Transition probabilities for the simple random walk on the Sierpinski graph

Non-Gaussian upper and lower bounds are obtained for the transition probabilities of the simple random walk on the Sierpinski graph, the pre-fractal associated with the Sierpinski gasket. They are of the same form as bounds previously obtained for the transition density of Brownian motion on the Sierpinski gasket, subject to a scale restriction. A comparison with transition density bounds for random walks on general graphs demonstrates that this restriction represents the scale at which the pre-fractal graph starts to look like the fractal gasket

A systematic review on the meaning of the concept 'AIDS Orphan':confusion over definitions and implications for care

Global publications on the international AIDS epidemic report on the existence of an ever-increasing number of orphans and vulnerable children. It has been suggested that by the end of this decade there will be in excess of 25 million AIDS orphans globally, an issue which will require understanding and organisation of long-term medical, psychological and social support. This study provides a systematic review to examine the use, overuse and misuse of the term orphan and explores the benefits and limitations of this approach. It then summarises the knowledge on orphans to date. Using a search strategy of published studies and recent conference abstracts, 383 papers were identified where the concept of AIDS and Orphan was raised. The papers were systematically coded and reviewed to understand when and how a child is labelled an orphan, and to summarise the effect of orphanhood on outcome measures, most notably psychologically and physically. All controlled studies published prior to 2006 were reviewed. A consistent picture of negative effects of parental death (however defined) on a wide range of physical, socioeconomic and psychological outcomes were recorded. Seventeen studies met criteria for in-depth review (empirical, fully published, control group). The majority of studies are cross-sectional (two are longitudinal) and employ a very wide array of measures - both standardised and study specific. This detailed analysis shows a mixed picture on outcome. Although most studies report some negative effects, there are often no differences and some evidence of protective effects from quality of subsequent care and economic assistance. The lack of consistent measures and the blurring of definitions are stumbling blocks in this are