On p-adic lattices and Grassmannians

It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive group G over a field k, carry the geometric structure of an inductive limit of projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for G. From the point of view of number theory it would be interesting to obtain an analogous geometric interpretation of quotients of the form G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of p-typical Witt vectors, k is a perfect field of characteristic p and G is a reductive group scheme over W(k). The present paper is an attempt to describe which constructions carry over from the function field case to the p-adic case, more precisely to the situation of the p-adic affine Grassmannian for the special linear group G=SL_n. We start with a description of the R-valued points of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R), where R is a perfect k-algebra. In order to obtain a link with geometry we further construct projective k-subvarieties of the multigraded Hilbert scheme which map equivariantly to the p-adic affine Grassmannian. The images of these morphisms play the role of Schubert varieties in the p-adic setting. Further, for any reduced k-algebra R these morphisms induce bijective maps between the sets of R-valued points of the respective open orbits in the multigraded Hilbert scheme and the corresponding Schubert cells of the p-adic affine Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math. Zeitschrift, of the previously published preprint "On p-adic loop groups and Grassmannians

Rational isogenies from irrational endomorphisms

In this paper, we introduce a polynomial-time algorithm to compute a connecting $\mathcal{O}$-ideal between two supersingular elliptic curves over $\mathbb{F}_p$ with common $\mathbb{F}_p$-endomorphism ring $\mathcal{O}$, given a description of their full endomorphism rings. This algorithm provides a reduction of the security of the CSIDH cryptosystem to the problem of computing endomorphism rings of supersingular elliptic curves. A similar reduction for SIDH appeared at Asiacrypt 2016, but relies on totally different techniques. Furthermore, we also show that any supersingular elliptic curve constructed using the complex-multiplication method can be located precisely in the supersingular isogeny graph by explicitly deriving a path to a known base curve. This result prohibits the use of such curves as a building block for a hash function into the supersingular isogeny graph

Unravelling the novel Higgs mechanism in (2+1)d Chern-Simons theories

Chern-Simons gauge theories in 2+1 dimensions with multiple gauge fields exhibit novel properties that are analysed here in some detail. A striking feature is the possibility of a non-propagating Chern-Simons field acquiring a massless propagating mode via a Higgs mechanism. This novel Higgs mechanism, originally discovered in the context of M-theory, is studied here without reference to M-theory or supersymmetry. It is revealed as a variant of topological mass generation and shown to arise only when Chern-Simons and mass matrices are not simultaneously diagonalisable. Sufficient conditions are found for it to occur. It is speculated that some analogue of the NHM could occur in theories of condensed-matter systems similar to those exhibiting the fractional quantum Hall effect, as well as in 2+1 dimensional gravity.Comment: 28 page

Effects of Astragalus Polysaccharide on Immune Responses of Porcine PBMC Stimulated with PRRSV or CSFV

BACKGROUND: Astragalus polysaccharide (APS) has been used as an immunomodulator that can enhance immune responses, whereas the immunomodulatory effects of APS on porcine peripheral blood mononuclear cells (PBMCs) exposed to porcine reproductive and respiratory syndrome virus (PRRSV) and classical swine fever virus (CSFV) have not been investigated. METHODOLOGY/PRINCIPAL FINDINGS: Porcine PBMCs were cultured in complete RPMI media in the presence of the R98-strain of PRRSV (5×10(4) TCID(50)/ml) or C-strain of CSFV (10(3) TCID(50)/ml) with or without APS. The expression of mRNA for CD28, cytotoxic T-lymphocyte antigen 4 (CTLA-4), transforming growth factor-β (TGF-β), interleukin 2 (IL-2) and IL-10 was assayed by TaqMan real-time RT-PCR. The expression of mRNA for CD28 and CTLA-4 increased at 24 h after stimulation of PBMCs with CSFV and the increased production of CTLA-4 was confirmed by western blot analysis, whereas the increases were inhibited by the addition of APS. In addition, APS alone upregulated IL-2 and TGF-β mRNA expression in PBMCs and the addition of APS had the capacity to prevent a further increase in IL-2 mRNA expression in PBMCs during CSFV or PRRSV infection, but had no effect on TGF-β mRNA expression. The production of tumor necrosis factor-alpha (TNF-α) increased at 12 h after stimulation with PRRSV or CSFV, but not with PRRSV plus APS or CSFV plus APS, whereas the addition of APS to PBMCs infected with PRRSV or CSFV promoted IL-10 mRNA expression. CONCLUSIONS: We suggested that APS had immunomodulatory effects on cells exposed to PRRSV or CSFV. It might be that APS via different mechanisms affects the activities of immune cells during either PRRSV or CSFV infection. This possibility warrants further studies to evaluate whether APS would be an effective adjuvant in vaccines against PRRSV or CSFV

How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A

We show how cyclic (f,σ,δ)-codes over finite rings canonically induce a Z-lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f. This construction generalizes the one using certain σ-constacyclic codes by Ducoat and Oggier, which used quotients of orders in non-commutative associative division algebras defined by f, and can be viewed as a generalization of the classical Construction A for lattices from linear codes. It has the potential to be applied to coset coding, in particular to wire-tap coding. Previous results by Ducoat and Oggier are obtained as special cases

