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In this work we improve the dynamic-evolutionary framework of two massive clusters at intermediate redshifts: Cl 0024+17 at $z \sim 0.4$ and MS 0451-03 at $z \sim 0.5$. The spectroscopic galaxy members were selected from Moran et al. (2007a), which combine optical and UV imaging with spectroscopy. Using a set of dynamic estimators with different approaches, our results show that both Cl 0024+17 and MS 0451-03 are non-relaxed systems with distinct dynamical configurations. Cl 0024+17 exhibits a disturbed kinematics, displaying significant gaps and a velocity dispersion profile suggesting a merger. This is confirmed by the presence of previously reported substructures and new ones identified in this study. MS 0451-03 appears less disturbed than Cl 0024+17, indicating by the significant segregation between late and early-type galaxies, with the latter occupying more central regions of the projected phase-space. However, five previously unobserved substructures and non-Gaussianity in the velocity distribution indicate that MS 0451-03 is also out of equilibrium. In both clusters, there are substructures infalling onto the systems, indicating key moments in their assembly histories and potential effects on the pre-processing of galaxies within these subgroups. This is suggested by the high percentage of early-type galaxies outside $R_{200}$ (approximately $83\%$) in the case of CL 0024+17. This work reinforces the importance of more detailed dynamical analysis of clusters to better characterize their evolutionary picture., Comment: Accepted for publication in MNRAS, 16 pages, 11 Figures

Galaxies infalling into clusters undergo both star-formation quenching and morphological transformation due to environmental effects. We investigate these processes and their timescales using a local sample of 20,191 cluster and 11,674 field galaxies from SDSS. By analysing morphology as a function of distance from the star-formation main sequence, we show that environmental influence is especially pronounced for low-mass galaxies, which emerge from the green valley with early-type morphologies before their star formation is fully suppressed. Using the galaxies' positions in the clusters' Projected Phase Space, we examine the evolution of blue cloud, green valley, and red sequence fractions as a function of time since infall. Interestingly, the green valley fraction remains constant with time since infall, suggesting a balanced flow of galaxies in and out of this class. We estimate that galaxies less massive than $10^{10}\rm M_{\odot}$ spend approximately 0.4 Gyr in the green valley. By comparing quenched and early-type populations, we provide further evidence for the ``slow-then-rapid'' quenching model and suggest that it can also be applied to morphological transitions. Our results indicate that morphological transformation occurs at larger radii than complete star-formation quenching. About 75% of galaxies undergoing morphological transition in clusters are spirals evolving into S0s, suggesting that infalling galaxies retain their disks, while massive ellipticals are relics of early merger events. Finally, we show it takes approximately 2.5 and 1.2 Gyr after the delay-time ($\sim 3.8 {\rm Gyr}$) for the population of low mass galaxies in clusters to reach a 50% threshold in quenched and early-type fraction, respectively. These findings suggest morphological transition precedes full star formation quenching, with both processes possibly being causally linked., Comment: 14 pages, 10 figures

We investigate the role that dense environments have on the quenching of star formation and the transformation of morphology for a sample of galaxies selected from the Sloan Digital Sky Survey. We make a distinction between galaxies falling into groups $(13 \leq \log{(M_{\text{halo}}/M_{\odot})} < 14)$ and clusters $(\log{(M_{\text{halo}}/M_{\odot})} \geq 14)$, and compare to a large sample of field galaxies. Using galaxy position in projected phase space as a proxy for time since infall, we study how galaxy specific star formation rate (sSFR) and morphology, parameterized by the bulge-to-total light ratio (B/T), change over time. After controlling for stellar mass, we find clear trends of increasing quenched and elliptical fractions as functions of infall time for galaxies falling into both groups and clusters. The trends are strongest for low mass galaxies falling into clusters. By computing quenching and morphological transformation timescales, we find evidence that star formation quenching occurs faster than morphological transformation in both environments. Comparing field galaxies to recently infalling galaxies, we determine there is pre-processing of both star formation and morphology, with pre-processing affecting star formation rates more strongly. Our analysis favours quenching mechanisms that act quickly to suppress star formation, while other mechanisms that act on longer timescales transform morphology through bulge growth and disc fading., Comment: 14 pages, 12 figures, accepted by MNRAS

We exploit a sample of 80,000 SDSS central galaxies to investigate the effect of AGN feedback on their evolution. We trace the demographics of optically-selected AGN (Seyferts) as a function of their internal properties and environment. We find that the preeminence of AGN as the dominant ionising mechanism increases with stellar mass, overtaking star-formation for galaxies with $M_\text{stellar} \geq 10^{11}M_\odot$. The AGN fraction changes systematically with the galaxies' star-formation activity. Within the blue cloud, this fraction increases as star-formation activity declines, reaching a maximum near the green valley ($\sim 17 \pm 4\%$), followed by a decrease as the galaxies transition into the red sequence. This systematic trend provides evidence that AGN feedback plays a key role in regulating and suppressing star formation. In general, Seyfert central galaxies achieve an early-type morphology while they still host residual star formation. This suggests that, in all environments, the morphology of Seyfert galaxies evolves from late- to early-type before their star formation is fully quenched. Stellar mass plays an important role in this morphological transformation: while low mass systems tend to emerge from the green valley with an elliptical morphology (T-Type $\sim -2.5 \pm 0.7$), their high-mass counterparts maintain a spiral morphology deeper into the red sequence. In high-stellar-mass centrals, the fraction of Seyferts increases from early- to late-type galaxies, indicating that AGN feedback may be linked with the morphology and its transformation. Our analysis further suggests that AGN are fuelled by their own host halo gas reservoir, but when in group centrals can also increase their gas reservoir via interactions with satellite galaxies., Comment: 13 pages, 11 figures, accepted for publication in the MNRAS

