Résumé. Ce texte est mon mémoire de M2. Il traite de la dynamiquequantique des quantifiés d’automorphismes linéaire du tore, après le tempsd’Ehrenfest. Je montre que, dans la base des paquets d’ondes, la “matrice”du propagateur associé est bien approchée par des sommes de Birkhoff denilrotations sur le tore.
Published in Sports biomechanics
Combining biomechanics and motor control, the aim of this study was to investigate the limit cycle dynamics during the high bar longswing across the UK elite gymnastics pathway age groupings. Senior, junior and development gymnasts (N = 30) performed three sets of eight consecutive longswings on the high bar. The centre of mass motion was examined ...
High-dimensional dynamical systems often require computationally intensive physics-based simulations, making full physical space data assimilation impractical. Latent data assimilation methods perform assimilation in reduced-order latent space for efficiency but struggle with complex, nonlinear state-observation mappings. Recent solutions like Gene...
In this empirical article, we introduce INNAprop, an optimization algorithm that combines the INNA method with the RMSprop adaptive gradient scaling. It leverages second-order information and rescaling while keeping the memory requirements of standard DL methods as AdamW or SGD with momentum.After having recalled our geometrical motivations, we pro...
Resting-state functional magnetic resonance imaging evolves through a repertoire of functional connectivity patterns which might reflect ongoing cognition, as well as the contents of conscious awareness. We investigated whether the dynamic exploration of these states can provide robust and generalizable markers for the state of consciousness in hum...
A growing field in machine learning is to develop computationally friendly algorithms optimized for classification of sensor data at the edge. As many sensors respond to different stimuli with different dynamics, the sensor dynamics may provide valuable information for classification. The problem of determining which of the dynamics has generated a...
This is the opening talk of the First Meeting of the ANR TeMPlex project, Topological Methods for the Planet's Dynamics. In these slides, I present a historical background tracing the development from Branched Manifold Analysis through Homologies (BraMAH), introduced in 1999, to the mathematical concept of the templex, formulated in 2022. The templ...
In the context of an increasing popularity of data-driven models to represent dynamical systems, many machine learning-based implementations of the Koopman operator have recently been proposed. However, the vast majority of those works are limited to deterministic predictions, while the knowledge of uncertainty is critical in fields like meteorolog...
We study the optimization of resource allocation in bacteria evolving in periodic environments. We use a dynamical model of the metabolism of these microorganisms with a control variable representing the allocation of protein precursors. We mathematically define the objective of maximizing the long-term growth of a given cell. We carry out a theore...
