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Quasi-periodic eruptions (QPEs) are an extreme X-ray variability phenomenon associated with low-mass supermassive black holes. First discovered in the nucleus of the galaxy GSN 069, they have been so far securely detected in five other galaxies, including RX J1301.9+2747. When detected, the out-of-QPE emission (quiescence) is consistent with the high-energy tail of thermal emission from an accretion disk. We present the X-ray and radio properties of RX J1301.9+2747, both in quiescence and during QPEs. We analyse X-ray data taken during five XMM-Newton observations between 2000 and 2022. The last three observations were taken in coordination with radio observations with the Karl G. Jansky Very Large Array. We also make use of EXOSAT, ROSAT, and Chandra archival observations taken between 1983 and 2009. XMM-Newton detected 34 QPEs of which 8 have significantly lower amplitudes than the others. No correlated radio/X-ray variability was observed during QPEs. In terms of timing properties, the QPEs in RX J1301.9+2747 do not exhibit the striking regularity observed in the discovery source GSN 069. In fact there is no clear repetition pattern between QPEs: the average time separation between their peaks is about four hours, but it can be as short as one, and as long as six hours. The QPE spectral properties of RX J1301.9+2747 as a function of energy are however very similar to those of GSN 069 and of other QPE sources. The quiescent emission of RX J1301.9+2747 is more complex than that of GSN 069, as it requires a soft X-ray excess-like component in addition to the thermal emission from the accretion disk. Its long-term X-ray quiescent flux variations are of low-amplitude and not strictly monotonic, with a general decay over $\sim 22$ years. We discuss our observational results in terms of some of the ideas and models that have been proposed so far for the physical origin of QPEs., Comment: Accepted for publication in Astronomy & Astrophysics. 22 pages and 17 figures in the main text; 11 pages, 5 tables, and 4 figures in the Appendix. Abstract shortened to comply with arXiv requirements

Using data from the first flight of SPIDER and from Planck HFI, we probe the properties of polarized emission from interstellar dust in the SPIDER observing region. Component separation algorithms operating in both the spatial and harmonic domains are applied to probe their consistency and to quantify modeling errors associated with their assumptions. Analyses spanning the full SPIDER region demonstrate that i) the spectral energy distribution of diffuse Galactic dust emission is broadly consistent with a modified-blackbody (MBB) model with a spectral index of $\beta_\mathrm{d}=1.45\pm0.05$ $(1.47\pm0.06)$ for $E$ ($B$)-mode polarization, slightly lower than that reported by Planck for the full sky; ii) its angular power spectrum is broadly consistent with a power law; and iii) there is no significant detection of line-of-sight decorrelation of the astrophysical polarization. The size of the SPIDER region further allows for a statistically meaningful analysis of the variation in foreground properties within it. Assuming a fixed dust temperature $T_\mathrm{d}=19.6$ K, an analysis of two independent sub-regions of that field results in inferred values of $\beta_\mathrm{d}=1.52\pm0.06$ and $\beta_\mathrm{d}=1.09\pm0.09$, which are inconsistent at the $3.9\,\sigma$ level. Furthermore, a joint analysis of SPIDER and Planck 217 and 353 GHz data within a subset of the SPIDER region is inconsistent with a simple MBB at more than $3\,\sigma$, assuming a common morphology of polarized dust emission over the full range of frequencies. These modeling uncertainties have a small--but non-negligible--impact on limits on the cosmological tensor-to-scalar ratio derived from the \spider dataset. The fidelity of the component separation approaches of future CMB polarization experiments may thus have a significant impact on their constraining power., Comment: 21 pages, 15 figures

