Commensurability classes of hyperbolic Coxeter groups

AbstractIn this paper, we classify all the hyperbolic Coxeter n-simplex reflection groups up to wide-commensurability for all n⩾3. We also determine all the subgroup relationships among the groups

Loop operators and S-duality from curves on Riemann surfaces

We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn's classification of homotopy classes of non-self-intersecting curves on an associated Riemann surface--the same surface which characterizes the gauge theory. Our analysis provides an explicit prediction for the action of S-duality on loop operators in these theories which we check against the known duality transformation in several examples.Comment: 41 page

Superpotentials for M-theory on a G_2 holonomy manifold and Triality symmetry

For $M$-theory on the $G_2$ holonomy manifold given by the cone on {\bf S^3}\x {\bf S^3} we consider the superpotential generated by membrane instantons and study its transformations properties, especially under monodromy transformations and triality symmetry. We find that the latter symmetry is, essentially, even a symmetry of the superpotential. As in Seiberg/Witten theory, where a flat bundle given by the periods of an universal elliptic curve over the $u$-plane occurs, here a flat bundle related to the Heisenberg group appears and the relevant universal object over the moduli space is related to hyperbolic geometry.Comment: 58 pages, latex; references adde

an overview of the MHONGOOSE survey: Observing nearby galaxies with MeerKAT

© Copyright owned by the author(s). MHONGOOSE is a deep survey of the neutral hydrogen distribution in a representative sample of 30 nearby disk and dwarf galaxies with H I masses from ∼ 106 to ∼ 1011 M, and luminosities from MR ∼ 12 to MR ∼ −22. The sample is selected to uniformly cover the available range in log(MHI). Our extremely deep observations, down to H I column density limits of well below 1018 cm−2 — or a few hundred times fainter than the typical H I disks in galaxies — will directly detect the effects of cold accretion from the intergalactic medium and the links with the cosmic web. These observations will be the first ever to probe the very low-column density neutral gas in galaxies at these high resolutions. Combination with data at other wavelengths, most of it already available, will enable accurate modeling of the properties and evolution of the mass components in these galaxies and link these with the effects of environment, dark matter distribution, and other fundamental properties such as halo mass and angular momentum. MHONGOOSE can already start addressing some of the SKA-1 science goals and will provide a comprehensive inventory of the processes driving the transformation and evolution of galaxies in the nearby universe at high resolution and over 5 orders of magnitude in column density. It will be a Nearby Galaxies Legacy Survey that will be unsurpassed until the advent of the SKA, and can serve as a highly visible, lasting statement of MeerKAT’s capabilities

QCD Corrections to Spin Dependent Drell-Yan and a Global Subtraction Scheme

We present QCD corrections to the Drell-Yan process in the transversely polarized, longitudinally polarized and unpolarized cases. The analytical results are presented in a form valid for all $n$-dimensional regularization schemes. A universal mass factorization scheme is presented in which the results reduce to those of dimensional reduction. The connection between the parton distributions and fragmentation functions of dimensional reduction and those of dimensional regularization is elucidated in a simple manner. Numerical results are presented for proton-proton collisions at energies relevant to RHIC (Relativistic Heavy Ion Collider). The perturbative stability of the transverse and longitudinal asymmetries is investigated.Comment: 18 pages, 8 figures in 1 postscript fil

Investigation of hospital discharge cases and SARS-CoV-2 introduction into Lothian care homes

Background The first epidemic wave of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) in Scotland resulted in high case numbers and mortality in care homes. In Lothian, over one-third of care homes reported an outbreak, while there was limited testing of hospital patients discharged to care homes. Aim To investigate patients discharged from hospitals as a source of SARS-CoV-2 introduction into care homes during the first epidemic wave. Methods A clinical review was performed for all patients discharges from hospitals to care homes from 1st March 2020 to 31st May 2020. Episodes were ruled out based on coronavirus disease 2019 (COVID-19) test history, clinical assessment at discharge, whole-genome sequencing (WGS) data and an infectious period of 14 days. Clinical samples were processed for WGS, and consensus genomes generated were used for analysis using Cluster Investigation and Virus Epidemiological Tool software. Patient timelines were obtained using electronic hospital records. Findings In total, 787 patients discharged from hospitals to care homes were identified. Of these, 776 (99%) were ruled out for subsequent introduction of SARS-CoV-2 into care homes. However, for 10 episodes, the results were inconclusive as there was low genomic diversity in consensus genomes or no sequencing data were available. Only one discharge episode had a genomic, time and location link to positive cases during hospital admission, leading to 10 positive cases in their care home. Conclusion The majority of patients discharged from hospitals were ruled out for introduction of SARS-CoV-2 into care homes, highlighting the importance of screening all new admissions when faced with a novel emerging virus and no available vaccine

Buckling tests of sandwich cylindrical shells with and without cut-outs

The results of buckling tests performed during the project DESICOS funded by the European Commission in the FP7 Programme are here presented. The tested structures are sandwich cylindrical shells that consist of reduced models of a component of the Ariane 5 launcher: the Dual Launch System. In particular, the scaled component is studied with and without the presence of cut-outs. Before performing the tests, the geometric imperfections as well as the thickness variations were measured. The tests were performed using the buckling testing equipment of Politecnico di Milano. The results of the tests contributed to understand the complex phenomenon of buckling of sandwich cylindrical shells, and to study the effect of initial geometric imperfections. They were also used to validate finite element models useful for the design of future launcher structures, and to set-up a probabilistic approach for the buckling analysis of cylindrical shells