Some finiteness results in the category U

This note investigate some finiteness properties of the category U of unstable modules. One shows finiteness properties for the injective resolution of finitely generated unstable modules. One also shows a stabilization result under Frobenius twist for Ext-groups

Sur la torsion de Frobenius de la cat\'egorie des modules instables

In the category $\mathcal{P}_{d}$ of strict polynomial functors, the morphisms between extension groups induced by the Frobenius twist are injective. In \cite{Cuo14a}, the category $\mathcal{P}_{d}$ is proved to be a full sub-category of the category $\mathcal{U}$ of unstable modules \textit{via} Hai's functor. The Frobenius twist is extended to the category $\mathcal{U}$ but remains mysterious there. This article aims to study the Frobenius twist and its effects on the extension groups of unstable modules. We compute explicitly several extension groups and show that in these cases, the morphisms induced by the Frobenius twist are injective. These results are obtained by constructing the minimal injective resolution of the free unstable module $F(1)$.Comment: in French. Change of references thanks to a remark by Professor Wilberd van der Kalle

Homogeneous strict polynomial functors as unstable modules

A relation between Schur algebras and the Steenrod algebra is shown in [Hai10] where to each strict polynomial functor the author naturally associates an unstable module. We show that the restriction of Hai's functor to a sub-category of strict polynomial functors of a given degree is fully faithful

Research method detection human face in video streams

То же на с. 58-6

In silico study of legume and legume-type lectins

Dissertation supervisor: Dr. Gary Stacey.Includes vita.In contemporary biological research, bioinformatics and computational biology are essential fields that can help biologists solve and understand complex biological problems and mechanisms. Indeed, recent advances in DNA sequencing technology have helped us to gain insight into the origin, distribution, and evolution of genes and gene families in living organisms. A large-scale genomic study was conducted to search for putative proteins containing the legume-type lectin domain (LLDP) across kingdoms, followed by comprehensive genomics and phylogenetic analyses. Many homologous sequences of the plant LLDP family were newly identified in bacteria and lower eukaryotes, but far fewer than those found universally in land plants. Analyses of the evolution of LLDP genes across kingdoms revealed that members share a common ancestor suggesting a species-specific divergence and expansion of members of the LLDP family in plants. Detailed investigation of LLDP gene pools in sequenced genomes demonstrates that segmental and tandem duplications are two key factors in the rapid expansion of this family in land plants. Calculation of nucleotide substitution rates shows that purifying selection is likely the main driving force for stabilizing selection and evolution of the soybean LLDP genes. Analysis of soybean LLDP gene expression suggests that duplicate genes tend to differ and diverge regarding expression levels and expression partitioning in different studied tissues and development stages. A gene set enrichment study of soybean LLDPs demonstrated a functional conservation among members towards carbohydrate binding and kinase activity. In addition, molecular modeling and docking studies were also performed on the LLD domain of DORN1 protein, an important plant receptor-like kinase of the LLDP family, leading to the identification and in vitro characterization of its ligand-binding site and key binding residues interacting with an adenosine triphosphate substrate.Includes bibliographical references (pages 143-158)

Around conjectures of N. Kuhn

We discuss two extensions of results conjectured by Nick Kuhn about the non-realization of unstable algebras as the mod $p$ singular cohomology of a space, for $p$ a prime. The first extends and refines earlier work of the second and fourth authors, using Lannes' mapping space theorem. The second (for the prime $2$) is based on an analysis of the $-1$ and $-2$ columns of the Eilenberg-Moore spectral sequence, and of the associated extension. In both cases, the statements and proofs use the relationship between the categories of unstable modules and functors between \Fp-vector spaces. The second result in particular exhibits the power of the functorial approach

Some finiteness results in the category U

This note investigate some finiteness properties of the category U of unstable modules. One shows finiteness properties for the injective resolution of finitely generated unstable modules. One also shows a stabilization result under Frobenius twist for Ext-groups