Designing digital technologies and learning activities for different geometries

This chapter focuses on digital technologies and geometry education, a combination of topics that provides a suitable avenue for analysing closely the issues and challenges involved in designing and utilizing digital technologies for learning mathematics. In revealing these issues and challenges, the chapter examines the design of digital technologies and related forms of learning activities for a range of geometries, including Euclidean and co-ordinate geometries in two and three dimensions, and non-Euclidean geometries such as spherical, hyperbolic and fractal geometry. This analysis reveals the decisions that designers take when designing for different geometries on the flat computer screen. Such decisions are not only about the geometry but also about the learner in terms of supporting their perceptions of what are the key features of geometry

Determining the quality of mathematical software using reference data sets

This paper describes a methodology for evaluating the numerical accuracy of software that performs mathematical calculations. The authors explain how this methodology extends the concept of metrological traceability, which is fundamental to measurement, to include software quality. Overviews of two European Union-funded projects are also presented. The first project developed an infrastructure to allow software to be verified by testing, via the internet, using reference data sets. The primary focus of the project was software used within systems that make physical measurements. The second project, currently underway, explores using this infrastructure to verify mathematical software used within general scientific and engineering disciplines. Publications on using reference data sets for the verification of mathematical software are usually intended for a readership specialising in measurement science or mathematics. This paper is aimed at a more general readership, in particular software quality specialists and computer scientists. Further engagement with experts in these disciplines will be helpful to the continued development of this application of software quality

The perceived social impacts of the 2006 World Cup on Munich residents

All major sporting events result in a variety of impacts upon the host community. To date, the majority of existing studies have focused upon the wider economic impacts, with few empirical studies of the social impacts upon local residents. This paper explores the perceived impacts of the 2006 Football World Cup upon residents of one of the host cities–Munich. Using a multi-stage sampling technique, 180 Munich residents were randomly selected. Of these, 132 agreed to participate in face-to-face interviews. Findings from the study suggested that the impacts were largely perceived as positive by residents, especially in terms of urban regeneration, increased sense of security, positive fan behaviour and the general atmosphere surrounding the event. Negative impacts, such as increased crime, prostitution, and displacement of local residents were perceived by fewer respondents. Further analysis demonstrates that such perceptions are not dependent upon socio-demographic factors such as age, gender or length of residence in the city

Ranking expansion terms using partial and ostensive evidence

In this paper we examine the problem of ranking candidate expansion terms for query expansion. We show, by an extension to the traditional F4 scheme, how partial relevance assessments (how relevant a document is) and ostensive evidence (when a document was assessed relevant) can be incorporated into a term ranking function. We then investigate this new term ranking function in three user experiments, examining the performance of our function for automatic and interactive query expansion. We show that the new function not only suggests terms that are preferred by searchers but suggests terms that can lead to more use of expansion terms

Bayesian Inference in Estimation of Distribution Algorithms

Metaheuristics such as Estimation of Distribution Algorithms and the Cross-Entropy method use probabilistic modelling and inference to generate candidate solutions in optimization problems. The model fitting task in this class of algorithms has largely been carried out to date based on maximum likelihood. An alternative approach that is prevalent in statistics and machine learning is to use Bayesian inference. In this paper, we provide a framework for the application of Bayesian inference techniques in probabilistic model-based optimization. Based on this framework, a simple continuous Bayesian Estimation of Distribution Algorithm is described. We evaluate and compare this algorithm experimentally with its maximum likelihood equivalent, UMDAG c

Focussed microwave heating using degenerate and non-degenerate cavity modes

Microwave ovens have long been recognised as a means of reducing heating times versus conventional convection ovens. The principle design feature is based on the procurement of uniform heating within any material placed in the interior of the microwave cavity oven. Materials within the oven are subjected to a degree of heating dependent on their electromagnetic properties. For many applications, it is desirable to maintain control over the distribution of heat deposition. This can be achieved through focussing of the electromagnetic field within the cavity. Two new mechanisms are identified where an increased level of control over the heating pattern and its location could be advantageous. The research described within this thesis aims to improve heating selectivity in microwave cavity ovens by the identification and enhanced control of modal patterns in degenerate and non-degenerate resonators. This is achieved through the analysis of two novel oven arrangements. The first of these addresses the requirement for highly selective heating in hyperthermia treatment. It is demonstrated that proper selection of a forced degenerate mode set can lead to an enhancement in field focussing within the centre of the cavity through constructive and destructive interference of the fields in each mode pattern. It is found that a highly selective peak of field can be produced within the centre of a large cylindrical waveguide cavity for the purpose of hyperthermia treatment. The peak is produced using a quasi degenerate mode set excited at approximately 1:3GHz. The second example presents an open oven design for the curing of epoxy and encapsulant materials within the micro-electronics packaging industry. It is intended that the oven be placed on the arm of a precision alignment machine such that the curing and placement stages of production be combined, suggesting an increase in production efficiency. Two excitation schemes are presented based on the coupling of quasi degenerate mode sets through a wide frequency range and the excitation of a single high order mode enabling uniform field distribution for heating of encapsulant material and increased selective heating through spatial alignment of modal field peaks, respectively. Experimental results demonstrate the viability of the open-ended microwave oven for curing. Both proposed excitation methods within the open oven design are investigated with results presented. Optimisation of the heating fields is achieved through inclusion of lowloss materials within the oven. Curing of an encapsulant material covering a commercial chip package is achieved and the overall design validated