Assessing the Robustness of the Clock Transition in a Mononuclear S = 1 Ni(II) Complex Spin Qubit

International audienceNi(II) complexes with an integer spin S = 1 that behave as clock transition spin qubits at zero magnetic field are resilient to magnetic fluctuations of the spin bath, while Co(II) complexes with a half-integer spin (S = 3/2) lose their coherence when they are subject to the same fluctuating magnetic field as the Ni(II) ones. These findings demonstrate that adequately designed Ni(II) complexes are excellent candidates for spin qubits

Contrôle de la proportion de fausses découvertes dans des modèles linéaires massivement univariés à l'aide du bootstrap résiduel

International audienceIn this article we develop a method for performing post hoc inference of the False Discovery Proportion (FDP) over multiple contrasts of interest in the mass-univariate linear model. To do so we use the residual bootstrap to simulate from the distribution of the null contrasts. We combine the bootstrap with the post hoc inference bounds of Blanchard et al (2020) and prove that doing so provides simultaneous asymptotic control of the FDP over all subsets of hypotheses. We demonstrate, via simulations, that our approach provides simultaneous control of the FDP over all subsets and is typically more powerful than existing, state of the art, parametric methods. We illustrate our approach on functional Magnetic Resonance Imaging data from the Human Connectome project and on a transcriptomic dataset of chronic obstructive pulmonary disease.Dans cet article, nous développons une méthode permettant de réaliser une inférence post hoc sur la Proportion de Fausse Découverte (False Discovery Proportion, FDP) pour plusieurs contrastes d'intérêt dans le cadre du modèle linéaire massivement univarié. Pour ce faire, nous utilisons le bootstrap des résidus afin d'échantillonner dans la distribution des contrastes sous l'hypothèse nulle. Nous combinons cette approche par bootstrap avec les bornes d'inférence post hoc proposées par Blanchard et al. (2020) et démontrons que cette combinaison permet d'assurer un contrôle asymptotique simultané du FDP sur tous les sous-ensembles d'hypothèses. Nous montrons, à travers des simulations, que notre approche garantit ce contrôle simultané du FDP tout en étant généralement plus puissante que les méthodes paramétriques de l'état de l'art. Nous illustrons notre approche à l'aide de données d'imagerie par résonance magnétique fonctionnelle issues du Human Connectome Project et d'un jeu de données transcriptomiques sur la bronchopneumopathie chronique obstructive

Optimisation bayésienne d'un réseau neuronal léger et précis pour la prédiction des performances aérodynamiques

International audienceEnsuring high accuracy and efficiency of predictive models is paramount in the aerospace industry, particularly in the context of multidisciplinary design and optimization processes. These processes often require numerous evaluations of complex objective functions, which can be computationally expensive and time-consuming. To build efficient and accurate predictive models, we propose a new approach that leverages Bayesian Optimization (BO) to optimize the hyper-parameters of a lightweight and accurate Neural Network (NN) for aerodynamic performance prediction. To clearly describe the interplay between design variables, hierarchical and categorical kernels are used in the BO formulation. We demonstrate the efficiency of our approach through two comprehensive case studies, where the optimized NN significantly outperforms baseline models and other publicly available NNs in terms of accuracy and parameter efficiency. For the drag coefficient prediction task, the Mean Absolute Percentage Error (MAPE) of our optimized model drops from 0.1433% to 0.0163%, which is nearly an order of magnitude improvement over the baseline model. Additionally, our model achieves a MAPE of 0.82% on a benchmark aircraft self-noise prediction problem, significantly outperforming existing models (where their MAPE values are around 2 to 3%) while requiring less computational resources. The results highlight the potential of our framework to enhance the scalability and performance of NNs in large-scale MDO problems, offering a promising solution for the aerospace industry.Garantir la précision et l'efficacité des modèles prédictifs est primordial dans l'industrie aérospatiale, en particulier dans le contexte des processus de conception et d'optimisation multidisciplinaires. Ces processus nécessitent souvent de nombreuses évaluations de fonctions objectives complexes, ce qui peut être coûteux en temps et en argent. Pour construire des modèles prédictifs efficaces et précis, nous proposons une nouvelle approche qui s'appuie sur l'optimisation bayésienne (BO) pour optimiser les hyperparamètres d'un réseau neuronal (NN) léger et précis pour la prédiction des performances aérodynamiques. Pour décrire clairement l'interaction entre les variables de conception, des noyaux hiérarchiques et catégoriels sont utilisés dans la formulation BO. Nous démontrons l'efficacité de notre approche à travers deux études de cas complètes, où le réseau neuronal optimisé surpasse de manière significative les modèles de base et d'autres réseaux neuronaux publiquement disponibles en termes de précision et d'efficacité des paramètres. Pour la tâche de prédiction du coefficient de traînée, l'erreur absolue moyenne en pourcentage (MAPE) de notre modèle optimisé passe de 0,1433 % à 0,0163 %, ce qui représente une amélioration de près d'un ordre de grandeur par rapport au modèle de base. En outre, notre modèle atteint un MAPE de 0,82 % sur un problème de référence de prédiction du bruit propre d'un avion, ce qui est nettement supérieur aux modèles existants (dont les valeurs MAPE sont de l'ordre de 2 à 3 %) tout en nécessitant moins de ressources informatiques. Les résultats soulignent le potentiel de notre cadre pour améliorer l'évolutivité et la performance des NN dans les MDO à grande échelle

