Hamiltonians of spherical Galaxies in action-angle coordinates

We present a simple formula for the Hamiltonian in terms of the actions for spherically symmetric, scale-free potentials. The Hamiltonian is a power-law or logarithmic function of a linear combination of the actions. Our expression reduces to the well-known results for the familiar cases of the harmonic oscillator and the Kepler potential. For other power-laws, as well as for the singular isothermal sphere, it is exact for the radial and circular orbits, and very accurate for general orbits. Numerical tests show that the errors are always small, with mean errors across a grid of actions always less than 1 % and maximum errors less than 2.5 %. Simple first-order corrections can reduce mean errors to less than 0.6 % and maximum errors to less than 1 %. We use our new result to show that :[1] the misalignment angle between debris in a stream and a progenitor is always very nearly zero in spherical scale-free potentials, demonstrating that streams can be sometimes well approximated by orbits, [2] the effects of an adiabatic change in the stellar density profile in the inner regions of a galaxy weaken any existing 1/r density cusp, which is reduced to $1/r^{1/3}$. More generally, we derive the full range of adiabatic cusp transformations and show how to relate the starting cusp index to the final cusp index. It follows that adiabatic transformations can never erase a dark matter cusp.AW and AB acknowledge the support of STFC

Absolutism, Relativism and Anarchy: Alain Locke and William James on Value Pluralism

This paper aims to compare the pluralistic theories of James and Locke on the three criteria by which Locke proposes that any pluralistic axiology should be assessed: normativity, objectivity and loyalty. A pluralistic account of value must be able to account for the normativity of particular value systems without appealing to universal standards. It must be able to provide some objective ground for value so that different values can be constructively compared across cultures, without becoming monistic. And it must provide an account which still allows people to find their particular values meaningful and motivating, whilst at the same time encouraging tolerance for differing values. The conclusion of the paper will be that, despite Locke's accusation of anarchism, James's appeal to a limited form of realism means that his theory is better placed to meet these three criteria

Kidnapping an ugly child: is William James a pragmaticist?

Since the term ‘pragmatism’ was first coined, there have been debates about who is or is not a ‘real’ pragmatist, and what that might mean. The division most often drawn in contemporary pragmatist scholarship is between William James and Charles Peirce. Peirce is said to present a version of pragmatism which is scientific, logical and objective about truth, whereas James presents a version which is nominalistic, subjectivistic and leads to relativism. The first person to set out this division was in fact Peirce himself, when he distinguished his own ‘pragmaticism’ from the broad pragmatism of James and others. Peirce sets out six criteria which defines ‘pragmaticism’: the pragmatic maxim; a number of ‘preliminary propositions’; prope-positivism; metaphysical inquiry; critical common-sensism; and scholastic realism. This paper sets out to argue that in fact James meets each of these criteria, and should be seen as a ‘pragmaticist’ by Peirce’s own lights

Models of bars - I. Flattish profiles for early-type galaxies

We introduce a simple family of barred galaxy models with flat rotation curves. They are built by convolving the axisymmetric logarithmic model with a needle density. The density contours in the bar region are highly triaxial and elongated, but become spheroidal in the outer parts. The mass distribution differs markedly from the elliptical shape assumed in other analytical models, like Ferrers or Freeman bars. The surface density profile along the bar major axis is flattish, as befits models for bars in early-type galaxies (SB0, SBa). The 2D orbital structure of the models is analysed with surfaces of section and characteristic diagrams and it reveals qualitatively new features. For some pattern speeds, additional Lagrange points can exist along the major axis and give rise to off-centred, trapped orbits. When the bar is weak, the orbital structure is very simple, comprising just prograde, aligned x1 orbits and retrograde anti-aligned x4 orbits. As the bar strength increases, the x1 family becomes unstable and vanishes, with propeller orbits dominating the characteristic diagram

