Related papers: Universal tree structures in directed polymers and…
Ultrametric trees are trees whose leaves lie at the same distance from the root. They are used to model the genealogy of a population of particles co-existing at the same point in time. We show how the boundary of an ultrametric tree, like…
The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…
We compute the continuous bounded cohomology of the full automorphism groups of regular trees in all positive degrees, with coefficients arising from any irreducible continuous unitary representations. To the author's knowledge, this seems…
We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we…
A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…
Polymers consisting of more than one type of monomer, known as copolymers, are vital to both living and synthetic systems. Copolymerisation has been studied theoretically in a number of contexts, often by considering a Markov process in…
The evolution of an inhomogeneous universe composed entirely of matter is followed from an early, nearly uniform state until the time when the inhomogeneities have begun to grow large. The particular distribution of matter studied in this…
We deal with the existence of universal members in a given cardinality for several classes. First we deal with classes of Abelian groups, specifically with the existence of universal members in cardinalities which are strong limit singular…
Ignoring the differences between countries, human reproductive and dispersal behaviors can be described by some standardized models, so whether there is a universal law of population growth hidden in the abundant and unstructured data from…
We study the evolution of the population genealogy in the classic neutral Moran Model of finite size and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise…
We consider two varieties of labeled rooted trees, and the probability that a vertex chosen from all vertices of all trees of a given size uniformly at random has a given rank. We prove that this probability converges to a limit as the tree…
Given a subset of size $k$ of a very large universe a randomized way to find this subset could consist of deleting half of the universe and then searching the remaining part. With a probability of $2^{-k}$ one will succeed. By probability…
We review the statistical properties of the genealogies of a few models of evolution. In the asexual case, selection leads to coalescence times which grow logarithmically with the size of the population in contrast with the linear growth of…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
We demonstrate that the melting curves of various model systems of interacting particles collapse to (or are located very close to) a universal master curve on a plane of appropriately chosen scaled variables. The physics behind this…
Recovery of population size history from molecular sequence data is an important problem in population genetics. Inference commonly relies on a coalescent model linking the population size history to genealogies. The high computational cost…
In sexual populations, selection operates neither on the whole genome, which is repeatedly taken apart and reassembled by recombination, nor on individual alleles that are tightly linked to the chromosomal neighborhood. The resulting…
A method for creating a forest of model trees to fit samples of a function defined on images is described in several steps: down-sampling the images, determining a tree's hyperplanes, applying convolutions to the hyperplanes to handle small…
We consider the problem of drawing multiple gene trees inside a single species tree in order to visualize multispecies coalescent trees. Specifically, the drawing of the species tree fills a rectangle in which each of its edges is…
In the context of percolation in a regular tree, we study the size of the largest cluster and the length of the longest run starting within the first d generations. As d tends to infinity, we prove almost sure and weak convergence results.