Blocks of Lie Superalgebras of Type W(n)

We calculate the blocks of the category of finite-dimensional representations of W(0,n), with n > 2, and show that all are of wild type. As an application, we show that the centre of the universal enveloping algebra is trivial.Comment: 14 pages, AMS-LaTeX, XY-Pic figures; revised versio

Linear algebra meets Lie algebra: the Kostant-Wallach theory

In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.Comment: 27 pages, LaTeX; abstract adde

MicroRNA-Biogenesis and Pre-mRNA Splicing Crosstalk

MicroRNAs (miRNAs) are often hosted in introns of protein-coding genes. Given that the same transcriptional unit can potentially give rise to both miRNA and mRNA transcripts raises the intriguing question of the level of interaction between these processes. Recent studies from transcription, pre-mRNA splicing, and miRNA-processing perspectives have investigated these relationships and yielded interesting, yet somewhat controversial findings. Here we discuss major studies in the field

Computational Complexity and Numerical Stability of Linear Problems

We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the algebraic complexity theory as well as the general error analysis for matrix multiplication and related problems. We emphasize the central role played by the matrix multiplication problem and discuss historical and modern approaches to its solution.Comment: 16 pages; updated to reflect referees' remarks; to appear in Proceedings of the 5th European Congress of Mathematic

Computational Complexity and Numerical Stability of Linear Problems

We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the algebraic complexity theory as well as the general error analysis for matrix multiplication and related problems. We emphasize the central role played by the matrix multiplication problem and discuss historical and modern approaches to its solution.Comment: 16 pages; updated to reflect referees' remarks; to appear in Proceedings of the 5th European Congress of Mathematic

An Evolutionary Perspective of Animal MicroRNAs and Their Targets

MicroRNAs (miRNAs) are short noncoding RNAs that regulate gene expression through translational inhibition or mRNA degradation by binding to sequences on the target mRNA. miRNA regulation appears to be the most abundant mode of posttranscriptional regulation affecting ∼50% of the transcriptome. miRNA genes are often clustered and/or located in introns, and each targets a variable and often large number of mRNAs. Here we discuss the genomic architecture of animal miRNA genes and their evolving interaction with their target mRNAs

A quantum-trace determinantal formula for matrix commutators, and applications

AbstractIn this paper, we establish a determinantal formula for 2×2 matrix commutators [X,Y]=XY-YX over a commutative ring, using (among other invariants) the quantum traces of X and Y. Special forms of this determinantal formula include a “trace version”, and a “supertrace version”. Some applications of these formulas are given to the study of value sets of binary quadratic forms, the factorization of 2×2 integral matrices, and the solution of certain simultaneous diophantine equations over commutative rings

miRNAminer: A tool for homologous microRNA gene search

<p>Abstract</p> <p>Background</p> <p>MicroRNAs (miRNAs), present in most metazoans, are small non-coding RNAs that control gene expression by negatively regulating translation through binding to the 3'UTR of mRNA transcripts. Previously, experimental and computational methods were used to construct miRNA gene repositories agreeing with careful submission guidelines.</p> <p>Results</p> <p>An algorithm we developed – miRNAminer – is used for homologous conserved miRNA gene search in several animal species. Given a search query, candidate homologs from different species are tested for their known miRNA properties, such as secondary structure, energy and alignment and conservation, in order to asses their fidelity. When applying miRNAminer on seven mammalian species we identified several hundreds of high-confidence homologous miRNAs increasing the total collection of (miRbase) miRNAs, in these species, by more than 50%. miRNAminer uses stringent criteria and exhibits high sensitivity and specificity.</p> <p>Conclusion</p> <p>We present – miRNAminer – the first web-server for homologous miRNA gene search in animals. miRNAminer can be used to identify conserved homolog miRNA genes and can also be used prior to depositing miRNAs in public databases. miRNAminer is available at <url>http://pag.csail.mit.edu/mirnaminer</url>.</p