Search

We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as the central limit theorem holds for the partial sum normalized by $n^{-1/2}$. %The conditions are expressed in terms of projective criteria. This result applies to the empirical distribution function in $L^p(\mu)$, where $p\geq 2$ and $\mu$ is a real $\sigma$-finite measure: under some $\tau$-mixing conditions we obtain a rate of order $O(n^{-(p-2)/2})$. In the real case, our result leads to new conditions to reach the optimal rates of convergence in terms of Wasserstein distances of order $p\in ]2,3]$.

Representing and quantifying Minimal Residual Disease (MRD) in Acute Myeloid Leukemia (AML), a type of cancer that affects the blood and bone marrow, is essential in the prognosis and follow-up of AML patients. As traditional cytological analysis cannot detect leukemia cells below 5\%, the analysis of flow cytometry dataset is expected to provide more reliable results. In this paper, we explore statistical learning methods based on optimal transport (OT) to achieve a relevant low-dimensional representation of multi-patient flow cytometry measurements (FCM) datasets considered as high-dimensional probability distributions. Using the framework of OT, we justify the use of the K-means algorithm for dimensionality reduction of multiple large-scale point clouds through mean measure quantization by merging all the data into a single point cloud. After this quantization step, the visualization of the intra and inter-patients FCM variability is carried out by embedding low-dimensional quantized probability measures into a linear space using either Wasserstein Principal Component Analysis (PCA) through linearized OT or log-ratio PCA of compositional data. Using a publicly available FCM dataset and a FCM dataset from Bordeaux University Hospital, we demonstrate the benefits of our approach over the popular kernel mean embedding technique for statistical learning from multiple high-dimensional probability distributions. We also highlight the usefulness of our methodology for low-dimensional projection and clustering patient measurements according to their level of MRD in AML from FCM. In particular, our OT-based approach allows a relevant and informative two-dimensional representation of the results of the FlowSom algorithm, a state-of-the-art method for the detection of MRD in AML using multi-patient FCM.

The first generation of ELT instruments includes an optical-infrared high-resolution spectrograph, indicated as ELT-HIRES and recently christened ANDES (ArmazoNes high Dispersion Echelle Spectrograph). ANDES consists of three fibre-fed spectrographs ([U]BV, RIZ, YJH) providing a spectral resolution of $\sim$100,000 with a minimum simultaneous wavelength coverage of 0.4-1.8 $\mu$m with the goal of extending it to 0.35-2.4 $\mu$m with the addition of a U arm to the BV spectrograph and a separate K band spectrograph. It operates both in seeing- and diffraction-limited conditions and the fibre feeding allows several, interchangeable observing modes including a single conjugated adaptive optics module and a small diffraction-limited integral field unit in the NIR. Modularity and fibre-feeding allow ANDES to be placed partly on the ELT Nasmyth platform and partly in the Coud\'e room. ANDES has a wide range of groundbreaking science cases spanning nearly all areas of research in astrophysics and even fundamental physics. Among the top science cases, there are the detection of biosignatures from exoplanet atmospheres, finding the fingerprints of the first generation of stars, tests on the stability of Nature's fundamental couplings, and the direct detection of the cosmic acceleration. The ANDES project is carried forward by a large international consortium, composed of 35 Institutes from 13 countries, forming a team of almost 300 scientists and engineers which include the majority of the scientific and technical expertise in the field that can be found in ESO member states., Comment: SPIE astronomical telescope and instrumentation 2024, in press

Tools from optimal transport (OT) theory have recently been used to define a notion of quantile function for directional data. In practice, regularization is mandatory for applications that require out-of-sample estimates. To this end, we introduce a regularized estimator built from entropic optimal transport, by extending the definition of the entropic map to the spherical setting. We propose a stochastic algorithm to directly solve a continuous OT problem between the uniform distribution and a target distribution, by expanding Kantorovich potentials in the basis of spherical harmonics. In addition, we define the directional Monge-Kantorovich depth, a companion concept for OT-based quantiles. We show that it benefits from desirable properties related to Liu-Zuo-Serfling axioms for the statistical analysis of directional data. Building on our regularized estimators, we illustrate the benefits of our methodology for data analysis.

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.

Context: Traditional one-dimensional (1D) hydrostatic model atmospheres introduce systematic modelling errors into spectroscopic analyses of FGK-type stars. Aims: We present an updated version of the STAGGER-grid of 3D model atmospheres, and explore the accuracy of post-processing methods in preparation for spectral synthesis. Methods: New and old models were (re)computed following an updated workflow, including an updated opacity binning technique. Spectroscopic tests were performed in 3D LTE for a grid of 216 fictitious Fe I lines, spanning a wide range in oscillator strength, excitation potential and central wavelength, and eight model atmospheres that cover the stellar atmospheric parameter range (Teff, log g, [Fe/H]) of FGK-type stars. Using this grid, the impact of vertical and horizontal resolution, and temporal sampling of model atmospheres on spectroscopic diagnostics was tested. Results: We find that downsampling the horizontal mesh from its original size of 240 x 240 grid cells to 80 x 80 cells, i.e. sampling every third grid cell, introduces minimal errors on the equivalent width and normalized line flux across the line and stellar parameter space. Regarding temporal sampling, we find that sampling ten statistically independent snapshots is sufficient to accurately model the shape of spectral line profiles. For equivalent widths, a subsample consisting of only two snapshots is sufficient, introducing an abundance error of less than 0.015 dex. Conclusions: We have computed 32 new model atmospheres and recomputed 116 old model atmospheres present in the original grid. The public release of the STAGGER-grid contains 243 models, excluding models with [Fe/H] = -4.00, and the processed snapshots can be used to improve the accuracy of spectroscopic analyses.

