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The vertical evolution of galactic discs is governed by the sub-structures within them. We examine the diversity of kinematic sub-structure present in the first 12 galaxies observed from the GECKOS survey, a VLT/MUSE large programme providing a systematic study of 35 edge-on, Milky Way-mass disc galaxies. Employing the nGIST analysis pipeline, we derive the mean line-of-sight stellar velocity ($V_{\star}$), velocity dispersion ($\sigma_{\star}$), skew ($h_{3}$), and kurtosis ($h_{4}$) for the sample, and examine 2D maps and 1D line profiles. Visually, the majority of this sample (8/12) are found to possess boxy-peanut bulges and host the corresponding kinematic structure predicted for stellar bars viewed in projection. Four galaxies exhibit strong evidence for the presence of nuclear discs, including central $h_{3}$-$V_{\star}$ anti-correlations, `croissant'-shaped central depressions in $\sigma_{\star}$ maps, strong gradients in $h_{3}$, and positive $h_{4}$ plateaus over the expected nuclear disc extent. The strength of the $h_{3}$ feature corresponds to the size of the nuclear disc, measured from the $h_{3}$ turnover radius. We can explain the features within the kinematic maps of all sample galaxies via disc structure(s) alone. We do not find any need to invoke the existence of dispersion-dominated bulges. Obtaining the specialised data products for this paper and the broader GECKOS survey required significant development of existing integral field spectroscopic (IFS) analysis tools. Therefore, we also present the nGIST pipeline: a modern, sophisticated, and easy-to-use pipeline for the analysis of galaxy IFS data. We conclude that the variety of kinematic sub-structures seen in GECKOS galaxies requires a contemporary view of galaxy morphology, expanding on the traditional view of galaxy structure, and uniting the kinematic complexity observed in the Milky Way with the extragalactic., Comment: 32 pages (9 of which are appendix), 26 figures, submitted to A&A. Comments welcome!

Galaxies grow through star formation (in-situ) and accretion (ex-situ) of other galaxies. Reconstructing the relative contribution of these two growth channels is crucial for constraining the processes of galaxy formation in a cosmological context. In this on-going work, we utilize a conditional variational autoencoder along with a normalizing flow - trained on a state-of-the-art cosmological simulation - in an attempt to infer the posterior distribution of the 2D ex-situ stellar mass distribution of galaxies solely from observable two-dimensional maps of their stellar mass, kinematics, age and metallicity. Such maps are typically obtained from large Integral Field Unit Surveys such as MaNGA. We find that the average posterior provides an estimate of the resolved accretion histories of galaxies with a mean ~10% error per pixel. We show that the use of a normalizing flow to conditionally sample the latent space results in a smaller reconstruction error. Due to the probabilistic nature of our architecture, the uncertainty of our predictions can also be quantified. To our knowledge, this is the first attempt to infer the 2D ex-situ fraction maps from observable maps., Comment: 6 pages, 3 figures

Let $(f,g): (S,s) \to (\mathbb{C}^2, 0)$ be a finite morphism from a germ of normal complex analytic surface to the germ of $\mathbb{C}^2$ at the origin. We show that the affine algebraic curve in $\mathbb{C}^2$ defined by the initial Newton polynomial of a defining series of the discriminant germ of $(f,g)$ depends up to toric automorphisms only on the germs of curves defined by $f$ and $g$. This result generalizes a theorem of Gryszka, Gwo\'zdziewicz and Parusi\'nski, which is the special case in which $(S,s)$ is smooth. Our proof uses a common generalization of formulas of L\^e and Casas-Alvero for the intersection number of the discriminant with a germ of plane curve. It uses also a theorem of Delgado and Maugendre characterizing the special members of pencils of curves on normal surface singularities. We apply it to the pencils generated by all pairs $(f^b, g^a)$, for varying positive integral exponents $a, b$, following a strategy initiated by Gwo\'zdziewicz. This is similar to the Eudoxian method of comparison of magnitudes by comparing the sizes of their positive integral multiples., Comment: 27 pages, 3 figures