PROXDDP: Proximal Constrained Trajectory Optimization

International audienceTrajectory optimization has been a popular choice for motion generation and control in robotics for at least a decade. Several numerical approaches have exhibited the required speed to enable online computation of trajectories for real-time of various systems, including complex robots. Many of these said are based on the differential dynamic programming (DDP) algorithm – initially designed for unconstrained trajectory optimization problems – and its variants, which are relatively easy to implement and provide good runtime performance. However, several problems in robot control call for using constrained formulations (e.g. torque limits, obstacle avoidance), from which several difficulties arise when trying to adapt DDP-type methods: numerical stability, computational efficiency, and constraint satisfaction.In this article, we leverage proximal methods for constrained optimization and introduce a DDP-type method for fast, constrained trajectory optimization suited for model-predictive control (MPC) applications with easy warm-starting.Compared to earlier solvers, our approach effectively manages hard constraints without warm-start limitations and exhibits good convergence behavior. We provide a complete implementation as part of an open-source and flexible C++ trajectory optimization library called ALIGATOR. These algorithmic contributions are validated through several trajectory planning scenarios from the robotics literature and the real-time whole-body MPC of a quadruped robot

Représentations dérivées des variétés de caractères quantiques

Quantum moduli algebras $\mathcal{L}_{g,n}^{\mathrm{inv}}(H)$ were introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche in the context of quantization of character varieties of surfaces and exist for any quasitriangular Hopf algebra $H$. In this paper we construct representations of $\mathcal{L}_{g,n}^{\mathrm{inv}}(H)$ on cohomology spaces $\mathrm{Ext}_H^m(X,M)$ for all $m \geq 0$, where $X$ is any $H$-module and $M$ is any $\mathcal{L}_{g,n}(H)$-module endowed with a compatible $H$-module structure. As a corollary and under suitable assumptions on $H$, we obtain projective representations of mapping class groups of surfaces on such Ext spaces. This recovers the projective representations constructed by Lentner-Mierach-Schweigert-Sommerhäuser from Lyubashenko theory, when the category $\mathcal{C} = H\text{-}\mathrm{mod}$ is used in their construction. Other topological applications are matrix-valued invariants of knots in thickened surfaces and representations of skein algebras on Ext spaces

Sensitivity-Aware Model Predictive Control for Robots with Parametric Uncertainty

International audienceThis paper introduces a computationally efficient robust Model Predictive Control (MPC) scheme for controlling nonlinear systems affected by parametric uncertainties in their models. The approach leverages the recent notion of closedloop state sensitivity and the associated ellipsoidal tubes of perturbed trajectories for taking into account online time-varying restrictions on state and input constraints. This makes the MPC controller "aware" of potential additional requirements needed to cope with parametric uncertainty, thus significantly improving the tracking performance and success rates during navigation in constrained environments. One key contribution lies in the introduction of a computationally efficient robust MPC formulation with a comparable computational complexity to a standard MPC (i.e., an MPC not explicitly dealing with parametric uncertainty). An extensive simulation campaign is presented to demonstrate the effectiveness of the proposed approach in handling parametric uncertainties and enhancing task performance, safety, and overall robustness. Furthermore, we also provide an experimental validation that shows the feasibility of the approach in real-world conditions and corroborates the statistical findings of the simulation campaign. The versatility and efficiency of the proposed method make it therefore a valuable tool for real-time control of robots subject to non-negligible uncertainty in their models

Planning under Uncertainties with Closed-Loop Sensitivity: Recent Results and Perspectives

International audienceThis paper presents a comprehensive summary of recent advancements in motion planning under parametric uncertainties, focusing on the application of closed-loop state sensitivity. This concept provides a framework for quantifying how deviations in model parameters affect the behavior of a system in closed-loop, facilitating the generation of robust trajectories. Various methods have been proposed to improve the resilience of robotic systems to model inaccuracies. However, these approaches often face challenges such as computational complexity and limitations in real-time applications. This paper synthesizes key results from several recent works, highlighting the development of techniques that optimize trajectory robustness while reducing computational overhead. Additionally, we outline the practical applications of these methods, discussing their validation through simulations and experiments on robotic systems subject to non-negligible uncertainties in their models

Automated growth of AlAs/GaAs Bragg mirror with real-time feedback reflectometry.

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"Coinvestment games under uncertainty"

National audienceThere are many business situations in which investments by a supplier and a producer (“coinvest-ments") are both necessary for either of them to grasp a business opportunity. For instance, better quality tanks are needed to manufacture reliable hydrogen-powered vehicles. One of these two firms, typically the one facing a lower cost, may be more willing to invest, but the cautionary attitude of the other delays the coinvestment. We model supply-chain interactions in a classical tractable way to derive the firms’ net present values (NPVs) upon coinvestment and determine their Nash equilibrium investment (timing) strategies. Firms coinvest when the real options of the weaker firm is ‘deep in the money.’ These business situations are likely to be affected by evolving market circumstances, in particular due to changes in the demand dynamics or endogenous decision (by, say, the supplier) to conduct research and development (R&D). We investigate related model extensions, which confirm the robustness of our key result

Anomalous propagators and the particle-particle channel: Bethe-Salpeter equation

19 pages, 8 figuresInternational audienceThe Bethe-Salpeter equation has been extensively employed to compute the two-body electron-hole propagator and its poles which correspond to the neutral excitation energies of the system. Through a different time-ordering, the two-body Green's function can also describe the propagation of two electrons or two holes. The corresponding poles are the double ionization potentials and double electron affinities of the system. In this work, a Bethe-Salpeter equation for the two-body particle-particle propagator is derived within the linear-response formalism using a pairing field and anomalous propagators. This framework allows us to compute kernels corresponding to different self-energy approximations ($GW$, $T$-matrix, and second-Born) as in the usual electron-hole case. The performance of these various kernels is gauged for singlet and triplet valence double ionization potentials using a set of 23 small molecules. The description of double core hole states is also analyzed