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Discrete Poincaré inequalities: a review on proofs, equivalent formulations, and behavior of constants
No full textInternational audienceWe investigate discrete Poincaré inequalities on piecewise polynomial subspaces of the Sobolev spaces H(curl, ω) and H(div, ω) in three space dimensions. We characterize the dependence of the constants on the continuous-level constants, the shape regularity and cardinality of the underlying tetrahedral mesh, and the polynomial degree. One important focus is on meshes being local patches (stars) of tetrahedra from a larger tetrahedral mesh. We also review various equivalent results to the discrete Poincaré inequalities, namely stability of discrete constrained minimization problems, discrete inf-sup conditions, bounds on operator norms of piecewise polynomial vector potential operators (Poincaré maps), and existence of graph-stable commuting projections
Tutorial – Topological image analysis based on morphological hierarchies
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Deformation of synthetic rock salt investigated by X-Ray micro-computed tomography: Effect of brine, confining pressure and loading rate
No full textInternational audienceThe development of micro-cracks in rock salt has been studied in 3D. In order to investigate the influence of brine, dry and humid materials have been synthetized by powder compaction. We present results of in situ X-Ray micro-tomography triaxial tests performed on the PSICHE beamline of Synchrotron SOLEIL. We have explored different loading rates and confining pressures for both types of synthetic rock salt
Effect of Pore Fluid Chemistry on the Hydro-Mechanical Behaviour of Poorly Indurated Boom Clay
No full textInternational audienceEffect of Pore Fluid Chemistry on the Hydro-Mechanical Behaviour of Poorly Indurated Boom Cla
What kind of cars do people drive? Including fuel type and emission standards in a car ownership model
No full textInternational audienceCar ownership models are essential for understanding travel behavior and informing transportation policy decisions. However, previous research on car ownership modeling has not addressed the determinants of car ownership related to pollutant emissions such as fuel type or emission standard. This study seeks to fill this gap by comparing the performance of several classification models in predicting the number of cars owned by households, their fuel type and their Euro norm (i.e. car age), while also investigating the significance of explanatory variables. These variables include socioeconomic characteristics, as well as mobility-related variables such as commuting distance, parking availability, and public transportation accessibility to the home and workplace. The methodology is applied to the Paris region. We find that logistic regression performs similarly to supervised learning models, even slightly outperforming them, except for car age estimation in which gradient boosting performs better. Our results show that income and commuting distance jointly have a preponderant explanatory effect on the type of car owned, particularly income for electric cars. This work paves the way for future research evaluating transportation policies related to household car ownership by allowing a deeper understanding of the determinants of the type of car owned by households and by providing the trained classifiers as open data
Decreasing Entropic Regularization Averaged Gradient for Semi-Discrete Optimal Transport
No full textInternational audienceAdding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while still benefiting from the acceleration provided by regularization, a natural solver would adaptively decrease the regularization as it approaches the solution. Although some algorithms heuristically implement this idea, their theoretical guarantees and the extent of their acceleration compared to using a fixed regularization remain largely open. In the setting of semi-discrete OT, where the source measure is continuous and the target is discrete, we prove that decreasing the regularization can indeed accelerate convergence. To this end, we introduce DRAG: Decreasing (entropic) Regularization Averaged Gradient, a stochastic gradient descent algorithm where the regularization decreases with the number of optimization steps. We provide a theoretical analysis showing that DRAG benefits from decreasing regularization compared to a fixed scheme, achieving an unbiased sample and iteration complexity for both the OT cost and the potential estimation, and a rate for the OT map. Our theoretical findings are supported by numerical experiments that validate the effectiveness of DRAG and highlight its practical advantages
La ventilation en rénovation : un rendez-vous manqué entre habitants et artisans