Cosmic voids, distinguished by their low-density environment, provide a unique opportunity to explore the interplay between the cosmic environment and the processes of galaxy formation and evolution. Data on the molecular gas has been scarce so far. In this paper, we continue previous research done in the CO-CAVITY pilot project to study the molecular gas content and properties in void galaxies to search for possible differences compared to galaxies that inhabit denser structures. We observed at the IRAM 30 m telescope the CO(1-0) and CO(2-1) emission of 106 void galaxies selected from the CAVITY survey. Together with data from the literature, we obtained a sample of 200 void galaxies with CO data. We conducted a comprehensive comparison of the specific star formation rate (sSFR = SFR/M$_*$), the molecular gas fraction (MH$_2$/M$_*$), and the star formation efficiency (SFE = SFR/MH$_2$) between the void galaxies and a comparison sample of galaxies in filaments and walls, selected from the xCOLD GASS survey. We found no statistically significant difference between void galaxies and the comparison sample in the molecular gas fraction as a function of stellar mass for galaxies on the star-forming main sequence (SFMS). However, for void galaxies, the SFE was found to be constant across all stellar mass bins, while there is a decreasing trend with M$_*$ for the comparison sample. Finally, we found some indications for a smaller dynamical range in the molecular gas fraction as a function of distance to the SFMS in void galaxies. Overall, our analysis finds that the molecular gas properties of void galaxies are not very different from denser environments. The physical origin of the most significant difference that we found - a constant SFE as a function of stellar mass in void galaxies - is unclear and requires further investigation and higher-resolution data., Comment: 26 pages, 9 figures. Accepted for publication in A&A

The ability to discover new materials with desirable properties is critical for numerous applications from helping mitigate climate change to advances in next generation computing hardware. AI has the potential to accelerate materials discovery and design by more effectively exploring the chemical space compared to other computational methods or by trial-and-error. While substantial progress has been made on AI for materials data, benchmarks, and models, a barrier that has emerged is the lack of publicly available training data and open pre-trained models. To address this, we present a Meta FAIR release of the Open Materials 2024 (OMat24) large-scale open dataset and an accompanying set of pre-trained models. OMat24 contains over 110 million density functional theory (DFT) calculations focused on structural and compositional diversity. Our EquiformerV2 models achieve state-of-the-art performance on the Matbench Discovery leaderboard and are capable of predicting ground-state stability and formation energies to an F1 score above 0.9 and an accuracy of 20 meV/atom, respectively. We explore the impact of model size, auxiliary denoising objectives, and fine-tuning on performance across a range of datasets including OMat24, MPtraj, and Alexandria. The open release of the OMat24 dataset and models enables the research community to build upon our efforts and drive further advancements in AI-assisted materials science., Comment: 19 pages

In this paper we describe the factorization of the higher order polars of a generic branch in its equisingularity class. We generalize the results of Casas-Alvero and Hefez-Hernandes-Hern\'andez to higher order polars.

Far-from-equilibrium phenomena unveil the intricate principles of complex systems, including snowflake growth and fluid turbulence, with broad applications ranging from foreign exchange trading to climate modeling. A recurring feature across these systems is the emergence of a spectral cascade, where energy is transferred across the system's length scales, following a simple power law. The statistical theory of weak wave turbulence, in which only leading order interactions are considered, successfully predicts scaling laws for stationary states in idealised scenarios. Realistic conditions, such as finite size and amplitude effects, and strong dissipation, remain beyond our current understanding. Lacking comprehensive theoretical insight, we experimentally trace the formation of a spectral cascade under these conditions. Using an externally driven fluid-fluid interface, we successfully resolve individual wave modes and track their real-time evolution from one to few to many. This process culminates in a steady state whose power spectral density is fully characterised by a power-law scaling. We further quantify specific interactions through statistical correlations to reveal a hierarchy in the wave-mixing order, thus confirming a key assumption of weak-wave turbulence. We present a comprehensive time-evolution analysis that is crucial in identifying critical points where the interface undergoes significant changes. Our findings validate that the interfacial dynamics can be effectively modelled using a weakly nonlinear Lagrangian theory, enabling us to explore its applicability to other out-of-equilibrium systems. Notably, we uncover intriguing connections to reheating scenarios following cosmic inflation in the early universe.

