Koszul duality and mixed Hodge modules

We prove that on a certain class of smooth complex varieties (those with "affine even stratifications"), the category of mixed Hodge modules is "almost" Koszul: it becomes Koszul after a few unwanted extensions are eliminated. We also give an equivalence between perverse sheaves on such a variety and modules for a certain graded ring, obtaining a formality result as a corollary. For flag varieties, these results were proved earlier by Beilinson-Ginzburg-Soergel using a rather different construction.Comment: 26 pages. v4: added Proposition 3.9; streamlined Section 4; other minor correction

Perverse coherent sheaves and the geometry of special pieces in the unipotent variety

Let X be a scheme of finite type over a Noetherian base scheme S admitting a dualizing complex, and let U be an open subset whose complement has codimension at least 2. We extend the Deligne-Bezrukavnikov theory of perverse coherent sheaves by showing that a coherent middle extension (or intersection cohomology) functor from perverse sheaves on U to perverse sheaves on X may be defined for a much broader class of perversities than has previously been known. We also introduce a derived category version of the coherent middle extension functor. Under suitable hypotheses, we introduce a construction (called "S2-extension") in terms of perverse coherent sheaves of algebras on X that takes a finite morphism to U and extends it in a canonical way to a finite morphism to X. In particular, this construction gives a canonical "S2-ification" of appropriate X. The construction also has applications to the "Macaulayfication" problem, and it is particularly well-behaved when X is Gorenstein. Our main goal, however, is to address a conjecture of Lusztig on the geometry of special pieces (certain subvarieties of the unipotent variety of a reductive algebraic group). The conjecture asserts in part that each special piece is the quotient of some variety (previously unknown in the exceptional groups and in positive characteristic) by the action of a certain finite group. We use S2-extension to give a uniform construction of the desired variety.Comment: 30 pages; minor corrections and addition

Staggered sheaves on partial flag varieties

Staggered t-structures are a class of t-structures on derived categories of equivariant coherent sheaves. In this Note, we show that the derived category of coherent sheaves on a partial flag variety, equivariant for a Borel subgroup, admits a staggered t-structure with the property that all objects in its heart have finite length. As a consequence, we obtain a basis for its equivariant K-theory consisting of simple staggered sheaves. To cite this article: P.N. Achar, D.S. Sage, C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences

A study to evaluate the in-vivo anticancer activity of ethanolic extract of Holoptelea integrifolia leaves against Ehrlich ascites carcinoma model using Swiss albino mice

Background: Herbs having ethnomedical uses is one of the best approaches in searching novel anticancer drugs. The aim of the present study is to evaluate the anticancer activity of ethanolic extract of Holoptelea integrifolia leaves against Ehrlich ascites carcinoma induced liquid tumor model using Swiss Albino mice.Methods: Acute toxicity test was performed using Wistar albino rats before starting the in-vivo anticancer activity, were the MTD was more than 5000 mg/kg. Animals were divided into six groups of six animals each. 250mg/kg and 500 mg/kg of ethanolic extract of HI leaves, was administered orally for 9 days and Cisplatin (3.5 mg/kg, i.p., single dose). Various parameters like Change in body weight, Mean Survival Time, Percentage Increase in Life Span, Hematological & Biochemical parameters were assessed.Results: All the parameters were considerably restored towards the normal values. HIAL500mg/kg showed more significant results than 250 mg/kg. Hence 500mg/kg was taken for combination study with standard drug Cisplatin.Conclusions: On the basis of the above result it was suggested that, the in-vivo anticancer activity of ethanolic extract of Holoptelea integrifolia leaves possess significant anticancer property with the dose dependent effect. This may probably due to the presence of phytochemicals such as alkaloids, phenols and flavonoids

Multipartite entanglement in fermionic systems via a geometric measure

We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-1/2 fermions distributed over 2L modes (single particle states). The measure is defined on the 2L qubit space isomorphic to the Fock space for 2L single particle states. This entanglement measure is defined for a given partition of 2L modes containing m >= 2 subsets. Thus this measure applies to m <= 2L partite fermionic system where L is any finite number, giving the number of sites. The Hilbert spaces associated with these subsets may have different dimensions. Further, we have defined the local quantum operations with respect to a given partition of modes. This definition is generic and unifies different ways of dividing a fermionic system into subsystems. We have shown, using a representative case, that the geometric measure is invariant under local unitaries corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems. To the best of our knowledge, there is no usable entanglement measure of m > 3 partite fermionic systems in the literature, so that this is the first measure of multipartite entanglement for fermionic systems going beyond the bipartite and tripartite cases.Comment: 25 pages, 8 figure

Anticariogenic Activity of Lagerstroemia speciosa (L.)

Dental caries is the common infectious diseases of the oral cavity and is caused mainly by oral streptococci. The present study was carried out to investigate the anticariogenic activity of methanol extract of Lagerstroemia speciosa (L.) (Lythraceae) leaves. The inhibitory efficacy of methanol extract was tested against 12 oral isolates of Streptococcus mutans by Agar well diffusion method. The broth cultures of bacteria were swabbed uniformly on sterile Brain heart infusion agar plates and wells of 6mm were punched in the inoculated plates. Standard antibiotic and different  concentrations of extract were transferred into labeled wells. Zone of inhibition was measured after incubation. The extract caused a  concentration dependent inhibition of cariogenic isolates. Inhibition caused by standard antibiotic was higher than the methanol extract. Preliminary phytochemical analysis showed the presence of saponins, glycosides,  tannins and terpenoids. The result of the present study reveals that  methanol extract showed significant inhibitory activity against cariogenic isolates. The inhibitory efficacy of extract against cariogenic isolates could be due to the presence of these metabolites. In suitable form, the leaves could be used to treat dental caries