On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes

We show that if $G$ is an infinitesimal elementary supergroup scheme of height $\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally homeomorphic to the variety $\mathcal{N}_r(G)$ of supergroup homomorphisms $\rho: \mathbb{M}_r \rightarrow G$ from a certain (non-algebraic) affine supergroup scheme $\mathbb{M}_r$ into $G$. In the case $r=1$, we further identify the cohomological support variety of a finite-dimensional $G$-supermodule $M$ as a subset of $\mathcal{N}_1(G)$. We then discuss how our methods, when combined with recently-announced results by Benson, Iyengar, Krause, and Pevtsova, can be applied to extend the homeomorphism $\mathcal{N}_r(G) \cong |G|$ to arbitrary infinitesimal unipotent supergroup schemes.Comment: Fixed some algebra misidentifications, primarily in Sections 1.3 and 3.3. Simplified the proof of Proposition 3.3.

Cohomology for infinitesimal unipotent algebraic and quantum groups

In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple algebraic group $G$, a parabolic subgroup $P_J$, and its unipotent radical $U_J$, we determine the ring structure of the cohomology ring $H^\bullet((U_J)_1,k)$. We also obtain new results on computing $H^\bullet((P_J)_1,L(\lambda))$ as an $L_J$-module where $L(\lambda)$ is a simple $G$-module with high weight $\lambda$ in the closure of the bottom $p$-alcove. Finally, we provide generalizations of all our results to the quantum situation.Comment: 18 pages. Some proofs streamlined over previous version. Additional details added to some proofs in Section

Finite Schur filtration dimension for modules over an algebra with Schur filtration

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N 2^N. Let G act rationally on a finitely generated commutative k-algebra A. Assume that A as a G-module has a good filtration or a Schur filtration. Let M be a noetherian A-module with compatible G action. Then M has finite good/Schur filtration dimension, so that there are at most finitely many nonzero H^i(G,M). Moreover these H^i(G,M) are noetherian modules over the ring of invariants A^G. Our main tool is a resolution involving Schur functors of the ideal of the diagonal in a product of Grassmannians.Comment: 22 pages; final versio

An improved method of computing geometrical potential force (GPF) employed in the segmentation of 3D and 4D medical images

The geometric potential force (GPF) used in segmentation of medical images is in general a robustmethod. However, calculation of the GPF is often time consuming and slow. In the present work, wepropose several methods for improving the GPF calculation and evaluate their efficiency against theoriginal method. Among different methods investigated, the procedure that combines Riesz transformand integration by part provides the fastest solution. Both static and dynamic images have been employedto demonstrate the efficacy of the proposed methods

A case of septicaemic anthrax in an intravenous drug user

<p><b>Background:</b> In 2000, Ringertz et al described the first case of systemic anthrax caused by injecting heroin contaminated with anthrax. In 2008, there were 574 drug related deaths in Scotland, of which 336 were associated with heroin and or morphine. We report a rare case of septicaemic anthrax caused by injecting heroin contaminated with anthrax in Scotland.</p> <p><b>Case Presentation:</b> A 32 year old intravenous drug user (IVDU), presented with a 12 hour history of increasing purulent discharge from a chronic sinus in his left groin. He had a tachycardia, pyrexia, leukocytosis and an elevated C-reactive protein (CRP). He was treated with Vancomycin, Clindamycin, Ciprofloxacin, Gentamicin and Metronidazole. Blood cultures grew Bacillus anthracis within 24 hours of presentation. He had a computed tomography (CT) scan and magnetic resonance imagining (MRI) of his abdomen, pelvis and thighs performed. These showed inflammatory change relating to the iliopsoas and an area of necrosis in the adductor magnus.</p> <p>He underwent an exploration of his left thigh. This revealed chronically indurated subcutaneous tissues with no evidence of a collection or necrotic muscle. Treatment with Vancomycin, Ciprofloxacin and Clindamycin continued for 14 days. Negative Pressure Wound Therapy (NPWT) device was applied utilising the Venturi™ wound sealing kit. Following 4 weeks of treatment, the wound dimensions had reduced by 77%.</p> <p><b>Conclusions:</b> Although systemic anthrax infection is rare, it should be considered when faced with severe cutaneous infection in IVDU patients. This case shows that patients with significant bacteraemia may present with no signs of haemodynamic compromise. Prompt recognition and treatment with high dose IV antimicrobial therapy increases the likelihood of survival. The use of simple wound therapy adjuncts such as NPWT can give excellent wound healing results.</p&gt

