Search

The Kraichnan-Leith-Batchelor (KLB) inverse energy cascade is a hallmark of 2D turbulence, with its theoretical energy spectrum observed in both Direct Numerical Simulations (DNS) and laboratory experiments. Surprisingly, however, we show that the effective diffusivity of 2D turbulent flows significantly departs from the KLB scaling prediction. We illustrate this phenomenon based on a suite of DNS of 2D turbulent flows forced at intermediate wavenumber and damped by weak linear or quadratic drag. We derive alternate scaling predictions based on the emergence of intense, isolated vortices causing spatially intermittent frictional dissipation localized within the small vortex cores. The predictions quantitatively match DNS data. This study points to a universal large-scale organization of 2D turbulent flows in physical space, bridging standard 2D Navier-Stokes turbulence with large-scale geophysical turbulence., Comment: 6 pages, 3 figures

We study the kernel instrumental variable algorithm of \citet{singh2019kernel}, a nonparametric two-stage least squares (2SLS) procedure which has demonstrated strong empirical performance. We provide a convergence analysis that covers both the identified and unidentified settings: when the structural function cannot be identified, we show that the kernel NPIV estimator converges to the IV solution with minimum norm. Crucially, our convergence is with respect to the strong $L_2$-norm, rather than a pseudo-norm. Additionally, we characterize the smoothness of the target function without relying on the instrument, instead leveraging a new description of the projected subspace size (this being closely related to the link condition in inverse learning literature). With the subspace size description and under standard kernel learning assumptions, we derive, for the first time, the minimax optimal learning rate for kernel NPIV in the strong $L_2$-norm. Our result demonstrates that the strength of the instrument is essential to achieve efficient learning. We also improve the original kernel NPIV algorithm by adopting a general spectral regularization in stage 1 regression. The modified regularization can overcome the saturation effect of Tikhonov regularization.

The Laboratory of Mechanics and Acoustics in Marseilles (France) was created in 1941, under the name of Centre de Recherches Scientifiques, Industrielles et Maritimes (CRSIM). But it was actually issued from the French Naval Research Center created in Toulon by the French Navy to work on submarine detection during World War I. LMA is therefore the result of a long and quite amazing story with several moves and even more name changes. It benefited from all these events and is today established in a new campus with large facilities specially designed for its latest research activities. This article presents the story in some details, summarize the evolution of the research domains through all these years and finally gives a description of the LMA today.

This paper demonstrates the first on-chip frequency multiplexed readout of two co-integrated single-electron transistors without the need for bulky resonators. We characterize single electron dynamics in both single electron transistors at 4.2K before validating their simultaneous readout within 2.2{\mu}s, achieving a 99.9% fidelity with a 1MHz frequency spacing. This experimental demonstration paves the way towards resonator-free large-scale quantum-classical architectures that would be required for future universal and reprogrammable quantum computers.

Graphene is a promising material for the development of applications in nanoelectronic devices, but the lack of a band gap necessitates the search for ways to tune its electronic properties. In addition to doping, defects, and nanoribbons, a more radical alternative is the development of 2D forms with structures that are in clear departure from the honeycomb lattice, such as graphynes, with the distinctive property of involving carbon atoms with both hybridizations sp and sp2. The density and details of how the acetylenic links are distributed allow for a variety of electronic signatures. Here we propose a graphyne system based on the recently synthesized biphenylene monolayer. We demonstrate that this system features highly localized states with a spin-polarized semiconducting configuration. We study its stability and show that the system's structural details directly influence its highly anisotropic electronic properties. Finally, we show that the symmetry of the frontier states can be further tuned by modulating the size of the acetylenic chains forming the system., Comment: 14 pages, 7 figures

We report the existence of hydrostatic equilibrium states for a composite body made of two rigidly rotating, homogeneous layers bounded by spheroidal surfaces, where the core has a prolate shape. These new configurations require an oblate envelope that spins faster than the core. No solution with a prolate envelope is found. For some parameters, the prolate core can even be at rest. Numerical experiments based on the self-consistent field method support this result in the case of heterogeneous layers with polytropic equations of state. The possible cancellation of the first gravitational moment, $J_2$, is discussed., Comment: Accepted for publication in A&A. 7 pages, 4 figures, 4 tables

Ecological systems often exhibit complex nonlinear dynamics like oscillations, chaos, and regime shifts. Universal dynamic equations have shown promise in modeling complex dynamics by combining known functional forms with neural networks that represent unknown relationships. However, these methods do not yet accommodate the forms of uncertainty common to ecological datasets. To address this limitation, we developed state-space universal dynamic equations by combining universal differential equations with a state-space modeling framework, accounting for uncertainty. We tested this framework on two simulated and two empirical case studies and found that this method can recover nonlinear biological interactions that produce complex behaviors, including chaos and regime shifts. Their forecasting performance is context-dependent, with the best performance being achieved on chaotic and oscillating time series. This new approach leveraging both ecological theory and data-driven machine learning offers a promising new way to make accurate and useful predictions of ecosystem change.

