Cohomology of osp(1∣2)\frak {osp}(1|2) acting on the space of bilinear differential operators on the superspace R1∣1\mathbb{R}^{1|1}

We compute the first cohomology of the ortosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$ on the (1,1)-dimensional real superspace with coefficients in the superspace $\frak{D}_{\lambda,\nu;\mu}$ of bilinear differential operators acting on weighted densities. This work is the simplest superization of a result by Bouarroudj [Cohomology of the vector fields Lie algebras on $\mathbb{R}\mathbb{P}^1$ acting on bilinear differential operators, International Journal of Geometric Methods in Modern Physics (2005), {\bf 2}; N 1, 23-40]

The Binary Invariant Differential Operators on Weighted Densities on the superspace R1∣n\mathbb{R}^{1|n} and Cohomology

Over the $(1,n)$-dimensional real superspace, $n>1$, we classify $\mathcal{K}(n)$-invariant binary differential operators acting on the superspaces of weighted densities, where $\mathcal{K}(n)$ is the Lie superalgebra of contact vector fields. This result allows us to compute the first differential cohomology of %the Lie superalgebra $\mathcal{K}(n)$ with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities--a superisation of a result by Feigin and Fuchs. We explicitly give 1-cocycles spanning these cohomology spaces

Driving factors of the potentially toxic and harmful species of Prorocentrum Ehrenberg in a semi-enclosed Mediterranean lagoon (Tunisia, SW Mediterranean)

We analysed the dynamics of the potentially toxic and harmful species of Prorocentrum Ehrenberg in Bizerte lagoon (important aquaculture area, Northern Tunisia), substantiating the possible driving forces (temperature, salinity and nutrients), based on a two years database. We revealed that Prorocentrum spp. blooms of high magnitude (104 - 105 cells l-1) occurred mostly during the period of late winter to early spring. We found five species of Prorocentrum, two of which, P. lima and P. cordatum, the most common during the field, are confirmed agents of Diarrhetic Shellfish Poisoning in various regions of the world ocean. Prorocentrum sp., P. micans, and P. gracile were however present only sporadically but with high cell abundances, exemplifying bloom densities. Canonical correspondence analysis revealed that P. minimum and P. lima were much more abundant in eutrophied waters characterized here by high Chl a biomass, while P. gracile species occurred principally in warm waters. Furthermore, Prorocentrum sp. and P. micans seemed more likely to proliferate in saline waters with high concentrations of inorganic nutrients (nitrate, ammonia and phosphate). Our study calls attention to a possible intensification of DSP events in the Bizerte lagoon, given the propensity of Prorocentrum spp. to proliferate in a eutrophied system

Sorting by reversals, block interchanges, tandem duplications, and deletions

<p>Abstract</p> <p>Background</p> <p>Finding sequences of evolutionary operations that transform one genome into another is a classic problem in comparative genomics. While most of the genome rearrangement algorithms assume that there is exactly one copy of each gene in both genomes, this does not reflect the biological reality very well – most of the studied genomes contain duplicated gene content, which has to be removed before applying those algorithms. However, dealing with unequal gene content is a very challenging task, and only few algorithms allow operations like duplications and deletions. Almost all of these algorithms restrict these operations to have a fixed size.</p> <p>Results</p> <p>In this paper, we present a heuristic algorithm to sort an ancestral genome (with unique gene content) into a genome of a descendant (with arbitrary gene content) by reversals, block interchanges, tandem duplications, and deletions, where tandem duplications and deletions are of arbitrary size.</p> <p>Conclusion</p> <p>Experimental results show that our algorithm finds sorting sequences that are close to an optimal sorting sequence when the ancestor and the descendant are closely related. The quality of the results decreases when the genomes get more diverged or the genome size increases. Nevertheless, the calculated distances give a good approximation of the true evolutionary distances.</p

Solid State Electronics Laboratory Semiannual report, Feb. - Sep. 1969

Design and performance of miniaturized portable heart rate and electrocardiographic monitoring system for prolonged space flight

A framework for orthology assignment from gene rearrangement data

Abstract. Gene rearrangements have successfully been used in phylogenetic reconstruction and comparative genomics, but usually under the assumption that all genomes have the same gene content and that no gene is duplicated. While these assumptions allow one to work with organellar genomes, they are too restrictive when comparing nuclear genomes. The main challenge is how to deal with gene families, specifically, how to identify orthologs. While searching for orthologies is a common task in computational biology, it is usually done using sequence data. We approach that problem using gene rearrangement data, provide an optimization framework in which to phrase the problem, and present some preliminary theoretical results.

A Unifying Model of Genome Evolution Under Parsimony

We present a data structure called a history graph that offers a practical basis for the analysis of genome evolution. It conceptually simplifies the study of parsimonious evolutionary histories by representing both substitutions and double cut and join (DCJ) rearrangements in the presence of duplications. The problem of constructing parsimonious history graphs thus subsumes related maximum parsimony problems in the fields of phylogenetic reconstruction and genome rearrangement. We show that tractable functions can be used to define upper and lower bounds on the minimum number of substitutions and DCJ rearrangements needed to explain any history graph. These bounds become tight for a special type of unambiguous history graph called an ancestral variation graph (AVG), which constrains in its combinatorial structure the number of operations required. We finally demonstrate that for a given history graph $G$, a finite set of AVGs describe all parsimonious interpretations of $G$, and this set can be explored with a few sampling moves.Comment: 52 pages, 24 figure

Efficient algorithms for analyzing segmental duplications with deletions and inversions in genomes

Background: Segmental duplications, or low-copy repeats, are common in mammalian genomes. In the human genome, most segmental duplications are mosaics comprised of multiple duplicated fragments. This complex genomic organization complicates analysis of the evolutionary history of these sequences. One model proposed to explain this mosaic patterns is a model of repeated aggregation and subsequent duplication of genomic sequences. Results: We describe a polynomial-time exact algorithm to compute duplication distance, a genomic distance defined as the most parsimonious way to build a target string by repeatedly copying substrings of a fixed source string. This distance models the process of repeated aggregation and duplication. We also describe extensions of this distance to include certain types of substring deletions and inversions. Finally, we provide an description of a sequence of duplication events as a context-free grammar (CFG). Conclusion: These new genomic distances will permit more biologically realistic analyses of segmental duplications in genomes.