Approximating the minimum directed tree cover

Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a rooted directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover problem (DTCP) is to find a directed tree cover of minimum cost. The problem is known to be $NP$-hard. In this paper, we show that the weighted Set Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to approximate DTCP with the same ratio as for SCP. We show that this expectation can be satisfied in some way by designing a purely combinatorial approximation algorithm for the DTCP and proving that the approximation ratio of the algorithm is $\max\{2, \ln(D^+)\}$ with $D^+$ is the maximum outgoing degree of the nodes in $G$.Comment: 13 page

Convergence of high-order interpolation schemes in shear layer modelling

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.Capturing flow discontinuities and calculate energy dissipation across the shock wave correctly are challenging numerical simulation problem. Several highly accurate numerical interpolation schemes are employed to capture the shock waves developing in shear flow in shallow waters for two convective Froude numbers. The simulation starts from a small disturbance to the hyperbolic tangent (TANH) based velocity profile. The subsequent linear and nonlinear development of the shear instabilities are obtained from the numerical simulation using the second-order MINMOD, the third-order ULTIMATE-QUICK and the fifth-order WENO schemes. The computational error is evaluated using progressively smaller grid sizes. The number of nodes over a wave length are /x = /y = 16, 32, 64, 128, 256, and 512. The grid refinement determines the accuracy of the simulation and the order of convergence for each scheme. It also determines the dependence of the wave radiation and energy dissipation on the grid size.cf201

Influence of Vancomycin Minimum Inhibitory Concentration on the Outcome of Methicillin-Susceptible Staphylococcus aureus Left-Sided Infective Endocarditis Treated with Anti-staphylococcal Beta-Lactam Antibiotics; a Prospective Cohort Study by the International Collaboration on Endocarditis

Objectives: Left-sided methicillin-susceptible Staphylococcus aureus (MSSA) endocarditis treated with cloxacillin has a poorer prognosis when the vancomycin minimum inhibitory concentration (MIC) is ≥1.5 mg/L. We aimed to validate this using the International Collaboration on Endocarditis cohort and to analyse whether specific genetic characteristics were associated with a high vancomycin MIC (≥1.5 mg/L) phenotype. Methods: All patients with left-sided MSSA infective endocarditis treated with antistaphylococcal β-lactam antibiotics between 2000 and 2006 with available isolates were included. Vancomycin MIC was determined by Etest as either high (≥1.5 mg/L) or low (<1.5 mg/L). Isolates underwent spa typing to infer clonal complexes and multiplex PCR for identifying virulence genes. Univariate analysis was performed to evaluate the association between in-hospital and 1-year mortality, and vancomycin MIC phenotype. Results: Sixty-two cases met the inclusion criteria. Vancomycin MIC was low in 28 cases (45%) and high in 34 cases (55%). No significant differences in patient demographic data or characteristics of infection were observed between patients with infective endocarditis due to high and low vancomycin MIC isolates. Isolates with high and low vancomycin MIC had similar distributions of virulence genes and clonal lineages. In-hospital and 1-year mortality did not differ significantly between the two groups (32% (9/28) vs. 27% (9/34), p 0.780; and 43% (12/28) vs. 29% (10/34), p 0.298, for low and high vancomycin MIC respectively). Conclusions: In this international cohort of patients with left-sided MSSA endocarditis treated with antistaphylococcal β-lactams, vancomycin MIC phenotype was not associated with patient demographics, clinical outcome or virulence gene repertoire

Search for jet extinction in the inclusive jet-pT spectrum from proton-proton collisions at s=8 TeV

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published articles title, journal citation, and DOI.The first search at the LHC for the extinction of QCD jet production is presented, using data collected with the CMS detector corresponding to an integrated luminosity of 10.7  fb−1 of proton-proton collisions at a center-of-mass energy of 8 TeV. The extinction model studied in this analysis is motivated by the search for signatures of strong gravity at the TeV scale (terascale gravity) and assumes the existence of string couplings in the strong-coupling limit. In this limit, the string model predicts the suppression of all high-transverse-momentum standard model processes, including jet production, beyond a certain energy scale. To test this prediction, the measured transverse-momentum spectrum is compared to the theoretical prediction of the standard model. No significant deficit of events is found at high transverse momentum. A 95% confidence level lower limit of 3.3 TeV is set on the extinction mass scale