We show that the bunkbed conjecture remains true when gluing along a vertex. As immediate corollaries, we obtain that the bunkbed conjecture is true for forests and that a minimal counterexample to the bunkbed conjecture is 2-connected., Comment: 9 pages, 2 figures

Semiconductor quantum dot arrays are a promising platform to perform spin-based error-corrected quantum computation with large numbers of qubits. However, due to the diverging number of possible charge configurations combined with the limited sensitivity of large-footprint charge sensors, achieving single-spin occupancy in each dot in a growing quantum dot array is exceedingly complex. Therefore, to scale-up a spin-based architecture we must change how individual charges are readout and controlled. Here, we demonstrate single-spin occupancy of each dot in a foundry-fabricated array by combining two methods. 1/ Loading a finite number of electrons into the quantum dot array; simplifying electrostatic tuning by isolating the array from the reservoirs. 2/ Deploying multiplex gate-based reflectometry to dispersively probe charge tunneling and spin states without charge sensors or reservoirs. Our isolated arrays probed by embedded multiplex readout can be readily electrostatically tuned. They are thus a viable, scalable approach for spin-based quantum architectures., Comment: 15 pages 5 figures

Single-photon sources (SPS) hold the potential to enhance the performance of quantum key distribution (QKD). QKD systems using SPS often require cryogenic cooling, while recent QKD attempts using SPS operating at room-temperature have failed to achieve long-distance transmission due to the SPS not operating at telecommunication wavelength. In this work, we have successfully demonstrated QKD using a room-temperature SPS at telecommunication wavelength. The SPS used in this work is based on point defects hosted by gallium nitride (GaN) thin films grown on sapphire substrates. We employed a time-bin and phase encoding scheme to perform the BB84 and reference-frame-independent QKD protocols over a 33 km fiber spool, achieving a secure key rate of $7.58\times 10^{-7}$ per pulse. Moreover, we also implemented a metropolitan QKD experiment over a 30 km deployed fiber, achieving a secure key rate of $6.06\times 10^{-8}$ per pulse. These results broaden the prospects for future use of SPS in commercial QKD applications.

Single photon sources (SPSs) are directly applicable in quantum key distribution (QKD) because they allow the implementation of the canonical BB84 protocol. To date, QKD implementations using SPS are not widespread because of the need for cryogenic operation, or frequency conversion to a wavelength efficiently transmitted over telecommunication fibers. We report an observation of polarization-encoded QKD using a room-temperature telecom SPS based on a GaN defect. A field test over 3.5 km of deployed fiber with 4.0 dB loss yielded a secure key rate of 585.9~bps. Further testing in a 32.5 km fiber spool (attenuation of 11.2 dB), which exhibited substantially lower polarization mode dispersion, yielded a secure key rate of 50.4 bps. Both results exhibited a quantum bit error rate (QBER) of approximately 5%. These results illustrate the potential of the GaN defects for supporting polarization-encoded quantum communication.

Cell motility is connected to the spontaneous symmetry breaking of a circular shape. In https://doi.org/10.1103/PhysRevLett.110.078102, Blanch-Mercader and Casademunt perfomed a nonlinear analysis of the minimal model proposed by Callan and Jones https://doi.org/10.1103/PhysRevLett.100.258106 and numerically conjectured the existence of traveling solutions once that symmetry is broken. In this work, we prove analytically that conjecture by means of nonlinear bifurcation techniques.

Solid-state defects susceptible of spin manipulation hold great promise for scalable quantum technology. To broaden their utility, operating at room temperature and emitting in the telecom wavelength range are desired, eliminating cryogenic requirements and leveraging existing optical fiber infrastructure for transmitting the quantum information. To that end, we report that telecom single photon emitters (SPEs) in gallium nitride (GaN) exhibit optically detected magnetic resonance (ODMR) at room temperature. The analysis of ODMR as a function of magnetic field orientation enables the determination of the orientation of the spin quantization axis with respect to the GaN crystalline lattice. The optical transitions dynamics are analyzed to gain further insight into the transition rates dominating ODMR. Our findings, coupled with GaN's mature fabrication technology, could facilitate the realization of scalable quantum technology.

