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Parallel geodesics and minimal stable length of random groups
No full text21 pagesWe show that for any pair of long enough parallel geodesics in a random group G(m, d) with m generators at density d < 1/6, there is a van Kampen diagram having only one layer of faces. Using this result, we give an upper bound, depending only on d, of the number of pairwise parallel geodesics in G(m, d) when d < 1/6. As an application, we show that the minimal stable length of a random group at density d < 1/6 is exactly 1
Associations indépendantes de la pollution de l’air et des conditions météorologiques avec les hospitalisations pour maladies circulatoires et respiratoires dans la métropole de Lyon, France (2012–2019) : une analyse à retards distribués non linéaire.
No full textInternational audienceThe impact of air pollution on respiratory and circulatory diseases is a major public health topic. The present study examines the impact of air pollution and weather on hospital admissions for circulatory and respiratory diseases in adults in the Lyon metropolitan area, France. A quasi-Poisson generalized linear model, along with a distributed lag nonlinear model (DLNM), was used to investigate the nonlinear exposure-response relationships of air pollutants and weather variables on daily adult hospital admissions from 2012 to 2019. Subgroup analyses by age, French deprivation index (FDep), and Charlson comorbidity index (CCI) were performed. Based on cumulative effects over the entire lag range, results showed that for respiratory admissions, CO at the 99th percentile was positively associated with overall admissions, and admissions of patients aged ≥ 65 years, FDep>1, and CCI = {0, 1} . PM10>75th percentile was negatively associated with overall admissions and admissions of patients aged ≥ 65, FDep=1 or >1, and CCI = {0, 1} . Ox below the median was positively associated with admissions in patients aged ≥ 65, and negatively associated at the 75th percentile. Temperature at the 99th percentile was negatively associated with overall admissions, and admissions in patients categorized as FDep=1 and CCI>1. Rainfall at the 99th percentile was negatively associated with admissions in patients categorized as CCI = {0, 1} . For circulatory admissions, only wind speed above the median was positively associated with overall admissions and admissions of patients categorized as FDep=1. Lag-specific associations revealed heterogeneous temporal patterns across exposures and subgroups
History-Aware Sequence Modeling for Authentic Learner Profiling in the Age of Generative AI
No full textGenerative AI tools (e.g., ChatGPT, DeepSeek, Copilot) enable students to delegate learning tasks, obscuring authentic learning behaviors and the critical transition from declarative to procedural knowledge. Current learning analytics and AI detectors focus on coarse-grained outputs, failing to capture the nuanced dynamics of learning processes in generative AI-integrated contexts. However, identifying patterns beyond memorization such as using ChatGPT for initial hints or scaffolding remains challenging when learners orchestrate interactions between reasoning, AI assistants, and digital environments. We introduce Auth-LP (Authentic Learner Profiling), a history-aware sequence modeling framework that profiles authentic learning by analyzing timestamped event sequences (e.g., Prompted, AskGenAI, HelpSeeking, HintRequest) in educational contexts integrating generative AI. The framework bridges task-level learner-AI assistant interactions by identifying behavioral states such as Engaged, Struggling, AI-Dependent, and Gaming the System. Auth-LP integrates visual analytics (e.g., heatmaps, radar charts) to gracefully monitor profile transitions as students' behavioral states evolve throughout the learning process. It enables educators to distinguish genuine skill development and learning agency from AI-assisted outputs, informing learning analytics design and enhancing personalized guidance. Our findings, based on a proof of concept conducted within the écri+ project, demonstrate that history-aware sequence modeling supports authentic learner profiling and trustworthy assessment, fostering Human-AI synergy for augmented learning in AI-augmented education.</div
Visualization of surface wave generation and tail wave formation in acoustic Wood anomalies
No full textInternational audienceAcoustic Wood anomalies are phenomena characterized by sharp amplitude peaks and dips at specific frequencies in the spectra of the waves reflected from periodic surfaces. Theoretical studies proposed the double mode conversion theory, suggesting bulk waves convert to surface waves at periodic rough surfaces and reconvert to bulk waves, which then interfere with specular reflections (main waves) as delayed reflected components (tail waves). However, experimental validation remains incomplete. This study clarifies the relationship between surface waves and tail waves through visualization of wave propagation processes and identifies causes of changes in tail wave formation due to periodic surface geometry. Pulse-echo experiments were conducted using carbon steel specimens with rectangular periodic profiles of varying pitch and depth. Finite-difference time-domain simulations visualized ultrasonic wave propagation under identical experimental conditions. Simulation data showed good agreement with experimental data, validating the simulation approach. Amplitude spectral analysis revealed that the surface waves and tail waves had common frequency characteristics, confirming the double mode conversion assumption. The simulations successfully visualized surface waves generation, propagation, and reconversion to bulk waves, demonstrating tail wave formation from surface waves in detail
Involutions de Möbius
No full textWe revisit and extend the classical theory of M\"obius involutions, presenting a unified geometric framework that highlights their ubiquity and utility in similarity geometry and mathematical physics. We analyze compositions of spiral similarities, clarifying how dilation factors, rotation angles, and the often‑overlooked relations among fixed points interact under composition. Reinterpreting these phenomena via M\"obius involutions yields simpler proofs and sharper structural insights. We treat indirect involutions (inversions), give a complete account of three pairwise commuting inversions, and prove Ramondou’s recent conjecture on elliptic and hyperbolic pencils of circles. Finally, we introduce a novel similarity geometry on pairs of points exchanged by a fixed M\"obius involution, define collinearity and concyclicity in this setting, and present applications that simultaneously exchange multiple classical point pairs. The results synthesize historical sources with new observations and demonstrate that M\"obius involutions are both fundamental and practically powerful in geometry