Coral reefs are vital ecosystems that are under increasing threat due to local human impacts and climate change. Efficient and accurate monitoring of coral reefs is crucial for their conservation and management. In this paper, we present an automatic coral detection system utilizing the You Only Look Once (YOLO) deep learning model, which is specifically tailored for underwater imagery analysis. To train and evaluate our system, we employ a dataset consisting of 400 original underwater images. We increased the number of annotated images to 580 through image manipulation using data augmentation techniques, which can improve the model's performance by providing more diverse examples for training. The dataset is carefully collected from underwater videos that capture various coral reef environments, species, and lighting conditions. Our system leverages the YOLOv5 algorithm's real-time object detection capabilities, enabling efficient and accurate coral detection. We used YOLOv5 to extract discriminating features from the annotated dataset, enabling the system to generalize, including previously unseen underwater images. The successful implementation of the automatic coral detection system with YOLOv5 on our original image dataset highlights the potential of advanced computer vision techniques for coral reef research and conservation. Further research will focus on refining the algorithm to handle challenging underwater image conditions, and expanding the dataset to incorporate a wider range of coral species and spatio-temporal variations.

High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed data. To this end, we suppose that the set of observed predictors (or features) is a random matrix with a variance profile and with dimensions growing at a proportional rate. Assuming a random effect model, we study the predictive risk of the ridge estimator for linear regression with such a variance profile. In this setting, we provide deterministic equivalents of this risk and of the degree of freedom of the ridge estimator. For certain class of variance profile, our work highlights the emergence of the well-known double descent phenomenon in high-dimensional regression for the minimum norm least-squares estimator when the ridge regularization parameter goes to zero. We also exhibit variance profiles for which the shape of this predictive risk differs from double descent. The proofs of our results are based on tools from random matrix theory in the presence of a variance profile that have not been considered so far to study regression models. Numerical experiments are provided to show the accuracy of the aforementioned deterministic equivalents on the computation of the predictive risk of ridge regression. We also investigate the similarities and differences that exist with the standard setting of independent and identically distributed data.

In an ideal perfectly straight multimode fiber with a circular-core, the symmetry ensures that rotating the input wavefront leads to a corresponding rotation of the output wavefront. This invariant property, known as the rotational memory effect (RME), remains independent of the typically unknown output profile. The RME thus offers significant potential for imaging and telecommunication applications. However, in real-life fibers, this effect is degraded by intrinsic imperfections and external perturbations, and is challenging to observe because of its acute sensitivity to misalignments and aberrations in the optical setup. Thanks to processing involving a spatial light modulator, we efficiently overcome these measurement biases, allowing for precise quantification of the RME. We establish an experimental and theoretical framework for studying and manipulating the RME in multimode fibers. Theoretical predictions are consistent with experimental data and simulations, connecting the shape of the angular-dependent correlation of the RME to the geometrical properties of the core deformation. This work opens the road for accurate characterization of the distributed disorder originating from the fabrication process and calibration-less imaging in multimode fibers.

We extend the central limit theorem under the Dedecker-Rio condition to adapted stationary and ergodic sequences of random variables taking values in a class of smooth Banach spaces. This result applies to the case of random variables taking values in $L^p(\mu)$, with $2 \leq p < \infty$ and $\mu$ a $\sigma$-finite real measure. As an application we give a sufficient condition for empirical processes indexed by Sobolev balls to satisfy the central limit theorem, and discuss about the optimality of these conditions.

We propose center-outward superquantile and expected shortfall functions, with applications to multivariate risk measurements, extending the standard notion of value at risk and conditional value at risk from the real line to $\mathbb{R}^d$. Our new concepts are built upon the recent definition of Monge-Kantorovich quantiles based on the theory of optimal transport, and they provide a natural way to characterize multivariate tail probabilities and central areas of point clouds. They preserve the univariate interpretation of a typical observation that lies beyond or ahead a quantile, but in a meaningful multivariate way. We show that they characterize random vectors and their convergence in distribution, which underlines their importance. Our new concepts are illustrated on both simulated and real datasets.

We report about element specific measurements of ultrafast demagnetization and magnetization precession damping in Permalloy (Py) thin films. Magnetization dynamics induced by optical pump at $1.5$eV is probed simultaneously at the $M_{2,3}$ edges of Ni and Fe with High order Harmonics for moderate demagnetization rates (less than $50$%). The role of the intersublattice exchange interaction on both longitudinal and transverse dynamics is analyzed with a Landau Lifshitz Bloch description of ferromagnetically coupled Fe and Ni sublattices. It is shown that the intersublattice exchange interaction governs the dissipation during demagnetization as well as precession damping of the magnetization vector., Comment: 8 pages, 5 figures

We introduce a new stochastic algorithm for solving entropic optimal transport (EOT) between two absolutely continuous probability measures $\mu$ and $\nu$. Our work is motivated by the specific setting of Monge-Kantorovich quantiles where the source measure $\mu$ is either the uniform distribution on the unit hypercube or the spherical uniform distribution. Using the knowledge of the source measure, we propose to parametrize a Kantorovich dual potential by its Fourier coefficients. In this way, each iteration of our stochastic algorithm reduces to two Fourier transforms that enables us to make use of the Fast Fourier Transform (FFT) in order to implement a fast numerical method to solve EOT. We study the almost sure convergence of our stochastic algorithm that takes its values in an infinite-dimensional Banach space. Then, using numerical experiments, we illustrate the performances of our approach on the computation of regularized Monge-Kantorovich quantiles. In particular, we investigate the potential benefits of entropic regularization for the smooth estimation of multivariate quantiles using data sampled from the target measure $\nu$., Comment: 32 pages, 5 figures

Stellar granulation generates fluctuations in photometric and spectroscopic data whose properties depend on the stellar type, composition, and evolutionary state. In this study, we aim to detect the signatures of stellar granulation, link spectroscopic and photometric signatures of convection for main-sequence stars, and test predictions from 3D hydrodynamic models. For the first time, we observed two bright stars (Teff = 5833 K and 6205 K) with high-precision observations taken simultaneously with CHEOPS and ESPRESSO. We analyzed the properties of the stellar granulation signal in each individual data set. We compared them to Kepler observations and 3D hydrodynamic models. While isolating the granulation-induced changes by attenuating the p-mode oscillation signals, we studied the relationship between photometric and spectroscopic observables. The signature of stellar granulation is detected and precisely characterized for the hotter F star in the CHEOPS and ESPRESSO observations. For the cooler G star, we obtain a clear detection in the CHEOPS dataset only. The TESS observations are blind to this stellar signal. Based on CHEOPS observations, we show that the inferred properties of stellar granulation are in agreement with both Kepler observations and hydrodynamic models. Comparing their periodograms, we observe a strong link between spectroscopic and photometric observables. Correlations of this stellar signal in the time domain (flux vs RV) and with specific spectroscopic observables (shape of the cross-correlation functions) are however difficult to isolate due to signal-to-noise dependent variations. In the context of the upcoming PLATO mission and the extreme precision RV surveys, a thorough understanding of the properties of the stellar granulation signal is needed. The CHEOPS and ESPRESSO observations pave the way for detailed analyses of this stellar process., Comment: Accepted to A&A, 30 pages, 21 figures, 10 tables (one online)

We present here the new results obtained with the INPOP planetary ephemerides and BepiColombo radio-science simulations. We give new constraints for the classic General Relativity tests in terms of violation of the PPN parameters $\beta$ and $\gamma$ and the time variation of the gravitational constant G. We also present new limits for the mass of the graviton and finally we obtain new acceptable intervals for the dilaton parameters $\alpha_{0}$, $\alpha_{T}$ and $\alpha_{G}$. Besides these tests of gravitation, we also study the possibility of detecting the Sun core rotation., Comment: arXiv admin note: substantial text overlap with arXiv:2111.04499

This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics. Wasserstein estimators are defined as solutions of variational problems whose objective function involves the use of an optimal transport cost between probability measures. Such estimators can be regularized by replacing the optimal transport cost by its regularized version using an entropy penalty on the transport plan. The use of such a regularization has a potentially significant smoothing effect on the resulting estimators. In this work, we investigate its potential benefits on the approximation and estimation properties of regularized Wasserstein estimators. Our main contribution is to discuss how entropic regularization may reach, at a lower computational cost, statistical performances that are comparable to those of un-regularized Wasserstein estimators in statistical learning problems involving distributional data analysis. To this end, we present new theoretical results on the convergence of regularized Wasserstein estimators. We also study their numerical performances using simulated and real data in the supervised learning problem of proportions estimation in mixture models using optimal transport., Comment: 45 pages, 12 figures

This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling these time-dependent probability measures as random objects in the Wasserstein space, we propose a new auto-regressive model for the statistical analysis of multivariate distributional time series. Using the theory of iterated random function systems, results on the existence, uniqueness and stationarity of the solution of such a model are provided. We also propose a consistent estimator for the auto-regressive coefficients of this model. Due to the simplex constraints that we impose on the model coefficients, the proposed estimator that is learned under these constraints, naturally has a sparse structure. The sparsity allows the application of the proposed model in learning a graph of temporal dependency from multivariate distributional time series. We explore the numerical performances of our estimation procedure using simulated data. To shed some light on the benefits of our approach for real data analysis, we also apply this methodology to a data set made of observations from age distribution in different countries.

The detection of small exoplanets with the radial velocity (RV) technique is limited by various poorly known noise sources of instrumental and stellar origin. As a consequence, current detection techniques often fail to provide reliable estimates of the significance levels of detection tests (p-values). We designed an RV detection procedure that provides reliable p-value estimates while accounting for the various noise sources. The method can incorporate ancillary information about the noise (e.g., stellar activity indicators) and specific data- or context-driven data (e.g., instrumental measurements, simulations of stellar variability) . The detection part of the procedure uses a detection test that is applied to a standardized periodogram. Standardization allows an autocalibration of the noise sources with partially unknown statistics. The estimation of the p-value of the test output is based on dedicated Monte Carlo simulations that allow handling unknown parameters. The procedure is versatile in the sense that the specific pair (periodogram and test) is chosen by the user. We demonstrate by extensive numerical experiments on synthetic and real RV data from the Sun and aCenB that the proposed method reliably allows estimating the p-values. The method also provides a way to evaluate the dependence of the estimated p-values that are attributed to a reported detection on modeling errors. It is a critical point for RV planet detection at low signal-to-noise ratio to evaluate this dependence. The python algorithms are available on GitHub. Accurate estimation of p-values when unknown parameters are involved is an important but only recently addressed question in the field of RV detection. Although this work presents a method to do this, the statistical literature discussed in this paper may trigger the development of other strategies., Comment: 19 pages, 11 figures, accepted to A&A

Addressing a real world sequential decision problem with Reinforcement Learning (RL) usually starts with the use of a simulated environment that mimics real conditions. We present a novel open source RL environment for realistic crop management tasks. gym-DSSAT is a gym interface to the Decision Support System for Agrotechnology Transfer (DSSAT), a high fidelity crop simulator. DSSAT has been developped over the last 30 years and is widely recognized by agronomists. gym-DSSAT comes with predefined simulations based on real world maize experiments. The environment is as easy to use as any gym environment. We provide performance baselines using basic RL algorithms. We also briefly outline how the monolithic DSSAT simulator written in Fortran has been turned into a Python RL environment. Our methodology is generic and may be applied to similar simulators. We report on very preliminary experimental results which suggest that RL can help researchers to improve sustainability of fertilization and irrigation practices.

High-precision photometric data from space missions have improved our understanding of stellar granulation. These observations have shown with precision the stochastic brightness fluctuations of stars across the HR diagram, allowing us to better understand how stellar surface convection reacts to a change in stellar parameters. These fluctuations need to be understood and quantified in order to improve the detection and characterization of exoplanets. In this work, we provide new scaling relations of two characteristic properties of the brightness fluctuations time series, the standard deviation ($\sigma$) and the auto-correlation time ($\tau\rm_{eff}$). This was done by using long time series of 3D stellar atmosphere models at different metallicities and across the HR diagram, generated with a 3D radiative hydrodynamical code: the STAGGER code. We compared our synthetic granulation properties with the values of a large sample of Kepler stars, and analyzed selected stars with accurate stellar parameters from the Kepler LEGACY sample. Our 3D models showed that $\sigma\propto\nu\rm_{max}^{-0.567\pm0.012}$ and $\tau\rm_{eff}\propto\nu\rm_{max}^{-0.997\pm0.018}$ for stars at solar metallicity. We showed that both $\sigma$ and $\tau\rm_{eff}$ decrease with metallicity, although the metallicity dependence is more significant on $\sigma$. Unlike previous studies, we found very good agreement between $\sigma$ from Kepler targets and the 3D models at $\log{g}\leq3.5$, and a good correlation between the stars and models with $\log{g}\geq3.5$. For $\tau\rm_{eff}$, we found that the 3D models reproduced well the Kepler LEGACY star values. Overall, this study shows that 3D stellar atmosphere models reproduce the granulation properties of stars across the HR diagram., Comment: Accepted for publication in MNRAS

