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In engineering, models are often used to represent the behavior of a system. Estimators are then needed to approximate the values of the model's parameters based on observations. This approximation implies a difference between the values predicted by the model and the observations that have been made. It creates an uncertainty that can lead to dangerous decision making. Interval analysis tools can be used to guarantee some properties of an estimator, even when the estimator itself doesn't rely on interval analysis (Adam, 2019) (Adam, 2015). This paper contributes to this dynamic by proposing an interval-based and guaranteed method to validate a nonlinear estimator. It is based on the Moore-Skelboe algorithm (van Emden, 2004). This method returns a guaranteed maximum error that the estimator will never exceed. We will show that we can guarantee properties even when working with non-guaranteed estimators such as neural networks., Comment: REC 2024, Oct 2024, Beijing, China

Quasi-static time series (QSTS) simulations have great potential for evaluating the grid's ability to accommodate the large-scale integration of distributed energy resources. However, as grids expand and operate closer to their limits, iterative power flow solvers, central to QSTS simulations, become computationally prohibitive and face increasing convergence issues. Neural power flow solvers provide a promising alternative, speeding up power flow computations by 3 to 4 orders of magnitude, though they are costly to train. In this paper, we envision how recently introduced grid foundation models could improve the economic viability of neural power flow solvers. Conceptually, these models amortize training costs by serving as a foundation for a range of grid operation and planning tasks beyond power flow solving, with only minimal fine-tuning required. We call for collaboration between the AI and power grid communities to develop and open-source these models, enabling all operators, even those with limited resources, to benefit from AI without building solutions from scratch., Comment: Equal contributors: A.P. and F.M.; Lead contact: A.P

Foundation models (FMs) currently dominate news headlines. They employ advanced deep learning architectures to extract structural information autonomously from vast datasets through self-supervision. The resulting rich representations of complex systems and dynamics can be applied to many downstream applications. Therefore, FMs can find uses in electric power grids, challenged by the energy transition and climate change. In this paper, we call for the development of, and state why we believe in, the potential of FMs for electric grids. We highlight their strengths and weaknesses amidst the challenges of a changing grid. We argue that an FM learning from diverse grid data and topologies could unlock transformative capabilities, pioneering a new approach in leveraging AI to redefine how we manage complexity and uncertainty in the electric grid. Finally, we discuss a power grid FM concept, namely GridFM, based on graph neural networks and show how different downstream tasks benefit., Comment: Major equal contributors: H.F.H., T.B., B.G., L.S.A.M., A.P., A.V., J.W.; Significant equal contributors: J.B., A.B.M., S.C., I.F., B.H., R.J., K.K., V.M., F.M., M.D.M., O.R., H.S., L.X., E.S.Y., A.Z.; Other equal contributors: A.J.B., R.J.B., B.P.B., J.S., S.S; Lead contact: H.F.H

In graph theory, the minimum directed feedback vertex set (FVS) problem consists in identifying the smallest subsets of vertices in a directed graph whose deletion renders the directed graph acyclic. Although being known as NP-hard since 1972, this problem can be solved in a reasonable time on small instances, or on instances having special combinatorial structure. In this paper we investigate graph reductions preserving all or some minimum FVS and focus on their properties, especially the Church-Rosser property, also called confluence. The Church-Rosser property implies the irrelevance of reduction order, leading to a unique directed graph. The study seeks the largest subset of reductions with the Church-Rosser property and explores the adaptability of reductions to meet this criterion. Addressing these questions is crucial, as it may impact algorithmic implications, allowing for parallelization and speeding up sequential algorithms., Comment: In Proceedings GASCom 2024, arXiv:2406.14588

Hydro-Quebec (HQ) is a vertically integrated utility that produces, transmits, and distributes most of the electricity in the province of Quebec. The power grid it operates has a particular architecture created by large hydroelectric dams located far north and the extensive 735kV transmission grid that allows the generated power to reach the majority of the load located thousands of kilometers away in the southern region of Quebec. The specificity of the grid has led HQ to develop monitoring tools responsible for generating so-called stability limits. Those stability limits take into account several nonlinear phenomena such as angular stability, frequency stability, or voltage stability. Since generation planning and operation tools rely mostly on mixed integer linear programming formulation, HQ had to adapt its tools to integrate stability limits into them. This paper presents the challenges it faced, especially considering its reserve monitoring tool and unit commitment tool., Comment: 12 pages, 7 figures, 7 tables, 1 algorithm

