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Limite haute-fréquence pour les équations de Klein-Gordon-Maxwell
No full textThe Klein-Gordon-Maxwell equations are used in several physical contexts, as a simple model for gauge theories,in quantum electrodynamics... As for other hyperbolic or elliptic equations, it is interesting to study the behaviorof high-frequency solutions. Especially at the limit, when the wavelength tends to 0.In the case of the vacuum Einstein equations, the Burnett conjecture states that a high-frequency limit of solutions (in a sense to be specified)is a solution to the massless Einstein-Vlasov equations. This phenomenon of backreaction is linked to the nonlinearities of the Einstein equations.For KGM, the nonlinearities are weaker and have a more flexible structure, which suggests the existence of more singular high-frequency solutions.Moreover, the presence of the Planck constant h (representative of the quantum effects in KGM) in the equationsallows the study of another type of high-frequency solutions, the ones appearing at the semi-classical limit,that is, when h tends to 0.The aim of this thesis will be to identify possible limits (semi-classical or not) for sequences of high-frequency solutionsto the Klein-Gordon-Maxwell equations and to understand which relativistic fluid or kinetic system are they solution to. To do so, several methods will be used: geometric optics,semi-classical analysis, modulated energy method, study of simplified equation (nonlinear Klein-Gordon)...Les équations de Klein-Gordon-Maxwell sont utilisées dans plusieurs contextes physiques, comme modèle simple pour les théories de jauge, en électrodynamique quantique... Comme pour d'autres équations hyperboliques ou elliptiques, il est intéressant d'étudier le comportement des solutions haute fréquence. Notamment à la limite, quand la longueur d'onde tend vers 0. Dans le cas des équations d'Einstein dans le vide, la conjecture de Burnett dit qu'une limite haute-fréquence de solutions (dans un sens à préciser) est solution des équations d'Einstein-Vlasov sans masse. Ce phénomène de rectification est lié aux non-linéarités des équations d'Einstein. Pour KGM, les non-linéarités sont plus faibles et ont une structureplus souple, ce qui laisse présager l'existence de solutions haute-fréquence plus singulières. De plus, la présence de la constante de Planck h (manifestation du caractère quantique de KGM) dans les équations donne lieu à l'étude d'un autre type de solutions haute-fréquence, celles apparaissant à la limite semi-classique,c'est-à-dire quand h tend vers 0. Le but de cette thèse sera d'identifier des limites (semi-classiques ou non) possibles pour des suites de solutions haute-fréquence aux équations de Klein-Gordon-Maxwell et de comprendre de quels systèmes de type fluides ou cinétiques relativistes elles sont solutions. Pour ce faire, plusieurs méthodes seront utilisées : l'optique géométrique,l'analyse semi-classique, les méthodes d'énergies modulées, l'étude d'équations plus simples (Klein-Gordon non linéaire)..
Graph Neural Network Generalization with Gaussian Mixture Model Based Augmentation
No full textInternational audienceGraph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when training data is limited in size or diversity. To address these issues, we introduce a theoretical framework using Rademacher complexity to compute a regret bound on the generalization error and then characterize the effect of data augmentation. This framework informs the design of GRATIN, an efficient graph data augmentation algorithm leveraging the capability of Gaussian Mixture Models (GMMs) to approximate any distribution. Our approach not only outperforms existing augmentation techniques in terms of generalization but also offers improved time complexity, making it highly suitable for real-world applications. Our code is publicly available at: https://github.com/abbahaddou/GRATIN
Search for light pseudoscalar bosons, pair-produced in Higgs boson decays in the four-electron final state in proton-proton collisions at = 13 TeV
No full textInternational audienceA search for pairs of light neutral pseudoscalar bosons (A) resulting from the decay of a Higgs boson is performed. The search is conducted using LHC proton-proton collision data at = 13 TeV, collected with the CMS detector in 20162018 and corresponding to an integrated luminosity of 138 fb. The A boson decays into a highly collimated electron-positron pair. A novel multivariate algorithm using tracks and calorimeter information is developed to identify these distinctive signatures, and events are selected with two such merged electron-positron pairs. No significant excess above the standard model background predictions is observed. Upper limits on the branching fraction for H AA 4e are set at 95% confidence level, for masses between 10 and 100 MeV and proper decay lengths below 100 m, reaching branching fraction sensitivities as low as 10. This is the first search for Higgs boson decays to four electrons via light pseudoscalars at the LHC. It significantly improves the experimental sensitivity to axion-like particles with masses below 100 MeV
