On Vanishing of {K}ronecker Coefficients

It is shown that: (1) The problem of deciding positivity of Kronecker coefficients is NP-hard. (2) There exists a positive ($\# P$)-formula for a subclass of Kronecker coefficients whose positivity is NP-hard to decide. (3) For any $0 < \epsilon \le 1$, there exists $0<a<1$ such that, for all $m$, there exist $\Omega(2^{m^a})$ partition triples $(\lambda,\mu,\mu)$ in the Kronecker cone such that: (a) the Kronecker coefficient $k^\lambda_{\mu,\mu}$ is zero, (b) the height of $\mu$ is $m$, (c) the height of $\lambda$ is $\le m^\epsilon$, and (d) $|\lambda|= |\mu| \le m^3$. The last result takes a step towards proving the existence of occurrence-based representation-theoretic obstructions in the context of the GCT approach to the permanent vs. determinant problem. Its proof also illustrates the effectiveness of the explicit proof strategy of GCT

P02-07. High Concentrations of Interleukin-15 and Low Concentrations of CCL5 in Breast Milk are Associated with Protection against Postnatal HIV Transmission

Background: Natural variations in IL-15 concentration have not been investigated for an association with an immune-protection against HIV. Given IL-15's central role in anti-HIV immunity, we hypothesized that higher concentrations of IL-15 in breast milk may protect against postnatal mother-to-child HIV transmission. Methods: In a case-control study nested within a clinical trial in Zambia, we compared IL-15 concentrations in breast milk of 22 HIV-infected women who transmitted HIV to their infants through breastfeeding with those of 72 who did not, as well as 18 HIV-uninfected women. Breast milk HIV RNA quantity, sodium, CXCL12, CCL5, and IL-8 concentrations were measured as well as maternal plasma HIV RNA concentrations and CD4 cell count. We used logistic regression modeling to adjust for potential confounders. Results: Higher concentrations of IL-15 in breast milk (adjusted odds ratio [AOR]: 0.01 per log10 pg/ml increase, 95% confidence interval [CI]: <0.001 to 0.3) were associated with protection against postnatal HIV transmission in univariate analysis and after adjusting for maternal CD4 cell counts, breast milk HIV RNA, CCL5, CXCL12, and IL-8 concentrations. Breast milk IL-15 concentration correlated with breast milk sodium, the other cytokines and HIV RNA concentration. It was inversely correlated with infant birth weight and tended to be higher in 1 week than in 1 month post-partum samples. Breast milk CCL5 concentrations were associated with increased risk of HIV transmission (AOR: 12.7 95% CI: 1.6 to 102.0) in adjusted analysis. Breast milk CXCL12 and IL-8 concentrations were not independently associated with transmission. Conclusion: High concentration of IL-15 were associated with a protection against breastfeeding HIV transmission after adjusting for other pro-inflammatory cytokines, HIV RNA in breast milk, and maternal CD4 cell count. These results corroborate a protective role of IL-15-mediated cellular immunity against HIV transmission during breastfeeding. They are informative for vaccination studies using IL-15 as an adjuvant

A Bose gas in a single-beam optical dipole trap

We study an ultracold Bose gas in an optical dipole trap consisting of one single focused laser beam. An analytical expression for the corresponding density of states beyond the usual harmonic approximation is obtained. We are thus able to discuss the existence of a critical temperature for Bose-Einstein condensation and find that the phase transition must be enabled by a cutoff near the threshold. Moreover, we study the dynamics of evaporative cooling and observe significant deviations from the findings for the well-established harmonic approximation. Furthermore, we investigate Bose-Einstein condensates in such a trap in Thomas-Fermi approximation and determine analytical expressions for chemical potential, internal energy and Thomas-Fermi radii beyond the usual harmonic approximation

Stellar (n,gamma) cross sections of p-process isotopes PartI: 102Pd, 120Te, 130,132Ba,and 156Dy

We have investigated the (n,gamma) cross sections of p-process isotopes with the activation technique. The measurements were carried out at the Karlsruhe Van de Graaff accelerator using the 7Li(p,n)7Be source for simulating a Maxwellian neutron distribution of kT = 25 keV. Stellar cross section measurements are reported for the light p-process isotopes 102Pd, 120Te, 130,132Ba, and 156Dy. In a following paper the cross sections of 168Yb, 180W, 184Os, 190Pt, and 196Hg will be discussed. The data are extrapolated to p-process energies by including information from evaluated nuclear data libraries. The results are compared to standard Hauser-Feshbach models frequently used in astrophysics.Comment: 13 pages, 4 figure

Physics Analysis Expert PAX: First Applications

PAX (Physics Analysis Expert) is a novel, C++ based toolkit designed to assist teams in particle physics data analysis issues. The core of PAX are event interpretation containers, holding relevant information about and possible interpretations of a physics event. Providing this new level of abstraction beyond the results of the detector reconstruction programs, PAX facilitates the buildup and use of modern analysis factories. Class structure and user command syntax of PAX are set up to support expert teams as well as newcomers in preparing for the challenges expected to arise in the data analysis at future hadron colliders.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 7 pages, LaTeX, 10 eps figures. PSN THLT00

Dynamics of Warm-Absorbing Gas in Seyfert Galaxies: NGC 5548

A hydromagnetic (MHD) wind from a clumpy molecular accretion disk is invoked to explain observations of warm absorbing (WA) gas in UVX from Sy galaxies. This paper focuses on two issues: (1) compatibility of kinematics and dynamics of MHD wind with the observed properties of WAs; and (2) relationship between the UVX absorptions. We provide an in-depth comparison between the MHD model and the Sy 1 galaxy NGC 5548, which at high spectral resolution exhibits a number of discrete UV absorption components. We find that: (1) the total column densities of Ovii, Oviii and H, are reproduced by constraining the UV ion column densities of Civ and Nv in each component to lie within a factor of 2 of their observed values and optimizing over the possible sets of component ionization states and Civ column densities; (2) the WA exists in the outer part of the wind and is not a continuation of the flow in the BLR; and (3) the WA extends in radial and polar directions and is ionization-stratified. X-ray absorption is found to be heavily biased towards smaller r, and UV absorption originates at larger distances from the central continuum source. We show that the discrete absorption components along the line-of-sight are intrinsically clumpy. Density differences between kinematic components result in a range of ionization and recombination timescales. We further test the applicability of the MHD wind to WAs in general, by constructing a quasi-continuous flow model, and extending it to arbitrary aspect angles. We estimate the fraction of Sy 1s having detectable WAs with larger Ovii column density than Oviii, and the range of total H column densities. We also find that the ratio of Ovii to Oviii optical depths can serve as a new diagnostic of AGN aspect angle.Comment: Latex, 8 postscript figures. Astrophysical Journal, 536, June 10, in pres