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The Gaia-ESO Survey is a public spectroscopic survey that has targeted $\gtrsim10^5$ stars covering all major components of the Milky Way from the end of 2011 to 2018, delivering its public final release in May 2022. Unlike other spectroscopic surveys, Gaia-ESO is the only survey that observed stars across all spectral types with dedicated, specialised analyses: from O ($T_\mathrm{eff} \sim 30,000-52,000$~K) all the way to K-M ($\gtrsim$3,500~K). The physics throughout these stellar regimes varies significantly, which has previously prohibited any detailed comparisons between stars of significantly different type. In the final data release (internal data release 6) of the Gaia-ESO Survey, we provide the final database containing a large number of products such as radial velocities, stellar parameters and elemental abundances, rotational velocity, and also, e.g., activity and accretion indicators in young stars and membership probability in star clusters for more than 114,000 stars. The spectral analysis is coordinated by a number of Working Groups (WGs) within the Survey, which specialise in the various stellar samples. Common targets are analysed across WGs to allow for comparisons (and calibrations) amongst instrumental setups and spectral types. Here we describe the procedures employed to ensure all Survey results are placed on a common scale to arrive at a single set of recommended results for all Survey collaborators to use. We also present some general quality and consistency checks performed over all Survey results., Comment: A&A accepted, minor revision, 36 pages, 38 figures

MITICA (Megavolt ITER Injector & Concept Advancement), the full scale prototype of ITER Heating Neutral Beam, is under realization at the Neutral Beam Test Facility (Padova, Italy). It is designed to deliver 16.5 MW to ITER plasma, obtained by accelerating negative Deuterium ions up to 1 MeV for a total ion current of 40 A and then neutralized. MITICA Acceleration Power Supply is composed of several non-standard equipment, beyond industrial standard for insulation voltage level (-1 MVdc) and dimensions. Voltage withstand tests (up to 1.265 MVdc) have been performed in five subsequent steps (from 2018 to 2019), according to the installation progress, after connecting equipment belonging to different procurements. During integrated commissioning, started in 2021, two breakdowns occurred in a position of the HV plant not still identified, so they could be occurred either in air or in SF6. To identify the locations of possible weak insulation points, the existing diagnostics for partial discharge detection (the precursor of breakdowns) as a first step have been improved on air-insulated parts by consisting in a set of instrumentation, like capacitive probes and off-the-shelf instruments for AC application (acoustic and electromagnetic sensors). The paper deals with the instruments qualification to assess their suitability for DC usage and then with the investigation performed in MITICA, in particular: 1) sensitivity assessment campaign, with artificially produced corona effect to identify the minimum threshold of each diagnostics 2) voltage application to MITICA plant, moving the instrumentation around equipment and increasing progressively the voltage looking for corona phenomena to identify possible weak insulation points., Comment: Nine pages, twelve figures, accepted manuscript of a paper published in Fusion Engineering and Design

PBC J2333.9-2343 is a giant radio galaxy at z = 0.047 with a bright central core associated to a blazar nucleus. If the nuclear blazar jet is a new phase of the jet activity, then the small orientation angle suggest a dramatic change of the jet direction. We present observations obtained between September 2018 and January 2019 (cadence larger than three days) with Effeslberg, SMARTS-1.3m, ZTF, ATLAS, Swift, and Fermi-LAT, and between April-July 2019 (daily cadence) with SMARTS-1.3m and ATLAS. Large (>2x) flux increases are observed on timescales shorter than a month, which are interpreted as flaring events. The cross correlation between the SMARTS-1.3m monitoring in the NIR and optical shows that these data do not show significant time lag within the measured errors. A comparison of the optical variability properties between non-blazars and blazars AGN shows that PBC J2333.9-2343 has properties more comparable to the latter. The SED of the nucleus shows two peaks, that were fitted with a one zone leptonic model. Our data and modelling shows that the high energy peak is dominated by External Compton from the dusty torus with mild contribution from Inverse Compton from the jet. The derived jet angle of 3 degrees is also typical of a blazar. Therefore, we confirm the presence of a blazar-like core in the center of this giant radio galaxy, likely a Flat Spectrum Radio Quasar with peculiar properties., Comment: Accepted for publication in MNRAS. 15 pages, 6 figures, 2 appendix including tables and figures

