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Hierarchical Bayesian Estimation of COVID-19 Reproduction Number
No full textInternational audienceAssessing the intensity of a epidemic, such as the COVID-19 pandemic, during the epidemic outbreak, constitutes a significant technical challenge with high societal stakes. Elaborating on classical epidemiological models, this work aims to define a hierarchical Bayesian model that permits the robust estimation of the temporal evolution of the pandemic intensity despite highly corrupted daily new infection counts. It also outputs uncertainty assessment, in the form of credibility intervals robust to the priors choice, accounting for uncertainties on model parameters. The estimation is performed by carefully designed Monte Carlo samplers. The relevance of the proposed estimation procedure is illustrated on real COVID-19 pandemic data for several countries and periods, made available from the Johns Hopkins University repository
Numerical simulation of Lugiato-Lefever equation for Kerr combs generation in Fabry-Perot resonators
No full textLugiato-Lefever equation (LLE) is a nonlinear Schrödinger equation with damping, detuning and driving terms, introduced as a model for Kerr combs generation in ring-shape resonators and more recently, in the form of a variant, in Fabry-Perot (FP) resonators. The aim of this paper is to present some numerical methods that complement each other to solve the LLE in its general form both in the dynamic and in the steady state regimes. We also provide some mathematical properties of the LLE likely to help the understanding and interpretation of the numerical simulation results
Complete Upper Bound Hierarchies for Spectral Minimum in Noncommutative Polynomial Optimization
No full textThis is the full/expanded/comprehensive version of the preliminary report https://laas.hal.science/hal-04440949v1This work addresses the problem of computing the spectral minimum (ground state energy) of a noncommutative polynomial subject to finitely many noncommutative polynomial constraints.Building on the Helton-McCullough Positivstellensatz, the Navascués-Pironio-Acı́n (NPA) hierarchy provides a sequence of lower bounds that converge to the spectral minimum under mild assumptions on the constraint set. Each of these bounds can be computed via semidefinite programming.In this paper, we develop complementary, complete hierarchies of upper bounds for the spectral minimum. These are noncommutative counterparts to Lasserre’s upper bound hierarchies for polynomial optimization. Each upper bound is obtained by solving a generalized eigenvalue problem. The proposed hierarchies are applicable to optimization problems in both bounded and unbounded operator algebras, as illustrated through a range of examples
A comparative study of gellan gum and xanthan gum versus commercial vehicles as pharmaceutical thickening agents in oral suspensions
No full textInternational audiencePharmaceutical oral suspensions are the main form used for patients with dysphagia. Compounding these forms is challenging because they are thermodynamically unstable but must remain physically stable. Ready-to-use vehicles such as Inorpha® or Orablend® exist but these are not optimal, and physical stability can be improved using a thickening or suspending agent. High-acyl gellan gum is a European food additive (E418), also used in pharmaceutical preparations, as a gelling agent, stabilizer or thickener but never as a suspending agent. This study aimed to investigate and characterize the properties of high-acyl gellan gum as a suspending agent and to compare it with ready-to-use vehicles and with another suspending agent, xanthan gum. Rheological behaviour, sedimentation and resuspension of vehicles were studied with and without irbesartan used as a model insoluble drug. Viscosity stability was studied for 90 days at room temperature and controlled temperature. We show that the high-acyl gellan gum vehicle offers the best viscosity and stability results for use in pharmaceutical suspensions because it exhibits stable homogeneity and viscosity in time, regardless of storage temperature, and is compatible with safe administration in dysphagic patients after 90 days. High-acyl gellan gum appears to be a good suspending agent for pharmaceutical suspensions
Etude d'un nouveau schéma IMEX Volumes Finis bas Mach d'ordre 2 et peu oscillant pour les équations d'Euler complet
No full textInternational audienceIn this work, we propose and study an Implicit-Explicit (IMEX) finite volume scheme for the compressible Euler system which preserves the low Mach number limit. IMEX schemes are based on a flux splitting into a part treated explicitly and a part treated implicitly. We choose the flux splitting introduced by E. Toro and M.E. Vázquez-Cendón for ensuring the recognition of contact discontinuities and shear waves. Then, based on this flux splitting, we propose first and second order new linear asymptotic preserving (AP) schemes in the low Mach number limit. We prove that the schemes are asymptotically consistent, that is they degenerate into a consistent discretization of the incompressible system when the Mach number is sufficiently small. We perform a Fourier stability analysis on the linearized system around a constant state showing that the first order scheme is L 2 stable under a CFL condition independent of the Mach number. This proves the asymptotic stability in the linear case. We show one-dimensional and two-dimensional results which prove the good behavior of our scheme in all-Mach number regimes. Furthermore, we construct a low-diffusive TVD first-order scheme by interpolating the first-order in time scheme with a second-order one.Dans cet article, nous proposons et étudions un schéma de volumes finis implicite-explicite (IMEX) pour le système d'Euler compressible qui préserve la limite bas Mach. Les schémas IMEX sont basés sur une division du flux en une partie traitée explicitement et une partie traitée implicitement. Nous choisissons la décomposition de flux introduite par E. Toro et M.E. Vázquez-Cendón pour assurer la préservation des discontinuités de contact et des ondes de cisaillement. Ensuite, sur la base de cette décomposition de flux, nous proposons de nouveaux schémas linéaires du premier et du second ordre asymptotiquement préservants (AP) dans la limite des faibles nombres de Mach. Nous prouvons que les schémas sont asymptotiquement coonsistants, c'est-à-dire qu'ils dégénèrent en une discrétisation consistante du système incompressible lorsque le nombre de Mach est suffisamment petit. Nous effectuons une analyse de stabilité de Fourier sur le système linéarisé autour d'un état constant, montrant que le schéma du premier ordre est L 2 stable sous une condition CFL indépendante du nombre de Mach. Cela prouve la stabilité asymptotique dans le cas linéaire. Nous montrons des résultats unidimensionnels et bidimensionnels qui prouvent le bon comportement de notre schéma dans tous les régimes du nombre de Mach. Par ailleurs, nous construisons un schéma TVD du premier ordre faiblement diffusif en interpolant le schéma du premier ordre en temps avec un schéma du second ordre
