Condensation of the roots of real random polynomials on the real axis

We introduce a family of real random polynomials of degree n whose coefficients a_k are symmetric independent Gaussian variables with variance = e^{-k^\alpha}, indexed by a real \alpha \geq 0. We compute exactly the mean number of real roots for large n. As \alpha is varied, one finds three different phases. First, for 0 \leq \alpha \sim (\frac{2}{\pi}) \log{n}. For 1 < \alpha < 2, there is an intermediate phase where grows algebraically with a continuously varying exponent, \sim \frac{2}{\pi} \sqrt{\frac{\alpha-1}{\alpha}} n^{\alpha/2}. And finally for \alpha > 2, one finds a third phase where \sim n. This family of real random polynomials thus exhibits a condensation of their roots on the real line in the sense that, for large n, a finite fraction of their roots /n are real. This condensation occurs via a localization of the real roots around the values \pm \exp{[\frac{\alpha}{2}(k+{1/2})^{\alpha-1} ]}, 1 \ll k \leq n.Comment: 13 pages, 2 figure

A Universal Vertical Stellar Density Distribution Law for the Galaxy

We reduced the observational logarithmic space densities in the vertical direction up to 8 kpc from the galactic plane, for stars with absolute magnitudes (5,6], (6,7] and [5,10] in the fields #0952+5245 and SA114, to a single exponential density law. One of three parameters in the quadratic expression of the density law corresponds to the local space density for stars with absolute magnitudes in question. There is no need of any definition for scaleheights or population types. We confirm with the arguments of non-discrete thin and thick discs for our Galaxy and propose a single structure up to several kiloparsecs from the galactic plane. The logarithmic space densities evaluated by this law for the ELAIS field fit to the observational ones. Whereas, there are considerable offsets for the logarithmic space densities produced by two sets of classical galactic model parameters from the observational ones, for the same field.Comment: 9 pages, 1 figure and 10 tables, accepted for publication in Astrophysics & Space Scienc

Overcoming challenges to data quality in the ASPREE clinical trial

© 2019 The Author(s). Background: Large-scale studies risk generating inaccurate and missing data due to the complexity of data collection. Technology has the potential to improve data quality by providing operational support to data collectors. However, this potential is under-explored in community-based trials. The Aspirin in reducing events in the elderly (ASPREE) trial developed a data suite that was specifically designed to support data collectors: the ASPREE Web Accessible Relational Database (AWARD). This paper describes AWARD and the impact of system design on data quality. Methods: AWARD's operational requirements, conceptual design, key challenges and design solutions for data quality are presented. Impact of design features is assessed through comparison of baseline data collected prior to implementation of key functionality (n = 1000) with data collected post implementation (n = 18,114). Overall data quality is assessed according to data category. Results: At baseline, implementation of user-driven functionality reduced staff error (from 0.3% to 0.01%), out-of-range data entry (from 0.14% to 0.04%) and protocol deviations (from 0.4% to 0.08%). In the longitudinal data set, which contained more than 39 million data values collected within AWARD, 96.6% of data values were entered within specified query range or found to be accurate upon querying. The remaining data were missing (3.4%). Participant non-attendance at scheduled study activity was the most common cause of missing data. Costs associated with cleaning data in ASPREE were lower than expected compared with reports from other trials. Conclusions: Clinical trials undertake complex operational activity in order to collect data, but technology rarely provides sufficient support. We find the AWARD suite provides proof of principle that designing technology to support data collectors can mitigate known causes of poor data quality and produce higher-quality data. Health information technology (IT) products that support the conduct of scheduled activity in addition to traditional data entry will enhance community-based clinical trials. A standardised framework for reporting data quality would aid comparisons across clinical trials

Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant

We present semi-analytical solutions to the background equations describing the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann equations, in the presence of dust, curvature and a cosmological constant Lambda. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius. Hence, these solutions describe the complete space time of a collapsing spherical object in an expanding universe. In the appendix we present for completeness a solution of the Friedmann equations in the additional presence of radiation, only valid for the Robertson-Walker metric.Comment: 23 pages, one figure. Numerical module for evaluation of the solutions released at http://web.physik.rwth-aachen.de/download/valkenburg/ColLambda/ Matches published version, published under Open Access. Note change of titl

'An outsider in our midst': narratives of Neil Lennon, soccer and ethno-religious igotry in the Scottish press

