Nested simulation is typically used to estimate the functional of a conditional expectation. Considerable research has been performed on point estimation for various functionals. However, the quantification of the statistical uncertainty in the point estimator, for instance, using confidence intervals (CIs), has not been extensively investigated. In this article, we establish central limit theorems with the asymptotically optimal convergence rate of Γ−1false/3$$ {\Gamma}^{-1/3} $$ for nested simulation with different forms of functionals, where normalΓ$$ \Gamma $$ denotes the total computational effort. Based on these theorems, we develop a unified CI framework that can ensure that both the mean squared error of the point estimator and CI width attain the optimal convergence rate. Numerical examples are presented, and the results are found to be consistent with the theoretical results. Experimental results demonstrate that the proposed framework outperforms the existing methods for CI construction in terms of the CI widths and convergence rates.
Background
Long non-coding RNAs (lncRNAs) are substantial to wide varity of biological processes and pathogenesis processes of ischemic stroke. Houshiheisan (HSHS), a typical prescription of traditional Chinese medicine, has outstanding efficacy in treating stroke, although the comprehensive molecular mechanism of its therapeutic effect has remained obscure up to now.
Methods
In this work, we induced a ischemic stroke rat model by permanent middle cerebral artery occlusion (MCAO). The microarray expression profile of lncRNAs and mRNAs was used to investigate various possible roles and molecular mechanism of HSHS in treating MCAO rats.
Results
HSHS improved the neurological deficit and alleviated the pathological damage after cerebral ischemia. The Clariom D Assay (rat, Affymetrix) showed that 8128 mRNAs and 3022 lncRNAs differentially expressed between sham group and model group, and 868 mRNAs and 836 lncRNAs between HSHS and model groups. Among the three groups, the intersections (666 mRNAs and 288 lncRNAs) were chosen and analyzed. GO and KEGG analysis disclosed that the majority of overlapping mRNAs were enriched in Axon guidance, Autophagy, PI3K-AKT signaling pathway and mTOR signaling pathway. Pathway network, protein-protein network and molecular complex detection analysis identified significant hub genes, e.g., Rock2, Rps6kb1, Wnt4, IL-6 and so on. Furthermore, we explored dynamic interactions between the dysregulated lncRNAs and mRNAs by lncRNA-mRNA network analysis. Finally, qRT-PCR verified expressions of the critical differentially expressed lncRNAs and mRNAs within the three groups.
Conclusion
Our results indicate that these differentially expressed lncRNAs may affect pathological processes of ischemic stroke by regulating co-expressed mRNAs, providing novel insight in regarding lncRNAs’ involvement in the treatment of ischemic stroke.
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