Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

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.

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.

Sediment transfer and accumulation in two contrasting salt marsh/mudflat systems: the Seine estuary (France) and the Medway estuary (UK)

Understanding the dynamics of fine sediment transport across the upper intertidal zone is critical in managing the erosion and accretion of intertidal areas, and in managed realignment/estuarine habitat recreation strategies. This paper examines the transfer of sediments between salt marsh and mudflat environments in two contrasting macrotidal estuaries: the Seine (France) and the Medway (UK), using data collected during two joint field seasons undertaken by the Anglo-French RIMEW project (Rives-Manche Estuary Watch). High-resolution ADCP, Altimeter, OBS and ASM measurements from mudflat and marsh surface environments have been combined with sediment trap data to examine short-term sediment transport processes under spring tide and storm flow conditions. In addition, the longer-term accumulation of sediment in each salt marsh system has been examined via radiometric dating of sediment cores. In the Seine, rapid sediment accumulation and expansion of salt marsh areas, and subsequent loss of open intertidal mudflats, is a major problem, and the data collected here indicate a distinct net landward flux of sediments into the marsh interior. Suspended sediment fluxes are much higher than in the Medway estuary (averaging 0.09 g/m(3)/s), and vertical accumulation rates at the salt marsh/mudflat boundary exceed 3 cm/y. Suspended sediment data collected during storm surge conditions indicate that significant in-wash of fine sediments into the marsh interior can occur during (and following) these high-magnitude events. In contrast to the Seine, the Medway is undergoing erosion and general loss of salt marsh areas. Suspended sediment fluxes are of the order of 0.03 g/m(3)/s, and the marsh system here has much lower rates of vertical accretion (sediment accumulation rates are ca. 4 mm/y). Current velocity data for the Medway site indicate higher velocities on the ebb tide than occur on the flood tide, which may be sufficient to remobilise sediments deposited on the previous tide and so force net removal of material from the marsh.