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This study introduces a novel frequency-based data-driven controller for adaptive optics, using power spectral density for optimization while ensuring stability criteria. It addresses disturbance rejection, command amplitude constraints and system transfer functions through convex optimization to obtain an optimal control in an infinite input response filter form. Evaluated within the SAXO+ project, it demonstrates efficacy under diverse atmospheric conditions and operational scenarios. The proposed controller is tested in both standard and disentangled adaptive optics schemes, showcasing its adaptability and performance. Experimental validation is conducted using the COMPASS simulation tool, affirming the controller's promise for enhancing adaptive optics systems in real-world applications.

Wavefunction forms based on products of electron pairs are usually constructed as closed-shell singlets, which is insufficient when the molecular state has a nonzero spin or when the chemistry is determined by $d$- or $f-$electrons. A set of two-electron forms are considered as explicit couplings of second-quantized operators to open-shell singlets. Geminal wavefunctions are constructed and their structure is elaborated. Numerical results for small model systems clearly demonstrate improvement over closed-shell singlet pairs.

Exoplanets form from circumstellar protoplanetary discs whose fundamental properties (notably their extent, composition, mass, temperature and lifetime) depend on the host star properties, such as their mass and luminosity. B-stars are among the most massive stars and their protoplanetary discs test extreme conditions for exoplanet formation. This paper investigates the frequency of giant planet companions around young B-stars (median age of 16 Myr) in the Scorpius-Centaurus association, the closest association containing a large population of B-stars. We systematically search for massive exoplanets with the high-contrast direct imaging instrument SPHERE using the data from the BEAST survey, that targets an homogeneous sample of young B-stars from the wide Sco-Cen association. We derive accurate detection limits in case of non-detections. We found evidence in previous papers for two substellar companions around 42 stars. The masses of these companions are straddling the ~13 Jupiter mass deuterium burning limit but their mass ratio with respect to their host star is close to that of Jupiter. We derive a frequency of such massive planetary mass companions around B stars of 11-5+7%, accounting for the survey sensitivity. The discoveries of substellar companions bcen b and mu2sco B happened after only few stars in the survey had been observed, raising the possibility that massive Jovian planets might be common around B-stars. However our statistical analysis show that the occurrence rate of such planets is similar around B-stars and around solar-type stars of similar age, while B-star companions exhibit low mass ratios and larger semi-major axis., Comment: Accepted in A&A

This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network improves scalability and convergence rates compared to the single level method. Tested on a Poisson equation with Dirichlet boundary conditions, the two-level deep DDM demonstrates superior performance, maintaining efficient convergence regardless of the number of subdomains. This advance provides a more scalable and effective approach to solving complex partial differential equations with machine learning., Comment: Preprint proceeding format

We revisit the standard ``telescoping sum'' argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of the requested accuracy $\epsilon$. While bounds obtained using the standard argument typically are of the form $\mathcal{O}(\epsilon^{-\alpha})$ for some positive $\alpha$, the refined results are of the form $o(\epsilon^{-\alpha})$. We then explore to which known algorithms our refined bounds are applicable and finally describe an example showing how close the standard and refined bounds can be., Comment: 10 ages, 1 figure

A new decoder for the SIF test problems of the CUTEst collection is described, which produces problem files allowing the computation of values and derivatives of the objective function and constraints of most \cutest\ problems directly within ``native'' Matlab, Python or Julia, without any additional installation or interfacing with MEX files or Fortran programs. When used with Matlab, the new problem files optionally support reduced-precision computations.

A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity bound for finding first-order critical points. The method is noise-tolerant and the inexactness conditions required for convergence depend on the history of past steps. Applications to cases where derivative evaluation is inexact and to minimization of finite sums by sampling are discussed. Numerical experiments on large binary classification problems illustrate the potential of the new method., Comment: 32 pages, 9 figures

A parametric class of trust-region algorithms for constrained nonconvex optimization is analyzed, where the objective function is never computed. By defining appropriate first-order stationarity criteria, we are able to extend the Adagrad method to the newly considered problem and retrieve the standard complexity rate of the projected gradient method that uses both the gradient and objective function values. Furthermore, we propose an additional iteration-dependent scaling with slightly inferior theoretical guarantees. In both cases, the bounds are essentially sharp, and curvature information can be used to compute the stepsize. Initial experimental results for noisy bound-constrained instances illustrate the benefits of the objective-free approach.

In this paper, we introduce a novel discriminative loss function with large margin in the context of Deep Learning. This loss boosts the discriminative power of neural nets, represented by intra-class compactness and inter-class separability. On the one hand, the class compactness is ensured by close distance of samples of the same class to each other. On the other hand, the inter-class separability is boosted by a margin loss that ensures the minimum distance of each class to its closest boundary. All the terms in our loss have an explicit meaning, giving a direct view of the feature space obtained. We analyze mathematically the relation between compactness and margin term, giving a guideline about the impact of the hyper-parameters on the learned features. Moreover, we also analyze properties of the gradient of the loss with respect to the parameters of the neural net. Based on this, we design a strategy called partial momentum updating that enjoys simultaneously stability and consistency in training. Furthermore, we also investigate generalization errors to have better theoretical insights. Our loss function systematically boosts the test accuracy of models compared to the standard softmax loss in our experiments.