The alignment of the second velocity moment tensor in galaxies

We show that provided the principal axes of the second velocity moment tensor of a stellar population are generally unequal and are oriented perpendicular to a set of orthogonal surfaces at each point, then those surfaces must be confocal quadric surfaces and the potential must be separable or Stäckel. This is true under the mild assumption that the even part of the distribution function (DF) is invariant under time reversal vi → −vi of each velocity component. In particular, if the second velocity moment tensor is everywhere exactly aligned in spherical polar coordinates, then the potential must be of separable or Stäckel form (excepting degenerate cases where two or more of the semiaxes of ellipsoid are everywhere the same). The theorem also has restrictive consequences for alignment in cylindrical polar coordinates, which is used in the popular Jeans Anisotropic Models (JAM) of Cappellari. We analyse data on the radial velocities and proper motions of a sample of ∼7300 stars in the stellar halo of the Milky Way. We provide the distributions of the tilt angles or misalignments from both the spherical polar coordinate systems. We show that in this sample the misalignment is always small (usually within 3°) for Galactocentric radii between ∼6 and ∼11 kpc. The velocity anisotropy is very radially biased (β ≈ 0.7), and almost invariant across the volume in our study. Finally, we construct a triaxial stellar halo in a triaxial NFW dark matter halo using a made-to-measure method. Despite the triaxiality of the potential, the velocity ellipsoid of the stellar halo is nearly spherically aligned within ∼6° for large regions of space, particularly outside the scale radius of the stellar halo. We conclude that the second velocity moment ellipsoid can be close to spherically aligned for a much wider class of potentials than the strong constraints that arise from exact alignment might suggest

Occupational lung diseases among former goldminers in two labour sending areas

Objectives. To compare and contrast the prevalence of pneumoconiosis in two groups of former migrant mineworkers in southern Africa, and to examine the effectiveness of the South African compensation system for occupational lung diseases.Design. Comparison of two cross-sectional studies and follow-up data on compensation results.Setting. The village of Thamaga, Botswana and the rural area of Libode, Eastern Cape, South Africa.Subjects. Two hundred and thirty-four former underground mineworkers in Thamaga, and 238 in Libode. Main outcome measures. Prevalence and severity of pneumoconiosis, prevalence of radiological signs of tuberculosis (TB), Medical Bureau for Occupational Diseases (MBOD) certification committee decisions, and compensation results.Results. Prevalence of pneumoconiosis ≥ 2/ 1 was 15.4% in Libode and 13.6% in Thamaga. Significantly more Libode than Thamaga subjects (51.1% versus 29.0%) reported past TB treatment Radiological signs of pulmonary TB were also more prevalent in Libode (33.3% v. 23.9%). Twenty-six per cent of Libode men and 16.1% of Thamaga men were certified with compensable disease. Libode payments were finalised within 30 months, whereas Thamaga cases only began receiving payments 52 months after medical  examination, with 11 cases still pending 66 months after medical examination.Conclusion. There was a high prevalence of pneumoconiosis in both study groups. Many men were eligible for compensation but were previously uncompensated. The higher rate of compensable disease in the Libode group may relate to the higher prevalence of TB, as well as more active follow-up by the study group, including a large number of appeals. Socio-political changes in South Africa between 1994 and 1996 may also have influenced compensation results

Features of GBA-associated Parkinson’s disease at presentation in the UK Tracking Parkinson’s study

Objectives: To examine the influence of the glucocerebrosidase (GBA) mutation carrier state on age at onset of Parkinson’s disease (PD), the motor phenotype and cognitive function at baseline assessment in a large cohort of UK patients. We also analysed the prevalence of mood and behavioural problems that may confound the assessment of cognitive function. Methods: We prospectively recruited patients with PD in the Tracking Parkinson’s study. We fully sequenced the GBA gene in all recently diagnosed patients (≤3.5 years). We examined cognitive (Montreal Cognitive Assessment) and motor (Movement Disorder Society Unified Parkinson’s Disease Rating Scale part 3) function at a baseline assessment, at an average of 1.3 years after diagnosis. We used logistic regression to determine predictors of PD with mild cognitive impairment and PD with dementia. Results: We studied 1893 patients with PD: 48 (2.5%) were heterozygous carriers for known Gaucher’s disease (GD) causing pathogenic mutations; 117 (6.2%) had non-synonymous variants, previously associated with PD, and 28 (1.5%) patients carried variants of unknown significance in the GBA gene. L444P was the most common pathogenic GBA mutation. Patients with pathogenic GBA mutations were on average 5 years younger at disease onset compared with non-carriers (P=0.02). PD patients with GD-causing mutations did not have an increased family risk of PD. Patients with GBA mutations were more likely to present with the postural instability gait difficulty phenotype compared with non-carriers (P=0.02). Patients carrying pathogenic mutations in GBA had more advanced Hoehn and Yahr stage after adjustment for age and disease duration compared with non-carriers (P=0.005). There were no differences in cognitive function between GBA mutation carriers and non-carriers at this early disease stage. Conclusions: Our study confirms the influence of GBA mutations on the age of onset, disease severity and motor phenotype in patients with PD. Cognition did not differ between GBA mutation carriers and non-carriers at baseline, implying that cognitive impairment/dementia, reported in other studies at a later disease stage, is not present in recently diagnosed cases. This offers an important window of opportunity for potential disease-modifying therapy that may protect against the development of dementia in GBA-PD. Clinical trial registration: NCT02881099; Results

