Related papers: Structured coalescents, coagulation equations and …
Branching processes are classical growth models in cell kinetics. In their construction, it is usually assumed that cell lifetimes are independent random variables, which has been proved false in experiments. Models of dependent lifetimes…
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
We consider a critical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We are interested in the event $\mathcal{A}_i(n)$ that all individuals alive at time $n$ are offspring of the…
Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…
Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the…
We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of the Pitman sampling formula in Pitman (2006) and the birth-and-death process with immigration studied in…
We introduce a low dimensional function of the site frequency spectrum that is tailor-made for distinguishing coalescent models with multiple mergers from Kingman coalescent models with population growth, and use this function to construct…
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
Stochastic models that incorporate birth, death and immigration (also called birth-death and innovation models) are ubiquitous and applicable to many research topics such as quantifying species sizes in ecological populations, describing…
In this work, we study general Dirichlet coalescents, which are a family of Xi-coalecents constructed from i.i.d mass partitions, and are an extension of the symmetric coalescent. This class of models is motivated by population models with…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
For a continuous state branching process with two types of individuals which are subject to selection and density dependent competition, we characterize the joint evolution of population size, type configurations and genealogies as the…
We model the evolution of two competing populations $U_t, V_t $ by a two-dimensional size-dependent branching process. The population characteristics are assumed to be close to each other, as in a resident-mutant situation. Given that $U_t…
The deterministic selection-recombination equation describes the evolution of the genetic type composition of a population under selection and recombination in a law of large numbers regime. So far, an explicit solution has seemed out of…
This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
Spatial models where growth is limited to the edge of the expansions have been instrumental to understand the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular…
We study the effect of biological confounders on the model selection problem between Kingman coalescents with population growth, and Xi-coalescents involving simultaneous multiple mergers. We use a low dimensional, computationally tractable…