In a wide range of practical problems, such as forming operations and impact tests, assuming that one of the contacting bodies is rigid is an excellent approximation to the physical phenomenon. In this work, the well-established dual mortar method is adopted to enforce interface constraints in the finite deformation frictionless contact of rigid and deformable bodies. The efficiency of the nonlinear contact algorithm proposed here is based on two main contributions. Firstly, a variational formulation of the method using the so-called Petrov-Galerkin scheme is investigated, as it unlocks a significant simplification by removing the need to explicitly evaluate the dual basis functions. The corresponding first-order dual mortar interpolation is presented in detail. Particular focus is, then, placed on the extension for second-order interpolation by employing a piecewise linear interpolation scheme, which critically retains the geometrical information of the finite element mesh. Secondly, a new definition for the nodal orthonormal moving frame attached to each contact node is suggested. It reduces the geometrical coupling between the nodes and consequently decreases the stiffness matrix bandwidth. The proposed contributions decrease the computational complexity of dual mortar methods for rigid/deformable interaction, especially in the three-dimensional setting, while preserving accuracy and robustness.

We have investigated the structure of the Hercules supercluster (SCL160) based on data originally extracted from the Sloan Digital Sky Survey SDSS-DR7. We have traced the mass distribution in the field through the numerical density-weighted by the $r^\prime$-luminosity of the galaxies and classified them based on their spatial position and redshift. This has allowed us not only to address the kinematics of the supercluster as a whole, but also the internal kinematic of each cluster, which was no further explored before. We have confirmed that the Hercules supercluster is composed of the galaxy clusters A2147, A2151, and A2152. A2151 consists of five subclusters, A2147 on two and A2152 on at least two. They form the heart of the Hercules supercluster. We also have found two other gravitationally bond clusters, increasing, therefore, the known members of the supercluster. We have estimated a total mass of $2.1\pm0.2 \times 10^{15}$ M$_\odot$ for the Hercules supercluster. To determine the dynamical masses in this work, we have resorted to the $M_{200}-\sigma$ scaling relation and the caustic technique. Comparing both methods with simulated data of bimodal merging clusters, we found the caustic, as well as the $\sigma$-based masses, are biased through the merger age, showing a boost just after the pericentric passage. This is not in line with the principle of the caustic method that affirms it is not depending on the cluster dynamical state., Comment: 20 pages, 11 figures, 7 tables - Accepted for publication in MNRAS

We present a study of a sample of 254 clusters from the SDSS-DR7 Yang Catalog and an auxiliary sample of field galaxies to perform a detailed investigation on how galaxy quenching depends on both environment and galaxy stellar mass. Our samples are restricted to 0.03$\leq$z$\leq$0.1 and we only consider clusters with $\rm log(M_{halo}/M_{\odot}) \geq 14$. Comparing properties of field and cluster galaxies in the Blue Cloud, Green Valley and Red Sequence, we find evidence that field galaxies in the red sequence hosted star formation events $\rm 2.1 \pm 0.7$ Gyr ago, on average, more recently than galaxies in cluster environments. Dissecting the star formation rate vs stellar mass diagram we show how morphology rapidly changes after reaching the green valley region, while the star formation rate keeps decreasing. In addition, we use the relation between location in the projected phase space and infall time to explore the time delay between morphological and specific Star Formation Rate variations. We estimate that the transition from late to early-type morphology happens in $\rm \Delta t_{inf} \sim$1 Gyr, whereas the quenching of star formation takes $\sim$3 Gyr. The time-scale we estimate for morphological transitions is similar to the expected for the delayed-then-rapid quenching model. Therefore, we suggest that the delay phase is characterized mostly by morphological transition, which then contributes morphological quenching as an additional ingredient in galaxy evolution., Comment: 18 pages, 10 Figures, Accepted for Publication in the Monthly Notices of the Royal Astronomical Society

By way of the projected phase-space (PPS), we investigate the relation between galaxy properties and cluster environment in a subsample of groups from the Yang Catalog. The sample is split according to the gaussianity of the velocity distribution in the group into gaussian (G) and non-gaussian (NG). Our sample is limited to massive clusters with $\rm M_{200} \geq 10^{14} M_{\odot}$ and $\rm 0.03\leq z \leq 0.1$. NG clusters are more massive, less concentrated and have an excess of faint galaxies compared to G clusters. NG clusters show mixed distributions of galaxy properties in the PPS compared to the G case. Using the relation between infall time and locus on the PPS, we find that, on average, NG clusters accreted $\rm \sim 10^{11}\,M_{\odot}$ more stellar mass in the last $\sim 5$ Gyr than G clusters. The relation between galaxy properties and infall time is significantly different for galaxies in G and NG systems. The more mixed distribution in the PPS of NG clusters translates into shallower relations with infall time. Faint galaxies whose first crossing of the cluster virial radius happened 2-4 Gyr ago in NG clusters are older and more metal-rich than in G systems. All these results suggest that NG clusters experience a higher accretion of pre-processed galaxies, which characterizes G and NG clusters as different environments to study galaxy evolution., Comment: Accepted for publication in MNRAS, 17 pages, 9 Figures

