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We investigate the stellar Mass-Metallicity Relation (MZR) using a sample of 637 quiescent galaxies with 10.4 <= log(M*/M ) < 11.7 selected from the LEGA-C survey at 0.6 <= z <= 1. We derive mass-weighted stellar metallicities using full-spectral fitting. We find that while lower-mass galaxies are both metal -rich and -poor, there are no metal-poor galaxies at high masses, and that metallicity is bounded at low values by a mass-dependent lower limit. This lower limit increases with mass, empirically defining a MEtallicity-Mass Exclusion (MEME) zone. We find that the spectral index MgFe = \sqrt{Mgb \times Fe4383}, a proxy for the stellar metallicity, also shows a mass-dependent lower limit resembling the MEME relation. Crucially, MgFe is independent of stellar population models and fitting methods. By constructing the Metallicity Enrichment Histories, we find that, after the first Gyr, the Star Formation History of galaxies has a mild impact on the observed metallicity distribution. Finally, from the average formation times, we find that galaxies populate differently the metallicity-mass plane at different cosmic times, and that the MEME limit is recovered by galaxies that formed at z >= 3. Our work suggests that the stellar metallicity of quiescent galaxies is bounded by a lower limit which increases with the stellar mass. On the other hand, low-mass galaxies can have metallicities as high as galaxies ~1 dex more massive. This suggests that, at log(M*/M ) >= 10.4, rather than lower-mass galaxies being systematically less metallic, the observed MZR might be a consequence of the lack of massive, metal-poor galaxies., Comment: Accepted for publication in A&A

Most of the analyses concerning signed networks have focused on the balance theory, hence identifying frustration with undirected, triadic motifs having an odd number of negative edges; much less attention has been paid to their directed counterparts. To fill this gap, we focus on signed, directed connections, with the aim of exploring the notion of frustration in such a context. When dealing with signed, directed edges, frustration is a multi-faceted concept, admitting different definitions at different scales: if we limit ourselves to consider cycles of length two, frustration is related to reciprocity, i.e. the tendency of edges to admit the presence of partners pointing in the opposite direction. As the reciprocity of signed networks is still poorly understood, we adopt a principled approach for its study, defining quantities and introducing models to consistently capture empirical patterns of the kind. In order to quantify the tendency of empirical networks to form either mutualistic or antagonistic cycles of length two, we extend the Exponential Random Graphs framework to binary, directed, signed networks with global and local constraints and, then, compare the empirical abundance of the aforementioned patterns with the one expected under each model. We find that the (directed extension of the) balance theory is not capable of providing a consistent explanation of the patterns characterising the directed, signed networks considered in this work. Although part of the ambiguities can be solved by adopting a coarser definition of balance, our results call for a different theory, accounting for the directionality of edges in a coherent manner. In any case, the evidence that the empirical, signed networks can be highly reciprocated leads us to recommend to explicitly account for the role played by bidirectional dyads in determining frustration at higher levels (e.g. the triadic one)., Comment: 35 pages, 9 figures, 4 tables

The Extremely Large Telescopes (ELTs), thanks to their large apertures and cutting-edge Multi-Conjugate Adaptive Optics (MCAO) systems, promise to deliver sharper and deeper data even than the JWST. SHARP is a concept study for a near-IR (0.95-2.45 $\mu$m) spectrograph conceived to fully exploit the collecting area and the angular resolution of the upcoming generation of ELTs. In particular, SHARP is designed for the 2nd port of MORFEO@ELT. Composed of a Multi-Object Spectrograph, NEXUS, and a multi-Integral Field Unit, VESPER, MORFEO-SHARP will deliver high angular ($\sim$30 mas) and spectral (R$\simeq$300, 2000, 6000, 17000) resolution, outperforming NIRSpec@JWST (100 mas). SHARP will enable studies of the nearby Universe and the early Universe in unprecedented detail. NEXUS is fed by a configurable slit system deploying up to 30 slits with $\sim$2.4 arcsec length and adjustable width, over a field of about 1.2"$\times$1.2" (35 mas/pix). Each slit is fed by an inversion prism able to rotate by an arbitrary angle the field that can be seen by the slit. VESPER is composed of 12 probes of 1.7"$\times$1.5" each (spaxel 31 mas) probing a field 24"$\times$70". SHARP is conceived to exploit the ELTs apertures reaching the faintest flux and the sharpest angular resolution by joining the sensitivity of NEXUS and the high spatial sampling of VESPER to MORFEO capabilities. This article provides an overview of the scientific design drivers, their solutions, and the resulting optical design of the instrument achieving the required optical performance., Comment: Proceedings of the SPIE Astronomical Telescopes and Instrumentation 2024, Volume 13096, Paper No. 130965I, 11 pp, 11 figs

