Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures

In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key criteria is that the procedures should scale to large data sets. In this regard we find that the formal calculation of the Bayes factor for a dependent-vs.-independent DPM joint probability measure is not feasible computationally. To address this we present Bayesian diagnostic measures for characterising evidence against a "null model" of pairwise independence. In simulation studies, as well as for a real data analysis, we show that our approach provides a useful tool for the exploratory nonparametric Bayesian analysis of large multivariate data sets

Two-sample Bayesian Nonparametric Hypothesis Testing

In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples $\mathbf{y}^{\scriptscriptstyle(1)}\;$\stackrel{\scriptscriptstyle{iid}}{\s im}$\;F^{\scriptscriptstyle(1)}$ and $\mathbf{y}^{\scriptscriptstyle(2 )}\;$\stackrel{\scriptscriptstyle{iid}}{\sim}$\;F^{\scriptscriptstyle( 2)}$, with $F^{\scriptscriptstyle(1)},F^{\scriptscriptstyle(2)}$ unknown, we wish to evaluate the evidence for the null hypothesis $H_0:F^{\scriptscriptstyle(1)}\equiv F^{\scriptscriptstyle(2)}$ versus the alternative $H_1:F^{\scriptscriptstyle(1)}\neq F^{\scriptscriptstyle(2)}$. Our method is based upon a nonparametric P\'{o}lya tree prior centered either subjectively or using an empirical procedure. We show that the P\'{o}lya tree prior leads to an analytic expression for the marginal likelihood under the two hypotheses and hence an explicit measure of the probability of the null $\mathrm{Pr}(H_0|\{\mathbf {y}^{\scriptscriptstyle(1)},\mathbf{y}^{\scriptscriptstyle(2)}\}\mathbf{)}$.Comment: Published at http://dx.doi.org/10.1214/14-BA914 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Advanced modelling of ovoid balls

Sports played with an ovoid ball may be considered as minority sports in comparison to the numerous games played with spherical balls, however the ovoid ball market is considerable, with $84million spent on the purchasing of American footballs in the US alone (SGMA 2007b). In comparison to spherical balls, it is apparent that little research has been performed on ovoid types, which presented an opportunity for a detailed study into their dynamic properties in game related situations. With the development of this knowledge new ball design concepts have been investigated to improve consistency and performance, allowing manufacturers to create balls with improved physical characteristics. Experimental procedures have been created which allow the dynamic behaviour of an ovoid ball to be characterised. It was found that the measured parameters varied depending upon the position of impact, orientation angle of the ball and the position of the valve at impact. The inclusion of the valve within a rugby ball creates a non uniform mass distribution resulting in unstable rotation about the axis with the intermediate moment of inertia. This unstable rotation results in the ball performing a series of half twists, thus increasing the drag force during the flight and wobble. Prototype rugby balls have been manufactured with various mass distributions, allowing the effect on the unstable rotation to be analysed. Results showed that the inclusion of multiple valves, within the dynamically balanced bladder, resulted in stable rotation about all ptinciple axes. FE models have been created with isotropic and anisotropic material properties, with all models validated using experimental procedures. Results suggest that the anisotropic FE simulation accurately predicts the coefficient of restitution, contact time and deformation during experimental testing, and as a result it can be used to predict the dynamic behaviour of a rugby ball during various impact scenarios. Using a thermo-bonded construction, it was shown that a novel rugby ball could be developed with a unique carcass configuration and outer panels with increased design flexibility. A number of carcass designs, based upon mathematical shapes, have been created which increase the consistency of the dynamic behaviour of the ball when impacted at different locations.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Design of a force acquisition system for high-energy short-duration impacts

This paper describes a novel force acquisition system capable of measuring the force profiles of high-energy short-duration impacts. This force acquisition system was used to test dynamically a cricket leg guard and to create a contour map of the peak transmitted forces across the garment’s surface. The cricket leg guard was found to provide most protection in the central shin and knee regions, areas most likely to be impacted normally and so to receive the highest-energy impacts. The use of this system will enable a dynamic test procedure to be developed to mimic impact conditions encountered during a game, allowing optimization of cricket pad designs for specific impacts