This work focuses on minimizing the eigenvalue of a noncommutative polynomial subject to a finite number of noncommutative polynomial inequality constraints. Based on the Helton-McCullough Positivstellensatz, the noncommutative analog of Lasserre's moment-sum of squares hierarchy provides a sequence of lower bounds converging to the minimal eigenvalue, under mild assumptions on the constraint set. Each lower bound can be obtained by solving a semidefinite program. We derive complementary converging hierarchies of upper bounds. They are noncommutative analogues of the upper bound hierarchies due to Lasserre for minimizing polynomials over compact sets. Each upper bound can be obtained by solving a generalized eigenvalue problem., Comment: 4 pages

We analyze Bell inequalities violations in photonic experiments for which the measurement apparatuses are restricted to homodyne measurements. Through numerical optimization of the Clauser-Horne-Shimony-Holt inequality over homodyne measurements and binning choices, we demonstrate large violations for states with a bounded number of photons. When considering states defined within qubit local subspaces of two Fock states, such as NOON states, a violation is observed solely within the qubit Fock space spanned by zero and two photons. For more generic states, large violations are obtained. Significant violations are observed even for states containing three photons locally and under realistic values of noise and losses. We propose concrete implementations to achieve such violations, opening new avenues for Bell experiments with homodyne detectors., Comment: 7+4 pages, 5+2 figures

We study a graph-theoretic problem in the Penrose P2-graphs which are the dual graphs of Penrose tilings by kites and darts. Using substitutions, local isomorphism and other properties of Penrose tilings, we construct a family of arbitrarily large induced subtrees of Penrose graphs with the largest possible number of leaves for a given number $n$ of vertices. These subtrees are called fully leafed induced subtrees. We denote their number of leaves $L_{P2}(n)$ for any non-negative integer $n$, and the sequence $\left(L_{P2}(n)\right)_{n\in\mathbb{N}}$ is called the leaf function of Penrose P2-graphs. We present exact and recursive formulae for $L_{P2}(n)$, as well as an infinite sequence of fully leafed induced subtrees, which are caterpillar graphs. In particular, our proof relies on the construction of a finite graded poset of 3-internal-regular subtrees., Comment: 21 pages, 19 figures

In the last years, several variants of transformers have emerged. In this paper, we compare different transformer-based models for solving the reverse dictionary task and explore their use in the context of a serious game called The Dictionary Game.

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock like salt, gypsum or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the mass-transfer and the flow leads to the formation of remarkable patterns, like scallop patterns in caves. We emphasize the common presence of very sharp shapes and spikes, despite the diversity of hydrodynamic conditions and the nature of the soluble materials. We explain the generic emergence of such spikes in dissolution processes by a geometrical approach. Singularities at the interface emerge as a consequence of the erosion directed in the normal direction, when the surface displays curvature variations, like those associated to a dissolution pattern. First, we demonstrate the presence of singular structures in natural interfaces shaped by dissolution. Then, we propose simple surface evolution models of increasing complexity demonstrating the emergence of spikes and allowing us to explain at long term by coarsening the formation of cellular structures. Finally, we perform a dissolution pattern experiment driven by solutal convection and we report the emergence of a cellular pattern following well the model predictions. Although the precise prediction of dissolution shapes necessitates to perform a complete hydrodynamic study, we show that the characteristic spikes which are reported ultimately for dissolution shapes are explained generically by geometrical arguments due to the surface evolution. These findings can be applied to other ablation patterns, reported for example in melting ice., Comment: 14 pages, 8 figures

We describe an experimental concept at the National Ignition Facility for specifically tailored spherical implosions to compress hydrogen to extreme densities (up to $\sim$800$\times$ solid density, electron number density n$_e$$\sim$4$\times$10$^{25}$ cm$^{-3}$ ) at moderate temperatures (T$\sim$200 eV), i.e., to conditions, which are relevant to the interiors of red dwarf stars. The dense plasma will be probed by laser-generated x-ray radiation of different photon energy to determine the plasma opacity due to collisional (free-free) absorption and Thomson scattering. The obtained results will benchmark radiation transport models, which in the case for free-free absorption show strong deviations at conditions relevant to red dwarfs. This very first experimental test of free-free opacity models at these extreme states will help to constrain where inside those celestial objects energy transport is dominated by radiation or convection. Moreover, our study will inform models for other important processes in dense plasmas, which are based on electron-ion collisions, e.g., stopping of swift ions or electron-ion temperature relaxation.

