions of stationary time series using window functions. Proofs are given for areal estimators, but they are also valid for lineal and point estimators with slight modifications. Finally we show that stationary Boolean models satisfy the relevant assumptions reasonably well.

scholarly journals The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping

2002 ◽  
Vol 31 (1) ◽  
pp. 11-21 ◽  
Author(s):  
Hongwen Guo ◽  
Dihe Hu
Keyword(s):  
Hausdorff Dimension ◽  
Hausdorff Measure ◽  
Intersection Property ◽  
Random Sets ◽  
Hausdorff Measures ◽  
Open Set Condition ◽  
Finite Intersection ◽  
Open Set ◽  
Finite Intersection Property

We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have positive and finite Hausdorff measures, which in certain extent generalize some of the known results, about random recursive fractals.

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