Related papers: Reinforced Galton--Watson processes III: Empirical…
We give a realization of the stable L\'evy forest of a given size conditioned by its mass from the path of the unconditioned forest. Then, we prove an invariance principle for this conditioned forest by considering $k$ independent…
We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated…
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.
The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death…
In populations competing for resources, it is natural to ask whether consuming fewer resources provides any selective advantage. To answer this question, we propose a Wright- Fisher model with two types of individuals: the inefficient…
We describe a Bayesian formalism for analyzing individual gravitational-wave events in light of the rest of an observed population. This analysis reveals how the idea of a "population-informed prior" arises naturally from a suitable…
We analyze the interactions between division, mutation and selection in a simplified evolutionary model, assuming that the population observed can be classified into fitness levels. The construction of our mathematical framework is…
Understanding the interplay between recombination and resampling is a significant challenge in mathematical population genetics and of great practical relevance. Asymptotic results about the distribution of samples when recombination is…
In this article, we prove a joint large deviation principle in $n$ for the \emph{empirical pair measure} and \emph{ empirical offspring measure} of critical multitype Galton-Watson trees conditioned to have exactly $n$ vertices in the weak…
Evolution by Natural Selection is a process by which progeny inherit some properties from their progenitors with small variation. These properties are subject to Natural Selection and are called adaptive traits and carriers of the latter…
We consider conditioned Galton-Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe…
We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are…
In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a ''mating function'' and form couples of different types. We assume that this function is superadditive,…
It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in…
We consider two processes that have been used to study gene duplication, Watterson's [Genetics 105 (1983) 745--766] double recessive null model and Lynch and Force's [Genetics 154 (2000) 459--473] subfunctionalization model. Though the…
We study the asymptotic behavior of small deviation probabilities for the critical Galton-Watson processes with infinite variance of the offspring sizes of particles and apply the obtained result to investigate the structure of a reduced…
We propose a novel class of count time series models alternative to the classic Galton-Watson process with immigration (GWI) and Bernoulli offspring. A new offspring mechanism is developed and its properties are explored. This novel…
We consider the critical Galton-Watson process with overlapping generations stemming from a single founder. Assuming that both the variance of the offspring number and the average generation length are finite, we establish the convergence…
Branching Processes in a Random Environment (BPREs) $(Z_n:n\geq0)$ are a generalization of Galton Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. We determine here the upper large…
Machine Learning techniques have been used to teach computer programs how to play games as complicated as Chess and Go. These were achieved using powerful tools such as Neural Networks and Parallel Computing on Supercomputers. In this…