In Vapor Cycle Systems, the mass flow sensor playsa key role for different monitoring and control purposes. However,physical sensors can be inaccurate, heavy, cumbersome, expensive orhighly sensitive to vibrations, which is especially problematic whenembedded into an aircraft. The conception of a virtual sensor, basedon other standard sensors, is a good alternative. This paper has twomain objectives. Firstly, a data-driven model using a ConvolutionalNeural Network is proposed to estimate the mass flow of thecompressor. We show that it significantly outperforms the standardPolynomial Regression model (thermodynamic maps), in terms of thestandard MSE metric and Engineer Performance metrics. Secondly,a semi-automatic segmentation method is proposed to compute theEngineer Performance metrics for real datasets, as the standard MSEmetric may pose risks in analyzing the dynamic behavior of VaporCycle Systems.

The analysis of several spectroscopic surveys indicates the presence of a bimodality between the disc stars in the abundance ratio space of [${\alpha}$/Fe] versus [Fe/H]. The two stellar groups are commonly referred to as the high-${\alpha}$ and low-${\alpha}$ sequences. Some models capable of reproducing such a bimodality, invoke the presence of a hiatus in the star formation history in our Galaxy, whereas other models explain the two sequences by means of stellar migration. Our aim is to show that the existence of the gap in the star formation rate between high-$\alpha$ and low-$\alpha$ is evident in the stars of APOGEE DR17, if one plots [Fe/$\alpha$] versus [$\alpha$/H], thus confirming previous suggestions by Gratton et al. (1996) and Fuhrmann (1998). Then we try to interpret the data by means of detailed chemical models. We compare the APOGEE DR17 red giant stars with the predictions of a detailed chemical evolution model based on the two-infall paradigm, taking also into account possible accretion of dwarf satellites. The APOGEE DR17 abundance ratios [Fe/$\alpha$] versus [$\alpha$/H] exhibit a sharp increase of [Fe/$\alpha$] at a nearly constant [$\alpha$/H] (where $\alpha$ elements considered are Mg, Si, O) during the transition between the two disc phases. This observation strongly supports the hypothesis that a hiatus in star formation occurred during this evolutionary phase. Notably, the most pronounced growth in the [Fe/$\alpha$] versus [$\alpha$/H] relation is observed for oxygen, as this element is exclusively synthesised in core-collapse supernovae. A chemical model predicting a stop in the star formation of a duration of roughly 3.5 Gyr, and where the high-$\alpha$ disc starts forming from pre-enriched gas by a previous encounter with a dwarf galaxy can well explain the observations., Comment: Accepted for publication in Astronomy and Astrophysics (A&A), 16 pages, 13 figures

We carried out very deep VLT/SPHERE imaging polarimetry of the nearby system Eps Eri based on 38.5 hours of integration time with a 600 - 900 nm broadband filter to search for polarized scattered light from a planet or from circumstellar dust using AO, coronagraphy, high precision differential polarimetry, and angular differential imaging. We have improved several data reduction and post-processing techniques and also developed new ones to further increase the sensitivity of SPHERE/ZIMPOL. The data provide unprecedented contrast limits, but no significant detection of a point source or an extended signal from circumstellar dust. For each observing epoch, we obtained a point source contrast for the polarized intensity between $2\cdot 10^{-8}$ and $4\cdot 10^{-8}$ at the expected separation of the planet Eps Eri b of 1'' near quadrature phase. The polarimetric contrast limits are about six to 50 times better than the intensity limits because polarimetric imaging is much more efficient in speckle suppression. Combining the entire 14-month data set to the search for a planet moving on a Keplerian orbit with the K-Stacker software further improves the contrast limits by a factor of about two, to about $8 \cdot 10^{-9}$ at 1''. This would allow the detection of a planet with a radius of about 2.5 Jupiter radii. The surface brightness contrast limits achieved for the polarized intensity from an extended scattering region are about 15 mag arcsec$^{-2}$ at 1'', or up to 3 mag arcsec$^{-2}$ deeper than previous limits. For Eps Eri, these limits exclude the presence of a narrow dust ring and they constrain the dust properties. This study shows that the polarimetric contrast limits for reflecting planets with SPHERE/ZIMPOL can be improved to a level $<10^{-8}$ simply by collecting more data over many nights and using the K-Stacker software., Comment: 26 pages, 20 figures, 5 tables. Accepted for publication in A&A