Méthodes Probabilistes Avancées pour l’Amplification de la Confidentialité : Approches Coopératives et Non Coopératives
No full textFrom drawing statistical conclusions to training machine learning models, data collection has undoubtedly become an essential part of modern technologies. Over the years, this has led to increasing privacy concerns, especially in sensitive applications. To address these concerns and reassure users, the frameworks of Differential Privacy (DP) and Quantitative Information Flow (QIF) have been widely studied, which quantify the amount of information an analyst can gain after observing a system.The thesis explores mechanisms that enhance privacy in two different scenarios: (a) when users cooperate with each other to orchestrate a common defense strategy and (b) when users do not cooperate and each must rely on their own approach.In the first case, we build upon the shuffle model of DP, where users obfuscate their data before a trusted shuffler mixes it and then releases it to the analyst. The blending effect of shuffling is refined using varying encoding schemes that significantly limit the amount of user information available to the analyst, without affecting the accuracy of the result. The thesis studies this approach in location data, combining shuffling with metric privacy (a variant of DP for domains equipped with a notion of distance) and then in Federated Learning to protect against Source Inference Attacks (which aim to identify exactly which client trained a given data point).Finally, in non-cooperative settings, the thesis analyzes, using QIF, a user’s optimal strategy to obfuscate their own secret based on the observed submitted secrets of others, under linear constraints. This approach is then applied to defending against Website Fingerprinting attacks. In this scenario, an administrator seeks to make their site’s behavior resemble some other websites, which they wish to mimic. As cooperation with these other sites is not possible, the administrator has to design their defense based solely on the observed behavior of the other sites.De la formulation de conclusions statistiques à l’entraînement de modèles d’apprentissage automatique, la collecte de données est indéniablement devenue une composante essentielle des technologies modernes. Au fil des années, cela a soulevé des préoccupations croissantes en matière de confidentialité, en particulier dans les applications sensibles. Pour répondre à ces inquiétudes et rassurer les utilisateurs, les cadres de la Differential Privacy (DP) et du Quantitative Information Flow (QIF) ont été largement étudiés, permettant de quantifier la quantité d’information qu’un analyste peut obtenir après avoir observé un système.Cette thèse explore des mécanismes renforçant la confidentialité dans deux scénarios distincts : (a) lorsque les utilisateurs coopèrent pour orchestrer une stratégie de défense commune, et (b) lorsque les utilisateurs ne coopèrent pas et doivent chacun s’appuyer sur leur propre approche.Dans le premier cas, nous nous appuyons sur le modèle de mélange (shuffle model) de la DP, où les utilisateurs obfusquent leurs données avant qu’un mélangeur de confiance ne les combine et les publie ensuite à l’analyste. L’effet de mélange est affiné grâce à divers schémas d’encodage qui limitent considérablement la quantité d’information utilisateur accessible à l’analyste, sans compromettre l’exactitude du résultat. Cette approche est étudiée dans le cadre des données de localisation, en combinant le mélange avec la metric privacy (une variante de DP adaptée aux domaines munis d’une notion de distance), puis dans l’apprentissage fédéré afin de se protéger contre les Source Inference Attacks (qui visent à identifier précisément quel client a entraîné un point de données donné).Enfin, dans des contextes non coopératifs, la thèse analyse, à l’aide du QIF, la stratégie optimale d’un utilisateur pour obfusquer son propre secret en se basant sur les secrets soumis par d’autres, sous des contraintes linéaires. Cette approche est ensuite appliquée à la défense contre les attaques de fingerprinting de sites Web. Dans ce scénario, un administrateur cherche à faire en sorte que le comportement de son site ressemble à celui d’autres sites qu’il souhaite imiter. Comme la coopération avec ces autres sites est impossible, l’administrateur doit concevoir sa défense uniquement sur la base du comportement observé de ces sites
A Constraint Opinion Model
No full textInternational audienceThis paper introduces a generalised opinion model that extends the standard DeGroot model by representing agents' opinions and influences as soft constraints rather than single real values. This allows for modelling scenarios beyond the scope of the DeGroot model, such as agents sharing partial information and preferences, engaging in discussions on multiple topics simultaneously, and representing opinions with different degrees of uncertainty. By considering soft constraints as influences, the proposed model captures also situations where agents impose conditions on how others' opinions are integrated during belief revision. Finally, the flexibility offered by soft constraints allows us to introduce a novel polarisation measure that takes advantage of this generalised framework
