Non-Weyl Resonance Asymptotics for Quantum Graphs

We consider the resonances of a quantum graph $\mathcal G$ that consists of a compact part with one or more infinite leads attached to it. We discuss the leading term of the asymptotics of the number of resonances of $\mathcal G$ in a disc of a large radius. We call $\mathcal G$ a \emph{Weyl graph} if the coefficient in front of this leading term coincides with the volume of the compact part of $\mathcal G$. We give an explicit topological criterion for a graph to be Weyl. In the final section we analyze a particular example in some detail to explain how the transition from the Weyl to the non-Weyl case occurs.Comment: 29 pages, 2 figure

Discrete Nodal Domain Theorems

We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem

Non-Weyl asymptotics for quantum graphs with general coupling conditions

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in case of Kirchhoff or anti-Kirchhoff conditions, while for graphs without permutation numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight helping to understand what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with nonequal edge weights.Comment: minor changes, to appear in Pierre Duclos memorial issue of J. Phys. A: Math. Theo

LpL^p-Spectral theory of locally symmetric spaces with QQ-rank one

We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=\Gamma\backslash X$ with finite volume and arithmetic fundamental group $\Gamma$ whose universal covering $X$ is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one

Surge in Expression of Carboxylesterase 1 During the Post-neonatal Stage Enables a Rapid Gain of the Capacity to Activate the Anti-influenza Prodrug Oseltamivir

Background. Oseltamivir, a widely used anti-influenza drug, is hydrolytically activated by carboxylesterase 1 (CES1). The expression of this carboxylesterase is developmentally regulated. This study was performed to determine when after birth infants acquire competence of activating this prodrug. Methods. Liver tissue samples were collected and divided into 5 age groups: group 1 (1-31 d old), group 2 (35-70 d old), group 3 (89-119 d old), group 4 (123-198 d old), and group 5 (>18 years of age). These samples were analyzed for oseltamivir hydrolysis and CES1 expression. Results. Liver samples in group 1 expressed the lowest level of CES1 with the lowest hydrolytic activity toward oseltamivir. A 4-7-fold increase between groups 1 and 2 (1-31 vs 35-70 d of age) was detected in the hydrolysis and expression analyses, respectively. Liver samples in the other 3 pediatric groups (35-198 d of age) exhibited similar expression and hydrolysis levels. Overall, liver samples in group 1 had CES1 expression and hydrolysis levels that were 10% of those of adults, whereas liver samples in the other 3 pediatric groups had levels that were ∼50% of adult levels. Conclusions. The post-neonatal surge in CES1 expression ensures the hydrolytic capacity to be gained rapidly after birth in infants, but the larger variability during this period suggests that caution should be exercised on the extrapolated dosing regimens of ester drugs from other age group

Probing the Inner Disk Emission of the Herbig Ae Stars HD 163296 and HD 190073

The physical processes occurring within the inner few astronomical units of proto-planetary disks surrounding Herbig Ae stars are crucial to setting the environment in which the outer planet-forming disk evolves and put critical constraints on the processes of accretion and planet migration. We present the most complete published sample of high angular resolution H- and K-band observations of the stars HD 163296 and HD 190073, including 30 previously unpublished nights of observations of the former and 45 nights of the latter with the CHARA long-baseline interferometer, in addition to archival VLTI data. We confirm previous observations suggesting significant near-infrared emission originates within the putative dust evaporation front of HD 163296 and show this is the case for HD 190073 as well. The H- and K-band sizes are the same within $(3 \pm 3)\%$ for HD 163296 and within $(6 \pm 10)\%$ for HD 190073. The radial surface brightness profiles for both disks are remarkably Gaussian-like with little or no sign of the sharp edge expected for a dust evaporation front. Coupled with spectral energy distribution analysis, our direct measurements of the stellar flux component at H and K bands suggest that HD 190073 is much younger (<400 kyr) and more massive (~5.6 M$_\odot$) than previously thought, mainly as a consequence of the new Gaia distance (891 pc).Comment: 19 pages, 6 figure

Preliminary imaging results from the second Mercury encounter

The second Mercury encounter has resulted in the acquisition of about 360 pictures of the south polar regions which provide a reliable cartographic and geologic tie between the two sides of the planet photographed on the first encounter. Stereoscopic coverage of large areas of the southern hemisphere was obtained by combining Mercury 1 and 2 pictures taken at different viewing angles. The south polar regions consist of heavily cratered terrain and intercrater plains interspersed with patches of smooth plains. No large areas of smooth plains similar to those surrounding Caloris occur in the south polar regions. No new types of terrain have been recognized, but lobate scarps are common. The second largest basin seen by Mariner 10 (∼600-km diameter) has been confirmed on the new photography. At high solar elevations the surface displays an abundance of rays and rayed craters

Insights into high-risk multiple myeloma from an analysis of the role of PHF19 in cancer

Despite improvements in outcome, 15-25% of newly diagnosed multiple myeloma (MM) patients have treatment resistant high-risk (HR) disease with a poor survival. The lack of a genetic basis for HR has focused attention on the role played by epigenetic changes. Aberrant expression and somatic mutations affecting genes involved in the regulation of tri-methylation of the lysine (K) 27 on histone 3 H3 (H3K27me3) are common in cancer. H3K27me3 is catalyzed by EZH2, the catalytic subunit of the Polycomb Repressive Complex 2 (PRC2). The deregulation of H3K27me3 has been shown to be involved in oncogenic transformation and tumor progression in a variety of hematological malignancies including MM. Recently we have shown that aberrant overexpression of the PRC2 subunit PHD Finger Protein 19 (PHF19) is the most significant overall contributor to HR status further focusing attention on the role played by epigenetic change in MM. By modulating both the PRC2/EZH2 catalytic activity and recruitment, PHF19 regulates the expression of key genes involved in cell growth and differentiation. Here we review the expression, regulation and function of PHF19 both in normal and the pathological contexts of solid cancers and MM. We present evidence that strongly implicates PHF19 in the regulation of genes important in cell cycle and the genetic stability of MM cells making it highly relevant to HR MM behavior. A detailed understanding of the normal and pathological functions of PHF19 will allow us to design therapeutic strategies able to target aggressive subsets of MM