A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discuss the prior distribution of the parameter and we generate samples from the posterior distribution by using Markov Chain Monte Carlo (MCMC) methods. Finally, we illustrate our method analyzing real data associated with COVID-19 in a specific region located at the south of Spain.Ministerio de Economía y Competitividad. Gobierno de España; 2014-2020 ERDF Operational Programme; Consejería de Economía, Conocimiento, Empresas y Universidad.Junta de Andalucí

On a property of Lorenz curves with monotone elasticity and its application to the study of inequality by using tax data

The Lorenz curve is the most widely used graphical tool for describing and comparing inequality of income distributions. In this paper, we show that the elasticity of this curve is an indicator of the effect, in terms of inequality, of a truncation of the income distribution. As an application, we consider tax returns as equivalent to the truncation from below of a hypothetical income distribution. Then, we replace this hypothetical distribution by the income distribution obtained from a general household survey and use the dual Lorenz curve to anticipate this effect

Corona-Australis DANCe I. Revisiting the census of stars with Gaia-DR2 data

Context. Corona-Australis is one of the nearest regions to the Sun with recent and ongoing star formation, but the current picture of its stellar (and substellar) content is not complete yet. Aims. We take advantage of the second data release of the Gaia space mission to revisit the stellar census and search for additional members of the young stellar association in Corona-Australis. Methods. We applied a probabilistic method to infer membership probabilities based on a multidimensional astrometric and photometric data set over a field of 128 deg(2) around the dark clouds of the region. Results. We identify 313 high-probability candidate members to the Corona-Australis association, 262 of which had never been reported as members before. Our sample of members covers the magnitude range between G greater than or similar to 5 mag and G less than or similar to 20 mag, and it reveals the existence of two kinematically and spatially distinct subgroups. There is a distributed "off-cloud" population of stars located in the north of the dark clouds that is twice as numerous as the historically known "on-cloud" population that is concentrated around the densest cores. By comparing the location of the stars in the HR-diagram with evolutionary models, we show that these two populations are younger than 10 Myr. Based on their infrared excess emission, we identify 28 Class II and 215 Class III stars among the sources with available infrared photometry, and we conclude that the frequency of Class II stars (i.e. "disc-bearing" stars) in the on-cloud region is twice as large as compared to the off-cloud population. The distance derived for the Corona-Australis region based on this updated census is d = 149.4(-0.4)(+0.4) pc, which exceeds previous estimates by about 20 pc. Conclusions. In this paper we provide the most complete census of stars in Corona-Australis available to date that can be confirmed with Gaia data. Furthermore, we report on the discovery of an extended and more evolved population of young stars beyond the region of the dark clouds, which was extensively surveyed in the past

Kalkayotl: A cluster distance inference code

Context. The high-precision parallax data of the Gaia mission allows for significant improvements in the distance determination to stellar clusters and their stars. In order to obtain accurate and precise distance determinations, systematics such as parallax spatial correlations need to be accounted for, especially with regard to stars in small sky regions. Aims. Our aim is to provide the astrophysical community with a free and open code designed to simultaneously infer cluster parameters (i.e., distance and size) and distances to the cluster stars using Gaia parallax measurements. The code includes cluster-oriented prior families and it is specifically designed to deal with the Gaia parallax spatial correlations. Methods. A Bayesian hierarchical model is created to allow for the inference of both the cluster parameters and distances to its stars. Results. Using synthetic data that mimics Gaia parallax uncertainties and spatial correlations, we observe that our cluster-oriented prior families result in distance estimates with smaller errors than those obtained with an exponentially decreasing space density prior. In addition, the treatment of the parallax spatial correlations minimizes errors in the estimated cluster size and stellar distances, and avoids the underestimation of uncertainties. Although neglecting the parallax spatial correlations has no impact on the accuracy of cluster distance determinations, it underestimates the uncertainties and may result in measurements that are incompatible with the true value (i.e., falling beyond the 2 sigma uncertainties). Conclusions. The combination of prior knowledge with the treatment of Gaia parallax spatial correlations produces accurate (error < 10%) and trustworthy estimates (i.e., true values contained within the 2 sigma uncertainties) of cluster distances for clusters up to similar to 5 kpc, along with cluster sizes for clusters up to similar to 1 kpc