Temporal dynamics of aquatic communities and implications for pond conservation

Conservation through the protection of particular habitats is predicated on the assumption that the conservation value of those habitats is stable. We test this assumption for ponds by investigating temporal variation in macroinvertebrate and macrophyte communities over a 10-year period in northwest England. We surveyed 51 ponds in northern England in 1995/6 and again in 2006, identifying all macrophytes (167 species) and all macroinvertebrates (221 species, excluding Diptera) to species. The alpha-diversity, beta-diversity and conservation value of these ponds were compared between surveys. We find that invertebrate species richness increased from an average of 29. 5 species to 39. 8 species between surveys. Invertebrate gamma-diversity also increased between the two surveys from 181 species to 201 species. However, this increase in diversity was accompanied by a decrease in beta-diversity. Plant alpha-, beta and gamma-diversity remained approximately constant between the two periods. However, increased proportions of grass species and a complete loss of charophytes suggests that the communities are undergoing succession. Conservation value was not correlated between sampling periods in either plants or invertebrates. This was confirmed by comparing ponds that had been disturbed with those that had no history of disturbance to demonstrate that levels of correlation between surveys were approximately equal in each group of ponds. This study has three important conservation implications: (i) a pond with high diversity or high conservation value may not remain that way and so it is unwise to base pond conservation measures upon protecting currently-speciose habitats; (ii) maximising pond gamma-diversity requires a combination of late and early succession ponds, especially for invertebrates; and (iii) invertebrate and plant communities in ponds may require different management strategies if succession occurs at varying rates in the two groups

Exploring differential item functioning in the SF-36 by demographic, clinical, psychological and social factors in an osteoarthritis population

The SF-36 is a very commonly used generic measure of health outcome in osteoarthritis (OA). An important, but frequently overlooked, aspect of validating health outcome measures is to establish if items work in the same way across subgroup of a population. That is, if respondents have the same 'true' level of outcome, does the item give the same score in different subgroups or is it biased towards one subgroup or another. Differential item functioning (DIF) can identify items that may be biased for one group or another and has been applied to measuring patient reported outcomes. Items may show DIF for different conditions and between cultures, however the SF-36 has not been specifically examined in an osteoarthritis population nor in a UK population. Hence, the aim of the study was to apply the DIF method to the SF-36 for a UK OA population. The sample comprised a community sample of 763 people with OA who participated in the Somerset and Avon Survey of Health. The SF-36 was explored for DIF with respect to demographic, social, clinical and psychological factors. Well developed ordinal regression models were used to identify DIF items. Results: DIF items were found by age (6 items), employment status (6 items), social class (2 items), mood (2 items), hip v knee (2 items), social deprivation (1 item) and body mass index (1 item). Although the impact of the DIF items rarely had a significant effect on the conclusions of group comparisons, in most cases there was a significant change in effect size. Overall, the SF-36 performed well with only a small number of DIF items identified, a reassuring finding in view of the frequent use of the SF-36 in OA. Nevertheless, where DIF items were identified it would be advisable to analyse data taking account of DIF items, especially when age effects are the focus of interest