Program Veri¿cation in the presence of complex numbers, functions with branch cuts etc

Abstract-In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as "does the lowlevel arithmetic implement the high-level mathematics". Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more dif¿cult than expected: for example the complex function log is not continuous, writing down a program to compute an inverse function is more complicated than just solving an equation, and many algebraic simpli¿cation rules are not universally valid. The good news is that these problems are theoretically capable of being solved, and are practically close to being solved, but not yet solved, in several real-world examples. However, there is still a long way to go before implementations match the theoretical possibilities

A “piano movers” problem reformulated

Abstract-It has long been known that cylindrical algebraic decompositions (CADs) can in theory be used for robot motion planning. However, in practice even the simplest examples can be too complicated to tackle. We consider in detail a "Piano Mover's Problem" which considers moving an infinitesimally thin piano (or ladder) through a right-angled corridor. Producing a CAD for the original formulation of this problem is still infeasible after 25 years of improvements in both CAD theory and computer hardware. We review some alternative formulations in the literature which use differing levels of geometric analysis before input to a CAD algorithm. Simpler formulations allow CAD to easily address the question of the existence of a path. We provide a new formulation for which both a CAD can be constructed and from which an actual path could be determined if one exists, and analyse the CADs produced using this approach for variations of the problem. This emphasises the importance of the precise formulation of such problems for CAD. We analyse the formulations and their CADs considering a variety of heuristics and general criteria, leading to conclusions about tackling other problems of this form

Meat and Nicotinamide:A Causal Role in Human Evolution, History, and Demographics

Hunting for meat was a critical step in all animal and human evolution. A key brain-trophic element in meat is vitamin B 3 /nicotinamide. The supply of meat and nicotinamide steadily increased from the Cambrian origin of animal predators ratcheting ever larger brains. This culminated in the 3-million-year evolution of Homo sapiens and our overall demographic success. We view human evolution, recent history, and agricultural and demographic transitions in the light of meat and nicotinamide intake. A biochemical and immunological switch is highlighted that affects fertility in the ‘de novo’ tryptophan-to-kynurenine-nicotinamide ‘immune tolerance’ pathway. Longevity relates to nicotinamide adenine dinucleotide consumer pathways. High meat intake correlates with moderate fertility, high intelligence, good health, and longevity with consequent population stability, whereas low meat/high cereal intake (short of starvation) correlates with high fertility, disease, and population booms and busts. Too high a meat intake and fertility falls below replacement levels. Reducing variances in meat consumption might help stabilise population growth and improve human capital

Branch cuts in maple 17

Abstract Accurate and comprehensible knowledge about the position of branch cuts is essential for correctly working with multi-valued functions, such as the square root and logarithm. We discuss the new tools in Maple 17 for calculating and visualising the branch cuts of such functions, and others built up from them. The cuts are described in an intuitive and accurate form, offering substantial improvement on the descriptions previously available

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\u2013Dindo Grades III\u2013V). 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\u20132.96, P < 0.001), whereas obese patients undergoing surgery for benign indications were at decreased risk (OR 0.59, 95% CI 0.46\u20130.75, 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