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General reproducing properties in RKHS with application to derivative and integral operators
No full textIn this paper, we consider the reproducing property in Reproducing Kernel Hilbert Spaces (RKHS). We establish a reproducing property for the closure of the class of combinations of composition operators under minimal conditions. This allows to revisit the sufficient conditions for the reproducing property to hold for the derivative operator, as well as for the existence of the mean embedding function. These results provide a framework of application of the representer theorem for regularized learning algorithms that involve data for function values, gradients, or any other operator from the considered class.Dans cet article, nous considérons la propriété reproduisante dans les espaces de Hilbert à noyaux reproduisants (RKHS). Nous établissons une propriété de reproduction pour l'adhérence de la classe des combinaisons d'opérateurs de composition sous des conditions minimales. Cela nous permet de revisiter les conditions suffisantes pour que la propriété de reproduction soit valable pour l'opérateur dérivé, ainsi que pour l'existence de la fonction mean embedding. Ces résultats donnent un cadre d'application du théorème du représentant pour les algorithmes d'apprentissage régularisés qui impliquent des données sur les valeurs de fonctions, les gradients ou tout autre opérateur de la classe considérée
AKiRa: Augmentation Kit on Rays for optical video generation
No full textInternational audienceRecent advances in text-conditioned video diffusion have greatly improved video quality. However, these methods offer limited or sometimes no control to users on camera aspects, including dynamic camera motion, zoom, distorted lens and focus shifts. These motion and optical aspects are crucial for adding controllability and cinematic elements to generation frameworks, ultimately resulting in visual content that draws focus, enhances mood, and guides emotions according to filmmakers' controls. In this paper, we aim to close the gap between controllable video generation and camera optics. To achieve this, we propose AKiRa (Augmentation Kit on Rays), a novel augmentation framework that builds and trains a camera adapter with a complex camera model over an existing video generation backbone. It enables fine-tuned control over camera motion as well as complex optical parameters (focal length, distortion, aperture) to achieve cinematic effects such as zoom, fisheye effect, and bokeh. Extensive experiments demonstrate AKiRa's effectiveness in combining and composing camera optics while outperforming all state-of-the-art methods. This work sets a new landmark in controlled and optically enhanced video generation, paving the way for future camera diffusion methods
Formulation en transformation finie du principe d’écart d’équilibre discret : application à l’estimation directe de paramètres à partir de mesures de champs
No full textInternational audienceThe Equilibrium Gap Method (EGM) is a direct model parameter identification method, i.e., that does not require any resolution of the model. It has been extensively studied in the context of small strains but not thoroughly investigated for large strains. In this article, we propose a novel formulation of the EGM, valid in large strains, and applicable to both boundary and body forces, when full-field measurements are available. Our formulation is based on a recently proposed continuous formulation and consistent discretization of the equilibrium gap principle. Additionally, we developed an estimation pipeline to quantify the robustness of our new EGM formulation to noise, and we compared its performance to other classical estimation methods, namely the Finite Element Model Updating (FEMU) method and the Virtual Fields Method (VFM). Our robustness quantification pipeline involves generating synthetic data from a reference model through two methods: by adding noise to the reference displacement, or by generating noisy images and performing motion tracking with the Equilibrium Gap principle used as mechanical regularization. While the quality of estimation using our new EGM formulation is poor with the first data generation method, it improves drastically with the second method. Since the second method of synthetic data generation closely mimics experimental processes, the EGM, when combined with motion tracking with Equilibrium Gap regularization, demonstrates reasonable noise robustness. Thus, it is a promising option for direct parameter estimation from full-field measurements.La méthode de l’écart d’équilibre (EGM) est une méthode directe d’identification de paramètres de modèles, c’est-à-dire qu’elle ne nécessite aucune résolution du modèle. Elle a été largement étudiée dans le contexte des petites déformations, mais n’a pas fait l’objet d’un examen approfondi pour les grandes défor- mations. Dans cet article, nous proposons une nouvelle formulation de l’EGM, valable pour les grandes dé- formations et applicable à la fois aux forces surfaciques et aux forces volumiques, lorsque des mesures plein champ sont disponibles. Notre approche est basée sur une formulation continue et une discrétisation consis- tante du principe de l’écart d’équilibre récemment proposées. En outre, nous avons développé un pipeline pour quantifier la robustesse de notre nouvelle formulation EGM au bruit, et nous avons comparé ses perfor- mances à d’autres méthodes d’estimation classiques, à savoir la méthode « Finite Element Method Updating » (FEMU) et la méthode des champs virtuels (VFM). Notre pipeline de quantification de la robustesse implique la génération de données synthétiques à partir d’un modèle de référence via deux méthodes potentielles : soit en ajoutant du bruit au déplacement de référence, soit en générant des images bruitées et en effectuant un suivi de mouvement avec le principe de l’écart d’équilibre utilisé comme régularisation mécanique. Alors que la qualité de l’estimation utilisant notre nouvelle formulation EGM est faible avec la première méthode de génération de données, elle s’améliore considérablement avec la seconde méthode. Étant donné que la deuxième méthode de génération de données synthétiques reproduit fidèlement les processus expérimen- taux, l’EGM, lorsqu’elle est associée au suivi des mouvements avec régularisation de l’écart d’équilibre, fait preuve d’une robustesse raisonnable face au bruit. Il s’agit donc d’une option prometteuse pour l’estimation directe de paramètres à partir de mesures plein champ
First direct observation of a wakefield generated with structured light
