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Contrary to conventional massive MIMO cellular configurations plagued by inter-cell interference, cell-free massive MIMO systems distribute network resources across the coverage area, enabling users to connect with multiple access points (APs) and boosting both system capacity and fairness across user. In such systems, one critical functionality is the association between APs and users: determining the optimal association is indeed a combinatorial problem of prohibitive complexity. In this paper, a solution based on deep learning is thus proposed to solve the user clustering problem aimed at maximizing the sum spectral efficiency while controlling the number of active connections. The proposed solution can scale effectively with the number of users, leveraging long short-term memory cells to operate without the need for retraining. Numerical results show the effectiveness of the proposed solution, even in the presence of imperfect channel state information due to pilot contamination., Comment: Accepted to 25th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2024

In this paper, we introduce a novel post-processing algorithm that is both model-agnostic and does not require the sensitive attribute at test time. In addition, our algorithm is explicitly designed to enforce minimal changes between biased and debiased predictions; a property that, while highly desirable, is rarely prioritized as an explicit objective in fairness literature. Our approach leverages a multiplicative factor applied to the logit value of probability scores produced by a black-box classifier. We demonstrate the efficacy of our method through empirical evaluations, comparing its performance against other four debiasing algorithms on two widely used datasets in fairness research.

Superclusters are the largest-scale environments where a number of galaxy clusters interact with each other through minor/major mergers and grow via accretion along cosmic filaments. We focus on the A3528 complex in the core of the Shapley Supercluster. This system includes three clusters, A3528 (composed itself by two sub-clusters, namely A3528N and A3528S), A3532 and A3530, and presents a mildly active dynamical state. We study how minor mergers affect the evolution of radio galaxies and whether they are able to re-accelerate relativistic electrons in the ICM. We used observations from the uGMRT (Band 3, 4 and 5) and MeerKAT (L-band) telescopes to obtain images and spectral index maps over a wide frequency band and spatial resolutions. We compare these data with those from the SRG/eROSITA X-ray telescope. We detect faint diffuse radio emission associated with the radio galaxies. The BCGs in A3528S and A3532 show filaments of diffuse radio emission which extend for $\sim200-400$ kpc out of the radio galaxy. The spectral index of these filaments is extremely steep and almost constant ($\alpha\sim -2, -2.5$). Contrary to the radio tails in A3528N, the spectral properties of these radio filaments are not consistent with standard models of plasma ageing. We also detect roundish diffuse radio emission around the BCG in A3528S which could be classified as a radio mini-halo. The radio tail in this cluster appears longer that in earlier detections, being $\sim300$ kpc long at all frequencies. We linked the presence of extended radio emission in the form of filaments and threads in the A3528 complex with the effect of minor mergers. This is reinforced by the increasing X-ray fluctuations in correspondence with the radio extended emission in A3528S. Despite the less energy involved, our findings support the hypothesis that these events can re-energise plasma originating from radio galaxies., Comment: 28 pages, 23 figures and 5 tables; accepted for publication in Astronomy & Astrophysics

Fix integers $r\geq 4$ and $i\geq 2$. Let $C$ be a non-degenerate, reduced and irreducible complex projective curve in $\mathbb P^r$, of degree $d$, not contained in a hypersurface of degree $\leq i$. Let $p_a(C)$ be the arithmetic genus of $C$. Continuing previous research, under the assumption $d\gg \max\{r,i\}$, in the present paper we exhibit a Castelnuovo bound $G_0(r;d,i)$ for $p_a(C)$. In general, we do not know whether this bound is sharp. However, we are able to prove it is sharp when $i=2$, $r=6$ and $d\equiv 0,3,6$ (mod $9$). Moreover, when $i=2$, $r\geq 9$, $r$ is divisible by $3$, and $d\equiv 0$ (mod $r(r+3)/6$), we prove that if $G_0(r;d,i)$ is not sharp, then for the maximal value of $p_a(C)$ there are only three possibilities. The case in which $i=2$ and $r$ is not divisible by $3$ has already been examined in the literature. We give some information on the extremal curves., Comment: 19 pages

