Related papers: Stochastic and deterministic modelling of cell mig…

Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including…

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…

In this paper we consider deterministic limits of molecular stochastic systems with finite and infinite degrees of freedom. The method to obtain the deterministic vector field is based on the continuum limit of such microscopic systems…

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response.…

Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in diverse tissue environments to accomplish a wide variety of biological phenomena, viz. embryonic development, wound healing, and tumor…

Nowadays, we are surrounded by a large number of complex phenomena ranging from rumor spreading, social norms formation to rise of new economic trends and disruption of traditional businesses. To deal with such phenomena,Complex Adaptive…

Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…

Discrete choice models (DCMs) have been widely utilized in various scientific fields, especially economics, for many years. These models consider a stochastic environment influencing each decision maker's choices. Extensive research has…

Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…

We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…

Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…

In this paper we develop a probabilistic micro-scale compartmental model and use it to study macro-scale properties of axonal transport, the process by which intracellular cargo is moved in the axons of neurons. By directly modeling the…

Biological movement patterns can sometimes be quasi linear with abrupt changes in direction and speed, as in plastids in root cells investigated here. For the analysis of such changes we propose a new stochastic model for movement along…

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The…

Big data, including applications with high security requirements, are often collected and stored on multiple heterogeneous devices, such as mobile devices, drones and vehicles. Due to the limitations of communication costs and security…

An agent-based model (ABM) is a computational model in which the local interactions of autonomous agents with each other and with their environment give rise to global properties within a given domain. As the detail and complexity of these…

We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…

Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tighly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting…

Statistical clustering in dynamic networks aims to identify groups of nodes with similar or distinct internal connectivity patterns as the network evolves over time. While early research primarily focused on static Stochastic Block Models…

There is a rich literature on microscopic models for opinion dynamics; most of them fall into one of two categories - agent-based models or differential equation models - with a general understanding that the two are connected in certain…