Statistics of cross sections of Voronoi tessellations.

In this paper, we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in order to obtain analytical results, Voronoi cells are approximated to spheres. First, the probability density function for the lengths of the radii of the sections is derived and it is shown that it is related to the Meijer G function; its properties are discussed and comparisons are made with the numerical results.

Mean number of visits to sites in Levy flights.

Formulas are derived to compute the mean number of times a site has been visited during symmetric Levy flights. Unrestricted Levy flights are considered first, for lattices of any dimension: conditions for the existence of finite asymptotic maps of the visits over the lattice are analyzed and a connection is made with the transience of the flight. In particular it is shown that flights on lattices of dimension greater than 1 are always transient.

Number of times a site is visited in two-dimensional random walks.

In this paper, formulas are derived to compute the mean number of times a site has been visited in a random walk on a two-dimensional lattice. Asymmetric random walks are considered, with or without drift, for different boundary conditions. It is shown that in case of absorbing boundaries the mean number of visits reaches stationary values over the lattice; comparisons with a Monte Carlo simulation are also presented.

Elongation factor 1-alpha sequences do not support an early divergence of the Acoela.

The phylogenetic position of the Acoela is a key problem in the understanding of metazoan evolution. Recent studies based on 18S ribosomal DNA (rDNA) sequences have placed the Acoela in an extremely basal position as the sister group to all other extant triploblastic animals, suggesting that the phylum Platyhelminthes is polyphyletic. In order to test the results obtained with 18S rDNA, we sequenced elongation factor 1-alpha (EF1a) for the acoel Convoluta roscoffensis and five species of Turbellaria (two polyclads, Leptoplana tremellaris, and Prostheceraeus vittatus, and three triclads, Crenobia alpina, Schmidtea polychroa, and Girardia tigrina).