Recent advancements in multimodal Variational AutoEncoders (VAEs) have highlighted their potential for modeling complex data from multiple modalities. However, many existing approaches use relatively straightforward aggregating schemes that may not fully capture the complex dynamics present between different modalities. This work introduces a novel multimodal VAE that incorporates a Markov Random Field (MRF) into both the prior and posterior distributions. This integration aims to capture complex intermodal interactions more effectively. Unlike previous models, our approach is specifically designed to model and leverage the intricacies of these relationships, enabling a more faithful representation of multimodal data. Our experiments demonstrate that our model performs competitively on the standard PolyMNIST dataset and shows superior performance in managing complex intermodal dependencies in a specially designed synthetic dataset, intended to test intricate relationships.

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

This work deals with a problem of assigning periodic tasks to employees in such a way that each employee performs each task with the same frequency in the long term. The motivation comes from a collaboration with the SNCF, the main French railway company. An almost complete solution is provided under the form of a necessary and sufficient condition that can be checked in polynomial time. A complementary discussion about possible extensions is also proposed.

We focus on multi-domain Neural Machine Translation, with the goal of developing efficient models which can handle data from various domains seen during training and are robust to domains unseen during training. We hypothesize that Sparse Mixture-of-Experts (SMoE) models are a good fit for this task, as they enable efficient model scaling, which helps to accommodate a variety of multi-domain data, and allow flexible sharing of parameters between domains, potentially enabling knowledge transfer between similar domains and limiting negative transfer. We conduct a series of experiments aimed at validating the utility of SMoE for the multi-domain scenario, and find that a straightforward width scaling of Transformer is a simpler and surprisingly more efficient approach in practice, and reaches the same performance level as SMoE. We also search for a better recipe for robustness of multi-domain systems, highlighting the importance of mixing-in a generic domain, i.e. Paracrawl, and introducing a simple technique, domain randomization.

Context. Planets with radii of between 2-4 RE closely orbiting solar-type stars are of significant importance for studying the transition from rocky to giant planets. Aims. Our goal is to determine the mass of a transiting planet around the very bright F6 star HD 73344 . This star exhibits high activity and has a rotation period that is close to the orbital period of the planet. Methods. The transiting planet, initially a K2 candidate, is confirmed through TESS observations . We refined its parameters and rule out a false positive with Spitzer observations. We analyzed high-precision RV data from the SOPHIE and HIRES spectrographs. We conducted separate and joint analyses using the PASTIS software. We used a novel observing strategy, targeting the star at high cadence for two consecutive nights with SOPHIE to understand the short-term stellar variability. We modeled stellar noise with two Gaussian processes. Results. High-cadence RV observations provide better constraints on stellar variability and precise orbital parameters for the transiting planet. The derived mean density suggests a sub-Neptune-type composition, but uncertainties in the planet's mass prevent a detailed characterization. In addition, we find a periodic signal in the RV data that we attribute to the signature of a nontransiting exoplanet, without totally excluding the possibility of a nonplanetary origin. Dynamical analyses confirm the stability of the two-planet system and provide constraints on the inclination of the candidate planet; these findings favor a near-coplanar system. Conclusions. While the transiting planet orbits the bright star at a short period, stellar activity prevented us from precise mass measurements. Long-term RV tracking of this planet could improve this measurement, as well as our understanding of the activity of the host star., Comment: Accepted for publication in Astronomy and Astrophysics

We study theoretical properties of a broad class of regularized algorithms with vector-valued output. These spectral algorithms include kernel ridge regression, kernel principal component regression, various implementations of gradient descent and many more. Our contributions are twofold. First, we rigorously confirm the so-called saturation effect for ridge regression with vector-valued output by deriving a novel lower bound on learning rates; this bound is shown to be suboptimal when the smoothness of the regression function exceeds a certain level. Second, we present the upper bound for the finite sample risk general vector-valued spectral algorithms, applicable to both well-specified and misspecified scenarios (where the true regression function lies outside of the hypothesis space) which is minimax optimal in various regimes. All of our results explicitly allow the case of infinite-dimensional output variables, proving consistency of recent practical applications.

