Effects of local mutations in quadratic iterations

We introduce mutations in replication systems, in which the intact copying mechanism is performed by discrete iterations of a complex quadratic map. More specifically, we consider a "correct" function acting on the complex plane (representing the space of genes to be copied). A "mutation" is a different ("erroneous") map acting on a complex locus of given radius r around a mutation focal point. The effect of the mutation is interpolated radially to eventually recover the original map when reaching an outer radius R. We call the resulting map a "mutated" map. In the theoretical framework of mutated iterations, we study how a mutation (replication error) affects the temporal evolution of the system, on both a local and global scale (from cell diffetentiation to tumor formation). We use the Julia set of the system to quantify simultaneously the long-term behavior of the entire space under mutated maps. We analyze how the position, timing and size of the mutation can alter the topology of the Julia set, hence the system's long-term evolution, its progression into disease, but also its ability to recover or heal. In the context of genetics, mutated iterations may help shed some light on aspects such as the importance of location, size and type of mutation when evaluating a system's prognosis, and of customizing intervention.Comment: 15 pages, 15 figures, 7 reference

The development and validation of a scoring tool to predict the operative duration of elective laparoscopic cholecystectomy

Background: The ability to accurately predict operative duration has the potential to optimise theatre efficiency and utilisation, thus reducing costs and increasing staff and patient satisfaction. With laparoscopic cholecystectomy being one of the most commonly performed procedures worldwide, a tool to predict operative duration could be extremely beneficial to healthcare organisations. Methods: Data collected from the CholeS study on patients undergoing cholecystectomy in UK and Irish hospitals between 04/2014 and 05/2014 were used to study operative duration. A multivariable binary logistic regression model was produced in order to identify significant independent predictors of long (> 90 min) operations. The resulting model was converted to a risk score, which was subsequently validated on second cohort of patients using ROC curves. Results: After exclusions, data were available for 7227 patients in the derivation (CholeS) cohort. The median operative duration was 60 min (interquartile range 45–85), with 17.7% of operations lasting longer than 90 min. Ten factors were found to be significant independent predictors of operative durations > 90 min, including ASA, age, previous surgical admissions, BMI, gallbladder wall thickness and CBD diameter. A risk score was then produced from these factors, and applied to a cohort of 2405 patients from a tertiary centre for external validation. This returned an area under the ROC curve of 0.708 (SE = 0.013, p  90 min increasing more than eightfold from 5.1 to 41.8% in the extremes of the score. Conclusion: The scoring tool produced in this study was found to be significantly predictive of long operative durations on validation in an external cohort. As such, the tool may have the potential to enable organisations to better organise theatre lists and deliver greater efficiencies in care