Global Solvability in Functional Spaces for Smooth Nonsingular Vector Fields in the Plane

We address some global solvability issues for classes of smooth nonsingular vector fields $L$ in the plane related to cohomological equations $Lu=f$ in geometry and dynamical systems. The first main result is that $L$ is not surjective in $C^\infty(\R^2)$ iff the geometrical condition -- the existence of separatrix strips -- holds. Next, for nonsurjective vector fields, we demonstrate that if the RHS $f$ has at most infra-exponential growth in the separatrix strips we can find a global weak solution $L^1_{loc}$ near the boundaries of the separatrix strips. Finally we investigate the global solvability for perturbations with zero order p.d.o. We provide examples showing that our estimates are sharp.Comment: 22 pages, 2 figures, submitted to the PDE volume of the proceedings of the ISAAC2009 conferenc

The potential role of statins in the treatment and prevention of oesophageal adenocarcinoma

Oesophageal adenocarcinoma (OAC) is an aggressive malignancy with a very poor prognosis overall. Barrett’s oesophagus (BO) is the only known precursor lesion. Emerging preclinical evidence indicates statins, medications commonly used in the primary and secondary prevention of cardiovascular disease, inhibit proliferation, promote apoptosis and limit invasiveness of OAC. Inhibition of the mevalonate pathway depletes downstream products involved in candidate growth-signalling cascades. This research aimed to determine: (1) associations between statin use after diagnosis of oesophageal carcinoma (OC) and mortality outcomes; (2) the feasibility of assessing adjuvant statin therapy in patients with operable OAC in a future phase III randomised controlled trial; and (3) associations between statin use and malignant progression to high-grade dysplasia (HGD)/OAC in BO populations. In a cohort of 4445 patients with OC in a large primary care dataset, the General Practice Research Database, post-diagnostic statin use was associated with significant reductions in OC-specific and all-cause mortality. Significant associations were demonstrated in patients with OAC but not in oesophageal squamous cell carcinoma. A multi-centre, double-blind, parallel group, randomised, placebo-controlled feasibility trial of adjuvant statin therapy recruited patients with operable OAC. In total, 32 patients were randomised (1:1) to simvastatin (40mg) or matched placebo. Treatment started from the date of discharge following surgery and continued for up to one year. The trial estimated recruitment, retention, drug absorption, adherence, safety, quality of life, generalisability, and mortality outcomes. The feasibility of a future phase III trial was demonstrated; and derived feasibility estimates inform its design and conduct. A nested case-control analysis of a cohort with BO registered with the United Kingdom National Barrett’s Oesophagus Registry (UKBOR) demonstrated no significant associations between statin use and malignant progression. Significant dose and duration-response relationships were not demonstrated

Efficacy and safety profile of statins in patients with cancer: a systematic review of randomised controlled trials

PURPOSE: A growing body of preclinical and observational research suggests that statins have potential as a therapeutic strategy in patients with cancer. This systematic review of randomised controlled trials (RCTs) in patients with solid tumours aimed to determine the efficacy of statin therapy on mortality outcomes, their safety profile and the risk of bias of included studies. METHODS: Full-text articles comparing statin therapy versus control in solid tumours and reporting mortality outcomes were identified from Medline and Embase from conception to February 2020. A systematic review with qualitative (primarily) and quantitative synthesis was conducted. This systematic review was prospectively registered (Prospero registration CRD42018116364). RESULTS: Eleven trials of 2165 patients were included. Primary tumour sites investigated included lung, colorectal, gastro-oesophageal, pancreatic and liver. Most trials recruited patients with advanced malignancy and used sub-maximal statin doses for relatively short durations. Aside from one trial which demonstrated benefit with allocation to pravastatin 40 mg in hepatocellular carcinoma, the remaining ten trials did not demonstrate efficacy with statins. The pooled hazard ratio for all-cause mortality with allocation to pravastatin in patients with hepatocellular carcinoma in two trials was 0.69 (95% confidence interval CI 0.30-1.61). Study estimates were imprecise. There were no clinically important differences in statin-related adverse events between groups. Overall, included trials were deemed low risk of bias. CONCLUSION: The trial evidence is not sufficiently robust to confirm or refute the efficacy and safety of statins in patients with solid malignant tumours. Study and patient characteristics may explain this uncertainty. The potential role of high-dose statins in adjuvant settings deserves further research

