Related papers: Stochastic and deterministic modelling of cell mig…

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…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…

How far is neuroepithelial cell proliferation in the developing central nervous system a deterministic process? Or, to put it in a more precise way, how accurately can it be described by a deterministic mathematical model? To provide tracks…

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which…

In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…

We analyze the dynamics of agent--based models (ABMs) from a Markovian perspective and derive explicit statements about the possibility of linking a microscopic agent model to the dynamical processes of macroscopic observables that are…

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…

The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…

To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…

In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…

The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migration of cell populations driven by this non-local form of…

In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a…

Fluctuating environments pose tremendous challenges to bacterial populations. It is observed in numerous bacterial species that individual cells can stochastically switch among multiple phenotypes for the population to survive in rapidly…

Cell size control and homeostasis is a major topic in cell biology yet to be fully understood. Several growth laws like the timer, adder, and sizer were proposed, and mathematical approaches that model cell growth and division were…

Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…

We consider a multiscale stochastic compartmental model with three types of cells (stem cells, immature cells and mature cells) which combines cell proliferation and cell differentiation. We derive a hydrodynamic limit when the number of…

Background. It is assumed that the introduction of stochastic in mathematical model makes it more adequate. But there is virtually no methods of coordinated (depended on structure of the system) stochastic introduction into deterministic…

The dynamics of affective decision making is considered for an intelligent network composed of agents with different types of memory: long-term and short-term memory. The consideration is based on probabilistic affective decision theory,…

This article outlines a method for automatically generating models of dynamic decision-making that both have strong predictive power and are interpretable in human terms. This is useful for designing empirically grounded agent-based…

Decision making algorithms are used in a multitude of different applications. Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable…