Grünbaum introduced measures of symmetry for convex bodies that measure how far a given convex body is from a centrally symmetric one. Here, we introduce new measures of symmetry that measure how far a given convex body is from one with “enough symmetries”. To define these new measures of symmetry, we use affine covariant points. We give examples of convex bodies whose affine covariant points a...

The point density in a single-scan terrestrial laser scanner (TLS) point cloud is very dense close to the scanner and gets sparser as the distance from the scanner increases. A full circular scan can contain tens of millions of points, which is impractical for most algorithms that work on point data. The number of points can be reduced by taking a sample of the original data. We have studied wh...

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...

We present a fast algorithm for kernel summation problems in high-dimensions. These problems appear in computational physics, numerical approximation, non-parametric statistics, and machine learning. In our context, the sums depend on a kernel function that is a pair potential defined on a dataset of points in a high-dimensional Euclidean space. A direct evaluation of the sum scales quadratical...

This paper presents a brief history of the concept of player types starting with Bartles’s work on MUDs and continuing to more recent, empirical research. Player types are not a defined concept and any categorization of players or users needs to occur within the context of a particular application or domain. Play-personas are suggested as a useful tool that can be used to put player type resear...

In-water viewing of sharks by tourists has become a popular and lucrative industry. There is some concern that interactions with tourists with ecotourism operations might harm sharks through disruption of behaviours. Here, we analysed five years of whale shark (Rhincodon typus) encounter data by an ecotourism industry at Ningaloo Reef, Western Australia, to assess the impact of ecotourism inter...