The star formation efficiency (SFE) has been shown to vary across different environments, particularly within galactic starbursts and deep within the bulges of galaxies. Various quenching mechanisms may be responsible, ranging from galactic dynamics to feedback from active galactic nuclei (AGN). Here, we use spatially-resolved observations of warm ionised gas emission lines from the imaging Fourier transform spectrograph SITELLE at the Canada-France-Hawaii Telescope (CFHT) and cold molecular gas (CO(2-1)) from the Atacama Large Millimeter/sub-millimeter Array (ALMA) to study the SFE in the bulge of the AGN-host galaxy NGC 3169. After distinguishing star-forming regions from AGN-ionised regions using emission-line ratio diagnostics, we measure spatially-resolved molecular gas depletion times (\tau_dep = 1/SFE) with a spatial resolution of \approx 100 pc within a galactocentric radius of 1.8 kpc. We identify a star-forming ring located at radii 1.25 \pm 0.6 kpc with an average \tau_dep of 0.3 Gyr. At radii < 0.9 kpc, however, the molecular gas surface densities and depletion times increase with decreasing radius, the latter reaching approximately 2.3 Gyr at a radius \approx 500 pc. Based on analyses of the gas kinematics and comparisons with simulations, we identify AGN feedback, bulge morphology and dynamics as the possible causes of the radial profile of SFE observed in the central region of NGC 3169., Comment: 25 pages, 15 figures, accepted for publication in MNRAS

We show we can control an epidemic reaction-diffusion on a directed, and heterogeneous, network by redirecting the flows, thanks to the optimisation of well-designed loss functions, in particular the basic reproduction number of the model. We provide a final size relation linking the basic reproduction number to the epidemic final sizes, for diffusions around a reference diffusion with basic reproduction number less than 1. Experimentally, we show control is possible for different topologies, network heterogeneity levels, and speeds of diffusion. Our experimental results highlight the relevance of the basic reproduction number loss, compared to more straightforward losses.

We report a user-friendly software environment for battery data science. It is designed to streamline data management, data cleaning, and data analysis to help bridge the gap between the domain expertise of most battery scientists and the tools needed as the field becomes increasingly data intensive. The software solution suitable for ingesting battery test data from disparate sources. By aggregating data in an intelligent way, users can streamline routine data analysis tasks and leverage Jupyter Notebook functionality to build advanced scripts and analytics, thereby making battery engineering teams more productive.

Quantum theory predicts the existence of genuinely tripartite-entangled states, which cannot be obtained from local operations over any bipartite entangled states and unlimited shared randomness. Some of us recently proved that this feature is a fundamental signature of quantum theory. The state $\left|{GHZ}_3\right\rangle=(\left|000\right\rangle+\left|111\right\rangle)/\sqrt{2}$ gives rise to tripartite quantum correlations which cannot be explained by any causal theory limited to bipartite nonclassical common causes of any kind (generalising entanglement) assisted with unlimited shared randomness. Hence, any conceivable physical theory which would reproduce quantum predictions will necessarily include genuinely tripartite resources. In this work, we verify that such tripartite correlations are experimentally achievable. We derive a new device-independent witness capable of falsifying causal theories wherein nonclassical resources are merely bipartite. Using a high-performance photonic $\left|{GHZ}_3\right\rangle$ states with fidelities of $ 0.9741\pm0.002$, we provide a clear experimental violation of that witness by more than $26.3$ standard deviation, under the locality and fair sampling assumption. We generalise our work to the $\left|{GHZ}_4\right\rangle$ state, obtaining correlations which cannot be explained by any causal theory limited to tripartite nonclassical common causes assisted with unlimited shared randomness., Comment: See related work by Ya-Li Mao et al. (arXiv:2201.12753). 12 pages (7 of appendices), 5 figures (2 in appendices). H.C., M-O.R. and C.Z contributed equally to this work

An experimental program is currently underway at the National Ignition Facility (NIF) to compress deuterium and tritium (DT) fuel to densities and temperatures sufficient to achieve fusion and energy gain. The primary approach being investigated is indirect drive inertial confinement fusion (ICF), where a high-Z radiation cavity (a hohlraum) is heated by lasers, converting the incident energy into x-ray radiation which in turn drives the DT fuel filled capsule causing it to implode. Previous experiments reported DT fuel gain exceeding unity [O.A. Hurricane et al., Nature 506, 343 (2014)] and then exceeding the kinetic energy of the imploding fuel [S. Le Pape et al., Phys. Rev. Lett. 120, 245003 (2018)]. We report on recent experiments that have achieved record fusion neutron yields on NIF, greater than 100 kJ with momentary fusion powers exceeding 1PW, and have for the first time entered the burning plasma regime where fusion alpha-heating of the fuel exceeds the energy delivered to the fuel via compression. This was accomplished by increasing the size of the high-density carbon (HDC) capsule, increasing energy coupling, while controlling symmetry and implosion design parameters. Two tactics were successful in controlling the radiation flux symmetry and therefore the implosion symmetry: transferring energy between laser cones via plasma waves, and changing the shape of the hohlraum. In conducting these experiments, we controlled for known sources of degradation. Herein we show how these experiments were performed to produce record performance, and demonstrate the data fidelity leading us to conclude that these shots have entered the burning plasma regime.