Geant4 is an object-oriented toolkit for the simulation of the passage of particles through matter. Its development was initially motivated by the requirements of physics experiments at high energy hadron colliders under construction in the last decade of the 20th century. Since its release in 1998, it has been exploited in many different applicative fields, including space science, nuclear physics, medical physics and archaeology. Its valuable support to scientific discovery is demonstrated by more than 16000 citations received in the past 25 years, including notable citations for main discoveries in different fields. This accomplishment shows that well designed software plays a key role in enabling scientific advancement. In this paper we discuss the key principles and the innovative decisions at the basis of Geant4, which made it a game changer in high energy physics and related fields, and outline some considerations regarding future directions., Comment: Accepted for publication in Future Generation Computer Systems

Community detection algorithms try to extract a mesoscale structure from the available network data, generally avoiding any explicit assumption regarding the quantity and quality of information conveyed by specific sets of edges. In this paper, we show that the core of ideological/discursive communities on X/Twitter can be effectively identified by uncovering the most informative interactions in an authors-audience bipartite network through a maximum-entropy null model. The analysis is performed considering three X/Twitter datasets related to the main political events of 2022 in Italy, using as benchmarks four state-of-the-art algorithms - three descriptive, one inferential -, and manually annotating nearly 300 verified users based on their political affiliation. In terms of information content, the communities obtained with the entropy-based algorithm are comparable to those obtained with some of the benchmarks. However, such a methodology on the authors-audience bipartite network: uses just a small sample of the available data to identify the central users of each community; returns a neater partition of the user set in just a few, easy to interpret, communities; clusters well-known political figures in a way that better matches the political alliances when compared with the benchmarks. Our results provide an important insight into online debates, highlighting that online interaction networks are mostly shaped by the activity of a small set of users who enjoy public visibility even outside social media.

This paper describes an experimental evaluation aimed at detecting the users' perception of the robot's empathic abilities during a conversation. The results have been then analyzed to search for a possible relationship between the perceived empathy and the attribution of mental states to the robot, namely the user's perception of the robot's mental qualities as compared to humans. The involved sample consisted of 68 subjects, including 34 adults and 34 between teenagers and children. By conducting the experiment with both adult and child participants, make possible to compare the results obtained from each group and identify any differences in perception between the various age groups.

For U.S. presidential elections, most states use the so-called winner-take-all system, in which the state's presidential electors are awarded to the winning political party in the state after a popular vote phase, regardless of the actual margin of victory. Therefore, election campaigns are especially intense in states where there is no clear direction on which party will be the winning party. These states are often referred to as swing states. To measure the impact of such an election law on the campaigns, we analyze the Twitter activity surrounding the 2020 US preelection debate, with a particular focus on the spread of disinformation. We find that about 88% of the online traffic was associated with swing states. In addition, the sharing of links to unreliable news sources is significantly more prevalent in tweets associated with swing states: in this case, untrustworthy tweets are predominantly generated by automated accounts. Furthermore, we observe that the debate is mostly led by two main communities, one with a predominantly Republican affiliation and the other with accounts of different political orientations. Most of the disinformation comes from the former., Comment: arXiv admin note: text overlap with arXiv:2303.12474

With the primary goal of raising readers' awareness of misinformation phenomena, extensive efforts have been made by both academic institutions and independent organizations to develop methodologies for assessing the trustworthiness of online news publishers. Unfortunately, existing approaches are costly and face critical scalability challenges. This study presents a novel framework for assessing the trustworthiness of online news publishers using user interactions on social media platforms. The proposed methodology provides a versatile solution that serves the dual purpose of i) identifying verifiable online publishers and ii) automatically performing an initial estimation of the trustworthiness of previously unclassified online news outlets., Comment: A pre-final version of the paper accepted at WebSci'24

