Random waves on T3\mathbb{T}^3: nodal area variance and lattice point correlations

We consider the ensemble of random Gaussian Laplace eigenfunctions on $\mathbb{T}^3=\mathbb{R}^3/\mathbb{Z}^3$ (`$3d$ arithmetic random waves'), and study the distribution of their nodal surface area. The expected area is proportional to the square root of the eigenvalue, or `energy', of the eigenfunction. We show that the nodal area variance obeys an asymptotic law. The resulting asymptotic formula is closely related to the angular distribution and correlations of lattice points lying on spheres.Comment: To appear in IMR

Moral Imagination: The Missing Component in Global Health

Benatar explores the underlying reasons for our failure to make adequate progress in improving global health

Global Health Challenges: The Need for an Expanded Discourse on Bioethics

Benatar and colleagues argue that the world has changed profoundly since the birth of modern bioethics in the 1960s, and that bioethics needs to address today's global health problems

Performance Measurement Under Increasing Environmental Uncertainty In The Context of Interval Type-2 Fuzzy Logic Based Robotic Sailing

Performance measurement of robotic controllers based on fuzzy logic, operating under uncertainty, is a subject area which has been somewhat ignored in the current literature. In this paper standard measures such as RMSE are shown to be inappropriate for use under conditions where the environmental uncertainty changes significantly between experiments. An overview of current methods which have been applied by other authors is presented, followed by a design of a more sophisticated method of comparison. This method is then applied to a robotic control problem to observe its outcome compared with a single measure. Results show that the technique described provides a more robust method of performance comparison than less complex methods allowing better comparisons to be drawn.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013

The humanistic side of medical education

The hope of teaching the humanities in medicine is that improvement in attitude and practice may result from sensitising students to the many complex social and ethical issues faced in healthcare, and through providing them with insight into the role of moral reasoning in ranking potential solutions with justifying reasons and transparency

Adult reactions to multiple trauma

A dissertation submitted to the Faculty of Arts. University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the Degree of Master of Arts (Clinical Psycholoqy). Johannesburg, August 1996This study aims to explore the relationship between intrusion and avoidance symptoms as described in the diagnostic category in the DSM-IV (American Psychiatric Association, 1994) and frequency and level of exposure to traumatogenic events. The effects of lay counselling after the event were taken into account in the analysis, and the sample consisted of voluntary First National Bank employees, who were exposed to more than one bank robbery between December 1989 and 1992. The hypotheses of the study were that an increasing number of exposures to potentially traumatogenic events, and increasing levels of exposure to potentially traurnatoqenic events would be related to the development of avoidant and intrusion symptoms. Further, it was hypothesised that the interaction of these two variables would also be significantly related to the development of avoidant and intrusive symptoms and the nature of this interaction was explored. The scale used to measure the symptoms was the impact of Events Scale (Horowitz, 1979). Level of exposure was measured on a four point scale, which included extreme exposure with physical injury; direct threat and coafrontatlon: indirect contact with the perpetrators, and the fourth category was indirect exposure, or secondary victimisation. The results indicated that level of exposure had a significant relationship with the development of both intrusion and avoidance symptoms. Contrary to expectations, frequency of exposure was not found to be related to symptomology and it was speculated that this might have been because of the crudeness of the measure. In this regard it is of note that level of exposure as measured in this study included frequency of exposure. The results indicated further that post trauma counselling was not significantly related to symptomology. The implications of these findings were discussed in the light of the general literature in PTSD