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

The Kervaire-Laudenbach conjecture and presentations of simple groups

The statement ``no nonabelian simple group can be obtained from a nonsimple group by adding one generator and one relator" 1) is equivalent to the Kervaire--Laudenbach conjecture; 2) becomes true under the additional assumption that the initial nonsimple group is either finite or torsion-free. Key words: Kervaire--Laudenbach conjecture, relative presentations, simple groups, car motion, cocar comotion. AMS MSC: 20E32, 20F05, 20F06.Comment: 20 pages, 13 figure

Applications of p-deficiency and p-largeness

We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is Golod-Shafarevich, and has a finite index subgroup which is Golod-Shafarevich for the remaining primes. We also generalise a result of Grigorchuk on Coxeter groups to odd primes.Comment: 23 page

Septic arthritis in an in vivo murine model induced by Staphylococcus aureus:a comparison between actions of the haemolysin toxin and the effects of the host immune response

AIMS: Staphylococcus aureus is a major cause of septic arthritis, and in vitro studies suggest α haemolysin (Hla) is responsible for chondrocyte death. We used an in vivo murine joint model to compare inoculation with wild type S. aureus 8325-4 with a Hla-deficient strain DU1090 on chondrocyte viability, tissue histology, and joint biomechanics. The aim was to compare the actions of S. aureus Hla alone with those of the animal’s immune response to infection. METHODS: Adult male C57Bl/6 mice (n = 75) were randomized into three groups to receive 1.0 to 1.4 × 10(7) colony-forming units (CFUs)/ml of 8325-4, DU1090, or saline into the right stifle joint. Chondrocyte death was assessed by confocal microscopy. Histological changes to inoculated joints were graded for inflammatory responses along with gait, weight changes, and limb swelling. RESULTS: Chondrocyte death was greater with 8325-4 (96.2% (SD 5.5%); p < 0.001) than DU1090 (28.9% (SD 16.0%); p = 0.009) and both were higher than controls (3.8% (SD 1.2%)). Histology revealed cartilage/bone damage with 8325-4 or DU1090 compared to controls (p = 0.010). Both infected groups lost weight (p = 0.006 for both) and experienced limb swelling (p = 0.043 and p = 0.018, respectively). Joints inoculated with bacteria showed significant alterations in gait cycle with a decreased stance phase, increased swing phase, and a corresponding decrease in swing speed. CONCLUSION: Murine joints inoculated with Hla-producing 8325-4 experienced significantly more chondrocyte death than those with DU1090, which lack the toxin. This was despite similar immune responses, indicating that Hla was the major cause of chondrocyte death. Hla-deficient DU1090 also elevated chondrocyte death compared to controls, suggesting a smaller additional deleterious role of the immune system on cartilage. Cite this article: Bone Joint Res 2022;11(9):669–678

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.

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

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