Pulsar Timing Array (PTA) collaborations reported evidence of a nano-Hz stochastic gravitational wave background (sGWB) compatible with an adiabatically inspiraling population of massive black hole binaries (MBHBs). Despite the large uncertainties, the relatively flat spectral slope of the recovered signal suggests a possible prominent role of MBHB dynamical coupling with the environment or/and the presence of an eccentric MBHB population. This work aims at studying the capabilities of future PTA experiments to detect single MBHBs under the realistic assumption that the sGWB is originated from an eccentric binary population coupled with its environment. To this end, we generalize the standard signal-to-noise ratio (SNR) and Fisher Information Matrix calculations used in PTA for circular MBHBs to the case of eccentric systems. We consider an ideal 10-year MeerKAT and 30-year SKA PTAs and apply our method over a wide number of simulated eccentric MBHB populations. We find that the number of resolvable MBHBs for the SKA (MeerKAT) PTA is ${\sim}\,30$ ($4$) at $\rm SNR\,{>}\,5$ (${>}\,3$), featuring an increasing trend for larger eccentricity values of the MBHB population. This is the result of eccentric MBHBs at ${\lesssim}\,10^{-9}\, \rm Hz$ emitting part of their power at high harmonics, thus reaching the PTA sensitivity band. Our results also indicate that resolved MBHBs do not follow the eccentricity distribution of the underlying MBHB population, but prefer low eccentricity values (${<}\,0.6$). Finally, the recovery of binary intrinsic properties and sky-localization do not depend on the system eccentricity, while orbital parameters such as eccentricity and initial orbital phase show clear trends. Although simplified, our results show that SKA will enable the detection of tens of MBHBs, projecting us into the era of precision gravitational wave astronomy at nano-Hz frequencies., Comment: 17 pages, 11 figures, submitted to A&A

Motivated by the recent discovery of superconductivity in twisted bilayer WSe$_2$, we analyze the correlated physics in this system in the framework of a continuum model for the moir\'e superlattice. Using the symmetries in a fine-tuned limit of the system, we identify the strong-coupling ground states and their fate when the perturbations caused by finite bandwidth, displacement field, and the phase of the intralayer potential are taken into account. We classify the superconducting instabilities and, employing a spin-fermion-like model, study the superconducting instabilities in proximity to these insulating particle-hole orders. This reveals that only a neighboring intervalley coherent phase (with zero or finite wave vector) is naturally consistent with the observed superconducting state. Depending on details, the superconductor will be nodal or a chiral gapped state while further including electron-phonon coupling leads to a fully gapped, time-reversal symmetric pairing state., Comment: 11 pages, 9 figures

According to the hierarchical formation paradigm, galaxies form through mergers of smaller entities and massive black holes (MBHs), if lurking at their centers, migrate to the nucleus of the newly formed galaxy, where they form binary systems. The formation and evolution of MBH binaries, and in particular their coalescence timescale, is very relevant for current and future facilities aimed at detecting the gravitational-wave signal produced by the MBH close to coalescence. While most of the studies targeting this process are based on hydrodynamic simulations, the high computational cost makes a complete parameter space exploration prohibitive. Semi-analytic approaches represent a valid alternative, but they require ad-hoc prescriptions for the mass loss of the merging galaxies in minor mergers due to tidal stripping, which is not commonly considered or at most modelled assuming very idealised geometries. In this work, we propose a novel, effective model for the tidal stripping in axisymmetric potentials, to be implemented in semi-analytic models. We validate our semi-analytic approach against N-body simulations considering different galaxy sizes, inclinations, and eccentricities, finding only a moderate dependence on the orbit eccentricity. In particular, we find that, for almost circular orbits, our model mildly overestimates the mass loss, and this is due to the adjustment of the stellar distribution after the mass is removed. Nonetheless, the model exhibits a very good agreement with simulations in all the considered conditions, and thus represents an extremely powerful addition to semi-analytic calculations., Comment: 15 pages, 8 figures, 2 tables. Accepted for publication on A&A

Quasi-periodic eruptions (QPEs) are repeated X-ray flares from galactic nuclei. Despite some diversity in the recurrence and amplitude of eruptions, their striking regularity has motivated theorists to associate QPEs with orbital systems. Among the known QPE sources, eRO-QPE2 has shown the most regular flare timing and luminosity since its discovery. We report here on its long-term evolution over $\sim3.3\,$yr from discovery and find that: i) the average QPE recurrence time per epoch has decreased over time, albeit not at a uniform rate; ii) the distinct alternation between consecutive long and short recurrence times found at discovery has not been significant since; iii) the spectral properties, namely flux and temperature of both eruptions and quiescence components, have remained remarkably consistent within uncertainties. We attempted to interpret these results as orbital period and eccentricity decay coupled with orbital and disk precession. However, since gaps between observations are too long, we are not able to distinguish between an evolution dominated by just a decreasing trend, or by large modulations (e.g. due to the precession frequencies at play). In the former case, the observed period decrease is roughly consistent with that of a star losing orbital energy due to hydrodynamic gas drag from disk collisions, although the related eccentricity decay is too fast and additional modulations have to contribute too. In the latter case, no conclusive remarks are possible on the orbital evolution and the nature of the orbiter due to the many effects at play. However, these two cases come with distinctive predictions for future X-ray data: in the former, we expect all future observations to show a shorter recurrence time than the latest epoch, while in the latter we expect some future observations to be found with a larger recurrence, hence an apparent temporary period increase., Comment: Version updated after re-submission to A&A with minor revisions. Appendix B in v1 was moved to the main text