Very metal-poor stars contain crucial information on the Milky Way's infancy. In our previous study \citep{Plotnikova_2022} we derived a mean age of $\sim$ 13.7 Gyr for a sample of these stars in the Sun's vicinity. In this work, we investigate the chemical and kinematics properties of these stars with the goal of obtaining some insights on their origin and their parent population. We did not find any Al-Mg anti-correlation, which lead us to the conclusion that these stars did not form in globular clusters, while the detailed analysis of their orbital parameters reveals that these stars are most probably associated with the pristine Bulge of the Milky Way. We then sketch a scenario for the formation of the Milky Way in which the first structure to form was the Bulge through rapid collapse. The other components have grown later on, with a significant contribution of accreted structures., Comment: 13 pages, 10 figures, accepted for publication in the Astrophysical Journal

We make use of recent estimates for the parameters of the Milky Way's halo globular clusters and study the influence of the galactic bar on the dynamics of these clusters by computing their orbits. We use both an axisymmetric and non-axisymmetric galactic potentials, which include the rotating elongated bar/bulge structure. We account for observational errors both in the positions and in the velocities of the globular clusters and explore the influence of the bar on cluster's evolution. This is contained in the angular momentum-total energy plane, (Lz,E), which is widely exploited as an indicator of the groups of globular clusters that originated from the same accretion event. Particular attention is devoted to the Gaia-Sausage/Enceladus and Pontus structures identified recently as two independent accretion events. Our study shows that it is not possible to identify GSE and Pontus as different merger events., Comment: 17 pages, 9 figures

UNICEF Innocenti's Report Card 17 explores how the 43 Organisation for Economic Co-operation and Development (OECD) and/or the European Union (EU) countries are faring in providing healthy environments for children. Do children have clean water to drink? Do they have good-quality air to breathe? Are their homes free of lead and mould? How many children live in overcrowded homes? How many have access to green play spaces, safe from road traffic? Data show that a nation's wealth does not guarantee a healthy environment. Far too many children are deprived of a healthy home, irreversibly damaging their current and future well-being. Beyond children's immediate environments, over-consumption in some of the world's richest countries is destroying children's environments globally. This threatens both children worldwide and future generations. To provide all children with safe and healthy environments, governments, policymakers, businesses and all stakeholders are called to act on a set of policy recommendations. The report focuses on the following questions: (1) How do environmental factors affect children's well-being? (2) How are many of the world's richest countries faring in terms of providing a healthy environment in which children can live, develop and thrive? and (3) What actions can these countries take to improve the environments in which children live? [This report was written with contributions from Dominic Richardson, Gunilla Olsson, Celine Little, Dagna Rams, Gro Dehli Villanger, Nicole Quattrini, Tim Huijts, Mirza Balaj and Terje Eikemo.]

Predicting future resource demand in Cloud Computing is essential for optimizing the trade-off between serving customers' requests efficiently and minimizing the provisioning cost. Modelling prediction uncertainty is also desirable to better inform the resource decision-making process, but research in this field is under-investigated. In this paper, we propose univariate and bivariate Bayesian deep learning models that provide predictions of future workload demand and its uncertainty. We run extensive experiments on Google and Alibaba clusters, where we first train our models with datasets from different cloud providers and compare them with LSTM-based baselines. Results show that modelling the uncertainty of predictions has a positive impact on performance, especially on service level metrics, because uncertainty quantification can be tailored to desired target service levels that are critical in cloud applications. Moreover, we investigate whether our models benefit transfer learning capabilities across different domains, i.e. dataset distributions. Experiments on the same workload datasets reveal that acceptable transfer learning performance can be achieved within the same provider (because distributions are more similar). Also, domain knowledge does not transfer when the source and target domains are very different (e.g. from different providers), but this performance degradation can be mitigated by increasing the training set size of the source domain.