We measure the Out-of-domain uncertainty in the prediction of Neural Networks using a statistical notion called ``Lens Depth'' (LD) combined with Fermat Distance, which is able to capture precisely the ``depth'' of a point with respect to a distribution in feature space, without any assumption about the form of distribution. Our method has no trainable parameter. The method is applicable to any classification model as it is applied directly in feature space at test time and does not intervene in training process. As such, it does not impact the performance of the original model. The proposed method gives excellent qualitative result on toy datasets and can give competitive or better uncertainty estimation on standard deep learning datasets compared to strong baseline methods., Comment: 12 pages

Dynamical masses of young planets aged between 10 and 200 Myr detected in imaging play a crucial role in shaping models of giant planet formation. Regrettably, only a few such objects possess these characteristics. Furthermore, the evolutionary pattern of young sub-stellar companions in near-infrared colour-magnitude diagrams might diverge from free-floating objects, possibly due to differing formation processes. The recent identification of a giant planet around AF Lep, part of the beta Pic moving group (BPMG), encouraged us to re-examine these points. We considered updated dynamical masses and luminosities for the sub-stellar objects in the BPMG. In addition, we compared the properties of sub-stellar companions and free-floating objects in the BPMG and other young associations remapping the positions of the objects in the colour-magnitude diagram into a dustiness-temperature plane. We found that cold-start evolutionary models do not reproduce the mass-luminosity relation for sub-stellar companions in the BPMG. This aligns rather closely with predictions from 'hot start' scenarios and is consistent with recent planet formation models. We obtain rather good agreement with masses from photometry and the remapping approach compared to actual dynamical masses. We also found a strong suggestion that the near-infrared colour-magnitude diagram for young companions is different from that of free-floating objects belonging to the same young associations. If confirmed by further data, this last result would imply that cloud settling - which likely causes the transition between L and T spectral type - occurs at a lower effective temperature in young companions than in free-floating objects. This might tentatively be explained with a different chemical composition., Comment: Accepted on Astronomy and Astrophysics. 19 pages, 12 figures

Recently, combining high-contrast imaging and space astrometry we found that Jupiter-like (JL) planets are frequent in the beta Pic moving group (BPMG) around those stars where their orbit can be stable, prompting further analysis and discussion. We broaden our previous analysis to other young nearby associations to determine the frequency, mass, and separation of companions in general and JL in particular and their dependencies on the mass and age of the associations. We collected available data about companions including those revealed by visual observations, eclipses, spectroscopy, and astrometry. We determined search completeness and found that it is very high for stellar companions, while completeness corrections are still large for JL companions. Once these corrections are included, we found a high frequency of companions, both stellar (>0.52+/-0.03) and JL (0.57+/-0.11). The two populations are separated by a gap that corresponds to the brown dwarf desert. Within the population of massive companions, we found trends in frequency, separation, and mass ratios with stellar mass. Planetary companions pile up in the region just outside the ice line and we found them to be frequent once completeness was considered. The frequency of JL planets decreases with the overall mass and possibly the age of the association. We tentatively identify the two populations as due to disk fragmentation and core accretion, respectively. The distributions of stellar companions with a semi-major axis <1000 au is well reproduced by a simple model of formation by disk fragmentation. The observed trends with stellar mass can be explained by a shorter but much more intense phase of accretion onto the disk of massive stars and by a more steady and prolonged accretion on solar-type stars. Possible explanations for the trends in the population of JL planets with association mass and age are briefly discussed., Comment: Accepted by Astronomy and Astrophysics, 52 pages, 23 figures

Planets in binary systems are a fascinating and yet poorly understood phenomenon. Since there are only a few known large-separation systems in which both components host planets, characterizing them is a key target for planetary science. In this paper, we aim to carry out an exhaustive analysis of the interesting XO-2 system, where one component appears to be a system with only one planet, while the other has at least three planets. Over the last 9 years, we have collected 39 spectra of XO-2N and 106 spectra of XO-2S with the High Accuracy Radial velocity Planet Searcher for the Northern emisphere (HARPS-N) in the framework of the Global Architecture of Planetary Systems project, from which we derived precise radial velocity and activity indicator measurements. Additional spectroscopic data from the High Resolution Echelle Spectrometer and from the High Dispersion Spectrograph, and the older HARPS-N data presented in previous papers, have also been used to increase the total time span. We also used photometric data from TESS to search for potential transits that have not been detected yet. For our analysis, we mainly used PyORBIT, an advanced Python tool for the Bayesian analysis of RVs, activity indicators, and light curves. We found evidence for an additional long-period planet around XO-2S and characterized the activity cycle likely responsible for the long-term RV trend noticed for XO-2N. The new candidate is an example of a Jovian analog with $m\sin i \sim 3.7$ M$_J$, $a \sim 5.5$ au, and $e = 0.09$. We also analyzed the stability and detection limits to get some hints about the possible presence of additional planets. Our results show that the planetary system of XO-2S is at least one order of magnitude more massive than that of XO-2N. The implications of these findings for the interpretation of the previously known abundance difference between components are also discussed.

