A view of canonical extension

This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties are given. In particular, they are doubly algebraic lattices and their interval topologies agree with their double Scott topologies and make them Priestley topological algebras.Comment: 24 pages, 2 figures. Presented at the Eighth International Tbilisi Symposium on Language, Logic and Computation Bakuriani, Georgia, September 21-25 200

Modal satisfiability via SMT solving

Modal logics extend classical propositional logic, and they are robustly decidable. Whereas most existing decision procedures for modal logics are based on tableau constructions, we propose a framework for obtaining decision procedures by adding instantiation rules to standard SAT and SMT solvers. Soundness, completeness, and termination of the procedures can be proved in a uniform and elementary way for the basic modal logic and some extensions.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Fontaine, Pascal. Université de Lorraine; Francia.Fil: Fontaine, Pascal. National Institute for Research in Digital Science and Technology; Francia.Fil: Merz, Stephan. Université de Lorraine; Francia.Fil: Merz, Stephan. National Institute for Research in Digital Science and Technology; Francia.Ciencias de la Computació

Analysis of LIGO data for gravitational waves from binary neutron stars

We report on a search for gravitational waves from coalescing compact binary systems in the Milky Way and the Magellanic Clouds. The analysis uses data taken by two of the three LIGO interferometers during the first LIGO science run and illustrates a method of setting upper limits on inspiral event rates using interferometer data. The analysis pipeline is described with particular attention to data selection and coincidence between the two interferometers. We establish an observational upper limit of $\mathcal{R}<$1.7 \times 10^{2}$per year per Milky Way Equivalent Galaxy (MWEG), with 90coalescence rate of binary systems in which each component has a mass in the range 1--3$M_\odot$.Comment: 17 pages, 9 figure

Cross-ancestry genome-wide association analysis of corneal thickness strengthens link between complex and Mendelian eye diseases

Central corneal thickness (CCT) is a highly heritable trait associated with complex eye diseases such as keratoconus and glaucoma. We perform a genome-wide association meta-analysis of CCT and identify 19 novel regions. In addition to adding support for known connective tissue-related pathways, pathway analyses uncover previously unreported gene sets. Remarkably, >20% of the CCT-loci are near or within Mendelian disorder genes. These included FBN1, ADAMTS2 and TGFB2 which associate with connective tissue disorders (Marfan, Ehlers-Danlos and Loeys-Dietz syndromes), and the LUM-DCN-KERA gene complex involved in myopia, corneal dystrophies and cornea plana. Using index CCT-increasing variants, we find a significant inverse correlation in effect sizes between CCT and keratoconus (r =-0.62, P = 5.30 × 10-5) but not between CCT and primary open-angle glaucoma (r =-0.17, P = 0.2). Our findings provide evidence for shared genetic influences between CCT and keratoconus, and implicate candidate genes acting in collagen and extracellular matrix regulation

Broad-scale patterns of body size in squamate reptiles of Europe and North America

Aim To document geographical interspecific patterns of body size of European and North American squamate reptile assemblages and explore the relationship between body size patterns and environmental gradients. Location North America and western Europe. Methods We processed distribution maps for native species of squamate reptiles to document interspecific spatial variation of body size at a grain size of 110 x 110 km. We also examined seven environmental variables linked to four hypotheses possibly influencing body size gradients. We used simple and multiple regression, evaluated using information theory, to identify the set of models best supported by the data. Results Europe is characterized by clear latitudinal trends in body size, whereas geographical variation in body size in North America is complex. There is a consistent association of mean body size with measures of ambient energy in both regions, although lizards increase in size northwards whereas snakes show the opposite pattern. Our best models accounted for almost 60% of the variation in body size of lizards and snakes within Europe, but the proportions of variance explained in North America were less than 20%. Main conclusions Although body size influences the energy balance of thermoregulating ectotherms, inconsistent biogeographical patterns and contrasting associations with energy in lizards and snakes suggest that no single mechanism can explain variation of reptile body size in the northern temperate zone

Measurement of the View the tt production cross-section using eμ events with b-tagged jets in pp collisions at √s = 13 TeV with the ATLAS detector

This paper describes a measurement of the inclusive top quark pair production cross-section (σtt¯) with a data sample of 3.2 fb−1 of proton–proton collisions at a centre-of-mass energy of √s = 13 TeV, collected in 2015 by the ATLAS detector at the LHC. This measurement uses events with an opposite-charge electron–muon pair in the final state. Jets containing b-quarks are tagged using an algorithm based on track impact parameters and reconstructed secondary vertices. The numbers of events with exactly one and exactly two b-tagged jets are counted and used to determine simultaneously σtt¯ and the efficiency to reconstruct and b-tag a jet from a top quark decay, thereby minimising the associated systematic uncertainties. The cross-section is measured to be: σtt¯ = 818 ± 8 (stat) ± 27 (syst) ± 19 (lumi) ± 12 (beam) pb, where the four uncertainties arise from data statistics, experimental and theoretical systematic effects, the integrated luminosity and the LHC beam energy, giving a total relative uncertainty of 4.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. A fiducial measurement corresponding to the experimental acceptance of the leptons is also presented