The software is available as supplementary material.

Abstract.The non-negative matrix factorization (NMF) determines a lower rank approximation of a matrixis given and nonnegativity is imposed on all components of the factors £ 7 ¥ 8 § © @ 9and £ 7 ¥ A 9 B © @. The NMF has attracted much attention for over a decade and has been successfully applied to numerous data analysis problems. In applications where the components of the data are necessarily nonnegative such as chemical concentrations in experimental results or pixels in digital images, the NMF provides a more relevant interpretation of the results since it gives non-subtractive combinations of non-negative basis vectors. In this paper, we introduce an algorithm for the NMF based on alternating non-negativity constrained least squares (NMF/ANLS) and the active set based fast algorithm for non-negativity constrained least squares with multiple right hand side vectors, and discuss its convergence properties and a rigorous convergence criterion based on the Karush-Kuhn-Tucker (KKT) conditions. In addition, we also describe algorithms for sparse NMFs and regularized NMF. We show how we impose a sparsity constraint on one of the factors by C E D -norm minimization and discuss its convergence properties. Our algorithms are compared to other commonly used NMF algorithms in the literature on several test data sets in terms of their convergence behavior.

Layered transition-metal dichalcogenides hold promise for making ultrathin-film photovoltaic devices with a combination of excellent photovoltaic performance, superior flexibility, long lifetime, and low manufacturing cost. Engineering the proper band structures of such layered materials is essential to realize such potential. Here, we present a plasma-assisted doping approach for significantly improving the photovoltaic response in multilayer MoS2. In this work, we fabricated and characterized photovoltaic devices with a vertically stacked indium tin oxide electrode/multilayer MoS2/metal electrode structure. Utilizing a plasma-induced p-doping approach, we are able to form p-n junctions in MoS2 layers that facilitate the collection of photogenerated carriers, enhance the photovoltages, and decrease reverse dark currents. Using plasma-assisted doping processes, we have demonstrated MoS2-based photovoltaic devices exhibiting very high short-circuit photocurrent density values up to 20.9 mA/cm(2) and reasonably good power-conversion efficiencies up to 2.8% under AM1.5G illumination, as well as high external quantum efficiencies. We believe that this work provides important scientific insights for leveraging the optoelectronic properties of emerging atomically layered two-dimensional materials for photovoltaic and other optoelectronic applications.

Single-nucleotide polymorphisms (SNP) associated with polygenetic disorders, such as breast cancer (BC), can create, destroy, or modify microRNA (miRNA) binding sites; however, the extent to which SNPs interfere with miRNA gene regulation and affect cancer susceptibility remains largely unknown. We hypothesize that disruption of miRNA target binding by SNPs is a widespread mechanism relevant to cancer susceptibility. To test this, we analyzed SNPs known to be associated with BC risk, in silico and in vitro, for their ability to modify miRNA binding sites and miRNA gene regulation and referred to these as target SNPs. We identified rs1982073-TGFB1 and rs1799782-XRCC1 as target SNPs, whose alleles could modulate gene expression by differential interaction with miR-187 and miR-138, respectively. Genome-wide bioinformatics analysis predicted ∼64% of transcribed SNPs as target SNPs that can modify (increase/decrease) the binding energy of putative miRNA::mRNA duplexes by >90%. To assess whether target SNPs are implicated in BC susceptibility, we conducted a case-control population study and observed that germline occurrence of rs799917-BRCA1 and rs334348-TGFR1 significantly varies among populations with different risks of developing BC. Luciferase activity of target SNPs, allelic variants, and protein levels in cancer cell lines with different genotypes showed differential regulation of target genes following overexpression of the two interacting miRNAs (miR-638 and miR-628-5p). Therefore, we propose that transcribed target SNPs alter miRNA gene regulation and, consequently, protein expression, contributing to the likelihood of cancer susceptibility, by a novel mechanism of subtle gene regulation. Cancer Res; 70(7); 2789-98. ©2010 AACR.