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A Noetherian approach to invariants for the statics and dynamics of elastic rods
No full textInternational audienceThe static-dynamic analogy discovered by Gustav Kirchhoff in 1859 shows that the statics of an elastic beam is equivalent to the dynamics of a spinning top. This analogy, where time and angular velocity are, for example, equivalent to arclength and curvatures,allows the use of Emmy Noether's 1918 theorem on continuous symmetries to unravel a quantity that is invariant along elastic rods at equilibrium. A spinning top having a Lagrangian independent of time will have its mechanical energy constant in time.In the same manner, an elastic rod with uniform elastic properties will have the sum of its curvature energy and its tension force uniform along the structure. This arclength invariance property is known in simple cases, but the present approach generalises it to more complex scenarios where extensibility, shear, conservative loads (\eg gravity), and contact are involved.Moreover, still using Noether's theorem and bringing to light the continuous symmetries of the Lagrangian of the variational approach, we recover all known invariants for the statics and dynamics of rods and ribbons, including configurational invariants. Furthermore, we show how the arclength invariant may be used to obtain pivotal information on some landmark elastic rod problems, including confinement buckling, sliding sleeves, or plectonemes.Finally, we extend the approach to vibrations.Overall, this paper is an attempt to explain, unify and extend all previous results on rod invariants thanks to the beautiful Noetherian formalism, and to show its practical use on a few relevant applications
Analyse de sensibilité quantitative pour l'équation de Fokker-Planck par rapport à la distance de Wasserstein
No full textWe analyze the sensitivity of solutions to the Fokker-Planck equation with respect to some unknown parameter. Our main result is to provide quantitative upper bounds for the -Wasserstein distance between two solutions with different parameters, for every . We are able to give two proofs of this result, the first relying on synchronous coupling between two solutions of an SDE, and another one that relies on the differentiation of Kantorovitch dual formulation of optimal transport. We also provide more specific bounds in the case of the overdamped Langevin process, for which we are able to compare convergence to the invariant measure and sensitivity to the parameter.Nous analysons la sensibilité des solutions de l'équation de Fokker-Planck par rapport à un paramètre inconnu. Notre principal résultat est de fournir des bornes supérieures quantitatives pour la distance de Wasserstein d'ordre entre deux solutions correspondant à des paramètres différents. Nous donnons deux preuves de ce résultat, une première reposant sur un couplage synchrone entre deux solutions à une EDS, et une autre qui repose sur la différentiation de la formulation duale de Kantorovitch du transport optimal. Nous considérons aussi le processus de Langevin dans un second temps, pour lequel nous prouvons des bornes légerement différentes afin de comparer convergence vers une mesure invariante et sensibilité au paramètre
Restoring hand grasping for patients with a complete tetraplegia with selective epineural stimulation: a parsimonious thus relevant clinical approach
No full textInternational audienceAbstractBackground: We explored epineural stimulation as a parsimonious approach to restore wrist and finger functions in individuals with complete tetraplegia.Methods: Two epineural multicontact cuff electrodes were implanted in four participants with complete tetraplegia for 28 days. The electrodes were wrapped around two nerves above the elbow, the median nerve and the radial nerve, respectively. The electrodes were connected via percutaneous cables to an external 56-channels electrical stimulator. Electrical stimulation parameters and electrode configurations were empirically adjusted to evoke hand gestures. Voluntary actions by the participant (e.g., muscle contractions, shoulder movements, or button presses) were associated with specific 3D current configurations to enable the triggering of diverse pre-programmed stimulation sequences.Results: The electrodes remained in place throughout the entire month, with no technical failure observed. The impedance of the contacts remained stable over time. The activation thresholds of the standard bipolar configuration (so called “Ring”) also demonstrated good stability across sessions. Participants were able to perform at least six functional tasks. P1 and P2 were assigned six preselected tasks — derived from the Motor Capacities Scale (MCS) — while P3 and P4 were given five preselected tasks — two of which were derived from the Motor Capacities Scale (MCS) — as well as five additional self-chosen tasks. An analytical evaluation was applied to the tasks derived from the MCS. The other tasks were graded using a binary outcome: success or failure. Execution times were also analyzed. For P3 and P4, a functional assessment was carried out based on perceived usefulness, usability (System Usability Scale), performance, satisfaction and acceptability with an emphasis on a user-centered approach by the Canadian Occupational Performance Measure. Conclusions: This article summarizes the observations made during a one-month follow-up of four participants with complete motor deficit of the wrists and hands who experienced epineural stimulation with the use of electrodes implanted around two arm nerves. This minimalist approach in terms of implanted components enabled them to perform various daily tasks without external assistance. The results — in terms of tolerance, electrode stability and functional success — pave the way for a new neuroprosthetic solution.Clinical trial registration numbers: NCT04306328 and NCT0555591
Subdiffusive fractional limit of a jump-renewal equation
