Related papers: On the Calibration of a Size-Structured Population…
Bacterial colonies can form a wide variety of shapes and structures based on ambient and internal conditions. To help understand the mechanisms that determine the structure of and the diversity within these colonies, various numerical…
How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells on average, add a fixed size (volume) from birth to…
We develop a simple computational model for cell boundary evolution in plastic deformation. We study the cell boundary size distribution and cell boundary misorientation distribution that experimentally have been found to have scaling forms…
This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…
Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…
The growth of a population is often modeled as branching process where each individual at the end of its life is replaced by a certain number of offspring. An example of these branching models is the Bellman-Harris process, where the…
In bioequivalence design, power analyses dictate how much data must be collected to detect the absence of clinically important effects. Power is computed as a tail probability in the sampling distribution of the pertinent test statistics.…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
Compartmental models are used in epidemiology to capture the evolution of infectious diseases such as COVID-19 in a population by assigning members of it to compartments with labels such as susceptible, infected, and recovered. In a…
Population quantiles are important parameters in many applications. Enthusiasm for the development of effective statistical inference procedures for quantiles and their functions has been high for the past decade. In this article, we study…
We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…
That data follow a Gompertz distribution is a widely used assumption in diverse fields of applied sciences, e.g., in biology or when analysing survival times. Since misspecified models may lead to false conclusions, assessing the fit of the…
Fundamental mechanisms governing cell size control and homeostasis are still poorly understood. The relationship between sizes at division and birth in single cells is used as a metric to categorize the basis of size homeostasis [1-3].…
The quality of the inferences we make from pathogen sequence data is determined by the number and composition of pathogen sequences that make up the sample used to drive that inference. However, there remains limited guidance on how to best…
In a multicellular organism different cell types express a gene in different amounts. Samples from which gene expression levels can be measured typically contain a mixture of different cell types, the resulting measurements thus give only…
This paper studies the bounded confidence model on growing fully-mixed populations. In this model, in addition to the usual opinion clusters, significant secondary clusters of smaller size appear systematically, while those secondary…
We propose a new numerical scheme designed for a wide class of structured population models based on the idea of operator splitting and particle approximations. This scheme is related to the Escalator Boxcar Train (EBT) method commonly used…
Colombi et al. 1999 (paper I) investigated the counts-in-cells statistics and their respective errors in the $\tau$CDM Virgo Hubble Volume simulation. This extremely large $N$-body experiment also allows a numerical investigation of the…
This study introduces a novel epidemiological model that expands upon the Kermack-McKendrick model by incorporating the age of infection and reinfection. By including infection age, we can classify participants, which enables a more…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…