We review some geometric criteria and prove a refined version, that yield existence of capillary surfaces in tubes $\Omega\times \mathbb{R}$ in a gravity free environment, in the case of physical interest, that is, for bounded, open, and simply connected $\Omega \subset \mathbb{R}^2$. These criteria rely on suitable weak one-sided bounds on the curvature of the boundary of the cross-section $\Omega$., Comment: 16 pages, 4 figures

We prove a lower bound for the Cheeger constant of a cylinder $\Omega\times (0,L)$, where $\Omega$ is an open and bounded set. As a consequence, we obtain existence of minimizers for the shape functional defined as the ratio between the first Dirichlet eigenvalue of the $p$-Laplacian and the $p$-th power of the Cheeger constant, within the class of bounded convex sets in any $\mathbb{R}^N$. This positively solves open conjectures raised by Parini (J. Convex Anal. (2017)) and by Briani-Buttazzo-Prinari (Ann. Mat. Pura Appl. (2023))., Comment: 13 pages, 1 figure, accepted paper 2024, to appear

We study Cheeger and $p$-eigenvalue partition problems depending on a given evaluation function $\Phi$ for $p\in[1,\infty)$. We prove existence and regularity of minima, relations among the problems, convergence, and stability with respect to $p$ and to $\Phi$., Comment: 33 pages. Due to a miscommunication, we received one report after publication. This version incorporates the report's feedback and corrects the statement of Lemma 4.17 by adding a missing hypothesis

The INSPIRE project has built the largest sample of ultra-compact massive galaxies (UCMGs) at 0.12, and the other stellar population parameters.We use the Full-Index-Fitting method to fit the INSPIRE spectra to single stellar population (SSP) models. This allows us to measure, for the first time, the low-mass end slope of the IMF, as well as stellar metallicity [M/H], [Mg/Fe], [Ti/Fe] and [Na/Fe] ratios, and study correlations between them and the DoR. Similarly to normal-sized galaxies, UCMGs with larger stellar masses have overall higher metallicities. We found a correlation between the low-mass end of the IMF slope and the DoR, that, however, breaks down for systems with a more extended SFH. An even stronger dependency is found between the IMF and the fraction of mass formed at high-z. At equal velocity dispersion and metallicity, galaxies with a higher DoR have a dwarf-richer IMF than that of low-DoR counterparts. This might indicate that the cosmic epoch and formation mechanisms influence the fragmentation of the star formation cloud and hence might be the explanation for IMF variations detected in massive ETGs., Comment: 16 pages, 11 figures, submitted to MNRAS

Current Total Skin Electron Therapy (TSET) Stanford technique for cutaneous lymphoma, established in the 70's, involves a unique irradiation setup, i.e. patient's position and beam arrangement, for all patients with ensuing great variability in dose distribution and difficult dose optimization. A Geant4-based simulation has been developed to explore the possibility of personalizing the dose to each patient's anatomy. To achieve this optimization of the treatment method, this project enrolls different aspects of the clinical and computational techniques: starting with the knowledge of the experimental parameters involving TSET practice, passing through an innovative approach to model the patient's anatomy, a precise description of the electron beam and a validated configuration of the physics models handling the interactions of the electrons and of secondary particles. The Geant4-based simulation models the patient as a tessellated solid derived from the optical scan of her/his body, realistically reproduces the irradiation environment in detail and calculates the energy deposition corresponding to each facet of the patient's scanned surface. The resulting three-dimensional dose distribution constitutes the basis for the personalization of the medical treatement as appropriate to each patient's specific characteristics., Comment: Presented at the 2022 IEEE Nuclear Science Symposium

Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and properties that are implicit in universal algebra and algebraic theories. In particular, it is shown that the category of groups with a compatible action of a truss T (also called pointed T-modules) is isomorphic to the category of modules over the ring R(T) universally associated to the truss. This is widely used in the explicit description of free objects. Next, it is proven that the category of heaps of modules over T is isomorphic to the category of affine modules over R(T) and, in order to make the picture complete, that (in the unital case) these are in turn equivalent to a specific subcategory of the slice category of pointed T-modules over R(T). These correspondences and properties are then used to describe explicitly various (co)limits and to compare short exact sequences in the Barr-exact category of heaps of T-modules with short exact sequences as defined previously., Comment: 28 pages, comments are welcome

Making the first steps towards a classification of simple partial comodules, we give a general construction for partial comodules of a Hopf algebra \(H\) using central idempotents in right coideal subalgebras and show that any \(1\)-dimensional partial comodule is of that form. We conjecture that in fact all finite-dimensional simple partial \(H\)-comodules arise this way. For \(H = kG\) for some finite group \(G\), we give conditions for the constructed partial comodule to be simple, and we determine when two of them are isomorphic. If \(H = kG^*,\) then our construction recovers the work of M. Dokuchaev and N. Zhukavets. We also study the partial modules and comodules of the non-commutative non-cocommutative Kac-Paljutkin algebra \(\mathcal{A}\).

