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We present an analysis of the structure, kinematics, and chemo-dynamical properties of the Milky Way bulge using data from OGLE, APOGEE, and Gaia. Firstly, we identified 2,156 ab-type RR Lyrae stars (RRabs) from OGLE-IV, then through their apocenters derived from orbital integration, we distinguished three populations: the central bulge RRabs, the inner bulge RRabs and halo interlopers. Inner bulge RRabs kinematically align with the Galactic bar, while central bulge RRabs show slower rotation with lower velocity dispersion, which do not trace the bar. Higher velocity dispersion stars were identified as halo interlopers. Then, orbital analysis of 28,188 APOGEE Red Clump and Red Giant Branch stars revealed kinematic properties consistent with RRabs, and chemical abundance distribution displayed a bimodal stellar density pattern, suggesting complex star evolution histories and also slightly different star formation histories for the inner bulge and central bulge. The differences in the density distribution on the $|\mathrm{Z}|_{\text{max}}$-eccentricity plane for the central bulge, inner bulge, and halo regions are clearly detected. Finally, the chemodynamical analysis of 301,485 Gaia DR3 red giants without orbital integration indicated that metal-rich bulge stars form a bar-like structure, while metal-poor bulge stars are dominated by velocity dispersion. It is found that the classification of bulge stars based on orbital parameters, rather than solely on metallicity, provides a more accurate population separation. Our results also support that secular evolution of the Galactic disk is the primary origin of the bulge, and boxy/peanut (B-P) bulge population might be more dominant than X-shape bulge population., Comment: 24 pages, 20 figures

We study the structure, interstellar absorption, color-magnitude diagrams, kinematics, and dynamical state of embedded star clusters in the star-forming region associated with the giant molecular cloud G174+2.5. Our investigation is based on photometric data from the UKIDSS Galactic Plane Survey catalog and astrometric data from the Gaia DR3 catalogs. First, we recover all the known embedded clusters and candidate clusters in the region using surface density maps. Then, for the detected clusters, we determine their general parameters: the center positions, radii, number of stars, and reddening. To evaluate the reddening, we use both the NICEST algorithm and the Q-method. Both methods produce consistent extinction maps in the regions of the four studied clusters. However, the Q-method yields a much smaller color scatter in the CMD. For four clusters in particular (S235~North-West, S235~A-B-C, S235~Central, and S235~East1+East2), we were able to compute individual membership probabilities, the cluster distances, the cluster masses, and their average proper motions. By building on these results, we have studied the clusters' kinematics and dynamics. Moreover, we estimate the mass of the gas component and the star formation efficiency (SFE) in the regions of these four clusters. Finally, we provide an estimate of the total energy of the stellar and gas components in the area of these four clusters to determine whether the clusters are bound (here we consider a `cluster' as the system `stars + gas'). The gravitational bound strongly depends on the region for which we estimate the gas mass. If we consider the mass of the entire cloud, all these four clusters turn out to be bound., Comment: 30 pages, 16 figures, accepted for publication in the Astronomical Journal

In this study we address whether the age--metallicity relation (AMR) deviates from the expected trend of metallicity increasing smoothly with age. We also show the presence (or absence) of two populations, as recently claimed using a relatively small dataset. Moreover, we studied the Milky Way thin disk's chemical evolution using solar twins, including the effect of radial migration and accretion events. In particular, we exploited high-resolution spectroscopy of a large sample of solar twins in tandem with an accurate age determination to investigate the Milky Way thin disk age--metallicity relationship. Additionally, we derived the stars' birth radius and studied the chemical evolution of the thin disk. We discovered that statistical and selection biases can lead to a misinterpretation of the observational data. An accurate accounting of all the uncertainties led us to detect no separation in the AMR into different populations for solar twins around the Sun (-0.3 < [Fe/H] < 0.3 dex). This lead us to the conclusion that the thin disk was formed relatively smoothly. For the main scenario of the Milky Way thin disk formation, we suggest that the main mechanism for reaching today's chemical composition around the Sun is radial migration with the possible contribution of well-known accretion events such as Gaia-Enceladus/Sausage (GES) and Sagittarius (Sgr).

Logic Tensor Networks (LTN) is a Neuro-Symbolic framework that effectively incorporates deep learning and logical reasoning. In particular, LTN allows defining a logical knowledge base and using it as the objective of a neural model. This makes learning by logical reasoning possible as the parameters of the model are optimized by minimizing a loss function composed of a set of logical formulas expressing facts about the learning task. The framework learns via gradient-descent optimization. Fuzzy logic, a relaxation of classical logic permitting continuous truth values in the interval [0,1], makes this learning possible. Specifically, the training of an LTN consists of three steps. Firstly, (1) the training data is used to ground the formulas. Then, (2) the formulas are evaluated, and the loss function is computed. Lastly, (3) the gradients are back-propagated through the logical computational graph, and the weights of the neural model are changed so the knowledge base is maximally satisfied. LTNtorch is the fully documented and tested PyTorch implementation of Logic Tensor Networks. This paper presents the formalization of LTN and how LTNtorch implements it. Moreover, it provides a basic binary classification example., Comment: 5 pages, 2 figures

The advent of powerful neural classifiers has increased interest in problems that require both learning and reasoning. These problems are critical for understanding important properties of models, such as trustworthiness, generalization, interpretability, and compliance to safety and structural constraints. However, recent research observed that tasks requiring both learning and reasoning on background knowledge often suffer from reasoning shortcuts (RSs): predictors can solve the downstream reasoning task without associating the correct concepts to the high-dimensional data. To address this issue, we introduce rsbench, a comprehensive benchmark suite designed to systematically evaluate the impact of RSs on models by providing easy access to highly customizable tasks affected by RSs. Furthermore, rsbench implements common metrics for evaluating concept quality and introduces novel formal verification procedures for assessing the presence of RSs in learning tasks. Using rsbench, we highlight that obtaining high quality concepts in both purely neural and neuro-symbolic models is a far-from-solved problem. rsbench is available at: https://unitn-sml.github.io/rsbench.

The Li abundance observed in pre-main sequence and main sequence late-type stars is strongly age-dependent, but also shows a complex pattern depending on several parameters, such as rotation, chromospheric activity and metallicity. The best way to calibrate these effects, with the aim of studying Li as an age indicator for FGK stars, is to calibrate coeval groups of stars, such as open clusters (OCs) and associations. We present a considerable target sample of 42 OCs and associations, ranging from 1 Myr to 5 Gyr, observed within the Gaia-ESO survey (GES), and using the latest data provided by GES iDR6 and the most recent release of Gaia that was then available, EDR3. As part of this study, we update and improve the membership analysis for all 20 OCs presented in our previous article. We perform detailed membership analyses for all target clusters to identify likely candidates, using all available parameters provided by GES and based on numerous criteria: from radial velocity distributions, to the astrometry and photometry provided by Gaia, to gravity indicators, [Fe/H] metallicity, and Li content. We obtain updated lists of cluster members for the whole target sample, as well as a selection of Li-rich giant contaminants obtained as an additional result of the membership process. Each selection of cluster candidates was thoroughly contrasted with numerous existing membership studies using data from Gaia to ensure the most robust results. These final cluster selections will be used in the third and last paper of this series, which reports the results of a comparative study characterising the observable Li dispersion in each cluster and analysing its dependence on several parameters, allowing us to calibrate a Li-age relation and obtain a series of empirical Li envelopes for key ages in our sample., Comment: 83 pages, 246 figures. To be published in A&A, accepted January 27, 2024

We use a Kernel Density Estimator method to evaluate the stellar velocity dispersion in the open cluster NGC 2571. We derive the 3-D velocity dispersion using both proper motions as extracted from Gaia DR3 and single epoch radial velocities as obtained with the instrument FLAMES at ESO VLT. The mean-square velocity along the line-of-sight is found to be larger than the one in the tangential direction by a factor in the interval [6,8]. We argue that the most likely explanation for such an occurrence is the presence of a significant quantity of unresolved binary and multiple stars in the radial velocity sample. Special attention should be paid to single line spectroscopic binaries (SB1) since in this case we observe the spectral lines of the primary component only, and therefore the derived radial velocity is not the velocity of the binary system center of mass. To investigate this scenario, we performed numerical experiments at varying the fractional abundance of SB1 in the observed sample. These experiments show that the increase of the mean-square radial velocity depends actually on the fractional abundance of SB1 to a power in the range of [0.39,0.45]. We used the 3-D velocity dispersion obtained by the dispersions in the tangential directions and the assumption that the radial velocity dispersion is the same as a tangential one to estimate the virial cluster mass and the cluster mass taking into account the gravitational field of the Galaxy and the non-stationarity of the cluster. These estimates are $650\pm30 \; M_\odot$ and $310\pm80 \; M_\odot$, respectively, and they are in substantial agreement with the photometric cluster mass., Comment: 16 pages, 7 figures, accepted for publication in the Astronomical Journal

Building on the recent release of a new \emph{Gaia}-based blue straggler star catalog in Galactic open star clusters (OCs), we explored the properties of these stars in a cluster sample spanning a wide range in fundamental parameters. We employed \emph{Gaia} EDR3 to assess the membership of any individual blue or yellow straggler to their parent cluster. We then made use of the \texttt{ASteCA} code to estimate the fundamental parameters of the selected clusters, in particular, the binary fraction. With all this at hand, we critically revisited the relation of the blue straggler population and the latter. For the first time, we found a correlation between the number of blue stragglers and the host cluster binary fraction and binaries. This supports the hypothesis that binary evolution is the most viable scenario of straggler formation in Galactic star clusters. The distribution of blue stragglers in the Gaia color-magnitude diagram was then compared with a suite of composite evolutionary sequences derived from binary evolutionary models that were run by exploring a range of binary parameters: age, mass ratio, period, and so forth. The excellent comparison between the bulk distribution of blue stragglers and the composite evolutionary sequences loci further supports the binary origin of most stragglers in OCs and paves the way for a detailed study of individual blue stragglers, Comment: 15 pages, in press in Astronomy and Astrophysics

AIMS. We derive the morphology of the stellar component in the outer halo volume, and search for possible overdensities due to substructures therein. METHODS. We made use of some of the data releases of the spectroscopic survey LAMOST DR8-DR9 in tandem with distance determinations for two subsamples, that is, of K-giants and M-giants, respectively, making up 60,000 stars. These distance are obtained through Bayesian techniques that derive absolute magnitudes as a function of measured spectroscopic parameters. Our calculation of the density from these catalogues requires: (1) derivation of the selection function; and (2) a correction for the convolution of the distance errors, which we carried out with Lucy's inversion of the corresponding integral equation. RESULTS. The stellar density distribution of the outer halo (distance to the Galactic centre, $r_G$, of between 25 and 90 kpc) is a smooth monotonously decreasing function with a dependence of approximately $\rho \propto r_G^{-n}$, with $n=4.6\pm 0.4$ for K-giants and $n=4.5\pm 0.2$ for M-giants, and with a insignificant oblateness. The value of $n$ is independent of the angular distance to the Sagittarius tidal stream plane, which is what would be expected if such a stream did not exist in the anticenter positions or had a negligible imprint in the density distribution in the outer halo. Apart from random fluctuations or minor anomalies in some lines of sight, we do not see substructures superimposed in the outer halo volume within the resolution that we are using and limited by the error bars. This constrains the mass of over- and under-densities in the outer halo to be of $\lesssim 10^3$ M$_\odot $/deg$^2$, whereas the total mass of the stellar halo, including inner and outer parts, is $\sim 7\times 10^8$ M$_\odot $., Comment: 11 pages, 14 figures, accepted to be published in A&A

It has long been recognized that it is not enough for a Recommender System (RS) to provide recommendations based only on their relevance to users. Among many other criteria, the set of recommendations may need to be diverse. Diversity is one way of handling recommendation uncertainty and ensuring that recommendations offer users a meaningful choice. The literature reports many ways of measuring diversity and improving the diversity of a set of recommendations, most notably by re-ranking and selecting from a larger set of candidate recommendations. Driven by promising insights from the literature on how to incorporate versatile Large Language Models (LLMs) into the RS pipeline, in this paper we show how LLMs can be used for diversity re-ranking. We begin with an informal study that verifies that LLMs can be used for re-ranking tasks and do have some understanding of the concept of item diversity. Then, we design a more rigorous methodology where LLMs are prompted to generate a diverse ranking from a candidate ranking using various prompt templates with different re-ranking instructions in a zero-shot fashion. We conduct comprehensive experiments testing state-of-the-art LLMs from the GPT and Llama families. We compare their re-ranking capabilities with random re-ranking and various traditional re-ranking methods from the literature. We open-source the code of our experiments for reproducibility. Our findings suggest that the trade-offs (in terms of performance and costs, among others) of LLM-based re-rankers are superior to those of random re-rankers but, as yet, inferior to the ones of traditional re-rankers. However, the LLM approach is promising. LLMs exhibit improved performance on many natural language processing and recommendation tasks and lower inference costs. Given these trends, we can expect LLM-based re-ranking to become more competitive soon., Comment: 32 pages, 2 figures

Time crystals (TCs) are many-body systems displaying spontaneous breaking of time translation symmetry. Here, we demonstrate a TC using driven-dissipative condensates of microcavity exciton-polaritons, spontaneously formed from an incoherent particle bath. In contrast to other realizations, the TC phases can be controlled by the power of continuous-wave non-resonant optical drive exciting the condensate and optomechanical interactions with phonons. Those phases are for increasing power: (i) Larmor precession of pseudo-spins - a signature of continuous TC, (ii) locking of the frequency of precession to self-sustained coherent phonons - stabilized TC, (iii) doubling of TC frequency by phonons - a discrete TC with continuous excitation. These results establish microcavity polaritons as a platform for the investigation of time-broken symmetry in non-hermitian systems., Comment: 25 pages; 15 figures

The ubiquitous phenomenon of synchronization is inherently characteristic of dynamical dissipative non-linear systems. In particular, synchronization has been theoretically and experimentally demonstrated for exciton-polariton condensates with time-independent coupling. Unlike that case, we theoretically investigate the effects of a fixed mechanical harmonic driving, i.e., a coherent phonon population, that induces time modulation in the coupling of two coupled condensates. Our model applies both to electrically generated modulation, through coherent bulk acoustic waves, and to self-induced optomechanical vibrations. We consider linear as well as quadratic phonon-displacement-induced modulations of the polariton coupling. Peculiar asynchronously locked phases are found and analyzed in the context of synchronization and Josephson-type oscillations phenomena that appear in the non-driven case. Notably, Arnold tongues corresponding to the asynchronously locked phases emerge at condensate detunings that correspond to integer numbers of the mechanical frequency and also to rational fractions of it. Unlocked quasiperiodic and chaotic regimes can also be reached. In particular, the phonon-induced fractional locking frequencies arrange in a Farey sequence that produces a devil's staircase of the steady-state dressed detuning between the condensates. Importantly, both polariton-polariton and reservoir-polariton interactions facilitate the realization of coherent phonon-induced asynchronously locked phases. The relation to recent experiments on optomechanically driven condensates in arrays of polariton traps is discussed., Comment: 18 pages, 9 figures

With the unprecedented increase of known star clusters, quick and modern tools are needed for their analysis. In this work, we develop an artificial neural network trained on synthetic clusters to estimate the age, metallicity, extinction, and distance of $Gaia$ open clusters. We implement a novel technique to extract features from the colour-magnitude diagram of clusters by means of the QuadTree tool and we adopt a multi-band approach. We obtain reliable parameters for $\sim 5400$ clusters. We demonstrate the effectiveness of our methodology in accurately determining crucial parameters of $Gaia$ open clusters by performing a comprehensive scientific validation. In particular, with our analysis we have been able to reproduce the Galactic metallicity gradient as it is observed by high-resolution spectroscopic surveys. This demonstrates that our method reliably extracts information on metallicity from colour-magnitude diagrams (CMDs) of stellar clusters. For the sample of clusters studied, we find an intriguing systematic older age compared to previous analyses present in the literature. This work introduces a novel approach to feature extraction using a QuadTree algorithm, effectively tracing sequences in CMDs despite photometric errors and outliers. The adoption of ANNs, rather than Convolutional Neural Networks, maintains the full positional information and improves performance, while also demonstrating the potential for deriving clusters' parameters from simultaneous analysis of multiple photometric bands, beneficial for upcoming telescopes like the Vera Rubin Observatory. The implementation of ANN tools with robust isochrone fit techniques could provide further improvements in the quest for open clusters' parameters., Comment: 24 pages, 15 figures, Accepted in The Astronomical Journal. Temporally, data produced in this work are available at https://phisicslollo0.github.io/cavallo23.html

In this study we estimate the stellar ages of LAMOST DR8 Red Giant Branch (RGB) stars based on the Gradient Boosting Decision Tree algorithm (GBDT). We used 2,643 RGB stars extracted from the APOKASC-2 astero-seismological catalog as training data-set. After selecting the parameterses ([$\alpha$/Fe], [C/Fe], T$_{eff}$, [N/Fe], [C/H], log g) highly correlated with age using GBDT, we apply the same GBDT method to the new catalog of more than 590,000 stars classified as RGB stars. The test data-set shows that the median relative error is around 11.6$\%$ for the method. We also compare the predicted ages of RGB stars with other studies (e.g., based on APOGEE), and find systematic differences. The final uncertainty is about 15 to 30$\%$ compared to open clusters' ages. Then we present the spatial distribution of the RGB sample having an age determination, which could recreate the expected result, and discuss systematic biases. All these diagnostics show that one can apply the GBDT method to other stellar samples to estimate atmospheric parameters and age., Comment: 17 pages, 17 figures, Accepted for publication in The Astrophysical Journal

Detailed analysis of kinematics of the Milky Way disk in the solar neighborhood based on the GAIA DR3 catalog reveals the existence of peculiarities in the stellar velocity distribution perpendicular to the galactic plane. We study the influence of resonances -- the outer Lindblad resonance and the outer vertical Lindblad resonance -- of a rotating bar with stellar oscillations perpendicular to the plane of the disk, and their role in shaping the spatial and the velocity distributions of stars. We find that the $Z$ and $V_Z$ distributions of stars with respect to $L_Z$ are affected by the outer Lindblad resonance. The existence of bar resonance with stellar oscillations perpendicular to the plane of the disk is demonstrated for a long (large semi-axis 5 kpc) and fast rotating bar with $\Omega_{b}= 60.0$ $km~s^{-1}~kpc^{-1}$. We show also that, in the model with the long and fast rotating bar, some stars in the 2:1 OLR region deviate far from their original places, entering the bar region. A combination of resonance excitation of stellar motions at the 2:1 OLR region together with strong interaction of the stars with the bar potential leads to the formation of the group of 'escapees', i.e., stars that deviate in $R$ and $Z$ -- directions at large distances from the resonance region. Simulations, however, do not demonstrate any noticeable effect on $V_Z$-distribution of stars in the solar neighborhood, Comment: 21 pages, 12 figures