We study the network reconstruction problem for an epidemic reaction-diffusion. These models are an extension of deterministic, compartmental models to a graph setting, where the reactions within the nodes are coupled by a diffusion. We study the influence of the diffusion rate, and the network topology, on the reconstruction and prediction problems, both from a theoretical and experimental standpoint.Results first show that for almost every network, the reconstruction problem is identifiable. Then, we show that the faster the diffusion, the harder the reconstruction, but that increasing the sampling rate may help in this respect.Second, we demonstrate that it is possible to classify symmetrical networks generating the same trajectories, and that the prediction problem can still be solved satisfyingly, even when the network topology makes exact reconstruction difficult.

A review is made of the field of contextuality in quantum mechanics. We study the historical emergence of the concept from philosophical and logical issues. We present and compare the main theoretical frameworks that have been derived. Finally, we focus on the complex task of establishing experimental tests of contextuality. Throughout this work, we try to show that the conceptualisation of contextuality has progressed through different complementary perspectives, before summoning them together to analyse the signification of contextuality experiments. Doing so, we argue that contextuality emerged as a discrete logical problem and developed into a quantifiable quantum resource., Comment: 47 pages, 8 figures

Spatial Atomic Layer Deposition (SALD) is a recent approach that is up to two orders of magnitude faster than conventional ALD, and that can be performed at atmospheric pressure and even in the open air. Previous works have exploited these assets to focus on the possibility of high-rate, large-area deposition for scaling up into mass production. Conversely, here we show that SALD indeed represents an ideal platform for the selective deposition of functional materials by proper design and miniaturization of SALD close-proximity heads. In particular, we have used the potential offered by 3D printing to fabricate custom close-proximity SALD injection heads. By using 3D printing, the heads can be easily designed and readily modified to obtain different deposition areas, free-form patterns, and even complex multimaterial structures. The heads can be printed in different materials to adjust to the chemistry of the precursors and the deposition conditions used. Polymeric heads can be used as cheap (even disposable) heads that are both used for performing deposition and for prototyping and optimization purposes. Finally, by designing a miniaturized head with circular concentric gas channels, 3D printing of functional materials can be performed with nanometric resolution in Z. This constitutes a new 3D printing approach based on gaseous precursors. Because the selective deposition strategies presented here are based on the SALD process, conformal and continuous thin films of functional materials can be printed at low temperatures and with high deposition rate in the open air. Our approach represents a new versatile way of printing functional materials and devices with spatial and topological control, thus extending the potential of SALD and ALD in general, and opening a new avenue in the field of area-selective deposition of functional materials., Comment: 20 pages, 4 figures

Between 2004 and 2017, spectral observations have been gathered by the Visual and Infrared Mapping Spectrometer (VIMS) on-board Cassini (Brown et al., 2004) during 23 Enceladus close encounters, in addition to more distant surveys. The objective of the present study is to produce a global hyperspectral mosaic of the complete VIMS data set of Enceladus in order to highlight spectral variations among the different geological units. This requires the selection of the best observations in terms of spatial resolution and illumination conditions. We have carried out a detailed investigation of the photometric behavior at several key wavelengths (1.35, 1.5, 1.65, 1.8, 2.0, 2.25, 2.55 and 3.6 ${\mu}$m), characteristics of the infrared spectra of water ice. We propose a new photometric function, based on the model of Shkuratov et al. (2011). When combined, corrected mosaics at different wavelengths reveal heterogeneous areas, in particular in the terrains surrounding the Tiger Stripes on the South Pole and in the northern hemisphere around 30{\deg}N, 90{\deg}W. Those areas appear mainly correlated to tectonized units, indicating an endogenous origin, potentially driven by seafloor hotspots., Comment: Erratum: Fix south polar grid longitudes in Figures 9 and 11

