Related papers: Branching within branching II: Limit theorems
During batch growth on mixtures of two growth-limiting substrates, microbes consume the substrates either sequentially or simultaneously. These growth patterns are manifested in all types of bacteria and yeasts. The ubiquity of these growth…
It has long been known that antibiotic treatment will not completely kill off a bacteria population. For many species a small fraction of bacteria is not sensitive to antibiotics. These bacteria are said to persist. Recently it has been…
We study sufficient conditions for the belonging of random process to certain Besov space and for the Central Limit Theorem (CLT) in these spaces. We investigate also the non-asymptotic tail behavior of normed sums of centered random…
A packed community of exponentially proliferating microbes will spread in size exponentially. However, due to nutrient depletion, mechanical constraints, or other limitations, exponential proliferation is not indefinite, and the spreading…
Bursting cells lead to ambient RNA that contaminates sequencing data. This process is especially problematic in perturbation experiments where transcription factors are implanted into cells to determine their effects. The presence of…
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.
The paper discusses the continuous-time Markov Branching Process allowing Immigration. We are considering a critical case for which the second moment of offspring law and the first moment of immigration law are possibly infinite. Assuming…
In this paper we study the central limit theorem and its functional form for random fields which are not started from their equilibrium, but rather under the measure conditioned by the past sigma field. The initial class considered is that…
Segregation of populations is a key question in evolution theory. One important aspect is the relation between spatial organization and the population's composition. Here we study a specific example -- sectors in expanding bacterial…
A continuous-time particle system on the real line satisfying the branching property and an exponential integrability condition is called a branching L\'evy process, and its law is characterized by a triplet $(\sigma^2,a,\Lambda)$. We…
We study the Stochastic Thermodynamics of cell growth and division using a theoretical framework based on branching processes with resetting. Cell division may be split into two sub-processes: branching, by which a given cell gives birth to…
We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical…
The focus of this article is studying an optimal control problem for branching diffusion processes. Initially, we introduce the problem in its strong formulation and expand it to include linearly growing drifts. Then, we present a relaxed…
We compute the posterior distributions of the initial population and parameter of binary branching processes, in the limit of a large number of generations. We compare this Bayesian procedure with a more na\"ive one, based on hitting times…
We introduce a model called Host-Pathogen game for studying biological competitions. Notably, we focus on the invasive dynamics of external agents, like bacteria, within a host organism. The former are mapped to a population of defectors…
In this paper, a special sequence of controlled branching processes is considered. We provide a simple set of sufficient conditions for the weak convergence of such processes to a weak solution to a kind of continuous branching processes…
We consider the limiting behaviour of the point processes associated with a branching random walk with supercritical branching mechanism and balanced regularly varying step size. Assuming that the underlying branching process satisfies…
We prove distributional limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains those obtained from non-integrable observables over certain piecewise…
Consider a heavy-tailed branching process (denoted by $Z_{n}$) in random environments, under the condition which infers that $\mathbb{E}\log m(\xi_{0})=\infty$. We show that (1) there exists no proper $c_{n}$ such that $\{Z_{n}/c_{n}\}$ has…
We consider a spatial stochastic model for a pathogen population growing inside a host that attempts to eliminate the pathogens through its immune system. The pathogen population is divided into different types. A pathogen can either…