Injection moulding: properties customization by varying process conditions

Injection moulding: properties customization by varying process condition

The application of simulation to the understanding of football flight

This paper demonstrates the value of using a flight model in the analysis of the flight of a football, and explores the complexity of the model required to produce useful results. Two specific aspects of the simulation are addressed: the need to include a model of spin decay and the requirement to include a full aerodynamic drag profile as a function of Reynolds number rather than a single indicative value. Both are aspects of the ball performance that are experimentally intensive to obtain. The simulated flights show that the inclusion of spin degradation is important if flight validation is the objective, but that it may be unnecessary in a comparative study. The simple analytical model of spin degradation is shown to overestimate the reduction in lateral deviation when compared to experimentally acquired data. Therefore, the experimental method is preferred. The analysis of the shape of the drag profile (drag coefficient against Reynolds number) is explored, and it is shown from the simulated flights that post-critical coefficients of drag have the greatest effect on trajectories, and an average drag value is sufficient for most modelled scenarios

Complex injection moulded components - Bridging the knowledge gap

Injection moulding is the predominant manufacturing process enabling the production of precise and consistent polymeric parts at a high volume. The final performance of those parts is critically dependent on their melt flow history and the current approach of testing simplified specimens produced by idealized melt flow conditions to specify new or enhanced materials is therefore not sufficient, since final parts often feature a more complex geometry. The purpose of this research is to highlight this omission by conducting high velocity impact and quasi-static tensile tests on PA-12 specimens obtained from a new concept injection moulding tool. This mould allows controlled modification of the material flow by adding specific mould tool design features which lead to the creation of a weld line, flow hesitation, or combination of both of these irregular flow phenomena and is therefore an improved representation of final injection moulded components. Furthermore, test specimens representing simplified as well as more complex geometries can be obtained from the same moulded samples, guaranteeing identical applied process conditions. The occurring microstructural differences due to the diverse melt flow history are verified using optical microscopy and Differential Scanning Calorimetry

The aerodynamic performance of a range of FIFA-approved footballs

Much discussion surrounds the flight of a football especially that perceived as irregular and is typically done so with little understanding of the aerodynamic effects or substantive evidence of the path taken. This work establishes that for a range of FIFA approved balls there is a significant variation in aerodynamic performance. This paper describes the methods used for mounting stationary and spinning footballs in a wind tunnel enabling accurate force data to be obtained, and the analysis techniques used. The approach has been to investigate a number of scenarios: Non-spinning Reynolds Sweep, Unsteady Loads, Orientation Sensitivity (Yaw Sweep) and Spinning Reynolds Sweep. The techniques are applied to a number of footballs with differing constructions and the results reported. To put the aerodynamic data into context the results are applied in a flight model to predict the potential differences in the behaviour of each ball in the air. The paper concludes that although the drag characteristics are different for the different balls tested the simulation suggests that this has only a limited effect on the flight of the ball. It is also shown that the unsteadiness of the aerodynamic loads is unlikely to be responsible for unpredictable behaviour. However, it is also shown that there are significant differences in the lateral aerodynamic forces for a range of FIFA approved match balls, and that these aerodynamic differences have a significant effect on the flight path for both spinning and for slowly rotating balls

Processing of in-plant mechanically recycled PA-12

The increasing public awareness and demand for a more sustainable handling of the earth’s resources has led to the idea/ concept of a circular economy. Within this concept materials will be re-used in a closed loop system rather than being down-cycled or inappropriately managed (disposed via landfill) at the end of their life-cycle. Based on previous research, Polyamide 12 (PA-12) is a promising material candidate in the sports and leisure sector and its ability for being reprocessed via injection molding has been investigated. While other PAs tend to show a decrease in impact properties on mechanical recycling, PA-12 is shown to be able to overcome these problems when reprocessed at a higher melt temperature, yielding samples with improved impact properties compared to the primary material