The structure of one-relator relative presentations and their centres

Suppose that G is a nontrivial torsion-free group and w is a word in the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\} such that the word w' obtained from w by erasing all letters belonging to G is not a proper power in the free group F(x_1,...,x_n). We show how to reduce the study of the relative presentation \^G= to the case n=1. It turns out that an "n-variable" group \^G can be constructed from similar "one-variable" groups using an explicit construction similar to wreath product. As an illustration, we prove that, for n>1, the centre of \^G is always trivial. For n=1, the centre of \^G is also almost always trivial; there are several exceptions, and all of them are known.Comment: 15 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm . V4: the intoduction is rewritten; Section 1 is extended; a short introduction to Secton 5 is added; some misprints are corrected and some cosmetic improvements are mad

Risk of cancer following primary total hip replacement or primary resurfacing arthroplasty of the hip : A retrospective cohort study in Scotland

Acknowledgements: We are grateful to Lee Barnsdale, Doug Clark, and Richard Dobbie for advice and assistance with data preparation before analysis, and to the three anonymous referees for their helpful comments and suggestions.Peer reviewedPublisher PD

Patient enablement requires physician empathy: a cross-sectional study of general practice consultations in areas of high and low socioeconomic deprivation in Scotland

<b>Background</b> Patient 'enablement' is a term closely aligned with 'empowerment' and its measurement in a general practice consultation has been operationalised in the widely used patient enablement instrument (PEI), a patient-rated measure of consultation outcome. However, there is limited knowledge regarding the factors that influence enablement, particularly the effect of socio-economic deprivation. The aim of the study is to assess the factors influencing patient enablement in GP consultations in areas of high and low deprivation.<p></p> <b>Methods</b> A questionnaire study was carried out on 3,044 patients attending 26 GPs (16 in areas of high socio-economic deprivation and 10 in low deprivation areas, in the west of Scotland). Patient expectation (confidence that the doctor would be able to help) was recorded prior to the consultation. PEI, GP empathy (measured by the CARE Measure), and a range of other measures and variables were recorded after the consultation. Data analysis employed multi-level modelling and multivariate analyses with the PEI as the dependant variable.<p></p> <b>Results</b> Although numerous variables showed a univariate association with patient enablement, only four factors were independently predictive after multilevel multivariate analysis; patients with multimorbidity of 3 or more long-term conditions (reflecting poor chronic general health), and those consulting about a long-standing problem had reduced enablement scores in both affluent and deprived areas. In deprived areas, emotional distress (GHQ-caseness) had an additional negative effect on enablement. Perceived GP empathy had a positive effect on enablement in both affluent and deprived areas. Maximal patient enablement was never found with low empathy.<p></p> <b>Conclusions</b> Although other factors influence patient enablement, the patients' perceptions of the doctors' empathy is of key importance in patient enablement in general practice consultations in both high and low deprivation settings

Measurement of Respiratory Chain Enzyme Activity in Human Renal Biopsy Specimens

Background: Mitochondrial disorders can present as kidney disease in children and be difficult to diagnose. Measurement of mitochondrial function in kidney tissue may help diagnosis. This study was to assess the feasibility of obtaining renal samples and analysing them for respiratory chain enzyme activity. Methods: The subjects were children undergoing a routine diagnostic renal biopsy, in whom a clinical condition of renal inflammation, scarring and primary metabolic disorder was unlikely. A fresh sample of kidney was snap frozen and later assayed for the activities of respiratory chain enzyme complexes I, II/III, and IV using spectrophotometric enzyme assay, and expressed as a ratio of citrate synthase activity. Results: The range of respiratory chain enzyme activity for complex I was 0.161 to 0.866 (mean 0.404, SD 0.2), for complex II/III was 0.021 to 0.318 (mean 0.177, SD 0.095) and for complex IV was 0.001 to 0.025 (mean 0.015, SD 0.006). There were correlations between the different activities but not between them and the age of the children or a measure of the amount of chronic damage in the kidneys. Conclusion: It is feasible to measure respiratory chain enzyme activity in routine renal biopsy specimens

Scottish theme towns: have new identities enhanced development?

