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Unbalanced L1 optimal transport for vector valued measures and application to Full Waveform Inversion
No full textInternational audienceOptimal transport has recently started to be successfully employed to define misfit or loss functions in inverse problems. However, it is a problem intrinsically defined for positive (probability) measures and therefore strategies are needed for its applications in more general settings of interest. In this paper we introduce an unbalanced optimal transport problem for vector valued measures starting from the optimal transport. By lifting data in a self-dual cone of a higher dimensional vector space, we show that one can recover a meaningful transport problem. We show that the favorable computational complexity of the problem, an advantage compared to other formulations of optimal transport, is inherited by our vector extension. We consider both a one-homogeneous and a two-homogeneous penalization for the imbalance of mass, the latter being potentially relevant for applications to physics based problems. In particular, we demonstrate the potential of our strategy for full waveform inversion, an inverse problem for high resolution seismic imaging
Stochastic sewing lemma on Wasserstein space
No full textInternational audienceThe stochastic sewing lemma recently introduced by Le~(2020) allows to construct a unique limit process from a doubly indexed stochastic process that satisfies some regularity. This lemma is stated in a given probability space on which these processes are defined. The present paper develops a version of this lemma for probability measures: from a doubly indexed family of maps on the set of probability measures that have a suitable probabilistic representation, we are able to construct a limit flow of maps on the probability measures. This result complements and improves the existing result coming from the classical sewing lemma. It is applied to the case of law-dependent jump SDEs for which we obtain weak existence result as well as the uniqueness of the marginal laws
Théorème ergodique pour les chaînes de Markov branchantes indexées par des arbres avec des formes arbitraires
No full textInternational audienceWe prove an ergodic theorem for Markov chains indexed by the Ulam-Harris-Neveu tree over large subsets with arbitrary shape under two assumptions: with high probability, two vertices in the large subset are far from each other and have their common ancestor close to the root. The assumption on the common ancestor can be replaced by some regularity assumption on the Markov transition kernel. We verify that those assumptions are satisfied for some usual trees. Finally, with Markov-Chain Monte-Carlo considerations in mind, we prove when the underlying Markov chain is stationary and reversible that the Markov chain, that is the line graph, yields minimal variance for the empirical average estimator among trees with a given number of nodes.Nous démontrons un théorème ergodique pour des chaînes de Markov indexées par l'arbre d'Ulam-Harris-Neveu sur des grands sous-ensembles de forme arbitraire, sous deux hypothèses : avec grande probabilité, deux sommets du grand sous-ensemble sont éloignés l’un de l’autre et ont leur ancêtre commun proche de la racine. L’hypothèse sur l’ancêtre commun peut être remplacée par une hypothèse de régularité sur le noyau de transition de la chaîne de Markov. Nous vérifions que ces hypothèses sont satisfaites pour certains arbres usuels. Enfin, motivés par des considérations liées aux méthodes de Monte-Carlo par chaînes de Markov, nous prouvons que lorsque la chaîne de Markov sous-jacente est stationnaire et réversible, cette chaîne de Markov, autrement dit le graphe ligne, minimise la variance de l’estimateur de la moyenne empirique parmi les arbres ayant un nombre donné de nœuds
Energetically Consistent Eddy-Diffusivity Mass-Flux Convective Schemes: 1. Theory and Models
No full textInternational audienceThis paper presents a self‐contained derivation, from first principles, of a convective vertical mixing scheme based on the Eddy‐Diffusivity Mass‐Flux (EDMF) approach. This type of closure separates vertical turbulent fluxes into two components: an eddy‐diffusivity (ED) which accounts for local small‐scale mixing in a nearly isotropic environment, and a mass‐flux (MF) transport term, which represents the non‐local transport driven by vertically coherent plumes. Using the multi‐fluid averaging underlying the MF concept, we review consistent energy budgets between resolved and subgrid scales for seawater and dry atmosphere, in anelastic and Boussinesq frameworks. We demonstrate that when using an EDMF scheme, closed energy budgets can be recovered if: (a) bulk production terms of turbulent kinetic energy (TKE) by shear buoyancy include MF contributions; (b) boundary conditions are consistent with EDMF, to avoid spurious energy fluxes at the boundary. Furthermore, we show that lateral mixing, due to either entrainment or detrainment induces a net production of TKE via the shear term, with enhanced production under increased horizontal drag. We also provide constraints on boundary conditions to ensure mathematical consistency. Throughout the theoretical development, we maintain transparency regarding underlying assumptions. In a companion paper (Perrot and Lemarié (2024, https://hal.science/hal‐04666049 ); hereafter Part II) we assess the validity of these hypotheses, and analyze the sensitivity of the scheme to modeling choices against Large Eddy Simulations (LES) and observational data on oceanic convection. Part II also details an energy‐conserving discretization and quantifies energy biases in inconsistent formulations
Sick of Working from Home?
