Related papers: A multitype Galton-Watson model for rejuvenating c…
We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational…
Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by…
Consider an arbitrary large population at the present time, originated at an unspecified arbitrary large time in the past, where individuals in the same generation reproduce independently, forward in time, with the same offspring…
We prove a scaling limit theorem for two-type Galton-Waston branching processes with interaction. The limit theorem gives rise to a class of mixed state branching processes with interaction using to simulate the evolution for cell division…
We study multi-type Bienaym\'e-Galton-Watson processes with linear-fractional reproduction laws using various analytical tools like contour process, spinal representation, Perron-Frobenius theorem for countable matrices, renewal theory. For…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
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…
Branching processes model the evolution of populations of agents that randomly generate offsprings. These processes, more patently Galton-Watson processes, are widely used to model biological, social, cognitive, and technological phenomena,…
We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but increasing sets of types. A pathwise approach is…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. First, we introduce a new theoretical framework, reaction-diffusion system on `chemical species…
The simple Galton--Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of…
The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this…
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent…
Stem cell regeneration is a crucial biological process for most self-renewing tissues during the development and maintenance of tissue homeostasis. In developing the mathematical models of stem cell regeneration and tissue development, cell…
This paper deals with branching processes in varying environment, namely, whose offspring distributions depend on the generations. We provide sufficient conditions for survival or extinction which rely only on the first and second moments…
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…
We provide deviation inequalities for properly normalized sums of bifurcating Markov chains on Galton-Watson tree. These processes are extension of bifurcating Markov chains (which was introduced by Guyon to detect cellular aging from cell…
Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical…
A properly scaled critical Galton-Watson process converges to a continuous state critical branching process $\xi(\cdot)$ as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping…
In this paper we consider a model based on branching process theory for the proliferation and the dissemination network of T cells in the adaptive immune response. A multi-type Galton Watson branching process is assumed as the basic…