Collecting accurate and fine-grain information about the music people like, dislike and actually listen to has long been a challenge for sociologists. As millions of people now use online music streaming services, research can build upon the individual listening history data that are collected by these platforms. Individual interviews in particular can benefit from such data, by allowing the interviewers to immerse themselves in the musical universe of consenting respondents, and thus ask them contextualized questions and get more precise answers. Designing a visual exploration tool allowing such an immersion is however difficult, because of the volume and heterogeneity of the listening data, the unequal "visual literacy" of the prospective users, or the interviewers' potential lack of knowledge of the music listened to by the respondents. In this case study we discuss the design and evaluation of such a tool. Designed with social scientists, its purpose is to help them in preparing and conducting semi-structured interviews that address various aspects of the listening experience. It was evaluated during thirty interviews with consenting users of a streaming platform in France., Comment: Preprint of the paper to be presented at ACM CHI Conference on Human Factors in Computing Systems (CHI'22), Case Studies track, 10 pages, 5 figures

We introduce the SAPP (Stellar Abundances and atmospheric Parameters Pipeline), the prototype of the code that will be used to determine parameters of stars observed within the core program of the PLATO space mission. The pipeline is based on the Bayesian inference and provides effective temperature, surface gravity, metallicity, chemical abundances, and luminosity. The code in its more general version can have a much wider range of applications. It can also provide masses, ages, and radii of stars and can be used for stars of stellar types not targeted by the PLATO core program, such as red giants. We validate the code on a set of 27 benchmark stars that includes 19 FGK-type dwarfs, 6 GK-type sub-giants, and 2 red giants. Our results suggest that combining various observables is the optimal approach, as it allows to break degeneracies between different parameters and yields more accurate values of stellar parameters and more realistic uncertainties. For the PLATO core sample, we obtain a typical uncertainty of 27 ($\rm{syst.}$) $\pm$ 37 ($\rm{stat.}$) K for T$_{\rm{eff}}$, 0.00 $\pm$ 0.01 dex for log$g$, 0.02 $\pm$ 0.02 dex for metallicity [Fe/H], -0.01 $\pm$ 0.03 R$_\odot$ for radii, -0.01 $\pm$ 0.05 M$_\odot$ for stellar masses, and -0.14 $\pm$ 0.63 Gyrs for ages. We also show that the best results are obtained by combining the $\nu_{max}$ scaling relation and stellar spectra. This resolves the notorious problem of degeneracies, which is particularly important for F-type stars., Comment: 25 pages, 42 figures, accepted for publication in A&A

We give here a detailed description of the latest INPOP planetary ephemerides INPOP20a. We test the sensitivity of the Sun oblateness determination obtained with INPOP to different models for the Sun core rotation. We also present new evaluations of possible GRT violations with the PPN parameters $\beta$,$\gamma$ and $\dot{\mu}/\mu$. With a new method for selecting acceptable alternative ephemerides we provide conservative limits of about $7.16 \times 10^{-5}$ and $7.49 \times 10^{-5}$ for $\beta-1$ and $\gamma-1$ respectively using the present day planetary data samples. We also present simulations of Bepi-Colombo range tracking data and their impact on planetary ephemeris construction. We show that the use of future BC range observations should improve these estimates, in particular $\gamma$. Finally, interesting perspectives for the detection of the Sun core rotation seem to be reachable thanks to the BC mission and its accurate range measurements in the GRT frame., Comment: Proceedings of the IAU Symposium 364 "Multi-scale dynamics of space objects"

The focus is on the statistical analysis of matrix-valued time series, where data is collected over a network of sensors, typically at spatial locations, over time. Each sensor records a vector of features at each time point, creating a vectorial time series for each sensor. The goal is to identify the dependency structure among these sensors and represent it with a graph. When only one feature per sensor is observed, vector auto-regressive (VAR) models are commonly used to infer Granger causality, resulting in a causal graph. The first contribution extends VAR models to matrix-variate models for the purpose of graph learning. Additionally, two online procedures are proposed for both low and high dimensions, enabling rapid updates of coefficient estimates as new samples arrive. In the high-dimensional setting, a novel Lasso-type approach is introduced, and homotopy algorithms are developed for online learning. An adaptive tuning procedure for the regularization parameter is also provided. Given that the application of auto-regressive models to data typically requires detrending, which is not feasible in an online context, the proposed AR models are augmented by incorporating trend as an additional parameter, with a particular focus on periodic trends. The online algorithms are adapted to these augmented data models, allowing for simultaneous learning of the graph and trend from streaming samples. Numerical experiments using both synthetic and real data demonstrate the effectiveness of the proposed methods.

We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete, while the target measure is assumed to be discrete. To solve the semi-dual formulation of such a regularized and semi-discrete optimal transportation problem, we propose to consider a stochastic Gauss-Newton algorithm that uses a sequence of data sampled from the source measure. This algorithm is shown to be adaptive to the geometry of the underlying convex optimization problem with no important hyperparameter to be accurately tuned. We establish the almost sure convergence and the asymptotic normality of various estimators of interest that are constructed from this stochastic Gauss-Newton algorithm. We also analyze their non-asymptotic rates of convergence for the expected quadratic risk in the absence of strong convexity of the underlying objective function. The results of numerical experiments from simulated data are also reported to illustrate the finite sample properties of this Gauss-Newton algorithm for stochastic regularized optimal transport, and to show its advantages over the use of the stochastic gradient descent, stochastic Newton and ADAM algorithms.

