Related papers: Stochastic and deterministic modelling of cell mig…
As ecologists increasingly adopt stochastic models over deterministic ones, the question arises: when is this a positive development and when is this an unnecessary complication? While deterministic models -- like the Lotka-Volterra model…
Branching processes are a class of continuous-time Markov chains (CTMCs) prevalent for modeling stochastic population dynamics in ecology, biology, epidemiology, and many other fields. The transient or finite-time behavior of these systems…
Agent-Based Models (ABMs) are powerful tools for studying emergent properties in complex systems. In ABMs, agent behaviors are governed by local interactions and stochastic rules. However, these rules are, in general, non-differentiable,…
Stochastic systems in biology often exhibit substantial variability within and between cells. This variability, as well as having dramatic functional consequences, provides information about the underlying details of the system's behaviour.…
The advent of single-cell technology has significantly improved our understanding of cellular states and subpopulations in various tissues under normal and diseased conditions by employing data-driven approaches such as clustering and…
Cell migration is a fundamental process involved in physiological phenomena such as the immune response and morphogenesis, but also in pathological processes, such as the development of tumor metastasis. These functions are effectively…
Epidemiological models can not only be used to forecast the course of a pandemic like COVID-19, but also to propose and design non-pharmaceutical interventions such as school and work closing. In general, the design of optimal policies…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
Collective cell migration plays a central role in tissue development, morphogenesis, wound repair and cancer progression. With the growing realization that physical forces mediate cell motility in development and physiology, a key…
Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular…
This paper studies identification and estimation of a class of dynamic models in which the decision maker (DM) is uncertain about the data-generating process. The DM surrounds a benchmark model that he or she fears is misspecified by a set…
The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
We propose a hybrid deterministic and stochastic approach to achieve extended time scales in atomistic simulations that combines the strengths of molecular dynamics (MD) and Monte Carlo (MC) simulations in an easy-to-implement way. The…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Research into somatic mutations in cancer cell DNA and their role in tumour growth and progression between successive stages is crucial for improving our understanding of cancer evolution. Mathematical and computer modelling can provide…
Stochastic gradient methods enable learning probabilistic models from large amounts of data. While large step-sizes (learning rates) have shown to be best for least-squares (e.g., Gaussian noise) once combined with parameter averaging,…
Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms…