Scientific Publications of the University of Toulouse II Le Mirail
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The Zermelo Navigation Problem on the 2-Sphere of Revolution: An Optimal Control Perspective with Applications to Micromagnetism
No full textInternational audienceThis article presents geometric optimal control techniques for analyzing geodesics in time-optimal Zermelo navigation problems on 2-spheres of revolution. We classify the problem by analyzing the pair , which represents the current (or wind) and the Riemannian metric. Using the maximum principle, the dynamics of geodesics are described by a Hamiltonian vector field on the cotangent bundle . Our primary motivation is the application to micromagnetism, specifically spin magnetization reversal in ferromagnetic ellipsoidal samples. This model depends on four parameters and the amplitude of the applied magnetic field. The problem is formulated as a Zermelo navigation on the 2-sphere, where geodesics are classified as elliptic, hyperbolic, or abnormal. We demonstrate that the transition set , which separates weak and strong current domains, is critical for understanding optimality. A key result shows that abnormal geodesics intersect this set with semi-cubical cusp singularities, a phenomenon we term the Landau–Lifshitz billiard. The analysis of the transition set's connected components is complex and complemented by algebraic geometry and symbolic computations. We further reveal that hyperbolic geodesics lose optimality at their second intersection with the abnormal arc. Our numerical simulations complement this analysis by computing conjugate and cut loci, wavefronts, and accessibility sets, providing new insights into optimal magnetization switching under bounded control
Le generazioni future nella Carta dell’Ambiente: una causa in piena espansione, un diritto in ritardo
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Invariants raffinés pour les surfaces abéliennes : entre polynomialité et modularité
No full textTropical refined invariants for toric surfaces, introduced Block and Göttsche, are obtained couting tropical curves with a Laurent polynomial multiplicity. Brugallé and Jaramillo-Puentes then exhibited a polynomial behavior of the coefficients of this Laurent polynomial, seen as function on the curve degree. The authors provided explicit formula for small genus, involving quasi-modular forms.Inspired by the toric setting, the first-named author defined refined invariants for abelian surfaces and extended the polynomiality result. In this paper, we further study this regularity for abelian surfaces, providing explicit formulas involving quasi-modular forms. This resonates with the small genus cases of the toric setting
A Gaussian surrogate of partially observed stochastic processes using Wasserstein metric
No full textInternational audienceApproximating the evolution of probability measures for nonlinear stochastic differential equations (SDEs) and the associated nonlinear filtering problems is a challenging problem, as it involves solving high-dimensional differential equations. In contrast to classical variational inference methods, which address this challenge by minimizing the Kullback-Leibler (KL) divergence between the true and approximate distributions, we propose a Wasserstein-based variational framework for approximating the laws of stochastic systems. In particular, instead of minimizing the KL divergence, our approach minimizes the Wasserstein-2 () distance between the joint probability distributions of the state and observation processes. This formulation respects the underlying transport geometry and results in evolution equations for Gaussian parameters that provide an approximation of the dynamics of the true measure. An illustration is provided for some of our results with the help of an academic example
Testing the testing effect on prolific: when retrieval practice fails to boost learning
No full textInternational audienceThe testing effect-whereby retrieving information through testing improves long-term retention more than restudying-is one of the most robust and welldocumented phenomena in educational psychology. However, its replicability in online crowdsourced settings remains uncertain. In this paper, we report two preliminary experiments examining whether the testing effect can be detected in studies conducted on Prolific, a platform widely used for behavioral and educational research. Although not conceived as direct replications, both studies relied on validated learning materials and incorporated key methodological features known to enhance the testing effect, including delayed posttests, corrective feedback, and both factual and application-based outcome measures. In both experiments, participants were randomly assigned to a retrieval-practice (test) or restudy condition. No significant differences were found between groups at delayed test, despite multiple safeguards aimed at promoting participant engagement (e.g., prescreening filters, attention checks, fair compensation). These null findings suggest that investigating learning phenomena that require sustained cognitive engagement may be more challenging with crowdsource samples. We argue that the absence of the testing effect in our studies is unlikely to reflect a theoretical limitation of the effect itself, but rather highlights challenges inherent to online research environments. While platforms like Prolific offer valuable advantages in terms of speed and sample diversity, their constraints should be carefully considered when studying learning effects that depend on deep engagement with learning materia
Ancrage relationnel et écriture en ligne des personnages en fanfiction
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Is mild intellectual disability associated with a rhythmic skills impairment? A developmental perspective
No full textInternational audienceBackgroundWhile rhythm is an essential component of human development that contributes to both cognitive abilities and interactive behaviors, to date, research on rhythmic skills in individuals with mild intellectual disability (MID) – whose intellectual and adaptive functioning is impaired – is almost non-existent. If rhythmic abilities were deficient in these individuals, they could constitute a factor limiting their social integration and autonomy in daily life, that clinicians cannot neglect in their support.AimsThe aim of our study was to better understand rhythm perception and production abilities and their development between 10 and 15 years and 16–21 years in individuals with idiopathic MID, compared to typically developing (TD) individuals.Methods and proceduresFifty-seven MID and sixty-eight TD participants matched on chronological age were tested in a rhythm discrimination task and a rhythm production task, including two spontaneous motor tempo (SMT) recording and a synchronization-continuation phase in which they had to produce rhythms that were identical, slower or faster than their own SMT, and this with three different response modalities.Outcomes and resultsParticipants with MID performed worse than TD participants on all rhythmic tasks, while exhibiting a faster and more unstable SMT.Conclusions and implicationsThese findings suggest the existence of a deficit in both rhythmic perception and production skills in individuals with MID, compared to TD individuals. Our study thus helps to demonstrate the importance of a standardized assessment of rhythmic abilities and the role of these abilities in rehabilitation protocols for patients
Multi-view Surface Reconstruction Using Normal and Reflectance Cues
No full textInternational audienceAchieving high-fidelity 3D surface reconstruction while preserving fine details remains challenging, especially in the presence of materials with complex reflectance properties and without a dense-view setup. In this paper, we introduce a versatile framework that incorporates multi-view normal and optionally reflectance maps into radiance-based surface reconstruction. Our approach employs a pixelwise joint re-parametrization of reflectance and surface normals, representing them as a vector of radiances under simulated, varying illumination. This formulation enables seamless incorporation into standard surface reconstruction pipelines, such as traditional multi-view stereo (MVS) frameworks or modern neural volume rendering (NVR) ones. Combined with the latter, our approach achieves state-of-the-art performance on multi-view photometric stereo (MVPS) benchmark datasets, including DiLiGenT-MV, LUCES-MV and Skoltech3D. In particular, our method excels in reconstructing finegrained details and handling challenging visibility conditions. The present paper is an extended version of the earlier conference paper by Brument et al. (in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024), featuring an accelerated and more robust algorithm as well as a broader empirical evaluation. The code and data relative to this article is available at https://github.com/RobinBruneau/RNb-NeuS2