Two dimensional matrices with binary (0/1) entries are a common data structure in many research fields. Examples include ecology, economics, mathematics, physics, psychometrics and others. Because the columns and rows of these matrices represent distinct entities, they can equivalently be expressed as a pair of bipartite networks that are linked by projection. A variety of diversity statistics and network metrics can then be used to quantify patterns in these matrices and networks. But what should these patterns be compared to? In all of these disciplines, researchers have recognized the necessity of comparing an empirical matrix to a benchmark set of "null" matrices created by randomizing certain elements of the original data. This common need has nevertheless promoted the independent development of methodologies by researchers who come from different backgrounds and use different terminology. Here, we provide a multidisciplinary review of randomization techniques for matrices representing binary, bipartite networks. We aim to translate the concepts from different technical domains into a common language that is accessible to a broad scientific audience. Specifically, after briefly reviewing examples of binary matrix structures across different fields, we introduce the major approaches and common strategies for randomizing these matrices. We then explore the details of and performance of specific techniques, and discuss their limitations and computational challenges. In particular, we focus on the conceptual importance and implementation of structural constraints on the randomization, such as preserving row or columns sums of the original matrix in each of the randomized matrices. Our review serves both as a guide for empiricists in different disciplines, as well as a reference point for researchers working on theoretical and methodological developments in matrix randomization methods.

This paper presents the third data release of the INvestigating Stellar Population In RElics (INSPIRE) project, comprising 52 ultra-compact massive galaxies (UCMGs) observed with the X-Shooter spectrograph. We measure integrated stellar velocity dispersion, [Mg/Fe] abundances, ages, and metallicities for all the INSPIRE objects. We thus infer star formation histories and confirm the existence of a degree of relicness (DoR), defined in terms of the fraction of stellar mass formed by $z=2$, the time at which a galaxy has assembled 75\% of its mass, and the final assembly time. Objects with a high DoR assembled their stellar mass at early epochs, while low-DoR objects show a non-negligible fraction of later-formed populations and hence a spread in ages and metallicities. A higher DoR correlates with larger [Mg/Fe], super-solar metallicity, and larger velocity dispersion values. The 52 UMCGs span a large range of DoR from 0.83 to 0.06, with 38 of them having formed more than 75\% of their mass by $z=2$. Of these, nine are extreme relics (DoR$>0.7$), since they formed the totality ($>99\%$) of their stellar mass by redshift $z=2$. The remaining 14 UCMGs cannot be considered relics, as they are characterised by more extended star formation histories. With INSPIRE, we built the first sizeable sample of relics outside the local Universe, up to $z\sim0.4$, increasing the number of confirmed relics by a factor of $>10$, and opening up an important window to explain the mass assembly of massive galaxies in the high-z Universe., Comment: accepted for publication on MNRAS, 20 pages, 15 figures, 3 tables

Let A be a k-algebra over a commutative ring k. By the renowned Tannaka-Krein reconstruction, liftings of the monoidal structure from k-modules to A-modules correspond to bialgebra structures on A and liftings of the closed monoidal structure correspond to Hopf algebra structures on A. In this paper, we determine conditions on A that correspond to liftings of the closed structure alone, i.e. without considering the monoidal one, which lead to the notion of what we call a gabi-algebra. First, we tackle the question from the general perspective of monads, then we focus on the set-theoretic and the linear setting. Our main and most surprising result is that a normal gabi-algebra, that is an algebra A whose category of modules is (associative and unital normal) closed with closed forgetful functor to k-modules, is automatically a Hopf algebra (thus justifying our title)., Comment: 40 pages, comments are welcome

We exhibit a bijective correspondence between certain left ideal coideals in a Hopf algebroid for which the resulting quotient is a coequalizer and certain right coideal subrings which are themselves an equalizer, remarkably improving a recent result of the author obtained in collaboration with L. El Kaoutit, A. Ghobadi and J. Vercruysse. Interpreting this result in the Hopf algebra setting provides a bijective correspondence which extends the previously known cases., Comment: 13 pages, comments are welcome

We construct automorphisms of $\mathbb{C}^2$ with a cycle of escaping Fatou components, on which there are exactly two limit functions, both of rank 1. On each such Fatou component, the limit sets for these limit functions are two disjoint hyperbolic subsets of the line at infinity.