Stellar magnetic activity induces both distortions and Doppler-shifts in the absorption line profiles of Sun-like stars. Those effects produce apparent radial velocity (RV) signals which greatly hamper the search for potentially habitable, Earth-like planets. In this work, we investigate these distortions in the Sun using cross-correlation functions (CCFs), derived from intensive monitoring with the high-precision spectrograph HARPS-N. We show that the RV signal arising from line-shape variations on time-scales associated with the solar rotation and activity cycle can be robustly extracted from the data, reducing the RV dispersion by half. Once these have been corrected, activity-induced Doppler-shifts remain, that are modulated at the solar rotation period, and that are most effectively modelled in the time domain, using Gaussian Processes (GPs). Planet signatures are still best retrieved with multi-dimensonal GPs, when activity is jointly modelled from the raw RVs and indicators of the line width or of the Ca II H and K emission. After GP modelling, the residual RVs exhibit a dispersion of 0.6-0.8 m/s, likely to be dominated by signals induced by super-granulation. Finally, we find that the statistical properties of the RVs evolve significantly over time, and that this evolution is primarily driven by sunspots, which control the smoothness of the signal. Such evolution, which reduces the sensitivity to long-period planet signatures, is no longer seen in the activity-induced Doppler-shifts, which is promising for long term RV monitoring surveys such as the Terra Hunting Experiment or the PLATO follow-up campaign., Comment: Accepted by MNRAS on the 2024 May 20. 17 pages, 14 figures (plus 8 pages of Appendix, 9 Appendix figures)

Stellar variability strongly impacts the search for low-mass exoplanets with radial velocity techniques. Two types of planet-free time series can be used to quantify this impact: models and direct solar observations after a subtraction of the Solar System planetary contribution. Comparing these approaches is necessary for simulations. Our objective is to validate the amplitude of the convective blueshift in plages used in our previous works, particularly in blind tests, with HARPS-N solar data. We applied our model to the structures observed at the time of observations and compared the radial velocity time series. To complete our diagnosis, we studied the observed radial velocities separately for each diffraction order derived from the individual cross-correlation functions, as well as our line-by-line radial velocities. We find that our previous model had been underestimating the amplitude of the convective blueshift inhibition by a factor of about 2. A direct estimation of the convective blueshift in the spectra explains the difference with previous estimations obtained with MDI/SOHO Dopplergrams, based on the properties of the Ni line. We identified several instrumental systematics: the presence of a 2 m/s peak-to-peak signal with a period of about 200 days in radial velocity and bisector, which could be due to periodic detector warm-ups, a systematic dependence of the long-term trend on wavelength possibly related to the variability of the continuum over time, and/or an offset in radial velocity after the interruption of several months in Oct. 2017. A large amplitude in the convective blueshift inhibition of (360 m/s) must be used when building synthetic times series for blind tests. The presence of instrumental systematics should also be taken into account when using sophisticated methods based on line properties to mitigate stellar activity when searching for very weak signals., Comment: Paper accepted in Astronomy and Astrophysics

Physics-Informed Neural Networks (PINNs) have gained considerable interest in diverse engineering domains thanks to their capacity to integrate physical laws into deep learning models. Recently, geometry-aware PINN-based approaches that employ the strong form of underlying physical system equations have been developed with the aim of integrating geometric information into PINNs. Despite ongoing research, the assessment of PINNs in problems with various geometries remains an active area of investigation. In this work, we introduce a novel physics-informed framework named the Geometry-Aware Deep Energy Method (GADEM) for solving structural mechanics problems on different geometries. As the weak form of the physical system equation (or the energy-based approach) has demonstrated clear advantages compared to the strong form for solving solid mechanics problems, GADEM employs the weak form and aims to infer the solution on multiple shapes of geometries. Integrating a geometry-aware framework into an energy-based method results in an effective physics-informed deep learning model in terms of accuracy and computational cost. Different ways to represent the geometric information and to encode the geometric latent vectors are investigated in this work. We introduce a loss function of GADEM which is minimized based on the potential energy of all considered geometries. An adaptive learning method is also employed for the sampling of collocation points to enhance the performance of GADEM. We present some applications of GADEM to solve solid mechanics problems, including a loading simulation of a toy tire involving contact mechanics and large deformation hyperelasticity. The numerical results of this work demonstrate the remarkable capability of GADEM to infer the solution on various and new shapes of geometries using only one trained model., Comment: 28 pages, 26 figures, 4 tables

