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By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R^d of Ginibre's Fermi-Dirac gas of such loops. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford and Ruelle if the underlying potential is positive. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.
Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.
Since 2011 the Comorian Island of Mayotte has been France’s 101st département, thereby becoming part of the European Union. As a result, France has consolidated and strengthened its strategic position in the Indian Ocean. With the change of political status in 2011, new developments have occurred in Mayotte. It is still unclear whether the expected economic boom, extensive social benefits or injection of EU regional funds can help to alleviate poverty and raise living standards. There is concern, however, that massive immigration to Mayotte from the surrounding territories is diminishing any progress and will continue to do so. Not only France but also the EU will have to adapt to new immigration problems due to this new external border. In this situation one thing is clear: the language contact between French and the local languages, which is the result of political developments, is leading to new dynamics. The diglossic situation east of Africa, between French as the dominant language and local languages like Shimaoré or Shibushi spoken in Mayotte will become more marked in the next few years.