7 papers
A note on application of mean-field limit to non-exchangeable non-conservative systems
Piotr Gwiazda, Katarzyna Ryszewska
In this paper we apply the newly developed theory of extended graphons to a certain class of non-exchangeable, non-conservative problems. We establish the mean-field limit by provi…
Asynchronous exponential growth for structured population models in measure space
Christian Düll, József Z. Farkas, Piotr Gwiazda +1
This paper studies the asymptotic behaviour of a structured population model on the space of nonnegative Radon measures. Such formulations naturally arise when solutions develop co…
Operator splitting algorithm for structured population models on metric spaces
Carolin Lindow, Christian Düll, Piotr Gwiazda +2
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of…
Beyond Bayesian Inference: The Correlation Integral Likelihood Framework and Gradient Flow Methods for Deterministic Sampling
Piotr Gwiazda, Alexey Kazarnikov, Anna Marciniak-Czochra +1
Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due t…
Stochastic parabolic equations in Musielak-Orlicz spaces with discontinuous in time N-function
Piotr Gwiazda, Jakub Woźnicki, Aneta Wróblewska-KamiÅska +1
We consider a stochastic parabolic partial differential equation with Dirichlet boundary conditions, multiplicative stochastic noise, and a monotone parabolic operator A. The growt…
Lipschitz stability for Bayesian inference in porous medium tissue growth models
Tomasz DÄbiec, Piotr Gwiazda, BÅażej Miasojedow +3
We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive rela…