Monochromatic gamma-ray signals constitute a potential smoking gun signature for annihilating or decaying dark matter particles that could relatively easily be distinguished from astrophysical or instrumental backgrounds. We provide an updated assessment of the sensitivity of the Cherenkov Telescope Array (CTA) to such signals, based on observations of the Galactic centre region as well as of selected dwarf spheroidal galaxies. We find that current limits and detection prospects for dark matter masses above 300 GeV will be significantly improved, by up to an order of magnitude in the multi-TeV range. This demonstrates that CTA will set a new standard for gamma-ray astronomy also in this respect, as the world's largest and most sensitive high-energy gamma-ray observatory, in particular due to its exquisite energy resolution at TeV energies and the adopted observational strategy focussing on regions with large dark matter densities. Throughout our analysis, we use up-to-date instrument response functions, and we thoroughly model the effect of instrumental systematic uncertainties in our statistical treatment. We further present results for other potential signatures with sharp spectral features, e.g.~box-shaped spectra, that would likewise very clearly point to a particle dark matter origin., Comment: 44 pages JCAP style (excluding author list and references), 19 figures; minor changes to match published version

The chromospheric emission estimated in the core of different lines, such as Ca II H & K, Na D1 and D2, and Halpha, is not always correlated between lines, as the Ca II H & K and Halpha emission time series are anti-correlated for a few percent of the stars, contrary to what is observed on the Sun. This puzzling result has been observed for both solar-type and M stars. Our objective is to characterise these relationships in more detail using complementary criteria, based on a set of spectra obtained with HARPS for a large sample of M dwarfs, to evaluate whether or not additional processes are required to explain the observations. We analysed the time average and variability of the Ca, Na, and Halpha emissions for 177 M0-M8 stars. We computed synthetic Halpha time series based on different assumptions of plage properties. The statistical properties of our sample, in terms of correlations and slopes between indices at different timescales, differ from what we previously obtained for FGK stars, with fewer stars with a null correlation, and a weaker dependence of the correlations on timescale. However, there can be a large dispersion from one season to another for stars. We find a clear indication of a change in the slope sign from the relation between averaged Ca (or Na) and Halpha for the most massive M dwarfs, as well as a change in slope in the Na-Ca relation. At this stage, we are not able to find simple plage properties that, alone, are sufficient to reproduce the observations. Simulations shows that it is not straightforward to compare the temporal variability correlation and the integrated indices and demonstrate the need for complex activity patterns to explain some of the observations. We conclude that the relation between these indices exhibits a large diversity in behaviour. More detailed simulations with complex activity patterns are necessary to understand these observations., Comment: Paper accepted in Astronomy and Astrophysics 15 January 2024

We introduce Brain-Artificial Intelligence Interfaces (BAIs) as a new class of Brain-Computer Interfaces (BCIs). Unlike conventional BCIs, which rely on intact cognitive capabilities, BAIs leverage the power of artificial intelligence to replace parts of the neuro-cognitive processing pipeline. BAIs allow users to accomplish complex tasks by providing high-level intentions, while a pre-trained AI agent determines low-level details. This approach enlarges the target audience of BCIs to individuals with cognitive impairments, a population often excluded from the benefits of conventional BCIs. We present the general concept of BAIs and illustrate the potential of this new approach with a Conversational BAI based on EEG. In particular, we show in an experiment with simulated phone conversations that the Conversational BAI enables complex communication without the need to generate language. Our work thus demonstrates, for the first time, the ability of a speech neuroprosthesis to enable fluent communication in realistic scenarios with non-invasive technologies., Comment: 16 pages (39 with supplementary meterial), 6 figures

In this paper, we present Partially Stochastic Infinitely Deep Bayesian Neural Networks, a novel family of architectures that integrates partial stochasticity into the framework of infinitely deep neural networks. Our new class of architectures is designed to improve the computational efficiency of existing architectures at training and inference time. To do this, we leverage the advantages of partial stochasticity in the infinite-depth limit which include the benefits of full stochasticity e.g. robustness, uncertainty quantification, and memory efficiency, whilst improving their limitations around computational complexity. We present a variety of architectural configurations, offering flexibility in network design including different methods for weight partition. We also provide mathematical guarantees on the expressivity of our models by establishing that our network family qualifies as Universal Conditional Distribution Approximators. Lastly, empirical evaluations across multiple tasks show that our proposed architectures achieve better downstream task performance and uncertainty quantification than their counterparts while being significantly more efficient. The code can be found at \url{https://github.com/Sergio20f/part_stoch_inf_deep}, Comment: 17 pages including supplementary material. Accepted at ICML 2024

