D-modules on Spaces of Rational Maps and on other Generic Data

Let X be an algebraic curve. We study the problem of parametrizing geometric data over X, which is only generically defined. E.g., parametrizing generically defined (aka rational) maps from X to a fixed target scheme Y. There are three methods for constructing functors of points for such moduli problems (all originally due to Drinfeld), and we show that the resulting functors are equivalent in the fppf Grothendieck topology. As an application, we obtain three presentations for the category of D-modules "on" B (K) \G (A) /G (O), and we combine results about this category coming from the different presentations.Comment: 55 page

Compactifications and algebraic completions of Limit groups

In this paper we consider the existence of dense embeddings of Limit groups in locally compact groups generalizing earlier work of Breuillard, Gelander, Souto and Storm [GBSS] where surface groups were considered. Our main results are proved in the context of compact groups and algebraic groups over local fields. In addition we prove a generalization of the classical Baumslag lemma which is a useful tool for generating eventually faithful sequences of homomorphisms. The last section is dedicated to correct a mistake from [BGSS] and to get rid of the even genus assumption.Comment: v2: Substantial changes to sections 7 and 8.2. Typos corrected. References added. v3: Acknowledgement correcte

UTAP: User-friendly Transcriptome Analysis Pipeline

Abstract Background RNA-Seq technology is routinely used to characterize the transcriptome, and to detect gene expression differences among cell types, genotypes and conditions. Advances in short-read sequencing instruments such as Illumina Next-Seq have yielded easy-to-operate machines, with high throughput, at a lower price per base. However, processing this data requires bioinformatics expertise to tailor and execute specific solutions for each type of library preparation. Results In order to enable fast and user-friendly data analysis, we developed an intuitive and scalable transcriptome pipeline that executes the full process, starting from cDNA sequences derived by RNA-Seq [Nat Rev Genet 10:57-63, 2009] and bulk MARS-Seq [Science 343:776-779, 2014] and ending with sets of differentially expressed genes. Output files are placed in structured folders, and results summaries are provided in rich and comprehensive reports, containing dozens of plots, tables and links. Conclusion Our User-friendly Transcriptome Analysis Pipeline (UTAP) is an open source, web-based intuitive platform available to the biomedical research community, enabling researchers to efficiently and accurately analyse transcriptome sequence data