Aims. We aim to expand the atmospheric exploration of AF Lep b by modeling all available observations obtained with SPHERE at VLT (between 0.95-1.65, at 2.105, and 2.253 $\mu$m, and NIRC2 at Keck (at 3.8 $\mu$m) with self-consistent atmospheric models. Methods. To understand the physical properties of this exoplanet, we used ForMoSA. This forward-modeling code compares observations with grids of pre-computed synthetic atmospheric spectra using Bayesian inference methods. We used Exo-REM, an atmospheric radiative-convective equilibrium model, including the effects of non-equilibrium processes and clouds. Results. From the atmospheric modeling we derive solutions at a low effective temperature of ~750 K. Our analysis also favors a metal-rich atmosphere (>0.4) and solar to super-solar carbon-to-oxygen ratio (~0.6). We tested the robustness of the estimated values for each parameter by cross-validating our models using the leave-one-out strategy, where all points are used iteratively as validation points. Our results indicate that the photometry point at 3.8 $\mu$m strongly drives the metal-rich and super-solar carbon-to-oxygen solutions. Conclusions. Our atmospheric forward-modeling analysis strongly supports the planetary nature of AF Lep b. Its spectral energy distribution is consistent with that of a young, cold, early-T super-Jovian planet. We recover physically consistent solutions for the surface gravity and radius, which allows us to reconcile atmospheric forward modeling with evolutionary models, in agreement with the previously published complementary analysis done by retrievals. Finally, we identified that future data at longer wavelengths are mandatory before concluding about the metal-rich nature of AF Lep b., Comment: 7 pages, 7 figures, 6 tables. Accepted for publication on the 9th of January 2024 in A&A

The intrinsic variability due to the magnetic activity of young active stars is one of the main challenges in detecting and characterising exoplanets. We present a method able to model the stellar photosphere and its surface inhomogeneities (starspots) in young/active and fast-rotating stars, based on the cross-correlation function (CCF) technique, to extract information about the spot configuration of the star. Within the Global Architecture of Planetary Systems (GAPS) Project at the Telescopio Nazionale Galileo, we analysed more than 300 spectra of the young planet-hosting star V1298 Tau provided by HARPS-N high-resolution spectrograph. By applying the SpotCCF model to the CCFs we extracted the spot configuration (latitude, longitude and projected filling factor) of this star, and also provided the new RVs time series of this target. We find that the features identified in the CCF profiles of V1298 Tau are modulated by the stellar rotation, supporting our assumption that they are caused by starspots. The analysis suggests a differential rotation velocity of the star with lower rotation at higher latitudes. Also, we find that SpotCCF provides an improvement in RVs extraction with a significantly lower dispersion with respect to the commonly used pipelines, with consequent mitigation of the stellar activity contribution modulated with stellar rotation. A detection sensitivity test, by the direct injection of a planetary signal into the data, confirmed that the SpotCCF model improves the sensitivity and ability to recover planetary signals. Our method enables the modelling of the stellar photosphere, extracting the spot configuration of young/active and rapidly rotating stars. It also allows for the extraction of optimised RV time series, thereby enhancing our detection capabilities for new exoplanets and advancing our understanding of stellar activity., Comment: 18 pages, 20 figures, accepted by A&A

Context. Different theories have been developed to explain the origins and properties of close-in giant planets, but none of them alone can explain all of the properties of the warm Jupiters (WJs, Porb = 10 - 200 days). One of the most intriguing characteristics of WJs is that they have a wide range of orbital eccentricities, challenging our understanding of their formation and evolution. Aims. The investigation of these systems is crucial in order to put constraints on formation and evolution theories. TESS is providing a significant sample of transiting WJs around stars bright enough to allow spectroscopic follow-up studies. Methods. We carried out a radial velocity (RV) follow-up study of the TESS candidate TOI-4515 b with the high-resolution spectrograph HARPS-N in the context of the GAPS project, the aim of which is to characterize young giant planets, and the TRES and FEROS spectrographs. We then performed a joint analysis of the HARPS-N, TRES, FEROS, and TESS data in order to fully characterize this planetary system. Results. We find that TOI-4515 b orbits a 1.2 Gyr-old G-star, has an orbital period of Pb = 15.266446 +- 0.000013 days, a mass of Mb = 2.01 +- 0.05 MJ, and a radius of Rb = 1.09 +- 0.04 RJ. We also find an eccentricity of e = 0.46 +- 0.01, placing this planet among the WJs with highly eccentric orbits. As no additional companion has been detected, this high eccentricity might be the consequence of past violent scattering events., Comment: 20 pages, 16 figures

We investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of the numerical simulators have inconsistent dimensions across the multilevel hierarchy. This requires the introduction of grid transfer operators borrowed from multigrid methods. Starting from a simple 1D illustration, we demonstrate numerically that the resulting MLMC estimator deteriorates the estimation of high-frequency components of the discretized expectation field compared to a Monte Carlo (MC) estimator. By adapting mathematical tools initially developed for multigrid methods, we perform a theoretical spectral analysis of the MLMC estimator of the expectation of discretized random fields, in the specific case of linear, symmetric and circulant simulators. This analysis provides a spectral decomposition of the variance into contributions associated with each scale component of the discretized field. We then propose improved MLMC estimators using a filtering mechanism similar to the smoothing process of multigrid methods. The filtering operators improve the estimation of both the small- and large-scale components of the variance, resulting in a reduction of the total variance of the estimator. These improvements are quantified for the specific class of simulators considered in our spectral analysis. The resulting filtered MLMC (F-MLMC) estimator is applied to the problem of estimating the discretized variance field of a diffusion-based covariance operator, which amounts to estimating the expectation of a discretized random field. The numerical experiments support the conclusions of the theoretical analysis even with non-linear simulators, and demonstrate the improvements brought by the proposed F-MLMC estimator compared to both a crude MC and an unfiltered MLMC estimator.

Context. The study of protoplanetary disks is fundamental to understand their evolution and interaction with the surrounding environment, and to constrain planet formation mechanisms. Aims. We aim at characterising the young binary system HD 34700 A, which shows a wealth of structures. Methods. Taking advantage of the high-contrast imaging instruments SPHERE at the VLT, LMIRCam at the LBT, and of ALMA observations, we analyse this system at multiple wavelengths. We study the rings and spiral arms morphology and the scattering properties of the dust. We discuss the possible causes of all the observed features. Results. We detect for the first time, in the H${\alpha}$ band, a ring extending from $\sim$65 au to ${\sim}$120 au, inside the ring already known from recent studies. These two have different physical and geometrical properties. Based on the scattering properties, the outer ring may consist of grains of typical size $a_{out} > 4 {\mu}m$, while the inner ring of smaller grains ($a_{in} <= 0.4 {\mu m}$). Two extended logarithmic spiral arms stem from opposite sides of the disk. The outer ring appears as a spiral arm itself, with a variable radial distance from the centre and extended substructures. ALMA data confirm the presence of a millimetric dust substructure centred just outside the outer ring, and detect misaligned gas rotation patterns for HD 34700 A and B. Conclusions. The complexity of HD 34700 A, revealed by the variety of observed features, suggests the existence of one or more disk-shaping physical mechanisms. Possible scenarios, compatible with our findings, involve the presence inside the disk of a yet undetected planet of several Jupiter masses and the system interaction with the surroundings by means of gas cloudlet capture or flybys. Further observations with JWST/MIRI or ALMA (gas kinematics) could shed more light on these., Comment: Accepted for publication on A&A. 14 + 5 pages, 9 + 7 figures (text + appendix)

An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this random approximation technique does not affect the method's convergence nor its evaluation complexity for the search of an $\epsilon$-approximate first-order critical point, which is $\mathcal{O}(\epsilon^{-(p+1)/p})$, where $p$ is the order of derivatives used. A variant of the algorithm using approximate Hessian matrices is also analyzed and shown to require at most $\mathcal{O}(\epsilon^{-2})$ evaluations. Preliminary numerical tests show that the random-subspace technique can significantly improve performance on some problems, albeit, unsurprisingly, not for all., Comment: 23 pages

Radial velocity surveys suggest that the Solar System may be unusual and that Jupiter-like planets have a frequency <20% around solar-type stars. However, they may be much more common in one of the closest associations in the solar neighbourhood. Young moving stellar groups are the best targets for direct imaging of exoplanets and four massive Jupiter-like planets have been already discovered in the nearby young beta Pic Moving Group (BPMG) via high-contrast imaging, and four others were suggested via high precision astrometry by the European Space Agency's Gaia satellite. Here we analyze 30 stars in BPMG and show that 20 of them might potentially host a Jupiter-like planet as their orbits would be stable. Considering incompleteness in observations, our results suggest that Jupiter-like planets may be more common than previously found. The next Gaia data release will likely confirm our prediction., Comment: 21 pages. Final edited version published on Nature Communications available at URL: https://www.nature.com/articles/s41467-023-41665-0

We discuss the properties of companions to B stars in the Scorpius-Centaurus association (age ~15 Myr, 181 B-stars). We gathered available data combining high contrast imaging samples with evidence of companions from Gaia, from eclipsing binaries, and from spectroscopy. We evaluated the completeness of the binary search and estimated the mass and semi-major axis for all detected companions. These data provide a complete sample of stellar secondaries for separation >3 au, and they are highly informative as to closer companions. We found evidence for 200 companions around 181 stars. The fraction of single star is 15.2\pm 4.1% for stars with M_A>3.5 Msun while it is 31.5\pm 5.9% for lower-mass stars. The median semi-major axis of the orbits of the companions is smaller for B than in A stars, confirming a turn-over previously found for OB stars. The mass distribution of the very wide (a>1000 au) and closer companions is different. Very few companions of massive stars M_A>5.0 Msun have a mass below solar and even fewer are M stars with a semi-major axis <1000 au. The scarcity of low-mass companions extends throughout the whole sample. Most early B stars are in compact systems with massive secondaries, while lower-mass stars are mainly in wider systems with a larger spread in mass ratios. We interpret our results as the formation of secondaries with a semi-major axis <1000 au (about 80% of the total) by fragmentation of the disk of the primary and selective mass accretion on the secondaries. The observed trends with primary mass may be explained by a more prolonged phase of accretion episodes on the disk and by a more effective inward migration. We detected twelve new stellar companions from the BEAST survey and of a new BD companion at 9.6 arcsec from HIP74752 using Gaia data, and we discuss the cases of possible BD and low-mass stellar companions to HIP59173, HIP62058, and HIP64053., Comment: Accepted on Astronomy and Astrophysics, 31 pages, 24 figures

