Judging the ‘passability’ of dynamic gaps in a virtual rugby environment

Affordances have recently been proposed as a guiding principle in perception–action research in sport (Fajen, Riley, & Turvey, 2009). In the present study, perception of the ’passability’ affordance of a gap between two approaching defenders in rugby is explored. A simplified rugby gap closure scenario was created using immersive, interactive virtual reality technology where 14 novice participants (attacker) judged the passability of the gap between two virtual defenders via a perceptual judgment (button press) task. The scenario was modeled according to tau theory (Lee, 1976) and a psychophysical function was fitted to the response data. Results revealed that a tau-based informational quantity could account for 82% of the variance in the data. Findings suggest that the passability affordance in this case, is defined by this variable and participants were able to use it in order to inform prospective judgments as to passability. These findings contribute to our understanding of affordances and how they may be defined in this particular sporting scenario; however, some limitations regarding methodology, such as decoupling perception and action are also acknowledged.

Confirming the Existence of Gaps and Depletions in the Irish Oak Tree-Ring Record

In the course of building the 7000 year Belfast long oak chronology a series of depletion problems were encountered. These problems were overcome by 1984 when the completion of the long chronology was announced. The solution to the bridging of the various ‘gaps’ in the Irish chronology lay in the use of long sections of oak chronology from Britain. Now that a quarter of a century has elapsed and large numbers of additional oak samples, and site assemblages, have been accumulated it seems reasonable to review the ‘gaps’ in order to see if the Irish chronology could now be constructed without the use of British material. That is, are the depletion periods in the Irish chronology still evident, and if so, what might they imply about past conditions and human populations? The perhaps surprising conclusion is that the original depletions are still evident after 25 years of quasi-random sampling by archaeologists and palaeoecologists throughout Ireland.

Separable Banach lattices on which every bounded linear operator is regular

We give a complete description of those separable Banach lattices E with the property that every bounded linear from E into itself is the difference of two positive operators.

Mass media and polarisation processes in the bounded confidence model of opinion dynamics

This paper presents a social simulation in which we add an additional layer of mass media communication to the social network 'bounded confidence' model of Deffuant et al (2000). A population of agents on a lattice with continuous opinions and bounded confidence adjust their opinions on the basis of binary social network interactions between neighbours or communication with a fixed opinion. There are two mechanisms for interaction. 'Social interaction' occurs between neighbours on a lattice and 'mass communication' adjusts opinions based on an agent interacting with a fixed opinion. Two new variables are added, polarisation: the degree to which two mass media opinions differ, and broadcast ratio: the number of social interactions for each mass media communication. Four dynamical regimes are observed, fragmented, double extreme convergence, a state of persistent opinion exchange leading to single extreme convergence and a disordered state. Double extreme convergence is found where agents are less willing to change opinion and mass media communications are common or where there is moderate willingness to change opinion and a high frequency of mass media communications. Single extreme convergence is found where there is moderate willingness to change opinion and a lower frequency of mass media communication. A period of persistent opinion exchange precedes single extreme convergence, it is characterized by the formation of two opposing groups of opinion separated by a gradient of opinion exchange. With even very low frequencies of mass media communications this results in a move to central opinions followed by a global drift to one extreme as one of the opposing groups of opinion dominates. A similar pattern of findings is observed for Neumann and Moore neighbourhoods.

Completely bounded disjointness preserving operators between Fourier algebras

In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. © 2011 Elsevier Inc.