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

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

Theoretical investigation on the possibility of preparing left-handed materials in metallic magnetic granular composites

We investigate the possibility of preparing left-handed materials in metallic magnetic granular composites. Based on the effective medium approximation, we show that by incorporating metallic magnetic nanoparticles into an appropriate insulating matrix and controlling the directions of magnetization of metallic magnetic components and their volume fraction, it may be possible to prepare a composite medium of low eddy current loss which is left-handed for electromagnetic waves propagating in some special direction and polarization in a frequency region near the ferromagnetic resonance frequency. This composite may be easier to make on an industrial scale. In addition, its physical properties may be easily tuned by rotating the magnetization locally.Comment: 5 figure

Meaningful values of the EQ-5D-3L in patients undergoing primary knee arthroplasty

AIMS: The aim of this study was to report the meaningful values of the EuroQol five-dimension three-level questionnaire (EQ-5D-3L) and EuroQol visual analogue scale (EQ-VAS) in patients undergoing primary knee arthroplasty (KA). METHODS: This is a retrospective study of patients undergoing primary KA for osteoarthritis in a university teaching hospital (Royal Infirmary of Edinburgh) (1 January 2013 to 31 December 2019). Pre- and postoperative (one-year) data were prospectively collected for 3,181 patients (median age 69.9 years (interquartile range (IQR) 64.2 to 76.1); females, n = 1,745 (54.9%); median BMI 30.1 kg/m(2) (IQR 26.6 to 34.2)). The reliability of the EQ-5D-3L was measured using Cronbach’s alpha. Responsiveness was determined by calculating the anchor-based minimal clinically important difference (MCID), the minimal important change (MIC) (cohort and individual), the patient-acceptable symptom state (PASS) predictive of satisfaction, and the minimal detectable change at 90% confidence intervals (MDC-90). RESULTS: The EQ-5D-3L demonstrated good internal consistency with an overall Cronbach alpha of 0.75 (preoperative) and 0.88 (postoperative), respectively. The MCID for the Index score was 0.085 (95% confidence interval (CI) 0.042 to 0.127) and EQ-VAS was 6.41 (95% CI 3.497 to 9.323). The MIC(COHORT) was 0.289 for the EQ-5D and 5.27 for the EQ-VAS. However, the MIC(INDIVIDUAL) for both the EQ-5D-3L Index (0.105) and EQ-VAS (-1) demonstrated poor-to-acceptable reliability. The MDC-90 was 0.023 for the EQ-5D-3L Index and 1.0 for the EQ-VAS. The PASS for the postoperative EQ-5D-3L Index and EQ-VAS scores predictive of patient satisfaction were 0.708 and 77.0, respectively. CONCLUSION: The meaningful values of the EQ-5D-3L Index and EQ-VAS scores can be used to measure clinically relevant changes in health-related quality of life in patients undergoing primary KA. Cite this article: Bone Joint Res 2022;11(9):619–628

Economical adjunction of square roots to groups

How large must an overgroup of a given group be in order to contain a square root of any element of the initial group? We give an almost exact answer to this question (the obtained estimate is at most twice worse than the best possible) and state several related open questions.Comment: 5 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2: minor correction

CD248+ stromal cells are associated with progressive chronic kidney disease

Stromal fibroblasts are the primary cells of the kidney that produce fibrotic matrix. CD248 is a stromal marker expressed on fibroblasts and pericytes within the human kidney. Here, we tested whether CD248 expression in the kidney colocalizes with fibrosis and if it is associated with known determinants of chronic kidney disease (CKD). CD248 expression was located and quantified in situ by immunohistochemistry in kidney biopsies from 93 patients with IgA nephropathy and compared with 22 archived biopsies encompassing normal kidney tissue as control. In normal kidney tissue, CD248 was expressed by resident pericytes, stromal fibroblasts, and was upregulated in human CKD. The expression was linked to known determinants of renal progression. This relationship was maintained in a multivariate analysis with CD248 expression linked to renal survival. CD248 was expressed by a population of α-smooth muscle actin (SMA)+ myofibroblasts and α-SMA− stromal cells but not expressed on CD45+ leukocytes. Thus, CD248 defines a subset of stromal cells, including but not limited to some myofibroblasts, linked to albuminuria and tubulointerstitial damage during tissue remodeling in CKD

Effective electronic response of a system of metallic cylinders

The electronic response of a composite consisting of aligned metallic cylinders in vacuum is investigated, on the basis of photonic band structure calculations. The effective long-wavelength dielectric response function is computed, as a function of the filling fraction. A spectral representation of the effective response is considered, and the surface mode strengths and positions are analyzed. The range of validity of a Maxwell-Garnett-like approach is discussed, and the impact of our results on absorption spectra and electron energy-loss phenomena is addressed.Comment: 15 pages, 6 figures, to appear in Phys. Rev.

Para-adventure: A hyper-dynamic problem for the inclusive coach

Recent research has recognized sports coaching as complex, chaotic, and cognitively taxing for coaches. Against this backdrop, the present paper explores challenges faced by high-level coaches working with disabled performers. Specifically, it seeks to understand how coaches create mental models of performance in adventure sports and para-canoe. Five coaches were purposively sampled and underwent a semi-structured interview. A thematic analysis revealed conceptualizing the mental model as being mechanically-related for all and as including a social construction within the para-canoe coaches. Reflection on the coaching process and on personal characteristics were perceived as important to individualized inclusive coaching. Coach training should particularly emphasize the need for critical judgment and decision making skills within a similarly oriented social structure of coaches and support staff where applicable

Type II Supernovae as Probes of Cosmology

- Constraining the cosmological parameters and understanding Dark Energy have tremendous implications for the nature of the Universe and its physical laws. - The pervasive limit of systematic uncertainties reached by cosmography based on Cepheids and Type Ia supernovae (SNe Ia) warrants a search for complementary approaches. - Type II SNe have been shown to offer such a path. Their distances can be well constrained by luminosity-based or geometric methods. Competing, complementary, and concerted efforts are underway, to explore and exploit those objects that are extremely well matched to next generation facilities. Spectroscopic follow-up will be enabled by space- based and 20-40 meter class telescopes. - Some systematic uncertainties of Type II SNe, such as reddening by dust and metallicity effects, are bound to be different from those of SNe Ia. Their stellar progenitors are known, promising better leverage on cosmic evolution. In addition, their rate - which closely tracks the ongoing star formation rate - is expected to rise significantly with look- back time, ensuring an adequate supply of distant examples. - These data will competitively constrain the dark energy equation of state, allow the determination of the Hubble constant to 5%, and promote our understanding of the processes involved in the last dramatic phases of massive stellar evolution.Comment: Science white paper, submitted to the Decadal committee Astro201

Rapid genotype imputation from sequence without reference panels

Inexpensive genotyping methods are essential for genetic studies requiring large sample sizes. In human studies, array-based microarrays and high-density haplotype reference panels allow efficient genotype imputation for this purpose. However, these resources are typically unavailable in non-human settings. Here we describe a method (STITCH) for imputation based only on sequencing read data, without requiring additional reference panels or array data. We demonstrate its applicability even in settings of extremely low sequencing coverage, by accurately imputing 5.7 million SNPs at a mean r(2) value of 0.98 in 2,073 outbred laboratory mice (0.15× sequencing coverage). In a sample of 11,670 Han Chinese (1.7× coverage), we achieve accuracy similar to that of alternative approaches that require a reference panel, demonstrating that our approach can work for genetically diverse populations. Our method enables straightforward progression from low-coverage sequence to imputed genotypes, overcoming barriers that at present restrict the application of genome-wide association study technology outside humans