Closed geodesics and billiards on quadrics related to elliptic KdV solutions

We consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards. Namely, generic complex invariant manifolds are not Abelian varieties, and the billiard map is no more algebraic. A Poncelet-like theorem for such system is known. We give explicit sufficient conditions both for closed geodesics and periodic billiard orbits on Q and discuss their relation with the elliptic KdV solutions and elliptic Calogero systemComment: 23 pages, Latex, 1 figure Postscrip

Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian

In this paper the Galilean, scaling and translational self--similarity conditions for the AKNS hierarchy are analysed geometrically in terms of the infinite dimensional Grassmannian. The string equations found recently by non--scaling limit analysis of the one--matrix model are shown to correspond to the Galilean self--similarity condition for this hierarchy. We describe, in terms of the initial data for the zero--curvature 1--form of the AKNS hierarchy, the moduli space of these self--similar solutions in the Sato Grassmannian. As a byproduct we characterize the points in the Segal--Wilson Grassmannian corresponding to the Sachs rational solutions of the AKNS equation and to the Nakamura--Hirota rational solutions of the NLS equation. An explicit 1--parameter family of Galilean self--similar solutions of the AKNS equation and the associated solution to the NLS equation is determined.Comment: 25 pages in AMS-LaTe

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

EmrR-Dependent Upregulation of the Efflux Pump EmrCAB Contributes to Antibiotic Resistance in Chromobacterium violaceum

Chromobacterium violaceum is an environmental Gram-negative bacterium that causes infections in humans. Treatment of C. violaceum infections is difficult and little is known about the mechanisms of antibiotic resistance in this bacterium. In this work, we identified mutations in the MarR family transcription factor EmrR and in the protein GyrA as key determinants of quinolone resistance in C. violaceum, and we defined EmrR as a repressor of the MFS-type efflux pump EmrCAB. Null deletion of emrR caused increased resistance to nalidixic acid, but not to other quinolones or antibiotics of different classes. Moreover, the ΔemrR mutant showed decreased production of the purple pigment violacein. Importantly, we isolated C. violaceum spontaneous nalidixic acid-resistant mutants with a point mutation in the DNA-binding domain of EmrR (R92H), with antibiotic resistance profile similar to that of the ΔemrR mutant. Other spontaneous mutants with high MIC values for nalidixic acid and increased resistance to fluoroquinolones presented point mutations in the gene gyrA. Using DNA microarray, Northern blot and EMSA assays, we demonstrated that EmrR represses directly a few dozen genes, including the emrCAB operon and other genes related to transport, oxidative stress and virulence. This EmrR repression on emrCAB was relieved by salicylate. Although mutation of the C. violaceum emrCAB operon had no effect in antibiotic susceptibility or violacein production, deletion of emrCAB in an emrR mutant background restored antibiotic susceptibility and violacein production in the ΔemrR mutant. Using a biosensor reporter strain, we demonstrated that the lack of pigment production in ΔemrR correlates with the accumulation of quorum-sensing molecules in the cell supernatant of this mutant strain. Therefore, our data revealed that overexpression of the efflux pump EmrCAB via mutation and/or derepression of EmrR confers quinolone resistance and alters quorum-sensing signaling in C. violaceum, and that point mutation in emrR can contribute to emergence of antibiotic resistance in bacteria

Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians

The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems under study include the shallow water equation and Dym type equation. The classes of solutions are described in terms of theta-functions and their singular limits by using new parameterizations. A qualitative description of real valued solutions is provided

Fuchs versus Painlev\'e

We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e VI. We then show that the polynomiality of the expressions of the correlation functions (and form factors) in terms of the complete elliptic integral of the first and second kind, $K$ and $E$, is a straight consequence of the fact that the differential operators corresponding to the entries of Toeplitz-like determinants, are equivalent to the second order operator $L_E$ which has $E$ as solution (or, for off-diagonal correlations to the direct sum of $L_E$ and $d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $\Pi_1$, the Jacobi's form of the complete elliptic integral of the third kind (or equivalently two second order linear partial differential operators associated with Appell functions, where one of these operators can be seen as a deformation of $L_E$). We finally explore the generalizations, to the anisotropic Ising models, of the links we made, in two previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and elliptic curves. In particular the elliptic representation of Painlev\'e VI has to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of Difference Equations, SIDE VII meeting held in Melbourne during July 200

Cell walls of the dimorphic fungal pathogens Sporothrix schenckii and Sporothrix brasiliensis exhibit bilaminate structures and sloughing of extensive and intact layers

This work was supported by the Fundação Carlos Chagas de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), grants E-26/202.974/2015 and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), grants 229755/2013-5, Brazil. LMLB is a senior research fellow of CNPq and Faperj. NG acknowledged support from the Wellcome Trust (Trust (097377, 101873, 200208) and MRC Centre for Medical Mycology (MR/N006364/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

African trypanosomes evade immune clearance by O-glycosylation of the VSG surface coat

The African trypanosome, Trypanosoma brucei spp., is a paradigm for antigenic variation, the orchestrated alteration of cell surface molecules to evade host immunity. The parasite elicits robust antibody-mediated immune responses to its Variant Surface Glycoprotein (VSG) coat, but evades immune clearance by repeatedly accessing a large genetic VSG repertoire and “switching” to antigenically distinct VSGs. This persistent immune evasion has been ascribed exclusively to amino acid variance on the VSG surface presented by a conserved underlying protein architecture. We establish here that this model does not account for the scope of VSG structural and biochemical diversity. The 1.4Å resolution crystal structure of variant VSG3 manifests heretofore unappreciated divergence in the tertiary fold and oligomeric state. The structure also reveals an O linked carbohydrate on the top surface of VSG3, a modification previously unknown in African trypanosomes. Mass spectrometric analysis indicates that this O -glycosylation site is heterogeneously occupied in VSG3 by 0 to 3 hexose residues and is also present in other VSGs. We demonstrate that this O -glycosylation increases parasite virulence by impairing the generation of protective immunity. These data alter the paradigm of antigenic variation by the African trypanosome, expanding VSG variability beyond amino acid sequence to include surface posttranslational modifications with immunomodulatory impact