Phase transition and percolation in Gibbsian particle models

We discuss the interrelation between phase transitions in interacting lattice or continuum models, and the existence of infinite clusters in suitable random-graph models. In particular, we describe a random-geometric approach to the phase transition in the continuum Ising model of two species of particles with soft or hard interspecies repulsion. We comment also on the related area-interaction process and on perfect simulation.Comment: Survey article, 25 page

Nucleotide repeats in mitochondrial genome determine human lifespan

Direct nucleotide repeats can facilitate deletions of segments of mitochondrial genome1, leading to a wide range of neuromuscular disorders1,2 as well as aging2,3 in humans. We hypothesized that the number of the direct perfect repeats in human mitochondrial genomes influences longevity through the formation of harmful mtDNA deletions in the somatic cells. The analysis of the complete mitochondrial genomes of 762 unrelated Japanese individuals4-6 reveals a negative correlation between the abundance of the direct perfect repeats and the expected longevity. This association is largely due to the disruption of the common repeat (8470,13447) by a point mutation 8473C which occurred at the origin of the D4a haplogroup characterized by extreme longevity in Japan7. Our results provide the first evidence for correlation between the number of nucleotide repeats and the lifespan on intraspecific level

Supercritical multitype branching processes: the ancestral types of typical individuals

For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population averages of ancestral types (conditioned on non-extinction), and identify the mutation process describing the type evolution along typical lineages. An important tool is a representation of the family tree in terms of a suitable size-biased tree with trunk. As a by-product, this representation allows a `conceptual proof' (in the sense of Kurtz, Lyons, Pemantle, Peres 1997) of the continuous-time version of the Kesten-Stigum theorem.Comment: 23 pages, 1 figure; minor additions, added reference