The Calar Alto Void Integral-field Treasury surveY (CAVITY) is a legacy project aimed at characterising the population of galaxies inhabiting voids, which are the most under-dense regions of the cosmic web, located in the Local Universe. This paper describes the first public data release (DR1) of CAVITY, comprising science-grade optical data cubes for the initial 100 out of a total of $\sim$300 galaxies in the Local Universe ($0.005 < z < 0.050$). These data were acquired using the integral-field spectrograph PMAS/PPak mounted on the 3.5m telescope at the Calar Alto observatory. The DR1 galaxy sample encompasses diverse characteristics in the color-magnitude space, morphological type, stellar mass, and gas ionisation conditions, providing a rich resource for addressing key questions in galaxy evolution through spatially resolved spectroscopy. The galaxies in this study were observed with the low-resolution V500 set-up, spanning the wavelength range 3745-7500 \AA, with a spectral resolution of 6.0 \AA\ (FWHM). Here, we describe the data reduction and characteristics and data structure of the CAVITY datasets essential for their scientific utilisation, highlighting such concerns as vignetting effects, as well as the identification of bad pixels and management of spatially correlated noise. We also provide instructions for accessing the CAVITY datasets and associated ancillary data through the project's dedicated database., Comment: 17 pages, 9 figures, 5 tables. Accepted for publication in A&A (replacement after minor language edits)

At the same time that artificial intelligence is becoming popular, concern and the need for regulation is growing, including among other requirements the data privacy. In this context, Federated Learning is proposed as a solution to data privacy concerns derived from different source data scenarios due to its distributed learning. The defense mechanisms proposed in literature are just focused on defending against adversarial attacks and the performance, leaving aside other important qualities such as explainability, fairness to poor quality clients, dynamism in terms of attacks configuration and generality in terms of being resilient against different kinds of attacks. In this work, we propose RAB$^2$-DEF, a $\textbf{r}$esilient $\textbf{a}$gainst $\textbf{b}\text{yzantine}$ and $\textbf{b}$ackdoor attacks which is $\textbf{d}$ynamic, $\textbf{e}$xplainable and $\textbf{f}$air to poor clients using local linear explanations. We test the performance of RAB$^2$-DEF in image datasets and both byzantine and backdoor attacks considering the state-of-the-art defenses and achieve that RAB$^2$-DEF is a proper defense at the same time that it boosts the other qualities towards trustworthy artificial intelligence.

We aim to trace the evolution of eight edge-on star-forming disc galaxies through the analysis of stellar population properties of their thin and thick discs. These galaxies have relatively low stellar masses (4 $\times$ 10$^9$ to 6 $\times$ 10$^{10}$ $M_{\odot}$). We use Multi-Unit Spectroscopic Explorer (MUSE) observations and full-spectrum fitting to produce spatially resolved maps of ages, metallicities and [Mg/Fe]-abundances and extract the star formation histories of stellar discs. Our maps show thick discs that are on average older, more metal-poor and more [Mg/Fe]-enhanced than thin discs. However, age differences between thin and thick discs are small (around 2 Gyr) and the thick discs are younger than previously observed in more massive and more quiescent galaxies. Both thin and thick discs show mostly sub-solar metallicities, and the vertical metallicity gradient is milder than previously observed in similar studies. [Mg/Fe] differences between thick and thin discs are not sharp. The star formation histories of thick discs extend down to recent times, although most of the mass in young stars was formed in thin discs. Our findings show thick discs that are different from old quiescent thick discs previously observed in galaxies of different morphologies and/or different masses. We propose that thick discs in these galaxies did not form quickly at high redshift, but slowly in an extended time. Also, the thin discs formed slowly, however, a larger mass fraction was created at very recent times., Comment: 20 pages, 9 figures, submitted to A&A

This proposal outlines the future plans of the Brazilian High-Energy Physics (HEP) community for upcoming collider experiments. With the construction of new particle colliders on the horizon and the ongoing operation of the High-Luminosity LHC, several research groups in Brazil have put forward technical proposals, covering both hardware and software contributions, as part of the Brazilian contribution to the global effort. The primary goal remains to foster a unified effort within the Brazilian HEP community, optimizing resources and expertise to deliver a high-impact contribution to the international HEP community., Comment: 24 pages, submitted to the Latin American Strategy Forum for Research Infrastructure