Estimation basée sur la forêt aléatoire de la mesure d'analyse de sensibilité globale orientée quantile
No full textThis thesis is devoted to the estimation and application of Quantile-Oriented Sensitivity Analysis (QOSA) measures, including the first-order QOSA indices, the total QOSA indices, and the Quantile-Oriented Shapley Effects (QOSE) indices, which provide a natural and interpretable extension when input variables are dependent. Compared with variance-based measures, QOSA indices are both more robust and more informative, as they capture distributional features beyond variance. Our first contribution is the development of a new quantile-oriented random forest, which achieves performance comparable to other state-of-the-art random forest approaches for quantile regression. Building on this tool, we integrate the projected algorithm to estimate conditional quantiles given a subset of inputs. This enables the estimation of QOSA indices through a straightforward plug-in procedure. We establish consistency results for the conditional quantile estimators and three type QOSA indices. The final part of the thesis focuses on the application of QOSE in meteorology. We demonstrate that QOSE indices can effectively identify and rank the most influential input variables, thereby offering practical guidance for model simplification and for allocating computational resources more efficiently.Cette thèse est consacrée à l'estimation et à l'application des mesures d'analyse de sensibilité orientée quantile (QOSA), incluant les indices QOSA de premier ordre, les indices QOSA totaux et les indices d'effets Shapley orientés quantile (QOSE). Ces mesures offrent une extension naturelle et interprétable lorsque les variables d'entrée sont dépendantes. Comparés aux mesures basées sur la variance, les indices QOSA sont à la fois plus robustes et plus informatifs, car ils capturent les caractéristiques distributionnelles au-delà de la variance. Notre première contribution est le développement d'une nouvelle forêt aléatoire orientée quantile, dont les performances sont comparables à celles des autres approches de pointe en matière de régression quantile. En nous appuyant sur cet outil, nous intégrons l'algorithme projeté pour estimer les quantiles conditionnels à partir d'un sous-ensemble d'entrées. Ceci permet l'estimation des indices QOSA grâce à une procédure simple de plug-in. Nous établissons des résultats de consistance pour les estimateurs de quantiles conditionnels et trois indices QOSA de type. La dernière partie de la thèse porte sur l'application de la QOSE en météorologie. Nous démontrons que les indices QOSE peuvent identifier et classer efficacement les variables d’entrée les plus influentes, offrant ainsi des conseils pratiques pour la simplification des modèles et pour l’allocation plus efficace des ressources de calcul
Computing the degreewidth of a digraph is hard
No full textGiven a digraph, an ordering of its vertices defines a backedge graph, namely the undirected graph whose edges correspond to the arcs pointing backwards with respect to the order. The degreewidth of a digraph is the minimum over all ordering of the maximum degree of the backedge graph. We answer an open question by Keeney and Lokshtanov [WG 2024], proving that it is NP-hard to determine whether an oriented graph has degreewidth at most 1, which settles the last open case for oriented graphs. We complement this result with a general discussion on parameters defined using backedge graphs and their relations to classical parameters
Some aspects of topological dynamics of Polish groups: With an introduction to descriptive set theory
No full textInternational audienceThe first half of these notes presents some aspects of the theory of continuous actions of Polish groups on compact spaces, leading to the Kechris--Pestov--Todorcevic correspondence. The second part provides an introduction to descriptive set theory and culminates in a proof, due to B. Miller, of the G_0 dichotomy theorem due to Kechris, Solecki and Todorcevic
Dynamical analysis and numerical simulation of a reaction-diffusion model for microbial decomposition of organic matter in 3D soil structure
No full textMicrobial decomposition of organic matter in soil is a fundamental process in the global carbon cycle, directly influencing soil health, fertility, and greenhouse gas emissions. This paper presents a dynamic analysis and numerical simulation of a reaction-diffusion model that describes microbial decomposition of organic matter within a three dimensional soil structure. We investigate the interactions between {Microbial Biomass} (MB) and organic substrates, as well as the diffusion of various compounds through the soil matrix, using nonlinear parabolic partial differential equations. Our study provides proofs for the existence and uniqueness of solutions, as well as an analysis of asymptotic behavior. Notably, our investigation reveals the presence of a global attractor, where any solution, regardless of initial conditions, tends to converge. To illustrate the practical implications of our findings, we have developed a numerical tool to simulate the long-term behavior of the system with reasonable computational expense. This tool provides a visual proof of the global attractor for a validated set of biological parameters in a real sandy loam soil sample captured using 3D tomography imagery
Global Hopf Bifurcation Analysis for a Delayed Nicholson's Blowflies Model with Constant Reproductive Supply
No full textWe investigate the dynamics of a delayed Nicholson's blowflies equation incorporating a constant reproductive supply that influences both density-dependent competition and egg production. The existence and local stability of the positive equilibrium are characterized via the analysis of the associated implicit and characteristic equations. Both local and global Hopf bifurcations are examined to establish conditions for the emergence of periodic solutions. Analytical and numerical results show that increasing the reproductive supply can restore the stability of the positive equilibrium by increasing the critical delay for the onset of Hopf bifurcation, in parameter regimes where sustained oscillations would otherwise occur