No full textIn this paper, we consider an age-structured jump model that arises as a description of continuous time random walks with infinite mean waiting time between jumps. We prove that under a suitable rescaling, this equation converges in the long time large scale limit to a time fractional subdiffusion equation
Demystifying Performer Attention: Handle Genome-Length Sequences Efficiently
No full texthttps://thekhair.github.io/This document provides a comprehensive tutorial on attention mechanisms, starting from the fundamental self-attention mechanism and progressing to the efficient Performer attention. We explain all mathematical concepts with clarity, using gene sequence analysis as a motivating example throughout. The document includes stepby-step explanations, comparative analyses, practical examples, and complete PyTorch implementation code for Performer attention. All concepts are presented in an accessible manner suitable for both beginners and experienced practitioners in machine learning and computational biology.This document provides a comprehensive tutorial on attention mechanisms, starting from the fundamental self-attention mechanism and progressing to the efficientPerformer attention. We explain all mathematical concepts with clarity, using gene sequence analysis as a motivating example throughout. The document includes step-by-step explanations, comparative analyses, practical examples, and complete PyTorch implementation code for Performer attention. All concepts are presented in an accessible manner suitable for both beginners and experienced practitioners in machine learning and computational biology
Geometric Time-Dependent Density Functional Theory
No full textWe provide a new formulation of Time-Dependent Density Functional Theory (TDDFT) based on the geometric structure of the set of states constrained to have a fixed density. Orbital-free TDDFT is formulated using a hydrodynamics equation involving a new universal density-to-current functional map. In the corresponding Kohn--Sham equation, the density is reproduced using a non-local operator. Numerical simulations for one-dimensional soft-Coulomb systems are provided
PaRAMHTRS (Philology And Resolution of Abbreviations in Manuscripts obtained by HTR at Scale)
No full textNational audienc
RL-finetuning LLMs from on- and off-policy data with a single algorithm
No full textInternational audienceWe introduce a novel reinforcement learning algorithm (AGRO, for Any-Generation Reward Optimization) for fine-tuning large-language models. AGRO leverages the concept of generation consistency, which states that the optimal policy satisfies the notion of consistency across any possible generation of the model. We derive algorithms that find optimal solutions via the sample-based policy gradient and provide theoretical guarantees on their convergence. Our experiments demonstrate the effectiveness of AGRO in both on-policy and off-policy settings, showing improved performance on the mathematical reasoning dataset over baseline algorithms
The -resolvent estimates for the Dirac operator on hyperbolic and spherical spaces
No full textThis seminal paper marks the beginning of our investigation into on the spectral theory based on -spectrum applied to the Dirac operator on manifolds. Specifically, we examine in detail the cases of the Dirac operator on hyperbolic space and the Dirac operator on the spherical space, where these operators, and their squares and , can be written in a very explicit form. This fact is very important for the application of the spectral theory on the -spectrum. In fact, let denote a (right) linear Clifford operator, the -spectrum is associated with a second-order polynomial in the operator , specifically the operator defined as This allows us to associate to the Dirac operator boundary conditions that can be of Dirichlet type but also of Robin-like type. Moreover, our theory is not limited to Hilbert modules; it is applicable to Banach modules as well. The spectral theory based on the -spectrum has gained increasing attention in recent years, particularly as it aims to provide quaternionic quantum mechanics with a solid mathematical foundation from the perspective of spectral theory. This theory was extended to Clifford operators, and more recently, the spectral theorem has been adapted to this broader context. The -spectrum is crucial for defining the so-called -functional calculus for quaternionic and Clifford operators in various forms. This includes bounded as well as unbounded operators, where suitable estimates of sectorial and bi-sectorial type for the -resolvent operator are essential for the convergence of the Dunford integrals in this setting
Production of polyhydroxyalkanoates by Halomonas sp. HG01, a halophilic bacterium from northern Peru, using various carbon sources: metabolic and genomic analysis
No full textInternational audienceHalomonas sp. HG01, a moderate halophilic bacterium isolated from a northern Peru salt mine, is promising as a polyhydroxyalkanoate (PHA) producer. Experimental data and genome analysis were used to evaluate its capabilities. Shaken flask experiments revealed that HG01 can accumulate 70-86 wt.% poly(3-hydroxybutyrate) [P(3HB)] from various carbon sources, including glucose, sucrose, and fructose. In a fed-batch bioreactor, it achieved a cell dry weight (CDW) of 12.2 g/L with 63% P(3HB) content after 72 hours. The PHA synthase enzyme exhibited substrate specificity for C4 to C5 compounds. HG01 strain also produced poly(3hydroxybutyrate-co-3-hydroxyvalerate) [P(3HB-co-3HV)] from propionic and valeric acids, with a maximum 3HV content of 25.53 mol% monomers into the polymer (69.40 %wt) when valeric acid was used. The complete bacterial 3.66 Mbp genome sequence revealed metabolic pathways for carbohydrate and fatty acid catabolism, PHA biosynthesis, and stress tolerance factor. This genetic information enhances our understanding of PHA synthesis and supports the development of metabolic engineering strategies, positioning Halomonas sp. HG01 as a promising candidate for biotechnological applications