Whether common ancestors of eukaryotes and prokaryotes had introns is one of the oldest unanswered questions in molecular evolution. Recently completed genome sequences have been used for comprehensive analyses of exon-intron organization in orthologous genes of diverse organisms, leading to more refined work on intron evolution. Large sets of intron presence-absence data require rigorous theor...

Although genes have specific phenotypic consequences in a given species, this functional relationship can clearly change during the course of evolution. Many cases of evolutionary dissociations between homologous genes and homologous morphological features are now known. These dissociations have interesting and important implications for understanding the genetic basis for evolutionary change i...

Symmetric homology of a unital algebra A over a commutative ground ring k has been defined using derived functors and the symmetric bar construction of Fiedorowicz, in an analogous way as cyclic, dihedral or quaternionic homology has been defined. In this paper, it is found that the HS∗(A) admits Dyer-Lashoff homology operations, and indeed, there is a Pontryagin product structure making HS∗(A)...

This text is a preliminary version of material used for a course at the University of Copenhagen, part of ”Workshop and Masterclass on Homological stability” August 26-30, 2013. This lecture concerns the method developped, in collaboration with Aurélien Djament, in [DV10] and used in [Dja12] and [DVa] to compute the stable homology of a family of groups with coefficients given by a polynomial f...

This text is a preliminary version of material used for a course at the University of Copenhagen, part of ”Workshop and Masterclass on Homological stability” August 26-30, 2013. This lecture concerns the method developped, in collaboration with Aurélien Djament, in [DV10] and used in [Dja12] and [DVa] to compute the stable homology of a family of groups with coefficients given by a polynomial f...

A homology stratification is a filtered space with local homology groups constant on strata. Despite being used by Goresky and MacPherson [3] in their proof of topological invariance of intersection homology, homology stratifications do not appear to have been studied in any detail and their properties remain obscure. Here we use them to present a simplified version of the Goresky–MacPherson pr...

We compute the equivariant $KO$-homology of classifying space for proper actions $\textrm{SL}_3(\mathbb{Z})$ and $\textrm{GL}_3(\mathbb{Z})$. also Bredon homology $K$-homology spaces $\textrm{PSL}_2(\mathbb{Z}[\frac{1}{p}])$ $\textrm{SL}_2(\mathbb{Z}[\frac{1}{p}])$ each prime $p$. Finally, we prove Unstable Gromov-Lawson-Rosenberg Conjecture a large class groups whose maximal finite subgroups a...

In the post genomic era a possibility of theoretical prediction of protein structure from sequence of amino acids is one of the most important and challenging goals of molecular biology. High complexity of the problem requires simplification of molecular models and very efficient computational tools. Proposed here model of protein structure, dynamics and interaction scheme assumes a single inte...