Related papers: A deterministic model for the occurrence and dynam…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Large-scale dynamical properties of complete chromosome DNA sequences of eukaryotes are considered. By the proposed deterministic models with intermittency and symbolic dynamics we describe a wide spectrum of large-scale patterns inherent…
We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather,…
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the…
The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based…
We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to…
At what level does selective pressure effectively act? When considering the reproductive dynamics of interacting and mutating agents, it has long been debated whether selection is better understood by focusing on the individual or if…
The evolution of the adaptive immune system is characterized by changes in the relative abundances of the B- and T-cell clones that make up its repertoires. To fully capture this evolution, we need to describe the complex dynamics of the…
Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at…
A model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters. The model represents biological individuals that die or reproduce at rates depending…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other…
Stem cells have the potential to produce lineages of non-stem cell populations (differentiated cells) via a ubiquitous hierarchal division scheme. Differentiation of a stem cell into (partially) differentiated cells can happen either…
Our interest is in multiplex network data with multiple network samples observed across the same set of nodes. Examples originate from a variety of fields, including brain connectivity, international trade networks, and social networks,…
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a…
Here, we consider an SIS epidemic model where the individuals are distributed on several distinct patches. We construct a stochastic model and then prove that it converges to a deterministic model as the total population size tends to…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
The organization of cells within tissues plays a vital role in various biological processes, including development and morphogenesis. As a result, understanding how cells self-organize in tissues has been an active area of research. In our…
The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in…