Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct new Lagrangian ROMs. We show that the new Lagrangian ROMs are orders of magnitude more accurate than the standard Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis

Global gene expression analysis reveals reduced abundance of putative microRNA targets in human prostate tumours

<p>Abstract</p> <p>Background</p> <p>Recently, microRNAs (miRNAs) have taken centre stage in the field of human molecular oncology. Several studies have shown that miRNA profiling analyses offer new possibilities in cancer classification, diagnosis and prognosis. However, the function of miRNAs that are dysregulated in tumours remains largely a mystery. Global analysis of miRNA-target gene expression has helped illuminate the role of miRNAs in developmental gene expression programs, but such an approach has not been reported in cancer transcriptomics.</p> <p>Results</p> <p>In this study, we globally analysed the expression patterns of miRNA target genes in prostate cancer by using several public microarray datasets. Intriguingly, we found that, in contrast to global mRNA transcript levels, putative miRNA targets showed a reduced abundance in prostate tumours relative to benign prostate tissue. Additionally, the down-regulation of these miRNA targets positively correlated with the number of types of miRNA target-sites in the 3' untranslated regions of these targets. Further investigation revealed that the globally low expression was mainly driven by the targets of 36 specific miRNAs that were reported to be up-regulated in prostate cancer by a miRNA expression profiling study. We also found that the transcript levels of miRNA targets were lower in androgen-independent prostate cancer than in androgen-dependent prostate cancer. Moreover, when the global analysis was extended to four other cancers, significant differences in transcript levels between miRNA targets and total mRNA backgrounds were found.</p> <p>Conclusion</p> <p>Global gene expression analysis, along with further investigation, suggests that miRNA targets have a significantly reduced transcript abundance in prostate cancer, when compared with the combined pool of all mRNAs. The abnormal expression pattern of miRNA targets in human cancer could be a common feature of the human cancer transcriptome. Our study may help to shed new light on the functional roles of miRNAs in cancer transcriptomics.</p

Predicting miRNA-disease associations based on multi-view information fusion

MicroRNAs (miRNAs) play an important role in various biological processes and their abnormal expression could lead to the occurrence of diseases. Exploring the potential relationships between miRNAs and diseases can contribute to the diagnosis and treatment of complex diseases. The increasing databases storing miRNA and disease information provide opportunities to develop computational methods for discovering unobserved disease-related miRNAs, but there are still some challenges in how to effectively learn and fuse information from multi-source data. In this study, we propose a multi-view information fusion based method for miRNA-disease association (MDA)prediction, named MVIFMDA. Firstly, multiple heterogeneous networks are constructed by combining the known MDAs and different similarities of miRNAs and diseases based on multi-source information. Secondly, the topology features of miRNAs and diseases are obtained by using the graph convolutional network to each heterogeneous network view, respectively. Moreover, we design the attention strategy at the topology representation level to adaptively fuse representations including different structural information. Meanwhile, we learn the attribute representations of miRNAs and diseases from their similarity attribute views with convolutional neural networks, respectively. Finally, the complicated associations between miRNAs and diseases are reconstructed by applying a bilinear decoder to the combined features, which combine topology and attribute representations. Experimental results on the public dataset demonstrate that our proposed model consistently outperforms baseline methods. The case studies further show the ability of the MVIFMDA model for inferring underlying associations between miRNAs and diseases