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

A two-fluid model for tissue growth within\ud a dynamic flow environment

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study (Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89).\ud \ud The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a mechanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population

Environment of compact extragalactic radio sources

We have studied the interrelation of young AGN with their hosts. The objects of study are the young and powerful GPS and CSS radio sources. Due to their small size, GPS and CSS sources are excellent probes of this relation. Furhthermore, their young age allows us to compare them to the larger, old radio sources and establish a time-line evolution of this relation. Combining imaging and spectroscopy at UV, optical and radio wavelengths we find evidence of strong interaction between the host and the radio source. The presence and expansion of the radio source clearly affects the properties and evolution of the host. Furthermore, the radio source and host significantly affect each other's evolution. We describe our results and how these interactions take place.Comment: 6 pages. To appear in "Highlights of Spanisg astrophysics IV. Proceedings of the VII scientific meeting of the Spanish Astronomical Society". Editors: F. Figueras, J.M. Girart, M.Hernanz, C. Jordi. Springe

Spectral variability in faint high frequency peakers

We present the analysis of simultaneous multi-frequency Very Large Array (VLA) observations of 57 out of 61 sources from the ``faint'' high frequency peaker (HFP) sample carried out in various epochs. Sloan Digital Sky Survey (SDSS) data have been used to identify the optical counterpart of each radio source. From the analysis of the multi-epoch spectra we find that 24 sources do not show evidence of spectral variability, while 12 objects do not possess a peaked spectrum anymore at least in one of the observing epochs. Among the remaining 21 sources showing some degree of variability, we find that in 8 objects the spectral properties change consistently with the expectation for a radio source undergoing adiabatic expansion. The comparison between the variability and the optical identification suggests that the majority of radio sources hosted in galaxies likely represent the young radio source population, whereas the majority of those associated with quasars are part of a different population similar to flat-spectrum objects, which possess peaked spectra during short intervals of their life, as found in other samples of high-frequency peaking objects. The analysis of the optical images from the SDSS points out the presence of companions around 6 HFP hosted in galaxies, suggesting that young radio sources resides in groups.Comment: 16 pages, 5 figures; accepted for publication in MNRA

Multiscale analysis of pattern formation via intercellular signalling

Lateral inhibition, a juxtacrine signalling mechanism by which a cell adopting a particular fate inhibits neighbouring cells from doing likewise, has been shown to be a robust mechanism for the formation of fine-grained spatial patterns (in which adjacent cells in developing tissues diverge to achieve contrasting states of differentiation), provided that there is sufficiently strong feedback. The fine-grained nature of these patterns poses problems for analysis via traditional continuum methods since these require that significant variation takes place only over lengthscales much larger than an individual cell and such systems have therefore been investigated primarily using discrete methods. Here, however, we apply a multiscale method to derive systematically a continuum model from the discrete Delta-Notch signalling model of Collier \emph{et al.} (Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling, \emph{J. Theor. Biol.}, 183, 1996, 429--446) under particular assumptions on the parameters, which we use to analyse the generation of fine-grained patterns. We show that, on the macroscale, the contact-dependent juxtacrine signalling interaction manifests itself as linear diffusion, motivating the use of reaction-diffusion-based models for such cell-signalling systems. We also analyse the travelling-wave behaviour of our system, obtaining good quantitative agreement with the discrete system

The isolation of spatial patterning modes in a mathematical model of juxtacrine cell signalling

Juxtacrine signalling mechanisms are known to be crucial in tissue and organ development, leading to spatial patterns in gene expression. We investigate the patterning behaviour of a discrete model of juxtacrine cell signalling due to Owen \& Sherratt (\emph{Math. Biosci.}, 1998, {\bf 153}(2):125--150) in which ligand molecules, unoccupied receptors and bound ligand-receptor complexes are modelled. Feedback between the ligand and receptor production and the level of bound receptors is incorporated. By isolating two parameters associated with the feedback strength and employing numerical simulation, linear stability and bifurcation analysis, the pattern-forming behaviour of the model is analysed under regimes corresponding to lateral inhibition and induction. Linear analysis of this model fails to capture the patterning behaviour exhibited in numerical simulations. Via bifurcation analysis we show that, since the majority of periodic patterns fold subcritically from the homogeneous steady state, a wide variety of stable patterns exists at a given parameter set, providing an explanation for this failure. The dominant pattern is isolated via numerical simulation. Additionally, by sampling patterns of non-integer wavelength on a discrete mesh, we highlight a disparity between the continuous and discrete representations of signalling mechanisms: in the continuous case, patterns of arbitrary wavelength are possible, while sampling such patterns on a discrete mesh leads to longer wavelength harmonics being selected where the wavelength is rational; in the irrational case, the resulting aperiodic patterns exhibit `local periodicity', being constructed from distorted stable shorter-wavelength patterns. This feature is consistent with experimentally observed patterns, which typically display approximate short-range periodicity with defects

Extended emission around GPS radio sources

Extended radio emission detected around a sample of GHz Peaked Spectrum (GPS) radio sources is discussed. Evidence for extended emission which is related to the GPS source is found in 6 objects out of 33. Three objects are associated with quasars with core-jet pc-scale morphology, and three are identified with galaxies with symmetric (CSO) radio morphology. We conclude that the core-jet GPS quasars are likely to be beamed objects with a continuous supply of energy from the core to the kpc scale. It is also possible that low surface brightness extended radio emission is present in other GPS quasars but the emission is below our detection limit due to the high redshifts of the objects. On the other hand, the CSO/galaxies with extended large scale emission may be rejuvenated sources where the extended emission is the relic of previous activity. In general, the presence of large scale emission associated with GPS galaxies is uncommon, suggesting that in the context of the recurrent activity model, the time scale between subsequent bursts is in general longer than the radiative lifetime of the radio emission from the earlier activity.Comment: 18 paged, 18 figures, accepted for publication on A&

Atomic hydrogen in the one-sided "compact double" radio galaxy 2050+364

European VLBI Network spectral imaging of the "compact double" radio source 2050+364 in the UHF band at 1049 MHz has resolved the HI absorbing region, and has shown a faint continuum component to the North (N), in addition to the well-known East-West double (E, W). Re-examination of VLBI continuum images at multiple frequencies suggests that 2050+364 may well be a one-sided core-jet source, which appears as a double over a limited frequency range. One of the dominant features, W, would then be the innermost visible portion of the jet, and could be at or adjacent to the canonical radio core. The other, E, is probably related to shocks at a sudden bend of the jet, towards extended steep-spectrum region N. A remarkably deep and narrow HI absorption line component extends over the entire projected extent of 2050+364. It coincides in velocity with the [OIII] optical doublet lines to within 10 km/s. This HI absorption could arise in the atomic cores of NLR clouds, and the motion in the NLR is then remarkably coherent both along the line-of-sight and across a projected distance of > 300 pc on the plane of the sky. Broader, shallower HI absorption at lower velocities covers only the plausible core area W. This absorption could be due to gas which is either being entrained by the inner jet or is flowing out from the accretion region; it could be related to the BLR.Comment: 10 pages, 7 figures. Accepted in A&