We study the radio continuum emission of four galaxies experiencing ram-pressure stripping in four clusters of the Shapley supercluster at redshift z~0.05. Multi-band (235-1367 MHz) radio data, complemented by integral-field spectroscopy, allow us to detect and analyse in detail the non-thermal component both in the galaxy discs and the radio continuum tails. Three galaxies present radio continuum tails which are tens of kiloparsecs long. By deriving the radio spectral index in the inner and outer tails and comparing our findings with the distribution of the extraplanar ionised gas and the results of N-body/hydrodynamical simulations, we demonstrate that these tails are caused by the ram pressure which, together with the ionised gas, sweeps the magnetic field from the galaxy discs. We suggest that the radio continuum emission in these tails can be differently powered by (i) in situ star formation; (ii) relativistic electrons stripped from the disc; (iii) shock excitation or a combination of them. All the ram-pressure stripped galaxies are found in environments where cluster-cluster interactions occurred and/or are ongoing thus strongly supporting the thesis that cluster and group collisions and mergers may locally increase the ram pressure and trigger hydrodynamical interactions between the intracluster medium and the interstellar medium of galaxies., Comment: 18 pages, 14 figures, accepted for publication in MNRAS

When the Bekenstein-Hawking entropy is modified, ambiguity often arises concerning whether the Hawking temperature or the thermodynamic mass should be modified. The common practice, however, is to keep the black hole solution the same as that in general relativity. On the other hand, if Jacobson's method of deriving Einstein equations from thermodynamic is valid in the general settings, then given a generalized entropy one should first derive the corresponding modified gravity, and then look for the compatible black hole solution before investigating its thermodynamics. We comment on some properties and subtleties in this approach. In particular, we point out that generically generalized entropy would lead to a varying effective gravitational "constant" theory, where $G_\text{eff}$ depends on the horizon area. We discuss in what ways such theories are discernible from general relativity despite its seemingly jarring differences, and how to make sense of area-dependent field equations. As a consequence we show that in the Jacobson's approach, the standard quantum gravitational logarithmic correction to Bekenstein-Hawking entropy is equivalent to a running gravitational "constant". A horizon area dependent $G_\text{eff}$ could also lead to a coupling between black hole masses and cosmological expansion, a scenario that has been studied recently in the literature, but so far lacks strong theoretical motivation. In the Tsallis case, we show that the thermodynamic mass for a Schwarzschild black hole is just a constant multiple of its ADM mass, which is considerably simpler than the approach not utilizing the Jacobson's method., Comment: Minor changes; also added/fixed some references

A fraction of galaxy clusters harbor diffuse radio sources known as radio halos. The currently adopted scenario for their formation is based on second-order Fermi re-acceleration of seed electrons that is driven by merger-driven turbulence in the intra-cluster medium. This mechanism is expected to be inefficient, which implies that a significant fraction of halos should have very steep ($\alpha < -1.5$) energy spectra. We start investigating the potential and current limitations of the combination of the two surveys conducted by LOFAR, LoTSS (144 MHz) and LoLSS (54 MHz), to probe the origin of radio halos. We follow up the 20 radio halos detected in the DR1 of LoTSS, which covers the HETDEX field, with the LoLSS survey, and we study their spectral properties between 54 and 144 MHz. After the removal of compact sources, 9 halos were excluded due to unreliable halo flux density measurements at 54 MHz. Our main finding is that 7 out of 11 ($\sim$ 64%) exhibit an ultra-steep spectrum ($\alpha < -1.5$), which is a key prediction of turbulent re-acceleration models. We also note a tentative trend for more massive systems to host flatter halos, although the currently poor statistics does not allow for a deeper analysis. Our sample suffers from low angular resolution at 54 MHz, which limits the accuracy of the compact-sources subtraction. Nevertheless, this study is the first step towards providing compelling evidence for the existence of a large fraction of radio halos with very steep spectrum, which is a fundamental prediction of turbulent re-acceleration models. In this regard, the forthcoming second data release of LoLSS, along with the integration of LOFAR international stations and the instrumental upgrade to LOFAR2.0, will improve both the statistics and the low-frequency angular resolution, allowing to conclusively determine the origin of radio halos in galaxy clusters., Comment: A&A Letter; 11 pages, 12 figures