We measure the [${\alpha}$/Fe] abundances for 183 quiescent galaxies at z = 0.60 - 0.75 with stellar masses ranging 10.4 \leq log10 10.4 $\leq$ log10 (M$_*$ /M$_\odot$) $\leq$ 11.6 selected from the LEGA-C survey. We estimate [${\alpha}$/Fe] from the ratio of the spectral indices Mgb (${\lambda} \sim 5177$ {\AA}) and Fe4383, compared to predictions of simple stellar population models. We find that 91% of quiescents in our sample have supersolar [${\alpha}$/Fe], with an average value of [${\alpha}$/Fe] = +0.24 $\pm$ 0.01. We find no significant correlation between [${\alpha}$/Fe] and stellar metallicity, mass, velocity dispersion, and average formation time. Galaxies that formed the bulk of their stellar mass on time scales shorter than 1 Gyr follow the same [${\alpha}$/Fe] distribution as those which formed on longer time scales. In comparison to local early-type galaxies and to stacked spectra of quiescent galaxies at z = 0.38 and z = 0.07, we find that the average [${\alpha}$/Fe] has not changed between z = 0.75 and the present time. Our work shows that the vast majority of massive quiescent galaxies at z $\sim$ 0.7 are ${\alpha}$-enhanced, and that no detectable evolution of the average [${\alpha}$/Fe] has taken place over the last $\sim$ 6.5 Gyr., Comment: 12 pages, 10 figures, 2 tables, 1 appendix

Echo chambers, i.e. clusters of users exposed to news and opinions in line with their previous beliefs, were observed in many online debates on social platforms. We propose a completely unbiased entropy-based method for detecting echo chambers. The method is completely agnostic to the nature of the data. In the Italian Twitter debate about the Covid-19 vaccination, we find a limited presence of users in echo chambers (about 0.35% of all users). Nevertheless, their impact on the formation of a common discourse is strong, as users in echo chambers are responsible for nearly a third of the retweets in the original dataset. Moreover, in the case study observed, echo chambers appear to be a receptacle for disinformative content., Comment: 30 pages, 11 figures, 7 tables

We prove that, among weighted isotropic perimeters, only constant multiples of the Euclidean perimeter satisfy the monotonicity property on nested convex bodies. Although the analogous result fails for general weighted anisotropic perimeters, a similar characterization holds for radially-weighted anisotropic densities., Comment: 7 pages

We revise the procedure proposed by Balassa to infer comparative advantage, which is a standard tool, in Economics, to analyze specialization (of countries, regions, etc.). Balassa's approach compares the export of a product for each country with what would be expected from a benchmark based on the total volumes of countries and products flows. Based on results in the literature, we show that the implementation of Balassa's idea generates a bias: the prescription of the maximum likelihood used to calculate the parameters of the benchmark model conflicts with the model's definition. Moreover, Balassa's approach does not implement any statistical validation. Hence, we propose an alternative procedure to overcome such a limitation, based upon the framework of entropy maximisation and implementing a proper test of hypothesis: the `key products' of a country are, now, the ones whose production is significantly larger than expected, under a null-model constraining the same amount of information employed by Balassa's approach. What we found is that countries diversification is always observed, regardless of the strictness of the validation procedure. Besides, the ranking of countries' fitness is only partially affected by the details of the validation scheme employed for the analysis while large differences are found to affect the rankings of products Complexities. The routine for implementing the entropy-based filtering procedures employed here is freely available through the official Python Package Index PyPI.