Understanding the impact of digital platforms on user behavior presents foundational challenges, including issues related to polarization, misinformation dynamics, and variation in news consumption. Comparative analyses across platforms and over different years can provide critical insights into these phenomena. This study investigates the linguistic characteristics of user comments over 34 years, focusing on their complexity and temporal shifts. Utilizing a dataset of approximately 300 million English comments from eight diverse platforms and topics, we examine the vocabulary size and linguistic richness of user communications and their evolution over time. Our findings reveal consistent patterns of complexity across social media platforms and topics, characterized by a nearly universal reduction in text length, diminished lexical richness, but decreased repetitiveness. Despite these trends, users consistently introduce new words into their comments at a nearly constant rate. This analysis underscores that platforms only partially influence the complexity of user comments. Instead, it reflects a broader, universal pattern of human behaviour, suggesting intrinsic linguistic tendencies of users when interacting online.

Multi-task learning (MTL) is a powerful machine learning paradigm designed to leverage shared knowledge across tasks to improve generalization and performance. Previous works have proposed approaches to MTL that can be divided into feature learning, focused on the identification of a common feature representation, and task clustering, where similar tasks are grouped together. In this paper, we propose an MTL approach at the intersection between task clustering and feature transformation based on a two-phase iterative aggregation of targets and features. First, we propose a bias-variance analysis for regression models with additive Gaussian noise, where we provide a general expression of the asymptotic bias and variance of a task, considering a linear regression trained on aggregated input features and an aggregated target. Then, we exploit this analysis to provide a two-phase MTL algorithm (NonLinCTFA). Firstly, this method partitions the tasks into clusters and aggregates each obtained group of targets with their mean. Then, for each aggregated task, it aggregates subsets of features with their mean in a dimensionality reduction fashion. In both phases, a key aspect is to preserve the interpretability of the reduced targets and features through the aggregation with the mean, which is further motivated by applications to Earth science. Finally, we validate the algorithms on synthetic data, showing the effect of different parameters and real-world datasets, exploring the validity of the proposed methodology on classical datasets, recent baselines, and Earth science applications.

A long standing problem in the study of the under-hole-doped cuprates has been the description of the Fermi surfaces underlying the high magnetic field quantum oscillations, and their connection to the higher temperature pseudogap metal. Harrison and Sebastian (arXiv:1103.4181) proposed that the pseudogap `Fermi arcs' are reconstructed into an electron pocket by field-induced charge density wave order. But computations on such a model (Zhang and Mei, arXiv:1411.2098) show an unobserved additional oscillation frequency from a Fermi surface arising from the backsides of the hole pockets completing the Fermi arcs. We describe a transition from a fractionalized Fermi liquid (FL*) model of the pseudogap metal, to a metal with bi-directional charge density wave order without fractionalization. We show that the confinement of the fermionic spinon excitations of the FL* across this transition can eliminate the unobserved oscillation frequency.

Two-body relaxation may drive stars onto near-radial orbits around a massive black hole, resulting in a tidal disruption event (TDE). In some circumstances, stars are unlikely to undergo a single terminal disruption, but rather to have a sequence of many grazing encounters with the black hole. It has long been unclear what is the physical outcome of this sequence: each of these encounters can only liberate a small amount of stellar mass, but may significantly alter the orbit of the star. We study the phenomenon of repeating partial tidal disruptions (pTDEs) by building a semi-analytical model that accounts for mass loss and tidal excitation. In the empty loss cone regime, where two-body relaxation is weak, we estimate the number of consecutive partial disruptions that a star can undergo, on average, before being significantly affected by two-body encounters. We find that in this empty loss cone regime, a star will be destroyed in a sequence of weak pTDEs, possibly explaining the tension between the low observed TDE rate and its higher theoretical estimates., Comment: Open Journal of Astrophysics, accepted for publication