We aim to investigate how the local environment influences the star formation history (SFH) of galaxies residing in various large-scale environments. We categorise a sample of 9384 galaxies into the three primary large scale structures (voids, walls \& filaments, and clusters) and further classify them based on their local environment (as either "singlets" or group members), through a search of companion galaxies within sky-projected distances $\Delta r_p < 0.45$ Mpc and velocity differences $\Delta v < 160$ $\text{km s}^{-1}$. Subsequently, we explore these subsamples through SFH data from previous works. Throughout the study, galaxies are divided into long-timescale SFH galaxies (LT-SFH), which assemble their mass steadily along cosmic time, and short-timescale SFH galaxies (ST-SFH), which form their stars early. We then compare characteristic mass assembly look-back times. The distributions of mass assembly look-back times in ST-SFH galaxies are statistically different for singlets and groups. These differences are only found in LT-SFH galaxies when studying these distributions in stellar mass bins. Our results indicate that the large-scale environment is related to a delay in mass assembly of up to $\sim$2 Gyr, while this delay is $<$1 Gyr in the case of local environment. The effect of both kinds of environment is more significant in less massive galaxies, and in LT-SFHs. Our results are consistent with galaxies in groups assembling their stellar mass earlier than singlets, especially in voids and lower mass galaxies. Local environment plays a relevant role in stellar mass assembly times, although we find that large-scale structures also cause a delay in mass assembly, more so in the case of cluster galaxies., Comment: 7 pages, 4 figures. Accepted for publication in A&A

In this work, we analysed young stellar clusters with spatial and kinematic coherence in the Orion star-forming complex. For this study, we selected a sample of pre-main sequence candidates using parallaxes, proper motions and positions on the colour-magnitude diagram. After applying a hierarchical clustering algorithm in the 5D parameter space provided by Gaia DR3, we divided the recovered clusters into two regimes: Big Structures and Small Structures, defined by the number of detected stars per cluster. In the first regime, we found 13 stellar groups distributed along the declination axis in the regions where there is a high density of stars. In the second regime, we recovered 34 clusters classified into two types: 14 as small groups completely independent from the larger structures, including four candidates of new clusters, and 12 classified as sub-structures embedded within five larger clusters. Additionally, radial velocity data from APOGEE-2 and GALAH DR3 was included to study the phase space in some regions of the Orion complex. From the Big Structure regime, we found evidence of a general expansion in the Orion OB1 association over a common centre, giving a clue about the dynamical effects the region is undergoing. Likewise, in the Small Structure regime, the projected kinematics shows the ballistic expansion in the $\lambda$ Orionis association and the detection of likely events of clusters' close encounters in the OB1 association., Comment: 19 pages, 17 figures, 3 tables, accepted in MNRAS

The properties of metric perturbations are determined in the context of an expanding Universe governed by a modified theory of gravity with a non-minimal coupling between curvature and matter. We analyse the dynamics of the 6 components of a general helicity decomposition of the metric and stress-energy perturbations, consisting of scalar, vector and tensor sectors. The tensor polarisations are shown to still propagate luminally, in agreement with recent data from gravitational interferometry experiments, while their magnitude decays with an additional factor sourced by the nonminimal coupling. We show that the production of these modes is associated with a modified quadrupole formula at leading order. The vector perturbations still exhibit no radiative behaviour, although their temporal evolution is found to be modified, with spatial dependence remaining unaffected. We establish that the scalar perturbations can no longer be treated as identical. We investigate the scalar sector by writing the modified model as an equivalent two-field scalar-tensor theory and find the same scalar degrees of freedom as in previous literature. The different sectors are paired with the corresponding polarisation modes, which can be observationally measured by their effects on the relative motion of test particles, thus providing the possibility of testing the modified theory and constraining its parameters., Comment: 34 pages, 3 figures