Chamaeleon DANCe: Revisiting the stellar populations of Chamaeleon I and Chamaeleon II with Gaia-DR2 data

Context. Chamaeleon is the southernmost low-mass star-forming complex within 200 pc from the Sun. Its stellar population has been extensively studied in the past, but the current census of the stellar content is not complete yet and deserves further investigation.Aims. We take advantage of the second data release of the Gaia space mission to expand the census of stars in Chamaeleon and to revisit the properties of the stellar populations associated to the Chamaeleon I (Cha I) and Chamaeleon II (Cha II) dark clouds.Methods. We perform a membership analysis of the sources in the Gaia catalogue over a field of 100 deg(2) encompassing the Chamaeleon clouds, and use this new census of cluster members to investigate the 6D structure of the complex.Results. We identify 188 and 41 high-probability members of the stellar populations in Cha I and Cha II, respectively, including 19 and 7 new members. Our sample covers the magnitude range from G=6 to G=20 mag in Cha I, and from G=12 to G=18 mag in Cha II. We confirm that the northern and southern subgroups of Cha I are located at different distances ( 191.4(-0.8)(+0.8) 191 . 4 - 0.8 + 0.8 pc and 186.7(-1.0)(+1.0) 186 . 7 - 1.0 + 1.0 pc), but they exhibit the same space motion within the reported uncertainties. Cha II is located at a distance of 197.5(-0.9)(+1.0) 197 . 5 - 0.9 + 1.0 pc and exhibits a space motion that is consistent with Cha I within the admittedly large uncertainties on the spatial velocities of the stars that come from radial velocity data. The median age of the stars derived from the Hertzsprung-Russell diagram and stellar models is about 1-2 Myr, suggesting that they are somewhat younger than previously thought. We do not detect significant age differences between the Chamaeleon subgroups, but we show that Cha II exhibits a higher fraction of disc-bearing stars compared to Cha I.Conclusions. This study provides the most complete sample of cluster members associated to the Chamaeleon clouds that can be produced with Gaia data alone. We use this new census of stars to revisit the 6D structure of this region with unprecedented precision

KOBEsim: A Bayesian observing strategy algorithm for planet detection in radial velocity blind-search surveys

Context. Ground-based observing time is precious in the era of exoplanet follow-up and characterization, especially in high-precision radial velocity instruments. Blind-search radial velocity surveys thus require a dedicated observational strategy in order to optimize the observing time, which is particularly crucial for the detection of small rocky worlds at large orbital periods. Aims. We developed an algorithm with the purpose of improving the efficiency of radial velocity observations in the context of exoplanet searches, and we applied it to the K-dwarfs Orbited By habitable Exoplanets experiment. Our aim is to accelerate exoplanet confirmations or, alternatively, reject false signals as early as possible in order to save telescope time and increase the efficiency of both blind-search surveys and follow-up of transiting candidates. Methods. Once a minimum initial number of radial velocity datapoints is reached in such a way that a periodicity starts to emerge according to generalized Lomb-Scargle periodograms, that period is targeted with the proposed algorithm, named KOBEsim. The algorithm selects the next observing date that maximizes the Bayesian evidence for this periodicity in comparison with a model with no Keplerian orbits. Results. By means of simulated data, we proved that the algorithm accelerates the exoplanet detection, needing 29-33% fewer observations and a 41-47% smaller time span of the full dataset for low-mass planets (mp < 10 M⊕) in comparison with a conventional monotonic cadence strategy. For 20 M⊕ planets we found a 16% enhancement in the number of datapoints. We also tested KOBEsim with real data for a particular KOBE target and for the confirmed planet HD 102365 b. These two tests demonstrate that the strategy is capable of speeding up the detection by up to a factor of 2 (i.e., reducing both the time span and number of observations by half).14 página