HEV is a low-cost, versatile, high-quality ventilator, which has been designed in response to the COVID-19 pandemic. The ventilator is intended to be used both in and out of hospital intensive care units, and for both invasive and non-invasive ventilation. The hardware can be complemented with an external turbine for use in regions where compressed air supplies are not reliably available. The standard modes provided include PC-A/C(Pressure Assist Control),PC-A/C-PRVC(Pressure Regulated Volume Control), PC-PSV (Pressure Support Ventilation) and CPAP (Continuous Positive airway pressure). HEV is designed to support remote training and post market surveillance via a web interface and data logging to complement the standard touch screen operation, making it suitable for a wide range of geographical deployment. The HEV design places emphasis on the quality of the pressure curves and the reactivity of the trigger, delivering a global performance which will be applicable to ventilator needs beyond theCOVID-19 pandemic. This article describes the conceptual design and presents the prototype units together with their performance evaluation., Comment: 34 pages, 18 figures, Extended version of the article submitted to PNAS

Without a vaccine, the fight against the spreading of the coronavirus has focused on maintaining physical distance. To study the impact of such measures on inter-municipality traffic, we analyze a mobile dataset with the daily flow of people in Portugal in March and April 2020. We find that the reduction in inter-municipality traffic depends strongly on its initial outflow. In municipalities where the mobility is low, the outflow reduced by $10-20\%$ and this decrease was independent of the population size. Whereas, for municipalities of high mobility, the reduction was a monotonic increasing function of the population size and it even exceeded $60\%$ for the largest municipalities. As a consequence of such heterogeneities, there were significant structural changes on the most probable paths for the spreading of the virus, which must be considered when modeling the impact of control measures.

We analyze the dependence of galaxy evolution on cluster dynamical state and galaxy luminosities for a sample of 146 galaxy clusters from the Yang SDSS catalog. Clusters were split according to their velocity distribution in Gaussians (G) and Non-Gaussians (NG), and further divided by luminosity regime. We performed a classification in the Age-SSFR plane providing three classes: star-forming (SF), passive (PAS), and intermediate (GV -- green valley). We show that galaxies evolve in the same way in G and NG systems, but also suggest that their formation histories leads to different mixtures of galactic types and infall patterns. Separating the GV into star-forming and passive components, we find more bright galaxies in the passive mode of NG than in G systems. We also find more intermediate faint galaxies in the star-forming component of NG than in G systems. Our results suggest the GV as the stage where the transition from types Sab and Scd to S0 must be taking place, but the conversion between morphological types is independent of the dynamical stage of the clusters. Analyzing the velocity dispersion profiles, we find that objects recently infalling in clusters have a different composition between G and NG systems. While all galaxy types infall onto G systems, Sab and Scd dominate the infall onto NG systems. Finally, we find that faint Scd in the outskirts of NG systems present higher asymmetries relative to the mean asymmetry of field galaxies, suggesting environmental effects acting on these objects., Comment: Accepted for publication in MNRAS

Using new long-slit spectroscopy obtained with X-Shooter at ESO-VLT, we study, for the first time, radial gradients of optical and Near-Infrared IMF-sensitive features in a representative sample of galaxies at the very high-mass end of the galaxy population. The sample consists of seven early-type galaxies (ETGs) at $z\sim0.05$, with central velocity dispersion in the range $300<\sigma<350$km/s. Using state-of-art stellar population synthesis models, we fit a number of spectral indices, from different chemical species (including TiO's and Na indices), to constrain the IMF slope (i.e. the fraction of low-mass stars), as a function of galactocentric distance, over a radial range out to $\sim4$kpc. ETGs in our sample show a significant correlation of IMF slope and surface mass density. The bottom-heavy population (i.e. an excess of low-mass stars in the IMF) is confined to central galaxy regions with surface mass density above $\sim 10^{10} M_\odot kpc^{-2}$, or, alternatively, within a characteristic radius of $\sim2$~kpc. Radial distance, in physical units, and surface mass density, are the best correlators to IMF variations, with respect to other dynamical (e.g. velocity dispersion) and stellar population (e.g. metallicity) properties. Our results for the most massive galaxies suggest that there is no single parameter} that fully explains variations in the stellar IMF, but IMF radial profiles at z$\sim$0 rather result from the complex formation and mass accretion history of galaxy inner and outer regions., Comment: 23 pages, 13 figures, accepted for publication in MNRAS

This paper is the third of a series in which we investigate the discrimination between Gaussian (G) and Non-Gaussian (NG) clusters, based on the velocity distribution of the member galaxies. We study a sample of 177 groups from the Yang catalog in the redshift interval of 0.03 $\le$ z $\le$ 0.1 and masses $\ge$ 10$^{14} \rm M_{\odot}$. Examining the projected stellar mass density distributions of G and NG groups we find strong evidence of a higher infall rate in the outskirts of NG groups over the G ones. There is a 61\% excess of faint galaxies in NGs when contrasted with G groups, when integrating $\rm from ~ 0.8 ~to~ 2.0R/R_{200}$. The study of the Star Formation History (SFH) of ellipticals and spirals in the three main regions of the Projected Phase Space (PPS) reveals also that the star formation in faint spirals of NG groups is significantly different from their counterpart in the G groups. The assembled mass for Faint spirals varies from 59\% at 12.7 Gyr to 75\% at 8.0 Gyr, while in G systems this variation is from 82\% to 91\%. This finding may also be interpreted as a higher infall rate of gas rich systems in NG groups. This accretion process through the filaments, disturbing the velocity distribution and modifying not only the stellar population of the incoming galaxies but also their SFH, should be seriously considered in modelling galaxy evolution., Comment: 5 pages, 2 figures, Accepted to MNRAS Letters

Morphological classification is a key piece of information to define samples of galaxies aiming to study the large-scale structure of the universe. In essence, the challenge is to build up a robust methodology to perform a reliable morphological estimate from galaxy images. Here, we investigate how to substantially improve the galaxy classification within large datasets by mimicking human classification. We combine accurate visual classifications from the Galaxy Zoo project with machine and deep learning methodologies. We propose two distinct approaches for galaxy morphology: one based on non-parametric morphology and traditional machine learning algorithms; and another based on Deep Learning. To measure the input features for the traditional machine learning methodology, we have developed a system called CyMorph, with a novel non-parametric approach to study galaxy morphology. The main datasets employed comes from the Sloan Digital Sky Survey Data Release 7 (SDSS-DR7). We also discuss the class imbalance problem considering three classes. Performance of each model is mainly measured by Overall Accuracy (OA). A spectroscopic validation with astrophysical parameters is also provided for Decision Tree models to assess the quality of our morphological classification. In all of our samples, both Deep and Traditional Machine Learning approaches have over 94.5% OA to classify galaxies in two classes (elliptical and spiral). We compare our classification with state-of-the-art morphological classification from literature. Considering only two classes separation, we achieve 99% of overall accuracy in average when using our deep learning models, and 82% when using three classes. We provide a catalog with 670,560 galaxies containing our best results, including morphological metrics and classification., Comment: 19 pages, 14 figures and 4 tables. Published on Astronomy and Computing (online version: https://doi.org/10.1016/j.ascom.2019.100334). Printed version will be published on January 2020

We study deformations of holomorphic function germs $f:(X,0)\to\mathbb C$ where $(X,0)$ is an ICIS. We present conditions for these deformations to have constant Milnor number, Euler obstruction and Bruce-Roberts number.

To test the effectiveness of process discovery algorithms, a Process Discovery Contest (PDC) has been set up. This PDC uses a classification approach to measure this effectiveness: The better the discovered model can classify whether or not a new trace conforms to the event log, the better the discovery algorithm is supposed to be. Unfortunately, even the state-of-the-art fully-automated discovery algorithms score poorly on this classification. Even the best of these algorithms, the Inductive Miner, scored only 147 correct classified traces out of 200 traces on the PDC of 2017. This paper introduces the rule-based log skeleton model, which is closely related to the Declare constraint model, together with a way to classify traces using this model. This classification using log skeletons is shown to score better on the PDC of 2017 than state-of-the-art discovery algorithms: 194 out of 200. As a result, one can argue that the fully-automated algorithm to construct (or: discover) a log skeleton from an event log outperforms existing state-of-the-art fully-automated discovery algorithms., Comment: 16 pages with 9 figures, followed by an appendix of 14 pages with 17 figures

The primary difficulty in measuring dynamical masses of galaxy clusters from galaxy data lies in the separation between true cluster members from interloping galaxies along the line of sight. We study the impact of membership contamination and incompleteness on cluster mass estimates obtained with 25 commonly used techniques applied to nearly 1000 mock clusters. We show that all methods overestimate or underestimate cluster masses when applied to contaminated or incomplete galaxy samples respectively. This appears to be the main source of the intrinsic scatter in the mass scaling relation. Applying corrections based on a prior knowledge of contamination and incompleteness can reduce the scatter to the level of shot noise expected for poorly sampled clusters. We establish an empirical model quantifying the effect of imperfect membership on cluster mass estimation and discuss its universal and method-dependent features. We find that both imperfect membership and the response of the mass estimators depend on cluster mass, effectively causing a flattening of the estimated - true mass relation. Imperfect membership thus alters cluster counts determined from spectroscopic surveys, hence the cosmological parameters that depend on such counts., Comment: 18 pages, 11 figures, 3tables; accepted for publication in MNRAS