We investigate the ability of the Euclid telescope to detect galaxy-scale gravitational lenses. To do so, we perform a systematic visual inspection of the $0.7\,\rm{deg}^2$ Euclid ERO data towards the Perseus cluster using both the high-resolution VIS $I_{\scriptscriptstyle\rm E}$ band, and the lower resolution NISP bands. We inspect every extended source brighter than magnitude $23$ in $I_{\scriptscriptstyle\rm E}$ with $41$ expert human classifiers. This amounts to $12\,086$ stamps of $10^{\prime\prime}\,\times\,10^{\prime\prime}$. We find $3$ grade A and $13$ grade B candidates. We assess the validity of these $16$ candidates by modelling them and checking that they are consistent with a single source lensed by a plausible mass distribution. Five of the candidates pass this check, five others are rejected by the modelling and six are inconclusive. Extrapolating from the five successfully modelled candidates, we infer that the full $14\,000\,{\rm deg}^2$ of the Euclid Wide Survey should contain $100\,000^{+70\,000}_{-30\,000}$ galaxy-galaxy lenses that are both discoverable through visual inspection and have valid lens models. This is consistent with theoretical forecasts of $170\,000$ discoverable galaxy-galaxy lenses in Euclid. Our five modelled lenses have Einstein radii in the range $0.\!\!^{\prime\prime}68\,<\,\theta_\mathrm{E}\,<1.\!\!^{\prime\prime}24$, but their Einstein radius distribution is on the higher side when compared to theoretical forecasts. This suggests that our methodology is likely missing small Einstein radius systems. Whilst it is implausible to visually inspect the full Euclid data set, our results corroborate the promise that Euclid will ultimately deliver a sample of around $10^5$ galaxy-scale lenses., Comment: 21 pages, 20 figures, submitted to A&A

The hierarchical model of galaxy evolution suggests that the impact of mergers is substantial on the intricate processes that drive stellar assembly within a galaxy. However, accurately measuring the contribution of accretion to a galaxy's total stellar mass and its balance with in-situ star formation poses a persistent challenge, as it is neither directly observable nor easily inferred from observational properties. Here, we present theory-motivated predictions for the fraction of stellar mass originating from mergers in a statistically significant sample of nearby galaxies, using data from MaNGA. Employing a robust machine learning model trained on mock MaNGA analogs (MaNGIA) in turn obtained from a cosmological simulation (TNG50), we unveil that in-situ stellar mass dominates almost across the entire stellar mass spectrum (1e9Msun < M* < 1e12Msun). Only in more massive galaxies (M* > 1e11Msun) does accreted mass become a substantial contributor, reaching up to 35-40% of the total stellar mass. Notably, the ex-situ stellar mass in the nearby universe exhibits significant dependence on galaxy characteristics, with higher accreted fractions favored by elliptical, quenched galaxies and slow rotators, as well as galaxies at the center of more massive dark matter halos., Comment: 16 pages, 7 Figures. Accepted for publication

The Laser Interferometer Space Antenna (LISA) will be a space-borne gravitational wave (GW) detector to be launched in the next decade. Central to LISA data analysis is time-delay interferometry (TDI), a numerical procedure which drastically reduces otherwise overwhelming laser frequency noise. LISA data analysis is usually performed on sets of TDI variables, e.g. Michelson variables $(X, Y, Z)$ or quasiorthogonal variables $(A, E, T)$. We investigate a less standard TDI variable denoted $\kappa$ which depends on time, or frequency, and two parameters $(\beta, \lambda)$. This so-called coronagraphic TDI variable has the singular property of canceling GW signal when $(\beta, \lambda)$ tend to the sky position of the GW source. Thanks to this property, coronagraphic TDI has the potential to be an efficient model-agnostic method for sky localization of GW sources with LISA. Those characteristics make it relevant for low-latency searches and a possible glitch veto. Although briefly discussed in the literature, coronagraphic TDI has only been tested on theoretical grounds. In this paper we validate the applicability of $\kappa$ to sky localization of typical LISA sources, namely Galactic binaries (GBs) and massive black hole binaries (MBHBs), when considering a simplified LISA instrument. The goal of this paper is to pave the way for applications of coronagraphic TDI to practical LISA data analysis problems., Comment: 15 pages, 13 figures

