Vibrational modes of circular free plates under tension

The vibrational frequencies of a plate under tension are given by the eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem on the ball under natural (free) boundary conditions. In particular, the fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue --- are identified and found to have simple angular dependence.Comment: 17 pages. To be submitted for publication shortly

On colouring point visibility graphs

In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the problem of deciding whether the visibility graph of a point set is 5-colourable, is NP-complete. We give an example of a point visibility graph that has chromatic number 6 while its clique number is only 4

Neuroinflammation and structural injury of the fetal ovine brain following intra-amniotic Candida albicans exposure.

BackgroundIntra-amniotic Candida albicans (C. Albicans) infection is associated with preterm birth and high morbidity and mortality rates. Survivors are prone to adverse neurodevelopmental outcomes. The mechanisms leading to these adverse neonatal brain outcomes remain largely unknown. To better understand the mechanisms underlying C. albicans-induced fetal brain injury, we studied immunological responses and structural changes of the fetal brain in a well-established translational ovine model of intra-amniotic C. albicans infection. In addition, we tested whether these potential adverse outcomes of the fetal brain were improved in utero by antifungal treatment with fluconazole.MethodsPregnant ewes received an intra-amniotic injection of 10(7) colony-forming units C. albicans or saline (controls) at 3 or 5 days before preterm delivery at 0.8 of gestation (term ~ 150 days). Fetal intra-amniotic/intra-peritoneal injections of fluconazole or saline (controls) were administered 2 days after C. albicans exposure. Post mortem analyses for fungal burden, peripheral immune activation, neuroinflammation, and white matter/neuronal injury were performed to determine the effects of intra-amniotic C. albicans and fluconazole treatment.ResultsIntra-amniotic exposure to C. albicans caused a severe systemic inflammatory response, illustrated by a robust increase of plasma interleukin-6 concentrations. Cerebrospinal fluid cultures were positive for C. albicans in the majority of the 3-day C. albicans-exposed animals whereas no positive cultures were present in the 5-day C. albicans-exposed and fluconazole-treated animals. Although C. albicans was not detected in the brain parenchyma, a neuroinflammatory response in the hippocampus and white matter was seen which was characterized by increased microglial and astrocyte activation. These neuroinflammatory changes were accompanied by structural white matter injury. Intra-amniotic fluconazole reduced fetal mortality but did not attenuate neuroinflammation and white matter injury.ConclusionsIntra-amniotic C. albicans exposure provoked acute systemic and neuroinflammatory responses with concomitant white matter injury. Fluconazole treatment prevented systemic inflammation without attenuating cerebral inflammation and injury

Electronic structure of superconducting graphite intercalate compounds: The role of the interlayer state

Although not an intrinsic superconductor, it has been long--known that, when intercalated with certain dopants, graphite is capable of exhibiting superconductivity. Of the family of graphite--based materials which are known to superconduct, perhaps the most well--studied are the alkali metal--graphite intercalation compounds (GIC) and, of these, the most easily fabricated is the C${}_8$K system which exhibits a transition temperature $\bm{T_c\simeq 0.14}$K. By increasing the alkali metal concentration (through high pressure fabrication techniques), the transition temperature has been shown to increase to as much as $\bm 5$K in C${}_2$Na. Lately, in an important recent development, Weller \emph{et al.} have shown that, at ambient conditions, the intercalated compounds \cyb and \cca exhibit superconductivity with transition temperatures $\bm{T_c\simeq 6.5}$K and $\bm{11.5}$K respectively, in excess of that presently reported for other graphite--based compounds. We explore the architecture of the states near the Fermi level and identify characteristics of the electronic band structure generic to GICs. As expected, we find that charge transfer from the intercalant atoms to the graphene sheets results in the occupation of the $\bm\pi$--bands. Yet, remarkably, in all those -- and only those -- compounds that superconduct, we find that an interlayer state, which is well separated from the carbon sheets, also becomes occupied. We show that the energy of the interlayer band is controlled by a combination of its occupancy and the separation between the carbon layers.Comment: 4 Figures. Please see accompanying experimental manuscript "Superconductivity in the Intercalated Graphite Compounds C6Yb and C6Ca" by Weller et a

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Risk measures for direct real estate investments with non-normal or unknown return distributions

The volatility of returns is probably the most widely used risk measure for real estate. This is rather surprising since a number of studies have cast doubts on the view that volatility can capture the manifold risks attached to properties and corresponds to the risk attitude of investors. A central issue in this discussion is the statistical properties of real estate returns—in contrast to neoclassical capital market theory they are mostly non-normal and often unknown, which render many statistical measures useless. Based on a literature review and an analysis of data from Germany we provide evidence that volatility alone is inappropriate for measuring the risk of direct real estate. We use a unique data sample by IPD, which includes the total returns of 939 properties across different usage types (56% office, 20% retail, 8% others and 16% residential properties) from 1996 to 2009, the German IPD Index, and the German Property Index. The analysis of the distributional characteristics shows that German real estate returns in this period were not normally distributed and that a logistic distribution would have been a better fit. This is in line with most of the current literature on this subject and leads to the question which indicators are more appropriate to measure real estate risks. We suggest that a combination of quantitative and qualitative risk measures more adequately captures real estate risks and conforms better with investor attitudes to risk. Furthermore, we present criteria for the purpose of risk classification

Common Variants at 10 Genomic Loci Influence Hemoglobin A(1C) Levels via Glycemic and Nonglycemic Pathways