MultiNMRFit: A software to fit 1D and pseudo-2D NMR spectra
No full textNuclear Magnetic Resonance (NMR) is widely used for quantitative analysis of metabolic systems. Accurate extraction of NMR parameters -such as chemical shift, intensity, coupling constants, and linewidth -is essential for obtaining information on the structure, concentration, and isotopic composition of metabolites. We present MultiNMRFit, an open-source software designed for high-throughput analysis of one-dimensional NMR spectra, whether acquired individually or as pseudo-2D experiments. MultiNMRFit extracts signal parameters (e.g. intensity, area, chemical shift, and coupling constants) by fitting the experimental spectra using built-in or user-defined signal models that account for multiplicity, providing high flexibility along with robust and reproducible results. The software is accessible both as a Python library and via a graphical user interface, enabling intuitive use by end-users without computational expertise. We demonstrate the robustness and flexibility of MultiNMRFit on datasets collected in metabolomics and isotope labeling studies. Availability and Implementation. MultiNMRFit is implemented in Python 3 and was tested on Unix, Windows, and MacOS platforms. The source code and the documentation are freely distributed under GPL3 license at https://github.com/NMRTeamTBI/MultiNMRFit/
Sharp quantitative stability of the M\"obius group among sphere-valued maps in arbitrary dimension
No full text23 pagesInternational audienceIn this work we prove a sharp quantitative form of Liouville's theorem, which asserts that, for all , the weakly conformal maps of with degree are M\"obius transformations. In the case this estimate was first obtained by Bernand-Mantel, Muratov and Simon (Arch. Ration. Mech. Anal. 239(1):219-299, 2021), with different proofs given later on by Topping, and by Hirsch and the third author. The higher-dimensional case requires new arguments because it is genuinely nonlinear: the linearized version of the estimate involves quantities which cannot control the distance to M\"obius transformations in the conformally invariant Sobolev norm. Our main tool to circumvent this difficulty is an inequality introduced by Figalli and Zhang in their proof of a sharp stability estimate for the Sobolev inequality
Covariance parameter estimation of Gaussian processes with approximated functional inputs
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On the Mathematical foundations of Diffusion Monte Carlo
No full textInternational audienceThe Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of quantum systems. In this study, we present the first mathematically rigorous anal- ysis of this class of stochastic methods on non necessarily compact state spaces, including linear diffusions evolving in quadratic absorbing potentials, yielding what seems to be the first result of this type for this class of models. We present a novel and general mathematical framework with easily checked Lyapunov stability conditions that ensure the uniform-in-time convergence of Diffusion Monte Carlo estimates towards the top of the spectrum of Schr ̈odinger operators. For transient free evolutions, we also present a divergence blow up of the estimates w.r.t. the time horizon even when the asymptotic fluctuation variances are uniformly bounded. We also illustrate the impact of these results in the context of generalized coupled quan- tum harmonic oscillators with non necessarily reversible nor stable diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force
Isogeometric multipatch surface fitting in tomographic images: application to lattice structures
No full textInternational audienceAdditive manufacturing has enabled the production of cellular architected (lattice) structures known for their exceptional mechanical performances. However, the printed components often exhibit geometric defects on a scale close to that of lattice struts, leading to significant deviations in mechanical behavior when comparing simulations based on the as-designed (defect-free) geometry with experimental tests on the as-manufactured (imperfect) geometry. In this work, we develop a method to extract an analysis-suitable CAD-based geometry from 3D scan data. We start by building a multipatch B-spline surface model of the as-designed lattice boundary, and then deform it to match its as-manufactured counterpart observed in a volumetric image. To achieve this, key contributions include a data fitting metric based on the Virtual Image Correlation approach, combined with an image learning component; the integration of the membrane strain energy of the surface for regularization; the enforcement of higher continuity between patches where appropriate; an automatic estimation of the pose of the CAD object in the image; and the computation of a distance indicator map between the aligned CAD model and the as-manufactured surface. These elements enable comprehensive, accurate, and efficient measurement of geometric defects in lattice structures. Validated through various experiments, including those on a BCC lattice structure, this method achieves sub-voxel accuracy. Ultimately, it provides a compact and explicit representation of the as-manufactured geometry, maintaining the same CAD-based discretization as the initial design, and thereby facilitating quantitative defect assessment