For more than a decade scholars have been investigating the disinformation flow on social media contextually to societal events, like, e.g., elections. In this paper, we analyze the Twitter traffic related to the US 2020 pre-election debate and ask whether it mirrors the electoral system. The U.S. electoral system provides that, regardless of the actual vote gap, the premier candidate who received more votes in one state `takes' that state. Criticisms of this system have pointed out that election campaigns can be more intense in particular key states to achieve victory, so-called {\it swing states}. Our intuition is that election debate may cause more traffic on Twitter-and probably be more plagued by misinformation-when associated with swing states. The results mostly confirm the intuition. About 88\% of the entire traffic can be associated with swing states, and links to non-trustworthy news are shared far more in swing-related traffic than the same type of news in safe-related traffic. Considering traffic origin instead, non-trustworthy tweets generated by automated accounts, so-called social bots, are mostly associated with swing states. Our work sheds light on the role an electoral system plays in the evolution of online debates, with, in the spotlight, disinformation and social bots., Comment: 9 pages, 2 figures; Accepted @CySoc 2023, International Workshop on Cyber Social Threats, co-located with the ACM Web conference 2023, April 30, 2023. The present version is a preprint

The abundance of data about social relationships allows the human behavior to be analyzed as any other natural phenomenon. Here we focus on balance theory, stating that social actors tend to avoid establishing cycles with an odd number of negative links. This statement, however, can be supported only after a comparison with a benchmark. Since the existing ones disregard actors' heterogeneity, we extend Exponential Random Graphs to signed networks with both global and local constraints and employ them to assess the significance of empirical unbalanced patterns. We find that the nature of balance crucially depends on the null model: while homogeneous benchmarks favor the weak balance theory, according to which only triangles with one negative link should be under-represented, heterogeneous benchmarks favor the strong balance theory, according to which also triangles with all negative links should be under-represented. Biological networks, instead, display strong frustration under any benchmark, confirming that structural balance inherently characterizes social networks., Comment: 46 pages, 14 figures, 7 tables

This is the second data release (DR2) of the INvestigating Stellar Population In RElics (INSPIRE) project, comprising 21 new systems with observations completed before March 2022. For each system, we release four one-dimensional (1D) spectra to the ESO Science Archive, one spectrum for each arm of the X-Shooter spectrograph. In this paper, we focus on the line-of-sight velocity distribution, measuring integrated stellar velocity dispersions from the spectra, and assessing their robustness and the associated uncertainties. For each of the 21 new systems, we systematically investigated the effect of the parameters and set-ups of the full spectral fitting on the stellar velocity dispersion ($\sigma$) measurements. In particular, we tested how $\sigma$ changes when several parameters of the fit as well as the resolution and spectral coverage of the input spectra are varied. We found that the effect that causes the largest systematic uncertainties on $\sigma$ is the wavelength range used for the fit, especially for spectra with a lower signal-to-noise ratio (S/N $\leq$ 30). When using blue wavelengths (UVB arm) one generally underestimates the velocity dispersion (by $\sim$15 km/s). The values obtained from the near-IR (NIR) arm present a larger scatter because the quality of the spectra is lower. We finally compared our results with those in literature, finding a very good agreement overall. Joining results obtained in DR1 with those presented here, INSPIRE contains 40 ultra-compact massive galaxies, corresponding to 75% of the whole survey. By plotting these systems in a stellar mass-velocity dispersion diagram, we identify at least four highly reliable relic candidates among the new systems. Their velocity dispersion is larger than that of normal-sized galaxies of similar stellar mass., Comment: Accepted for publication, and in press on A&A

Satellite imagery is gaining popularity as a valuable tool to lower the impact on natural resources and increase profits for farmers. The purpose of this study is twofold: to mine the scientific literature to reveal the structure of this research domain, and to investigate to what extent scientific results can reach a wider public audience. To meet these two objectives, a Web of Science and a Twitter dataset were retrieved and analysed, respectively. For the academic literature, different performances of various countries were observed: the USA and China resulted as the leading actors, both in terms of published papers and employed researchers. Among the categorised keywords, "resolution", "Landsat", "yield", "wheat" and "multispectral" are the most used. Then, analysing the semantic network of the words used in the various abstracts, the different facets of the research in satellite remote sensing were detected. The importance of retrieving meteorological parameters through remote sensing and the broad use of vegetation indexes emerged from these analyses. As emerging topics, classification tasks for land use assessment and crop recognition stand out, alongside the use of hyperspectral sensors. Regarding the interaction of academia with the public, the analysis showed that it is practically absent on Twitter: most of the activity therein stems from private companies advertising their business. This shows that there is still a communication gap between academia and actors from other societal sectors., Comment: 30 pages, 13 figures. The version here is a draft, the final version can be found at the link: https://www.mdpi.com/2073-4395/13/2/576

