相关论文: The genealogy of a sample from a binary branching …

We investigate a network growth model in which the genealogy controls the evolution. In this model, a new node selects a random target node and links either to this target node, or to its parent, or to its grandparent, etc; all nodes from…

We consider a stochastic process that describes several particles interacting by either merging or annihilation. When two particles merge, they combine their masses; when annihilation occurs, only the particle of smallest mass survives.…

We revisit the spatial ${\lambda}$-Fleming-Viot process introduced in [1]. Particularly, we are interested in the time $T_0$ to the most recent common ancestor for two lineages. We distinguish between the case where the process acts on the…

We consider a critical branching process $Y_{n}$ in an i.i.d. random environment, in which one immigrant arrives at each generation. Let $% \mathcal{A}_{i}(n)$ be the event that all individuals alive at time $n$ are offspring of the…

We study coalescent processes conditional on the population pedigree under the exchangeable diploid bi-parental population model of \citet{BirknerEtAl2018}. While classical coalescent models average over all reproductive histories, thereby…

We present a coalescent process where three particles merge at each coagulation step. Using a random walk representation, we prove duality with a fragmentation process, whose fragmentation law we specify explicitly. Furthermore, we give a…

We consider inhomogeneous branching diffusions on an infinite domain of $\mathbb{R}^d$. The first aim of this article is to derive a general criterium under which the size process (number of particles) and the genealogy of the particle…

In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time. As the…

A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…

Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…

Determinantal point processes (DPPs) are a useful probabilistic model for selecting a small diverse subset out of a large collection of items, with applications in summarization, stochastic optimization, active learning and more. Given a…

We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying…

We consider a time-continuous branching random walk on a one-dimensional lattice on which there is one center (lattice point) of particle generation, called branching source. The generation of particles in the branching source is described…

An m-extracting procedure produces unbiased random bits from a loaded dice with m faces. A binarization takes inputs from an m-faced dice and produce bit sequences to be fed into a (binary) extracting procedure to obtain random bits. Thus,…

Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They are the simplest common model of concurrent programs that allows unbounded spawning of processes. In the probabilistic version of BPPs, every process generates…

Longitudinal molecular data of rapidly evolving viruses and pathogens provide information about disease spread and complement traditional surveillance approaches based on case count data. The coalescent is used to model the genealogy that…

An important problem in evolutionary genomics is to investigate whether a certain trait measured on each sample is associated with the sample phylogenetic tree. The phylogenetic tree represents the shared evolutionary history of the samples…

We observe $n$ sequences at each of $m$ sites, and assume that they have evolved from an ancestral sequence that forms the root of a binary tree of known topology and branch lengths, but the sequence states at internal nodes are unknown.…

We investigate the statistics of extremal path(s) (both the shortest and the longest) from the root to the bottom of a Cayley tree. The lengths of the edges are assumed to be independent identically distributed random variables drawn from a…

We consider the set of random Bienaym\'e-Galton-Watson trees with a bounded number of offspring and bounded number of generations as a statistical mechanics model: a random tree is a rooted subtree of the maximal tree; the spin at a given…