Computability and analysis: the legacy of Alan Turing

We discuss the legacy of Alan Turing and his impact on computability and analysis.Comment: 49 page

Average Weights and Power in Weighted Voting Games

We investigate a class of weighted voting games for which weights are randomly distributed over the standard probability simplex. We provide close-formed formulae for the expectation and density of the distribution of weight of the $k$-th largest player under the uniform distribution. We analyze the average voting power of the $k$-th largest player and its dependence on the quota, obtaining analytical and numerical results for small values of $n$ and a general theorem about the functional form of the relation between the average Penrose--Banzhaf power index and the quota for the uniform measure on the simplex. We also analyze the power of a collectivity to act (Coleman efficiency index) of random weighted voting games, obtaining analytical upper bounds therefor.Comment: 12 pages, 7 figure

A Computational Study of Genetic Crossover Operators for Multi-Objective Vehicle Routing Problem with Soft Time Windows

The article describes an investigation of the effectiveness of genetic algorithms for multi-objective combinatorial optimization (MOCO) by presenting an application for the vehicle routing problem with soft time windows. The work is motivated by the question, if and how the problem structure influences the effectiveness of different configurations of the genetic algorithm. Computational results are presented for different classes of vehicle routing problems, varying in their coverage with time windows, time window size, distribution and number of customers. The results are compared with a simple, but effective local search approach for multi-objective combinatorial optimization problems

The introduction of an holistic design approach through a teaching company scheme

Traditional design approaches separate the various functions of design such as material selection, performance modelling and tolerance specification into discrete entities. Whilst this allows more focused methods to be used at each stage, areas of conflict or benefit may be overlooked, and the designer is left to bring the loose ends together. This paper looks at a synthesis approach that draws upon a number of current design themes. The design process is considered along with various aspects such as product development, design-for-`X' methodologies and material selection. The need for the preservation of design knowledge and reasoning, the so called wh-? questions, within the process are considered along with various models of the design process. The paper draws these various aspects together to form a more holistic approach to design. The application of this technique within the Teaching Company Scheme is briefly discussed

Efficient option pricing with transaction costs

A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility-maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor’s basic portfolio selection problem without insertion of the option payoff into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no-transaction region, which leads to very efficient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational technique involves a discrete-time Markov chain approximation to a continuous-time singular stochastic optimal control problem. A general definition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

Teams and cardiac surgery

Motivation\ud Our study is designed to identify human factors that are a threat to the safety of children with heart disease.\ud \ud Research approach\ud After an initial observation period, we will apply a major safety intervention. We will then re-measure the occurrence and types of human factors in the operating room, and the incidence of adverse events, near misses and hospital death, to evaluate if there was a significant post-intervention reduction. \ud \ud Findings/design\ud We focus on challenges encountered during the training of the observers. Research Limitations\ud Because of the complexity of the OR, observations are necessarily subjective. \ud \ud Originality/Value\ud This work is original because of the systematic evaluation of a safety intevention and the training protocol for the observers.\ud \ud Take Away Message\ud Systematic and periodic assessment of observers is required when teamwork is observed in complex, dynamic settings

Analytical models for high performance milling. Part I: cutting forces, structural deformations and tolerance integrity

Milling is one of the most common manufacturing processes in industry. Despite recent advances in machining technology, productivity in milling is usually reduced due to the process limitations such as high cutting forces and stability. If milling conditions are not selected properly, the process may result in violations of machine limitations and part quality, or reduced productivity. The usual practice in machining operations is to use experience-based selection of cutting parameters which may not yield optimum conditions. In this two-part paper, milling force, part and tool deection, form error and stability models are presented. These methods can be used to check the process constraints as well as optimal selection of the cutting conditions for high performance milling. The use of the models in optimizing the process variables such as feed, depth of cut and spindle speed are demonstrated by simulations and experiments