Galois representations attached to automorphic forms on GL_2 over CM fields

In this paper we generalize the work of Harris-Soudry-Taylor and construct the compatible systems of two-dimensional Galois representations attached to cuspidal automorphic representations of cohomological type on GL_2 over a CM field with a suitable condition on their central characters. We also prove a local-global compatibility statement, up to semisimplification.Comment: 61 page

Is protocolised weaning that includes early extubation onto non-invasive ventilation more cost effective than protocolised weaning without non-invasive ventilation? Findings from the Breathe Study

Background Optimising techniques to wean patients from invasive mechanical ventilation (IMV) remains a key goal of intensive care practice. The use of non-invasive ventilation (NIV) as a weaning strategy (transitioning patients who are difficult to wean to early NIV) may reduce mortality, ventilator-associated pneumonia and intensive care unit (ICU) length of stay. Objectives Our objectives were to determine the cost effectiveness of protocolised weaning, including early extubation onto NIV, compared with weaning without NIV in a UK National Health Service setting. Methods We conducted an economic evaluation alongside a multicentre randomised controlled trial. Patients were randomised to either protocol-directed weaning from mechanical ventilation or ongoing IMV with daily spontaneous breathing trials. The primary efficacy outcome was time to liberation from ventilation. Bivariate regression of costs and quality-adjusted life-years (QALYs) provided estimates of the incremental cost per QALY and incremental net monetary benefit (INMB) overall and for subgroups [presence/absence of chronic obstructive pulmonary disease (COPD) and operative status]. Long-term cost effectiveness was determined through extrapolation of survival curves using flexible parametric modelling. Results NIV was associated with a mean INMB of £620 ($US885) (cost-effectiveness threshold of £20,000 per QALY) with a corresponding probability of 58$US6594 per QALY gained). Conclusions The probability of NIV being cost effective relative to weaning without NIV ranged between 57 and 59% overall and between 82 and 87% for the COPD subgroup

Plaster cast versus functional brace for non-surgical treatment of Achilles tendon rupture (UKSTAR) : a multicentre randomised controlled trial and economic evaluation

Background Patients with Achilles tendon rupture who have non-operative treatment have traditionally been treated with immobilisation of the tendon in plaster casts for several weeks. Functional bracing is an alternative non-operative treatment that allows earlier mobilisation, but evidence on its effectiveness and safety is scarce. The aim of the UKSTAR trial was to compare functional and quality-of-life outcomes and resource use in patients treated non-operatively with plaster cast versus functional brace. Methods UKSTAR was a pragmatic, superiority, multicentre, randomised controlled trial done at 39 hospitals in the UK. Patients (aged ≥16 years) who were being treated non-operatively for a primary Achilles tendon rupture at the participating centres were potentially eligible. The exclusion criteria were presenting more than 14 days after injury, previous rupture of the same Achilles tendon, or being unable to complete the questionnaires. Eligible participants were randomly assigned (1:1) to receive a plaster cast or functional brace using a centralised web-based system. Because the interventions were clearly visible, neither patients nor clinicians could be masked. Participants wore the intervention for 8 weeks. The primary outcome was patient-reported Achilles tendon rupture score (ATRS) at 9 months, analysed in the modified intention-to-treat population (all patients in the groups to which they were allocated, excluding participants who withdrew or died before providing any outcome data). The main safety outcome was the incidence of tendon re-rupture. Resource use was recorded from a health and personal social care perspective. The trial is registered with ISRCTN, ISRCTN62639639. Findings Between Aug 15, 2016, and May 31, 2018, 1451 patients were screened, of whom 540 participants (mean age 48·7 years, 79% male) were randomly allocated to receive plaster cast (n=266) or functional brace (n=274). 527 (98%) of 540 were included in the modified intention-to-treat population, and 13 (2%) were excluded because they withdrew or died before providing any outcome data. There was no difference in ATRS at 9 months post injury (cast group n=244, mean ATRS 74∙4 [SD 19∙8]; functional brace group n=259, ATRS 72∙8 [20∙4]; adjusted mean difference –1∙38 [95% CI –4∙9 to 2∙1], p=0·44). There was no difference in the rate of re-rupture of the tendon (17 [6%] of 266 in the plaster cast group vs 13 [5%] of 274 in the functional brace group, p=0·40). The mean total health and personal social care cost was £1181 for the plaster cast group and £1078 for the functional bract group (mean between-group difference –£103 [95% CI –289 to 84]). Interpretation Traditional plaster casting was not found to be superior to early weight-bearing in a functional brace, as measured by ATRS, in the management of patients treated non-surgically for Achilles tendon rupture. Clinicians may consider the use of early weight-bearing in a functional brace as a safe and cost-effective alternative to plaster casting