We prove local convergence of several notable gradient descent algorithms used in machine learning, for which standard stochastic gradient descent theory does not apply directly. This includes, first, online algorithms for recurrent models and dynamical systems, such as \emph{Real-time recurrent learning} (RTRL) and its computationally lighter approximations NoBackTrack and UORO; second, several adaptive algorithms such as RMSProp, online natural gradient, and Adam with $\beta^2\to 1$.Despite local convergence being a relatively weak requirement for a new optimization algorithm, no local analysis was available for these algorithms, as far as we knew. Analysis of these algorithms does not immediately follow from standard stochastic gradient (SGD) theory. In fact, Adam has been proved to lack local convergence in some simple situations \citep{j.2018on}. For recurrent models, online algorithms modify the parameter while the model is running, which further complicates the analysis with respect to simple SGD.Local convergence for these various algorithms results from a single, more general set of assumptions, in the setup of learning dynamical systems online. Thus, these results can cover other variants of the algorithms considered.We adopt an "ergodic" rather than probabilistic viewpoint, working with empirical time averages instead of probability distributions. This is more data-agnostic and creates differences with respect to standard SGD theory, especially for the range of possible learning rates. For instance, with cycling or per-epoch reshuffling over a finite dataset instead of pure i.i.d.\ sampling with replacement, empirical averages of gradients converge at rate $1/T$ instead of $1/\sqrt{T}$ (cycling acts as a variance reduction method), theoretically allowing for larger learning rates than in SGD.

Hybrid encoding of quantum information is a promising approach towards the realisation of optical quantum protocols. It combines advantages of continuous variables encoding, such as high efficiencies, with those of discrete variables, such as high fidelities. In particular, entangled hybrid states were shown to be a valuable ressource for quantum information protocols. In this work, we present a hybrid entanglement witness that can be implemented on currently available experiments and is robust to noise currently observed in quantum optical set-ups. The proposed witness is based on measurements of genuinely hybrid observables. The noise model we consider is general. It is formally characterised with Kraus operators since the considered hybrid system can be expressed in a finite dimension basis. A practical advantage of the witness is that it can be tested by measuring just a few experimentally available observables., Comment: 16 pages, 8 figures

Granular media (GM) present locomotor challenges for terrestrial and extraterrestrial devices because they can flow and solidify in response to localized intrusion of wheels, limbs, and bodies. While the development of airplanes and submarines is aided by understanding of hydrodynamics, fundamental theory does not yet exist to describe the complex interactions of locomotors with GM. In this paper, we use experimental, computational, and theoretical approaches to develop a terramechanics for bio-inspired locomotion in granular environments. We use a fluidized bed to prepare GM with a desired global packing fraction, and use empirical force measurements and the Discrete Element Method (DEM) to elucidate interaction mechanics during locomotion-relevant intrusions in GM such as vertical penetration and horizontal drag. We develop a resistive force theory (RFT) to account for more complex intrusions. We use these force models to understand the locomotor performance of two bio-inspired robots moving on and within GM.

In recent years, in France, computer learning (under the term of code) has entered the school curriculum, in primary and high school. This learning is also aimed at developing computer thinking to enable students, girls and boys, to start master all aspects of the digital world (science, technology, industry, culture). However, neither teachers, nor parents are trained to teach or educate on these topics. Furthermore, if the educational system progresses progressively towards these objectives, in everyday life and in professional context there is also a need for lifelong training in computer thinking. Large-scale projects on coding initiation are now quite successful in supporting the training of professionals in education on these topics. However, they require an infrastructure of people and important resources to maintain their level of efficiency. In order to further develop the objectives ofhelping people to demystify IT thinking, we aim to question here the way by which it is possible to conceive a concrete and operational initiative that addresses this issue. A huge challenge: Let's share a proposal here and discuss it., Comment: in French. Revue de l'EPI (Enseignement Public et Informatique), EPI, 2019

In this paper we address the problems of detecting objects of interest in a video and of estimating their locations, solely from the gaze directions of people present in the video. Objects can be indistinctly located inside or outside the camera field of view. We refer to this problem as extended gaze following. The contributions of the paper are the followings. First, we propose a novel spatial representation of the gaze directions adopting a top-view perspective. Second, we develop several convolutional encoder/decoder networks to predict object locations and compare them with heuristics and with classical learning-based approaches. Third, in order to train the proposed models, we generate a very large number of synthetic scenarios employing a probabilistic formulation. Finally, our methodology is empirically validated using a publicly available dataset., Comment: FG 2019