No full textInternational audienceVentilation is essential in large-scale energy renovations, but its improvement remains too marginal. This research note sheds light on the reasons for this observation through a sociological perspective and draws action pathways from it. On the inhabitants' side, ventilation is not an automatic reflex because it remains poorly understood. Relegated to the background in their renovation projects, the choices made lead to insufficient ventilation operation and counterproductive practices. On the installers' side, ventilation is an ancillary activity, which does not allow them to play a genuine advisory role. At every stage of the installation process, conditions prove unfavorable to the implementation of truly high-performance ventilation. Ultimately, the multiple dissonances between actors do not yet allow ventilation to meet the challenges of energy renovationLa ventilation est indispensable dans les rénovations énergétiques d’ampleur, mais son amélioration est encore trop marginale. Cette note de recherche éclaire les raisons de ce constat à travers un regard sociologique et en tire des pistes d’actions. Du côté des habitants, la ventilation n’est pas un réflexe car elle reste mal comprise. Reléguée au second plan dans leurs projets de travaux, les choix réalisés conduisent à un fonctionnement insuffisant de la ventilation et des pratiques contreproductives. Du côté des installateurs, la ventilation est une activité annexe, ce qui ne leur permet pas de jouer un véritable rôle de conseil. À chaque étape du parcours d’installation, des conditions s’avèrent défavorables à la mise en œuvre d’une ventilation effectivement performante. Au final, les multiples dissonances entre acteurs ne permettent pas encore à la ventilation d’être au rendez-vous de la rénovation énergétique
Qui gouverne ? Des problèmes économiques et sociaux à la gestion des transports du quotidien
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Fouille d'images par synthèse
No full textImage archives contain lots of hidden knowledge that researchers in the digital humanities would like to discover at scale. Much of this knowledge is hard to described through textual descriptions, or to properly ground them on visual evidence. Given collections of images with general predefined classification, for example the name of family of letters or that of a country, the goal of this thesis is to develop machine learning approaches that can mine informative visual structure hiding behind these image collections. Recent compositional synthesis methods can incorporate weak human labels to unsupervised approaches. The key idea of this thesis is to repurpose them towards reliable human-interpretable visual summarization, to provide a method that automatically identifies and summarizes informative visual structure. Our work focuses on two important challenges,The first challenge, is to summarize and help refine the typology existing typologies of handwritten characters. Character morphology has been central to the field of palaeography, where existing typologies are described through textual descriptions. The reliance of the literature on such descriptions prohibits a quantitative methodology that could ground qualitative observation and exploration across historical manuscript collections. Our first contribution, the "Learnable Typewriter," is a novel approach that learns an explicit decomposition of the script of a manuscript's text lines, into small images called sprites. Learning to reconstruct input text lines by composing sprites via differentiable transformations using weak-supervision, our method produces a concrete, interpretable summarization of a character’s morphology. This enables palaeographers to perform quantitative comparison that stands very close to the concrete visual evidence, captured through sprites. We validate this approach on various datasets of printed modern and historical fonts and ciphered texts, and two case studies on medieval manuscripts.The second challenge, is to extract and define the elements that best support a visual categorization of images in the context of their datasets. Different archives of historical, or cultural image datasets, are often associated with time or location, however finding their “visual genome” is hard to define through text and enumerate. In our second contribution, "Diffusion Models as Data Mining Tools", we leverage the abstract and scalable compositional synthesis capabilities of diffusion models to mine visual structure across versatile weakly labeled datasets. Through a "typicality" score that is based on the influence of a label to the denoising performance of the diffusion model, we rank and then cluster elements typical to specific labels. Unlike other approaches that rely on pairwise matching to discovery both frequent and discriminative patches, our diffusion based approach is linear, has more robust representations and can scale to versatile datasets of cars, portraits, geographical images, or scenes, that consist from thousands to millions of images. Using the diffusion model, we can directly translate images across location and mine co-typical, as well as make the model's sampling bias more interpretable.Les archives d'images contiennent une grande quantité de connaissances cachées que les chercheuses en sciences humaines numériques souhaitent découvrir à grande échelle. Une grande partie de ces connaissances est difficile à décrire par des descriptions textuelles, ou à fonder correctement sur des preuves visuelles. Étant donné des collections d'images avec des classifications générales prédéfinies, telles que le nom d'une famille de lettres ou celui d'un pays, l'objectif de cette thèse est de développer des approches d'apprentissage automatique permettant d'extraire la structure visuelle informative cachée derrière ces collections d'images. Les méthodes récentes de synthèse compositionnelle peuvent intégrer des étiquettes humaines faibles à des approches non supervisées. L'idée principale de cette thèse est de les réorienter vers un résumé visuel fiable et interprétable par l'homme, afin de fournir une méthode qui identifie et résume automatiquement la structure visuelle informative. Notre travail se concentre sur deux problèmes importants.Le premier probleme consiste à résumer et à affiner les typologies existantes des caractères manuscrits. La morphologie des caractères est au cœur du domaine de la paléographie, où les typologies existantes sont transmis à partir des descriptions textuelles. La dépendance de la littérature à ces descriptions empêche l'adoption d'une méthodologie quantitative qui pourrait fonder l'observation qualitative et l'exploration à travers des collections de manuscrits historiques. Notre première contribution, le "Learnable Typewriter", est une approche novatrice qui apprend une décomposition explicite du script des lignes de texte d'un manuscrit, en petites images appelées sprites. En apprenant à reconstruire les lignes de texte d'entrée en composant des sprites via des transformations différentiables utilisant une supervision faible, notre méthode produit une synthèse concrète et interprétable de la morphologie d'un caractère. Cela permet aux paléographes de réaliser des comparaisons quantitatives très proches de la preuve visuelle concrète, capturée par les sprites. Nous validons cette approche sur plusieurs ensembles de données de polices modernes et historiques imprimées, ainsi que sur des textes chiffrés, et deux études de cas sur des manuscrits médiévaux. Le deuxième problem consiste à extraire et à définir les éléments qui soutiennent le mieux une catégorisation visuelle des images dans le contexte de leurs ensembles de données. Différentes archives d'images historiques ou culturelles sont souvent associées au temps ou à la localisation, cependant, il est difficile de définir et d'énumérer leur "génome visuel" à travers du texte. Dans notre deuxième contribution, "Modèles de diffusion comme outils de fouille de données", nous exploitons les capacités abstraites et scalables de synthèse compositionnelle des modèles de diffusion pour extraire la structure visuelle à travers des ensembles de données faiblement étiquetés et polyvalents. Grâce à un score de "typicité" basé sur l'influence d'une étiquette sur la performance de débruitage du modèle de diffusion, nous classons puis regroupons les éléments typiques des étiquettes spécifiques. Contrairement à d'autres approches qui reposent sur une correspondance par paires pour découvrir des fragments fréquents et discriminants, notre approche basée sur la diffusion est linéaire, offre des représentations plus robustes et peut être mise à l'échelle pour des ensembles de données polyvalents d'images de voitures, de portraits, d'images géographiques ou de scènes, allant de milliers à des millions d'images. En utilisant le modèle de diffusion, nous pouvons directement traduire des images d'une localisation à l'autre et exploiter des éléments co-typiques, tout en rendant le biais d'échantillonnage du modèle plus interprétable
Computing gradient vector fields with Morse sequences
No full textInternational audienceWe rely on the framework of Morse sequences to enable the direct computation of gradient vector fields on simplicial complexes. A Morse sequence is a filtration from a subcomplex to a complex via elementary expansions and fillings, naturally encoding critical and regular simplexes. Maximal increasing and minimal decreasing schemes allow constructing these sequences, and are linked to algorithms like Random Discrete Morse and Coreduction. Extending the approach to cosimplicial complexes()allows for efficient computation using reductions, perforations, coreductions, and coperforations.We further generalize to -sequences, which are Morse sequences weighted by an arbitrary stack function , and provide algorithms to compute maximal and minimal sequences. A particular case is when the stack function is given through a vertex map, common in topological data analysis.For injective maps, the complex decomposes into lower stars, recovering established methods and enabling parallel computation; for non-injective maps, our approach applies directly without requiring perturbations. Thus, the paper adopts Morse sequences as a framework that simplifies and connects some important existing propagation-based methods, while also introducing new schemes that extend their scope and practical applicability