Related papers: A multitype Galton-Watson model for rejuvenating c…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. And the multi-types Galton-Watson forest is a random model of population growth without space or…
Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and…
Maintaining tissue homeostasis requires appropriate regulation of stem cell differentiation. The Waddington landscape posits that gene circuits in a cell form a potential landscape of different cell types, wherein cells follow attractors of…
The Doyle-Fuller-Newman (DFN) model is a common mechanistic model for lithium-ion batteries. The reaction rate constant and diffusivity within the DFN model are key parameters that directly affect the movement of lithium ions, thereby…
The evolutionary process has been modelled in many ways using both stochastic and deterministic models. We develop an algebraic model of evolution in a population of asexually reproducing organisms in which we represent a stochastic walk in…
We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the population. Parasites multiply randomly…
We examine the population growth system called Q-processes. This is defined by the Galton-Watson Branching system conditioned on non-extinction of its trajectory in the remote future. In this paper we observe the total progeny up to time…
We introduce multi-type Markov Branching trees, which are simple random population tree models where individuals are characterized by their size and type and give rise to (size,type)-children in a Galton-Watson fashion, with the rule that…
We introduce a general class of branching Markov processes for the modelling of a parasite infection in a cell population. Each cell contains a quantity of parasites which evolves as a diffusion with positive jumps. The drift, diffusive…
A host-parasite model is considered for a population of cells that can be of two types, A or B, and exhibits unilateral reproduction: while a B-cell always splits into two cells of the same type, the two daughter cells of an A-cell can be…
A multiphasic constitutive model of the skin that implicitly accounts for the process of intrinsic (i.e.\ chronological) ageing via variation of the constitutive parameters is proposed. The structurally-motivated constitutive formulation…
This paper investigates the stochastic fluctuations of the number of copies of a given protein in a cell. This problem has already been addressed in the past and closed-form expressions of the mean and variance have been obtained for a…
Bisexual Galton-Watson processes are discrete Markov chains where reproduction events are due to mating of males and females. Owing to this interaction, the standard branching property of Galton-Watson processes is lost. We prove tightness…
We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…
Some viruses, such as human immunodeficiency virus, can infect several types of cell populations. The age of infection can also affect the dynamics of infected cells and production of viral particles. In this work, we study a virus model…
Energy storage is a fundamental component for the development of sustainable and environment-aware technologies. One of the critical challenges that needs to be overcome is preserving the State of Health (SoH) in energy harvesting systems,…
We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of…
Application of some basic notions and statistics of ageing distributions used in mathematical theory of reliability including the Gini-type index is discussed as a methodological tool for investigation of human population ageing and…
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival…