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Positional Encoder Graph Neural Networks (PE-GNNs) are a leading approach for modeling continuous spatial data. However, they often fail to produce calibrated predictive distributions, limiting their effectiveness for uncertainty quantification. We introduce the Positional Encoder Graph Quantile Neural Network (PE-GQNN), a novel method that integrates PE-GNNs, Quantile Neural Networks, and recalibration techniques in a fully nonparametric framework, requiring minimal assumptions about the predictive distributions. We propose a new network architecture that, when combined with a quantile-based loss function, yields accurate and reliable probabilistic models without increasing computational complexity. Our approach provides a flexible, robust framework for conditional density estimation, applicable beyond spatial data contexts. We further introduce a structured method for incorporating a KNN predictor into the model while avoiding data leakage through the GNN layer operation. Experiments on benchmark datasets demonstrate that PE-GQNN significantly outperforms existing state-of-the-art methods in both predictive accuracy and uncertainty quantification., Comment: 17 main text pages, 4 figures

Artificial neural networks (ANNs) are highly flexible predictive models. However, reliably quantifying uncertainty for their predictions is a continuing challenge. There has been much recent work on "recalibration" of predictive distributions for ANNs, so that forecast probabilities for events of interest are consistent with certain frequency evaluations of them. Uncalibrated probabilistic forecasts are of limited use for many important decision-making tasks. To address this issue, we propose a localized recalibration of ANN predictive distributions using the dimension-reduced representation of the input provided by the ANN hidden layers. Our novel method draws inspiration from recalibration techniques used in the literature on approximate Bayesian computation and likelihood-free inference methods. Most existing calibration methods for ANNs can be thought of as calibrating either on the input layer, which is difficult when the input is high-dimensional, or the output layer, which may not be sufficiently flexible. Through a simulation study, we demonstrate that our method has good performance compared to alternative approaches, and explore the benefits that can be achieved by localizing the calibration based on different layers of the network. Finally, we apply our proposed method to a diamond price prediction problem, demonstrating the potential of our approach to improve prediction and uncertainty quantification in real-world applications., Comment: 25 pages, 5 figures

As evidenced by recent survey results, majority of asteroids are slow rotators (P>12 h), but lack spin and shape models due to selection bias. This bias is skewing our overall understanding of the spins, shapes, and sizes of asteroids, as well as of their other properties. Also, diameter determinations for large (>60km) and medium-sized asteroids (between 30 and 60 km) often vary by over 30% for multiple reasons. Our long-term project is focused on a few tens of slow rotators with periods of up to 60 hours. We aim to obtain their full light curves and reconstruct their spins and shapes. We also precisely scale the models, typically with an accuracy of a few percent. We used wide sets of dense light curves for spin and shape reconstructions via light-curve inversion. Precisely scaling them with thermal data was not possible here because of poor infrared data: large bodies are too bright for WISE mission. Therefore, we recently launched a campaign among stellar occultation observers, to scale these models and to verify the shape solutions, often allowing us to break the mirror pole ambiguity. The presented scheme resulted in shape models for 16 slow rotators, most of them for the first time. Fitting them to stellar occultations resolved previous inconsistencies in size determinations. For around half of the targets, this fitting also allowed us to identify a clearly preferred pole solution, thus removing the ambiguity inherent to light-curve inversion. We also address the influence of the uncertainty of the shape models on the derived diameters. Overall, our project has already provided reliable models for around 50 slow rotators. Such well-determined and scaled asteroid shapes will, e.g. constitute a solid basis for density determinations when coupled with mass information. Spin and shape models continue to fill the gaps caused by various biases., Comment: Accepted to Astronomy & Astrophysics. 12 pages + appendices

We present an observational and numerical study of the borderline hyperbolic comet C/2021 O3 (PANSTARRS) performed during its recent passage through the inner Solar system. Our observations were carried out at OASI and SOAR between 2021 October and 2022 January, and reveal a low level of activity relative to which was measured for other long-period comets. In addition, we observed a decrease in brightness as the comet got closer to the Sun. Our photometric data, obtained as C/2021 O3 approached perihelion on 2022 April 21, show that the comet was much less active than what is usually expected in the cases of long-period comets, with $Af\rho$ values more in line with those of short-period comets (specifically, the Jupiter Family Comets). On the other hand, the observed increase in the value of the spectral slope as the amount of dust in the coma decreased could indicate that the smaller dust particles were being dispersed from the coma by radiation pressure faster than they were injected by possible sublimation jets. The analysis of its orbital evolution suggests that C/2021 O3 could be a dynamically old comet, or perhaps a new one masquerading as a dynamically old comet, with a likely origin in the Solar system., Comment: 8 pages, 7 figures

The objective of this work is to characterise the onset of laterally asymmetric flow of viscoelastic solutions around a confined microfluidic cylinder, which was encountered in a recent study [Rodrigues et al., $\textit{J. Non-Newton. Fluid Mech.}$ $\textbf{289}$, 104406 (2020)]. To this end, two non-Newtonian fluids were employed in the same micro-geometry. Two microchannels were studied, both with a cylinder of diameter 75 $\mathrm{\mu}$m, aspect ratio (channel height over width) of 0.37 and blockage ratio (cylinder diameter over channel width) of 0.28, differing only on the width of the pressure taps, located 500 $\mathrm{\mu}$m up- and downstream from the respective cylinder face, on opposing walls. The working fluids consist of two poly(ethylene oxide) (PEO) solutions: a weakly shear-thinning elastic fluid and an elastic shear-thinning fluid. Micro-Particle Image Velocimetry ($\mathrm{\mu}$PIV) and streak imaging techniques were used to evaluate the flow over a Weissenberg number range: $100\leq Wi\leq500$, while maintaining a low Reynolds number, $Re<1$. The elastic shear-thinning solution showed laterally asymmetric flow past the cylinder with both pressure tap designs, while with the weakly shear-thinning solution asymmetric flow was only observed with the wider pressure tap intake. In both cases, the fluids preferentially chose the cylinder/wall gap opposing the upstream pressure tap, which was found to influence the flow greatly, seemingly associated with time-dependent flow and possibly the lateral flow asymmetry itself. This work brings to light the necessary compromise between optimal pressure tap design for quality pressure measurements and minimal flow interference, due to the increased susceptibility of elastic microfluidic flows to flow perturbations.

Results from the TESS mission showed that previous studies strngly underestimated the number of slow rotators, revealing the importance of studying those asteroids. For most slowly rotating asteroids (P > 12), no spin and shape model is available because of observation selection effects. This hampers determination of their thermal parameters and accurate sizes. We continue our campaign in minimising selection effects among main belt asteroids. Our targets are slow rotators with low light-curve amplitudes. The goal is to provide their scaled spin and shape models together with thermal inertia, albedo, and surface roughness to complete the statistics. Rich multi-apparition datasets of dense light curves are supplemented with data from Kepler and TESS. In addition to data in the visible range, we also use thermal data from infrared space observatories (IRAS, Akari and WISE) in a combined optimisation process using the Convex Inversion Thermophysical Model (CITPM). This novel method has so far been applied to only a few targets, and in this work we further validate the method. We present the models of 16 slow rotators. All provide good fits to both thermal and visible data. The obtained sizes are on average accurate at the 5% precision, with diameters in the range from 25 to 145 km. The rotation periods of our targets range from 11 to 59 hours, and the thermal inertia covers a wide range of values, from 2 to <400 SI units, not showing any correlation with the period. With this work we increase the sample of slow rotators with reliable spin and shape models and known thermal inertia by 40%. The thermal inertia values of our sample do not display a previously suggested increasing trend with rotation period, which might be due to their small skin depth., Comment: Accepted to Astronomy & Astrophysics. 10 pages + appendices

Analyses of data from spectroscopic and astrometric surveys have led to conflicting results concerning the vertical characteristics of the Milky Way. Ages are often used to provide clarity, but typical uncertainties of $>$ 40\,\% restrict the validity of the inferences made. Using the \textit{Kepler} APOKASC sample for context, we explore the global population trends of two K2 campaign fields (3 and 6), which extend further vertically out of the Galactic plane than APOKASC. We analyse the properties of red giant stars utilising three asteroseismic data analysis methods to cross-check and validate detections. The Bayesian inference tool PARAM is used to determine the stellar masses, radii and ages. Evidence of a pronounced red giant branch bump and an [$\alpha$/Fe] dependence on the position of the red clump is observed from the radii distribution of the K2 fields. Two peaks in the age distribution centred at $\sim$5 and and $\sim$12 Gyr are found using a sample with $\sigma_{\rm{age}}$ $<$ 35\,\%. In a comparison with \textit{Kepler}, we find the older peak to be more prominent for K2. This age bimodality is also observed based on a chemical selection of low- ($\leq$ 0.1) and high- ($>$ 0.1) [$\alpha$/Fe] stars. As a function of vertical distance from the Galactic mid-plane ($|Z|$), the age distribution shows a transition from a young to old stellar population with increasing $|Z|$ for the K2 fields. Further coverage of campaign targets with high resolution spectroscopy is required to increase the yield of precise ages achievable with asteroseismology., Comment: 17 pages, 16 figures. Accepted to MNRAS 01/08/2019. Updated manuscript

Very metal-poor halo stars are the best candidates for being among the oldest objects in our Galaxy. Samples of halo stars with age determination and detailed chemical composition measurements provide key information for constraining the nature of the first stellar generations and the nucleosynthesis in the metal-poor regime.} Age estimates are very uncertain and are available for only a small number of metal-poor stars. Here we present the first results of a pilot program aimed at deriving precise masses, ages and chemical abundances for metal-poor halo giants using asteroseismology, and high-resolution spectroscopy. We obtained high-resolution UVES spectra for four metal-poor RAVE stars observed by the K2 satellite. Seismic data obtained from K2 light curves helped improving spectroscopic temperatures, metallicities and individual chemical abundances. Mass and ages were derived using the code PARAM, investigating the effects of different assumptions (e.g. mass loss, [alpha/Fe]-enhancement). Orbits were computed using Gaia DR2 data. {The stars are found to be "normal" metal-poor halo stars (i.e. non C-enhanced), with an abundance pattern typical of old stars (i.e. alpha and Eu-enhanced), and with masses in the 0.80-1.0 M_sun range. The inferred model-dependent stellar ages are found to range from 7.4 to 13.0 Gyr, with uncertainties of ~ 30%-35%. We also provide revised masses and ages for metal-poor stars with Kepler seismic data from APOGEE survey and a set of M4 stars. {The present work shows that the combination of asteroseismology and high-resolution spectroscopy provides precise ages in the metal-poor regime. Most of the stars analysed in the present work (covering the metallicity range of [Fe/H] ~ -0.8 to -2 dex), are very old >9 Gyr (14 out of 19 stars ), and all of them are older than > 5 Gyr (within the 68 percentile confidence level)., Comment: 21 pages, 19 figures. Accepted

Bayesian simultaneous estimation of nonparametric quantile curves is a challenging problem, requiring a flexible and robust data model whilst satisfying the monotonicity or noncrossing constraints on the quantiles. This paper presents the use of the pyramid quantile regression method in the spline regression setting. In high dimensional problems, the choice of the pyramid locations becomes crucial for a robust parameter estimation. In this work we derive the optimal {pyramid locations which then allows us to propose an efficient} adaptive block-update MCMC scheme for posterior computation. Simulation studies show the proposed method provides estimates with significantly smaller errors and better empirical coverage probability when compared to existing alternative approaches. We illustrate the method with three real applications.

Deciphering the assembly history of the Milky Way is a formidable task, which becomes possible only if one can produce high-resolution chrono-chemo-kinematical maps of the Galaxy. Data from large-scale astrometric and spectroscopic surveys will soon provide us with a well-defined view of the current chemo-kinematical structure of the Milky Way, but will only enable a blurred view on the temporal sequence that led to the present-day Galaxy. As demonstrated by the (ongoing) exploitation of data from the pioneering photometric missions CoRoT, Kepler, and K2, asteroseismology provides the way forward: solar-like oscillating giants are excellent evolutionary clocks thanks to the availability of seismic constraints on their mass and to the tight age-initial-mass relation they adhere to. In this paper we identify five key outstanding questions relating to the formation and evolution of the Milky Way that will need precise and accurate ages for large samples of stars to be addressed, and we identify the requirements in terms of number of targets and the precision on the stellar properties that are needed to tackle such questions. By quantifying the asteroseismic yields expected from PLATO for red-giant stars, we demonstrate that these requirements are within the capabilities of the current instrument design, provided that observations are sufficiently long to identify the evolutionary state and allow robust and precise determination of acoustic-mode frequencies. This will allow us to harvest data of sufficient quality to reach a 10% precision in age. This is a fundamental pre-requisite to then reach the more ambitious goal of a similar level of accuracy, which will only be possible if we have to hand a careful appraisal of systematic uncertainties on age deriving from our limited understanding of stellar physics, a goal which conveniently falls within the main aims of PLATO's core science., Comment: 17 pages, 9 figures, accepted for publication in Astronomical Notes

Nowadays large spectroscopic surveys, like the Gaia-ESO Survey (GES), provide unique stellar databases for better investigating the formation and evolution of our Galaxy. Great attention must be paid to the accuracy of the basic stellar properties derived: large uncertainties in stellar parameters lead to large uncertainties in abundances, distances and ages. Asteroseismology has a key role in this context: when seismic information is combined with information derived from spectroscopic analysis, highly precise constraints on distances, masses, extinction and ages of Red Giants can be obtained. In the light of this promising joint-action, we started the CoRoT-GES collaboration. We present a set of 1,111 CoRoT stars, observed by GES from December 2011 to July 2014, these stars belong to the CoRoT field LRc01, pointing at the inner Galactic Disk. Among these stars, 534 have reliable global seismic parameters. By combining seismic informations and spectroscopy, we derived precise stellar parameters, ages, kinematic and orbital parameters and detailed element abundances for this sample of stars. We also show that, thanks to asteroseismology, we are able to obtain a higher precision than what can be achieved by the standard spectroscopic means. This sample of CoRoT Red Giants, spanning Galactocentric distances from 5 to 8 kpc and a wide age interval (1-13 Gyrs), provides us a representative sample for the inner disk population., Comment: 6 pages, 4 figures, to appear in Astronomische Nachrichten, special issue "Reconstruction the Milky Way's History: Spectroscopic surveys, Asteroseismology and Chemo-dynamical models", Guest Editors C. Chiappini, J. Montalban, and M. Steffen, AN 2016 (in press)

We present a set of 87 RAVE stars with detected solar like oscillations, observed during Campaign 1 of the K2 mission (RAVE K2-C1 sample). This dataset provides a useful benchmark for testing the gravities provided in RAVE Data Release 4 (DR4), and is key for the calibration of the RAVE Data Release 5 (DR5). In the present work, we use two different pipelines, GAUFRE (Valentini et al. 2013) and Sp_Ace (Boeche & Grebel 2016), to determine atmospheric parameters and abundances by fixing log(g) to the seismic one. Our strategy ensures highly consistent values among all stellar parameters, leading to more accurate chemical abundances. A comparison of the chemical abundances obtained here with and without the use of seismic log(g) information has shown that an underestimated (overestimated) gravity leads to an underestimated (overestimated) elemental abundance (e.g. [Mg/H] is underestimated by ~0.25 dex when the gravity is underestimated by 0.5 dex). We then perform a comparison between the seismic gravities and the spectroscopic gravities presented in the RAVE DR4 catalogue, extracting a calibration for log(g) of RAVE giants in the colour interval 0.50<(J - Ks)<0.85. Finally, we show a comparison of the distances, temperatures, extinctions (and ages) derived here for our RAVE K2-C1 sample with those derived in RAVE DR4 and DR5.DR5 performs better than DR4 thanks to the seismic calibration, although discrepancies can still be important for objects for which the difference between DR4/DR5 and seismic gravities differ by more than ~0.5 dex. The method illustrated in this work will be used for analysing RAVE targets present in the other K2 campaigns, in the framework of Galactic Archaeology investigations., Comment: 20 pages, 27 figures, accepted

Using combined asteroseismic and spectroscopic observations of 418 red-giant stars close to the Galactic disc plane (6 kpc $

Quantile regression models provide a wide picture of the conditional distributions of the response variable by capturing the effect of the covariates at different quantile levels. In most applications, the parametric form of those conditional distributions is unknown and varies across the covariate space, so fitting the given quantile levels simultaneously without relying on parametric assumptions is crucial. In this work we propose a Bayesian model for simultaneous linear quantile regression. More specifically, we propose to model the conditional distributions by using random probability measures known as quantile pyramids. Unlike many existing approaches, our framework allows us to specify meaningful priors on the conditional distributions, whilst retaining the flexibility afforded by the nonparametric error distribution formulation. Simulation studies demonstrate the flexibility of the proposed approach in estimating diverse scenarios, generally outperforming other competitive methods. The method is particularly promising for modelling the extremal quantiles. Applications to linear splines and extreme value analysis are also explored through real data examples.

In a companion paper, we have presented the combined asteroseismic-spectroscopic dataset obtained from CoRoT lightcurves and APOGEE infra-red spectra for 678 solar-like oscillating red giants in two fields of the Galactic disc (CoRoGEE). We have measured chemical abundance patterns, distances, and ages of these field stars which are spread over a large radial range of the Milky Way's disc. Here we show how to simulate this dataset using a chemodynamical Galaxy model. We also demonstrate how the observation procedure influences the accuracy of our estimated ages., Comment: 5 pages, 6 figures. To appear in Astronomische Nachrichten, special issue "Reconstruction the Milky Way's History: Spectroscopic surveys, Asteroseismology and Chemo-dynamical models", Guest Editors C. Chiappini, J. Montalb\'an, and M. Steffen

With the advent of the space missions CoRoT and Kepler, it has become feasible to determine precise asteroseismic masses and ages for large samples of red-giant stars. In this paper, we present the CoRoGEE dataset -- obtained from CoRoT lightcurves for 606 red giant stars in two fields of the Galactic disc which have been co-observed for an ancillary project of APOGEE. We have used the Bayesian parameter estimation code PARAM to calculate distances, extinctions, masses, and ages for these stars in a homogeneous analysis, resulting in relative statistical uncertainties of $\sim2\%$ in distance, $\sim4\%$ in radius, $\sim9\%$ in mass and $\sim25\%$ in age. We also assess systematic age uncertainties due to different input physics and mass loss. We discuss the correlation between ages and chemical abundance patterns of field stars over a large radial range of the Milky Way's disc (5 kpc $

Context. The availability of asteroseismic constraints for a large sample of red giant stars from the CoRoT and Kepler missions paves the way for various statistical studies of the seismic properties of stellar populations. Aims. We use the first detailed spectroscopic study of 19 CoRoT red-giant stars (Morel et al 2014) to compare theoretical stellar evolution models to observations of the open cluster NGC 6633 and field stars. Methods. In order to explore the effects of rotation-induced mixing and thermohaline instability, we compare surface abundances of carbon isotopic ratio and lithium with stellar evolution predictions. These chemicals are sensitive to extra-mixing on the red-giant branch. Results. We estimate mass, radius, and distance for each star using the seismic constraints. We note that the Hipparcos and seismic distances are different. However, the uncertainties are such that this may not be significant. Although the seismic distances for the cluster members are self consistent they are somewhat larger than the Hipparcos distance. This is an issue that should be considered elsewhere. Models including thermohaline instability and rotation-induced mixing, together with the seismically determined masses can explain the chemical properties of red-giants targets. However, with this sample of stars we cannot perform stringent tests of the current stellar models. Tighter constraints on the physics of the models would require the measurement of the core and surface rotation rates, and of the period spacing of gravity-dominated mixed modes. A larger number of stars with longer times series, as provided by Kepler or expected with Plato, would help for ensemble asteroseismology., Comment: Accepted 03/05/2015

We report the discovery of a group of apparently young CoRoT red-giant stars exhibiting enhanced [alpha/Fe] abundance ratios (as determined from APOGEE spectra) with respect to Solar values. Their existence is not explained by standard chemical evolution models of the Milky Way, and shows that the chemical-enrichment history of the Galactic disc is more complex. We find similar stars in previously published samples for which isochrone-ages could be robustly obtained, although in smaller relative numbers, which could explain why these stars have not received prior attention. The young [alpha/Fe]-rich stars are much more numerous in the CoRoT-APOGEE (CoRoGEE) inner-field sample than in any other high-resolution sample available at present, as only CoRoGEE can explore the inner-disc regions and provide ages for its field stars. The kinematic properties of the young [$\alpha$/Fe]-rich stars are not clearly thick-disc like, despite their rather large distances from the Galactic mid-plane. Our tentative interpretation of these and previous intriguing observations in the Milky Way is that these stars were formed close to the end of the Galactic bar, near corotation -- a region where gas can be kept inert for longer times, compared to other regions shocked more frequently by the passage of spiral arms. Moreover, that is where the mass return from older inner-disc stellar generations should be maximal (according to an inside-out disc-formation scenario), further diluting the in-situ gas. Other possibilities to explain these observations (e.g., a recent gas-accretion event) are also discussed., Comment: Letter in press in Astronomy and Astrophysics (5 pages, 4 figures + 2 pages Appendix)

In this paper, we study arithmetical and topological properties for a class of Rauzy fractals ${\mathcal R}_a$ given by the polynomial $x^3- ax^2+x-1$ where $a \geq 2$ is an integer. In particular, we prove the number of neighbors of ${\mathcal R}_a$ in the periodic tiling is equal to $8$. We also give explicitly an automaton that generates the boundary of ${\mathcal R}_a$. As a consequence, we prove that ${\mathcal R}_2$ is homeomorphic to a topological disk.