Spin chains and channels with memory

In most studies of the channel capacity of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error. This work has led to speculation that interesting non-analytic behaviour may occur in the capacity. Motivated by these observations, we connect the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables us the techniques of many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error. The models can display analogous behaviour to associated many-body systems, including `phase transitions'.Comment: V2: changes in presentation, some additional comments on generalisation. V3: In accordance with published version, most (but not all) details of proofs now included. A separate paper will shortly be submitted separately with all details and more result

An Economic analysis of the potential for precision farming in UK cereal production

The results from alternative spatial nitrogen application studies are analysed in economic terms and compared to the costs of precision farming hardware, software and other services for cereal crops in the UK. At current prices, the benefits of variable rate application of nitrogen exceed the returns from a uniform application by an average of £22 ha−1 The cost of the precision farming systems range from £5 to £18 ha−1 depending upon the system chosen for an area of 250 ha. The benefits outweigh the associated costs for cereal farms in excess of 80 ha for the lowest price system to 200–300 ha for the more sophisticated systems. The scale of benefits obtained depends upon the magnitude of the response to the treatment and the proportion of the field that will respond. To be cost effective, a farmed area of 250 ha of cereals, where 30% of the area will respond to variable treatment, requires an increase in crop yield in the responsive areas of between 0·25 and 1.00 t ha−1 (at £65 t−1) for the basic and most expensive precision farming systems, respectively

Using Geographic Information Systems to investigate variations in accessibility to ‘extended hours’ primary healthcare provision

There are ongoing policy concerns surrounding the difficulty in obtaining timely appointments to primary healthcare services and the potential impact on, for example, attendance at accident and emergency services and potential health outcomes. Using the case study of potential access to primary healthcare services in Wales, Geographic Information System (GIS)‐based tools that permit a consideration of population‐to‐provider ratios over space are used to examine variations in geographical accessibility to general practitioner (GP) surgeries offering appointment times outside of ‘core’ operating hours. Correlation analysis is used to explore the association of accessibility scores with potential demand for such services using UK Population Census data. Unlike the situation in England, there is a tendency for accessibility to those surgeries offering ‘extended’ hours of appointment times to be better for more deprived census areas in Wales. However, accessibility to surgeries offering appointments in the evening was associated with lower levels of working age population classed as ‘economically active’; that is, those who could be targeted beneficiaries of policies geared towards ‘extended’ appointment hours provision. Such models have the potential to identify spatial mismatches of different facets of primary healthcare, such as ‘extended’ hours provision available at GP surgeries, and are worthy of further investigation, especially in relation to policies targeted at particular demographic groups

High ions towards white dwarfs: circumstellar line shifts and stellar temperature

Based on a compilation of OVI, CIV, SiIV and NV data from IUE, FUSE, GHRS, STIS, and COS, we derive an anti- correlation between the stellar temperature and the high ion velocity shift w.r.t. to the photosphere, with positive (resp. negative) velocity shifts for the cooler (resp. hotter) white dwarfs. This trend probably reflects more than a single process, however such a dependence on the WD's temperature again favors a CS origin for a very large fraction of those ion absorptions, previously observed with IUE, HST-STIS, HST-GHRS, FUSE, and now COS, selecting objects for which absorption line radial velocities, stellar effective temperature and photospheric velocity can be found in the literature. Interestingly, and gas in near-equilibrium in the star vicinity. It is also probably significant that the temperature that corresponds to a null radial velocity, i.e. \simeq 50,000K, also corresponds to the threshold below which there is a dichotomy between pure or heavy elements atmospheres as well as some temperature estimates for and a form of balance between radiation pressure and gravitation. This is consistent with ubiquitous evaporation of orbiting dusty material. Together with the fact that the fraction of stars with (red-or blue-) shifted lines and the fraction of stars known to possess heavy species in their atmosphere are of the same order, such a velocity-temperature relationship is consistent with quasi-continuous evaporation of orbiting CS dusty material, followed by accretion and settling down in the photosphere. In view of these results, ion measurements close to the photospheric or the IS velocity should be interpreted with caution, especially for stars at intermediate temperatures. While tracing CS gas, they may be erroneously attributed to photospheric material or to the ISM, explaining the difficulty of finding a coherent pattern of the high ions in the local IS 3D distribution.Comment: Accepted by A&A. Body of paper identical to v1. This submission has a more appropriate truncation of the original abstrac

On the fundamental group of the complement of a complex hyperplane arrangement

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the complement to a line arrangement of a given combinatorial type with respect to isomorphisms inducing the canonical isomorphism of the first homology groups.Comment: 12 pages, Latex2e with AMSLaTeX 1.2, no figures; this last version is almost the same as published in Functional Analysis and its Applications 45:2 (2011), 137-14