The Resolvent Average for Positive Semidefinite Matrices

We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean. Some applications to matrix functions are also given

Compositions and convex combinations of asymptotically regular firmly nonexpansive mappings are also asymptotically regular

Because of Minty’s classical correspondence between firmly nonexpansive mappings and maximally monotone operators, the notion of a firmly nonexpansive mapping has proven to be of basic importance in fixed point theory, monotone operator theory, and convex optimization. In this note, we show that if finitely many firmly nonexpansive mappings defined on a real Hilbert space are given and each of these mappings is asymptotically regular, which is equivalent to saying that they have or “almost have” fixed points, then the same is true for their composition. This significantly generalizes the result by Bauschke from 2003 for the case of projectors (nearest point mappings). The proof resides in a Hilbert product space and it relies upon the Brezis-Haraux range approximation result. By working in a suitably scaled Hilbert product space, we also establish the asymptotic regularity of convex.Natural Sciences and Engineering Research Council of CanadaCanada Research Chair ProgramDirección General de Enseñanza SuperiorJunta de Andaluci

\u3cem\u3eStaphylococcus aureus\u3c/em\u3e Skin and Soft Tissue Infections at a Tertiary Hospital in Botswana

Objectives. To study the epidemiology of Staphylococcus aureus skin and soft-tissue infections (SSTIs) in hospitalised children and adults in Gaborone, Botswana, and to describe the changes in antimicrobial susceptibilities of S. aureus isolates over time. Methods. A retrospective cohort study evaluated SSTI isolates from January 2000 to December 2007 at Princess Marina Hospital (PMH), a large tertiary referral centre in Gaborone. Eligible subjects were those hospitalised at PMH during the study period who had a skin or soft-tissue culture yielding a bacterial or fungal pathogen. The primary outcome measure was a skin or soft-tissue culture yielding S. aureus. Secondary outcomes were the organism’s antimicrobial susceptibilities. Results. S. aureus was detected in 857 (35.8%) of single-organism SSTI cultures, and 194 (22.6%) of these isolates were methicillin resistant (MRSA). The proportion of MRSA isolates increased over time (linear test of trend: p=0.03 from 2000 to 2003), and MRSA isolates were more likely than methicillin-susceptible isolates to be resistant to commonly used antimicrobials recommended by the national SSTI treatment guideline. Conclusions. We report a high and increasing proportion of MRSA SSTIs in Gaborone. This high rate of MRSA resistance to currently recommended empiric antibiotics for SSTIs dictates the need for revising national guidelines and ongoing prospective surveillance of SSTIs in this setting

A comparison of course-related stressors in undergraduate problem-based learning (PBL) versus non-PBL medical programmes

Background: Medical students report high levels of stress related to their medical training as well as to other personal and financial factors. The aim of this study is to investigate whether there are differences in course-related stressors reported by medical students on undergraduate problem-based learning (PBL) and non-PBL programmes in the UK. Method: A cross-sectional study of second-year medical students in two UK medical schools (one PBL and one non-PBL programme) was conducted. A 16-question self-report questionnaire, derived from the Perceived Medical Student Stress Scale and the Higher Education Stress Inventory, was used to measure course-related stressors. Following univariate analysis of each stressor between groups, multivariate logistic regression was used to determine which stressors were the best predictors of each course type, while controlling for socio-demographic differences between the groups. Results: A total of 280 students responded. Compared to the non-PBL students (N = 197), the PBL students (N = 83) were significantly more likely to agree that: they did not know what the faculty expected of them (Odds Ratio (OR) = 0.38, p = 0.03); there were too many small group sessions facilitated only by students resulting in an unclear curriculum (OR = 0.04, p < 0.0001); and that there was a lack of opportunity to explore academic subjects of interest (OR = 0.40, p = 0.02). They were significantly more likely to disagree that: there was a lack of encouragement from teachers (OR = 3.11, p = 0.02); and that the medical course fostered a sense of anonymity and feelings of isolation amongst students (OR = 3.42, p = 0.008). Conclusion: There are significant differences in the perceived course-related stressors affecting medical students on PBL and non-PBL programmes. Course designers and student support services should therefore tailor their work to minimise, or help students cope with, the specific stressors on each course type to ensure optimum learning and wellbeing among our future doctors

Staphylococcus aureus skin and soft tissue infections at a tertiary hospital in Botswana

Objectives. To study the epidemiology of Staphylococcus aureus skin and soft-tissue infections (SSTIs) in hospitalised children and adults in Gaborone, Botswana, and to describe the changes in antimicrobial susceptibilities of S. aureus isolates over time. Methods. A retrospective cohort study evaluated SSTI isolates from January 2000 to December 2007 at Princess Marina Hospital (PMH), a large tertiary referral centre in Gaborone. Eligible subjects were those hospitalised at PMH during the study period who had a skin or soft-tissue culture yielding a bacterial or fungal pathogen. The primary outcome measure was a skin or soft-tissue culture yielding S. aureus. Secondary outcomes were the organism’s antimicrobial susceptibilities. Results. S. aureus was detected in 857 (35.8%) of single-organism SSTI cultures, and 194 (22.6%) of these isolates were methicillin resistant (MRSA). The proportion of MRSA isolates increased over time (linear test of trend: p=0.03 from 2000 to 2003), and MRSA isolates were more likely than methicillin-susceptible isolates to be resistant to commonly used antimicrobials recommended by the national SSTI treatment guideline. Conclusions. We report a high and increasing proportion of MRSA SSTIs in Gaborone. This high rate of MRSA resistance to currently recommended empiric antibiotics for SSTIs dictates the need for revising national guidelines and ongoing prospective surveillance of SSTIs in this setting