A prototype version of the Q & U bolometric interferometer for cosmology (QUBIC) underwent a campaign of testing in the laboratory at Astroparticle Physics and Cosmology laboratory in Paris (APC). The detection chain is currently made of 256 NbSi transition edge sensors (TES) cooled to 320 mK. The readout system is a 128:1 time domain multiplexing scheme based on 128 SQUIDs cooled at 1 K that are controlled and amplified by an SiGe application specific integrated circuit at 40 K. We report the performance of this readout chain and the characterization of the TES. The readout system has been functionally tested and characterized in the lab and in QUBIC. The low noise amplifier demonstrated a white noise level of 0.3 nV.Hz^-0.5. Characterizations of the QUBIC detectors and readout electronics includes the measurement of I-V curves, time constant and the noise equivalent power. The QUBIC TES bolometer array has approximately 80% detectors within operational parameters. It demonstrated a thermal decoupling compatible with a phonon noise of about 5.10^-17 W.Hz^-0.5 at 410 mK critical temperature. While still limited by microphonics from the pulse tubes and noise aliasing from readout system, the instrument noise equivalent power is about 2.10^-16 W.Hz^-0.5, enough for the demonstration of bolometric interferometry., Comment: Accepted for publication in JCAP

The Q $\&$ U Bolometric Interferometer for Cosmology (QUBIC) is a novel kind of polarimeter optimized for the measurement of the B-mode polarization of the Cosmic Microwave Background (CMB), which is one of the major challenges of observational cosmology. The signal is expected to be of the order of a few tens of nK, prone to instrumental systematic effects and polluted by various astrophysical foregrounds which can only be controlled through multichroic observations. QUBIC is designed to address these observational issues with a novel approach that combines the advantages of interferometry in terms of control of instrumental systematic effects with those of bolometric detectors in terms of wide-band, background-limited sensitivity. The QUBIC synthesized beam has a frequency-dependent shape that results in the ability to produce maps of the CMB polarization in multiple sub-bands within the two physical bands of the instrument (150 and 220 GHz). These features make QUBIC complementary to other instruments and makes it particularly well suited to characterize and remove Galactic foreground contamination. In this article, first of a series of eight, we give an overview of the QUBIC instrument design, the main results of the calibration campaign, and present the scientific program of QUBIC including not only the measurement of primordial B-modes, but also the measurement of Galactic foregrounds. We give forecasts for typical observations and measurements: with three years of integration on the sky and assuming perfect foreground removal as well as stable atmospheric conditions from our site in Argentina, our simulations show that we can achieve a statistical sensitivity to the effective tensor-to-scalar ratio (including primordial and foreground B-modes) $\sigma(r)=0.015$., Comment: 34 pages, 16 figures, accepted for publication by JCAP. Overview paper for a series of 8 QUBIC articles special JCAP edition dedicated to QUBIC

We experimentally validate a mode-dependent loss (MDL) estimation technique employing acorrection factor to remove the MDL estimation dependence on the SNR when using a minimum meansquare error (MMSE) equalizer. A reduction of the MDL estimation error is observed for both transmitter-side and in-span MDL emulation., Comment: Accepted for presentation at European Conference on Optical Communications (ECOC) 2020

Bolometric interferometry is a novel technique that has the ability to perform spectral imaging. A bolometric interferometer observes the sky in a wide frequency band and can reconstruct sky maps in several sub-bands within the physical band in post-processing of the data. This provides a powerful spectral method to discriminate between the cosmic microwave background (CMB) and astrophysical foregrounds. In this paper, the methodology is illustrated with examples based on the Q \& U Bolometric Interferometer for Cosmology (QUBIC) which is a ground-based instrument designed to measure the B-mode polarization of the sky at millimeter wavelengths. We consider the specific cases of point source reconstruction and Galactic dust mapping and we characterize the point spread function as a function of frequency. We study the noise properties of spectral imaging, especially the correlations between sub-bands, using end-to-end simulations together with a fast noise simulator. We conclude showing that spectral imaging performance are nearly optimal up to five sub-bands in the case of QUBIC., Comment: 27 pages, 18 figures. Accepted by JCAP on July 6, 2021. Second paper of series of 8 in a special JCAP edition on QUBIC

The capacity in space division multiplexing (SDM) systems with coupled channels is fundamentally limited by mode-dependent loss (MDL) and mode-dependent gain (MDG) generated in components and amplifiers. In these systems, MDL/MDG must be accurately estimated for performance analysis and troubleshooting. Most recent demonstrations of SDM with coupled channels perform MDL/MDG estimation by digital signal processing (DSP) techniques based on the coefficients of multiple-input multiple-output (MIMO) adaptive equalizers. Although these methods provide a valid indication of the order of magnitude of the accumulated MDL/MDG over the link, MIMO equalizers are usually updated according to the minimum mean square error (MMSE) criterion, which is known to depend on the channel signal-to-noise ratio (SNR). Therefore, MDL/MDG estimation techniques based on the adaptive filter coefficients are also impaired by noise. In this paper, we model analytically the influence of the SNR on DSP-based MDL/MDG estimation, and show that the technique is prone to errors. Based on the transfer function of MIMO MMSE equalizers, and assuming a known SNR, we calculate a correction factor that improves the estimation process in moderate levels of MDL/MDG and SNR. The correction factor is validated by simulation of a 6-mode long-haul transmission link, and experimentally using a 3-mode transmission link. The results confirm the limitations of the standard estimation method in scenarios of high additive noise and MDL/MDG, and indicate the correction factor as a possible solution in practical SDM scenarios.

We present the design, manufacturing and performance of the horn-switch system developed for the technological demonstrator of QUBIC (the $Q$\&$U$ Bolometric Interferometer for Cosmology). This system is constituted of 64 back-to-back dual-band (150\,GHz and 220\,GHz) corrugated feed-horns interspersed with mechanical switches used to select desired baselines during the instrument self-calibration. We manufactured the horns in aluminum platelets milled by photo-chemical etching and mechanically tightened with screws. The switches are based on steel blades that open and close the wave-guide between the back-to-back horns and are operated by miniaturized electromagnets. We also show the current development status of the feedhorn-switch system for the QUBIC full instrument, based on an array of 400 horn-switch assemblies., Comment: 30 pages, 28 figures. Accepted for submission to JCAP