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

We have learnt in the last decades that the majority of galaxies belong to high density regions interconnected in a sponge-like fashion. This large-scale structure is characterised by clusters, filaments, walls, where most galaxies concentrate, but also under-dense regions, called voids. The void regions and the galaxies within represent an ideal place for the study of galaxy formation and evolution as they are largely unaffected by the complex physical processes that transform galaxies in high-density environments. These void galaxies can hold the key as well to answer current challenges to the $\Lambda$CDM paradigm. The Calar Alto Void Integral-field Treasury surveY (CAVITY) is a Legacy project approved by the Calar Alto Observatory to obtain spatially resolved spectroscopic information of $\sim300$ void galaxies in the Local Universe (0.005 < z < 0.050) covering from -17.0 to -21.5 in $\rm r$ band absolute magnitude. It officially started in January 2021 and has been awarded 110 useful dark observing nights at the 3.5 m telescope using the PMAS spectrograph. Complementary follow-up projects including deep optical imaging, integrated, as well as resolved CO data, and integrated HI spectra, have joint the PMAS observations and naturally complete the scientific aim of characterising galaxies in cosmic voids. The extension data has been denominated CAVITY+. The data will be available to the whole community in different data releases, the first of which is planned for July 2024, and it will provide the community with PMAS data cubes for around 100 void galaxies through a user friendly, and well documented, database platform. We present here the survey, sample selection, data reduction, quality control schemes, science goals, and some examples of the scientific power of the CAVITY and CAVITY+ data., Comment: 19 pages, 11 figures. Accepted for publication in A&A - Replacement after A&A minor language edition

Linear scalar cosmological perturbations have increasing spectra in the contracting phase of bouncing models. We study the conditions for which these perturbations may collapse into primordial black holes and the hypothesis that these objects constitute a fraction of dark matter. We compute the critical density contrast that describes the collapse of matter perturbations in the flat-dust bounce model with a parametric solution, obtained from the Lemaitre-Tolman-Bondi metric that represents the spherical collapse. We discuss the inability of the Newtonian gauge to describe perturbations in contracting models as the perturbative hypothesis does not hold in such cases. We carry the calculations for a different Gauge choice and compute the perturbations power spectra numerically. Finally, assuming a Gaussian distribution, we compute the primordial black hole abundance with the Press-Schechter formalism and compare it with observational constraints. From our analysis, we conclude that the primordial black hole formation in a dust-dominated contracting phase does not lead to a significant mass fraction of primordial black holes in dark matter today., Comment: 39 pages, 8 figures

This paper studies Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators F that fails to be concave or convex in the space of symmetric matrices. In a first scenario, it is considered that F enjoys a small ellipticity aperture. In our second case, we study regularity results where the convexity of the superlevel (or sublevel) sets is verified, implying that the operator F is quasiconcave (or quasiconvex).

Most of the observed galaxies cannot be resolved into individual stars and are studied through their integrated spectrum using simple stellar populations (SSPs) models, with stellar libraries being a key ingredient in building them. Spectroscopic observations are increasingly being directed towards the near-infrared (NIR), where much is yet to be explored. SSPs in the NIR are still limited, and there are inconsistencies between different sets of models. One of the ways to minimize this problem is to have reliable NIR stellar libraries. The main goal of this work is to present SMARTY (mileS Moderate resolution neAr-infRared sTellar librarY) a ~0.9-2.4$\mu$m stellar spectral library composed of 31 stars observed with the Gemini Near-IR Spectrograph (GNIRS) at the 8.1m Gemini North telescope and make it available to the community. The stars were chosen from the SMARTY library, for which the atmospheric parameters are reliable (and well tested), to populate different regions of the Hertzsprung-Russell (HR) diagram. Furthermore, five of these stars have NIR spectra available that we use to assess the quality of SMARTY. The remaining 26 stars are presented for the first time in the NIR. We compared the observed SMARTY spectra with synthetic and interpolated spectra, finding a mean difference of ~20% in the equivalent widths and ~1% in the overall continuum shape in both sets of comparisons. We computed the spectrophotometric broadband magnitudes and colours and compared them with the 2MASS ones, resulting in mean differences up to 0.07 and 0.10mag in magnitudes and colours, respectively. In general, a small difference was noted between the SMARTY spectra corrected using the continuum from the interpolated and the theoretical stars.