The Gaia-ESO survey sample of massive OB stars in the Carina Nebula consists of 234 stars. The addition of brighter sources from the Galactic O-Star Spectroscopic Survey and additional sources from the literature allows us to create the most complete census of massive OB stars done so far in the region. It contains a total of 316 stars, being 18 of them in the background and four in the foreground. Of the 294 stellar systems in Car OB1, 74 are of O type, 214 are of non-supergiant B type and 6 are of WR or non-O supergiant (II to Ia) spectral class. We identify 20 spectroscopic binary systems with an O-star primary, of which 6 are reported for the first time, and another 18 with a B-star primary, of which 13 are new detections. The average observed double-lined binary fraction of O-type stars in the surveyed region is 0.35, which represents a lower limit. We find a good correlation between the spectroscopic n-qualifier and the projected rotational velocity of the stars. The fraction of candidate runaways among the stars with and without the n-qualifier is 4.4% and 2.4%, respectively, although non resolved double-lined binaries can be contaminating the fast rotators sample., Comment: Accepted for publication in A&A, 62 pages, 8 figures

In this study, we continue our project to search for unresolved binary and multiple systems in open clusters exploiting the photometric diagram (H-W2)-W1 vs W2-(BP-K) firstly introduced in \citet{Malofeeva+2022}. In particular, here we estimate the binary and multiple star ratios and the distribution of the component mass ratio $q$ in the Galactic clusters Alpha Persei, Praesepe, and NGC 1039. We have modified the procedure outlined in our first study \citep{Malofeeva+2022} making star counts automatic and by introducing bootstrapping for error estimation. Basing on this, we re-investigated the Pleiades star cluster in the same mass range as in our previous work and corrected an inaccuracy in the mass ratio $q$ distribution. The binary and multiple star ratio in the four clusters is then found to lie between 0.45$\pm$0.03 and 0.73$\pm$0.03. On the other hand, the ratio of systems with multiplicity more than 2 is between 0.06$\pm$0.01 and 0.09$\pm$0.02. The distribution of the component mass ratio $q$ is well fitted with a Gaussian having the mode between 0.22$\pm$0.04 and 0.52$\pm$0.01 and the dispersion between 0.10$\pm$0.02 and 0.35$\pm$0.07. All clusters show a large number of the very low-mass secondary components in the binary systems with primary components below 0.5 $M_{\odot}$., Comment: 16 pages, 12 figures, accepted for publication in the Astronomical Journal

The ages of the oldest and most metal-poor stars in the Milky Way bear important information on the age of the Universe and its standard model. We analyze a sample of 28 extremely metal-poor field stars in the solar vicinity culled from the literature and carefully determine their ages. To this aim, we critically make use of Gaia data to derive their distances and associated uncertainties. Particular attention has been paid to the estimate of the reddening and its effect on the derivation of stellar ages. We employed different reddenings and super-impose isochrones from different sources in the stars color-magnitude diagram built up with different photometric systems. We highlight subtle metallicity effects when using the Johnson photometry for low metallicity stars and finally adopt Gaia photometry. An automatic fitting method is devised to assign ages to each individual star taking into account the uncertainties in the input parameters. The mean age of the sample turns out to be $13.9 \pm 0.5$ Gyr using Padova isochrones, and $13.7 \pm 0.4$ Gyr using BASTI isochrones. We found also a group of very metal-poor stars ($\left[\frac{Fe}{H}\right]$: -2.7 -2.0 dex) with relatively young ages, in the range 8 --10 Gyr., Comment: 23 pages, 16 eps figures, accepted for publication in the Astrophysical Journal

We report the identification of a set of old super metal-rich dwarf stars with orbits of low eccentricity that reach a maximum height from the Galactic plane between ~0.5-1.5 kpc. We discuss their properties to understand their origins. We use data from the internal data release 6 of the Gaia-ESO Survey. We selected stars observed at high resolution with abundances of 21 species of 18 individual elements. We apply hierarchical clustering to group the stars with similar chemical abundances within the complete chemical abundance space. According to their chemical properties, this set of super metal-rich stars can be arranged into five subgroups. Four seem to follow a chemical enrichment flow, where nearly all abundances increase in lockstep with Fe. The fifth subgroup shows different chemical characteristics. All subgroups have the following features: median ages of the order of 7-9 Gyr, Solar or sub-Solar [Mg/Fe] ratios, maximum height between 0.5-1.5 kpc, low eccentricities, and a detachment from the expected metallicity gradient with guiding radius. The high metallicity of our stars is incompatible with a formation in the Solar neighbourhood. Their dynamic properties agree with theoretical expectations that these stars travelled from the inner Galaxy due to blurring and, most importantly, to churning. We suggest that most of this population's stars originated in the Milky Way's inner regions (inner disc and/or the bulge) and later migrated to the Solar neighbourhood. The region from where the stars originated had a complex chemical enrichment history, with contributions from supernovae types Ia and II and possibly asymptotic giant branch stars., Comment: 18 pages, 13 figures. Accepted for publication in A&A. Version after language proofs. The catalogue remains to be released. Abridged abstract to fit arxiv's requirements

The Gaia-ESO Survey (GES) is a large public spectroscopic survey that was carried out using the multi-object FLAMES spectrograph at the Very Large Telescope. The survey provides accurate radial velocities, stellar parameters, and elemental abundances for ~115,000 stars in all Milky Way components. In this paper we describe the method adopted in the final data release to derive lithium equivalent widths (EWs) and abundances. Lithium EWs were measured using two different approaches for FGK and M-type stars, to account for the intrinsic differences in the spectra. For FGK stars, we fitted the lithium line using Gaussian components, while direct integration over a predefined interval was adopted for M-type stars. Care was taken to ensure continuity between the two regimes. Abundances were derived using a new set of homogeneous curves of growth that were derived specifically for GES, and which were measured on a synthetic spectral grid consistently with the way the EWs were measured. The derived abundances were validated by comparison with those measured by other analysis groups using different methods. Lithium EWs were measured for ~40,000 stars, and abundances could be derived for ~38,000 of them. The vast majority of the measures (80%) have been obtained for stars in open cluster fields. The remaining objects are stars in globular clusters, or field stars in the Milky Way disc, bulge, and halo. The GES dataset of homogeneous lithium abundances described here will be valuable for our understanding of several processes, from stellar evolution and internal mixing in stars at different evolutionary stages to Galactic evolution., Comment: 15 pages, 15 figures. Accepted by Astronomy & Astrophysics

Binary stars are recognized to be important in driving the dynamical evolution of stellar systems and also in determining some of their observational features. In this study, we explore the role that binary stars have in modulating the estimates of the velocity dispersion of stellar systems. To this aim, we developed a tool which allows to investigate the dependence of synthetic velocity dispersion on a number of crucial quantities characterizing the binary content: binary fraction and the distributions of their mass ratio, eccentricity and semi-major axis. As an application, we evaluate the impact that binary stars have on the estimation of the dynamical mass of dwarf spheroidal and ultra-faint dwarf galaxies, finding that it can be particularly relevant, especially for low mass and low density systems. These results bear profound implications for the interpretation of the measured velocity dispersion in such systems, since it weakens or relieves the claim for the need of large amounts of dark matter., Comment: 15 pages, 7 figures, accepted for publication in the Astrophysical Journal

The Gaia-ESO Public Spectroscopic Survey is an ambitious project designed to obtain astrophysical parameters and elemental abundances for 100,000 stars, including large representative samples of the stellar populations in the Galaxy, and a well-defined sample of 60 (plus 20 archive) open clusters. We provide internally consistent results calibrated on benchmark stars and star clusters, extending across a very wide range of abundances and ages. This provides a legacy data set of intrinsic value, and equally a large wide-ranging dataset that is of value for homogenisation of other and future stellar surveys and Gaia's astrophysical parameters. This article provides an overview of the survey methodology, the scientific aims, and the implementation, including a description of the data processing for the GIRAFFE spectra. A companion paper (arXiv:2206.02901) introduces the survey results. Gaia-ESO aspires to quantify both random and systematic contributions to measurement uncertainties. Thus all available spectroscopic analysis techniques are utilised, each spectrum being analysed by up to several different analysis pipelines, with considerable effort being made to homogenise and calibrate the resulting parameters. We describe here the sequence of activities up to delivery of processed data products to the ESO Science Archive Facility for open use. The Gaia-ESO Survey obtained 202,000 spectra of 115,000 stars using 340 allocated VLT nights between December 2011 and January 2018 from GIRAFFE and UVES. The full consistently reduced final data set of spectra was released through the ESO Science Archive Facility in late 2020, with the full astrophysical parameters sets following in 2022., Comment: 38 pages. A&A in press

We present a spectroscopic analysis of the GIRAFFE and UVES data collected by the Gaia-ESO survey for the young open cluster NGC 3293. Archive spectra from the same instruments obtained in the framework of the `VLT-FLAMES survey of massive stars' are also analysed. Atmospheric parameters, non-LTE chemical abundances for six elements, or variability information are reported for a total of about 160 B stars spanning a wide range in terms of spectral types (B1 to B9.5) and rotation rate (up to 350 km/s). We take advantage of the multi-epoch observations to detect several binary systems or intrinsically line-profile variables. A deconvolution algorithm is used to infer the current, true (deprojected) rotational velocity distribution. We find a broad, Gaussian-like distribution peaking around 200-250 km/s. Although some stars populate the high-velocity tail, most stars in the cluster appear to rotate far from critical. We discuss the chemical properties of the cluster, including the low occurrence of abundance peculiarities in the late B stars and the paucity of objects showing CN-cycle burning products at their surface. We argue that the former result can largely be explained by the inhibition of diffusion effects because of fast rotation, while the latter is generally in accord with the predictions of single-star evolutionary models under the assumption of a wide range of initial spin rates at the onset of main-sequence evolution. However, we find some evidence for a less efficient mixing in two quite rapidly rotating stars that are among the most massive objects in our sample. Finally, we obtain a cluster age of ~20 Myrs through a detailed, star-to-star correction of our results for the effect of stellar rotation. This is significantly older than previous estimates from turn-off fitting that fully relied on classical, non-rotating isochrones. [abridged], Comment: 29 pages, 24 figures, accepted for publication in A&A

In the last 15 years different ground-based spectroscopic surveys have been started (and completed) with the general aim of delivering stellar parameters and elemental abundances for large samples of Galactic stars, complementing Gaia astrometry. Among those surveys, the Gaia-ESO Public Spectroscopic Survey (GES), the only one performed on a 8m class telescope, was designed to target 100,000 stars using FLAMES on the ESO VLT (both Giraffe and UVES spectrographs), covering all the Milky Way populations, with a special focus on open star clusters. This article provides an overview of the survey implementation (observations, data quality, analysis and its success, data products, and releases), of the open cluster survey, of the science results and potential, and of the survey legacy. A companion article (Gilmore et al.) reviews the overall survey motivation, strategy, Giraffe pipeline data reduction, organisation, and workflow. The GES has determined homogeneous good-quality radial velocities and stellar parameters for a large fraction of its more than 110,000 unique target stars. Elemental abundances were derived for up to 31 elements for targets observed with UVES. Lithium abundances are delivered for about 1/3 of the sample. The analysis and homogenisation strategies have proven to be successful; several science topics have been addressed by the Gaia-ESO consortium and the community, with many highlight results achieved. The final catalogue has been released through the ESO archive at the end of May 2022, including the complete set of advanced data products. In addition to these results, the Gaia-ESO Survey will leave a very important legacy, for several aspects and for many years to come., Comment: Accepted for publication in Astronomy and Astrophysics. 30 pages, 30 figures, 4 tables

We present a detailed analysis of kinematics of the Milky Way disk in solar neighborhood using GAIA DR3 catalog. To determine the local kinematics of the stellar disks of the Milky Way galaxy we use a complete sample of 278,228 red giant branch (RGB) stars distributed in a cylinder, centered at the Sun with a 1 kpc radius and half-height of 0.5 kpc. We determine separately the kinematical properties of RGB stars for each Galactic hemisphere in search for possible asymmetries. The kinematical properties of the RGB stars reveal the existence of two kinematically distinct components: the thin disk with mean velocities ${V_R}, {V_{\phi}}, {V_Z}$ of about -1, -239, 0 km s$^{-1}$ correspondingly and velocity dispersions $\sigma_R, \sigma_{\phi}, \sigma_Z$ of 31, 20 and 11 km s$^{-1}$, and the Thick disk with mean velocities components of about +1, -225, 0 km s$^{-1}$, and velocity dispersions of 49, 35, and 22 km s$^{-1}$. We find that up to 500 pc height above/below the galactic plane, Thick disk stars comprise about half the stars of the disk. Such high amount of RGB stars with Thick disk kinematics points at the secular evolution scenario origin for the Thick disk of the Milky Way galaxy., Comment: 14 pages, 9 figures

The recent rise in deep learning technologies fueled innovation and boosted scientific research. Their achievements enabled new research directions for deep generative modeling (DGM), an increasingly popular approach that can create novel and unseen data, starting from a given data set. As the technology shows promising applications, many ethical issues also arise. For example, their misuse can enable disinformation campaigns and powerful phishing attempts. Research also indicates different biases affect deep learning models, leading to social issues such as misrepresentation. In this work, we formulate a novel setting to deal with similar problems, showing that a repurposed anomaly detection system effectively generates novel data, avoiding generating specified unwanted data. We propose Variational Auto-encoding Binary Classifiers (V-ABC): a novel model that repurposes and extends the Auto-encoding Binary Classifier (ABC) anomaly detector, using the Variational Auto-encoder (VAE). We survey the limitations of existing approaches and explore many tools to show the model's inner workings in an interpretable way. This proposal has excellent potential for generative applications: models that rely on user-generated data could automatically filter out unwanted content, such as offensive language, obscene images, and misleading information., Comment: Accepted for presentation at the IJCNN at IEEE World Congress on Computational Intelligence (WCCI) 2022 and for publication in the conference proceedings published by IEEE. NOT camera ready

Galactic star clusters are known to harbour a significant amount of binary stars, yet their role in the dynamical evolution of the cluster as a whole is not comprehensively understood. We investigated the influence of binary stars on the total mass estimate for the case of the moderately populated Galactic star cluster NGC 225. The analysis of multi-epoch radial velocities of the 29 brightest cluster members, obtained over two observational campaigns, in 1990-1991 and in 2019-2020, yields a value of binary fraction of $\alpha =0.52$ (15 stars out of 29). Using theoretical isochrones and Monte Carlo simulations we found that the cluster mass increases at least 1.23 times when binaries are properly taken into account. By combining Gaia EDR3 photometric data with our spectroscopic observations, we derived estimates of NGC 225 fundamental parameters as follows: mean radial velocity $ = -9.8 \pm 0.7$ km s$^{-1}$, $\log(\tau)$=8.0-8.2 dex, distance $ D = 676 \pm 22$ pc, and colour excess $E(B-V) = 0.29 \pm 0.01$ mag.

The 6.4 keV Fe Ka emission line is a ubiquitous feature in X-ray spectra of AGN, and its properties track the interaction between the variable primary X-ray continuum and the surrounding structure from which it arises. We clarify the nature and origin of the narrow Fe Ka emission using X-ray spectral, timing, and imaging constraints, plus possible correlations to AGN and host galaxy properties, for 38 bright nearby AGN ($z<0.5$) from the BAT AGN Spectroscopic Survey. Modeling Chandra and XMM-Newton spectra, we computed line full-width half-maxima (FWHMs) and constructed Fe Ka line and 2-10 keV continuum light curves. The FWHM provides one estimate of the Fe Ka emitting region size, RFeKa, assuming virial motion. A second estimate comes from comparing the degree of correlation between the variability of the continuum and line-only light curves, compared to simulated light curves. Finally, we extracted Chandra radial profiles to place upper limits on RFeKa. We found that for 90% (21/24) of AGN with FWHM measurements, RFeKa is smaller than the fiducial dust sublimation radius, Rsub. Despite a wide range of variability properties, the constraints on the Fe Ka photon reprocessor size independently confirm that RFeKa is smaller than Rsub in 83% of AGN. Finally, the imaging analysis yields loose upper limits for all but two sources; notably, the Circinus Galaxy and NGC 1068 show significant but subdominant extended Fe Ka emission out to $\sim$100 and $\sim$800 pc, respectively. Based on independent constraints, we conclude that the majority of the narrow Fe Ka emission in typical AGN predominantly arises from regions smaller than and presumably inside Rsub, and thus it is associated either with the outer broad line region or outer accretion disk. However, the large diversity of continuum and narrow Fe Ka variability properties are not easily accommodated by a universal scenario., Comment: Accepted for publication in Astronomy and Astrophysics (A&A), 35 pages, 22 figures, 3 tables

Interpretability is having an increasingly important role in the design of machine learning algorithms. However, interpretable methods tend to be less accurate than their black-box counterparts. Among others, DNFs (Disjunctive Normal Forms) are arguably the most interpretable way to express a set of rules. In this paper, we propose an effective bottom-up extension of the popular FIND-S algorithm to learn DNF-type rulesets. The algorithm greedily finds a partition of the positive examples. The produced DNF is a set of conjunctive rules, each corresponding to the most specific rule consistent with a part of positive and all negative examples. We also propose two principled extensions of this method, approximating the Bayes Optimal Classifier by aggregating DNF decision rules. Finally, we provide a methodology to significantly improve the explainability of the learned rules while retaining their generalization capabilities. An extensive comparison with state-of-the-art symbolic and statistical methods on several benchmark data sets shows that our proposal provides an excellent balance between explainability and accuracy.