Related papers: A Three-dimensional tumor growth model and its bou…
We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation…
Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…
The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…
Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…
We analyze theoretically and experimentally the triadic resonance instability (TRI) of a plane inertial wave in a rotating fluid. Building on the classical triadic interaction equations between helical modes, we show by numerical…
Context: Numerous theoretical studies of the stellar dynamics of triple systems have been carried out, but fewer purely empirical studies that have addressed planetary orbits within these systems. Most of these empirical studies have been…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
We investigate the long-time dynamics and optimal control problem of a diffuse interface model that describes the growth of a tumor in presence of a nutrient and surrounded by host tissues. The state system consists of a Cahn-Hilliard type…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
Based on previous work for the static problem, in this paper we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out…
We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…
The clinical management of breast cancer depends on an accurate understanding of the tumor and its anatomical context to adjacent tissues and landmark structures. This context may be provided by semantic segmentation methods; however,…
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which…
This paper presents our investigation into the modification of a finite-width internal gravity wave beam arising from triadic resonance instability. We present both experimental and weakly non-linear modelling to examine this instability…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…
In this paper we make rigorous mathematical analysis to a free boundary problem modeling the growth of necrotic tumors. A remarkable feature of this free boundary problem is that it contains two different-type free surfaces: One is the…
This work intends to prove that strong instabilities may appear for high order geometric optics expansions of weakly stable quasilinear hyperbolic boundary value problems, when the forcing boundary term is perturbed by a small amplitude…
In this work, we explore various relevant aspects of the Smoothed Particle Hydrodynamics regarding Burger's equation. The stability, precision, and efficiency of the algorithm are investigated in terms of different implementations. In…
We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…