Search for the Zγ decay mode of new high-mass resonances in pp collisions at √s = 13 TeV with the ATLAS detector

This letter presents a search for narrow, high-mass resonances in the Zγ final state with the Z boson decaying into a pair of electrons or muons. The √s = 13 TeV pp collision data were recorded by the ATLAS detector at the CERN Large Hadron Collider and have an integrated luminosity of 140 fb−1. The data are found to be in agreement with the Standard Model background expectation. Upper limits are set on the resonance production cross section times the decay branching ratio into Zγ. For spin-0 resonances produced via gluon–gluon fusion, the observed limits at 95% confidence level vary between 65.5 fb and 0.6 fb, while for spin-2 resonances produced via gluon–gluon fusion (or quark–antiquark initial states) limits vary between 77.4 (76.1) fb and 0.6 (0.5) fb, for the mass range from 220 GeV to 3400 GeV

Search for heavy resonances decaying into a Z or W boson and a Higgs boson in final states with leptons and b-jets in 139 fb−1 of pp collisions at s√ = 13 TeV with the ATLAS detector

This article presents a search for new resonances decaying into a Z or W boson and a 125 GeV Higgs boson h, and it targets the νν¯¯¯bb¯¯, ℓ+ℓ−bb¯¯, or ℓ±νbb¯¯ final states, where ℓ = e or μ, in proton-proton collisions at s√ = 13 TeV. The data used correspond to a total integrated luminosity of 139 fb−1 collected by the ATLAS detector during Run 2 of the LHC at CERN. The search is conducted by examining the reconstructed invariant or transverse mass distributions of Zh or Wh candidates for evidence of a localised excess in the mass range from 220 GeV to 5 TeV. No significant excess is observed and 95% confidence-level upper limits between 1.3 pb and 0.3 fb are placed on the production cross section times branching fraction of neutral and charged spin-1 resonances and CP-odd scalar bosons. These limits are converted into constraints on the parameter space of the Heavy Vector Triplet model and the two-Higgs-doublet model

The ATLAS trigger system for LHC Run 3 and trigger performance in 2022

The ATLAS trigger system is a crucial component of the ATLAS experiment at the LHC. It is responsible for selecting events in line with the ATLAS physics programme. This paper presents an overview of the changes to the trigger and data acquisition system during the second long shutdown of the LHC, and shows the performance of the trigger system and its components in the proton-proton collisions during the 2022 commissioning period as well as its expected performance in proton-proton and heavy-ion collisions for the remainder of the third LHC data-taking period (2022–2025)

Evidence for the charge asymmetry in pp → tt¯ production at s√ = 13 TeV with the ATLAS detector

Inclusive and differential measurements of the top–antitop (tt¯) charge asymmetry Att¯C and the leptonic asymmetry Aℓℓ¯C are presented in proton–proton collisions at s√ = 13 TeV recorded by the ATLAS experiment at the CERN Large Hadron Collider. The measurement uses the complete Run 2 dataset, corresponding to an integrated luminosity of 139 fb−1, combines data in the single-lepton and dilepton channels, and employs reconstruction techniques adapted to both the resolved and boosted topologies. A Bayesian unfolding procedure is performed to correct for detector resolution and acceptance effects. The combined inclusive tt¯ charge asymmetry is measured to be Att¯C = 0.0068 ± 0.0015, which differs from zero by 4.7 standard deviations. Differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the tt¯ system. Both the inclusive and differential measurements are found to be compatible with the Standard Model predictions, at next-to-next-to-leading order in quantum chromodynamics perturbation theory with next-to-leading-order electroweak corrections. The measurements are interpreted in the framework of the Standard Model effective field theory, placing competitive bounds on several Wilson coefficients