Generalised Elliptic Functions

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two different approaches. These functions arise naturally as solutions to some of the important equations of mathematical physics and their differential equations, addition formulae, and applications have all been recent topics of study. The first approach discussed sees the functions defined as logarithmic derivatives of the sigma-function, a modified Riemann theta-function. We can make use of known properties of the sigma function to derive power series expansions and in turn the properties mentioned above. This approach has been extended to a wide range of non hyperelliptic and higher genus curves and an overview of recent results is given. The second approach defines the functions algebraically, after first modifying the curve into its equivariant form. This approach allows the use of representation theory to derive a range of results at lower computational cost. We discuss the development of this theory for hyperelliptic curves and how it may be extended in the future.Comment: 16 page

Effects of Diabetes and Insulin on α-amylase Messenger RNA Levels in Rat Parotid Glands

Previous studies have shown that amylase levels are reduced significantly in the pancreas and parotid gland of diabetic rats and that insulin reverses this effect and increases the secretory protein levels. In the pancreas, these changes in amylase protein levels are accompanied by parallel changes in amylase mRNA levels. In the present study, the effects of diabetes and subsequent insulin treatments on contents (per cell) of amylase protein and its mRNA in parotid glands were compared in rats rendered diabetic with an injection of a beta-cell toxin, streptozotocin (STZ). Both amylase protein and its mRNA contents were reduced significantly in diabetic rats, compared with control rats, and this reduction was reversed following insulin injections of diabetic rats. In insulin-injected diabetic rats, amylase protein contents increased before a detectable increase in amylase mRNA levels was seen. The mRNA contents of a non-secretory protein, actin, did not change during diabetogenesis or subsequent insulin treatments. The reductions in parotid contents of amylase and its mRNA in diabetic rats and the reversal of these changes by insulin are similar to those changes that occur in the pancreas under the same conditions. However, the magnitude of these changes in parotid glands was much smaller than in the pancreas, and the effect of insulin on amylase mRNA synthesis was not as immediate as in the latter gland.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67977/2/10.1177_00220345900690081001.pd

Critical care usage after major gastrointestinal and liver surgery: a prospective, multicentre observational study

Background Patient selection for critical care admission must balance patient safety with optimal resource allocation. This study aimed to determine the relationship between critical care admission, and postoperative mortality after abdominal surgery. Methods This prespecified secondary analysis of a multicentre, prospective, observational study included consecutive patients enrolled in the DISCOVER study from UK and Republic of Ireland undergoing major gastrointestinal and liver surgery between October and December 2014. The primary outcome was 30-day mortality. Multivariate logistic regression was used to explore associations between critical care admission (planned and unplanned) and mortality, and inter-centre variation in critical care admission after emergency laparotomy. Results Of 4529 patients included, 37.8% (n=1713) underwent planned critical care admissions from theatre. Some 3.1% (n=86/2816) admitted to ward-level care subsequently underwent unplanned critical care admission. Overall 30-day mortality was 2.9% (n=133/4519), and the risk-adjusted association between 30-day mortality and critical care admission was higher in unplanned [odds ratio (OR): 8.65, 95% confidence interval (CI): 3.51–19.97) than planned admissions (OR: 2.32, 95% CI: 1.43–3.85). Some 26.7% of patients (n=1210/4529) underwent emergency laparotomies. After adjustment, 49.3% (95% CI: 46.8–51.9%, P<0.001) were predicted to have planned critical care admissions, with 7% (n=10/145) of centres outside the 95% CI. Conclusions After risk adjustment, no 30-day survival benefit was identified for either planned or unplanned postoperative admissions to critical care within this cohort. This likely represents appropriate admission of the highest-risk patients. Planned admissions in selected, intermediate-risk patients may present a strategy to mitigate the risk of unplanned admission. Substantial inter-centre variation exists in planned critical care admissions after emergency laparotomies

Body mass index and complications following major gastrointestinal surgery: A prospective, international cohort study and meta-analysis

Aim Previous studies reported conflicting evidence on the effects of obesity on outcomes after gastrointestinal surgery. The aims of this study were to explore the relationship of obesity with major postoperative complications in an international cohort and to present a metaanalysis of all available prospective data. Methods This prospective, multicentre study included adults undergoing both elective and emergency gastrointestinal resection, reversal of stoma or formation of stoma. The primary end-point was 30-day major complications (Clavien–Dindo Grades III–V). A systematic search was undertaken for studies assessing the relationship between obesity and major complications after gastrointestinal surgery. Individual patient meta-analysis was used to analyse pooled results. Results This study included 2519 patients across 127 centres, of whom 560 (22.2%) were obese. Unadjusted major complication rates were lower in obese vs normal weight patients (13.0% vs 16.2%, respectively), but this did not reach statistical significance (P = 0.863) on multivariate analysis for patients having surgery for either malignant or benign conditions. Individual patient meta-analysis demonstrated that obese patients undergoing surgery formalignancy were at increased risk of major complications (OR 2.10, 95% CI 1.49–2.96, P < 0.001), whereas obese patients undergoing surgery for benign indications were at decreased risk (OR 0.59, 95% CI 0.46–0.75, P < 0.001) compared to normal weight patients. Conclusions In our international data, obesity was not found to be associated with major complications following gastrointestinal surgery. Meta-analysis of available prospective data made a novel finding of obesity being associated with different outcomes depending on whether patients were undergoing surgery for benign or malignant disease