In a digraph, a quasi-kernel is a subset of vertices that is independent and such that the shortest path from every vertex to this subset is of length at most two. The ``small quasi-kernel conjecture,'' proposed by Erd\H{o}s and Sz\'ekely in 1976, postulates that every sink-free digraph has a quasi-kernel whose size is within a fraction of the total number of vertices. The conjecture is even more precise with a $1/2$ ratio, but even with larger ratio, this property is known to hold only for few classes of graphs. The focus here is on small quasi-kernels in split graphs. This family of graphs has played a special role in the study of the conjecture since it was used to disprove a strengthening that postulated the existence of two disjoint quasi-kernels. The paper proves that every sink-free split digraph $D$ has a quasi-kernel of size at most $\frac{2}{3}|V(D)|$, and even of size at most two when the graph is an orientation of a complete split graph. It is also shown that computing a quasi-kernel of minimal size in a split digraph is W[2]-hard.

A rectangular graphyne sheet is composed of units similar to phenyl rings that are linked by acetylenic chains, as in hexagonal $\gamma$-graphyne. This system is organized over a rectangular lattice similar to that of the recently synthesized biphenylene network. We investigate the stability of this sheet from different perspectives and study its electronic structure. Rectangular graphyne is a semiconducting system in its pristine form and features a pair of highly localized states. These characteristics are correlated with the structural anisotropy of the system, since its frontier states behave like quasi--1D states embedded in the 2D lattice. We further consider modified systems in which longer acetylenic links are introduced. We discuss how a strategic choice of the position of these longer bridges can lead to specific changes of the electronic structure of the rectangular graphyne sheet.

We present the first optimal rates for infinite-dimensional vector-valued ridge regression on a continuous scale of norms that interpolate between $L_2$ and the hypothesis space, which we consider as a vector-valued reproducing kernel Hilbert space. These rates allow to treat the misspecified case in which the true regression function is not contained in the hypothesis space. We combine standard assumptions on the capacity of the hypothesis space with a novel tensor product construction of vector-valued interpolation spaces in order to characterize the smoothness of the regression function. Our upper bound not only attains the same rate as real-valued kernel ridge regression, but also removes the assumption that the target regression function is bounded. For the lower bound, we reduce the problem to the scalar setting using a projection argument. We show that these rates are optimal in most cases and independent of the dimension of the output space. We illustrate our results for the special case of vector-valued Sobolev spaces., Comment: Published JMLR version. arXiv admin note: text overlap with arXiv:2208.01711

We initiate a systematic study of quantum properties of finite graphs, namely, quantum asymmetry, quantum symmetry, and quantum isomorphism. We define the Schmidt alternative for a class of graphs, which reveals to be a useful tool for studying quantum symmetries of graphs. After showing that quantum isomorphic graphs have quantum isomorphic centers and connected components, we solve the aforementioned problems for the classes of cographs and forests. We also compute their quantum automorphism groups for the first time. In doing so, we extend to the noncommutative setting a theorem of Jordan. Using general results on $\mathcal F$-cographs, we extend the precedent results to $\mathcal G_5$-cographs and tree-cographs, two distinct strictly proper superclasses of cographs and forests respectively. Finally, we show that quantum isomorphic planar graphs are isomorphic., Comment: 50 pages, 1 figure. Two appendices added and some minor changes

This paper presents an analysis of the updated version of the Front-End Board (FEB) for the NectarCAM camera, developed for the Cherenkov Telescope Array Observatory (CTAO). The FEB is a critical component responsible for reading and converting signals from the camera's photo-multiplier tubes into digital data and generating module-level trigger signals. This study provides an overview of the design and performance of the new FEB version, including the use of an improved NECTAr3 chip with advanced features. The NECTAr3 chip contains a switched capacitor array for sampling signals at 1 GHz and a 12-bit analog-to-digital converter (ADC) for digitization upon receiving a trigger signal. The integration of the new NECTAr3 chip results in a significant reduction of NectarCAM's deadtime by an order of magnitude compared to the previous version. The paper also presents the results of laboratory testing, including measurements of timing performance, linearity, dynamic range, and deadtime, to characterize the new FEB's performance.