With the advent of wide-field cosmological surveys, we are approaching samples of hundreds of thousands of galaxy clusters. While such large numbers will help reduce statistical uncertainties, the control of systematics in cluster masses becomes ever more crucial. Here we examine the effects of an important source of systematic uncertainty in galaxy-based cluster mass estimation techniques: the presence of significant dynamical substructure. Dynamical substructure manifests as dynamically distinct subgroups in phase-space, indicating an 'unrelaxed' state. This issue affects around a quarter of clusters in a generally selected sample. We employ a set of mock clusters whose masses have been measured homogeneously with commonly-used galaxy-based mass estimation techniques (kinematic, richness, caustic, radial methods). We use these to study how the relation between observationally estimated and true cluster mass depends on the presence of substructure, as identified by various popular diagnostics. We find that the scatter for an ensemble of clusters does not increase dramatically for clusters with dynamical substructure. However, we find a systematic bias for all methods, such that clusters with significant substructure have higher measured masses than their relaxed counterparts. This bias depends on cluster mass: the most massive clusters are largely unaffected by the presence of significant substructure, but masses are significantly overestimated for lower mass clusters, by $\sim10\%$ at $10^{14}$ and $\geq20\%$ for $\leq10^{13.5}$. The use of cluster samples with different levels of substructure can, therefore, bias certain cosmological parameters up to a level comparable to the typical uncertainties in current cosmological studies., Comment: 14 pages, 8 figures, 3 tables. Submitted to MNRAS

Motivated by the existence of the relationship between the dynamical state of clusters and the shape of the velocity dispersion profiles (VDP), we study the VDPs for Gaussian (G) and Non-Gaussian (NG) systems for a subsample of clusters from the Yang catalog. The groups cover a redshift interval of $0.03\leq z\leq0.1$ with halo mass $\geq 10^{14}$M$_{\odot}$. We use a robust statistical method, Hellinger Distance, to classify the dynamical state of the systems according to their velocity distribution. The stacked VDP of each class, G and NG, is then determined using either Bright or Faint galaxies. The stacked VDP for G groups displays a central peak followed by a monotonically decreasing trend which indicates a predominance of radial orbits, with the Bright stacked VDP showing lower velocity dispersions in all radii. The distinct features we find in NG systems are manifested not only by the characteristic shape of VDP, with a depression in the central region, but also by a possible higher infall rate associated with galaxies in the Faint stacked VDP., Comment: 5 pages, 4 figures, accepted for publication in the MNRAS Letters

We investigate the dependence of stellar population properties of galaxies on group dynamical stage for a subsample of Yang catalog. We classify groups according to their galaxy velocity distribution into Gaussian (G) and Non-Gaussian (NG). Using two totally independent approaches we have shown that our measurement of Gaussianity is robust and reliable. Our sample covers Yang's groups in the redshift range 0.03 $\leq$ z $\leq$ 0.1 having mass $\geq$ 10$^{14} \rm M_{\odot}$. The new method, Hellinger Distance (HD), to determine whether a group has a velocity distribution Gaussian or Non-Gaussian is very effective in distinguishing between the two families. NG groups present halo masses higher than the G ones, confirming previous findings. Examining the Skewness and Kurtosis of the velocity distribution of G and NG groups, we find that faint galaxies in NG groups are mainly infalling for the first time into the groups. We show that considering only faint galaxies in the outskirts, those in NG groups are older and more metal rich than the ones in G groups. Also, examining the Projected Phase Space of cluster galaxies we see that bright and faint galactic systems in G groups are in dynamical equilibrium which does not seem to be the case in NG groups. These findings suggest that NG systems have a higher infall rate, assembling more galaxies which experienced preprocessing before entering the group., Comment: 55 pages, 5 Tables and 12 Figures. Accepted for publication in Astronomical Journal

This paper presents machine learning experiments performed over results of galaxy classification into elliptical (E) and spiral (S) with morphological parameters: concetration (CN), assimetry metrics (A3), smoothness metrics (S3), entropy (H) and gradient pattern analysis parameter (GA). Except concentration, all parameters performed a image segmentation pre-processing. For supervision and to compute confusion matrices, we used as true label the galaxy classification from GalaxyZoo. With a 48145 objects dataset after preprocessing (44760 galaxies labeled as S and 3385 as E), we performed experiments with Support Vector Machine (SVM) and Decision Tree (DT). Whit a 1962 objects balanced dataset, we applied K- means and Agglomerative Hierarchical Clustering. All experiments with supervision reached an Overall Accuracy OA >= 97%.

Statistical properties for the recurrence of particles in an oval billiard with a hole in the boundary are discussed. The hole is allowed to move in the boundary under two different types of motion: (i) counterclockwise periodic circulation with a fixed step length and; (ii) random movement around the boundary. After injecting an ensemble of particles through the hole we show that the surviving probability of the particles without recurring - without escaping - from the billiard is described by an exponential law and that the slope of the decay is proportional to the relative size of the hole. Since the phase space of the system exhibits islands of stability we show that there are preferred regions of escaping in the polar angle, hence given a partial answer to an open problem: {\it Where to place a hole in order to maximize or minimize a suitable defined measure of escaping}.

In this paper we analyse tiebreak results from some tennis players in order to investigate whether we are able to identify some strategy in this crucial moment of the game. We compared the observed results with a binomial distribution considering that the probabilities of winning or losing a point are equal. Using a $\chi^2$ test we found that, excepting some players, the greatest part of the results agrees with our hypothesis that there is no hidden strategy and the points in tiebreaks are merely aleatory.