We obtain an almost complete understanding of the mean-field phase diagram of the two-dimensional Hubbard model on a square lattice with a sizable next-nearest neighbor hopping and a moderate interaction strength. In particular, we clarify the nature of the transition region between the spiral and the stripe phase. Complementing previous [Phys. Rev. B 108, 035139 (2023)] real-space Hartree-Fock calculations on large finite lattices, we solve the mean-field equations for coplanar unidirectional magnetic order directly in the thermodynamic limit, and we determine the nature of the magnetic states right below the mean-field critical temperature $T^*$ by a Landau free energy analysis. While the magnetic order for filling factors $n \geq 1$ is always of N\'eel type, for $n \leq 1$ the following sequence of magnetic states is found as a function of increasing hole-doping: N\'eel, planar circular spiral, multi-spiral, and collinear spin-charge stripe states. Multi-spiral states are superpositions of several spirals with distinct wave vectors, and lead to concomitant charge order. We finally point out that nematic and charge orders inherited from the magnetic order can survive even in the presence of fluctuations, and we present a corresponding qualitative phase diagram., Comment: 14 pages, 7 figures

We propose a correspondence between topological order in 2+1d and Seifert three-manifolds together with a choice of ADE gauge group $G$. Topological order in 2+1d is known to be characterized in terms of modular tensor categories (MTCs), and we thus propose a relation between MTCs and Seifert three-manifolds. The correspondence defines for every Seifert manifold and choice of $G$ a fusion category, which we conjecture to be modular whenever the Seifert manifold has trivial first homology group with coefficients in the center of $G$. The construction determines the spins of anyons and their S-matrix, and provides a constructive way to determine the R- and F-symbols from simple building blocks. We explore the possibility that this correspondence provides an alternative classification of MTCs, which is put to the test by realizing all MTCs (unitary or non-unitary) with rank $r\leq 5$ in terms of Seifert manifolds and a choice of Lie group $G$., Comment: 9 pages + appendices

Topological defects and operators give a far-reaching generalization of symmetries of quantum fields. An auxiliary topological field theory in one dimension higher than the QFT of interest, known as the SymTFT, provides a natural way for capturing such operators. This gives a new perspective on several applications of symmetries, but fails to capture continuous non-Abelian symmetries. The main aim of this work is to fill this gap. Guided by geometric engineering and holography, we recover various known features of representation theory of the non-Abelian symmetry from a SymTFT viewpoint. Central to our approach is a duality between (flat) free Yang-Mills and non-Abelian BF theories. Our results extend naturally to models without supersymmetry., Comment: 6 pages, 4 figures

Quasi-Periodic Eruptions (QPEs) are luminous X-ray outbursts recurring on hour timescales, observed from the nuclei of a growing handful of nearby low-mass galaxies. Their physical origin is still debated, and usually modeled as (a) accretion disk instabilities or (b) interaction of a supermassive black hole (SMBH) with a lower mass companion in an extreme mass-ratio inspiral (EMRI). EMRI models can be tested with several predictions related to the short- and long-term behavior of QPEs. In this study, we report on the ongoing 3.5-year NICER and XMM-Newton monitoring campaign of eRO-QPE1, which is known to exhibit erratic QPEs that have been challenging for the simplest EMRI models to explain. We report 1) complex, non-monotonic evolution in the long-term trends of QPE energy output and inferred emitting area; 2) the disappearance of the QPEs (within NICER detectability) in October 2023, then reappearance by January 2024 at a luminosity $\sim$100x fainter (and temperature $\sim$3x cooler) than initial discovery; 3) radio non-detections with MeerKAT and VLA observations partly contemporaneous with our NICER campaign (though not during outbursts); and 4) the presence of a possible $\sim$6-day modulation of the QPE timing residuals, which aligns with the expected nodal precession timescale of the underlying accretion disk. Our results tentatively support EMRI-disk collision models powering the QPEs, and we demonstrate that the timing modulation of QPEs may be used to jointly constrain the SMBH spin and disk density profile., Comment: Accepted for publication in ApJ

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

Ultrafast electric-field control of emergent electronic and magnetic states at oxide interfaces offers exciting prospects for the development of new generations of energy-efficient devices. Here, we demonstrate that the electronic structure and emergent ferromagnetic interfacial state in epitaxial LaNiO3/CaMnO3 superlattices can be effectively controlled using intense single-cycle THz electric-field pulses. We employ a combination of polarization-dependent X-ray absorption spectroscopy with magnetic circular dichroism and X-ray resonant magnetic reflectivity to measure a detailed magneto-optical profile and thickness of the ferromagnetic interfacial layer. Then, we use time-resolved and temperature-dependent magneto-optical Kerr effect, along with transient optical reflectivity and transmissivity measurements, to disentangle multiple correlated electronic and magnetic processes driven by ultrafast high-field (~1 MV/cm) THz pulses. These processes include an initial sub-picosecond electronic response, consistent with non-equilibrium Joule heating; a rapid (~270 fs) demagnetization of the ferromagnetic interfacial layer, driven by THz-field-induced nonequilibrium spin-polarized currents; and subsequent multi-picosecond dynamics, possibly indicative of a change in the magnetic state of the superlattice due to the transfer of spin angular momentum to the lattice. Our findings shed light on the intricate interplay of electronic and magnetic phenomena in this strongly correlated material system, suggesting a promising avenue for efficient control of two-dimensional ferromagnetic states at oxide interfaces using ultrafast electric-field pulses.

We present the library lymph for the finite element numerical discretization of coupled multi-physics problems. lymph is a Matlab library for the discretization of partial differential equations based on high-order discontinuous Galerkin methods on polytopal grids (PolyDG) for spatial discretization coupled with suitable finite-difference time marching schemes. The objective of the paper is to introduce the library by describing it in terms of installation, input/output data, and code structure, highlighting - when necessary - key implementation aspects related to the method. A user guide, proceeding step-by-step in the implementation and solution of a Poisson problem, is also provided. In the last part of the paper, we show the results obtained for several differential problems, namely the Poisson problem, the heat equation, the elastodynamics system, and a multiphysics problem coupling poroelasticity and acoustic equations. Through these examples, we show the convergence properties and highlight some of the main features of the proposed method, i.e. geometric flexibility, high-order accuracy, and robustness with respect to heterogeneous physical parameters.

Pulsar Timing Array (PTA) experiments worldwide recently reported evidence of a nHz stochastic gravitational wave background (sGWB) compatible with the existence of slowly inspiralling massive black hole (MBH) binaries (MBHBs). The shape of the signal contains valuable information about the evolution of $z<1$ MBHs above $\rm 10^8 M_{\odot}$, suggesting a faster dynamical evolution of MBHBs towards the gravitational-wave-driven inspiral or a larger MBH growth than usually assumed. In this work, we investigate if the nHz sGWB could also provide constraints on the population of merging lower-mass MBHBs ($\rm {<} 10^7 \, M_{\odot}$) detectable by LISA. To this end, we use the $\texttt{L-Galaxies}$ semi-analytical model applied to the $\texttt{Millennium}$ suite of simulations. We generate a population of MBHs compatible simultaneously with current electromagnetic and nHz sGWB constraints by including the possibility that, in favourable environments, MBHs can accrete gas beyond the Eddington limit. The predictions of the model show that the global (integrated up to high-$z$) LISA detection rate is {\it not} significantly affected when compared to a fiducial model whose nHz sGWB signal is ${\sim}\,2$ times smaller. In both cases, the global rate yields ${\sim}\,12 \rm yr^{-1}$ and is dominated by systems of $\rm 10^{5-6} M_{\odot}$. The main differences are limited to low-$z$ ($z<3$), high-mass (${>}\rm 10^6\, M_{\odot}$) LISA MBHBs. The model compatible with the latest PTA results predicts up to ${\sim}\,1.6$ times more detections, with a rate of ${\sim}1\rm yr^{-1}$. We find that these LISA MBHB systems have 50\% probability of shining with bolometric luminosities $>10^{43}\rm erg/s$. Hence, in case PTA results are confirmed and given the current MBH modelling, our findings suggest there will be higher chances to perform multimessenger studies with LISA MBHB than previously expected., Comment: 16 pages; Submitted to A&A