The fundamental pro-groupoid of an affine 2-scheme

A natural question in the theory of Tannakian categories is: What if you don't remember \Forget? Working over an arbitrary commutative ring $R$, we prove that an answer to this question is given by the functor represented by the \'etale fundamental groupoid \pi_1(\spec(R)), i.e.\ the separable absolute Galois group of $R$ when it is a field. This gives a new definition for \'etale \pi_1(\spec(R)) in terms of the category of $R$-modules rather than the category of \'etale covers. More generally, we introduce a new notion of "commutative 2-ring" that includes both Grothendieck topoi and symmetric monoidal categories of modules, and define a notion of $\pi_1$ for the corresponding "affine 2-schemes." These results help to simplify and clarify some of the peculiarities of the \'etale fundamental group. For example, \'etale fundamental groups are not "true" groups but only profinite groups, and one cannot hope to recover more: the "Tannakian" functor represented by the \'etale fundamental group of a scheme preserves finite products but not all products.Comment: 46 pages + bibliography. Diagrams drawn in Tik

Association of tamoxifen use and reduced risk of contralateral breast cancer for BRCA1 and BRCA2 mutation carriers

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Designed Azolopyridinium Salts Block Protective Antigen Pores In Vitro and Protect Cells from Anthrax Toxin

Background:Several intracellular acting bacterial protein toxins of the AB-type, which are known to enter cells by endocytosis, are shown to produce channels. This holds true for protective antigen (PA), the binding component of the tripartite anthrax-toxin of Bacillus anthracis. Evidence has been presented that translocation of the enzymatic components of anthrax-toxin across the endosomal membrane of target cells and channel formation by the heptameric/octameric PA63 binding/translocation component are related phenomena. Chloroquine and some 4-aminoquinolones, known as potent drugs against Plasmodium falciparium infection of humans, block efficiently the PA63-channel in a dose dependent way.Methodology/Principal Findings:Here we demonstrate that related positively charged heterocyclic azolopyridinium salts block the PA63-channel in the μM range, when both, inhibitor and PA63 are added to the same side of the membrane, the cis-side, which corresponds to the lumen of acidified endosomal vesicles of target cells. Noise-analysis allowed the study of the kinetics of the plug formation by the heterocycles. In vivo experiments using J774A.1 macrophages demonstrated that the inhibitors of PA63-channel function also efficiently block intoxication of the cells by the combination lethal factor and PA63 in the same concentration range as they block the channels in vitro.Conclusions/Significance:These results strongly argue in favor of a transport of lethal factor through the PA63-channel and suggest that the heterocycles used in this study could represent attractive candidates for development of novel therapeutic strategies against anthrax. © 2013 Beitzinger et al

Lipofibromatous hamartoma of the median nerve

Lipofibromatous hamartoma is a rare tumour of peripheral nerves which is characterised by an excessive infiltration of the epineurium and perineurium by fibroadipose tissue. To the best of our knowledge, only approximately 88 cases are reported in the literature. We report a rare case of lipofibromatous hamartoma of the median nerve causing secondary carpal tunnel syndrome in a 25 year old patient. This patient was treated conservatively with decompression and biopsy and experienced a complete resolution of symptoms post-operatively. Magnetic resonance imaging may be used to diagnose this lesion as it has very distinctive characteristics. Multiple conditions have been associated with this lesion and a greater understanding of these associations may clarify the pathogenesis. The architecture of the tumour makes excision very challenging and the surgical management remains controversial. A review of the literature regarding the etiology, pathogenesis and surgical management of lipofibromatous hamartoma is included