Federated Learning (FL) has emerged as a promising approach for privacy-preserving machine learning, particularly in sensitive domains such as healthcare. In this context, the TRUSTroke project aims to leverage FL to assist clinicians in ischemic stroke prediction. This paper provides an overview of the TRUSTroke FL network infrastructure. The proposed architecture adopts a client-server model with a central Parameter Server (PS). We introduce a Docker-based design for the client nodes, offering a flexible solution for implementing FL processes in clinical settings. The impact of different communication protocols (HTTP or MQTT) on FL network operation is analyzed, with MQTT selected for its suitability in FL scenarios. A control plane to support the main operations required by FL processes is also proposed. The paper concludes with an analysis of security aspects of the FL architecture, addressing potential threats and proposing mitigation strategies to increase the trustworthiness level.

The connected sum construction, which takes as input Gorenstein rings and produces new Gorenstein rings, can be considered as an algebraic analogue for the topological construction having the same name. We determine the graded Betti numbers for connected sums of graded Artinian Gorenstein algebras. Along the way, we find the graded Betti numbers for fiber products of graded rings; an analogous result was obtained in the local case by Geller. We relate the connected sum construction to the doubling construction, which also produces Gorenstein rings. Specifically, we show that a connected sum of doublings is the doubling of a fiber product ring.

Low-frequency radio observations show an increasing number of radio galaxies located in galaxy clusters that display peculiar morphologies and spectral profiles. This is the result of the dynamical interaction of the galaxy with the surrounding medium. Studying this phenomenon is key to understanding the evolution of low-energy relativistic particles in the intracluster medium. We present a multi-frequency study of the three head-tail (HT) radio galaxies and the radio halo in the galaxy cluster ZwCl0634.1+4747. We make use of observations at four frequencies performed with LOFAR LBA (53 MHz), HBA (144 MHz), GMRT (323 MHz) and VLA (1518 MHz) data. The use of extremely low radio frequency observations, such as LOFAR at 53 and 144 MHz, allowed us to detect the extension of the tails up to a distance of ~ 1 Mpc. We extracted spectral profiles along the tails in order to identify possible departures from a pure ageing model, such as the Jaffe-Perola (JP) model, which only involves synchrotron and inverse-Compton losses. We found clear evidence of departures from this simple ageing model, such as surface brightness enhancement and spectral flattening along all of the tails. This can be interpreted as the consequence of particle re-acceleration along the tails. Possible explanations for this behaviour include the interaction between a shock and the radio tails or a turbulence-driven re-acceleration mechanism. We show that the latter scenario is able to reproduce the characteristic features that we observed in our profiles.

The Next Generation Very Large Array (ngVLA) is a planned radio interferometer providing unprecedented sensitivity at wavelengths between 21 cm and 3 mm. Its 263 antenna element array will be spatially distributed across North America to enable both superb low surface brightness recovery and sub-milliarcsecond angular resolution imaging. The project was developed by the international astronomy community under the lead of the National Radio Astronomy Observatory (NRAO), and is anticipated to be built between 2027 and 2037. Two workshops have been held in 2022 and 2023 with the goal to discuss and consolidate the scientific interests in the ngVLA within the German astronomical community. This community paper constitutes a collection of 48 science ideas which the German community aims to pursue with the ngVLA in the 2030s. This is not a complete list and the ideas are not developed at the level of a "Science Book", such that the present document is mainly meant provide a basis for further discussion within the community. As such, additional contributions are welcome, and will be considered for inclusion in future revisions., Comment: Version 2.0 (status June 18, 2024): 169 pages, comments and future contributions welcome [v2.0: 7 new science cases added, some minor revisions to other chapters]

We introduce and study a notion of Castelnuovo-Mumford regularity suitable for rational normal scroll surfaces. In this setting we prove analogs of some classical properties. We prove splitting criteria for coherent sheaves and a characterization of Ulrich bundles. Finally we study logarithmic bundles associated to arrangements of lines and rational curves.

