Judging where a ball will go: the case of curved free kicks in football

This study examined whether adding spin to a ball in the free kick situation in football affects a professional footballer's perception of the ball's future arrival position. Using a virtual reality set-up, participants observed the flight paths of aerodynamically realistic free kicks with (+/- 600 rpm) and without sidespin. With the viewpoint being fixed in the centre of the goal, participants had to judge whether the ball would have ended up in the goal or not. Results show that trajectories influenced by the Magnus force caused by sidespin gave rise to a significant shift in the percentage of goal responses. The resulting acceleration that causes the ball to continually change its heading direction as the trajectory unfolds does not seem to be taken into account by the participants when making goal judgments. We conclude that the visual system is not attuned to such accelerated motion, which may explain why goalkeepers appear to misjudge the future arrival point of such curved free kicks.

A contingent valuation of the 2012 London Olympic games - A regional perspective

Major sporting events such as the Olympics are usually assessed in terms of economic impacts. Recently, policy makers have begun to place greater emphasis on possible intangible effects (such as civic pride, legacy of sporting facilities) associated with such events. To date, little work has been carried out on quantifying these effects in a meaningful way. This study uses contingent valuation methodology to assess the value of the proposed 2012 London Olympic Games. The survey is carried out on the provincial city of Bath, approximately 2 hours west of London. Conducting the survey outside of London is justified on the basis that the organizers of London 2012 have emphasized the value of the event to the United Kingdom as a whole. The results suggest that positive intangible effects are associated with the event and residents outside of London are willing to pay toward funding.

Support vector machine classification for large data sets via minimum enclosing ball clustering

Support vector machine (SVM) is a powerful technique for data classification. Despite of its good theoretic foundations and high classification accuracy, normal SVM is not suitable for classification of large data sets, because the training complexity of SVM is highly dependent on the size of data set. This paper presents a novel SVM classification approach for large data sets by using minimum enclosing ball clustering. After the training data are partitioned by the proposed clustering method, the centers of the clusters are used for the first time SVM classification. Then we use the clusters whose centers are support vectors or those clusters which have different classes to perform the second time SVM classification. In this stage most data are removed. Several experimental results show that the approach proposed in this paper has good classification accuracy compared with classic SVM while the training is significantly faster than several other SVM classifiers.

Analysing orchestrations with risk profiles and angel-daemon games

In this paper game theory is used to analyse the effect of a number of service failures during the execution of a grid orchestration. A service failure may be catastrophic in that it causes an entire orchestration to fail. Alternatively, a grid manager may utilise alternative services in the case of failure, allowing an orchestration to recover, A risk profile provides a means of modelling situations in a way that is neither overly optimistic nor overly pessimistic. Risk profiles are analysed using angel and daemon games. A risk profile can be assigned a valuation through an analysis of the structure of its associated Nash equilibria. Some structural properties of valuation functions, that show their validity as a measure for risk, are given. Two main cases are considered, the assessment of Orc expressions and the arrangement of a meeting using reputations.

Cinderella comes to the Ball: Article 14 and the right to non-discrimination in the ECHR

Article 14 ECHR has often been derided as a Cinderella provision, but during the last few years, this has started to change. This article examines how Article 14 has developed, and may live up to its potential as a powerful non-discrimination principle. The case law developments in relation to the “ambit” requirement in Article 14, the development of indirect discrimination case law, and the approval of positive action, all point to a more substantive conception of equality, which offers protection to disadvantaged and vulnerable groups.

The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.

Optic variables used to judge future ball arrival position in expert and novice soccer players

Although many studies have looked at the perceptual-cognitive strategies used to make anticipatory judgments in sport, few have examined the informational invariants that our visual system may be attuned to. Using immersive interactive virtual reality to simulate the aerodynamics of the trajectory of a ball with and without sidespin, the present study examined the ability of expert and novice soccer players to make judgments about the ball's future arrival position. An analysis of their judgment responses showed how participants were strongly influenced by the ball's trajectory. The changes in trajectory caused by sidespin led to erroneous predictions about the ball's future arrival position. An analysis of potential informational variables that could explain these results points to the use of a first-order compound variable combining optical expansion and optical displacement.