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This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate approximation of the true image (or its gradient magnitude) through a neural network. Our approach operates without requiring prior knowledge of the noise intensity in the data and avoids the iterative recomputation of weights. Additionally, the paper includes a theoretical analysis of the proposed method, establishing its validity as a regularization approach. This framework integrates advanced neural network capabilities within a regularization context, thereby making the results of the networks interpretable. The results are promising as they enable high-quality reconstructions from limited-view tomographic measurements., Comment: 23 pages, 8 figures, submitted to journal for peer-review

Using the Event Horizon Telescope (EHT), the gravitationally lensed rings around the supermassive black holes (SMBHs) in Messier 87 (M87) and Sagittarius A* (Sgr A*) have now been successfully imaged at a resolution under 10 gravitational radii (R$_{\rm g}$ $ = \rm{GM/c^2}$). To expand studies beyond M87 and Sgr A*, we have constructed the Event Horizon and Environs (ETHER) sample, a comprehensive database encompassing approximately 3.15 million SMBH mass estimates, $\sim$ 20,000 Very-Long Baseline Interferometry (VLBI) radio flux densities, and $\sim$ 36,000 hard X-ray flux densities. This database is designed to identify and optimize target selection for the EHT and its upgrades on the ground and in space. We have identified a Gold Sample (GS) of nearby low-luminosity Active Galactic Nuclei (AGNs) within it that are ideal for studying jet bases and potentially imaging black hole shadows. We observed 27 of these AGNs using the EHT from 2022 to 2024, providing an opportunity to resolve and image accretion flows and jets at resolutions of $\leq$ 100 R$_{\rm g}$. Only a few SMBHs have sufficiently high enough flux density to be imaged at scales of $\leq$ 50 R$_{\rm g}$ with the present EHT. Among these are M87, Sgr A*, NGC4594 (Sombrero/M104), NGC4261, and NGC4374 (Messier 84/M84). Of these, NGC4261, Sombrero, and M84 have been observed and/or are scheduled for deep imaging with EHT+ALMA from 2023 to 2025. Sombrero, NGC4261, M84, NGC4278, and NGC5232 are clearly detected in our EHT+ALMA observations in 2022, indicating that the 230 GHz flux density from the accretion flows is significantly high. Ongoing imaging of the ETHER GS will enable measurements of black hole mass and spin, help constrain General Relativity, and enrich our understanding of jet launching and accretion inflows across a broad multi-parameter space, including black hole mass, spin, accretion rate, and orientation., Comment: 9 pages, 6 figures, 1 table, published in Proceedings of the 16th EVN Symposium, Ed. E. Ros, P. Benke, S.A. Dzib, I. Rottmann, & J.A. Zensus, Bonn: Max-Planck-Institut f\"ur Radioastronomie, 2024, pages 75-84, https://cloud.mpifr-bonn.mpg.de/index.php/s/BkX2CC2Xjn2aKR4

Sparse-view Computed Tomography (CT) is an emerging protocol designed to reduce X-ray dose radiation in medical imaging. Traditional Filtered Back Projection algorithm reconstructions suffer from severe artifacts due to sparse data. In contrast, Model-Based Iterative Reconstruction (MBIR) algorithms, though better at mitigating noise through regularization, are too computationally costly for clinical use. This paper introduces a novel technique, denoted as the Deep Guess acceleration scheme, using a trained neural network both to quicken the regularized MBIR and to enhance the reconstruction accuracy. We integrate state-of-the-art deep learning tools to initialize a clever starting guess for a proximal algorithm solving a non-convex model and thus computing an interpretable solution image in a few iterations. Experimental results on real CT images demonstrate the Deep Guess effectiveness in (very) sparse tomographic protocols, where it overcomes its mere variational counterpart and many data-driven approaches at the state of the art. We also consider a ground truth-free implementation and test the robustness of the proposed framework to noise.

We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast with second-order-in-time formulations, which require a CFL condition to guarantee stability, the methods we consider here are unconditionally stable without the need for stabilization terms. Along the lines of the work by M. Ferrari and S. Fraschini (2024), we address the stability analysis by studying the properties of the condition number of a family of matrices associated with the time discretization. Numerical tests validate the performance of the method.

