Principal forms X^2 + nY^2 representing many integers

In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X^2+nY^2. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n=2. In this paper, we prove that in fact this constant is unbounded as n runs through positive integers with a fixed number of prime divisors.Comment: 10 pages, title has been changed, Sections 2 and 3 are new, to appear in Abh. Math. Sem. Univ. Hambur

“Genetic and clinical findings in an ethnically diverse retinitis pigmentosa cohort associated with pathogenic variants in EYS”

Background and objectives: The EYS gene is an important cause of autosomal recessive retinitis pigmentosa (arRP). The objective of this study is to report on novel pathogenic variants in EYS and the range of associated phenotypes. / Subjects and methods: This retrospective case series at a tertiary referral centre for inherited retinal diseases describes patients with an IRD and at least two variants in the EYS gene. Phenotyping included multimodal retinal imaging; genotyping molecular genetic analysis using targeted next generation sequencing. Sanger sequencing verification and analysis of novel variants using in silico approaches to determine their predicted pathogenicity. / Results: Eight male and four female patients were included. Age at onset ranged from 11 to 62 years with variable symptom presentation; ten patients showed classical features of retinitis pigmentosa, albeit with great variation in disease severity and extent. Two patients had atypical phenotypes: one with localised inferior sector pigmentation and a mild RP phenotype with changes predominantly at the posterior pole. Eighteen variants in EYS were identified, located across the gene: six were novel. Eight variants were missense, two altered splicing, one was a whole exon duplication and the remainder were predicted to result in premature truncation of the protein. / Conclusion: The marked variability in severity and age of onset in most patients in this ethnically diverse cohort adds to growing evidence that that mild phenotypes are associated with EYS variants. Similarly, the two atypical cases add to the growing diversity of EYS disease as do the six novel pathogenic variants described

Laser-driven plasma waves in capillary tubes

The excitation of plasma waves over a length of up to 8 centimeters is, for the first time, demon- strated using laser guiding of intense laser pulses through hydrogen filled glass capillary tubes. The plasma waves are diagnosed by spectral analysis of the transmitted laser radiation. The dependence of the spectral redshift, measured as a function of filling pressure, capillary tube length and incident laser energy, is in excellent agreement with simulation results. The longitudinal accelerating field inferred from the simulations is in the range 1 -10 GV/m

Excitation Spectrum of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain:

The natural explanation of the excitation spectrum of the spin-1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum $k$ by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small $k$, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.Comment: 12 Pages REVTEX, Postscript file for the figures included. SKPH-94-C00

Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Pad\'{e} approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for all $d$, and achieve highly accelerated convergence of its expansions in powers of $q^2/m^2$ or $m^2/q^2$, for $d=4$.Comment: 25 pages, OUT--4102--43, BI--TP/92--5

False positive HIV diagnoses in resource limited settings: operational lessons learned for HIV programmes

Access to HIV diagnosis is life-saving; however the use of rapid diagnostic tests in combination is vulnerable to wrongly diagnosing HIV infection when both screening tests give a false positive result. Misclassification of HIV patients can also occur due to poor quality control, administrative errors and lack of supervision and training of staff. Médecins Sans Frontières discovered in 2004 that HIV negative individuals were enrolled in some HIV programmes. This paper describes the result of an audit of three sites to review testing practices, implement improved testing algorithms and offer re-testing to clients enrolled in the HIV clinic

Critical Behavior of Anisotropic Heisenberg Mixed-Spin Chains in a Field

We numerically investigate the critical behavior of the spin-(1,1/2) Heisenberg ferrimagnet with anisotropic exchange coupling in a magnetic field. A quantized magnetization plateau as a function of the field, appearing at a third of the saturated magnetization, is stable over whole the antiferromagnetic coupling region. The plateau vanishes in the ferromagnetic coupling region via the Kosterlitz-Thouless transition. Comparing the quantum and classical magnetization curves, we elucidate what are essential quantum effects.Comment: 5 pages, Revtex, with 7 eps figures, to appear in Phys. Rev. B (An extra ps figure (fig7.ps) is included for printing.

Effect of meteorological factors on clinical malaria risk among children: an assessment using village-based meteorological stations and community-based parasitological survey

<p>Abstract</p> <p>Background</p> <p>Temperature, rainfall and humidity have been widely associated with the dynamics of malaria vector population and, therefore, with spread of the disease. However, at the local scale, there is a lack of a systematic quantification of the effect of these factors on malaria transmission. Further, most attempts to quantify this effect are based on proxy meteorological data acquired from satellites or interpolated from a different scale. This has led to controversies about the contribution of climate change to malaria transmission risk among others. Our study addresses the original question of relating meteorological factors measured at the local scale with malaria infection, using data collected at the same time and scale.</p> <p>Methods</p> <p>676 children (6–59 months) were selected randomly from three ecologically different sites (urban and rural). During weekly home visits between December 1, 2003, and November 30, 2004, fieldworkers tested children with fever for clinical malaria. They also collected data on possible confounders monthly. Digital meteorological stations measured ambient temperature, humidity, and rainfall in each site. Logistic regression was used to estimate the risk of clinical malaria given the previous month's meteorological conditions.</p> <p>Results</p> <p>The overall incidence of clinical malaria over the study period was 1.07 episodes per child. Meteorological factors were associated with clinical malaria with mean temperature having the largest effect.</p> <p>Conclusion</p> <p>Temperature was the best predictor for clinical malaria among children under five. A systematic measurement of local temperature through ground stations and integration of such data in the routine health information system could support assessment of malaria transmission risk at the district level for well-targeted control efforts.</p

Excitation Spectra of Structurally Dimerized and Spin-Peierls Chains in a Magnetic Field

The dynamical spin structure factor and the Raman response are calculated for structurally dimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. In both cases there is a spin liquid phase composed of interacting singlet dimers at small fields h < h_c1, an incommensurate regime (h_c1 < h < h_c2) in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin polarized phase above an upper critical field h_c2. For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.Comment: RevTex, 10 pages with 8 eps figure

The Origin of the Cosmic Soft X-Ray Background: Optical Identification of an Extremely Deep ROSAT Survey

We present the results of the deepest optically identified X-ray survey yet made. The X-ray survey was made with the ROSAT PSPC and reaches a flux limit of 1.6x10^-15 erg cm^-2 s^-1 (0.5--2.0 keV). Above a flux limit of 2x10^-15 erg cm^-2 s^-1 we define a complete sample of 70 sources of which 59 are identified. Some (5) other sources have tentative identifications and in a further 4 the X-ray error-boxes are blank to R=23 mag. At the brighter flux levels (>= 10^-14 erg cm^-2 s^-1) we confirm the results of previous less deep X-ray surveys with 84% of the sources begin QSOs. At fainter fluxes, however, the survey is dominated by a population of galaxies with narrow optical emission lines (NELGs). In addition, a number of groups and clusters of galaxies are found at intermediate fluxes. Most of these are poor systems of low X-ray luminosity and are generally found at redshifts of > 0.3. Their numbers are consistent with a zero evolutionary scenario, in contrast to the situation for high luminosity clusters at the same redshift. We discuss the significance of these results to the determination of the cosmic soft X-ray background (XRB) and show that at 2x10^-15 erg cm^-2 s^-1, we have resolved more than 50% of the background. We also briefly consider the probable importance of NELG objects to the residual background and look at some of the properties of these unusual objects.Comment: 28 pages, LaTeX, 17 figures from 32 postscript files. Uses mn.sty and epsf.sty. Accepted by MNRAS. Revised version now contains data table. For more information see http://www.astro.soton.ac.uk/~amn/UKdee