Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

The influence of road networks on brown bear spatial distribution and habitat suitability in a human-modified landscape

Roads are human infrastructure that heavily affect wildlife, often with marked impacts on carnivores, including brown bears Ursus arctos. Here, we assessed the potential impact of road networks on the distribution of brown bears in the small, isolated and endangered Cantabrian population of north-western Spain. To ascertain whether local road networks affect brown bear spatial distribution, we first assessed potential influences on the distance of bear locations to roads using candidate models which included topographic variables, landcover types, bear age and reproductive status, traffic volume and road visibility. Then, we built two sets of habitat suitability models, both with and without roads, to discern the possible loss of habitat suitability caused by roads. The mean distance of bear locations to the nearest road was 968 ± 804 m and the closest road was a low traffic road in 72.5% of cases. Candidate models showed little influence of our variables on bear distance to the nearest road, with the exception of elevation. Habitat suitability models revealed that road networks in our study area seem to have almost no effect on brown bear habitat suitability, except for females with yearlings during the denning season. However, this result may also be a consequence of the fact that only a small proportion (16.5%) of the cells classified as suitable bear habitats were crossed by roads, that is, most of the roads are primarily located in unsuitable bear habitats in the Cantabrian Mountains. Compared to previous studies conducted in other populations, mainly North American ones, our findings might suggest a different response of Eurasian brown bears to roads due to a longer bear-human coexistence in Europe versus North America. However, the indirect approach used in our study does not exclude other detrimental effects, for example, road mortality, increased stress and movement pattern disruption, only detectable by more direct approaches such as telemetry.During this research, EG-B was financially supported by a FPU grant (FPU15-03429) from the Spanish Ministry of Science, Innovation and Universities. VP, EG-B, AMG and HRV were financially supported by the I + D + I Project PID2020-114181GB-I00 financed by the Spanish Ministry of Science and Innovation, the Agencia Estatal de Investigación (AEI) and the Fondo Europeo de Desarrollo Regional (FEDER, EU). AMG was supported by the Predoctoral Fellowship PRE2018-086102. AZA was financially supported by a Margarita Salas contract financed by the European Union-NextGenerationEU, Ministerio de Universidades y Plan de Recuperación, Transformación y Resiliencia, through the call of the Universidad de Oviedo (Asturias).Peer reviewe

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02

Role of age and comorbidities in mortality of patients with infective endocarditis

Purpose: The aim of this study was to analyse the characteristics of patients with IE in three groups of age and to assess the ability of age and the Charlson Comorbidity Index (CCI) to predict mortality. Methods: Prospective cohort study of all patients with IE included in the GAMES Spanish database between 2008 and 2015. Patients were stratified into three age groups:<65 years, 65 to 80 years, and = 80 years.The area under the receiver-operating characteristic (AUROC) curve was calculated to quantify the diagnostic accuracy of the CCI to predict mortality risk. Results: A total of 3120 patients with IE (1327 < 65 years;1291 65-80 years;502 = 80 years) were enrolled.Fever and heart failure were the most common presentations of IE, with no differences among age groups.Patients =80 years who underwent surgery were significantly lower compared with other age groups (14.3%, 65 years; 20.5%, 65-79 years; 31.3%, =80 years). In-hospital mortality was lower in the <65-year group (20.3%, <65 years;30.1%, 65-79 years;34.7%, =80 years;p < 0.001) as well as 1-year mortality (3.2%, <65 years; 5.5%, 65-80 years;7.6%, =80 years; p = 0.003).Independent predictors of mortality were age = 80 years (hazard ratio [HR]:2.78;95% confidence interval [CI]:2.32–3.34), CCI = 3 (HR:1.62; 95% CI:1.39–1.88), and non-performed surgery (HR:1.64;95% CI:11.16–1.58).When the three age groups were compared, the AUROC curve for CCI was significantly larger for patients aged <65 years(p < 0.001) for both in-hospital and 1-year mortality. Conclusion: There were no differences in the clinical presentation of IE between the groups. Age = 80 years, high comorbidity (measured by CCI), and non-performance of surgery were independent predictors of mortality in patients with IE.CCI could help to identify those patients with IE and surgical indication who present a lower risk of in-hospital and 1-year mortality after surgery, especially in the <65-year group

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

Search for TeV-scale gravity signatures in high-mass final states with leptons and jets with the ATLAS detector at sqrt [ s ] = 13TeV

A search for physics beyond the Standard Model, in final states with at least one high transverse momentum charged lepton (electron or muon) and two additional high transverse momentum leptons or jets, is performed using 3.2 fb−1 of proton–proton collision data recorded by the ATLAS detector at the Large Hadron Collider in 2015 at √s = 13 TeV. The upper end of the distribution of the scalar sum of the transverse momenta of leptons and jets is sensitive to the production of high-mass objects. No excess of events beyond Standard Model predictions is observed. Exclusion limits are set for models of microscopic black holes with two to six extra dimensions

Search for H→γγ produced in association with top quarks and constraints on the Yukawa coupling between the top quark and the Higgs boson using data taken at 7 TeV and 8 TeV with the ATLAS detector

A search is performed for Higgs bosons produced in association with top quarks using the diphoton decay mode of the Higgs boson. Selection requirements are optimized separately for leptonic and fully hadronic final states from the top quark decays. The dataset used corresponds to an integrated luminosity of 4.5 fb−14.5 fb−1 of proton–proton collisions at a center-of-mass energy of 7 TeV and 20.3 fb−1 at 8 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. No significant excess over the background prediction is observed and upper limits are set on the tt¯H production cross section. The observed exclusion upper limit at 95% confidence level is 6.7 times the predicted Standard Model cross section value. In addition, limits are set on the strength of the Yukawa coupling between the top quark and the Higgs boson, taking into account the dependence of the tt¯H and tH cross sections as well as the H→γγ branching fraction on the Yukawa coupling. Lower and upper limits at 95% confidence level are set at −1.3 and +8.0 times the Yukawa coupling strength in the Standard Model

Search for dark matter produced in association with a hadronically decaying vector boson in pp collisions at sqrt (s) = 13 TeV with the ATLAS detector

A search is presented for dark matter produced in association with a hadronically decaying W or Z boson using 3.2 fb−1 of pp collisions at View the MathML sources=13 TeV recorded by the ATLAS detector at the Large Hadron Collider. Events with a hadronic jet compatible with a W or Z boson and with large missing transverse momentum are analysed. The data are consistent with the Standard Model predictions and are interpreted in terms of both an effective field theory and a simplified model containing dark matter

Measurement of the cross section for isolated-photon plus jet production in pp collisions at √s=13 TeV using the ATLAS detector

The dynamics of isolated-photon production in association with a jet in proton–proton collisions at a centre-of-mass energy of 13 TeV are studied with the ATLAS detector at the LHC using a dataset with an integrated luminosity of 3.2 fb−1. Photons are required to have transverse energies above 125 GeV. Jets are identified using the anti- algorithm with radius parameter and required to have transverse momenta above 100 GeV. Measurements of isolated-photon plus jet cross sections are presented as functions of the leading-photon transverse energy, the leading-jet transverse momentum, the azimuthal angular separation between the photon and the jet, the photon–jet invariant mass and the scattering angle in the photon–jet centre-of-mass system. Tree-level plus parton-shower predictions from Sherpa and Pythia as well as next-to-leading-order QCD predictions from Jetphox and Sherpa are compared to the measurements