OBJECTIVE Glycated hemoglobin (HbA1c), used to monitor and diagnose diabetes, is influenced by average glycemia over a 2- to 3-month period. Genetic factors affecting expression, turnover, and abnormal glycation of hemoglobin could also be associated with increased levels of HbA1c. We aimed to identify such genetic factors and investigate the extent to which they influence diabetes classification based on HbA1c levels. RESEARCH DESIGN AND METHODS We studied associations with HbA1c in up to 46,368 nondiabetic adults of European descent from 23 genome-wide association studies (GWAS) and 8 cohorts with de novo genotyped single nucleotide polymorphisms (SNPs). We combined studies using inverse-variance meta-analysis and tested mediation by glycemia using conditional analyses. We estimated the global effect of HbA1c loci using a multilocus risk score, and used net reclassification to estimate genetic effects on diabetes screening. RESULTS Ten loci reached genome-wide significant association with HbA1c, including six new loci near FN3K (lead SNP/P value, rs1046896/P = 1.6 × 10−26), HFE (rs1800562/P = 2.6 × 10−20), TMPRSS6 (rs855791/P = 2.7 × 10−14), ANK1 (rs4737009/P = 6.1 × 10−12), SPTA1 (rs2779116/P = 2.8 × 10−9) and ATP11A/TUBGCP3 (rs7998202/P = 5.2 × 10−9), and four known HbA1c loci: HK1 (rs16926246/P = 3.1 × 10−54), MTNR1B (rs1387153/P = 4.0 × 10−11), GCK (rs1799884/P = 1.5 × 10−20) and G6PC2/ABCB11 (rs552976/P = 8.2 × 10−18). We show that associations with HbA1c are partly a function of hyperglycemia associated with 3 of the 10 loci (GCK, G6PC2 and MTNR1B). The seven nonglycemic loci accounted for a 0.19 (% HbA1c) difference between the extreme 10% tails of the risk score, and would reclassify ∼2% of a general white population screened for diabetes with HbA1c. CONCLUSIONS GWAS identified 10 genetic loci reproducibly associated with HbA1c. Six are novel and seven map to loci where rarer variants cause hereditary anemias and iron storage disorders. Common variants at these loci likely influence HbA1c levels via erythrocyte biology, and confer a small but detectable reclassification of diabetes diagnosis by HbA1c

A search for the decay modes B+/- to h+/- tau l

We present a search for the lepton flavor violating decay modes B+/- to h+/- tau l (h= K,pi; l= e,mu) using the BaBar data sample, which corresponds to 472 million BBbar pairs. The search uses events where one B meson is fully reconstructed in one of several hadronic final states. Using the momenta of the reconstructed B, h, and l candidates, we are able to fully determine the tau four-momentum. The resulting tau candidate mass is our main discriminant against combinatorial background. We see no evidence for B+/- to h+/- tau l decays and set a 90% confidence level upper limit on each branching fraction at the level of a few times 10^-5.Comment: 15 pages, 7 figures, submitted to Phys. Rev.

Evidence for an excess of B -> D(*) Tau Nu decays

Based on the full BaBar data sample, we report improved measurements of the ratios R(D(*)) = B(B -> D(*) Tau Nu)/B(B -> D(*) l Nu), where l is either e or mu. These ratios are sensitive to new physics contributions in the form of a charged Higgs boson. We measure R(D) = 0.440 +- 0.058 +- 0.042 and R(D*) = 0.332 +- 0.024 +- 0.018, which exceed the Standard Model expectations by 2.0 sigma and 2.7 sigma, respectively. Taken together, our results disagree with these expectations at the 3.4 sigma level. This excess cannot be explained by a charged Higgs boson in the type II two-Higgs-doublet model. We also report the observation of the decay B -> D Tau Nu, with a significance of 6.8 sigma.Comment: Expanded section on systematics, text corrections, improved the format of Figure 2 and included the effect of the change of the Tau polarization due to the charged Higg

Study of the reaction e^{+}e^{-} -->J/psi\pi^{+}\pi^{-} via initial-state radiation at BaBar

We study the process $e^+e^-\to J/\psi\pi^{+}\pi^{-}$ with initial-state-radiation events produced at the PEP-II asymmetric-energy collider. The data were recorded with the BaBar detector at center-of-mass energies 10.58 and 10.54 GeV, and correspond to an integrated luminosity of 454 $\mathrm{fb^{-1}}$. We investigate the $J/\psi \pi^{+}\pi^{-}$ mass distribution in the region from 3.5 to 5.5 $\mathrm{GeV/c^{2}}$. Below 3.7 $\mathrm{GeV/c^{2}}$ the $\psi(2S)$ signal dominates, and above 4 $\mathrm{GeV/c^{2}}$ there is a significant peak due to the Y(4260). A fit to the data in the range 3.74 -- 5.50 $\mathrm{GeV/c^{2}}$ yields a mass value $4244 \pm 5$ (stat) $\pm 4$ (syst)$\mathrm{MeV/c^{2}}$ and a width value $114 ^{+16}_{-15}$ (stat)$\pm 7$(syst)$\mathrm{MeV}$ for this state. We do not confirm the report from the Belle collaboration of a broad structure at 4.01 $\mathrm{GeV/c^{2}}$. In addition, we investigate the $\pi^{+}\pi^{-}$ system which results from Y(4260) decay