We derived stellar ages and metallicities [Z/H] for $\sim$70 passive early type galaxies (ETGs) selected from VANDELS survey over the redshift range 1.0$<$$z$$<$1.4 and stellar mass range 10$<$log(M$_*$/M$_\odot$)$<$11.6. We find significant systematics in their estimates depending on models and wavelength ranges considered. Using the full-spectrum fitting technique, we find that both [Z/H] and age increase with mass as for local ETGs. Age and metallicity sensitive spectral indices independently confirm these trends. According to EMILES models, for 67 per cent of the galaxies we find [Z/H]$>$0.0, a percentage which rises to $\sim$90 per cent for log(M$_*$/M$_\odot$)$>$11 where the mean metallicity is [Z/H]=0.17$\pm$0.1. A comparison with homogeneous measurements at similar and lower redshift does not show any metallicity evolution over the redshift range 0.0$11.0 host stellar populations with [Z/H]>0.05, formed over short timescales ($\Delta{t50}$$<$1 Gyr) at early epochs (t$_{form}$$<$2 Gyr), implying high star formation rates (SFR$>$100 M$_\odot$/yr) in high mass density regions (log($\Sigma_{1kpc}$)$>$10 M$_\odot$/kpc$^2$). This sharp picture tends to blur at lower masses: log(M$_*$/M$_\odot$)$\sim$10.6 galaxies can host either old stars with [Z/H]$<$0.0 or younger stars with [Z/H]$>$0.0, depending on the duration ($\Delta{t50}$) of the SF. The relations between galaxy mass, age and metallicities are therefore largely set up ab initio as part of the galaxy formation process. Mass, SFR and SF time-scale all contribute to shape up the stellar mass-metallicity relation with the mass that modulates metals retention., Comment: 18 pages + Appendix, 16 figures, 5 tables. Accepted for publication in MNRAS

A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our $p$-energy is defined through a relaxation process, where a suitable $p$-rotation of inscribed polygonals is adopted. The discrete $p$-rotation we choose has a geometric flavor: a polygonal is viewed as an approximation to a smooth curve and hence its discrete curvature is spread out into a smooth density. For any exponent $p$ greater than one, the $p$-energy is finite if and only if the arc-length parameterization of the curve has a second order summability with the same growth exponent. In that case, moreover, the energy agrees with the natural extension of the integral of the $p$-th power of the scalar curvature. Finally, a comparison with other definitions of discrete curvatures is discussed., Comment: 19 pages, 1 figure

We provide a correspondence between one-sided coideal subrings and one-sided ideal two-sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional conditions, this correspondence becomes bijective for Hopf algebroids. As an application, we investigate normal Hopf ideals in commutative Hopf algebroids (affine groupoid schemes) in connection with the study of normal affine subgroupoids.

Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose properties may be tuned upon the characteristics of a given population. In the present paper, we introduce the Fitness-Corrected Block Model, an adjustable-density variation of the well-known Degree-Corrected Block Model, and we show that the proposed construction yields a maximum entropy model. When the network is sparse, we derive an analytical expression for the degree distribution of the model that depends on just the constraints and the chosen fitness-distribution. Our model is perfectly suited to define maximum-entropy data-driven spatial social networks, where each block identifies vertices having similar position (e.g., residence) and age, and where the expected block-to-block adjacency matrix can be inferred from the available data. In this case, the sparse-regime approximation coincides with a phenomenological model where the probability of a link binding two individuals is directly proportional to their sociability and to the typical cohesion of their age-groups, whereas it decays as an inverse-power of their geographic distance. We support our analytical findings through simulations of a stylized urban area., Comment: 14 pages, 1 figure