We study the total density distribution in the central regions ($<\, 1$ effective radius, $R_{\rm e}$) of early-type galaxies (ETGs), using data from the SPIDER survey. We model each galaxy with two components (dark matter halo + stars), exploring different assumptions for the dark matter (DM) halo profile, and leaving stellar mass-to-light ($M_{\rm \star}/L$) ratios as free fitting parameters to the data. For a Navarro et al. (1996) profile, the slope of the total mass profile is non-universal. For the most massive and largest ETGs, the profile is isothermal in the central regions ($\sim R_{\rm e}/2$), while for the low-mass and smallest systems, the profile is steeper than isothermal, with slopes similar to those for a constant-M/L profile. For a concentration-mass relation steeper than that expected from simulations, the correlation of density slope with mass tends to flatten. Our results clearly point to a "non-homology" in the total mass distribution of ETGs, which simulations of galaxy formation suggest may be related to a varying role of dissipation with galaxy mass., Comment: 3 pages, 1 figure, to appear on the refereed Proceeding of the "The Universe of Digital Sky Surveys" conference held at the INAF--OAC, Naples, on 25th-28th november 2014, to be published on Astrophysics and Space Science Proceedings, edited by Longo, Napolitano, Marconi, Paolillo, Iodice

This article is the second in a series in which we perform an extensive comparison of various galaxy-based cluster mass estimation techniques that utilise the positions, velocities and colours of galaxies. Our aim is to quantify the scatter, systematic bias and completeness of cluster masses derived from a diverse set of 25 galaxy-based methods using two contrasting mock galaxy catalogues based on a sophisticated halo occupation model and a semi-analytic model. Analysing 968 clusters, we find a wide range in the RMS errors in log M200c delivered by the different methods (0.18 to 1.08 dex, i.e., a factor of ~1.5 to 12), with abundance matching and richness methods providing the best results, irrespective of the input model assumptions. In addition, certain methods produce a significant number of catastrophic cases where the mass is under- or over-estimated by a factor greater than 10. Given the steeply falling high-mass end of the cluster mass function, we recommend that richness or abundance matching-based methods are used in conjunction with these methods as a sanity check for studies selecting high mass clusters. We see a stronger correlation of the recovered to input number of galaxies for both catalogues in comparison with the group/cluster mass, however, this does not guarantee that the correct member galaxies are being selected. We do not observe significantly higher scatter for either mock galaxy catalogues. Our results have implications for cosmological analyses that utilise the masses, richnesses, or abundances of clusters, which have different uncertainties when different methods are used., Comment: 25 pages, 19 figures, 7 tables. Accepted for publication in MNRAS

We study the total density distribution in the central regions (~ 1 effective radius, $R_e$) of early-type galaxies (ETGs), using data from SPIDER and $\rm ATLAS^{3D}$. Our analysis extends the range of galaxy stellar mass ($M_{\star}$) probed by gravitational lensing, down to ~ $10^{10}\, \rm M_{\odot}$. We model each galaxy with two components (dark matter halo + stars), exploring different assumptions for the dark matter (DM) halo profile (i.e. NFW, NFW-contracted, and Burkert profiles), and leaving stellar mass-to-light ($M_{\star}/L$) ratios as free fitting parameters to the data. For all plausible halo models, the best-fitting $M_{\star}/L$, normalized to that for a Chabrier IMF, increases systematically with galaxy size and mass. For an NFW profile, the slope of the total mass profile is non-universal, independently of several ingredients in the modeling (e.g., halo contraction, anisotropy, and rotation velocity in ETGs). For the most massive ($M_{\star}$ ~ $10^{11.5} \, M_{\odot}$) or largest ($R_{\rm e}$ ~ $15 \, \rm kpc$) ETGs, the profile is isothermal in the central regions (~$R_{\rm e}/2$), while for the low-mass ($M_{\star}$ ~ $10^{10.2} \, M_\odot$) or smallest ($R_{\rm e}$ ~ $0.5 \, \rm kpc$) systems, the profile is steeper than isothermal, with slopes similar to those for a constant-$M/L$ profile. For a steeper concentration-mass relation than that expected from simulations, the correlation of density slope with galaxy mass tends to flatten, while correlations with $R_{\rm e}$ and velocity dispersions are more robust. Our results clearly point to a "non-homology" in the total mass distribution of ETGs, which simulations of galaxy formation suggest may be related to a varying role of dissipation with galaxy mass., Comment: 15 pages, 6 figures, 3 tables, MNRAS in press

A detailed analysis of how environment affects the star formation history of early-type galaxies (ETGs) is undertaken via high signal to noise ratio stacked spectra obtained from a sample of 20,977 ETGs (morphologically selected) from the SDSS-based SPIDER survey. Two major parameters are considered for the study: the central velocity dispersion (sigma), which relates to local drivers of star formation, and the mass of the host halo, which relates to environment-related effects. In addition, we separate the sample between centrals (the most massive galaxy in a halo) and satellites. We derive trends of age, metallicity, and [alpha/Fe] enhancement, with sigma. We confirm that the major driver of stellar population properties in ETGs is velocity dispersion, with a second-order effect associated to the central/satellite nature of the galaxy. No environmental dependence is detected for satellite ETGs, except at low sigma - where satellites in groups or in the outskirts of clusters tend to be younger than those in the central regions of clusters. In contrast, the trends for centrals show a significant dependence on halo mass. Central ETGs in groups (i.e. with a halo mass >10^12.5 M_Sun) have younger ages, lower [alpha/Fe], and higher internal reddening, than "isolated" systems (i.e. centrals residing in low-mass, <10^12.5 M_Sun, halos). Our findings imply that central ETGs in groups formed their stellar component over longer time scales than "isolated" centrals, mainly because of gas-rich interactions with their companion galaxies., Comment: 22 pages, 19 figures, accepted for publication in MNRAS

