On the compactness of the set of invariant Einstein metrics

Let $M = G/H$ be a connected simply connected homogeneous manifold of a compact, not necessarily connected Lie group $G$. We will assume that the isotropy $H$-module $\mathfrak {g/h}$ has a simple spectrum, i.e. irreducible submodules are mutually non-equivalent. There exists a convex Newton polytope $N=N(G,H)$, which was used for the estimation of the number of isolated complex solutions of the algebraic Einstein equation for invariant metrics on $G/H$ (up to scaling). Using the moment map, we identify the space $\mathcal{M}_1$ of invariant Riemannian metrics of volume 1 on $G/H$ with the interior of this polytope $N$. We associate with a point ${x \in \partial N}$ of the boundary a homogeneous Riemannian space (in general, only local) and we extend the Einstein equation to $\bar{\mathcal{M}_1}= N$. As an application of the Aleksevsky--Kimel'fel'd theorem, we prove that all solutions of the Einstein equation associated with points of the boundary are locally Euclidean. We describe explicitly the set $T\subset \partial N$ of solutions at the boundary together with its natural triangulation. Investigating the compactification $\bar{\mathcal{M}_1}$ of $\mathcal{M}_1$, we get an algebraic proof of the deep result by B\"ohm, Wang and Ziller about the compactness of the set $\mathcal{E}_1 \subset \mathcal{M}_1$ of Einstein metrics. The original proof by B\"ohm, Wang and Ziller was based on a different approach and did not use the simplicity of the spectrum. In Appendix we consider the non-symmetric K\"ahler homogeneous spaces $G/H$ with the second Betti number $b_2=1$. We write the normalized volumes $2,6,20,82,344$ of the corresponding Newton polytopes and discuss the number of complex solutions of the algebraic Einstein equation and the finiteness problem.Comment: 25 pages, 4 figures. Some proofs, 3 references, and Appendix adde

Celecoxib concentration predicts decrease in prostaglandin E2 concentrations in nipple aspirate fluid from high risk women

<p>Abstract</p> <p>Background</p> <p>Epidemiologic studies suggest that long term low dose celecoxib use significantly lowers breast cancer risk. We previously demonstrated that 400 mg celecoxib taken twice daily for 2 weeks lowered circulating plasma and breast nipple aspirate fluid (NAF) prostaglandin (PG)E₂concentrations in post- but not premenopausal high risk women. We hypothesized that circulating concentrations of celecoxib influenced PGE₂response, and that plasma levels of the drug are influenced by menopausal status. To address these hypotheses, the aims of the study were to determine: 1) if circulating plasma concentrations of celecoxib correlated with the change in plasma or NAF PGE₂concentrations from baseline to end of treatment, and 2) whether menopausal status influenced circulating levels of celecoxib.</p> <p>Methods</p> <p>Matched NAF and plasma were collected from 46 high risk women who were administered celecoxib twice daily for two weeks, 20 subjects receiving 200 mg and 26 subjects 400 mg of the agent. NAF and plasma samples were collected before and 2 weeks after taking celecoxib.</p> <p>Results</p> <p>In women taking 400 mg bid celecoxib, plasma concentrations of the agent correlated inversely with the change in NAF PGE₂levels from pre- to posttreatment. Nonsignificant trends toward higher celecoxib levels were observed in post- compared to premenopausal women. There was a significant decrease in NAF but not plasma PGE₂concentrations in postmenopausal women who took 400 mg celecoxib (p = 0.03).</p> <p>Conclusion</p> <p>In high risk women taking 400 mg celecoxib twice daily, plasma concentrations of celecoxib correlated with downregulation of PGE₂production by breast tissue. Strategies synergistic with celecoxib to downregulate PGE₂are of interest, in order to minimize the celecoxib dose required to have an effect.</p

