Categorification of persistent homology

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational Geometr

Flavour Universal Dynamical Electroweak Symmetry Breaking

The top condensate see-saw mechanism of Dobrescu and Hill allows electroweak symmetry to be broken while deferring the problem of flavour to an electroweak singlet, massive sector. We provide an extended version of the singlet sector that naturally accommodates realistic masses for all the standard model fermions, which play an equal role in breaking electroweak symmetry. The models result in a relatively light composite Higgs sector with masses typically in the range of (400-700)~GeV. In more complete models the dynamics will presumably be driven by a broken gauged family or flavour symmetry group. As an example of the higher scale dynamics a fully dynamical model of the quark sector with a GIM mechanism is presented, based on an earlier top condensation model of King using broken family gauge symmetry interactions (that model was itself based on a technicolour model of Georgi). The crucial extra ingredient is a reinterpretation of the condensates that form when several gauge groups become strong close to the same scale. A related technicolour model of Randall which naturally includes the leptons too may also be adapted to this scenario. We discuss the low energy constraints on the massive gauge bosons and scalars of these models as well as their phenomenology at the TeV scale.Comment: 22 pages, 3 fig

Ratios of anti-factor Xa to antithrombin activities of heparins as determined in recalcified human plasma

Anti-factor Xa and anti-thrombin activities of unfractionated (UF) and low molecular weight (LMW) heparins have been measured in human plasma and with purified human antithrombin III (ATIII) in the absence and presence of 1-5 mM calcium. The anti-factor Xa and antithrombin activities were measured directly, by assessing the heparin-dependent pseudo-first order rate constants of inactivation of human factor Xa or thrombin. These activities were studied with the 4th International Standard for UF heparin, the 1st International Standard for LMW heparin, CY216, enoxaparin, CY222, and the synthetic pentasaccharide. In plasma, calcium equally well increased the specific anti-factor Xa catalytic activities as compared to purified ATIII. That is, 1.5 mM calcium stimulated the UF standard heparin-catalysed inactivation of factor Xa 2.1-2.4 times. In the presence of the LMW heparins the effect of calcium was smaller (1.3-1.7 times), and in plasma there was no effect of calcium on the pentasaccharide-catalysed inactivation of factor Xa. Thus, the largest effects of calcium in the inactivation reaction of factor Xa is seen with UF standard heparin. Calcium reduced the anti-thrombin activities of all the heparin preparations studied about 1.5 times when purified ATIII was used, although in plasma this effect was less clear. Consequently, in the presence of 1.5 mM calcium the ratio of the anti-factor Xa to the anti-thrombin activities of UF standard heparin approximated those of the LMW heparins. The only exception was CY222, which under all conditions retained anti-factor Xa/anti-thrombin ratios significantly higher than those of UF standard heparin

Demographic transition and the real exchange rate in Australia: An empirical investigation

This article utilizes the empirical findings that age structure of the population affects saving, investment and capital flow and hypothesizes that age structure influences the real exchange rate. Based on this link, an empirical model is specified for Australia and estimated with annual data for the period 1970–2011. An autoregressive distributed lag model of cointegration indicates that Australia's real exchange rate is cointegrated with its productivity differential and the relative share of young dependents (0–14 years) in the population. Long-run estimates show that young cohort has an appreciating influence on the real exchange rate. Also, the short-run adjustment is substantial, with more than 65% of the disequilibrium corrected in a year

D* Production in Deep Inelastic Scattering at HERA

This paper presents measurements of D^{*\pm} production in deep inelastic scattering from collisions between 27.5 GeV positrons and 820 GeV protons. The data have been taken with the ZEUS detector at HERA. The decay channel $D^{*+}\to (D^0 \to K^- \pi^+) \pi^+$ (+ c.c.) has been used in the study. The $e^+p$ cross section for inclusive D^{*\pm} production with $5<Q^2<100 GeV^2$ and $y<0.7$ is 5.3 \pms 1.0 \pms 0.8 nb in the kinematic region {$1.3<p_T(D^{*\pm})<9.0$ GeV and $| \eta(D^{*\pm}) |<1.5$}. Differential cross sections as functions of p_T(D^{*\pm}), $\eta(D^{*\pm}), W$ and $Q^2$ are compared with next-to-leading order QCD calculations based on the photon-gluon fusion production mechanism. After an extrapolation of the cross section to the full kinematic region in p_T(D^{*\pm}) and $\eta$(D^{*\pm}), the charm contribution $F_2^{c\bar{c}}(x,Q^2)$ to the proton structure function is determined for Bjorken $x$ between 2 $\cdot$ 10$^{-4}$ and 5 $\cdot$ 10$^{-3}$.Comment: 17 pages including 4 figure

Observation of Scaling Violations in Scaled Momentum Distributions at HERA

Charged particle production has been measured in deep inelastic scattering (DIS) events over a large range of $x$ and $Q^2$ using the ZEUS detector. The evolution of the scaled momentum, $x_p$, with $Q^2,$ in the range 10 to 1280 $GeV^2$, has been investigated in the current fragmentation region of the Breit frame. The results show clear evidence, in a single experiment, for scaling violations in scaled momenta as a function of $Q^2$.Comment: 21 pages including 4 figures, to be published in Physics Letters B. Two references adde

Observation of hard scattering in photoproduction events with a large rapidity gap at HERA

Events with a large rapidity gap and total transverse energy greater than 5 GeV have been observed in quasi-real photoproduction at HERA with the ZEUS detector. The distribution of these events as a function of the $\gamma p$ centre of mass energy is consistent with diffractive scattering. For total transverse energies above 12 GeV, the hadronic final states show predominantly a two-jet structure with each jet having a transverse energy greater than 4 GeV. For the two-jet events, little energy flow is found outside the jets. This observation is consistent with the hard scattering of a quasi-real photon with a colourless object in the proton.Comment: 19 pages, latex, 4 figures appended as uuencoded fil

Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment

This paper describes an analysis of the angular distribution of W->enu and W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and the missing transverse energy, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw > 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables, revised author list, matches European Journal of Physics C versio

Observation of a new chi_b state in radiative transitions to Upsilon(1S) and Upsilon(2S) at ATLAS

The chi_b(nP) quarkonium states are produced in proton-proton collisions at the Large Hadron Collider (LHC) at sqrt(s) = 7 TeV and recorded by the ATLAS detector. Using a data sample corresponding to an integrated luminosity of 4.4 fb^-1, these states are reconstructed through their radiative decays to Upsilon(1S,2S) with Upsilon->mu+mu-. In addition to the mass peaks corresponding to the decay modes chi_b(1P,2P)->Upsilon(1S)gamma, a new structure centered at a mass of 10.530+/-0.005 (stat.)+/-0.009 (syst.) GeV is also observed, in both the Upsilon(1S)gamma and Upsilon(2S)gamma decay modes. This is interpreted as the chi_b(3P) system.Comment: 5 pages plus author list (18 pages total), 2 figures, 1 table, corrected author list, matches final version in Physical Review Letter