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

Assessing the Multiple Dimensions of the Self-Concept of Young Children: A Focus on Latinos

This study was designed to provide psychometric and developmental information for a caregiver report and observational measure of young children\u27s self-concept. The Caregiver Inventory of Self-Concept (elsC) and the Tasks for Observation of Self-Concept (lOSe) assess six domains: self-recognition, self-representation, selfdescription, self-assertion, self-evaluation, self-regulation. Mothers of 290 children aged 6 to 66 months reported on the presence of self-concept behaviors, and 75 of these children, aged 15 to 48 months, were observed. Coefficient alpha, an index of item-objective congruence, and factor analysis provided evidence for the reliability and validity of both measures. Between- and within-domain analyses found that the development of self-concept in young children followed the hypothesized progression (self-recognition, self-representation, self-description, self-assertion, selfevaluation, and self-regulation) on the ClSC but not on the TOSC

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

Validation of an abbreviated Treatment Satisfaction Questionnaire for Medication (TSQM-9) among patients on antihypertensive medications

<p>Abstract</p> <p>Background</p> <p>The 14-item Treatment Satisfaction Questionnaire for Medication (TSQM) Version 1.4 is a reliable and valid instrument to assess patients' satisfaction with medication, providing scores on four scales – side effects, effectiveness, convenience and global satisfaction. In naturalistic studies, administering the TSQM with the side effects domain could provoke the physician to assess the presence or absence of adverse events in a way that is clinically atypical, carrying the potential to interfere with routine medical care. As a result, an abbreviated 9-item TSQM (TSQM-9), derived from the TSQM Version 1.4 but without the five items of the side effects domain was created. In this study, an interactive voice response system (IVRS)-administered TSQM-9 was psychometrically evaluated among patients taking antihypertensive medication.</p> <p>Methods</p> <p>A total of 3,387 subjects were invited to participate in the study from an online panel who self-reported taking a prescribed antihypertensive medication. The subjects were asked to complete the IVRS-administered TSQM-9 at the start of the study, along with the modified Morisky scale, and again within 7 to 14 days. Standard psychometric analyses were conducted; including Cronbach's alpha, intraclass correlation coefficients, structural equation modeling, Spearman correlation coefficients and analysis of covariance (ANCOVA).</p> <p>Results</p> <p>A total of 396 subjects completed all the study procedures. Approximately 50% subjects were male with a good racial/ethnic mix: 58.3% white, 18.9% black, 17.7% Hispanic and 5.1% either Asian or other. There was evidence of construct validity of the TSQM-9 based on the structural equation modeling findings of the observed data fitting the Decisional Balance Model of Treatment Satisfaction even without the side effects domain. TSQM-9 domains had high internal consistency as evident from Cronbach's alpha values of 0.84 and greater. TSQM-9 domains also demonstrated good test-retest reliability with high intraclass correlation coefficients exceeding 0.70. As expected, the TSQM-9 domains were able to differentiate between individuals who were low, medium and high compliers of medication, with moderate to high effect sizes. There was evidence of convergent validity with significant correlations with the medication adherence scale.</p> <p>Conclusion</p> <p>The IVRS-administered TSQM-9 was found to be a reliable and valid measure to assess treatment satisfaction in naturalistic study designs, in which there is potential that the administration of the side effects domain of the TSQM would interfere with routine clinical care.</p

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

SEPARATION AND EXTRACTION OF PLUTONIUM IN MIXED WASTE

The Sonatol process uses ultrasonic agitation in fluorinated surfactant solutions to remove radioactive particles from surfaces. Filtering the suspended particles allows the solutions to be reused indefinitely. The current work applies the Sonatol process to the decontamination of heterogeneous legacy Pu-238 waste that exhibits excessive hydrogen gas generation, which prevents transportation of the waste to the Waste Isolation Pilot Plant. Bartlett Services, Inc. (BSI) designed and fabricated a prototype decontamination system within a replica of a Savannah River Site glovebox. In Phase I, BSI conducted cold testing with surrogate waste material to verify that the equipment, operating procedures, and test protocols would support testing with Pu-238 in Phase II. The surrogate waste material is representative of known constituents of legacy job control waste. Two sub-micron sized Pu-238 simulants were added to the surrogate waste so that decontamination could be tested. The first simulant was an Osram Sylvania Phosphor 2284C powder that fluoresces under ultraviolet light. The use of the fluorescent simulant allows rapid, inexpensive system startup testing because residuals can be assayed using a digital camera. The results of digital pixel analysis (DPA) are available immediately and do not require use of licensed material. The second simulant, which was used for integrated cold testing, was a cerium oxide powder that was activated in a research reactor neutron flux and assayed by photon spectroscopy. The surrogate transuranic (TRU) waste material was contaminated with Pu-238 simulants and loaded into the cleaning chamber, where the surrogates were ultrasonically agitated and rinsed. The decontaminated materials were then assayed for surface contamination by DPA to establish optimum operating parameters and provide process quality control. Selected samples were sent to the Massachusetts Institute of Technology for neutron activation analysis (NAA). NAA testing resulted in weighted average decontamination factors (DFs) in the range of 125 to 157 for the surrogate waste mixtures. The weighted DFs for the organic portion of the surrogate waste mixtures ranged from 66 to 140. The NAA DF for inorganic material was 370. Other than the removal of particulate contamination, the processed samples were unchanged by decontamination. Most NAA samples were irradiated after decontamination. However, several samples were irradiated in the reactor core prior to decontamination in order to investigate the possible interference of radiation induced imbedding of particles in organic materials. The radiation dose was in excess of 110 Mrad. The NAA DF for samples irradiated before decontamination was six

Tools for primal degenerate linear programs: IPS, DCA, and PE

ABSTRACT: This paper describes three recent tools for dealing with primal degeneracy in linear programming. The first one is the improved primal simplex (IPS) algorithm which turns degeneracy into a possible advantage. The constraints of the original problem are dynamically partitioned based on the numerical values of the current basic variables. The idea is to work only with those constraints that correspond to nondegenerate basic variables. This leads to a row-reduced problem which decreases the size of the current working basis. The main feature of IPS is that it provides a nondegenerate pivot at every iteration of the solution process until optimality is reached. To achieve such a result, a negative reduced cost convex combination of the variables at their bounds is selected, if any. This pricing step provides a necessary and sufficient optimality condition for linear programming. The second tool is the dynamic constraint aggregation (DCA), a constructive strategy specifically designed for set partitioning constraints. It heuristically aims to achieve the properties provided by the IPS methodology. We bridge the similarities and differences of IPS and DCA on set partitioning models. The final tool is the positive edge (PE) rule. It capitalizes on the compatibility definition to determine the status of a column vector and the associated variable during the reduced cost computation. Within IPS, the selection of a compatible variable to enter the basis ensures a nondegenerate pivot, hence PE permits a trade-off between strict improvement and high, reduced cost degenerate pivots. This added value is obtained without explicitly computing the updated column components in the simplex tableau. Ultimately, we establish tight bonds between these three tools by going back to the linear algebra framework from which emanates the so-called concept of subspace basis