The average inter-crossing number of equilateral random walks and polygons

In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = (3 In 2)/(8) approximate to 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance p apart and p is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of p. Our simulation result shows that the model in fact works very well for the entire range of p. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well.

Accès aux soins d'urgence: organisation et utilité de la chaîne des secours [Access to prehospital medical care: organization and utility of the chain of survival].

In order to be effective, access to prehospital care must be integrated into a system described as "the chain of survival". This system is composed of 5 essential phases: 1) basic help by witnesses; 2) call for help; 3) basic life support; 4) professional rescue and transport to the appropriate institution and 5) access to emergency ward and hospital management. Each phase is characterized by a specific organization, dedicated skills and means in order to increase the level of care brought to the patient. This article describes the organization, the utility and the specificity of the chain of survival allowing access to prehospital medical care in the western part of Switzerland.

Essential role of the Wnt pathway effector Tcf-1 for the establishment of functional CD8 T cell memory.

Immune protection from intracellular pathogens depends on the generation of terminally differentiated effector and of multipotent memory precursor CD8 T cells, which rapidly regenerate effector and memory cells during recurrent infection. The identification of factors and pathways involved in CD8 T cell differentiation is of obvious importance to improve vaccination strategies. Here, we show that mice lacking T cell factor 1 (Tcf-1), a nuclear effector of the canonical Wingless/Integration 1 (Wnt) signaling pathway, mount normal effector and effector memory CD8 T cell responses to infection with lymphocytic choriomeningitis virus (LCMV). However, Tcf-1-deficient CD8 T cells are selectively impaired in their ability to expand upon secondary challenge and to protect from recurrent virus infection. Tcf-1-deficient mice essentially lack CD8 memory precursor T cells, which is evident already at the peak of the primary response, suggesting that Tcf-1 programs CD8 memory cell fate. The function of Tcf-1 to establish CD8 T cell memory is dependent on the catenin-binding domain in Tcf-1 and requires the Tcf-1 coactivators and Wnt signaling intermediates beta-catenin and gamma-catenin. These findings demonstrate that the canonical Wnt signaling pathway plays an essential role for CD8 central memory T cell differentiation under physiological conditions in vivo. They raise the possibility that modulation of Wnt signaling may be exploited to improve the generation of CD8 memory T cells during vaccination or for therapies designed to promote sustained cytotoxic CD8 T cell responses against tumors.