Genus expansion for real Wishart matrices

We present an exact formula for moments and cumulants of several real compound Wishart matrices in terms of an Euler characteristic expansion, similar to the genus expansion for complex random matrices. We consider their asymptotic values in the large matrix limit: as in a genus expansion, the terms which survive in the large matrix limit are those with the greatest Euler characteristic, that is, either spheres or collections of spheres. This topological construction motivates an algebraic expression for the moments and cumulants in terms of the symmetric group. We examine the combinatorial properties distinguishing the leading order terms. By considering higher cumulants, we give a central limit-type theorem for the asymptotic distribution around the expected value

Observation of the Ankle and Evidence for a High-Energy Break in the Cosmic Ray Spectrum

We have measured the cosmic ray spectrum at energies above $10^{17}$ eV using the two air fluorescence detectors of the High Resolution Fly's Eye experiment operating in monocular mode. We describe the detector, PMT and atmospheric calibrations, and the analysis techniques for the two detectors. We fit the spectrum to models describing galactic and extragalactic sources. Our measured spectrum gives an observation of a feature known as the ``ankle'' near $3\times 10^{18}$ eV, and strong evidence for a suppression near $6\times 10^{19}$ eV.Comment: 14 pages, 9 figures. To appear in Physics Letters B. Accepted versio

Dietary nitrate supplementation increases fractional exhaled nitric oxide: implications for the assessment of airway health in athletes

Background: Fractional exhaled nitric oxide (FeNO) is a simple tool that has an established role in the assessment of airway inflammation in athletes. Specifically, FeNO provides information concerning asthma phenotypes, aetiology of respiratory symptoms, response to anti-inflammatory agents, course of disease and adherence to medication. It is recognised that FeNO can be influenced by a variety of external factors (e.g. atopic status, exercise, respiratory tract infection), however, there remains limited research concerning the impact of dietary nitrate ingestion. The primary aim of this study was therefore to evaluate the effect of acute dietary nitrate supplementation on FeNO and resting pulmonary function parameters. Method: The study was conducted as a randomised double-blind placebo-controlled trial. Thirty male endurance trained athletes (age: 28 ± 6 yrs; BMI: 23 ± 2 kg.m-2) free from cardio-respiratory and metabolic disease, and stable at time of study entry (i.e. entirely asymptomatic without recent respiratory tract infection) attended the laboratory on two separate occasions. On arrival to the laboratory, athletes consumed either 140ml nitrate-rich beetroot juice (15.2 mmol nitrate) (NIT) or nitrate-depleted beetroot juice (0 mmol nitrate) (PLA). In accordance with international guidelines all athletes performed resting FeNO and forced spirometry (2.5hrs post ingestion). Airway inflammation was evaluated using established FeNO thresholds: (intermediate [≥25ppb] and high [>50ppb]). Results: All athletes demonstrated normal baseline lung function (FEV1 % predicted >80%). A three-fold rise in resting FeNO was observed following NIT (median [IQR]): 32ppb [37] in comparison to PLA: 10ppb [12] (P0.05). Conclusion: Dietary nitrate ingestion should be considered when employing FeNO for the assessment of airway health in athletes. Our findings have implications concerning the decision to initiate or modify inhaler therapy. Further research is therefore required to determine the impact of chronic dietary nitrat

A Likelihood Method for Measuring the Ultrahigh Energy Cosmic Ray Composition

Air fluorescence detectors traditionally determine the dominant chemical composit ion of the ultrahigh energy cosmic ray flux by comparing the averaged slant depth of the shower maximum, $X_{max}$, as a function of energy to the slant depths expect ed for various hypothesized primaries. In this paper, we present a method to make a direct measurement of the expected mean number of protons and iron by comparing the shap es of the expected $X_{max}$ distributions to the distribution for data. The advantages of this method includes the use of information of the full distribution and its ability to calculate a flux for various cosmic ray compositi ons. The same method can be expanded to marginalize uncertainties due to choice of spectra, hadronic models and atmospheric parameters. We demonstrate the technique with independent simulated data samples from a parent sample of protons and iron. We accurately predict the number of protons and iron in the parent sample and show that the uncertainties are meaningful.Comment: 11 figures, 22 pages, accepted by Astroparticle Physic

Alternative Methods to Finding Patterns in HiRes Stereo Data

In this paper Ultra High Energy Cosmic Rays UHECRs data observed by the HiRes fluorescence detector in stereo mode is analyzed to search for events in the sky with an arrival direction lying on a great circle. Such structure is known as the arc structure. The arc structure is expected when the charged cosmic rays pass through the galactic magnetic field. The arcs searched for could represent a broad or a small scale anisotropy depending on the proposed source model for the UHECRs. The Arcs in this paper are looked for using Hough transform were Hough transform is a technique used to looking for patterns in images. No statistically significant arcs were found in this study

A Measurement of the Proton Structure Function F ⁣2(x,Q2)F_{\!2}(x,Q^2)

A measurement of the proton structure function $F_{\!2}(x,Q^2)$ is reported for momentum transfer squared $Q^2$ between 4.5 $GeV^2$ and 1600 $GeV^2$ and for Bjorken $x$ between $1.8\cdot10^{-4}$ and 0.13 using data collected by the HERA experiment H1 in 1993. It is observed that $F_{\!2}$ increases significantly with decreasing $x$, confirming our previous measurement made with one tenth of the data available in this analysis. The $Q^2$ dependence is approximately logarithmic over the full kinematic range covered. The subsample of deep inelastic events with a large pseudo-rapidity gap in the hadronic energy flow close to the proton remnant is used to measure the "diffractive" contribution to $F_{\!2}$.Comment: 32 pages, ps, appended as compressed, uuencoded fil