The Interface Region Imaging Spectrograph (IRIS) small explorer spacecraft provides simultaneous spectra and images of the photosphere, chromosphere, transition region, and corona with 0.33-0.4 arcsec spatial resolution, 2 s temporal resolution and 1 km/s velocity resolution over a field-of-view of up to 175 arcsec x 175 arcsec. IRIS was launched into a Sun-synchronous orbit on 27 June 2013 using a Pegasus-XL rocket and consists of a 19-cm UV telescope that feeds a slit-based dual-bandpass imaging spectrograph. IRIS obtains spectra in passbands from 1332-1358, 1389-1407 and 2783-2834 Angstrom including bright spectral lines formed in the chromosphere (Mg II h 2803 Angstrom and Mg II k 2796 Angstrom) and transition region (C II 1334/1335 Angstrom and Si IV 1394/1403 Angstrom). Slit-jaw images in four different passbands (C II 1330, Si IV 1400, Mg II k 2796 and Mg II wing 2830 Angstrom) can be taken simultaneously with spectral rasters that sample regions up to 130 arcsec x 175 arcsec at a variety of spatial samplings (from 0.33 arcsec and up). IRIS is sensitive to emission from plasma at temperatures between 5000 K and 10 MK and will advance our understanding of the flow of mass and energy through an interface region, formed by the chromosphere and transition region, between the photosphere and corona. This highly structured and dynamic region not only acts as the conduit of all mass and energy feeding into the corona and solar wind, it also requires an order of magnitude more energy to heat than the corona and solar wind combined. The IRIS investigation includes a strong numerical modeling component based on advanced radiative-MHD codes to facilitate interpretation of observations of this complex region. Approximately eight Gbytes of data (after compression) are acquired by IRIS each day and made available for unrestricted use within a few days of the observation., Comment: 53 pages, 15 figures

We introduce a new method to study the velocity distribution of galaxy systems, the Hellinger Distance (HD) - designed for detecting departures from a Gaussian velocity distribution. We define a relaxed galactic system as the one with unimodal velocity distribution and a normality deviation below a critical value (HD<0.05). In this work, we study the gaussian nature of the velocity distribution of the Berlind group sample, and of the FoF groups from the Millennium simulation. For the Berlind group sample (z<0.1), 67% of the systems are classified as relaxed, while for the Millennium sample we find 63% (z=0). We verify that in multimodal groups the average mass of modes in high multiplicity (N >= 20) systems are significantly larger than in low multiplicity ones (N<20), suggesting that groups experience a mass growth at an increasing virialization rate towards z=0, with larger systems accreting more massive subunits. We also investigate the connection between galaxy properties ([Fe/H], Age, eClass, g-r, R_petro and ) and the gaussianity of the velocity distribution of the groups. Bright galaxies (M_r <=-20.7) residing in the inner and outer regions of groups, do not show significant differences in the listed quantities regardless if the group has a Gaussian (G) or a Non-Gaussian (NG) velocity distribution. However, the situation is significantly different when we examine the faint galaxies (-20.7

We perform a spectroscopic study to constrain the stellar Initial Mass Function (IMF) by using a large sample of 24,781 early-type galaxies from the SDSS-based SPIDER survey. Clear evidence is found of a trend between IMF and central velocity dispersion, sigma0, evolving from a standard Kroupa/Chabrier IMF at 100km/s towards a more bottom-heavy IMF with increasing sigma0, becoming steeper than the Salpeter function at sigma0>220km/s. We analyze a variety of spectral indices, corrected to solar scale by means of semi-empirical correlations, and fitted simultaneously with extended MILES (MIUSCAT) stellar population models. Our analysis suggests that sigma0, rather than [alpha/Fe], drives the IMF variation. Although our analysis cannot discriminate between a single power-law (unimodal) and a low-mass (<0.5MSun) tapered (bimodal) IMF, we can robustly constrain the fraction in low-mass stars at birth, that is found to increase from 20% at sigma0~100km/s, up to 80% at sigma0~300km/s. Additional constraints can be provided with stellar mass-to-light (M/L) ratios: unimodal models predict M/L significantly larger than dynamical M/L, across the whole sigma0 range, whereas a bimodal IMF is compatible. Our results are robust against individual abundance variations. No significant variation is found in Na and Ca in addition to the expected change from the correlation between [alpha/Fe] and sigma0. [Abridged], Comment: 34 pages, 27 figures; V2. Accepted for publication in MNRAS

Radial trends of stellar populations in galaxies provide a valuable tool to understand the mechanisms of galaxy growth. In this paper, we present the first comprehensive analysis of optical-optical and optical-NIR colours, as a function of galaxy mass, out to the halo region (8Re) of early-type galaxies (ETGs). We select a sample of 674 massive ETGs (M*>3x10^10MSun) from the SDSS-based SPIDER survey. By comparing with a large range of population synthesis models, we derive robust constraints on the radial trends in age and metallicity. Metallicity is unambiguously found to decrease outwards, with a measurable steepening of the slope in the outer regions (Re10^11MSun). Furthermore, when segregating with respect to large scale environment, the age gradient is more significant in ETGs residing in higher density regions. These results shed light on the processes leading from the formation of the central core to the growth of the stellar envelope of massive galaxies. The fact that the populations in the outer regions are older and more metal-poor than in the core suggests a process whereby the envelope of massive galaxies is made up of accreted small satellites (i.e. minor mergers) whose stars were born during the first stages of galaxy formation., Comment: 20 pages, 13 figures, 10 tables. Accepted for publication in MNRAS