Adaptive Task Automata with Earliest-Deadline-First Scheduling

Adjusting to resource changes, dynamic environmental conditions, or new usage modes are some of the reasons why real-time embedded systems need to be adaptive. This requires a rigorous framework for designing such systems, to ensure that the adaptivity does not result in invalidating the system’s real-time constraints. To address this need, we have recently introduced adaptive task automata, a framework for modeling, verification, and schedulability analysis in adaptive, hard real-time embedded systems, assuming a fixed-priority scheduler. In this work, we extend the adaptive task automata framework to incorporate the earliest-deadline-first scheduling policy, as well as enable implementation of any other dynamic scheduling policy. To prove the decidability of our model, and at the same time maintain a manageable degree of conciseness, we show an encoding of our model as a network of timed automata with clock updates. To support this, we also show that reachability in our class of timed automata with updates is decidable. Our contribution helps to streamline the process of designing safety critical adaptive embedded systems

The association between physical activity and the risk of symptomatic Barrett’s oesophagus: a UK prospective cohort study

Background: Physical activity affects the functioning of the gastrointestinal system through both local and systemic effects and may play an important role in the aetiology of gastroesophageal reflux disease, Barrett’s oesophagus and oesophageal adenocarcinoma. We investigated, for the first time in a large prospective cohort study, associations between recreational and occupational levels of physical activity and the incidence of Barrett’s oesophagus. Participants and methods: The European Prospective Investigation of Cancer-Norfolk recruited 30 445 men and women between 1993 and 1997. Occupational and recreational levels of physical activity were measured using a baseline questionnaire. The cohort was followed up until 2015 to identify symptomatic cases of Barrett’s oesophagus. Cox proportional hazard regression estimated hazard ratios (HR) for physical activity and the development of disease. Results: Two hundred and three participants developed Barrett’s oesophagus (mean age: 70.6 years) the majority of whom were men (70.9%). There was an inverse association between standing occupations and disease risk [HR: 0.50, 95% confidence interval (CI): 0.31–0.82, P=0.006] when compared with sedentary jobs. Heavy manual occupations were positively associated with disease risk (HR: 1.66, 95% CI: 0.91–3.00), but conventional statistical significance was not reached (P=0.09). No associations were found between recreational activity and the risk of Barrett’s oesophagus (HR: 1.34, 95% CI: 0.72–2.50, P=0.35, highest vs. lowest levels of activity). Conclusion: Our study suggests that occupational levels of physical activity may be associated with the risk Barrett’s oesophagus. However, further work is required to confirm and describe specific occupations that may be protective

The association between preoperative cardiopulmonary exercise test variables and short-term morbidity following oesophagectomy: A hospital-based cohort study

Background: Postoperative complications after esophagectomy are thought to be associated with reduced fitness. This observational study explored the associations between aerobic fitness, as determined objectively by preoperative cardiopulmonary exercise testing (CPEX), and 30-day morbidity after esophagectomy. Methods: We retrospectively identified 254 consecutive patients who underwent esophagectomy at a single academic teaching hospital between September 2011 and March 2017. Postoperative complication data were measured using the Esophageal Complications Consensus Group definitions and graded using the Clavien-Dindo classification system of severity (blinded to cardiopulmonary exercise testing values). Associations between preoperative cardiopulmonary exercise testing variables and postoperative outcomes were estimated using logistic regression. Results: A total of 206 patients (77% male) were included in the analyses, with a mean age of 67 years (SD 9). The mean values for the maximal oxygen consumed at the peak of exercise (VO 2peak) and the anaerobic threshold were 21.1 mL/kg/min (SD 4.5) and 12.4 mL/kg/min (SD 2.8), respectively. The vast majority of patients (98.5%) had malignant disease—predominantly adenocarcinoma (84.5%), for which most received neoadjuvant chemotherapy (79%) and underwent minimally invasive Ivor Lewis esophagectomy (53%). Complications at postoperative day 30 occurred in 111 patients (54%), the majority of which were cardiopulmonary (72%). No associations were found between preoperative cardiopulmonary exercise testing variables and morbidity for either VO 2peak (OR 1.00, 95% CI 0.94–1.07) or anaerobic threshold (OR 0.98, 95% CI 0.89–1.09). Conclusion: Preoperative cardiopulmonary exercise testing variables were not associated with 30-day complications after esophagectomy. The findings do not support the use of cardiopulmonary exercise testing as an isolated preoperative screening tool to predict short-term morbidity after esophagectomy. This modestly sized observational work highlights the need for larger studies examining associations between preoperative cardiopulmonary exercise testing and outcomes after esophagectomy to look for consistency in our findings

