Related papers: Stochastic and deterministic modelling of cell mig…
Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of…
The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban…
Formal modelling provides a toolkit for understanding cultural dynamics, from individual decisions to recurring patterns of change. This chapter explains what models are and why they matter. Using a precise, shared language, they aid…
In this paper, we consider stochastic versions of three classical growth models given by ordinary differential equations (ODEs). Indeed we use stochastic versions of Von Bertalanffy, Gompertz, and Logistic differential equations as models.…
Quantifying the size of cell populations is crucial for understanding biological processes such as growth, injury repair, and disease progression. Often, experimental data offer information in the form of relative frequencies of distinct…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…
Cell migration in fibreous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response and cancer progression. During migration, individual cells can generate active…
Cellular Agent-Based Models are commonly employed to describe a variety biological systems. Over the course of the past years, many modeling tools have emerged which solve particular research questions. In this short opinion piece, we argue…
Agent-Based Models (ABMs) are often used to model migration and are increasingly used to simulate individual migrant decision-making and unfolding events through a sequence of heuristic if-then rules. However, ABMs lack the methods to embed…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
This paper presents a statistical block fading channel model for multiuser massive MIMO system. The proposed channel model is evolved from correlation based stochastic channel model (CBSCM) but in addition to the properties of CBSCM, it has…
Systematic exploration of Agent-Based Models (ABMs) is challenged by the curse of dimensionality and their inherent stochasticity. We present a multi-stage pipeline integrating the systematic design of experiments with machine learning…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Incorporating atomistic and molecular information into models of cellular behaviour is challenging because of a vast separation of spatial and temporal scales between processes happening at the atomic and cellular levels. Multiscale or…
Generators of space-time dynamics in bioimaging have become essential to build ground truth datasets for image processing algorithm evaluation such as biomolecule detectors and trackers, as well as to generate training datasets for deep…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions.…