Current experiments aimed at measuring the polarization of the Cosmic Microwave Background (CMB) use cryogenic detector arrays and cold optical systems to boost the mapping speed of the sky survey. For these reasons, large volume cryogenic systems, with large optical windows, working continuously for years, are needed. Here we report on the cryogenic system of the QUBIC (Q and U Bolometric Interferometer for Cosmology) experiment: we describe its design, fabrication, experimental optimization and validation in the Technological Demonstrator configuration. The QUBIC cryogenic system is based on a large volume cryostat, using two pulse-tube refrigerators to cool at ~3K a large (~1 m^3) volume, heavy (~165kg) instrument, including the cryogenic polarization modulator, the corrugated feedhorns array, and the lower temperature stages; a 4He evaporator cooling at ~1K the interferometer beam combiner; a 3He evaporator cooling at ~0.3K the focal-plane detector arrays. The cryogenic system has been tested and validated for more than 6 months of continuous operation. The detector arrays have reached a stable operating temperature of 0.33K, while the polarization modulator has been operated from a ~10K base temperature. The system has been tilted to cover the boresight elevation range 20 deg -90 deg without significant temperature variations. The instrument is now ready for deployment to the high Argentinean Andes., Comment: This is one of a series of papers on the QUBIC experiment status - This version of the paper matches the one accepted for publication on Journal of Cosmology and Astroparticle Physics

Inflation Gravity Waves B-Modes polarization detection is the ultimate goal of modern large angular scale cosmic microwave background (CMB) experiments around the world. A big effort is undergoing with the deployment of many ground-based, balloon-borne and satellite experiments using different methods to separate this faint polarized component from the incoming radiation. One of the largely used technique is the Stokes Polarimetry that uses a rotating half-wave plate (HWP) and a linear polarizer to separate and modulate the polarization components with low residual cross-polarization. This paper describes the QUBIC Stokes Polarimeter highlighting its design features and its performances. A common systematic with these devices is the generation of large spurious signals synchronous with the rotation and proportional to the emissivity of the optical elements. A key feature of the QUBIC Stokes Polarimeter is to operate at cryogenic temperature in order to minimize this unwanted component. Moving efficiently this large optical element at low temperature constitutes a big engineering challenge in order to reduce friction power dissipation. Big attention has been given during the designing phase to minimize the differential thermal contractions between parts. The rotation is driven by a stepper motor placed outside the cryostat to avoid thermal load dissipation at cryogenic temperature. The tests and the results presented in this work show that the QUBIC polarimeter can easily achieve a precision below 0.1{\deg} in positioning simply using the stepper motor precision and the optical absolute encoder. The rotation induces only few mK of extra power load on the second cryogenic stage (~ 8 K)., Comment: Part of a series of 8 papers on QUBIC to be submitted to a special issue of JCAP

The Q and U Bolometric Interferometer for Cosmology (QUBIC) is a ground-based experiment that aims to detect B-mode polarisation anisotropies in the CMB at angular scales around the l=100 recombination peak. Systematic errors make ground-based observations of B modes at millimetre wavelengths very challenging and QUBIC mitigates these problems in a somewhat complementary way to other existing or planned experiments using the novel technique of bolometric interferometry. This technique takes advantage of the sensitivity of an imager and the systematic error control of an interferometer. A cold reflective optical combiner superimposes there-emitted beams from 400 aperture feedhorns on two focal planes. A shielding system composedof a fixed groundshield, and a forebaffle that moves with the instrument, limits the impact of local contaminants. The modelling, design, manufacturing and preliminary measurements of the optical components are described in this paper., Comment: Part of a series of 8 papers on QUBIC to be published in a special issue of JCAP. Accepted for publication

A prototype version of the Q & U Bolometric Interferometer for Cosmology (QUBIC) underwent a campaign of testing in the laboratory at Astroparticle Physics and Cosmology in Paris. We report the results of this Technological Demonstrator which successfully shows the feasibility of the principle of Bolometric Interferometry. Characterization of QUBIC includes the measurement of the synthesized beam, the measurement of interference fringes, and the measurement of polarization performance. A modulated and frequency tunable millimetre-wave source in the telescope far-field is used to simulate a point source. The QUBIC pointing is scanned across the point source to produce beam maps. Polarization modulation is measured using a rotating Half Wave Plate. The measured beam matches well to the theoretical simulations and gives QUBIC the ability to do spectro imaging. The polarization performance is excellent with less than 0.5\% cross-polarization rejection. QUBIC is ready for deployment on the high altitude site at Alto Chorillo, Argentina to begin scientific operations., Comment: Part of a series of 8 papers on QUBIC accepted by JCAP for a special issue: https://iopscience.iop.org/journal/1475-7516/page/QUBIC_status_and_forecast

We report on the experimental observation of a simultaneous threefold wavelength and spatial conversion process at telecommunication wavelengths taking place in a 6-LP-mode graded-index few-mode fiber. The physical mechanism is based on parallel and phase-matched frequency-degenerated intermodal four-wave mixing (FD-IFWM) phenomena occurring between the fundamental mode and higher-order spatial modes. More precisely, a single high-power frequency-degenerated pump wave is simultaneously injected in the four spatial modes LP01, LP11, LP02 and LP31 of a 1.8-km long graded-index few-mode fiber together with three independent signals in the fundamental mode. By means of three parallel phase-matched FD-IFWM interactions, these initial signals are then simultaneously spatially and frequency converted from the fundamental mode to specific high-order modes. The influence of the differential modal group delay is also investigated and shows that the walk-off between the spatially multiplexed signals significantly limits the bandwidth of the conversion process for telecom applications.