This essay offers a critique of media narratives concerning soccer and those of 'difference' in contemporary Scotland, in particular those who have Irishness as their different identity. It examines certain newspaper narratives concerning Neil Lennon of Celtic FC during autumn 2005. During this period Lennon was characterized as a soccer villain. The commentaries drew on existing perceptions concerning his personality and style of play. More importantly Lennon's national identity (Irish) and his religious background (Catholic) were integrated into the narratives, marking him as an outsider in Scotland. These narratives resonate with public and private discourses of 'otherness' concerning the Irish Catholic diaspora community in Scotland. These broader discourses are manifest as ethno-religious prejudices directed against this community. The discourses of 'outsider' and 'otherness' that surround Lennon, Celtic FC and the Irish Catholic community expose the myth of Scotland's collective self-image as an egalitarian and inclusive society

Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets

The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole's accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a_* of the black hole (|a_*| < 1). The ten spins that have so far been measured by this continuum-fitting method range widely from a_* \approx 0 to a_* > 0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.Comment: 30 pages. Accepted for publication in Space Science Reviews. Also to appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher). Changes to Sections 5.2, 6.1 and 7.4. Section 7.4 responds to Russell et al. 2013 (MNRAS, 431, 405) who find no evidence for a correlation between the power of ballistic jets and black hole spi

Atom lasers: production, properties and prospects for precision inertial measurement

We review experimental progress on atom lasers out-coupled from Bose-Einstein condensates, and consider the properties of such beams in the context of precision inertial sensing. The atom laser is the matter-wave analog of the optical laser. Both devices rely on Bose-enhanced scattering to produce a macroscopically populated trapped mode that is output-coupled to produce an intense beam. In both cases, the beams often display highly desirable properties such as low divergence, high spectral flux and a simple spatial mode that make them useful in practical applications, as well as the potential to perform measurements at or below the quantum projection noise limit. Both devices display similar second-order correlations that differ from thermal sources. Because of these properties, atom lasers are a promising source for application to precision inertial measurements.Comment: This is a review paper. It contains 40 pages, including references and figure

Cervical spine immobilisation following blunt trauma in pre-hospital and emergency care: a systematic review

Objectives To assess whether different cervical spine immobilisation strategies (full immobilisation, movement minimisation or no immobilisation), impact neurological and/or other outcomes for patients with suspected cervical spinal injury in the pre-hospital and emergency department setting. Design Systematic review following Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. Data sources MEDLINE, EMBASE, CINAHL, Cochrane Library and two research registers were searched until September 2023. Eligibility criteria All comparative studies (prospective or retrospective) that examined the potential benefits and/or harms of immobilisation practices during pre-hospital and emergency care of patients with a potential cervical spine injury (pre-imaging) following blunt trauma. Data extraction and synthesis Two authors independently selected and extracted data. Risk of bias was appraised using the Cochrane ROBINS-I tool for non-randomised studies. Data were synthesised without meta-analysis. Results Six observational studies met the inclusion criteria. The methodological quality was variable, with most studies having serious or critical risk of bias. The effect of cervical spine immobilisation practices such as full immobilisation or movement minimisation during pre-hospital and emergency care did not show clear evidence of benefit for the prevention of neurological deterioration, spinal injuries and death compared with no immobilisation. However, increased pain, discomfort and anatomical complications were associated with collar application during immobilisation. Conclusions Despite the limited evidence, weak designs and limited generalisability, the available data suggest that pre-hospital cervical spine immobilisation (full immobilisation or movement minimisation) was of uncertain value due to the lack of demonstrable benefit and may lead to potential complications and adverse outcomes. High-quality randomised comparative studies are required to address this important question

Black Hole, Jet, and Disk: The Universal Engine

In this paper I review the results of our ongoing project to investigate the coupling between accretion disk and radio jet in galactic nuclei and stellar mass black holes. We find a good correlation between the UV bump luminosity and the radio luminosities of AGN, which improves upon the usual [OIII]/radio correlations. Taking mass and energy conservation in the jet/disk system into account we can successfully model the correlation for radio-loud and radio-weak quasars. We find that jets are comparable in power to the accretion disk luminosity, and the difference between radio-loud and radio-weak may correspond to two natural stages of the relativistic electron distribution -- assuming that radio weak quasars have jets as well. The distribution of flat- and steep-spectrum sources is explained by bulk Lorentz factors gamma_j ~ 5-10. The absence of radio-loud quasars below a critical optical luminosity coincides with the FR I/FR II break and could be explained by a powerdependent, ``closing'' torus. This points towards a different type of obscuring torus in radio-loud host galaxies which might be a consequence of past mergers (e.g. by the temporary formation of a binary black-hole). Interaction of the jet with the closing torus might in principle also help to make a jet radio-loud. Turning to stellar-mass black holes we find that galactic jet sources can be described with the same coupled jet/disk model as AGN which is suggestive of some kind of universal coupling between jet and accretion disk around compact objects.Comment: to appear in ``Jets from Stars and Galactic Nuclei'', Springer Lecture Notes, plain TeX, 16 pages, also at http://www.astro.umd.edu/~hfalcke/publications.htm