Project goals, target selection, and stellar characterization

The detection of habitable worlds is one of humanitya-s greatest endeavors. Thus far, astrobiological studies have shown that one of the most critical components for allowing life to develop is liquid water. Its chemical properties and its capacity to dissolve and, hence, transport other substances makes this constituent a key piece in this regard. As a consequence, looking for life as we know it is directly related to the search for liquid water. For a remote detection of life in distant planetary systems, this essentially means looking for planets in the so-called habitable zone. In this sense, K-dwarf stars are the perfect hosts to search for planets in this range of distances. Contrary to G-dwarfs, the habitable zone is closer, thus making planet detection easier using transit or radial velocity techniques. Contrary to M-dwarfs, stellar activity is on a much smaller scale, hence, it has a smaller impact in terms of both the detectability and the true habitability of the planet. Also, K-dwarfs are the quietest in terms of oscillations, and granulation noise. In spite of this, there is a dearth of planets in the habitable zone of K-dwarfs due to a lack of observing programs devoted to this parameter space. In response to a call for legacy programs of the Calar Alto observatory, we have initiated the first dedicated and systematic search for habitable planets around these stars: K-dwarfs Orbited By habitable Exoplanets (KOBE). This survey is monitoring the radial velocity of 50 carefully pre-selected K-dwarfs with the CARMENES instrument over five semesters, with an average of 90 data points per target. Based on planet occurrence rates convolved with our detectability limits, we expect to find 1.68 ± 0.25 planets per star in the KOBE sample. Furthermore, in half of the sample, we expect to find one of those planets within the habitable zone. Here, we describe the motivations, goals, and target selection for the project as well as the preliminary stellar characterization. © 2022 EDP Sciences. All rights reserved

On a property of Lorenz curves with monotone elasticity and its application to the study of inequality by using tax data

The Lorenz curve is the most widely used graphical tool for describing and comparing inequality of income distributions. In this paper, we show that the elasticity of this curve is an indicator of the effect, in terms of inequality, of a truncation of the income distribution. As an application, we consider tax returns as equivalent to the truncation from below of a hypothetical income distribution. Then, we replace this hypothetical distribution by the income distribution obtained from a general household survey and use the dual Lorenz curve to anticipate this effect

chi(1) Fornacis cluster DANCe Census of stars, structure, and kinematics of the cluster with Gaia-EDR3

Context. The chi(1) Fornacis cluster (Alessi 13) is one of a few open clusters of its age and distance in the Solar neighbourhood that ought to benefit from more attention as it can serve as a cornerstone for numerous future studies related to star and planet formation. Aims. We take advantage of the early installment of the third data release of the Gaia space mission in combination with archival data and our own observations, to expand the census of cluster members and revisit some properties of the cluster. Methods. We applied a probabilistic method to infer membership probabilities over a field of more than 1000 deg(2) to select the most likely cluster members and derive the distances, spatial velocities, and physical properties of the stars in this sample. Results. We identify 164 high-probability cluster members (including 61 new members) covering the magnitude range from 5.1 to 19.6 mag in the G-band. Our sample of cluster members is complete down to 0.04 M-circle dot. We derive the distance of 108.4 +/- 0.3 pc from Bayesian inference and confirm that the cluster is comoving with the Tucana-Horologium, Columba, and Carina young stellar associations. We investigate the kinematics of the cluster from a subsample of stars with measured radial velocities and we do not detect any significant expansion or rotation effects in the cluster. Our results suggest that the cluster is somewhat younger (about 30 Myr) than previously thought. Based on spectroscopic observations, we argue that the cluster is mass-segregated and that the distribution of spectral types shows little variation compared to other young stellar groups. Conclusions. In this study, we deliver the most complete census of cluster members that can be done with Gaia data alone and we use this new sample to provide an updated picture on the 6D structure of the cluster.This research has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 682903, P.I. H. Bouy), and from the French State in the framework of the "Investments for the future" Program, IdEx Bordeaux, reference ANR-10-IDEX-03-02. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This publication makes use of data products from theWidefield Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This publication makes use of VOSA, developed under the Spanish Virtual Observatory project supported by the Spanish MINECO through grant AyA2017-84089. VOSA has been partially updated by using funding from the European Union's Horizon 2020 Research and Innovation Programme, under Grant Agreement no 776403 (EXOPLANETS-A)