A survey of the UK benefit system

This paper describes all the main benefits in the UK system, giving details of rates and allowances, as well as numbers and types of claimants and levels of expenditure

The Kinematic and Plasma Properties of X-ray Knots in Cassiopeia A from the Chandra HETGS

We present high-resolution X-ray spectra from the young supernova remnant Cas A using a 70-ks observation taken by the Chandra High Energy Transmission Grating Spectrometer (HETGS). Line emission, dominated by Si and S ions, is used for high-resolution spectral analysis of many bright, narrow regions of Cas A to examine their kinematics and plasma state. These data allow a 3D reconstruction using the unprecedented X-ray kinematic results: we derive unambiguous Doppler shifts for these selected regions, with values ranging between -2500 and +4000 km/s. Plasma diagnostics of these regions, derived from line ratios of resolved He-like triplet lines and H-like lines of Si, indicate temperatures largely around 1 keV, which we model as O-rich reverse-shocked ejecta. The ionization age also does not vary considerably over these regions of the remnant. The gratings analysis was complemented by the non-dispersed spectra from the same dataset, which provided information on emission measure and elemental abundances for the selected Cas A regions. The derived electron density of X-ray emitting ejecta varies from 20 to 200 cm^{-3}. The measured abundances of Mg, Si, S and Ca are consistent with O being the dominant element in the Cas A plasma. With a diameter of 5 arcmin, Cas A is the largest source observed with the HETGS to date. We, therefore, describe the technique we use and some of the challenges we face in the HETGS data reduction from such an extended, complex object.Comment: 26 pages, 16 figures, evised version (minor changes), accepted for publication in ApJ (Oct 20 2006

Revisiting Multi-Subject Random Effects in fMRI: Advocating Prevalence Estimation

Random Effects analysis has been introduced into fMRI research in order to generalize findings from the study group to the whole population. Generalizing findings is obviously harder than detecting activation in the study group since in order to be significant, an activation has to be larger than the inter-subject variability. Indeed, detected regions are smaller when using random effect analysis versus fixed effects. The statistical assumptions behind the classic random effects model are that the effect in each location is normally distributed over subjects, and "activation" refers to a non-null mean effect. We argue this model is unrealistic compared to the true population variability, where, due to functional plasticity and registration anomalies, at each brain location some of the subjects are active and some are not. We propose a finite-Gaussian--mixture--random-effect. A model that amortizes between-subject spatial disagreement and quantifies it using the "prevalence" of activation at each location. This measure has several desirable properties: (a) It is more informative than the typical active/inactive paradigm. (b) In contrast to the hypothesis testing approach (thus t-maps) which are trivially rejected for large sample sizes, the larger the sample size, the more informative the prevalence statistic becomes. In this work we present a formal definition and an estimation procedure of this prevalence. The end result of the proposed analysis is a map of the prevalence at locations with significant activation, highlighting activations regions that are common over many brains

Asphericity and clumpiness in the winds of Luminous Blue Variables

We present the first systematic spectropolarimetric study of Luminous Blue Variables (LBVs) in the Galaxy and the Magellanic Clouds, in order to investigate the geometries of their winds. We find that at least half of our sample show changes in polarization across the strong H$\alpha$ emission line, indicating that the light from the stars is intrinsically polarized and therefore that asphericity already exists at the base of the wind. Multi-epoch spectropolarimetry on four targets reveals variability in their intrinsic polarization. Three of these, AG Car, HR Car and P Cyg, show a position angle (PA) of polarization which appears random with time. Such behaviour can be explained by the presence of strong wind-inhomogeneities, or `clumps' within the wind. Only one star, R 127, shows variability at a constant PA, and hence evidence for axi-symmetry as well as clumpiness. However, if viewed at low inclination, and at limited temporal sampling, such a wind would produce a seemingly random polarization of the type observed in the other three stars. Time-resolved spectropolarimetric monitoring of LBVs is therefore required to determine if LBV winds are axi-symmetric in general. The high fraction of LBVs ($>$ 50%) showing intrinsic polarization is to be compared with the lower $\sim$ 20-25 % for similar studies of their evolutionary neighbours, O supergiants and Wolf-Rayet stars. We anticipate that this higher incidence is due to the lower effective gravities of the LBVs, coupled with their variable temperatures within the bi-stability jump regime. This is also consistent with the higher incidence of wind asphericity that we find in LBVs with strong H$\alpha$ emission and recent (last $\sim$ 10 years) strong variability.Comment: 20 pages, 12 figures, accepted by A&