In this work we publish stellar velocity dispersions, sizes, and dynamical masses for 8 ultra-massive galaxies (UMGs; log($M$/M$_\odot>11$, $z\gtrsim3$) from the Massive Ancient Galaxies At $z>3$ NEar-infrared (MAGAZ3NE) Survey, more than doubling the number of such galaxies with velocity dispersion measurements at this epoch. Using the deep Keck/MOSFIRE and Keck/NIRES spectroscopy of these objects in the $H$- and $K$-bandpasses, we obtain large velocity dispersions of $\sim400$ km s$^{-1}$ for most of the objects, which are some of the highest stellar velocity dispersions measured, and $\sim40$\% larger than those measured for galaxies of similar mass at $z\sim1.7$. The sizes of these objects are also smaller by a factor of 1.5-3 compared to this same $z\sim1.7$ sample. We combine these large velocity dispersions and small sizes to obtain dynamical masses. The dynamical masses are similar to the stellar masses of these galaxies, consistent with a Chabrier initial mass function (IMF). Considered alongside previous studies of massive quiescent galaxies across $0.2

We extend a theorem, originally formulated by Blattner-Cohen-Montgomery for crossed products arising from Hopf algebras weakly acting on noncommutative algebras, to the realm of left Hopf algebroids. Our main motivation is an application to universal enveloping algebras of projective Lie-Rinehart algebras: for any given curved (resp. flat) connection, that is, a linear (resp. Lie-Rinehart) splitting of a Lie-Rinehart algebra extension, we provide a crossed (resp. smash) product decomposition of the associated universal enveloping algebra, and vice versa. As a geometric example, we describe the associative algebra generated by the invariant vector fields on the total space of a principal bundle as a crossed product of the algebra generated by the vertical ones and the algebra of differential operators on the base., Comment: 51 pages

To achieve sustainable development worldwide, the United Nations set 17 Sustainable Development Goals (SDGs) for humanity to reach by 2030. Society is involved in the challenge, with firms playing a crucial role. Thus, a key question is to what extent firms engage with the SDGs. Efforts to map firms' contributions have mainly focused on analysing companies' reports based on limited samples and non-real-time data. We present a novel interdisciplinary approach based on analysing big data from an online social network (Twitter) with complex network methods from statistical physics. By doing so, we provide a comprehensive and nearly real-time picture of firms' engagement with SDGs. Results show that: 1) SDGs themes tie conversations among major UK firms together; 2) the social dimension is predominant; 3) the attention to different SDGs themes varies depending on the community and sector firms belong to; 4) stakeholder engagement is higher on posts related to global challenges compared to general ones; 5) large UK companies and stakeholders generally behave differently from Italian ones. This paper provides theoretical contributions and practical implications relevant to firms, policymakers and management education. Most importantly, it provides a novel tool and a set of keywords to monitor the influence of the private sector on the implementation of the 2030 Agenda., Comment: 22 pages, 6 figures, 8 tables

Network theory has primarily focused on pairwise relationships, disregarding many-body interactions: neglecting them, however, can lead to misleading representations of complex systems. Hypergraphs represent an increasingly popular alternative for describing polyadic interactions: our innovation lies in leveraging the representation of hypergraphs based on the incidence matrix for extending the entropy-based framework to higher-order structures. In analogy with the Exponential Random Graphs, we name the members of this novel class of models Exponential Random Hypergraphs. Here, we focus on two explicit examples, i.e. the generalisations of the Erd\"os-R\'enyi Model and of the Configuration Model. After discussing their asymptotic properties, we employ them to analyse real-world configurations: more specifically, i) we extend the definition of several network quantities to hypergraphs, ii) compute their expected value under each null model and iii) compare it with the empirical one, in order to detect deviations from random behaviours. Differently from currently available techniques, ours is analytically tractable, scalable and effective in singling out the structural patterns of real-world hypergraphs differing significantly from those emerging as a consequence of simpler, structural constraints., Comment: 27 pages, 11 figures, 4 tables

Given an open, bounded, planar set $\Omega$, we consider its $p$-Cheeger sets and its isoperimetric sets. We study the set-valued map $\mathfrak{V}:[\frac12,+\infty)\rightarrow\mathcal{P}((0,|\Omega|])$ associating to each $p$ the set of volumes of $p$-Cheeger sets. We show that whenever $\Omega$ satisfies some geometric structural assumptions (convex sets are encompassed), the map is injective, and continuous in terms of $\Gamma$-convergence. Moreover, when restricted to $(\frac 12, 1)$ such a map is univalued and is in bijection with its image. As a consequence of our analysis we derive some fine boundary regularity result.