The automated analysis of flow cytometry measurements is an active research field. We introduce a new algorithm, referred to as CytOpT, using regularized optimal transport to directly estimate the different cell population proportions from a biological sample characterized with flow cytometry measurements. We rely on the regularized Wasserstein metric to compare cytometry measurements from different samples, thus accounting for possible mis-alignment of a given cell population across sample (due to technical variability from the technology of measurements). In this work, we rely on a supervised learning technique based on the Wasserstein metric that is used to estimate an optimal re-weighting of class proportions in a mixture model from a source distribution (with known segmentation into cell sub-populations) to fit a target distribution with unknown segmentation. Due to the high-dimensionality of flow cytometry data, we use stochastic algorithms to approximate the regularized Wasserstein metric to solve the optimization problem involved in the estimation of optimal weights representing the cell population proportions in the target distribution. Several flow cytometry data sets are used to illustrate the performances of CytOpT that are also compared to those of existing algorithms for automatic gating based on supervised learning., Comment: 25 pages, 17 figures

We have been monitoring the metal-poor Population II giant, HD 122563, for radial velocity variations since 2016 using the SONG telescope on Tenerife. We have detected the global seismic quantity, numax, which provides information related to the stellar parameters. By combining these data with complementary data, we derive a new precise surface gravity, radius and distance to the star. Our results are corroborated by using the parallax from Gaia DR2. We present these results and some of their implications., Comment: Proceedings of the French Astronomy Society Meeting, SF2A, June 2019; v2: typo in reported numax in Table, authors corrected

This paper is concerned by the problem of selecting an optimal sampling set of sensors over a network of time series for the purpose of signal recovery at non-observed sensors with a minimal reconstruction error. The problem is motivated by applications where time-dependent graph signals are collected over redundant networks. In this setting, one may wish to only use a subset of sensors to predict data streams over the whole collection of nodes in the underlying graph. A typical application is the possibility to reduce the power consumption in a network of sensors that may have limited battery supplies. We propose and compare various data-driven strategies to turn off a fixed number of sensors or equivalently to select a sampling set of nodes. We also relate our approach to the existing literature on sensor selection from multivariate data with a (possibly) underlying graph structure. Our methodology combines tools from multivariate time series analysis, graph signal processing, statistical learning in high-dimension and deep learning. To illustrate the performances of our approach, we report numerical experiments on the analysis of real data from bike sharing networks in different cities.

We report on the generation of four spatially multiplexed picosecond 40-GHz pulse trains in a km-long 6-LP multimode optical fiber. The principle of operation is based on the parallel nonlinear compression of initial beat-signals into well separated pulse trains owing to intra-modal multiple four-wave mixings. A series of four 40-GHz dual-frequency beatings at different wavelengths are simultaneously injected into the LP01, LP11, LP02 and LP12 modes of a 1.8-km long graded-index few-mode fiber. The combined effects of Kerr nonlinearity and anomalous chromatic dispersion lead to the simultaneous generation of four spatially multiplexed frequency combs which correspond in the temporal domain to the compression of these beat-signals into picosecond pulses. The temporal profiles of the output pulse-trains demultiplexed from each spatial mode show that well-separated picosecond pulses with negligible pedestals are then generated., Comment: arXiv admin note: text overlap with arXiv:2004.01485

We report on the experimental generation of spatially multiplexed picosecond 40-GHz pulse trains at telecommunication wavelengths by simultaneous intra-modal multiple four wave mixing and intermodal cross-phase modulation in km-long bi-modal and 6-LP-mode graded-index few-mode fibers. More precisely, an initial beat-signal injected into the fundamental mode is first nonlinearly compressed into well-separated pulses by means of an intra-modal multiple four-wave mixing process, while several group-velocity matched continuous-wave probe signals are injected into higher-order modes in such a way to develop similar pulsed profile thanks to an intermodal cross-phase modulation interaction. Specifically, by simultaneously exciting three higher-order modes (LP11, LP02 and LP31) of a 6-LP-mode fiber along group-velocity matched wavelengths with the fundamental mode, four spatially multiplexed 40-GHz picosecond pulse-trains are generated at selective wavelengths with negligible cross-talks between all the modes.

A magnetized bead in a magnetic field seeks to minimize its magnetic free energy by aligning its magnetic moment with the field direction and by moving towards the maximum of the field's intensity. However, when the bead is coupled to a substrate it is forced to roll. The two otherwise independent degrees of freedom, translation and rotation, become tightly coupled giving rise to subtle and often counterintuitive effects. Here we investigate one such, easily reproducible, yet stunning effect : A neodymium bead placed on top of a laboratory magnetic stirrer. When the stirrer's magnet spins at slow rates the bead naturally follows the field. However, surprisingly, at high spinning rates the bead suddenly inverts its direction and runs, to the surprise of the observer, in the opposite direction, against the driving field direction.This effect, experimentally investigated in [J.Magn.Magn.Matter, 476, 376-381, (2019)], is here comprehensively studied, with numerical simulations and a theoretical approach complementing experimental observations., Comment: 10 pages

Convective motions at the stellar surface generate a stochastic colored noise source in the radial velocity (RV) data. This noise impedes the detection of small exoplanets. Moreover, the unknown statistics (amplitude, distribution) related to this noise make it difficult to estimate the false alarm probability (FAP) for exoplanet detection tests. In this paper, we investigate the possibility of using 3D magneto-hydrodynamical simulations (MHD) of stellar convection to design detection methods that can provide both a reliable estimate of the FAP and a high detection power. We tested the realism of 3D simulations in producing solar RV by comparing them with the observed disk integrated velocities taken by the GOLF instrument on board the SOHO spacecraft. We presented a new detection method based on periodograms standardized by these simulated time series, applying several detection tests to these standarized periodograms. The power spectral density of the 3D synthetic convective noise is consistent with solar RV observations for short periods. For regularly sampled observations, the analytic expressions of FAP derived for several statistical tests applied to the periodogram standardized by 3D simulation noise are accurate. The adaptive tests considered in this work (Higher-Criticism, Berk-Jones), which are new in the exoplanet field, may offer better detection performance than classical tests (based on the highest periodogram value) in the case of multi-planetary systems and planets with eccentric orbits. 3D MHD simulations are now mature enough to produce reliable synthetic time series of the convective noise affecting RV data. These series can be used to access to the statistics of this noise and derive accurate FAP of tests that are a critical element in the detection of exoplanets down to the cm/s level., Comment: Accepted for publication in Astronomy and Astrophysics

The Q & U Bolometric Interferometer for Cosmology, QUBIC, is an innovative experiment designed to measure the polarization of the Cosmic Microwave Background and in particular the signature left therein by the inflationary expansion of the Universe. The expected signal is extremely faint, thus extreme sensitivity and systematic control are necessary in order to attempt this measurement. QUBIC addresses these requirements using an innovative approach combining the sensitivity of Transition Edge Sensor cryogenic bolometers, with the deep control of systematics characteristic of interferometers. This makes QUBIC unique with respect to others classical imagers experiments devoted to the CMB polarization. In this contribution we report a description of the QUBIC instrument including recent achievements and the demonstration of the bolometric interferometry performed in lab. QUBIC will be deployed at the observation site in Alto Chorrillos, in Argentina at the end of 2019., Comment: Accepted for publication in the Journal of Low Temperature Physics