Adjuvant Statin Therapy for Esophageal Adenocarcinoma: a cost-effectiveness analysis

Background: Emerging preclinical evidence indicates statins, medications commonly used in the prevention of cardiovascular disease, inhibit proliferation, promote apoptosis and limit invasiveness of esophageal adenocarcinoma (EAC). Population-based observational data demonstrates statin treatment after diagnosis of EAC is associated with significant reductions in all-cause and cancer-specific mortality. A feasibility study of adjuvant statin therapy following potentially curative resection for EAC has completed, with planned progression to a full phase III randomised controlled trial Aim: To estimate the cost-utility of statin therapy following surgical resection for EAC from an NHS perspective. Methods: A Markov model was developed to estimate the costs and outcomes (quality adjusted life years, QALYs) for hypothetical cohorts of patients with EAC exposed or not exposed to statins following potentially curative surgical resection. Model parameters were based on estimates from published observational and trial data. Costs, utilities and transition probabilities were modelled to reflect clinical practice from a payer’s perspective. Probabilistic and one-way sensitivity analyses were performed to account for uncertainty in key parameters. Results: Overall, a cost-saving of £6,781 per patient was realised with statin treatment compared to no statins. In probabilistic sensitivity analysis, 99% of all iterations were cost-saving and 99% of all iterations were less than £20,000 per QALY gained. These results were robust to changes in the price and effectiveness of statins. Conclusions: The cohort exposed to statins had lower costs and better QALY outcomes than the no statin cohort. Assuming a causal relationship between statin exposure and outcomes suggests that statins following resection of EAC is a cost-saving treatment

Single nucleotide polymorphisms and post-operative complications following major gastrointestinal surgery: A systematic review and meta-analysis

Background: The human genome is an under-researched area of pre-operative risk stratification. Studies of genetic polymorphisms and their associations with acute post-operative complications in gastrointestinal surgery have reported statistically significant results, but have varied in methodology, genetic variations studied, and conclusions reached. To provide clarity, we conducted a systematic review and meta-analysis of single nucleotide polymorphisms and their association with post-operative complications after major gastro-8 intestinal surgery. Methods: We performed a literature search using Ovid MEDLINE and Web of Science databases. Studies were included if they investigated genetic polymorphisms and their associations with post-operative complications after major gastrointestinal surgery. We extracted clinical and genetic data from each paper and assessed for quality against the STrengthening the REporting of Genetic Association Studies (STREGA) guidelines. Odds ratios were presented, with 95% confidence intervals, to assess strengths of association. We conducted a meta-analysis on TNF-alpha-308, which had been assessed in three papers. Results: Our search returned 68 papers, of which 5 were included after screening and full-text review. Twenty-two different single nucleotide polymorphisms (SNPs) were investigated in these studies. We found that all papers were genetic association studies, and had selected SNPs related to inflammation. The outcome investigated was most commonly post-operative infection, but also anastomotic leak and other non-infectious complications. Statistically significant associations were found for: TNF-alpha-308, IL-10-819, PTGS2-765 and IFN-gamma-874. There was significant variability in study quality and methodology. We conducted a meta-analysis on associations between the TNF-alpha-308 polymorphism and post-operative infection and report an OR of 1.18 (CI 0.27 – 5.21). Conclusions: We found biologically plausible associations between SNPs involved in inflammation and post-operative infection, but the available data were too limited and of insufficient quality to reach definitive conclusions. Further work is needed, including genome-wide association studies (GWAS)