In this paper we consider an appropriate ordering of the Laurent monomials $x^{i}y^{j}$, $i,j \in \mathbb{Z}$ that allows us to study sequences of orthogonal Laurent polynomials of the real variables $x$ and $y$ with respect to a positive Borel measure $\mu$ defined on $\mathbb{R}^2$ such that $\{ x=0 \}\cup \{ y=0 \} \not\in \textrm{supp}(\mu)$. This ordering is suitable for considering the {\em multiplication plus inverse multiplication operator} on each varibale $\left( x+\frac{1}{x}\right.$ and $\left. y+\frac{1}{y}\right)$, and as a result we obtain five-term recurrence relations, Christoffel-Darboux and confluent formulas for the reproducing kernel and a related Favard's theorem. A connection with the one variable case is also presented, along with some applications for future research.

We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first seeks a set of edges that leaves no disconnected nodes in the network; the second seeks a causal large connected component in the data. We tested these methods both for discrete synthetic and real data, and compared the results with those obtained for the PC algorithm, which we took as the benchmark. We show that this novel algorithm is generally faster and more accurate than the PC algorithm. The algorithm for determining the thresholds requires choosing a measure of causality. We tested our methods for Fisher Correlations, commonly used in PC algorithm (for instance in \cite{kalisch2005}), and further proposed a discrete and asymmetric measure of causality, that we called Net Influence, which provided very good results when inferring causal networks from discrete data. This metric allows for inferring directionality of the edges in the process of applying the thresholds, speeding up the inference of causal DAGs., Comment: 17 pages, 12 figures

The Universe is shaped as a web-like structure, formed by clusters, filaments, and walls that leave large volumes in between named voids. Galaxies in voids have been found to be of a later type, bluer, less massive, and to have a slower evolution than galaxies in denser environments (filaments and walls). However, the effect of the void environment on their stellar population properties is still unclear. We aim to address this question using 118 optical integral field unit datacubes from the Calar Alto Void Integral-field Treasury surveY (CAVITY), observed with the PMAS/PPaK spectrograph at the 3.5m telescope at the Calar Alto Observatory (Almer\'ia, Spain). We used the non-parametric full spectral fitting code STARLIGHT to estimate their stellar population properties: stellar mass, stellar mass surface density, age, star formation rate (SFR), and specific star formation rate (sSFR). We analysed the results through the global and spatially resolved properties. Then, we compared them with a control sample of galaxies in filaments and walls from the CALIFA survey, matched in stellar mass and morphological type. Key findings include void galaxies having a slightly higher half-light radius (HLR), lower stellar mass surface density, and younger ages across all morphological types, and slightly elevated SFR and sSFR (only significant enough for Sas). Many of these differences appear in the outer parts of spiral galaxies in voids (HLR > 1), which are younger and exhibit a higher sSFR, indicative of less evolved discs. This trend is also found for early-type spirals, suggesting a slower transition from star-forming to quiescent states in voids. Our analysis indicates that void galaxies, influenced by their surroundings, undergo a more gradual evolution, especially in their outer regions, with a more pronounced effect for low-mass galaxies., Comment: 24 pages, 22 figures, 5 tables. Accepted for publication in A&A. Updated references list

Given two images, we can estimate the relative camera pose between them by establishing image-to-image correspondences. Usually, correspondences are 2D-to-2D and the pose we estimate is defined only up to scale. Some applications, aiming at instant augmented reality anywhere, require scale-metric pose estimates, and hence, they rely on external depth estimators to recover the scale. We present MicKey, a keypoint matching pipeline that is able to predict metric correspondences in 3D camera space. By learning to match 3D coordinates across images, we are able to infer the metric relative pose without depth measurements. Depth measurements are also not required for training, nor are scene reconstructions or image overlap information. MicKey is supervised only by pairs of images and their relative poses. MicKey achieves state-of-the-art performance on the Map-Free Relocalisation benchmark while requiring less supervision than competing approaches.

