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We use the statistics of the VIPERS survey to investigate the relation between the surface mean stellar mass density Sigma=Mstar/(2*pi*Re^2) of massive passive galaxies (MPGs, Mstar>10^11 Msun) and their environment in the redshift range 0.52*10^11 Msun, we find an excess of MPGs with low Sigma and a deficit of high-Sigma MPGs in the densest regions wrt other environments. We interpret this result as due to the migration of some high-Sigma MPGs (<1% of the total population of MPGs) into low-Sigma MPGs, probably through mergers or cannibalism of small satellites. In summary, our results imply that the accretion of satellite galaxies has a marginal role in the mass-assembly history of most MPGs. We have previously found that the number density of VIPERS massive star-forming galaxies (MSFGs) declines rapidily from z=0.8 to z=0.5, which mirrors the rapid increase in the number density of MPGs. This indicates that the MSFGs at z>0.8 migrate to the MPG population. Here, we investigate the Sigma-delta relation of MSFGs at z>0.8 and find that it is consistent within 1 sigma with that of low-Sigma MPGs at z<0.8. Thus, the results of this and our previous paper show that MSFGs at z>0.8 are consistent in terms of number and environment with being the progenitors of low-Sigma MPGs at z<0.8., Comment: 12 pages, accepted for publication in A&A

The concept of metastable convergence was identified by Tao;it allows converting theorems about convergence into stronger theorems about uniform convergence. The Uniform Metastability Principle (UMP) states that if $T$ is a theorem about convergence, then the fact that $T$ is valid implies automatically that its (stronger) uniform version is valid, provided that $T$ can be stated in certain logical frameworks. In this paper we identify precisely the logical frameworks $L$ for which UMP holds. More precisely, we prove that the UMP holds for $L$ if and only if $L$ is a compact logic. We also prove a topological version of this equivalence. We conclude by proving new characterizations of logical compactness that yield additional information about the UMP.

Galaxy cluster counts in bins of mass and redshift have been shown to be a competitive probe to test cosmological models. This method requires an efficient blind detection of clusters from surveys with a well-known selection function and robust mass estimates. The Euclid wide survey will cover 15000 deg$^2$ of the sky in the optical and near-infrared bands, down to magnitude 24 in the $H$-band. The resulting data will make it possible to detect a large number of galaxy clusters spanning a wide-range of masses up to redshift $\sim 2$. This paper presents the final results of the Euclid Cluster Finder Challenge (CFC). The objective of these challenges was to select the cluster detection algorithms that best meet the requirements of the Euclid mission. The final CFC included six independent detection algorithms, based on different techniques, such as photometric redshift tomography, optimal filtering, hierarchical approach, wavelet and friend-of-friends algorithms. These algorithms were blindly applied to a mock galaxy catalog with representative Euclid-like properties. The relative performance of the algorithms was assessed by matching the resulting detections to known clusters in the simulations. Several matching procedures were tested, thus making it possible to estimate the associated systematic effects on completeness to $<3$%. All the tested algorithms are very competitive in terms of performance, with three of them reaching $>80$% completeness for a mean purity of 80% down to masses of $10^{14}$ M$_{\odot}$ and up to redshift $z=2$. Based on these results, two algorithms were selected to be implemented in the Euclid pipeline, the AMICO code, based on matched filtering, and the PZWav code, based on an adaptive wavelet approach. [abridged], Comment: A&A, in press. Only changes in affiliations and names between v1,v2,v3

We prove the impossibility of finding explicit finitary definitions of the spaces of Tsirelson and Schlumprecht in continuous first-order logic.

We use model theory of metric structures to prove the pointwise convergence, with a uniform metastability rate, of averages of a polynomial sequence $\{T_n\}$ (in Leibman's sense) of unitary transformations of a Hilbert space. As a special case, this applies to unitary sequences $\{U^{p(n)}\}$ where $p$ is a polynomial $\mathbb{Z}\to\mathbb{Z}$ and $U$ a fixed unitary operator; however, our convergence results hold for arbitrary Leibman sequences. As a case study, we show that the non-nilpotent "lamplighter group" $\mathbb{Z}\wr\mathbb{Z}$ is realized as the range of a suitable quadratic Leibman sequence. We also indicate how these convergence results generalize to arbitrary Folner averages of unitary polynomial actions of any abelian group $\mathbb{G}$ in place of $\mathbb{Z}$., Comment: To appear in Contemporary Mathematics, "Mexican Mathematicians around the World (Casa Matem\'atica Oaxaca, 2018)". This version adds a new subsection (2.2) proving that the range of some quadratic Leibman sequence realizes the non-nilpotent lamplighter group $\mathbb{Z}\wr\mathbb{Z}$