Many statistical studies are concerned with the analysis of observations organized in a matrix form whose elements are count data. When these observations are assumed to follow a Poisson or a multinomial distribution, it is of interest to focus on the estimation of either the intensity matrix (Poisson case) or the compositional matrix (multinomial case) when it is assumed to have a low rank structure. In this setting, it is proposed to construct an estimator minimizing the regularized negative log-likelihood by a nuclear norm penalty. Such an approach easily yields a low-rank matrix-valued estimator with positive entries which belongs to the set of row-stochastic matrices in the multinomial case. Then, as a main contribution, a data-driven procedure is constructed to select the regularization parameter in the construction of such estimators by minimizing (approximately) unbiased estimates of the Kullback-Leibler (KL) risk in such models, which generalize Stein's unbiased risk estimation originally proposed for Gaussian data. The evaluation of these quantities is a delicate problem, and novel methods are introduced to obtain accurate numerical approximation of such unbiased estimates. Simulated data are used to validate this way of selecting regularizing parameters for low-rank matrix estimation from count data. For data following a multinomial distribution, the performances of this approach are also compared to $K$-fold cross-validation. Examples from a survey study and metagenomics also illustrate the benefits of this methodology for real data analysis.

QUBIC (Q \& U Bolometric Interferometer for Cosmology) is an international ground-based experiment dedicated in the measurement of the polarized fluctuations of the Cosmic Microwave Background (CMB). It is based on bolometric interferometry, an original detection technique which combine the immunity to systematic effects of an interferometer with the sensitivity of low temperature incoherent detectors. QUBIC will be deployed in Argentina, at the Alto Chorrillos mountain site near San Antonio de los Cobres, in the Salta province. The QUBIC detection chain consists in 2048 NbSi Transition Edge Sensors (TESs) cooled to 350mK.The voltage-biased TESs are read out with Time Domain Multiplexing based on Superconducting QUantum Interference Devices (SQUIDs) at 1 K and a novel SiGe Application-Specific Integrated Circuit (ASIC) at 60 K allowing to reach an unprecedented multiplexing (MUX) factor equal to 128. The QUBIC experiment is currently being characterized in the lab with a reduced number of detectors before upgrading to the full instrument. I will present the last results of this characterization phase with a focus on the detectors and readout system., Comment: Conference proceedings submitted to the Journal of Low Temperature Physics for LTD18

This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on the use of Wasserstein distances and tools from optimal transport to analyse such data. In particular, we highlight the benefits of using the notions of barycenter and geodesic PCA in the Wasserstein space for the purpose of learning the principal modes of geometric variation in a dataset. In this setting, we discuss existing works and we present some research perspectives related to the emerging field of statistical optimal transport.

We study the eigenvalue distribution of a GUE matrix with a variance profile that is perturbed by an additive random matrix that may possess spikes. Our approach is guided by Voiculescu's notion of freeness with amalgamation over the diagonal and by the notion of deterministic equivalent. This allows to derive a fixed point equation to approximate the spectral distribution of certain deformed GUE matrices with a variance profile and to characterize the location of potential outliers in such models in a non-asymptotic setting. We also consider the singular values distribution of a rectangular Gaussian random matrix with a variance profile in a similar setting of additive perturbation. We discuss the application of this approach to the study of low-rank matrix denoising models in the presence of heteroscedastic noise, that is when the amount of variance in the observed data matrix may change from entry to entry. Numerical experiments are used to illustrate our results.

Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional data. However, current random forest approaches are not flexible enough to handle heterogeneous data such as curves, images and shapes. In this paper, we introduce Fr\'echet trees and Fr\'echet random forests, which allow to handle data for which input and output variables take values in general metric spaces. To this end, a new way of splitting the nodes of trees is introduced and the prediction procedures of trees and forests are generalized. Then, random forests out-of-bag error and variable importance score are naturally adapted. A consistency theorem for Fr\'echet regressogram predictor using data-driven partitions is given and applied to Fr\'echet purely uniformly random trees. The method is studied through several simulation scenarios on heterogeneous data combining longitudinal, image and scalar data. Finally, one real dataset about air quality is used to illustrate the use of the proposed method in practice.

The nearby metal-poor giant HD122563 is an important astrophysical laboratory for which to test stellar atmospheric and interior physics. It is also a benchmark star for which to calibrate methods to apply to large scale surveys. Recently it has been remeasured using various methodologies given the new high precision instruments at our disposal. However, inconsistencies in the observations and models have been found. In order to better characterise this star we have been measuring its radial velocities since 2016 using the Hertzsprung telescope (SONG network node). In this work we report the first detections of sun-like oscillations in this star, and to our knowledge, a detection in the most metal-poor giant to date. We apply the classical seismic scaling relation to derive a new surface gravity of $\log g_{\nu} = 1.39 \pm 0.01$ dex. Constraints on the mass imposed by its PopII giant classification then yield a radius of $30.8 \pm 1.0$ R$_{\odot}$. By coupling this with recent interferometric measurements we infer a distance to the star of 306 $\pm$ 9 pc. Data from the Gaia mission corroborates the distance hypothesis ($d_{\rm GDR2}$ = 290 $\pm$ 5 pc), and thus the updated fundamental parameters. We confirm the validity of the seismic scaling relation without corrections for surface gravity in metal-poor and evolved star regimes. The small discrepancy of 0.04 dex reduces to 0.02 dex by applying corrections to the scaling relations. The new constraints on the HR diagram ($L_{\odot} = 381 \pm 26$) reduce the disagreement between the stellar parameters and evolution models, however, a discrepancy still exists. Fine-tuned stellar evolution calculations show that this can be reconciled by changing the mixing-length parameter by an amount (--0.35) that is in agreement with predictions from recent 3D simulations and empirical results., Comment: Accepted for publication in A&A