An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation

We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane is non-relativistic and we show that it tends to violate the null energy condition and to render cosmological fluctuations ghosts. There nonetheless exists an interesting parameter space in which a stable phase of quasi-exponential expansion can be achieved while the induced gravity leaves non trivial imprints. We derive the exact second-order action governing the dynamics of linear perturbations and we show that it can be simply understood through a bimetric perspective. In the relativistic regime, we also calculate the dominant contribution to the primordial bispectrum and demonstrate that large non-Gaussianities of orthogonal shape can be generated, for the first time in a concrete model. More generally, we find that the sign and the shape of the bispectrum offer powerful diagnostics of the precise strength of the induced gravity.Comment: 34 pages including 9 figures, plus appendices and bibliography. Wordings changed and references added; matches version published in JCA

Enhanced generation of VUV radiation by four-wave mixing in mercury using pulsed laser vaporization

The efficiency of a coherent VUV source at 125 nm, based on 2-photon resonant four-wave mixing in mercury vapor, has been enhanced by up to 2 orders of magnitude. This enhancement was obtained by locally heating a liquid Hg surface with a pulsed excimer laser, resulting in a high density vapor plume in which the nonlinear interaction occurred. Energies up to 5 μJ (1 kW peak power) have been achieved while keeping the overall Hg cell at room temperature, avoiding the use of a complex heat pipe. We have observed a strong saturation of the VUV yield when peak power densities of the fundamental beams exceed the GW/cm2 range, as well as a large intensity-dependant broadening (up to ~30 cm-1) of the two-photon resonance. The source has potential applications for high resolution interference lithography and photochemistry

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt{s} = 1.96 TeV using Kinematic Characteristics of Lepton + Jets Events

We present a measurement of the top quark pair ttbar production cross section in ppbar collisions at a center-of-mass energy of 1.96 TeV using 230 pb**{-1} of data collected by the DO detector at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), large missing transverse energy, and at least four jets, and extract the ttbar content of the sample based on the kinematic characteristics of the events. For a top quark mass of 175 GeV, we measure sigma(ttbar) = 6.7 {+1.4-1.3} (stat) {+1.6- 1.1} (syst) +/-0.4 (lumi) pb, in good agreement with the standard model prediction.Comment: submitted to Phys.Rev.Let

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt(s)=1.96 TeV using Lepton + Jets Events with Lifetime b-tagging

We present a measurement of the top quark pair ($t\bar{t}$) production cross section ($\sigma_{t\bar{t}}$) in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV using 230 pb$^{-1}$ of data collected by the D0 experiment at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), missing transverse energy, and jets in the final state. We employ lifetime-based b-jet identification techniques to further enhance the $t\bar{t}$ purity of the selected sample. For a top quark mass of 175 GeV, we measure $\sigma_{t\bar{t}}=8.6^{+1.6}_{-1.5}(stat.+syst.)\pm 0.6(lumi.)$ pb, in agreement with the standard model expectation.Comment: 7 pages, 2 figures, 3 tables Submitted to Phys.Rev.Let

Temporal, spatial, and structural patterns of adult trembling aspen and white spruce mortality in Quebec's boreal forest

Temporal, spatial, and structural patterns of adult trembling aspen (Populus tremuloides Michx.) and white spruce (Picea glauca (Moench) Voss) mortality were studied in intact 150-year-old stands in the southwestern boreal forest of Quebec. For both species, mortality decreases (number of dead trees/total number of trees) with distance from the lake edge until 100-150 m, from which point it slightly increases. Strong peaks in mortality were found for 40- to 60-year-old aspen mainly between 1974 and 1992. Such mortality in relatively young aspen is likely related to competition for light from the dominant canopy trees. Also, the recruitment of this young aspen cohort is presumably the result of a stand breakup that occurred when the initial aspen-dominated stand was between 90 and 110 years old. For spruce, strong peaks in mortality were found in 110- to 150-year-old trees and they occurred mainly after 1980. No clear explanation could be found for these peaks, but we suggest that they may be related to senescence or weakening of the trees following the last spruce budworm outbreak. Suppressed and codominant aspen had a much higher mortality ratio than spruce in the same height class, while more surprisingly, no difference in mortality rate was found between dominant trees of the two species. Most spruce trees were found as standing dead, which leads us to reject the hypothesis that windthrow is an important cause of mortality for spruce in our forests

Measurement of the p-pbar -> Wgamma + X cross section at sqrt(s) = 1.96 TeV and WWgamma anomalous coupling limits

The WWgamma triple gauge boson coupling parameters are studied using p-pbar -> l nu gamma + X (l = e,mu) events at sqrt(s) = 1.96 TeV. The data were collected with the DO detector from an integrated luminosity of 162 pb^{-1} delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for p-pbar -> W(gamma) + X -> l nu gamma + X with E_T^{gamma} > 8 GeV and Delta R_{l gamma} > 0.7 is 14.8 +/- 1.6 (stat) +/- 1.0 (syst) +/- 1.0 (lum) pb. The one-dimensional 95% confidence level limits on anomalous couplings are -0.88 < Delta kappa_{gamma} < 0.96 and -0.20 < lambda_{gamma} < 0.20.Comment: Submitted to Phys. Rev. D Rapid Communication

Measurement of the Isolated Photon Cross Section in p-pbar Collisions at sqrt{s}=1.96 TeV

The cross section for the inclusive production of isolated photons has been measured in p anti-p collisions at sqrt{s}=1.96 TeV with the D0 detector at the Fermilab Tevatron Collider. The photons span transverse momenta 23 to 300 GeV and have pseudorapidity |eta|<0.9. The cross section is compared with the results from two next-to-leading order perturbative QCD calculations. The theoretical predictions agree with the measurement within uncertainties.Comment: 7 pages, 5 figures, submitted to Phys.Lett.

Search for W' bosons decaying to an electron and a neutrino with the D0 detector

This Letter describes the search for a new heavy charged gauge boson W' decaying into an electron and a neutrino. The data were collected with the D0 detector at the Fermilab Tevatron proton-antiproton Collider at a center-of-mass energy of 1.96 TeV, and correspond to an integrated luminosity of about 1 inverse femtobarn. Lacking any significant excess in the data in comparison with known processes, an upper limit is set on the production cross section times branching fraction, and a W' boson with mass below 1.00 TeV can be excluded at the 95% C.L., assuming standard-model-like couplings to fermions. This result significantly improves upon previous limits, and is the most stringent to date.Comment: submitted to Phys. Rev. Let