We present the results of a search for galaxy clusters and groups in the $\sim2$ square degree of the COSMOS field using all available X-ray observations from the XMM-Newton and Chandra observatories. We reach an X-ray flux limit of $3\times10^{-16}\;ergs\;cm^{-2}\;s^{-1}$ in 0.5--2 keV range, and identify 247 X-ray groups with $M_{200c}=8\times10^{12}-3\times10^{14}\;M_{\odot}$ at a redshift range of $0.08\leq z<1.53$, using the multiband photometric redshift and the master spectroscopic redshift catalogues of the COSMOS. The X-ray centres of groups are determined using high-resolution Chandra imaging. We investigate the relations between the offset of the brightest group galaxies (BGGs) from halo X-ray centre and group properties and compare with predictions from semi-analytic models and hydrodynamical simulations. We find that BGG offset decreases with both increasing halo mass and decreasing redshift with no strong dependence on the X-ray flux and SNR. We show that the BGG offset decreases as a function of increasing magnitude gap with no considerable redshift dependent trend. The stellar mass of BGGs in observations extends over a wider dynamic range compared to model predictions. At $z<0.5$, the central dominant BGGs become more massive than those with large offsets by up to 0.3dex, in agreement with model prediction. The observed and predicted lognormal scatter in the stellar mass of both low- and large-offset BGGs at fixed halo mass is $\sim0.3$dex., Comment: Accepted 2018 November 16 (MNRAS)

We present the version of the point source catalogue of the XXL Survey that was used, in part, in the first series of XXL papers. In this paper we release, in our database in Milan and at CDS: (i) the X-ray source catalogue with 26056 objects in two areas of 25 deg2; (ii) the associated multiwavelength catalogues with candidate counterparts of the X-ray sources in the infrared, near-infrared, optical, and ultraviolet (plus spectroscopic redshift when available); and (iii) a catalogue of spectroscopic redshifts recently obtained in the southern XXL area. We also present the basic properties of the X-ray point sources and their counterparts. Other catalogues described in the second series of XXL papers will be released contextually, and will constitute the second XXL data release., Comment: 19 pages, 11 figures, part of A&A Special Issue "The XXL Survey: second series" https://www.aanda.org/component/toc/?task=topic&id=927

In the currently debated context of using clusters of galaxies as cosmological probes, the need for well-defined cluster samples is critical. The XXL Survey has been specifically designed to provide a well characterised sample of some 500 X-ray detected clusters suitable for cosmological studies. The main goal of present article is to make public and describe the properties of the cluster catalogue in its present state, as well as of associated catalogues as super-clusters and fossil groups. We release a sample containing 365 clusters in total. We give the details of the follow-up observations and explain the procedure adopted to validate the cluster spectroscopic redshifts. Considering the whole XXL cluster sample, we have provided two types of selection, both complete in a particular sense: one based on flux-morphology criteria, and an alternative based on the [0.5-2] keV flux within one arcmin of the cluster centre. We have also provided X-ray temperature measurements for 80$\%$ of the clusters having a flux larger than 9$\times$10$^{-15}$$\rm \thinspace erg \, s^{-1} \, cm^{-2}$. Our cluster sample extends from z$\sim$0 to z$\sim$1.2, with one cluster at z$\sim$2. Clusters were identified through a mean number of six spectroscopically confirmed cluster members. Our updated luminosity function and luminosity-temperature relation are compatible with our previous determinations based on the 100 brightest clusters, but show smaller uncertainties. We also present an enlarged list of super-clusters and a sample of 18 possible fossil groups. This intermediate publication is the last before the final release of the complete XXL cluster catalogue when the ongoing C2 cluster spectroscopic follow-up is complete. It provides a unique inventory of medium-mass clusters over a 50~\dd\ area out to z$\sim$1., Comment: A&A, in press Shortened abstract Full catalogues available online, see paper

Context. We present an estimation of cosmological parameters with clusters of galaxies. Aims. We constrain the $\Omega_m$, $\sigma_8$, and $w$ parameters from a stand-alone sample of X-ray clusters detected in the 50 deg$^2$ XMM-XXL survey with a well-defined selection function. Methods. We analyse the redshift distribution of a sample comprising 178 high S/N clusters out to a redshift of unity. The cluster sample scaling relations are determined in a self-consistent manner. Results. In a lambda cold dark matter ($\Lambda$CDM) model, the cosmology favoured by the XXL clusters compares well with results derived from the Planck S-Z clusters for a totally different sample (mass/redshift range, selection biases, and scaling relations). However, with this preliminary sample and current mass calibration uncertainty, we find no inconsistency with the Planck CMB cosmology. If we relax the $w$ parameter, the Planck CMB uncertainties increase by a factor of $\sim$10 and become comparable with those from XXL clusters. Combining the two probes allows us to put constraints on $\Omega_m$=0.316$\pm$0.060, $\sigma_8$=0.814$\pm$0.054, and $w$=-1.02$\pm$0.20. Conclusions. This first self-consistent cosmological analysis of a sample of serendipitous XMM clusters already provides interesting insights into the constraining power of the XXL survey. Subsequent analysis will use a larger sample extending to lower confidence detections and include additional observable information, potentially improving posterior uncertainties by roughly a factor of 3., Comment: 11 pages, 5 figures, 5 tables, accepted as a letter by Astronomy & Astrophysics