Quantization of the N=2 Supersymmetric KdV Hierarchy

We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based on the $sl^{(1)}(2|1)$ affine algebra but with a new algebraic construction for the L-operator, different from the standard Drinfeld-Sokolov reduction. We construct the quantum monodromy matrix satisfying a special version of the reflection equation and show that in the classical limit, this object gives the monodromy matrix of N=2 supersymmetric KdV system. We also show that at both the classical and the quantum levels, the trace of the monodromy matrix (transfer matrix) is invariant under two supersymmetry transformations and the zero mode of the associated U(1) current.Comment: LaTeX2e, 12 page

The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice

We study completely integrable Hamiltonian systems whose monodromy matrices are related to the representatives for the set of gauge equivalence classes $\boldsymbol{\mathcal{M}}_F$ of polynomial matrices. Let $X$ be the algebraic curve given by the common characteristic equation for $\boldsymbol{\mathcal{M}}_F$. We construct the isomorphism from the set of representatives to an affine part of the Jacobi variety of $X$. This variety corresponds to the invariant manifold of the system, where the Hamiltonian flow is linearized. As the application, we discuss the algebraic completely integrability of the extended Lotka-Volterra lattice with a periodic boundary condition.Comment: Revised version, 26 page

Membrane-associated heparan sulfate is not required for rAAV-2 infection of human respiratory epithelia

BACKGROUND: Adeno-associated virus type 2 (AAV-2) attachment and internalization is thought to be mediated by host cell membrane-associated heparan sulfate proteoglycans (HSPG). Lack of HSPG on the apical membrane of respiratory epithelial cells has been identified as a reason for inefficient rAAV-2 infection in pulmonary applications in-vivo. The aim of this investigation was to determine the necessity of cell membrane HSPG for efficient infection by rAAV-2. RESULTS: Rates of transduction with rAAV2-CMV-EGFP3 in several different immortalized airway epithelial cell lines were determined at different multiplicities of infection (MOI) before and after removal of membrane HSPG by heparinase III. Removal of HSPG decreased the efficacy of infection with rAAV2 by only 30–35% at MOI ≤ 100 for all of respiratory cell lines tested, and had even less effect at an MOI of 1000. Studies in mutant Chinese Hamster Ovary cell lines known to be completely deficient in surface HSPG also demonstrated only moderate effect of absence of HSPG on rAAV-2 infection efficacy. However, mutant CHO cells lacking all membrane proteoglycans demonstrated dramatic reduction in susceptibility to rAAV-2 infection, suggesting a role of membrane glycosaminoglycans other than HSPG in mediating rAAV-2 infection. CONCLUSION: Lack of cell membrane HSPG in pulmonary epithelia and other cell lines results in only moderate decrease in susceptibility to rAAV-2 infection, and this decrease may be less important at high MOIs. Other cell membrane glycosaminoglycans can play a role in permitting attachment and subsequent rAAV-2 internalization. Targeting alternative membrane glycosaminoglycans may aid in improving the efficacy of rAAV-2 for pulmonary applications

Producing valid statistics when legislation, culture, and medical practices differ for births at or before the threshold of survival: Report of a European workshop

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Sylvester-t' Hooft generators of sl(n) and sl(n|n), and relations between them

Among the simple finite dimensional Lie algebras, only sl(n) possesses two automorphisms of finite order which have no common nonzero eigenvector with eigenvalue one. It turns out that these automorphisms are inner and form a pair of generators that allow one to generate all of sl(n) under bracketing. It seems that Sylvester was the first to mention these generators, but he used them as generators of the associative algebra of all n times n matrices Mat(n). These generators appear in the description of elliptic solutions of the classical Yang-Baxter equation, orthogonal decompositions of Lie algebras, 't Hooft's work on confinement operators in QCD, and various other instances. Here I give an algorithm which both generates sl(n) and explicitly describes a set of defining relations. For simple (up to center) Lie superalgebras, analogs of Sylvester generators exist only for sl(n|n). The relations for this case are also computed.Comment: 14 pages, 6 figure

The effective action of (2+1)-dimensional QED: the effect of finite fermion density

The effective action of (2+1)-dimensional QED with finite fermion density is calculated in a uniform electromagnetic field. It is shown that the integer quantum Hall effect and de Haas-van Alphen like phenomena in condensed matter physics are derived directly from the effective action.Comment: 10 pages, Revtex, No figure

Particle-hole symmetry and transport properties of the flux state in underdoped cuprates

