Gravitational Instantons, Confocal Quadrics and Separability of the Schr\"odinger and Hamilton-Jacobi equations

A hyperk\"ahler 4-metric with a triholomorphic SU(2) action gives rise to a family of confocal quadrics in Euclidean 3-space when cast in the canonical form of a hyperk\"ahler 4-metric metric with a triholomorphic circle action. Moreover, at least in the case of geodesics orthogonal to the U(1) fibres, both the covariant Schr\"odinger and the Hamilton-Jacobi equation is separable and the system integrable.Comment: 10 pages Late

Evolutionary bi-stability in pathogen transmission mode

Many pathogens transmit to new hosts by both infection (horizontal transmission) and transfer to the infected host's offspring (vertical transmission). These two transmission modes require speci®c adap- tations of the pathogen that can be mutually exclusive, resulting in a trade-off between horizontal and vertical transmission. We show that in mathematical models such trade-offs can lead to the simultaneous existence of two evolutionary stable states (evolutionary bi-stability) of allocation of resources to the two modes of transmission. We also show that jumping between evolutionary stable states can be induced by gradual environmental changes. Using quantitative PCR-based estimates of abundance in seed and vege- tative parts, we show that the pathogen of wheat, Phaeosphaeria nodorum, has jumped between two distinct states of transmission mode twice in the past 160 years, which, based on published evidence, we interpret as adaptation to environmental change. The ®nding of evolutionary bi-stability has impli- cations for human, animal and other plant diseases. An ill-judged change in a disease control programme could cause the pathogen to evolve a new, and possibly more damaging, combination of transmission modes. Similarly, environmental changes can shift the balance between transmission modes, with adverse effects on human, animal and plant health

Equilibrium solvation in quadrupolar solvents

We present a microscopic theory of equilibrium solvation in solvents with zero dipole moment and non-zero quadrupole moment (quadrupolar solvents). The theory is formulated in terms of autocorrelation functions of the quadrupolar polarization (structure factors). It can be therefore applied to an arbitrary dense quadrupolar solvent for which the structure factors are defined. We formulate a simple analytical perturbation treatment for the structure factors. The solute is described by coordinates, radii, and partial charges of constituent atoms. The theory is tested on Monte Carlo simulations of solvation in model quadrupolar solvents. It is also applied to the calculation of the activation barrier of electron transfer reactions in a cleft-shaped donor-acceptor complex dissolved in benzene with the structure factors of quadrupolar polarization obtained from Molecular Dynamics simulations.Comment: Submitted to J. Chem. Phys., 20 pages and 13 figure

The bolometric and UV attenuation in normal spiral galaxies of the Herschel Reference Survey

The dust in nearby galaxies absorbs a fraction of the UV-optical-near-infrared radiation produced by stars. This energy is consequently re-emitted in the infrared. We investigate the portion of the stellar radiation absorbed by spiral galaxies from the HRS by modelling their UV-to-submillimetre spectral energy distributions. Our models provide an attenuated and intrinsic SED from which we find that on average 32 % of all starlight is absorbed by dust. We define the UV heating fraction as the percentage of dust luminosity that comes from absorbed UV photons and find that this is 56 %, on average. This percentage varies with morphological type, with later types having significantly higher UV heating fractions. We find a strong correlation between the UV heating fraction and specific star formation rate and provide a power-law fit. Our models allow us to revisit the IRX-AFUV relations, and derive these quantities directly within a self-consistent framework. We calibrate this relation for different bins of NUV-r colour and provide simple relations to relate these parameters. We investigated the robustness of our method and we conclude that the derived parameters are reliable within the uncertainties which are inherent to the adopted SED model. This calls for a deeper investigation on how well extinction and attenuation can be determined through panchromatic SED modelling.Comment: 14 pages, 7 figures. Accepted for publication in Astronomy & Astrophysic

Dust emission at 8-mic and 24-mic as Diagnostics of HII Region Radiative Transfer

We use the Spitzer SAGE survey of the Magellanic Clouds to evaluate the relationship between the 8-mic PAH emission, 24-mic hot dust emission, and HII region radiative transfer. We confirm that in the higher-metallicity Large Magellanic Cloud, PAH destruction is sensitive to optically thin conditions in the nebular Lyman continuum: objects identified as optically thin candidates based on nebular ionization structure show 6 times lower median 8-mic surface brightness (0.18 mJy arcsec^-2) than their optically thick counterparts (1.2 mJy arcsec^-2). The 24-mic surface brightness also shows a factor of 3 offset between the two classes of objects (0.13 vs 0.44 mJy arcsec^-2, respectively), which is driven by the association between the very small dust grains and higher density gas found at higher nebular optical depths. In contrast, PAH and dust formation in the low-metallicity Small Magellanic Cloud is strongly inhibited such that we find no variation in either 8-mic or 24-mic emission between our optically thick and thin samples. This is attributable to extremely low PAH and dust production together with high, corrosive UV photon fluxes in this low-metallicity environment. The dust mass surface densities and gas-to-dust ratios determined from dust maps using Herschel HERITAGE survey data support this interpretation.Comment: Accepted to ApJ, May 15, 2017. 10 pages, 9 figure

OvMark: a user-friendly system for the identification of prognostic biomarkers in publically available ovarian cancer gene expression datasets

Background: Ovarian cancer has the lowest survival rate of all gynaecologic cancers and is characterised by a lack of early symptoms and frequent late stage diagnosis. There is a paucity of robust molecular markers that are independent of and complementary to clinical parameters such as disease stage and tumour grade. METHODS: We have developed a user-friendly, web-based system to evaluate the association of genes/miRNAs with outcome in ovarian cancer. The OvMark algorithm combines data from multiple microarray platforms (including probesets targeting miRNAs) and correlates them with clinical parameters (e.g. tumour grade, stage) and outcomes (disease free survival (DFS), overall survival). In total, OvMark combines 14 datasets from 7 different array platforms measuring the expression of ~17,000 genes and 341 miRNAs across 2,129 ovarian cancer samples. RESULTS: To demonstrate the utility of the system we confirmed the prognostic ability of 14 genes and 2 miRNAs known to play a role in ovarian cancer. Of these genes, CXCL12 was the most significant predictor of DFS (HR = 1.42, p-value = 2.42x10-6). Surprisingly, those genes found to have the greatest correlation with outcome have not been heavily studied in ovarian cancer, or in some cases in any cancer. For instance, the three genes with the greatest association with survival are SNAI3, VWA3A and DNAH12. CONCLUSIONS/IMPACT: OvMark is a powerful tool for examining putative gene/miRNA prognostic biomarkers in ovarian cancer (available at http://glados.ucd.ie/OvMark/index.html). The impact of this tool will be in the preliminary assessment of putative biomarkers in ovarian cancer, particularly for research groups with limited bioinformatics facilities