No full textInternational audienceWe explore the consequences of the development of home working for wages, hours worked and employee health in the post COVID era. We base our research strategy on a French law passed in 2017 to encourage telework agreements between employers and employees. In the months following the law, many establishments signed telework agreements, and we show that this subsequently led to a much greater development of home working in these establishments after the epidemic shock in 2020. This increase was particularly significant in mid-level occupations, and was followed by a deterioration in the health of the employees concerned, particularly men
Attrition in Randomized Controlled Trials: Using Tracking Information to Correct Bias
No full textInternational audienceThis paper analyzes the implications of attrition for the internal and external validity of the results of four randomized experiments and proposes a new method to correct for attrition bias. We find that not including those found during the intensive tracking can lead to a substantial overestimation or underestimation of the intention-to-treat effects, even when attrition without such tracking is balanced. We propose to correct for attrition using inverse probability weighting with estimates of weights that exploit the similarities between missing individuals and those found during an intensive tracking phase
Les mobilités domicile-travail au défi de la sobriété
No full textInternational audiencePourquoi les trois-quarts des trajets domicile-travail sont-ils toujours réalisés en voiture ? Et comment augmenter l’usage des modes de transport alternatifs (vélo, transports collectifs, covoiturage…) ? Cette communication explore les liens complexes entre le travail et les pratiques de mobilité
Imbalance Term in the TKE Budget over Waves
No full textInternational audienceIn an attempt to reconciliate air-sea momentum flux estimates derived from open sea observations, from large eddy simulation output fields, and from wind-wave tank measurements, a series of dedicated experiments were conducted in the wind-wave tank of the Large Air-Sea Facility of Marseille, France. The turbulent friction velocity, upon which the momentum flux depends, was estimated from wind measurements by applying four classical methods including the eddy-covariance method and the inertial-dissipation method. The collected data were used to investigate some characteristics of the waveinfluenced boundary layer that were predicted by previous simulations, and to quantify a wave-dependent term of the turbulent kinetic energy equation, the so-called imbalance term ϕ imb . Our results show that the turbulent stress decreases toward lower heights where the effect of waves is large, as in the simulations, and that ϕ imb is in the range 0.3 to 0.7, which is comparable to the value found with open sea data (0.4). These preliminary results have to be confirmed with wave-following probes, because the estimated eddy-covariance flux slightly varied with height, thus it could not be strictly considered to be equal to a constant total flux
Do suspended particles matter for wastewater-based epidemiology?
No full textInternational audienceAs wastewater-based epidemiology (WBE) continues to evolve and expand the range of targeted compounds, some limitations remain underexplored, particularly the sorption of targeted markers onto suspended particulate matter (SPM) in raw wastewater. This issue is crucial as it could lead to underestimations in retrospective calculations. While previous studies have addressed this topic, they have primarily focused on a limited range of analytes (e.g., illicit drugs and selected pharmaceuticals) and relied on small sample sizes, highlighting the need for further research. This study aims to bridge these gaps through a six-month monitoring campaign analyzing a broad range of WBE markers (pharmaceuticals, illicit drugs, and lifestyle biomarkers) in both the dissolved and the particulate phases. A dedicated analytical method based on pressurized liquid extraction and liquid chromatography coupled with tandem mass spectrometry allowed the assessment of daily loads and distribution behavior of these compounds, providing new insights into their relevance for WBE estimates. The results demonstrated that most compounds exhibited low sorption to SPM, confirming their reliability for WBE monitoring based solely on dissolved-phase measurements. Notably, this studyprovides the first clear assessment of the minimal sorption of tobacco and coffee biomarkers.However, significant sorption was observed for 11 molecules, including fluoxetine, THC-COOH, and methadone, revealing a “hidden load” that could bias estimates without proper correction. Log D proved to be a useful and better than log Kow predictor of sorption potential for ionized compounds but failed to accurately predict sorption for neutral species. Additionally, wastewater dilution due to urban runoff appeared to influence compound partitioning, potentially increasing their affinity for the solid phase. Nonetheless, potential changes in the organic composition of SPM do not appear to be the driving factor, as the studied material retained stable total organic carbon (TOC) levels, most likely due to in-sewer remobilization of organic deposits which share a similar signature with domestic wastewater effluent. Further investigations are needed to identify the key parameters influencing compound affinity for SPM and their potential implications for WBE applications
Bayesian inference of numerical modeling-based morphodynamics: Application to a dam-break over a mobile bed experiment
No full textInternational audienceNumerical modeling of morphodynamics presents significant challenges in engineering due to uncertainties arising from inaccurate inputs, model errors, and limited computing resources. Accurate results are essential for optimizing strategies and reducing costs. This paper presents a step-by-step Bayesian methodology to conduct an uncertainty analysis of 2D numerical modeling-based morphodynamics, exemplified by a dam-break over a sand bed experiment. Initially, uncertainties from prior knowledge are propagated through the dynamical model using the Monte Carlo technique. This approach estimates the relative influence of each input parameter on results, identifying the most relevant parameters and observations for Bayesian inference and creating a numerical database for emulator construction. Given the computationally intensive simulations of Markov chain Monte Carlo (MCMC) sampling, a neural network emulator is used to approximate the complex 2D numerical model efficiently. Subsequently, a Bayesian framework is employed to characterize input parameter uncertainty variability and produce probability-based predictions