Generalised Calogero-Moser models and universal Lax pair operators

Calogero-Moser models can be generalised for all of the finite reflection groups. These include models based on non-crystallographic root systems, that is the root systems of the finite reflection groups, H_3, H_4, and the dihedral group I_2(m), besides the well-known ones based on crystallographic root systems, namely those associated with Lie algebras. Universal Lax pair operators for all of the generalised Calogero-Moser models and for any choices of the potentials are constructed as linear combinations of the reflection operators. The consistency conditions are reduced to functional equations for the coefficient functions of the reflection operators in the Lax pair. There are only four types of such functional equations corresponding to the two-dimensional sub-root systems, A_2, B_2, G_2, and I_2(m). The root type and the minimal type Lax pairs, derived in our previous papers, are given as the simplest representations. The spectral parameter dependence plays an important role in the Lax pair operators, which bear a strong resemblance to the Dunkl operators, a powerful tool for solving quantum Calogero-Moser models.Comment: 37 pages, LaTeX2e, no macro, no figur

Establishing the potential for using routine data on Incapacity Benefit to assess the local impact of policy initiatives

<i>Background</i>: Incapacity Benefit (IB) is the key contributory benefit for people who are incapable of work because of illness or disability. <i>Methods</i>: The aims were to establish the utility of routinely collected data for local evaluation and to provide a descriptive epidemiology of the IB population in Glasgow and Scotland for the period 2000–05 using data supplied by the Department for Work and Pensions. <i>Results</i>: Glasgow's IB population is large in absolute and relative terms but is now falling, mainly due to a decrease in on flow. Claimants, tend to be older, have a poor work history and suffer from mental health problems. The rate of decline has been greater in Glasgow than Scotland, although the rate of on flow is still higher. <i>Conclusions</i>: Department for Work and Pensions (DWP) data can be used locally to provide important insights into the dynamics of the IB population. However, to be truly useful, more work needs to be undertaken to combine the DWP data with other information

A new code for parameter estimation in searches for gravitational waves from known pulsars

We describe the consistency testing of a new code for gravitational wave signal parameter estimation in known pulsar searches. The code uses an implementation of nested sampling to explore the likelihood volume. Using fake signals and simulated noise we compare this to a previous code that calculated the signal parameter posterior distributions on both a grid and using a crude Markov chain Monte Carlo (MCMC) method. We define a new parameterisation of two orientation angles of neutron stars used in the signal model (the initial phase and polarisation angle), which breaks a degeneracy between them and allows more efficient exploration of those parameters. Finally, we briefly describe potential areas for further study and the uses of this code in the future.Comment: Accepted for proceedings of Amaldi 9 meetin

Comparison of methods for estimating continuous distributions of relaxation times

The nonparametric estimation of the distribution of relaxation times approach is not as frequently used in the analysis of dispersed response of dielectric or conductive materials as are other immittance data analysis methods based on parametric curve fitting techniques. Nevertheless, such distributions can yield important information about the physical processes present in measured material. In this letter, we apply two quite different numerical inversion methods to estimate the distribution of relaxation times for glassy \lila\ dielectric frequency-response data at 225 \kelvin. Both methods yield unique distributions that agree very closely with the actual exact one accurately calculated from the corrected bulk-dispersion Kohlrausch model established independently by means of parametric data fit using the corrected modulus formalism method. The obtained distributions are also greatly superior to those estimated using approximate functions equations given in the literature.Comment: 4 pages and 4 figure

Introduction: culture mangling: conflict and dissonance in modern language studies

Introduction to the Culture Mangle volume. Locates the essays in the context of divergences and differences of preoccupation in cultural studies as practiced in the different areas of modern language studies in the UK and US. To this end the piece explores tensions and fault lines in constructions of territory, history and identity in various language area disciplines within modern language studies, concentrating notably on Aleksander Sokurov’s Russian Ark (2002), a lavish vision of the Hermitage museum’s reflective condensation of conflicting and desiring visions and articulations of cultural memory