We study the dynamical evolution of quasi-circular equal mass massive black hole binaries embedded in circumbinary discs from separations of $\sim 100R_{\rm g}$ down to the merger, following the post merger evolution. The binary orbit evolves owing to the presence of the gaseous disc and the addition of Post-Newtonian (PN) corrections up to the 2.5 PN order, therefore including the dissipative gravitational wave back-reaction. We investigate two cases of a relatively cold and warm circumbinary discs, with aspect ratios $H/R=0.03,\,0.1$ respectively, employing 3D hyper-Lagrangian resolution simulations with the {\sc gizmo}-MFM code. We extract spectral energy distributions and light curves in different frequency bands (i.e. X-ray, optical and UV) from the simulations. We find a clear two orders of magnitude drop in the X-ray flux right before merger if the disc is warm while we identify a significant increase in the UV flux regardless of the disc temperature. The optical flux shows clear distinctive modulations on the binary orbital period and on the cavity edge period, regardless of the disc temperature. We find that the presence of a cold disc can accelerate the coalescence of the binary by up to 130 seconds over the last five days of inspiral, implying a phase shift accumulation of about $\pi\,$radians compared to the binary evolution in vacuum. These differences are triggered by the presence of the gaseous disc and might have implications on the waveforms that can be in principle detected. We discuss the implications that these distinctive signatures might have for existing and upcoming time domain surveys and for multimessenger astronomy., Comment: 10 pages, A&A submitted

Terahertz time-domain spectroscopy (THz-TDS) employs sub-picosecond pulses to probe dielectric properties of materials giving as a result a 3-dimensional hyperspectral data cube. The spatial resolution of THz images is primarily limited by two sources: a non-zero THz beam waist and the acquisition step size. Acquisition with a small step size allows for the visualisation of smaller details in images at the expense of acquisition time, but the frequency-dependent point-spread function remains the biggest bottleneck for THz imaging. This work presents a super-resolution approach to restore THz time-domain images acquired with medium-to-big step sizes. The results show the optimized and robust performance for different frequency bands (from 0.5 to 3.5 THz) obtaining higher resolution and additionally removing effects of blur at lower frequencies and noise at higher frequencies., Comment: This work was presented at the Sixth International Workshop on Mobile Terahertz Systems (IWMTS)

We describe the design of two types of metamaterials aimed at enhancing terahertz field pulses that can be used to control the magnetic state in condensed matter systems. The first structure is a so-called "dragonfly" antenna, able to realize a five-fold enhancement of the impinging terahertz magnetic field, while preserving its broadband features. For currently available state-of-the-art table top sources, this leads to peak magnetic fields exceeding 1 T. The second structure is an octopole antenna aimed at enhancing a circularly-polarized terahertz electric field, while preserving its polarization state. We obtain a five-fold enhancement of the electric field, hence expected to exceed the 1 MV/cm peak amplitude. Both our structures can be readily fabricated on top of virtually any material., Comment: 7 pages, 5 figures

Massive black hole binaries (MBHBs) are binary systems formed by black holes with mass exceeding millions of solar masses, expected to form and evolve in the nuclei of galaxies. The extreme compact nature of such objects determines a loud and efficient emission of Gravitational Waves (GWs), which can be detected by the Pulsar Timing Array (PTA) experiment in the form of a Gravitational Wave Background (GWB), i.e. a superposition of GW signals coming from different sources. The modelling of the GWB requires some assumptions on the binary population and the exploration of the whole involved parameter space is prohibitive as it is computationally expensive. We here train a Neural Network (NN) model on a semi-analytical modelling of the GWB generated by an eccentric population of MBHBs that interact with the stellar environment. We then use the NN to predict the characteristics of the GW signal in regions of the parameter space that we did not sample analytically. The developed framework allows us to quickly predict the level, shape and variance of the GWB signals produced in different universe realisations., Comment: 8 pages, submitted to A&A

Massive black holes are key inhabitants of the nuclei of galaxies. Moreover, their astrophysical relevance has gained significant traction in recent years, thanks especially to the amazing results that are being (or will be) delivered by instruments such as the James Webb Space Telescope, Pulsar Timing Array projects and LISA. In this Chapter, we aim to detail a broad set of aspects related to the astrophysical nature of massive black holes embedded in galactic nuclei, with a particular focus on recent and upcoming advances in the field. In particular, we will address questions such as: What shapes the relations connecting the mass of massive black holes with the properties of their host galaxies? How do massive black holes form in the early Universe? What mechanisms keep on feeding them so that they can attain very large masses at z = 0? How do binaries composed of two massive black holes form and coalesce into a single, larger black hole? Here we present these topics from a mainly theoretical viewpoint and discuss how present and upcoming facilities may enhance our understanding of massive black holes in the near future., Comment: All authors equally contributed to the Chapter writing. To appear as Chapter 3 in the book "Black Holes in the Era of Gravitational Wave Astronomy", ed. Arca Sedda, Bortolas, Spera, pub. Elsevier

