Related papers: Detection of cellular aging in a Galton-Watson pro…
Understanding why we age is a long-lived open problem in evolutionary biology. Aging is prejudicial to the individual and evolutionary forces should prevent it, but many species show signs of senescence as individuals age. Here, I will…
Single-cell trajectory analysis aims to reconstruct the biological developmental processes of cells as they evolve over time, leveraging temporal correlations in gene expression. During cellular development, gene expression patterns…
Generalized non-autonomous linear celullar automata are systems of linear difference equations with many variables that can be seen as convolution equations in a discrete group. We study those systems from the stand point of the Galois…
Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number $r$, the $r$-neighbour bootstrap process is an update rule for vertices of a…
We introduce the notion of a hereditary property for rooted real trees and we also consider reduction of trees by a given hereditary property. Leaf-length erasure, also called trimming, is included as a special case of hereditary reduction.…
This article is an essay, both expository and argumentative, on the Galton-Watson process as a tool in the domain of Branching Processes. It is at the same time the author's ways to honour two distinguished scientists in this domain, both…
Li-ion batteries gradually lose their capacity with time and use; therefore, ageing forecasts are key to designs of battery powered systems. So far, cell-type-specific studies without standardised testing practices have lead to a variety of…
Reinforced Galton-Watson processes have been introduced in arxiv:2306.02476 as population models with non-overlapping generations, such that reproduction events along genealogical lines can be repeated at random. We investigate here some of…
We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects…
In a reinforced Galton-Watson process with reproduction law $\boldsymbol{\nu}$ and memory parameter $q\in(0,1)$, the number of children of a typical individual either, with probability $q$, repeats that of one of its forebears picked…
We investigate the genealogical structure of general critical or subcritical continuous-state branching processes. Analogously to the coding of a discrete tree by its contour function, this genealogical structure is coded by a real-valued…
Mutations can arise from the chance misincorporation of nucleotides during DNA replication or from DNA lesions that are not repaired correctly. We introduce a model that relates the source of mutations to their accumulation with cell…
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…
Lineage tracing, the determination and mapping of progeny arising from single cells, is an important approach enabling the elucidation of mechanisms underlying diverse biological processes ranging from development to disease. We developed a…
We investigate the range $\mathcal{R}_T$ of the diffusive biased walk $\mathbb{X}$ on a Galton-Watson tree $\mathbb{T}$ in random environment, that is to say the sub-tree of $\mathbb{T}$ of all distinct vertices visited by this walk up to…
We consider a continuous-time Bienaym\'e-Galton-Watson process with logistic competition in a regime of weak competition, or equivalently of a large carrying capacity. Individuals reproduce at random times independently of each other but…
Conventional Li-ion battery ageing models, such as electrochemical, semi-empirical and empirical models, require a significant amount of time and experimental resources to provide accurate predictions under realistic operating conditions.…
We consider a fragmentation of discrete trees where the internal vertices are deleted independently at a rate proportional to their degree. Informally, the associated cut-tree represents the genealogy of the nested connected components…
Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…
The Weibull function is widely used to describe skew distributions observed in nature. However, the origin of this ubiquity is not always obvious to explain. In the present paper, we consider the well-known Galton-Watson branching process…