Children’s Perceptions of Cohesion

The general purpose of the two studies reported here was to examine perceptions of team cohesiveness in children aged 9 to 12 years. In Study 1, focus groups were used to examine individual perceptions of cohesion from the perspective of group integration – the group as a totality. In Study 2, open-ended questionnaires were used to examine individual perceptions of cohesion from the perspective of individual attractions to the group. The results showed that children as young as nine years understand the phenomenon known as cohesion. They can discuss the group as a totality, the characteristics of cohesive and non-cohesive teams, and identify the major factors attracting them to and maintaining their involvement in the group. Also, the ability to clearly distinguish between task and social cohesion is present. The results provide insight into the world of child sport and emphasise the importance of group cohesion, affiliation, and other social constructs in children’s involvement and adherence to sport groups

Efficient algorithms for beacon routing in polygons

In a paper by Biro et al. [7], a novel twist on guarding in art galleries is introduced. A beacon is a fixed point with an attraction pull that can move points within the polygon. Points move greedily to monotonically decrease their Euclidean distance to the beacon by moving straight towards the beacon or sliding on the edges of the polygon. The beacon attracts a point if the point eventually reaches the beacon. Unlike most variations of the art gallery problem, the beacon attraction has the intriguing property of being asymmetric, leading to separate definitions of attraction region and inverse attraction region. The attraction region of a beacon is the set of points that it attracts. For a given point in the polygon, the inverse attraction region is the set of beacon locations that can attract the point. We first study the characteristics of beacon attraction. We consider the quality of a "successful" beacon attraction and provide an upper bound of $\sqrt{2}$ on the ratio between the length of the beacon trajectory and the length of the geodesic distance in a simple polygon. In addition, we provide an example of a polygon with holes in which this ratio is unbounded. Next we consider the problem of computing the shortest beacon watchtower in a polygonal terrain and present an $O(n \log n)$ time algorithm to solve this problem. In doing this, we introduce $O(n \log n)$ time algorithms to compute the beacon kernel and the inverse beacon kernel in a monotone polygon. We also prove that $\Omega(n \log n)$ time is a lower bound for computing the beacon kernel of a monotone polygon. Finally, we study the inverse attraction region of a point in a simple polygon. We present algorithms to efficiently compute the inverse attraction region of a point for simple, monotone, and terrain polygons with respective time complexities $O(n^2)$, $O(n \log n)$ and $O(n)$. We show that the inverse attraction region of a point in a simple polygon has linear complexity and the problem of computing the inverse attraction region has a lower bound of $\Omega(n \log n)$ in monotone polygons and consequently in simple polygons.