Let $R=K[x,y,z]$. A reduced plane curve $C=V(f)\subset \mathbf P^2$ is $free \ $ if its associated module of tangent derivations $\mathrm{Der}(f)$ is a free $R$-module, or equivalently if the corresponding sheaf $T_ {\mathbf P^2 }(-\log C)$ of vector fields tangent to $C$ splits as a direct sum of line bundles on $\mathbf P^2$. In general, free curves are difficult to find, and in this note, we describe a new method for constructing free curves in $\mathbf P^2$. The key tools in our approach are eigenschemes and pencils of curves, combined with an interpretation of Saito's criterion in this context. Previous constructions typically applied only to curves with quasihomogeneous singularities, which is not necessary in our approach. We illustrate our method by constructing large families of free curves.

Cosmological simulations predict the presence of warm hot thermal gas in the cosmic filaments that connect galaxy clusters. This gas is thought to constitute an important part of the missing baryons in the Universe. In addition to the thermal gas, cosmic filaments could contain a population of relativistic particles and magnetic fields. A detection of magnetic fields in filaments can constrain early magnetogenesis in the cosmos. So far, the resulting diffuse synchrotron emission has only been indirectly detected. We present our search for thermal and non-thermal diffuse emission from inter-cluster regions of 106 paired galaxy clusters by stacking the $0.6-2.3$~keV X-ray and 144~MHz radio data obtained with the eROSITA telescope on board the Spectrum-Roentgen-Gamma (SRG) observatory and LOw Frequency ARray (LOFAR), respectively. The stacked data do not show the presence of X-ray and radio diffuse emission in the inter-cluster regions. This could be due to the sensitivity of the data sets and/or the limited number of cluster pairs used in this study. Assuming a constant radio emissivity in the filaments, we find that the mean radio emissivity is not higher than $1.2\times10^{-44}\,{\rm erg \, s^{-1} \, cm^{-3} \, Hz^{-1}}$. Under equipartition conditions, our upper limit on the mean emissivity translates to an upper limit of $\sim75\,{\rm nG}$ for the mean magnetic field strength in the filaments, depending on the spectral index and the minimum energy cutoff. We discuss the constraint for the magnetic field strength in the context of the models for the formation of magnetic fields in cosmic filaments., Comment: Accepted for publication on MNRAS on June 5, 2023

Many galaxy clusters show diffuse cluster-scale emission in the form of radio halos, showing that magnetic fields and relativistic electrons are mixed in with the intra-cluster medium (ICM). There is general agreement that the origin of radio halos is connected to turbulence, generated during cluster mergers. Statistical studies of large samples of galaxy clusters in the radio band have the potential to unveil the connection between the properties of radio halos and the mass and dynamics of the host clusters. Previous studies have been limited to massive clusters and based on a small number of radio halos. The aim of this paper is to investigate the scaling relation between the radio power of radio halos and the mass of the host clusters at low frequencies and down to lower cluster masses. We analysed the clusters from the second catalogue of Planck Sunyaev Zel'dovich sources that lie within the 5634 sq deg covered by the second Data Release of the LOFAR Two-meter Sky Survey. We derived the correlation between the radio power and the mass of the host clusters and we investigated the distribution of clusters without radio halos with respect to the correlation. We use X-ray observations to classify the dynamical state of clusters and investigate its role on the power of radio halos. We found a correlation between the power of radio halos at 150 MHz and the mass of the host clusters down to 3e14 Msun. This correlation has a large scatter, part of which can be attributed to the different dynamical states of host clusters. We used two statistical test to show that the distribution of clusters with and without (upper limits) radio halos in the mass-radio power diagram is not compatible with a single correlation and that it is also not compatible with clusters being uniformly distributed below an upper envelope constituted by the correlation., Comment: 12 pages, 7 figures, submitted to A&A

