The Moment Problem for Continuous Positive Semidefinite Linear functionals

Let $\tau$ be a locally convex topology on the countable dimensional polynomial $\reals$-algebra \rx:=\reals[X_1,...,X_n]. Let $K$ be a closed subset of $\reals^n$, and let $M:=M_{\{g_1, ... g_s\}}$ be a finitely generated quadratic module in \rx. We investigate the following question: When is the cone \Pos(K) (of polynomials nonnegative on $K$) included in the closure of $M$? We give an interpretation of this inclusion with respect to representing continuous linear functionals by measures. We discuss several examples; we compute the closure of M=\sos with respect to weighted norm-$p$ topologies. We show that this closure coincides with the cone \Pos(K) where $K$ is a certain convex compact polyhedron.Comment: 14 page

Orthogonality constrained inverse regression to improve model selectivity and analyte predictions from vibrational spectroscopic measurements

In analytical chemistry spectroscopy is attractive for high-throughput quantification, which often relies on inverse regression, like partial least squares regression. Due to a multivariate nature of spectroscopic measurements an analyte can be quantified in presence of interferences. However, if the model is not fully selective against interferences, analyte predictions may be biased. The degree of model selectivity against an interferent is defined by the inner relation between the regression vector and the pure interfering signal. If the regression vector is orthogonal to the signal, this inner relation equals zero and the model is fully selective. The degree of model selectivity largely depends on calibration data quality. Strong correlations may deteriorate calibration data resulting in poorly selective models. We show this using a fructose-maltose model system. Furthermore, we modify the NIPALS algorithm to improve model selectivity when calibration data are deteriorated. This modification is done by incorporating a projection matrix into the algorithm, which constrains regression vector estimation to the null-space of known interfering signals. This way known interfering signals are handled, while unknown signals are accounted for by latent variables. We test the modified algorithm and compare it to the conventional NIPALS algorithm using both simulated and industrial process data. The industrial process data consist of mid-infrared measurements obtained on mixtures of beta-lactoglobulin (analyte of interest), and alpha-lactalbumin and caseinoglycomacropeptide (interfering species). The root mean squared error of beta-lactoglobulin (% w/w) predictions of a test set was 0.92 and 0.33 when applying the conventional and the modified NIPALS algorithm, respectively. Our modification of the algorithm returns simpler models with improved selectivity and analyte predictions. This paper shows how known interfering signals may be utilized in a direct fashion, while benefitting from a latent variable approach. The modified algorithm can be viewed as a fusion between ordinary least squares regression and partial least squares regression and may be very useful when knowledge of some (but not all) interfering species is available

Genome-wide association and Mendelian randomisation analysis provide insights into the pathogenesis of heart failure

Heart failure (HF) is a leading cause of morbidity and mortality worldwide. A small proportion of HF cases are attributable to monogenic cardiomyopathies and existing genome-wide association studies (GWAS) have yielded only limited insights, leaving the observed heritability of HF largely unexplained. We report results from a GWAS meta-analysis of HF comprising 47,309 cases and 930,014 controls. Twelve independent variants at 11 genomic loci are associated with HF, all of which demonstrate one or more associations with coronary artery disease (CAD), atrial fibrillation, or reduced left ventricular function, suggesting shared genetic aetiology. Functional analysis of non-CAD-associated loci implicate genes involved in cardiac development (MYOZ1, SYNPO2L), protein homoeostasis (BAG3), and cellular senescence (CDKN1A). Mendelian randomisation analysis supports causal roles for several HF risk factors, and demonstrates CAD-independent effects for atrial fibrillation, body mass index, and hypertension. These findings extend our knowledge of the pathways underlying HF and may inform new therapeutic strategies

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 strong gravity in multijet final states produced in pp collisions at √s=13 TeV using the ATLAS detector at the LHC

A search is conducted for new physics in multijet final states using 3.6 inverse femtobarns of data from proton-proton collisions at √s = 13TeV taken at the CERN Large Hadron Collider with the ATLAS detector. Events are selected containing at least three jets with scalar sum of jet transverse momenta (HT) greater than 1TeV. No excess is seen at large HT and limits are presented on new physics: models which produce final states containing at least three jets and having cross sections larger than 1.6 fb with HT > 5.8 TeV are excluded. Limits are also given in terms of new physics models of strong gravity that hypothesize additional space-time dimensions

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

The performance of the jet trigger for the ATLAS detector during 2011 data taking

The performance of the jet trigger for the ATLAS detector at the LHC during the 2011 data taking period is described. During 2011 the LHC provided proton–proton collisions with a centre-of-mass energy of 7 TeV and heavy ion collisions with a 2.76 TeV per nucleon–nucleon collision energy. The ATLAS trigger is a three level system designed to reduce the rate of events from the 40 MHz nominal maximum bunch crossing rate to the approximate 400 Hz which can be written to offline storage. The ATLAS jet trigger is the primary means for the online selection of events containing jets. Events are accepted by the trigger if they contain one or more jets above some transverse energy threshold. During 2011 data taking the jet trigger was fully efficient for jets with transverse energy above 25 GeV for triggers seeded randomly at Level 1. For triggers which require a jet to be identified at each of the three trigger levels, full efficiency is reached for offline jets with transverse energy above 60 GeV. Jets reconstructed in the final trigger level and corresponding to offline jets with transverse energy greater than 60 GeV, are reconstructed with a resolution in transverse energy with respect to offline jets, of better than 4 % in the central region and better than 2.5 % in the forward direction

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

Search for resonances in the mass distribution of jet pairs with one or two jets identified as b-jets in proton–proton collisions at √s=13TeV with the ATLAS detector

Searches for high-mass resonances in the dijet invariant mass spectrum with one or two jets identi-fied as b-jets are performed using an integrated luminosity of 3.2fb−1of proton–proton collisions with a centre-of-mass energy of √s=13TeVrecorded by the ATLAS detector at the Large Hadron Collider. Noevidence of anomalous phenomena is observed in the data, which are used to exclude, at 95%credibility level, excited b∗quarks with masses from 1.1TeVto 2.1TeVand leptophobic Z bosons with masses from 1.1TeVto 1.5TeV. Contributions of a Gaussian signal shape with effective cross sections ranging from approximately 0.4 to 0.001pb are also excluded in the mass range 1.5–5.0TeV