Search for the Decays B^0 -> D^{(*)+} D^{(*)-}

Using the CLEO-II data set we have searched for the Cabibbo-suppressed decays B^0 -> D^{(*)+} D^{(*)-}. For the decay B^0 -> D^{*+} D^{*-}, we observe one candidate signal event, with an expected background of 0.022 +/- 0.011 events. This yield corresponds to a branching fraction of Br(B^0 -> D^{*+} D^{*-}) = (5.3^{+7.1}_{-3.7}(stat) +/- 1.0(syst)) x 10^{-4} and an upper limit of Br(B^0 -> D^{*+} D^{*-}) D^{*\pm} D^\mp and B^0 -> D^+ D^-, no significant excess of signal above the expected background level is seen, and we calculate the 90% CL upper limits on the branching fractions to be Br(B^0 -> D^{*\pm} D^\mp) D^+ D^-) < 1.2 x 10^{-3}.Comment: 12 page postscript file also available through http://w4.lns.cornell.edu/public/CLNS, submitted to Physical Review Letter

ΛΛˉ\Lambda\bar{\Lambda} Production in Two-Photon Interactions at CLEO

Using the CLEO detector at the Cornell $e^+e^-$ storage ring, CESR, we study the two-photon production of $\Lambda \bar{\Lambda}$, making the first observation of $\gamma \gamma \to \Lambda \bar{\Lambda}$. We present the cross-section for $\gamma \gamma \to \Lambda \bar{\Lambda}$ as a function of the $\gamma \gamma$ center of mass energy and compare it to that predicted by the quark-diquark model.Comment: 10 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Observation of the Decay Ds+→ωπ+D_{s}^{+}\to \omega\pi^{+}

Using e+e- annihilation data collected by the CLEO~II detector at CESR, we have observed the decay Ds+ to omega pi+. This final state may be produced through the annihilation decay of the Ds+, or through final state interactions. We find a branching ratio of [Gamma(Ds+ to omega pi+)/Gamma(Ds+ to eta pi+)]=0.16+-0.04+-0.03, where the first error is statistical and the second is systematic.Comment: 9 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Validation of a susceptibility, benefits, and barrier scale for mammography screening among Peruvian women: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Perceived beliefs about breast cancer and breast cancer screening are important predictors for mammography utilization. This study adapted and validated the Champion's scale in Peru. This scale measures perceived susceptibility for breast cancer and perceived benefits and barriers for mammography.</p> <p>Methods</p> <p>A cross-sectional study was conducted among women ages 40 to 65 attending outpatient gynecology services in a public hospital in Peru. A group of experts developed and pre-tested a Spanish version of the Champion's scale to assess its comprehensibility (N = 20). Factor analysis, internal consistency, and test-retest reliability analyses were performed (N = 285). Concurrent validity compared scores from participants who had a mammogram and those who did not have it in the previous 15 months. T-test and multiple regression analysis adjusting for socio-demographic factors, mammography knowledge and other preventive behaviors were performed.</p> <p>Results</p> <p>The construct validity and reliability were optimal. Cronbach-Alpha coefficients were 0.75 (susceptibility), 0.72 (benefits) and 0.86 (barriers). Concurrent validity analysis showed an association between barriers and mammography screening use in bivariate (22.3 ± 6.7 vs. 30.2 ± 7.6; p < 0.001) and multiple regression analysis (OR = 0.28, 95% CI = 0.18-0.43). Ages 50-60 years (OR = 2.35, 95% CI = 1.19-4.65), history of prior Papanicolaou test (OR = 3.69, 95% CI = 1.84-7.40), and knowledge about breast cancer and mammography (OR = 3.69, 95% CI = 1.84-7.40) were also independently associated with mammography screening use.</p> <p>Conclusion</p> <p>Concurrent validity analysis showed that the Champion's scale has important limitations for assessing perceived susceptibility for breast cancer and perceived benefits for mammography among Peruvian women. There is still a need for developing valid and reliable instruments for measuring perceived beliefs about breast cancer and mammography screening among Peruvian women.</p