We present a velocity-resolved reverberation mapping analysis of the hypervariable quasar RM160 (SDSS J141041.25+531849.0) at z = 0.359 with 153 spectroscopic epochs of data representing a ten-year baseline (2013-2023). We split the baseline into two regimes based on the 3x flux increase in the light curve: a 'low state' phase during the years 2013-2019 and a 'high state' phase during the years 2022-2023. The velocity-resolved lag profiles (VRLP) indicate that gas with different kinematics dominates the line emission in different states. The H\b{eta} VRLP begins with a signature of inflow onto the BLR in the 'low state', while in the 'high state' it is flatter with less signature of inflow. The H{\alpha} VRLP begins consistent with a virialized BLR in the 'low state', while in the 'high state' shows a signature of inflow. The differences in the kinematics between the Balmer lines and between the 'low state' and the 'high state' suggests complex BLR dynamics. We find that the BLR radius and velocity (both FWHM and {\sigma}) do not obey a constant virial product throughout the monitoring period. We find that BLR lags and continuum luminosity are correlated, consistent with rapid response of the BLR gas to the illuminating continuum. The BLR kinematic profile changes in unpredictable ways that are not related to continuum changes and reverberation lag. Our observations indicate that non-virial kinematics can significantly contribute to observed line profiles, suggesting caution for black-hole mass estimation in luminous and highly varying quasars like RM160., Comment: 23 pages, 17 figures

We consider the focusing generalized Hartree equation in $H^1(\R^3)$ with a potential, \begin{equation*} iu_t + \Delta u - V(x)u + (I_\gamma \ast |u|^p )|u|^{p-2} u=0, \end{equation*} where $I_\gamma = \frac{1}{|x|^{3-\gamma}}$, $p \geq 2$ and $\gamma < 3$. In this paper, we prove scattering for the generalized Hartree equation with a potential in the intercritical case assuming radial initial data. The novelty of our approach lies in the use of a general mass-potential condition, incorporating the potential V, which extends the standard mass-energy framework. To this end, we employ a simplified method inspired by Dodson and Murphy \cite{Dod-Mur}, based on Tao's scattering criteria and Morawetz estimates. This approach provides a more straightforward proof of scattering compared to the traditional concentration-compactness/rigidity method of Kenig and Merle \cite{KENIG}., Comment: 20 pages

Contamination from singly ionized iron emission is one of the greatest obstacles to determining the intensity of emission lines in the UV and optical wavelength ranges. This study presents a comprehensive analysis of the FeII emission in the bright quasar RM 102, based on the most recent version of the CLOUDY software, with the goal of simultaneously reproducing UV and optical FeII emission. We employ a constant pressure model for the emitting clouds, instead of the customary constant density assumption. The allowed parameter range is broad, with metallicity up to 50 times the solar value and turbulent velocity up to 100 km s$^{-1}$ for a subset of models. We also consider geometrical effects that could enhance the visibility of the non-illuminated faces of the clouds, as well as additional mechanical heating. Our investigation reveals that the broad line region of RM 102 is characterized by highly metallic gas. The observed FeII features provide strong evidence for an inflow pattern geometry that favours the dark sides of clouds over isotropic emission. This study confirms the presence of chemically enriched gas in the broad line region of bright quasars, represented by RM 102, which is necessary to explain the strong FeII emission and its characteristic features. Additionally, we report that CLOUDY currently still lacks certain transitions in its atomic databases which prevents it from fully reproducing some observed FeII features in quasar spectra.

We present dynamical modeling of the broad-line region (BLR) for the highly variable AGN SDSS J141041.25+531849.0 ($z = 0.359$) using photometric and spectroscopic monitoring data from the Sloan Digital Sky Survey Reverberation Mapping project and the SDSS-V Black Hole Mapper program, spanning from early 2013 to early 2023. We model the geometry and kinematics of the BLR in the H$\beta$, H$\alpha$, and MgII, emission lines for three different time periods to measure the potential change of structure within the BLR across time and line species. We consistently find a moderately edge-on $(i_{\rm full-state} = 53.29^{\circ} \,{}^{+7.29}_{-6.55})$ thick-disk $(\theta_{\rm opn, \; full-state} = 54.86^{\circ} \,{}^{+5.83}_{-4.74})$ geometry for all BLRs, with a joint estimate for the mass of the supermassive black hole (SMBH) for each of three time periods, yielding $\log_{10}(M_{\rm BH} / M_{\odot}) = 7.66^{+0.12}_{-0.13}$ when using the full dataset. The inferred individual virial factor $f$ $\sim 1$ is significantly smaller than the average factor for a local sample of dynamically modeled AGNs. There is strong evidence for non-virial motion, with over $80\%$ of clouds on inflowing/outflowing orbits. We analyze the change in model parameters across emission lines, finding the radii of BLRs for the emission lines are consistent with the following relative sizes $R_{\rm H\beta} \lesssim R_{\rm MgII } \lesssim R_{\rm H\alpha}$. Comparing results across time, we find $R_{\rm low-state} \lesssim R_{\rm high-state}$, with the change in BLR size for H$\beta$, being more significant than for the other two lines. The data also reveal complex, time-evolving, and potentially transient dynamics of the BLR gas over decade-long timescales, encouraging for future dynamical modeling of fine-scale BLR kinematics., Comment: 32 pages, 16 figures, 4 tables. Submitted to ApJ

