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    ABSTRACT: We introduce an $\mathfrak{F}$-valued generalization of the Virasoro algebra, called the Frobenius-Virasoro algebra $\mathfrak{vir_F}$, where $\mathfrak{F}$ is a Frobenius algebra over $\mathbb{R}$. We also study Euler equations on the regular dual of $\mathfrak{vir_F}$, including the $\mathfrak{F}$-$\mathrm{KdV}$ equation and the $\mathfrak{F}$-$\mathrm{CH}$ equation and the $\mathfrak{F}$-$\mathrm{HS}$ equation, and discuss their Hamiltonian properties.
    Preview · Article · Feb 2014 · Journal of Geometry and Physics
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    ABSTRACT: A key paper in modelling patient recruitment in multi-centre clinical trials is that of Anisimov and Fedorov. They assume that the distribution of the number of patients in a given centre in a completed trial follows a Poisson distribution. In a second stage, the unknown parameter is assumed to come from a Gamma distribution. As is well known, the overall Gamma-Poisson mixture is a negative binomial. For forecasting time to completion, however, it is not the frequency domain that is important, but the time domain and that of Anisimov and Fedorov have also illustrated clearly the links between the two and the way in which a negative binomial in one corresponds to a type VI Pearson distribution in the other. They have also shown how one may use this to forecast time to completion in a trial in progress. However, it is not just necessary to forecast time to completion for trials in progress but also for trials that have yet to start. This suggests that what would be useful would be to add a higher level of the hierarchy: over all trials. We present one possible approach to doing this using an orthogonal parameterization of the Gamma distribution with parameters on the real line. The two parameters are modelled separately. This is illustrated using data from 18 trials. We make suggestions as to how this method could be applied in practice. Copyright © 2013 John Wiley & Sons, Ltd.
    No preview · Article · Dec 2013 · Statistics in Medicine
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    ABSTRACT: There is growing interest in links between poor health and socio-environmental inequalities (e.g. inferior housing, crime and industrial emissions) under the environmental justice agenda. The current project assessed associations between soil metal content, air pollution (NO2/PM10) and deprivation and health (respiratory case incidence) across Glasgow. This is the first time that both chemical land quality and air pollution have been assessed citywide in the context of deprivation and health for a major UK conurbation. Based on the dataset 'averages' for intermediate geography areas, generalised linear modelling of respiratory cases showed significant associations with overall soil metal concentration (p = 0.0367) and with deprivation (p < 0.0448). Of the individual soil metals, only nickel showed a significant relationship with respiratory cases (p = 0.0056). Whilst these associations could simply represent concordant lower soil metal concentrations and fewer respiratory cases in the rural versus the urban environment, they are interesting given (1) possible contributions from soil to air particulate loading and (2) known associations between airborne metals like nickel and health. This study also demonstrated a statistically significant correlation (-0.213; p < 0.05) between soil metal concentration and deprivation across Glasgow. This highlights the fact that despite numerous regeneration programmes, the legacy of environmental pollution remains in post-industrial areas of Glasgow many decades after heavy industry has declined. Further epidemiological investigations would be required to determine whether there are any causal links between soil quality and population health/well-being. However, the results of this study suggest that poor soil quality warrants greater consideration in future health and socio-environmental inequality assessments.
    Full-text · Article · Nov 2013 · Environmental Geochemistry and Health
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