Three small towns in southwest Scotland have recently been branded as distinct theme towns, based on books, artists and food. This is an attempt to make them more attractive to visitors and thereby improve their economy. The objective of this research is to establish whether the new identities possessed by the towns have enhanced their development. It is argued, using data reviewing the past decade, that they have all developed, albeit at different rates, in terms of the economy and culture. Moreover, it is maintained that social capital has been enhanced and is a factor whose importance has been under-appreciated by planners and observers of this type of process. The relevance of the new identity to the pre-branding identity is also seen as a factor in successful development and ideas of authenticity and heritage are brought to bear on the relationship

Blaming Bill Gates AGAIN! Misuse, overuse and misunderstanding of performance data in sport

Recently in Sport, Education and Society, Williams and Manley (2014) argued against the heavy reliance on technology in professional Rugby Union and elite sport in general. In summary, technology is presented as an elitist, ‘gold standard’ villain that management and coaches use to exert control and by which players lose autonomy, identity, motivation, social interactions and expertise. In this article we suggest that the sociological interpretations and implications offered by Williams and Manley may be somewhat limited when viewed in isolation. In doing so, we identify some core methodological issues in Williams and Manley’s study and critically consider important arguments for utilising technology; notably, to inform coach decision making and generate player empowerment. Secondly, we present a different, yet perhaps equally concerning, practice-oriented interpretation of the same results but from alternative coaching and expertise literature. Accordingly, we suggest that Williams and Manley have perhaps raised their alarm prematurely, inappropriately and on somewhat shaky foundations. We also hope to stimulate others to consider contrary positions, or at least to think about this topic in greater detail. More specifically, we encourage coaches and academics to think carefully about what technology is employed, how and why, and then the means by which these decisions are discussed with and, preferably, sold to players. Certainly, technology can significantly enhance coach decision making and practice, while also helping players to optimise their focus, empowerment and independence in knowing how to achieve their personal and collective goals

Preventive measures in infancy to reduce under-five mortality: a case-control study in The Gambia.

OBJECTIVE: To investigate the relationship between child mortality and common preventive interventions: vaccination, trained birthing attendants, tetanus toxoid during pregnancy, breastfeeding and vitamin A supplementation. METHODS: Case-control study in a population under demographic surveillance. Cases (n = 141) were children under five who died. Each was age and sex-matched to five controls (n = 705). Information was gathered by interviewing primary caregivers. RESULTS: All but one of the interventions - whether the mother had received tetanus toxoid during pregnancy - were protective against child mortality after multivariate analysis. Having a trained person assisting at child birth (OR 0.2 95% CI 0.1-0.4), receiving all vaccinations by 9 months of age (OR 0.1; 95% CI 0.01-0.3), being breastfed for more than 12 months (Children breastfed between 13 and 24 months OR 0.1 95% CI 0.03-0.3, more than 25 months OR 0.1 95% CI 0.01-0.5) and receiving vitamin A supplementation at or after 6 months of age (OR 0.05; 95% CI 0.01-0.2) were protective against child death. CONCLUSIONS: This study confirms the value of at least four available interventions in the prevention of under-five death in The Gambia. It is now important to identify those who are not receiving them and why, and to intervene to improve coverage across the population

Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem

The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts

The Movement of Salmon (Salmo Salar) Through an Estuary and a Fish-Pass

In this paper we have attempted to analyze in quantitative terms the behaviour of the salmon of the River Erne during the important phase of migration when the fish first enter brackish and fresh water

On Alternative Supermatrix Reduction

We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible superconformal-like transformations. The features of even- and odd-reduced supermatrices are investigated on a par. They can be unified into some kind of "sandwich" semigroups. Also we define a special module over even- and odd-reduced supermatrix sets, and the generalized Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced supermatrices represent semigroup bands and Rees matrix semigroups over a unit group.Comment: 22 pages, Standard LaTeX with AmS font