An edge-on debris disk was detected in 2015 around the young, nearby A0V star HD 110058. The disk showed features resembling those seen in the disk of beta Pictoris that could indicate the presence of a perturbing planetary-mass companion in the system. We investigated new and archival scattered light images of the disk in order to characterise its morphology and spectrum. In particular, we analysed the disk's warp to constrain the properties of possible planetary perturbers. Our work uses data from two VLT/SPHERE observations and archival data from HST/STIS. We measured the morphology of the disk by analysing vertical profiles along the length of the disk to extract the centroid spine position and vertical height. We extracted the surface brightness and reflectance spectrum of the disk. We detect the disk between 20 au (with SPHERE) and 150 au (with STIS), at a position angle of 159.6$^\circ\pm$0.6$^\circ$. Analysis of the spine shows an asymmetry between the two sides of the disk, with a 3.4$^\circ\pm$0.9$^\circ$ warp between ~20 au and 60 au. The disk is marginally vertically resolved in scattered light, with a vertical aspect ratio of 9.3$\pm$0.7% at 45 au. The extracted reflectance spectrum is featureless, flat between 0.95 micron and 1.1 micron, and red from 1.1 micron to 1.65 micron. The outer parts of the disk are also asymmetric with a tilt between the two sides compatible with a disk made of forward-scattering particles and seen not perfectly edge-on, suggesting an inclination of <84$^\circ$. The presence of an undetected planetary-mass companion on an inclined orbit with respect to the disk could explain the warp. The misalignment of the inner parts of the disk with respect to the outer disk suggests a warp that has not yet propagated to the outer parts of the disk, favouring the scenario of an inner perturber as the origin of the warp., Comment: 17 pages, 15 figures, 3 tables; accepted for publication in A&A

Observational data from space and ground-based campaigns reveal that the 10-30 Ma old V1298 Tau star hosts a compact and massive system of four planets. Mass estimates for the two outer giant planets point to unexpectedly high densities for their young ages. We investigate the formation of these two outermost giant planets, V1298 Tau b and e, and the present dynamical state of V1298 Tau's global architecture to shed light on the history of this young and peculiar extrasolar system. We perform detailed N-body simulations to explore the link between the densities of V1298 Tau b and e and their migration and accretion of planetesimals within the native circumstellar disk. We combine N-body simulations and the normalized angular momentum deficit (NAMD) analysis to characterize V1298 Tau's dynamical state and connect it to the formation history of the system. We search for outer planetary companions to constrain V1298 Tau's architecture and the extension of its primordial circumstellar disk. The high densities of V1298 Tau b and e suggest they formed quite distant from their host star, likely beyond the CO$_2$ snowline. The higher nominal density of V1298 Tau e suggests it formed farther out than V1298 Tau b. The current architecture of V1298 Tau is not characterized by resonant chains. Planet-planet scattering with an outer giant planet is the most likely cause for the instability, but our search for outer companions using SPHERE and GAIA observations excludes only the presence of planets more massive than 2 M$_\textrm{J}$. The most plausible scenario for V1298 Tau's formation is that the system is formed by convergent migration and resonant trapping of planets born in a compact and plausibly massive disk. The migration of V1298 Tau b and e leaves in its wake a dynamically excited protoplanetary disk and creates the conditions for the resonant chain breaking by planet-planet scattering., Comment: 19 pages, 11 figures, 5 tables. Accepted for publication on Astronomy and Astrophysics

Since 2019, the direct imaging B-star Exoplanet Abundance Study (BEAST) at SPHERE@VLT has been scanning the surroundings of young B-type stars in order to ascertain the ultimate frontiers of giant planet formation. Recently, the $17^{+3}_{-4}$ Myr HIP 81208 was found to host a close-in (~50 au) brown dwarf and a wider (~230 au) late M star around the central 2.6Msun primary. Alongside the continuation of the survey, we are undertaking a complete reanalysis of archival data aimed at improving detection performances so as to uncover additional low-mass companions. We present here a new reduction of the observations of HIP 81208 using PACO ASDI, a recent and powerful algorithm dedicated to processing high-contrast imaging datasets, as well as more classical algorithms and a dedicated PSF-subtraction approach. The combination of different techniques allowed for a reliable extraction of astrometric and photometric parameters. A previously undetected source was recovered at a short separation from the C component of the system. Proper motion analysis provided robust evidence for the gravitational bond of the object to HIP 81208 C. Orbiting C at a distance of ~20 au, this 15Mjup brown dwarf becomes the fourth object of the hierarchical HIP 81208 system. Among the several BEAST stars which are being found to host substellar companions, HIP 81208 stands out as a particularly striking system. As the first stellar binary system with substellar companions around each component ever found by direct imaging, it yields exquisite opportunities for thorough formation and dynamical follow-up studies., Comment: 12 pages, 9 figures, 5 tables. Accepted for publication as a Letter in Astronomy and Astrophysics, section 1. Letters to the Editor

