Related papers: Modelling physiologically structured populations: …
Microtubules (MTs) are dynamic protein filaments essential for intracellular organization and transport, particularly in long-lived cells such as neurons. The plus and minus ends of neuronal MTs switch between growth and shrinking phases,…
In this paper we first study partial regularity of weak solutions to the initial boundary value problem for the system $-\mbox{div}\left[(I+\mathbf{m}\otimes \mathbf{m})\nabla p\right]=S(x),\ \ \partial_t\mathbf{m}-D^2\Delta…
Cell lineage statistics is a powerful tool for inferring cellular parameters, such as division rate, death rate or the population growth rate. Yet, in practice such an analysis suffers from a basic problem: how should we treat incomplete…
We consider a class of dissipative stochastic differential equations (SDE's) with time-periodic coefficients in finite dimension, and the response of time-asymptotic probability measures induced by such SDE's to sufficiently regular, small…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very strong damping and quasi-periodic external forcing. We study…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
We analyze the asymptotic behavior of a partial differential equation (PDE) model for hematopoiesis. This PDE model is derived from the original agent-based model formulated by (Roeder et al., Nat. Med., 2006), and it describes the…
The structure of a network has a major effect on dynamical processes on that network. Many studies of the interplay between network structure and dynamics have focused on models of phenomena such as disease spread, opinion formation and…
Building on our recent work on {\em neuromimetic control theory}, new results on resilience and neuro-inspired quantization are reported. The term neuromimetic refers to the models having features that are characteristic of the neurobiology…
We construct viscosity solutions to the nonlinear evolution equation \eqref{p} below which generalizes the motion of level sets by mean curvature (the latter corresponds to the case $p = 1$) using the regularization scheme as in \cite{ES1}…
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…
The asymptotic behavior of some semilinear parabolic PDEs is analyzed by means of a "mean value" property. This property allows us to determine, by means of appropriate {\em{a priori}} estimates, some exponential decay results for suitable…
This paper addresses the problem of learning reaction-diffusion (RD) systems from data while ensuring physical consistency and well-posedness of the learned models. Building on a regularization-based framework for structured model learning,…
We study the classic pure selection integrodifferential equation, stemming from adaptative dynamics, in a measure framework by mean of duality approach. After providing a well posedness result under fairly general assumptions, we focus on…
In many biological processes heterogeneity within cell populations is an important issue. In this work we consider populations where the behavior of every single cell can be described by a system of ordinary differential equations.…
A reaction network consists of a finite number of species, which interact through predefined reaction channels. Traditionally such networks were modeled deterministically, but it is now well-established that when reactant copy numbers are…
The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space where the measure determines the abundance of individual…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…