Commutator methods for unitary operators

We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local finiteness of point spectrum. Large families of locally smooth operators are also exhibited. Half of the paper is dedicated to applications, and a special emphasize is put on the study of cocycles over irrational rotations. It is apparently the first time that commutator methods are applied in the context of rotation algebras, for the study of their generators.Comment: 15 page

Detecting communities using asymptotical Surprise

Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a community. We here analyze a recently proposed measure called surprise, which assesses the quality of the partition of a network into communities. In its current form, the formulation of surprise is rather difficult to analyze. We here therefore develop an accurate asymptotic approximation. This allows for the development of an efficient algorithm for optimizing surprise. Incidentally, this leads to a straightforward extension of surprise to weighted graphs. Additionally, the approximation makes it possible to analyze surprise more closely and compare it to other methods, especially modularity. We show that surprise is (nearly) unaffected by the well known resolution limit, a particular problem for modularity. However, surprise may tend to overestimate the number of communities, whereas they may be underestimated by modularity. In short, surprise works well in the limit of many small communities, whereas modularity works better in the limit of few large communities. In this sense, surprise is more discriminative than modularity, and may find communities where modularity fails to discern any structure

Point prevalence of surgical checklist use in Europe: relationship with hospital mortality

Background The prevalence of use of the World Health Organization surgical checklist is unknown. The clinical effectiveness of this intervention in improving postoperative outcomes is debated. Methods We undertook a retrospective analysis of data describing surgical checklist use from a 7 day cohort study of surgical outcomes in 28 European nations (European Surgical Outcomes Study, EuSOS). The analysis included hospitals recruiting >10 patients and excluding outlier hospitals above the 95th centile for mortality. Multivariate logistic regression and three-level hierarchical generalized mixed models were constructed to explore the relationship between surgical checklist use and hospital mortality. Findings are presented as crude and adjusted odds ratios (ORs) with 95% confidence intervals (CIs). Results A total of 45 591 patients from 426 hospitals were included in the analysis. A surgical checklist was used in 67.5% patients, with marked variation across countries (0-99.6% of patients). Surgical checklist exposure was associated with lower crude hospital mortality (OR 0.84, CI 0.75-0.94; P=0.002). This effect remained after adjustment for baseline risk factors in a multivariate model (adjusted OR 0.81, CI 0.70-0.94; P<0.005) and strengthened after adjusting for variations within countries and hospitals in a three-level generalized mixed model (adjusted OR 0.71, CI 0.58-0.85; P<0.001). Conclusions The use of surgical checklists varies across European nations. Reported use of a checklist was associated with lower mortality. This observation may represent a protective effect of the surgical checklist itself, or alternatively, may be an indirect indicator of the quality of perioperative care. Clinical trial registration The European Surgical Outcomes Study is registered with ClinicalTrials.gov, number NCT0120360

Erratum to: 36th International Symposium on Intensive Care and Emergency Medicine

[This corrects the article DOI: 10.1186/s13054-016-1208-6.]

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac

Epidemiology, practice of ventilation and outcome for patients at increased risk of postoperative pulmonary complications

BACKGROUND Limited information exists about the epidemiology and outcome of surgical patients at increased risk of postoperative pulmonary complications (PPCs), and how intraoperative ventilation was managed in these patients. OBJECTIVES To determine the incidence of surgical patients at increased risk of PPCs, and to compare the intraoperative ventilation management and postoperative outcomes with patients at low risk of PPCs. DESIGN This was a prospective international 1-week observational study using the ‘Assess Respiratory Risk in Surgical Patients in Catalonia risk score’ (ARISCAT score) for PPC for risk stratification. PATIENTS AND SETTING Adult patients requiring intraoperative ventilation during general anaesthesia for surgery in 146 hospitals across 29 countries. MAIN OUTCOME MEASURES The primary outcome was the incidence of patients at increased risk of PPCs based on the ARISCAT score. Secondary outcomes included intraoperative ventilatory management and clinical outcomes. RESULTS A total of 9864 patients fulfilled the inclusion criteria. The incidence of patients at increased risk was 28.4%. The most frequently chosen tidal volume (VT) size was 500 ml, or 7 to 9 ml kg1 predicted body weight, slightly lower in patients at increased risk of PPCs. Levels of positive end-expiratory pressure (PEEP) were slightly higher in patients at increased risk of PPCs, with 14.3% receiving more than 5 cmH2O PEEP compared with 7.6% in patients at low risk of PPCs (P < 0.001). Patients with a predicted preoperative increased risk of PPCs developed PPCs more frequently: 19 versus 7%, relative risk (RR) 3.16 (95% confidence interval 2.76 to 3.61), P < 0.001) and had longer hospital stays. The only ventilatory factor associated with the occurrence of PPCs was the peak pressure. CONCLUSION The incidence of patients with a predicted increased risk of PPCs is high. A large proportion of patients receive high VT and low PEEP levels. PPCs occur frequently in patients at increased risk, with worse clinical outcome