No full textInternational audienceThe use of structured light to control the phase velocity of the wake in laser-wakefield accelerators has generated significant interest for its ability to mitigate electron dephasing. Combining the diffraction-free properties of Bessel beams with spatio-temporal shaping of the pulse promises to enable acceleration with an unprecedented combination of long acceleration lengths and high gradients. This would facilitate the acceleration of electrons to energies above 100 GeV in existing laser facilities. In-depth understanding of the physical mechanisms involved is critical to achieving dephasing-free electron acceleration. Here we present the first experimental observation of wakefields generated by beams that were spatio-temporally sculpted and then focused with a long-focal-depth mirror, known as an axiparabola, which generates a quasi-Bessel beam. The resulting wakefield was imaged using femtosecond relativistic electron microscopy. Novel insights into this minimally explored regime include mapping the wakefield development over the focal depth and studying the effects of spatio-temporal manipulations of the beam on the structure and phase velocity of the wakefield. Such insights pave the way towards realizing the potential of structured-light based solutions to dephasing in laser-wakefield acceleration
Understanding Virtual Nodes: Oversquashing and Node Heterogeneity
No full textInternational audienceWhile message passing neural networks (MPNNs) have convincing success in a range of applications, they exhibit limitations such as the oversquashing problem and their inability to capture long-range interactions. Augmenting MPNNs with a virtual node (VN) removes the locality constraint of the layer aggregation and has been found to improve performance on a range of benchmarks. We provide a comprehensive theoretical analysis of the role of VNs and benefits thereof, through the lenses of oversquashing and sensitivity analysis. First, we characterize, precisely, how the improvement afforded by VNs on the mixing abilities of the network and hence in mitigating oversquashing, depends on the underlying topology. We then highlight that, unlike Graph-Transformers (GTs), classical instantiations of the VN are often constrained to assign uniform importance to different nodes. Consequently, we propose a variant of VN with the same computational complexity, which can have different sensitivity to nodes based on the graph structure. We show that this is an extremely effective and computationally efficient baseline for graph-level tasks
A Model of Post-2008 Monetary Policy
No full textWe introduce banks and bank reserves into the basic New Keynesian model and allow the central bank to set both the interest rate on reserves (IOR rate) and the nominal stock of reserves. Our model can account, in qualitative terms, for three key features of US inflation during the recent zero-lower-bound (ZLB) episodes: no significant deflation, little inflation volatility, and no significant inflation following quantitative-easing policies. Crucial to this result is our assumption that demand for bank reserves got close to satiation, but did not reach full satiation. We introduce liquid government bonds into the model to reconcile our non-satiation assumption with the fact that Treasury-bill rates were often below the IOR rate during the ZLB episodes. Looking ahead, we explore the implications of our model for the normalization of monetary policy and its operational framework (floor system)
Three-pion Bose-Einstein correlations measured in proton-proton collisions
No full textInternational audienceA study on the Bose-Einstein correlations for triplets of same-sign pions is presented. The analysis is performed using proton-proton collisions at a centre-of-mass energy of = 7 TeV, recorded by the LHCb experiment, corresponding to an integrated luminosity of 1.0 fb. For the first time, the results are interpreted in the core-halo model. The parameters of the model are determined in regions of charged-particle multiplicity. This measurement provides insight into the nature of hadronisation in terms of coherence, showing a coherent emission of pions
From Glosten-Milgrom to the whole limit order book and applications to financial regulation
No full textWe build an agent-based model for the order book with three types of market participants: an informed trader, a noise trader and competitive market makers. Using a Glosten-Milgrom like approach, we are able to deduce the whole limit order book (bid-ask spread and volume available at each price) from the interactions between the different agents. More precisely, we obtain a link between efficient price dynamic, proportion of trades due to the noise trader, traded volume, bid-ask spread and equilibrium limit order book state. With this model, we provide a relevant tool for regulators and market platforms. We show for example that it allows us to forecast consequences of a tick size change on the microstructure of an asset. It also enables us to value quantitatively the queue position of a limit order in the book
Estimation of extreme risk measures with neural networks
No full textNational audienceWe propose new parameterizations for neural networks in order to estimate extreme risk measures, such as conditional tail moments, in heavy-tailed settings. The proposed neural network estimator is able to extrapolate in the distribution tails thanks to an extension of the usual extreme-value second-order condition to an arbitrary order. The convergence rate of the uniform error between the log-conditional tail moment and its neural network approximation is established. The finite sample performance of the neural network estimator is compared to bias-reduced extreme-value competitors on simulated data. It is shown that our method outperforms them in difficult heavy-tailed situations where other estimators almost all fail. Finally, the neural network estimator is tested on real data to investigate the behavior of cryptocurrency extreme loss returns
Impact of the silica glass initial state on the thermal and structural properties of metamict-like silica glass
No full textInternational audienceThis study investigates the structural and thermal stability of metamict-like silica glass samples prepared through different thermomechanical pathways and then subjected to the same high dose of electron irradiation (11 GGy). Specifically, we compared Suprasil F300 silica glass samples treated with high-pressure high-temperature (HPHT) conditions followed by irradiation to those solely irradiated. Additionally, Suprasil CG samples were analyzed to investigate the effect of silica impurities (e.g. OH) on the resulting state. Using Raman and FTIR spectroscopy, along with photoluminescence spectroscopy, we analyzed the vibrational structure and point defects changes. The activation energy distribution of the densification relaxation process was calculated to assess its thermal stability in a reliable manner. The results demonstrate that, despite achieving similar densities and vibrational structures in the metamict-like state, the initial structure of silica significantly influences the thermal stability and the resulting point defects population