Abstract-We introduce a novel information criterion (NIC) for searching for the optimum weights of a two-layer linear neural network (NN). The NIC exhibits a single global maximum attained if and only if the weights span the (desired) principal subspace of a covariance matrix. The other stationary points of the NIC are (unstable) saddle points. We develop an adaptive algorithm based on the NIC for estimating and tracking the principal subspace of a vector sequence. The NIC algorithm provides a fast on-line learning of the optimum weights for the two-layer linear NN. We establish the connections between the NIC algorithm and the conventional mean-square-error (MSE) based algorithms such as Oja's algorithm, LMSER, PAST, APEX, and GHA. The NIC algorithm has several key advantages such as faster convergence, which is illustrated through analysis and simulation.
A class of fast subspace tracking methods such as the Oja method, the projection approximation subspace tracking (PAST) method, and the novel information criterion (NIC) method can be viewed as power-based methods. Unlike many non-power-based methods such as the Given's rotation based URV updating method and the operator restriction algorithm, the power-based methods with arbitrary initial conditions are convergent to the principal subspace of a vector sequence under a mild assumption. This paper elaborates on a natural version of the power method. The natural power method is shown to have the fastest convergence rate among the power-based methods. Three types of implementations of the natural power method are presented in detail, which require respectively O(n 2 p), O(np 2 ), and O(np) flops of computation at each iteration (update), where n is the dimension of the vector sequence and p is the dimension of the principal subspace. All of the three implementations are shown to be globally convergent under a mild assumption. The O(np) implementation of the natural power method is shown to be superior to the O(np) equivalent of the Oja, PAST, and NIC methods. Like all power-based methods, the natural power method can be easily modified via subspace deflation to track the principal components and, hence, the rank of the principal subspace.
Colorectal cancer (CRC) is one of the most common and deadly malignancies. Novel biomarkers for the diagnosis and prognosis of this disease must be identified. Besides, metabolism plays an essential role in the occurrence and development of CRC. This article aims to identify some critical prognosis-related metabolic genes (PRMGs) and construct a prognosis model of CRC patients for clinical use. We obtained the expression profiles of CRC from The Cancer Genome Atlas database (TCGA), then identified differentially expressed PRMGs by R and Perl software. Hub genes were filtered out by univariate Cox analysis and least absolute shrinkage and selection operator Cox analysis. We used functional enrichment analysis methods, such as Gene Ontology, Kyoto Encyclopedia of Genes and Genomes, and Gene Set Enrichment Analysis, to identify involved signaling pathways of PRMGs. The nomogram predicted overall survival (OS). Calibration traces were used to evaluate the consistency between the actual and the predicted survival rate. Finally, a prognostic model was constructed based on six metabolic genes (NAT2, XDH, GPX3, AKR1C4, SPHK1, and ADCY5), and the risk score was an independent prognostic prognosticator. Genetic expression and risk score were significantly correlated with clinicopathologic characteristics of CRC. A nomogram based on the clinicopathological feature of CRC and risk score accurately predicted the OS of individual CRC cancer patients. We also validated the results in the independent colorectal cancer cohorts GSE39582 and GSE87211. Our study demonstrates that the risk score is an independent prognostic biomarker and is closely correlated with the malignant clinicopathological characteristics of CRC patients. We also determined some metabolic genes associated with the survival and clinical stage of CRC as potential biomarkers for CRC diagnosis and treatment.
Impaired angiogenesis in diabetes is a key process contributing to ischemic diseases such as peripheral arterial disease. Epigenetic mechanisms, including those mediated by long non-coding RNAs are crucial links connecting diabetes and the related chronic tissue ischemia. Here we identify the LncRNA that Enhances Endothelial Nitric oxide synthase Expression (LEENE) as a regulator of angiogenesis and ischemic response. LEENE expression is decreased in diabetic conditions in cultured endothelial cells (EC), mouse hindlimb muscles, and human arteries.Inhibition of LEENE in human microvascular ECs reduces their angiogenic capacity with a dysregulated angiogenic gene program. Diabetic mice deficient in leene demonstrate impaired angiogenesis and perfusion following hindlimb ischemia. Importantly, overexpression of human LEENE rescues the impaired ischemic response in leene knockout mice at tissue functional and single-cell transcriptomic levels. Mechanistically, LEENE RNA promotes transcription of proangiogenic genes in ECs, such as KDR and eNOS, potentially by interacting with LEO1, a key component of RNA Polymerase II-associated factor complex and MYC, a crucial transcription factor for angiogenesis. Taken together, our findings demonstrate an essential role for LEENE in the regulation of angiogenesis and tissue perfusion. Functional enhancement of LEENE to restore angiogenesis for tissue repair and regeneration may represent a potential strategy to tackle ischemic vascular diseases.
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