This paper develops a networked federated learning algorithm to solve nonsmooth objective functions. To guarantee the confidentiality of the participants with respect to each other and potential eavesdroppers, we use the zero-concentrated differential privacy notion (zCDP). Privacy is achieved by perturbing the outcome of the computation at each client with a variance-decreasing Gaussian noise. ZCDP allows for better accuracy than the conventional $(\epsilon, \delta)$-DP and stronger guarantees than the more recent R\'enyi-DP by assuming adversaries aggregate all the exchanged messages. The proposed algorithm relies on the distributed Alternating Direction Method of Multipliers (ADMM) and uses the approximation of the augmented Lagrangian to handle nonsmooth objective functions. The developed private networked federated learning algorithm has a competitive privacy accuracy trade-off and handles nonsmooth and non-strongly convex problems. We provide complete theoretical proof for the privacy guarantees and the algorithm's convergence to the exact solution. We also prove under additional assumptions that the algorithm converges in $O(1/n)$ ADMM iterations. Finally, we observe the performance of the algorithm in a series of numerical simulations., Comment: 30 pages

The leading spectrographs used for exoplanets' sceince offer online data reduction softwares (DRS) that yield as an ancillary result the full-width at half-maximum (FWHM) of the cross-correlation function (CCF) that is used to estimate the radial velocity of the host star. The FWHM also contains information on the stellar projected rotational velocity vsini We wanted to establish a simple relationship to derive the vsini directly from the FWHM computed by the HARPS-N DRS in the case of slow-rotating solar-like stars. This may also help to recover the stellar inclination i, which in turn affects the exoplanets' parameters. We selected stars with an inclination of the spin axis compatible with 90 deg by looking at exoplanetary transiting systems with known small sky-projected obliquity: for these stars, we can presume that vsini is equal to stellar equatorial velocity veq. We derived their rotational periods from photometric time-series and their radii from SED fitting. This allowed us to recover their veq, which we could compare to the FWHM values of the CCFs obtained both with G2 and K5 spectral type masks. We obtained an empirical relation for each mask, useful for slow rotators (FWHM < 20 km/s). We applied them to 273 exoplanet-host stars observed with HARPS-N, obtaining homogeneous vsini measurements. We compared our results with the literature ones to confirm the reliability of our work, and we found a good agreement with the values found with more sophisticated methods for stars with log g > 3.5. We also tried our relations on HARPS and SOPHIE data, and we conclude that they can be used also on FWHM derived by HARPS DRS with G2 and K5 mask, and they may be adapted to the SOPHIE data as long as the spectra are taken in the high-resolution mode. We were also able to recover or constrain i for 12 objects with no prior vsini estimation., Comment: 15 pages, 16 figures, long table missing in arXiV version, accepted for publication in A\&A

Recent observations from B-star Exoplanet Abundance Study (BEAST) have illustrated the existence of sub-stellar companions around very massive stars. In this paper, we present the detection of two lower mass companions to a relatively nearby ($148.7^{+1.5}_{-1.3}$ pc), young ($17^{+3}_{-4}$ Myr), bright (V=$6.632\pm0.006$ mag), $2.58\pm0.06~ M_{\odot}$ B9V star HIP 81208 residing in the Sco-Cen association, using the Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument at the Very Large Telescope (VLT) in Chile. Analysis of the photometry obtained gives mass estimates of $67^{+6}_{-7}~M_J$ for the inner companion and $0.135^{+0.010}_{-0.013}~M_{\odot}$ for the outer companion, indicating the former to be most likely a brown dwarf and the latter to be a low-mass star. The system is compact but unusual, as the orbital planes of the two companions are likely close to orthogonal. The preliminary orbital solutions we derived for the system indicate that the star and the two companions are likely in a Kozai resonance, rendering the system dynamically very interesting for future studies., Comment: 18 pages, 14 figures, 5 tables Accepted for publication in the 10. Planets and planetary systems section of A&A

Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level methods from a block-coordinate point of view, we propose a multi-level algorithm for the solution of nonlinear optimization problems and analyze its evaluation complexity. We apply it to the solution of partial differential equations using physics-informed neural networks (PINNs) and show on a few test problems that the approach results in better solutions and significant computational savings