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

We present the generation of transient polarization gratings at the nanoscale, achieved using a tailored accelerator configuration of the FERMI free electron laser. We demonstrate the capabilities of such a transient polarization grating by comparing its induced dynamics with the ones triggered by a more conventional intensity grating on a thin film ferrimagnetic alloy. While the signal of the intensity grating is dominated by the thermoelastic response of the system, such a contribution is suppressed in the case of the polarization grating. This exposes helicity-dependent magnetization dynamics that have so-far remained hidden under the large thermally driven response. We anticipate nanoscale transient polarization gratings to become useful for the study of any physical, chemical and biological systems possessing chiral symmetry.

Electromagnetic waves possessing orbital angular momentum (OAM) are powerful tools for applications in optical communications, new quantum technologies and optical tweezers. Recently, they have attracted growing interest since they can be harnessed to detect peculiar helical dichroic effects in chiral molecular media and in magnetic nanostructures. In this work, we perform single-shot per position ptychography on a nanostructured object at a seeded free-electron laser, using extreme ultraviolet OAM beams of different topological charge order $\ell$ generated with spiral zone plates. By controlling $\ell$, we demonstrate how the structural features of OAM beam profile determine an improvement of about 30% in image resolution with respect to conventional Gaussian beam illumination. This result extends the capabilities of coherent diffraction imaging techniques, and paves the way for achieving time-resolved high-resolution (below 100 nm) microscopy on large area samples., Comment: M. Pancaldi and F. Guzzi contributed equally to this work

Machine learning algorithms are designed to capture complex relationships between features. In this context, the high dimensionality of data often results in poor model performance, with the risk of overfitting. Feature selection, the process of selecting a subset of relevant and non-redundant features, is, therefore, an essential step to mitigate these issues. However, classical feature selection approaches do not inspect the causal relationship between selected features and target, which can lead to misleading results in real-world applications. Causal discovery, instead, aims to identify causal relationships between features with observational data. In this paper, we propose a novel methodology at the intersection between feature selection and causal discovery, focusing on time series. We introduce a new causal feature selection approach that relies on the forward and backward feature selection procedures and leverages transfer entropy to estimate the causal flow of information from the features to the target in time series. Our approach enables the selection of features not only in terms of mere model performance but also captures the causal information flow. In this context, we provide theoretical guarantees on the regression and classification errors for both the exact and the finite-sample cases. Finally, we present numerical validations on synthetic and real-world regression problems, showing results competitive w.r.t. the considered baselines.

The Australian, Chinese, European, Indian, and North American pulsar timing array (PTA) collaborations recently reported, at varying levels, evidence for the presence of a nanohertz gravitational wave background (GWB). Given that each PTA made different choices in modeling their data, we perform a comparison of the GWB and individual pulsar noise parameters across the results reported from the PTAs that constitute the International Pulsar Timing Array (IPTA). We show that despite making different modeling choices, there is no significant difference in the GWB parameters that are measured by the different PTAs, agreeing within $1\sigma$. The pulsar noise parameters are also consistent between different PTAs for the majority of the pulsars included in these analyses. We bridge the differences in modeling choices by adopting a standardized noise model for all pulsars and PTAs, finding that under this model there is a reduction in the tension in the pulsar noise parameters. As part of this reanalysis, we "extended" each PTA's data set by adding extra pulsars that were not timed by that PTA. Under these extensions, we find better constraints on the GWB amplitude and a higher signal-to-noise ratio for the Hellings and Downs correlations. These extensions serve as a prelude to the benefits offered by a full combination of data across all pulsars in the IPTA, i.e., the IPTA's Data Release 3, which will involve not just adding in additional pulsars, but also including data from all three PTAs where any given pulsar is timed by more than as single PTA., Comment: 21 pages, 9 figures, submitted to ApJ