87 citations · 396 across the 37 of their papers we have counts for
39 papers
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…
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…
Instability mechanisms and far-from-equilibrium patterns in reaction-diffusion-ODE systems with multiple diffusion scales
Théo André, Szymon Cygan, Anna Marciniak-Czochra +1
Systems coupling diffusive and nondiffusive components exhibit mathematical phenomena absent in classical reaction-diffusion equations, arising from the singular nature of the vani…
Statistical parameter identification of mixed-mode patterns from a single experimental snapshot
Alexey Kazarnikov, Robert Scheichl, Irving R. Epstein +2
Parameter identification in pattern formation models from a single experimental snapshot is challenging, as traditional methods often require knowledge of initial conditions or tra…
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…
Structured Population Models on Polish spaces: A unified Approach including Graphs, Riemannian Manifolds and Measure Spaces to describe Dynamics of Heterogeneous Populations
Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra +1
This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes, dependent…
-limit for a sharp interface model related to pattern formation on biomembranes
Denis Brazke, Hans Knüpfer, Anna Marciniak-Czochra
We derive a macroscopic limit for a sharp interface version of a model proposed in [29] to investigate pattern formation due to competition of chemical and mechanical forces in bio…
Discontinuous stationary solutions to certain reaction-diffusion systems
Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied…
A Bayesian Approach to Modelling Biological Pattern Formation with Limited Data
Alexey Kazarnikov, Robert Scheichl, Heikki Haario +1
Pattern formation in biological tissues plays an important role in the development of living organisms. Since the classical work of Alan Turing, a pre-eminent way of modelling has…
Stability Results for Bounded Stationary Solutions of Reaction-Diffusion-ODE Systems
Chris Kowall, Anna Marciniak-Czochra, Finn Münnich
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of…
Stable discontinuous stationary solutions to reaction-diffusion-ODE systems
Szymon Cygan, Grzegorz Karch, Anna Marciniak-Czochra +1
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is…
Measure Differential Equation with a Nonlinear Growth/Decay Term
Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra +1
We obtain an existence result for a Measure Differential Equation with an additional nonlinear growth/decay term that may change the sign. The proof requires a modification of appr…
Long-time shadow limit for reaction-diffusion-ODE systems
Chris Kowall, Anna Marciniak-Czochra, Andro Mikelić
Shadow systems are an approximation of reaction-diffusion-type problems obtained in the infinite diffusion coefficient limit. They allow reducing complexity of the system and hence…
Instability of all regular stationary solutions to reaction-diffusion-ODE systems
Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch +1
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the conte…
Dynamical properties of feedback signalling in B lymphopoiesis: A mathematical modelling approach
Salvador Chulián, Alvaro Martínez-Rubio, Anna Marciniak-Czochra +7
Haematopoiesis is the process of generation of blood cells. Lymphopoiesis generates lymphocytes, the cells in charge of the adaptive immune response. Disruptions of this process ar…
Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation
Jan-Erik Busse, Silvia Cuadrado, Anna Marciniak-Czochra
In this paper we consider a system of non-linear integro-differential equations (IDEs) describing evolution of a clonally heterogeneous population of malignant white blood cells (l…
A structured population model of clonal selection in acute leukemias with multiple maturation stages
Tommaso Lorenzi, Anna Marciniak-Czochra, Thomas Stiehl
Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain un…
Asymptotic behaviour of a structured population model on a space of measures
József Z. Farkas, Piotr Gwiazda, Anna Marciniak-Czochra
In this paper we consider a physiologically structured population model with distributed states at birth, formulated on the space of non-negative Radon measures. Using a characteri…
Oscillations in a white blood cell production model with multiple differentiation stages
Franziska Knauer, Thomas Stiehl, Anna Marciniak-Czochra
In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analyti…
The Escalator Boxcar Train Method for a System of Aged-structured Equations in the Space of Measures
José A. Carrillo, Piotr Gwiazda, Karolina Kropielnicka +1
The Escalator Boxcar Train (EBT) method is a well known and widely used numerical method for one-dimensional structured population models of McKendrick-von Foerster type. Recently…
Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems
Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki +1
In this paper we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only desta…
Stable patterns with jump discontinuity in systems with Turing instability and hysteresis
Steffen Härting, Anna Marciniak-Czochra, Izumi Takagi
Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of…
The Escalator Boxcar Train method for a system of aged-structured equations
Piotr Gwiazda, Karolina Kropielnicka, Anna Marciniak-Czochra
The Escalator Boxcar Train method (EBT) is a numerical method for structured population models of McKendrick-von Foerster type. Those models consist of a certain class of hyperboli…
Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization
Thomas Carraro, Christian Goll, Anna Marciniak-Czochra +1
It is generally accepted that the effective velocity of a viscous flow over a porous bed satisfies the Beavers-Joseph slip law. To the contrary, in the case of a forced infiltratio…