We present the peculiar case of PSZ2G091.83+26.11 at z=0.822. This cluster hosts a Mpc-scale radio halo and an elongated radio source, whose location with the respect to the intracluster medium (ICM) distribution and to the cluster centre is not consistent with a simple merger scenario. We use VLA data at 1-4 GHz to investigate the spectral and polarisation properties of the diffuse radio emission. We combine them with previously published data from LOFAR n the 120-168 MHz band, and from the uGMRT at 250-500 and 550-900 MHz. We also complement the radio data with Chandra X-ray observations to compare the thermal and non-thermal emission of the cluster. The elongated radio emission is visible up to 3.0 GHz and has an integrated spectral index of $-1.24\pm0.03$, with a steepening from $-0.89\pm0.03$ to $-1.39\pm0.03$. These values correspond to Mach numbers $\mathcal{M}_{\rm radio,int}=3.0\pm0.19$ and $\mathcal{M}_{\rm radio,inj}=2.48\pm0.15$. Chandra data reveals a surface brightness discontinuity at the location of the radio source, with a compression factor of $\mathcal{C}=2.22^{+0.39}_{-0.30}$ (i.e. $\mathcal{M}_{\rm Xray}=1.93^{+0.42}_{-0.32}$). We also find that the source is polarised at GHz frequencies. We estimate an intrinsic polarisation fraction of $\sim0.2$, a Rotation Measure of $\sim50~{\rm rad~m^{-2}}$ (including the Galactic contribution) and an external depolarisation of $\sim60~{\rm rad~m^{-2}}$. The $B$-vectors are aligned with the major axis of the source, suggesting magnetic field compression. Hence, we classify this source as a radio relic. We also find a linear/super-linear correlation between the non-thermal and thermal emission. We propose an off-axis merger and/or multiple merger events to explain the position and orientation of the relic. Given the properties of the radio relic, we speculate that PSZ2G091.83+26.11 is in a fairly young merger state., Comment: 21 pages, 17 figures, 9 tables; accepted for publication in Astronomy & Astrophysics

Diffuse cluster-scale synchrotron radio emission is discovered in an increasing number of galaxy clusters in the form of radio halos (RHs), probing the presence of relativistic electrons and magnetic fields in the intra-cluster medium. The favoured scenario to explain their origin is that they trace turbulent regions generated during cluster mergers where particles are re-accelerated. In this framework, RHs are expected to probe cluster dynamics and are predicted to be more frequent in massive systems. Statistical studies are important to study the connection of RHs with cluster dynamics and to constrain theoretical models. Furthermore, low-frequency surveys can shed light on the existence of RHs with very steep radio-spectra, a key prediction of turbulent models. We study the properties of RHs from clusters of the second catalog of Planck Sunyaev Zel'dovich detected sources that lie within the 5634 deg^2 covered by the second Data Release (DR2) of the LOFAR Two-meter Sky Survey. We find that the number of observed RHs, their radio flux density and redshift distributions are in line with what is expected in the framework of the re-acceleration scenario. In addition, the fraction of clusters with RHs increases with the cluster mass, confirming the leading role of the gravitational process of cluster formation in the generation of RHs. These models predict a large fraction of RHs with very steep spectrum in the DR2 Planck sample, this will be tested in future studies, yet a comparison of the occurrence of halos in GMRT and LOFAR samples indeed shows a larger occurrence of RHs at lower frequencies suggesting the presence of a number of very steep spectrum RH that is preferentially detected by LOFAR. Using morphological information we confirm that RHs are preferentially located in merging systems and that the fraction of newly LOFAR discovered RHs is larger in less disturbed systems., Comment: 12 pages, 10 figures, accepted for publication in A&A