Transport properties are studied for the flux state with the gauge flux $\phi$ per plaquett, which may model the underdoped cuprates, with the emphasis on the particle-hole and parity/chiral symmetries.This model is reduced to the Dirac fermions in (2+1)D with a mass gap introduced by the antiferromagnetic (AF) long range order and/or the stripe formation. Without the mass gap, the Hall constant $R_H$ and the thermopower $S$ obey two-parameter scaling laws, and show the strong temperature dependence due to the recovery of the particle-hole symmetry at high temperature. The $x$-dependences of $\sigma_{xx} (\propto \sqrt{x})$ and $\sigma_{xy}$ (independent of $x$) are in a sharp contradiction with the experiments. (Here $x$ is the hole concentration.) Therefore there is no signature of the particle-hole symmetry or the massless Dirac fermions in the underdoped cuprates even above the Neel temperature $T_N$. With the mass gap introduced by the AF order, there occurs the parity anomaly for each of the Dirac fermions. However the contributions from different valleys and spins cancel with each other to result in no spontaneous Hall effect even if the time-reversal symmetry is broken with $\phi \ne \pi$. The effects of the stripes are also studied. The diagonal and vertical (horizontal) stripes have quite different influence on the transport properties. The suppression of $R_H$ occurs at low temperature only when (i) both the AF order and the vertical (horizontal) stripe coexist, and (ii) the average over the in-plane direction is taken. Discussions on the recent experiments are given from the viewpoint of these theoretical results.Comment: RevTeX, 14 pages, 11 figure

Novel associations for hypothyroidism include known autoimmune risk loci

Hypothyroidism is the most common thyroid disorder, affecting about 5% of the general population. Here we present the first large genome-wide association study of hypothyroidism, in 2,564 cases and 24,448 controls from the customer base of 23andMe, Inc., a personal genetics company. We identify four genome-wide significant associations, two of which are well known to be involved with a large spectrum of autoimmune diseases: rs6679677 near _PTPN22_ and rs3184504 in _SH2B3_ (p-values 3.5e-13 and 3.0e-11, respectively). We also report associations with rs4915077 near _VAV3_ (p-value 8.3e-11), another gene involved in immune function, and rs965513 near _FOXE1_ (p-value 3.1e-14). Of these, the association with _PTPN22_ confirms a recent small candidate gene study, and _FOXE1_ was previously known to be associated with thyroid-stimulating hormone (TSH) levels. Although _SH2B3_ has been previously linked with a number of autoimmune diseases, this is the first report of its association with thyroid disease. The _VAV3_ association is novel. These results suggest heterogeneity in the genetic etiology of hypothyroidism, implicating genes involved in both autoimmune disorders and thyroid function. Using a genetic risk profile score based on the top association from each of the four genome-wide significant regions in our study, the relative risk between the highest and lowest deciles of genetic risk is 2.1

Quantum Group as Semi-infinite Cohomology

We obtain the quantum group $SL_q(2)$ as semi-infinite cohomology of the Virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges $c+\bar{c}=26$. Each braided VOA is constructed from the free Fock space realization of the Virasoro algebra with an additional q-deformed harmonic oscillator degree of freedom. The braided VOA structure arises from the theory of local systems over configuration spaces and it yields an associative algebra structure on the cohomology. We explicitly provide the four cohomology classes that serve as the generators of $SL_q(2)$ and verify their relations. We also discuss the possible extensions of our construction and its connection to the Liouville model and minimal string theory.Comment: 50 pages, 7 figures, minor revisions, typos corrected, Communications in Mathematical Physics, in pres

Grifonin-1: A Small HIV-1 Entry Inhibitor Derived from the Algal Lectin, Griffithsin

Background: Griffithsin, a 121-residue protein isolated from a red algal Griffithsia sp., binds high mannose N-linked glycans of virus surface glycoproteins with extremely high affinity, a property that allows it to prevent the entry of primary isolates and laboratory strains of T- and M-tropic HIV-1. We used the sequence of a portion of griffithsin's sequence as a design template to create smaller peptides with antiviral and carbohydrate-binding properties. Methodology/Results: The new peptides derived from a trio of homologous β-sheet repeats that comprise the motifs responsible for its biological activity. Our most active antiviral peptide, grifonin-1 (GRFN-1), had an EC50 of 190.8±11.0 nM in in vitro TZM-bl assays and an EC50 of 546.6±66.1 nM in p24gag antigen release assays. GRFN-1 showed considerable structural plasticity, assuming different conformations in solvents that differed in polarity and hydrophobicity. Higher concentrations of GRFN-1 formed oligomers, based on intermolecular β-sheet interactions. Like its parent protein, GRFN-1 bound viral glycoproteins gp41 and gp120 via the N-linked glycans on their surface. Conclusion: Its substantial antiviral activity and low toxicity in vitro suggest that GRFN-1 and/or its derivatives may have therapeutic potential as topical and/or systemic agents directed against HIV-1