Serov, Alexander S. Laurent, François Floderer, Charlotte Perronet, Karen Favard, Cyril Muriaux, Delphine Westbrook, Nathalie Vestergaard, Christian L. Masson, Jean-Baptiste
Published in
Scientific Reports

We devise a method to detect and estimate forces in a heterogeneous environment based on experimentally recorded stochastic trajectories. In particular, we focus on systems modeled by the heterogeneous overdamped Langevin equation. Here, the observed drift includes a "spurious” force term when the diffusivity varies in space. We show how Bayesian i...

Buchwald, S Ciaramella, G Salomon, Julien

A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition of the reconstruction process and on an ansatz for the unknown operator obtained by an a priori chosen set of ...

Kojčić, Ivana Papadopoulo, Théodore Deriche, Rachid Deslauriers-Gauthier, Samuel

International audience

Sokolov, Alexander V. Voloshinov, Vladimir V.
Published in
Open Computer Science

The technology of formal quantitative estimation of the conformity of mathematical models to the available dataset is presented. The main purpose of the technology is to make the model selection decision-making process easier for the researcher. The method is a combination of approaches from the areas of data analysis, optimization and distributed ...

Hendriksen, Allard A. Pelt, Daniel M. Batenburg, K. Joost

Recovering a high-quality image from noisy indirect measurements is an important problem with many applications. For such inverse problems, supervised deep convolutional neural network (CNN)-based denoising methods have shown strong results, but the success of these supervised methods critically depends on the availability of a high-quality trainin...

Fokas, A. S. Dikaios, N. Kastis, G. A.
Published in
Journal of the Royal Society Interface

We introduce a novel methodology for predicting the time evolution of the number of individuals in a given country reported to be infected with SARS-CoV-2. This methodology, which is based on the synergy of explicit mathematical formulae and deep learning networks, yields algorithms whose input is only the existing data in the given country of the ...

Guliyev, Namig J.

We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions). Using these transformations, we obtain various direct and inverse spectral results for these probl...

Flinth, Axel De Gournay, Frédéric Weiss, Pierre

We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M(Ω) of Radon measures on a subset Ω of R d. Our main result states that under some regularity conditions, the method eventually converges linearly. Additionally, we prove that continuously optimizing the amplitudes of positions o...

rambour, clément Denis, Loïc Tupin, Florence Oriot, Hélène

—The resolution achieved by current Synthetic Aperture Radar (SAR) sensors provides detailed visualization of urban areas. Spaceborne sensors such as TerraSAR-X can be used to analyze large areas at a very high resolution. In addition, repeated passes of the satellite give access to temporal and interferometric information on the scene. Because of ...

Kochikov, I. V. Tikhonravov, A. V. Yagola, A. G.
Published in
Computational Mathematics and Mathematical Physics

AbstractA new computational approach is developed to evaluate the strength of the error self-compensation effect in the case of broadband optical monitoring of the multilayer coating deposition process. A new form of estimating the strength of the error self-compensation effect is suggested. Computational experiments simulating the deposition proce...