Combining Insertion and Deletion in RNA-editing Preserves Regularity

Inspired by RNA-editing as occurs in transcriptional processes in the living cell, we introduce an abstract notion of string adjustment, called guided rewriting. This formalism allows simultaneously inserting and deleting elements. We prove that guided rewriting preserves regularity: for every regular language its closure under guided rewriting is regular too. This contrasts an earlier abstraction of RNA-editing separating insertion and deletion for which it was proved that regularity is not preserved. The particular automaton construction here relies on an auxiliary notion of slice sequence which enables to sweep from left to right through a completed rewrite sequence.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347

Probing the evolving massive star population in Orion with kinematic and radioactive tracers

We assemble a census of the most massive stars in Orion, then use stellar isochrones to estimate their masses and ages, and use these results to establish the stellar content of Orion's individual OB associations. From this, our new population synthesis code is utilized to derive the history of the emission of UV radiation and kinetic energy of the material ejected by the massive stars, and also follow the ejection of the long-lived radioactive isotopes 26Al and 60Fe. In order to estimate the precision of our method, we compare and contrast three distinct representations of the massive stars. We compare the expected outputs with observations of 26Al gamma-ray signal and the extent of the Eridanus cavity. We find an integrated kinetic energy emitted by the massive stars of 1.8(+1.5-0.4)times 10^52 erg. This number is consistent with the energy thought to be required to create the Eridanus superbubble. We also find good agreement between our model and the observed 26Al signal, estimating a mass of 5.8(+2.7-2.5) times 10^-4 Msol of 26Al in the Orion region. Our population synthesis approach is demonstrated for the Orion region to reproduce three different kinds of observable outputs from massive stars in a consistent manner: Kinetic energy as manifested in ISM excavation, ionization as manifested in free-free emission, and nucleosynthesis ejecta as manifested in radioactivity gamma-rays. The good match between our model and the observables does not argue for considerable modifications of mass loss. If clumping effects turn out to be strong, other processes would need to be identified to compensate for their impact on massive-star outputs. Our population synthesis analysis jointly treats kinematic output and the return of radioactive isotopes, which proves a powerful extension of the methodology that constrains feedback from massive stars.Comment: Accepted for publication in A&A, 10 page

Fluids with quenched disorder: Scaling of the free energy barrier near critical points

In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of the critical point and the critical exponents. For Ising-like systems without quenched disorder, $P_L(m)$ becomes scale invariant at the critical point, where it assumes a characteristic bimodal shape featuring two overlapping peaks. In particular, the ratio between the value of $P_L(m)$ at the peaks ($P_{L, max}$) and the value at the minimum in-between ($P_{L, min}$) becomes $L$-independent at criticality. However, for Ising-like systems with quenched random fields, we argue that instead $\Delta F_L := \ln (P_{L, max} / P_{L, min}) \propto L^\theta$ should be observed, where $\theta>0$ is the "violation of hyperscaling" exponent. Since $\theta$ is substantially non-zero, the scaling of $\Delta F_L$ with system size should be easily detectable in simulations. For two fluid models with quenched disorder, $\Delta F_L$ versus $L$ was measured, and the expected scaling was confirmed. This provides further evidence that fluids with quenched disorder belong to the universality class of the random-field Ising model.Comment: sent to J. Phys. Cond. Mat