We propose two experiments suited for high school and/or undergraduate physics laboratory which are aimed to the discovery of the practical meaning and usefulness of the FFT analysis as a mathematical and graphical instrument, intended to discriminate different periodic signals in various situations, ranging from basic, demonstrative measurements to very complex, real-research experiments. In our proposal, quite inexpensive digital instruments can be used, yet with accurate out-of-the-box results., Comment: 7 pages, 5 figures

The demographic of circumstellar disks, the birthplaces of planets, is diverse and rich in disks featuring rings, gaps, spirals, filaments, and arcs. Many studies revealing these disk structures have focused on objects around single stars and disks in isolation. The scenario is more complex if binarity or multiplicity is involved; most stars are part of multiple systems in crowded star-forming regions. How does the presence of one or more stellar companions affect the shape and size of the circumstellar disks? Here we review the landscape of results from optical, infrared, and (sub-) millimeter observations of the effects of multiplicity on protoplanetary disks, emphasizing the demographic studies of nearby molecular clouds and the high-resolution studies of multiple disk systems., Comment: Invited review accepted in EPJ+

SARG is the high resolution spectrograph of TNG. It has been in operation since late spring 2000. SARG is a cross dispersed echelle spectrograph; it offers both single object and long slit (up to 26 arcsec) observing modes covering a spectral range from {\lambda}=0.37 up to 1 {\mu}m, with resolution ranging from R=29,000 up to R=164,000. Cross dispersion is provided by means of a selection of four grisms; interference filters may be used for the long slit mode (up to 26 arcsec). A dioptric camera images the cross dispersed spectra onto a mosaic of two 2048x4096 EEV CCDs (pixel size: 13.5 {\mu}m) allowing complete spectral coverage at all resolving power for {\AA} <0.8 {\mu}m. An iodine-absorbing cell allows to obtain high precision radial velocities. A Distributed Active Temperature Control System (DATCS) maintains constant the temperature of all spectrograph components at a preset value. Early results show that SARG works according to original specifications in terms of wavelength coverage, efficiency (measured peak efficiency is about 13%), resolution (maximum resolution R~164,000 using a 0.3 arcsec slit, R~144,000 using an image slicer), and stability (preliminary estimates of the radial velocity accuracy is ~5 m/s using the iodine cell and ~ 150 m/s without the cell)., Comment: 17 pages

A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is regularized with the square root of the current gradient and an additional term taking moderate negative curvature into account, a negative curvature step being taken only exceptionally. Practical variants have been detailed where the subspaces are chosen to be the full space, or Krylov subspaces. In the first case, the proposed method only requires the solution of a single linear system at nearly all iterations. We establish that at most $\mathcal{O}\left(|\log\epsilon|\,\epsilon^{-3/2}\right)$ evaluations of the problem's objective function and derivatives are needed for algorithms in the new class to obtain an $\epsilon$-approximate first-order minimizer, and at most $\mathcal{O}\left(|\log\epsilon|\,\epsilon^{-3}\right)$ to obtain a second-order one. Encouraging initial numerical experiments with two full-space and two Krylov-subspaces variants are finally presented., Comment: 32 pages, 2 Figure, 4 Tables

A class of multi-level algorithms for unconstrained nonlinear optimization is presented which does not require the evaluation of the objective function. The class contains the momentum-less AdaGrad method as a particular (single-level) instance. The choice of avoiding the evaluation of the objective function is intended to make the algorithms of the class less sensitive to noise, while the multi-level feature aims at reducing their computational cost. The evaluation complexity of these algorithms is analyzed and their behaviour in the presence of noise is then illustrated in the context of training deep neural networks for supervised learning applications., Comment: 29 pages, 4 figures

Aims. Using the direct imaging technique we searched for low mass companions around the star AF Lep that presents a significant proper motion anomaly (PMa) signal obtained from the comparison of Hipparcos and Gaia eDR3 catalogs. Methods. We observed AF Lep in two epochs with VLT/SPHERE using its subsystems IFS and IRDIS in the near-infrared (NIR) covering wavelengths ranging from the Y to the K spectral bands (between 0.95 and 2.3 {\mu}m). The data were then reduced using the high-contrast imaging techniques angular differential imaging (ADI) and spectral differential imaging (SDI) to be able to retrieve the signal from low mass companions of the star. Results. A faint companion was retrieved at a separation of ~0.335" from the star and with a position angle of ~70.5 deg in the first epoch and with a similar position in the second epoch. This corresponds to a projected separation of ~9 au. The extracted photometry allowed us to estimate for the companion a mass between 2 and 5 MJup. This mass is in good agreement with what is expected for the dynamic mass of the companion deduced using astrometric measures (5.2-5.5 MJup). This is the first companion with a mass well below the deuterium burning limit discovered coupling direct imaging with PMa measures. Orbit fitting done using the orvara tool allowed to further confirm the companion mass and to define its main orbital parameters., Comment: 10 pages, 8 Figures, accepted for publication on A&A