3,068 research outputs found

    Embedding Four-directional Paths on Convex Point Sets

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    A directed path whose edges are assigned labels "up", "down", "right", or "left" is called \emph{four-directional}, and \emph{three-directional} if at most three out of the four labels are used. A \emph{direction-consistent embedding} of an \mbox{nn-vertex} four-directional path PP on a set SS of nn points in the plane is a straight-line drawing of PP where each vertex of PP is mapped to a distinct point of SS and every edge points to the direction specified by its label. We study planar direction-consistent embeddings of three- and four-directional paths and provide a complete picture of the problem for convex point sets.Comment: 11 pages, full conference version including all proof

    β\beta-Stars or On Extending a Drawing of a Connected Subgraph

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    We consider the problem of extending the drawing of a subgraph of a given plane graph to a drawing of the entire graph using straight-line and polyline edges. We define the notion of star complexity of a polygon and show that a drawing ΓH\Gamma_H of an induced connected subgraph HH can be extended with at most min{h/2,β+log2(h)+1}\min\{ h/2, \beta + \log_2(h) + 1\} bends per edge, where β\beta is the largest star complexity of a face of ΓH\Gamma_H and hh is the size of the largest face of HH. This result significantly improves the previously known upper bound of 72V(H)72|V(H)| [5] for the case where HH is connected. We also show that our bound is worst case optimal up to a small additive constant. Additionally, we provide an indication of complexity of the problem of testing whether a star-shaped inner face can be extended to a straight-line drawing of the graph; this is in contrast to the fact that the same problem is solvable in linear time for the case of star-shaped outer face [9] and convex inner face [13].Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

    Crossing-Free Acyclic Hamiltonian Path Completion for Planar st-Digraphs

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    In this paper we study the problem of existence of a crossing-free acyclic hamiltonian path completion (for short, HP-completion) set for embedded upward planar digraphs. In the context of book embeddings, this question becomes: given an embedded upward planar digraph GG, determine whether there exists an upward 2-page book embedding of GG preserving the given planar embedding. Given an embedded stst-digraph GG which has a crossing-free HP-completion set, we show that there always exists a crossing-free HP-completion set with at most two edges per face of GG. For an embedded NN-free upward planar digraph GG, we show that there always exists a crossing-free acyclic HP-completion set for GG which, moreover, can be computed in linear time. For a width-kk embedded planar stst-digraph GG, we show that we can be efficiently test whether GG admits a crossing-free acyclic HP-completion set.Comment: Accepted to ISAAC200

    Planar Drawings of Fixed-Mobile Bigraphs

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    A fixed-mobile bigraph G is a bipartite graph such that the vertices of one partition set are given with fixed positions in the plane and the mobile vertices of the other part, together with the edges, must be added to the drawing. We assume that G is planar and study the problem of finding, for a given k >= 0, a planar poly-line drawing of G with at most k bends per edge. In the most general case, we show NP-hardness. For k=0 and under additional constraints on the positions of the fixed or mobile vertices, we either prove that the problem is polynomial-time solvable or prove that it belongs to NP. Finally, we present a polynomial-time testing algorithm for a certain type of "layered" 1-bend drawings

    Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

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    The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of sqrt(s) = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K_s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5% for central isolated hadrons and 1-3% for the final calorimeter jet energy scale.Comment: 24 pages plus author list (36 pages total), 23 figures, 1 table, submitted to European Physical Journal

    Measurement of the cross-section and charge asymmetry of WW bosons produced in proton-proton collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

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    This paper presents measurements of the W+μ+νW^+ \rightarrow \mu^+\nu and WμνW^- \rightarrow \mu^-\nu cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13

    Standalone vertex finding in the ATLAS muon spectrometer

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    A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon spectrometer is presented. The algorithm searches the region just upstream of or inside the muon spectrometer volume for multi-particle vertices that originate from the decay of particles with long decay paths. The performance of the algorithm is evaluated using both a sample of simulated Higgs boson events, in which the Higgs boson decays to long-lived neutral particles that in turn decay to bbar b final states, and pp collision data at √s = 7 TeV collected with the ATLAS detector at the LHC during 2011

    Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC

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    Measurements are presented of production properties and couplings of the recently discovered Higgs boson using the decays into boson pairs, H →γ γ, H → Z Z∗ →4l and H →W W∗ →lνlν. The results are based on the complete pp collision data sample recorded by the ATLAS experiment at the CERN Large Hadron Collider at centre-of-mass energies of √s = 7 TeV and √s = 8 TeV, corresponding to an integrated luminosity of about 25 fb−1. Evidence for Higgs boson production through vector-boson fusion is reported. Results of combined fits probing Higgs boson couplings to fermions and bosons, as well as anomalous contributions to loop-induced production and decay modes, are presented. All measurements are consistent with expectations for the Standard Model Higgs boson

    Search for chargino-neutralino production with mass splittings near the electroweak scale in three-lepton final states in √s=13 TeV pp collisions with the ATLAS detector

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    A search for supersymmetry through the pair production of electroweakinos with mass splittings near the electroweak scale and decaying via on-shell W and Z bosons is presented for a three-lepton final state. The analyzed proton-proton collision data taken at a center-of-mass energy of √s=13  TeV were collected between 2015 and 2018 by the ATLAS experiment at the Large Hadron Collider, corresponding to an integrated luminosity of 139  fb−1. A search, emulating the recursive jigsaw reconstruction technique with easily reproducible laboratory-frame variables, is performed. The two excesses observed in the 2015–2016 data recursive jigsaw analysis in the low-mass three-lepton phase space are reproduced. Results with the full data set are in agreement with the Standard Model expectations. They are interpreted to set exclusion limits at the 95% confidence level on simplified models of chargino-neutralino pair production for masses up to 345 GeV

    Measurement of the top quark-pair production cross section with ATLAS in pp collisions at \sqrt{s}=7\TeV

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    A measurement of the production cross-section for top quark pairs(\ttbar) in pppp collisions at \sqrt{s}=7 \TeV is presented using data recorded with the ATLAS detector at the Large Hadron Collider. Events are selected in two different topologies: single lepton (electron ee or muon μ\mu) with large missing transverse energy and at least four jets, and dilepton (eeee, μμ\mu\mu or eμe\mu) with large missing transverse energy and at least two jets. In a data sample of 2.9 pb-1, 37 candidate events are observed in the single-lepton topology and 9 events in the dilepton topology. The corresponding expected backgrounds from non-\ttbar Standard Model processes are estimated using data-driven methods and determined to be 12.2±3.912.2 \pm 3.9 events and 2.5±0.62.5 \pm 0.6 events, respectively. The kinematic properties of the selected events are consistent with SM \ttbar production. The inclusive top quark pair production cross-section is measured to be \sigmattbar=145 \pm 31 ^{+42}_{-27} pb where the first uncertainty is statistical and the second systematic. The measurement agrees with perturbative QCD calculations.Comment: 30 pages plus author list (50 pages total), 9 figures, 11 tables, CERN-PH number and final journal adde
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