An essential component of galaxy formation theory is the stellar initial mass function (IMF), that describes the parent distribution of stellar mass in star forming regions. We present observational evidence in a sample of early-type galaxies (ETGs) of a tight correlation between central velocity dispersion and the strength of several absorption features sensitive to the presence of low-mass stars. Our sample comprises ~40,000 ETGs from the SPIDER survey (z<0.1). The data, extracted from the Sloan Digital Sky Survey, are combined, rejecting both noisy data, and spectra with contamination from telluric lines, resulting in a set of 18 stacked spectra at high signal-to-noise ratio (S/N> 400 per A). A combined analysis of IMF-sensitive line strengths and spectral fitting is performed with the latest state-of the art population synthesis models (an extended version of the MILES models). A significant trend is found between IMF slope and velocity dispersion, towards an excess of low-mass stars in the most massive galaxies. Although we emphasize that accurate values of the IMF slope will require a detailed analysis of chemical composition (such as [a/Fe] or even individual element abundance ratios), the observed trends suggest that low-mass ETGs are better fit by a Kroupa-like IMF, whereas massive galaxies require bottom-heavy IMFs, exceeding the Salpeter slope at velocity dispersions above 200km/s., Comment: 5 pages, 4 figures, accepted for publication in MNRAS Letters

We present an X-ray follow-up, based on XMM plus Chandra, of six Fossil Group (FG) candidates identified in our previous work using SDSS and RASS data. Four candidates (out of six) exhibit extended X-ray emission, confirming them as true FGs. For the other two groups, the RASS emission has its origin as either an optically dull/X-ray bright AGN, or the blending of distinct X-ray sources. Using SDSS-DR7 data, we confirm, for all groups, the presence of an r-band magnitude gap between the seed elliptical and the second-rank galaxy. However, the gap value depends, up to 0.5mag, on how one estimates the seed galaxy total flux, which is greatly underestimated when using SDSS (relative to Sersic) magnitudes. This implies that many FGs may be actually missed when using SDSS data, a fact that should be carefully taken into account when comparing the observed number densities of FGs to the expectations from cosmological simulations. The similarity in the properties of seed--FG and non-fossil ellipticals, found in our previous study, extends to the sample of X-ray confirmed FGs, indicating that bright ellipticals in FGs do not represent a distinct population of galaxies. For one system, we also find that the velocity distribution of faint galaxies is bimodal, possibly showing that the system formed through the merging of two groups. This undermines the idea that all selected FGs form a population of true fossils., Comment: 9 pages, 3 figures. Submitted 01/12/2011 to MNRAS, referee report received 21/02/2012, accepted 22/02/2012

We analyze the central dark-matter (DM) content of \sim 4,500 massive (M* \gsim 10^{10} Msun), low-redshift (z<0.1), early-type galaxies (ETGs), with high-quality ugrizYJHK photometry and optical spectroscopy from SDSS and UKIDSS. We estimate the "central" fraction of DM within the K-band effective radius, \Re, using spherically symmetric isotropic galaxy models. We discuss the role of systematics. The main results of the present work are the following: (1) DM fractions increase systematically with both structural parameters and mass proxies, as in previous studies, and decrease with central stellar density. 2) All correlations involving DM fractions are caused by two fundamental ones with galaxy effective radius and central velocity dispersion. These correlations are independent of each other, so that ETGs populate a central-DM plane (DMP), i.e. a correlation among fraction of total-to-stellar mass, effective radius, and velocity dispersion, whose scatter along the total-to-stellar mass axis amounts to \sim 0.15 dex. (3) In general, under the assumption of an isothermal or a constant M/L profile for the total mass distribution, a Chabrier IMF is favoured with respect to a bottom-heavier Salpeter IMF, as the latter produces negative (i.e. unphysical) DM fractions for more than 50% of the galaxies in our sample. For a Chabrier IMF, the DM estimates agree with \LambdaCDM toy-galaxy models based on contracted DM-halo density profiles. We also find agreement with predictions from hydrodynamical simulations. (4) The central DM content of ETGs does not depend significantly on the environment where galaxies reside, with group and field ETGs having similar DM trends. (Abridged), Comment: 20 pages, 13 figures, 2 tables, accepted for publication on MNRAS, version including revisions after the referee's report and feedbacks from community

Classical systems of coupled harmonic oscillators are studied using the Carati-Galgani model. We investigate the consequences for Einstein's conjecture by considering that the exchanges of energy, in molecular collisions, follows the L\'evy type statistics. We develop a generalization of Planck's distribution admitting that there are analogous relations in the equilibrium quantum statistical mechanics of the relations found using the nonequilibrium classical statistical mechanics approach. The generalization of Planck's law based on the nonextensive statistical mechanics formalism is compatible with the our analysis., Comment: 10 pages, 3 figures