In the realm of Artificial Intelligence (AI), the need for privacy and security in data processing has become paramount. As AI applications continue to expand, the collection and handling of sensitive data raise concerns about individual privacy protection. Federated Learning (FL) emerges as a promising solution to address these challenges by enabling decentralized model training on local devices, thus preserving data privacy. This paper introduces FLEX: a FLEXible Federated Learning Framework designed to provide maximum flexibility in FL research experiments. By offering customizable features for data distribution, privacy parameters, and communication strategies, FLEX empowers researchers to innovate and develop novel FL techniques. The framework also includes libraries for specific FL implementations including: (1) anomalies, (2) blockchain, (3) adversarial attacks and defences, (4) natural language processing and (5) decision trees, enhancing its versatility and applicability in various domains. Overall, FLEX represents a significant advancement in FL research, facilitating the development of robust and efficient FL applications., Comment: Submitted to Information Fusion

Let $\mathcal{F}$ be a holomorphic foliation at $p\in\mathbb{C}^2$, and $B$ be a separatrix of $\mathcal{F}$. We prove the following Dimca-Greuel type inequality $3\mu_p(\mathcal{F},B)-4\tau_p(\mathcal{F},B)+GSV_p(\mathcal{F},B)\leq 0$, where $\mu_p(\mathcal{F},B)$ is the multiplicity of $\mathcal{F}$ along $B$, $\tau_p(\mathcal{F},B)$ is the dimension of the quotient of $\mathbb{C}\{x,y\}$ by the ideal generated by the components of any $1$-form defining $\mathcal{F}$ and any equation of $B$, and $GSV_p(\mathcal{F},B)$ is the \textit{G\'omez-Mont-Seade-Verjovsky index} of the foliation $\mathcal{F}$ with respect to $B$. As a consequence, we provide a new proof of the $\frac{4}{3}$-Dimca-Greuel conjecture for singularities of irreducible plane curve germs, with foliations ingredients, that differs from those given by Alberich-Carrami\~nana, Almir\'on, Blanco, Melle-Hern\'andez and Genzmer-Hernandes, but it is in line with the idea developed by Wang., Comment: 12 pages. We have modified the hypothesis of the main theorem and its proof

Let $K$ be a nonempty subset of a Banach space $X$. A mapping $T\colon K\to K$ is called $\mathfrak{cm}$-nonexpansive if for any sequence $(u_i)_{i=1}^\infty$ and $y$ in $K$, $\limsup_{i\to\infty} \sup_{A\subset\{1,\dots, n\}}\|\sum_{k\in A} \big(T u_{i+k} - Ty\big)\|\leq \limsup_{i\to\infty} \sup_{A\subset\{1,\dots, n\}}\|\sum_{k\in A} (u_{i+k} - y)\|$ for all $n\in\mathbb{N}$. As a subclass of the class of nonexpansive maps, its FPP is well-established in a wide variety of spaces. The main result of this paper is a fixed point result relating $\mathfrak{cm}$-nonexpansiveness, $\ell_1$ spreading models and Schauder bases with not-so-large basis constants. As a consequence, we deduce that Banach spaces with the weak Banach-Saks property have the fixed point property for $\mathfrak{cm}$-nonexpansive maps., Comment: In this new version we have improved the results obtained in order to more easily cover non-affine maps. arXiv admin note: text overlap with arXiv:2302.04323

The presently open problem of the Hubble tension is shown to be removed in the context of a modified theory of gravity with a non-minimal coupling between curvature and matter. By evolving the cosmological parameters that match the cosmic microwave background data until their values from direct late-time measurements, we obtain an agreement between different experimental methods without disrupting their individual validity. These modified gravity models are shown to provide adequate fits for other observational data from recent astrophysical surveys and to reproduce the late-time accelerated expansion of the Universe without the inclusion of a cosmological constant. This compatibility with observations presents further evidence of the versatility of these models in mimicking diverse cosmological phenomena in a unified manner., Comment: 12 pages, 6 figures, Final version with corrections from peer review