The Structure of Hopf Algebras Acting on Dihedral Extensions

We discuss isomorphism questions concerning the Hopf algebras that yield Hopf–Galois structures for a fixed separable field extension L/K. We study in detail the case where L/K is Galois with dihedral group Dp, p≥3 prime and give explicit descriptions of the Hopf algebras which act on L/K. We also determine when two such Hopf algebras are isomorphic, either as Hopf algebras or as algebras. For the case p=3 and a chosen L/K, we give the Wedderburn–Artin decompositions of the Hopf algebras

Distinct Regions of the Large Extracellular Domain of Tetraspanin CD9 Are Involved in the Control of Human Multinucleated Giant Cell Formation

Multinucleated giant cells, formed by the fusion of monocytes/macrophages, are features of chronic granulomatous inflammation associated with infections or the persistent presence of foreign material. The tetraspanins CD9 and CD81 regulate multinucleated giant cell formation: soluble recombinant proteins corresponding to the large extracellular domain (EC2) of human but not mouse CD9 can inhibit multinucleated giant cell formation, whereas human CD81 EC2 can antagonise this effect. Tetraspanin EC2 are all likely to have a conserved three helix sub-domain and a much less well-conserved or hypervariable sub-domain formed by short helices and interconnecting loops stabilised by two or more disulfide bridges. Using CD9/CD81 EC2 chimeras and point mutants we have mapped the specific regions of the CD9 EC2 involved in multinucleated giant cell formation. These were primarily located in two helices, one in each sub-domain. The cysteine residues involved in the formation of the disulfide bridges in CD9 EC2 were all essential for inhibitory activity but a conserved glycine residue in the tetraspanin-defining ‘CCG’ motif was not. A tyrosine residue in one of the active regions that is not conserved between human and mouse CD9 EC2, predicted to be solvent-exposed, was found to be only peripherally involved in this activity. We have defined two spatially-distinct sites on the CD9 EC2 that are required for inhibitory activity. Agents that target these sites could have therapeutic applications in diseases in which multinucleated giant cells play a pathogenic role

Dengue Virus Type 2 Infections of Aedes aegypti Are Modulated by the Mosquito's RNA Interference Pathway

A number of studies have shown that both innate and adaptive immune defense mechanisms greatly influence the course of human dengue virus (DENV) infections, but little is known about the innate immune response of the mosquito vector Aedes aegypti to arbovirus infection. We present evidence here that a major component of the mosquito innate immune response, RNA interference (RNAi), is an important modulator of mosquito infections. The RNAi response is triggered by double-stranded RNA (dsRNA), which occurs in the cytoplasm as a result of positive-sense RNA virus infection, leading to production of small interfering RNAs (siRNAs). These siRNAs are instrumental in degradation of viral mRNA with sequence homology to the dsRNA trigger and thereby inhibition of virus replication. We show that although dengue virus type 2 (DENV2) infection of Ae. aegypti cultured cells and oral infection of adult mosquitoes generated dsRNA and production of DENV2-specific siRNAs, virus replication and release of infectious virus persisted, suggesting viral circumvention of RNAi. We also show that DENV2 does not completely evade RNAi, since impairing the pathway by silencing expression of dcr2, r2d2, or ago2, genes encoding important sensor and effector proteins in the RNAi pathway, increased virus replication in the vector and decreased the extrinsic incubation period required for virus transmission. Our findings indicate a major role for RNAi as a determinant of DENV transmission by Ae. aegypti

RNA-seq analyses of blood-induced changes in gene expression in the mosquito vector species, Aedes aegypti

<p>Abstract</p> <p>Background</p> <p>Hematophagy is a common trait of insect vectors of disease. Extensive genome-wide transcriptional changes occur in mosquitoes after blood meals, and these are related to digestive and reproductive processes, among others. Studies of these changes are expected to reveal molecular targets for novel vector control and pathogen transmission-blocking strategies. The mosquito <it>Aedes aegypti </it>(Diptera, Culicidae), a vector of Dengue viruses, Yellow Fever Virus (YFV) and Chikungunya virus (CV), is the subject of this study to look at genome-wide changes in gene expression following a blood meal.</p> <p>Results</p> <p>Transcriptional changes that follow a blood meal in <it>Ae. aegypti </it>females were explored using RNA-seq technology. Over 30% of more than 18,000 investigated transcripts accumulate differentially in mosquitoes at five hours after a blood meal when compared to those fed only on sugar. Forty transcripts accumulate only in blood-fed mosquitoes. The list of regulated transcripts correlates with an enhancement of digestive activity and a suppression of environmental stimuli perception and innate immunity. The alignment of more than 65 million high-quality short reads to the <it>Ae. aegypti </it>reference genome permitted the refinement of the current annotation of transcript boundaries, as well as the discovery of novel transcripts, exons and splicing variants. <it>Cis</it>-regulatory elements (CRE) and <it>cis</it>-regulatory modules (CRM) enriched significantly at the 5'end flanking sequences of blood meal-regulated genes were identified.</p> <p>Conclusions</p> <p>This study provides the first global view of the changes in transcript accumulation elicited by a blood meal in <it>Ae. aegypti </it>females. This information permitted the identification of classes of potentially co-regulated genes and a description of biochemical and physiological events that occur immediately after blood feeding. The data presented here serve as a basis for novel vector control and pathogen transmission-blocking strategies including those in which the vectors are modified genetically to express anti-pathogen effector molecules.</p