A holographic non-uniqueness for the Helmholtz equation
No full textWe consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in , , outside the origin. We consider a sphere centered at the origin in . We show that the radiation solution on is not uniquely determined by the intensity of the total solution on . Extensions of this result to the case of other surfaces in place of are also mentioned. Our construction involves and develops technique of scattering on obstacles with Dirichlet boundary condition
Hawkes process with a diffusion-driven baseline: long-run behavior, inference, statistical tests
No full textInternational audienceEvent-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate Hawkes processes, in which the spontaneous rate of events is modulated by a diffusion process. This framework allows the point process to adapt dynamically to continuously evolving covariates, capturing both intrinsic self-excitation and external influences. In this article, we establish the probabilistic properties of the coupled process, proving stability and ergodicity under moderate assumptions. Classical functional results, including law of large numbers and mixing properties, are extended to this diffusiondriven setting. Building on these results, we study parametric inference for the Hawkes component: we derive consistency and asymptotic normality of the maximum likelihood estimator in the long-time regime, and derive stronger convergence results under additional assumptions on the covariate process. We further propose hypothesis testing procedures to assess the statistical relevance of the covariate. Simulation studies illustrate the validity of the asymptotic results and the effectiveness of the proposed inference methods. Overall, this work provides theoretical and practical foundations for diffusion-driven Hawkes models
The subtleties of three-dimensional radiative effects in contrails and cirrus clouds
No full textInternational audienceThe radiative effect of cirrus, contrails, and contrail cirrus affects the energy budget of the Earth and climate change. Those clouds, and especially contrails, are heterogeneous and their holes and sides exert three-dimensional radiative effects. This study uses the htrdr Monte Carlo radiative transfer code to investigate the sensitivity of the cloud radiative effect (CRE) to the geometrical dimensions and optical depth of optically thin ice clouds (cloud optical depth < 4), with particular emphasis on three-dimensional radiative effects. When the Sun is at zenith, an increase in cloud optical depth causes a linear increase in shortwave (SW) CRE but a saturation of longwave (LW) CRE, causing the net CRE to change sign from positive to negative. The optical depth at which this change in sign occurs depends on the cloud geometry. 3D effects make the one-dimensional SW and LW CREs more positive for a Sun at zenith, reaching the same order of magnitude as the 1D CRE itself for clouds with high aspect ratios. The angular dependence of ice crystal scattering strongly increases shortwave CRE when solar zenith angle increases. 3D effects change sign from positive at zenith to negative at large zenith angles as the Sun’s rays interact more with the cloud sides. Integrating instantaneous CRE and 3D effects over selected days of the year indicates compensation of SW with LW 3D effects for some cloud orientations, but 3D effects remain important in some cases. These results suggest that the 3D structure of cirrus and contrails needs to be considered to finely quantify their CRE and radiative forcing
Optimal exit from Uniswap v3 and best expected return for a liquidity provider
No full textWe analyze the profitability of liquidity providers’ (LPs) positions in Uniswap v3 by aggregating fee income and impermanent loss within an optimal stopping framework. Our first result shows that the liquidity burn should be optimized over one range at a time, rather than simultaneously. Second, without discounting future fees, there is no finite optimal liquidity burn time and indefinite liquidity provision is optimal. In this case, we derive closed-form expressions for the value of LP positions according to different price levels of liquidity burn. Third, with a discount factor, we introduce an equivalent rate of return and demonstrate that under a Black-Scholes model with volatility σ, the optimal return is approximately 0.425·σ2 (i.e. about 10%return for 50% volatility), and it is achieved by choosing the at-the-money range of liquidity. These results provide explicit formulas and strategic insights for LPs in Uniswap v3, and complement recent works on Uniswap v2 and fee modelling by highlighting the distinct impact of concentrated liquidity