Macdonald polynomials in superspace: conjectural definition and positivity conjectures

We introduce a conjectural construction for an extension to superspace of the Macdonald polynomials. The construction, which depends on certain orthogonality and triangularity relations, is tested for high degrees. We conjecture a simple form for the norm of the Macdonald polynomials in superspace, and a rather non-trivial expression for their evaluation. We study the limiting cases q=0 and q=\infty, which lead to two families of Hall-Littlewood polynomials in superspace. We also find that the Macdonald polynomials in superspace evaluated at q=t=0 or q=t=\infty seem to generalize naturally the Schur functions. In particular, their expansion coefficients in the corresponding Hall-Littlewood bases appear to be polynomials in t with nonnegative integer coefficients. More strikingly, we formulate a generalization of the Macdonald positivity conjecture to superspace: the expansion coefficients of the Macdonald superpolynomials expanded into a modified version of the Schur superpolynomial basis (the q=t=0 family) are polynomials in q and t with nonnegative integer coefficients.Comment: 18 page

Explicit formulas for the generalized Hermite polynomials in superspace

We provide explicit formulas for the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in superspace. The construction relies on the triangular action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions.Comment: 19 pages. This is a recasting of the second part of the first version of hep-th/0305038 which has been splitted in two articles. In this revised version, the introduction has been rewritten and a new appendix has been added. To appear in JP

Justice Florence Kerins Murray: The Legacy of a Pioneer in the Rhode Island Courts

This essay discusses the professional and personal life of Florence Kerins Murray (1916-2004), a senator and judge, whose career had a profound effect onRhode Islandgovernment, public service, and the judiciary. The author uses twenty oral history interviews conducted by the author from 2007-12 with men and women working in the courts, in state and local governments, in public service organizations, and in the media. The research was funded by a scholar grant from the Rhode Island Council on the Humanities

Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals

The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is invariant under the action of certain differential operators which include half the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit clusters of size at most k: they vanish when k+1 of their variables are identified, and they do not vanish when only k of them are identified. We generalize most of these properties to superspace using orthogonal eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular, we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N commuting variables and N anticommuting variables. We prove that the ideal {\mathcal I}^{(k,r)}_N is stable with respect to the action of the negative-half of the super-Virasoro algebra. In addition, we show that the Jack superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting variables are equal, and conjecture that they do not vanish when only k of them are identified. This allows us to conclude that the standard Jack polynomials with prescribed symmetry should satisfy similar clustering properties. Finally, we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for the subspace of symmetric superpolynomials in N variables that vanish when k+1 commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we present exceptions to an often made statement concerning the clustering property of the ordinary Jack polynomials for (k,r,N)-admissible partitions (see Footnote 2); 2) Conjecture 14 is substantiated with the extensive computational evidence presented in the new appendix C; 3) the various tests supporting Conjecture 16 are reporte

Understanding Maternity Care Coordination for Women Veterans Using an Integrated Care Model Approach

BACKGROUND: An increasing number of women veterans are using VA maternity benefits for their pregnancies. However, because the VA does not offer obstetrical care, women must seek maternity care from non-VA providers. The growing number of women using non-VA care has increased the importance of understanding how this care is integrated with ongoing VA medical and mental health services and how perceptions of care integration impact healthcare utilization. Therefore, we sought to understand these relationships among a sample of postpartum veterans utilizing VA maternity benefits. METHODS: We fielded a modified version of the Patient Perceptions of Integrated Care survey among a sample of postpartum veterans who had utilized VA maternity benefits for their pregnancies (n = 276). We assessed relationships between perceptions of six domains of patient-reported integrated care, indicating how well-integrated patients perceived the care received from VA and non-VA clinicians, and utilization of mental healthcare following pregnancy. RESULTS: Domain scores were highest for items focused on VA care, including test result communication and VA provider\u27s knowledge of patient\u27s medical conditions. Scores were lower for obstetrician\u27s knowledge of patient\u27s medical history. Women with depressive symptom scores indicative of depression rated test result communication as highly integrated, while women who received mental healthcare following pregnancy had low integrated care ratings for the Support for Medication and Home Health Management domain, indicating a lack of support for mental health conditions following pregnancy. DISCUSSION: Among a group of postpartum veterans, poor ratings of integrated care across some domains were associated with higher rates of mental healthcare use following pregnancy. Further assessment of integrated care by patients may assist VA providers and policymakers in developing systems to ensure integrated care for veterans who receive care outside the VA

Recombinant AAV Vectors for Enhanced Expression of Authentic IgG

Adeno-associated virus (AAV) has become a vector of choice for the treatment of a variety of genetic diseases that require safe and long-term delivery of a missing protein. Muscle-directed gene transfer for delivery of protective antibodies against AIDS viruses and other pathogens has been used experimentally in mice and monkeys. Here we examined a number of variations to AAV vector design for the ability to produce authentic immunoglobulin G (IgG) molecules. Expression of rhesus IgG from a single single-stranded AAV (ssAAV) vector (one vector approach) was compared to expression from two self-complementary AAV (scAAV) vectors, one for heavy chain and one for light chain (two vector approach). Both the one vector and the two vector approaches yielded considerable levels of expressed full-length IgG. A number of modifications to the ssAAV expression system were then examined for their ability to increase the efficiency of IgG expression. Inclusion of a furin cleavage sequence with a linker peptide just upstream of the 2A self-cleaving sequence from foot-and-mouth disease virus (F2A) increased IgG expression approximately 2 fold. Inclusion of these sequences also helped to ensure a proper sequence at the C-terminal end of the heavy chain. Inclusion of the post-transcriptional regulatory element from woodchuck hepatitis virus (WPRE) further increased IgG expression 1.5-2.0 fold. IgG1 versions of the two rhesus IgGs that were examined consistently expressed better than the IgG2 forms. In contrast to what has been reported for AAV2-mediated expression of other proteins, introduction of capsid mutations Y445F and Y731F did not increase ssAAV1-mediated expression of IgG as determined by transduction experiments in cell culture. Our findings provide a rational basis for AAV vector design for expression of authentic IgG

Some properties of angular integrals

We find new representations for Itzykson-Zuber like angular integrals for arbitrary beta, in particular for the orthogonal group O(n), the unitary group U(n) and the symplectic group Sp(2n). We rewrite the Haar measure integral, as a flat Lebesge measure integral, and we deduce some recursion formula on n. The same methods gives also the Shatashvili's type moments. Finally we prove that, in agreement with Brezin and Hikami's observation, the angular integrals are linear combinations of exponentials whose coefficients are polynomials in the reduced variables (x_i-x_j)(y_i-y_j).Comment: 43 pages, Late

Mapping the complete glycoproteome of virion-derived HIV-1 gp120 provides insights into broadly neutralizing antibody binding

The surface envelope glycoprotein (SU) of Human immunodeficiency virus type 1 (HIV-1), gp120SU plays an essential role in virus binding to target CD4+ T-cells and is a major vaccine target. Gp120 has remarkably high levels of N-linked glycosylation and there is considerable evidence that this “glycan shield” can help protect the virus from antibody-mediated neutralization. In recent years, however, it has become clear that gp120 glycosylation can also be included in the targets of recognition by some of the most potent broadly neutralizing antibodies. Knowing the site-specific glycosylation of gp120 can facilitate the rational design of glycopeptide antigens for HIV vaccine development. While most prior studies have focused on glycan analysis of recombinant forms of gp120, here we report the first systematic glycosylation site analysis of gp120 derived from virions produced by infected T lymphoid cells and show that a single site is exclusively substituted with complex glycans. These results should help guide the design of vaccine immunogens