Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Parallel implementation of the recurrence method for computing the power-spectral density of thin avalanche photodiodes

A simulation program has been developed to calculate the power-spectral density of thin avalanche photodiodes, which are used in optical networks. The program extends the time-domain analysis of the dead-space multiplication model to compute the autocorrelation function of the APD impulse response. However, the computation requires a large amount of memory space and is very time consuming. We describe our experiences in parallelizing the code using both MPI and OpenMP. Several array partitioning schemes and scheduling policies are implemented and tested Our results show that the OpenMP code is scalable up to 64 processors on an SGI Origin 2000 machine and has small average errors.

Debating the division of labour in healthcare in France and England

As Larson (1990) states, professions are historically specific and ‘there is no pattern of social closure around an occupation that is not inflected by the latter’s past, its specific activity and typical context of performance or…the political context in which closure is obtained.’ Larson’s work focuses particularly on the differences between the establishment of professions in France, where there was considerable state intervention, with that in the US and UK, both of which were more market-oriented. This paper is based on data from an evaluation of a large European exchange programme of staff between Kent and Lille, from 2005 to 2008 and discusses the division of labour in healthcare between two occupational groups, medicine and nursing, in England and in France. This division of labour has been extensively discussed in the UK, particularly since from the mid 1990s the nursing role has been extended and innovations such as nurse prescribing have been introduced, whereas such extended roles have not been introduced in France. The paper draws particularly on interview data from mental health practitioners, in which it is argued that whilst the English nurses may on the surface seem to have a wider range of competences and autonomy, in reality they are more constrained, as they operate under protocols and therefore do not exercise professional judgement. Not only do these data illustrate the centrality of professional judgement in discussions about practice, they also demonstrate the circularity of many debates on extended roles.