Context. It is well-established that shock waves in the intracluster medium launched by galaxy cluster mergers can produce synchrotron emission, which is visible to us at radio frequencies as radio relics. However, the particle acceleration mechanism producing these relics is still not fully understood. It is also unclear how relics relate to radio halos, which trace merger-induced turbulence in the intracluster medium. Aims. We aim to perform the first statistical analysis of radio relics in a mass-selected sample of galaxy clusters, using homogeneous observations. Methods. We analysed all relics observed by the Low Frequency Array Two Metre Sky Survey Data Release 2 (LoTSS DR2) at 144 MHz, hosted by galaxy clusters in the second Planck catalogue of SZ sources (PSZ2). We measured and compared the relic properties in a uniform, unbiased way. In particular, we developed a method to describe the characteristic downstream width in a statistical manner. Additionally, we searched for differences between radio relic-hosting clusters with and without radio halos. Results. We find that, in our sample, $\sim$ 10% of galaxy clusters host at least one radio relic. We confirm previous findings, at higher frequencies, of a correlation between the relic-cluster centre distance and the longest linear size, as well as the radio relic power and cluster mass. However, our findings suggest that we are still missing a population of low-power relics. We also find that relics are wider than theoretically expected, even with optimistic downstream conditions. Finally, we do not find evidence of a single property that separates relic-hosting clusters with and without radio halos., Comment: 28 pages, 17 figures. Accepted for publication in A&A

The hot plasma within merging galaxy clusters is predicted to be filled with shocks and turbulence that may convert part of their kinetic energy into relativistic electrons and magnetic fields generating synchrotron radiation. Analyzing Low Frequency Array (LOFAR) observations of the galaxy cluster Abell 2255, we show evidence of radio synchrotron emission distributed over very large scales of at least 5 megaparsec. The pervasive radio emission witnesses that shocks and turbulence efficiently transfer kinetic energy into relativistic particles and magnetic fields in a region that extends up to the cluster outskirts. The strength of the emission requires a magnetic field energy density at least 100 times higher than expected from a simple compression of primordial fields, presumably implying that dynamo operates efficiently also in the cluster periphery. It also suggests that nonthermal components may contribute substantially to the pressure of the intracluster medium in the cluster periphery., Comment: Published in Science Advances on Nov 2nd, 2022. 8 pages, 5 images

We exhibit a new proof, relying on bivariant theory, that the nilpotent cone is rationally smooth. Our approach enables us to prove a slightly more general statement.

The central regions of galaxy clusters are permeated by magnetic fields and filled with relativistic electrons. When clusters merge, the magnetic fields are amplified and relativistic electrons are re-accelerated by turbulence in the intra cluster medium. These electrons reach energies of 1 -- 10 GeV and, in the presence of magnetic fields, produce diffuse radio halos that typically cover an area of ~1 square Mpc. Here we report observations of four clusters whose radio halos are embedded in much more extended, diffuse radio emission, filling a volume 30 times larger than that of radio halos. The emissivity in these larger features is about 20 times lower than the emissivity in radio halos. We conclude that relativistic electrons and magnetic fields extend far beyond radio halos, and that the physical conditions in the outer regions of the clusters are quite different from those in the radio halos., Comment: 21 pages, 8 figures, Nature in press

Thanks to built-in immutability and persistence, the blockchain is often seen as a promising technology to certify information. However, when the information does not originate from the blockchain itself, its correctness cannot be taken for granted. To address this limitation, blockchain oracles -- services that validate external information before storing it in a blockchain -- were introduced. In particular, when the validation cannot be automated, oracles rely on humans that collaboratively cross-check external information. In this paper, we present DeepThought, a distributed human-based oracle that combines voting and reputation schemes. An empirical evaluation compares DeepThought with a state-of-the-art solution and shows that our approach achieves greater resistance to voters corruptions in different configurations.