Optimization algorithms for wireless systems play a fundamental role in improving their performance and efficiency. However, it is known that the complexity of conventional optimization algorithms in the literature often exponentially increases with the number of transmit antennas and communication users in the wireless system. Therefore, in the large scale regime, the astronomically large complexity of these optimization algorithms prohibits their use and prevents assessing large scale wireless systems performance under optimized conditions. To overcome this limitation, this work proposes instead the use of an unsupervised meta-learning based approach to directly perform non-convex optimization at significantly reduced complexity. To demonstrate the effectiveness of the proposed meta-learning based solution, the sum-rate (SR) maximization problem for the following three emerging 6G technologies is contemplated: hierarchical rate-splitting multiple access (H-RSMA), integrated sensing and communication (ISAC), and beyond-diagonal reconfigurable intelligent surfaces (BD-RIS). Through numerical results, it is demonstrated that the proposed meta-learning based optimization framework is able to successfully optimize the performance and also reveal unknown aspects of the operation in the large scale regime for the considered three 6G technologies.

We present the results of an investigation of a highly variable CIV broad absorption-line feature in the quasar SBS 1408+544 (z=2.337) that shows a significant shift in velocity over time. This source was observed as a part of the Sloan Digital Sky Survey Reverberation Mapping Project and the SDSS-V Black Hole Mapper Reverberation Mapping Project, and has been included in two previous studies, both of which identified significant variability in a high-velocity CIV broad absorption line (BAL) on timescales of just a few days in the quasar rest frame. Using ~130 spectra acquired over eight years of spectroscopic monitoring with SDSS, we have determined that this BAL is not only varying in strength, but is also systematically shifting to higher velocities. Using cross-correlation methods, we measure the velocity shifts (and corresponding acceleration) of the BAL on a wide range of timescales, measuring an overall velocity shift of delta v = -683 (+89, -84) km s-1 over the 8-year monitoring period. This corresponds to an average rest-frame acceleration of a=1.04 (+0.14, -0.13) cm s-2, though the magnitude of the acceleration on shorter timescales is not constant throughout. We place our measurements in the context of BAL-acceleration models and examine various possible causes of the observed velocity shift., Comment: Published in the Astrophysical Journal

This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary objective of the proposed optimization model is to achieve a good balance between denoising and the preservation of fine details and edges, overcoming the performance of the popular and largely used Total Variation (TV) regularization through the application of appropriate pixel-dependent weights. The proposed strategy leverages the role of gradient approximations for the computation of the space-variant TV weights. For this reason, a convolutional neural network is designed, to approximate both the ground truth image and its gradient using an elastic loss function in its training. Additionally, the paper provides a theoretical analysis of the proposed model, showing the uniqueness of its solution, and illustrates a Chambolle-Pock algorithm tailored to address the specific problem at hand. This comprehensive framework integrates innovative regularization techniques with advanced neural network capabilities, demonstrating promising results in achieving high-quality reconstructions from low-sampled tomographic data.

We present a set of new theoretical Fe II templates for bright quasars covering a wavelength range of 1000-10000 \AA\, based on the recent atomic database available in the C23.00 version of the photoionization code CLOUDY. We compute a grid of models for a range of incident photon flux, gas density, and multiple microturbulence velocities. We examine the equivalent widths (EWs) and the ratios of Fe II emission over various wavebands and compare them with observations. Our key results are: (1) The flux generated from the shielded side of the cloud is insufficient to describe the measured Fe II emission. (2) Despite using the newest atomic data we still confirm the long-standing problem that the predicted Fe II UV/optical ratio is significantly larger than that observed in the AGN spectra. (3) The Fe II UV/optical ratio is not significantly affected by the variations in the microturbulence and the metallicity. (4) The microturbulence can create an additional apparent velocity shift of up to 1000 km/s in the spectra. (5) There is no Fe II template based on a single set of physical parameters that can fit the observed UV to optical Fe II emission spectra. We shortly discuss the most likely effects responsible for the Fe II UV/optical mismatch problem: the assumption of the constant density clouds and the heating mechanism for Fe II emitting clouds., Comment: 34 pages, 27 figures, 3 tables, accepted for publication in the Astrophysical Journal Supplement (ApJS) series

"Changing-look" active galactic nuclei (CL-AGNs) challenge our basic ideas about the physics of accretion flows and circumnuclear gas around supermassive black holes. Using first-year Sloan Digital Sky Survey V (SDSS-V) repeated spectroscopy of nearly 29,000 previously known AGNs, combined with dedicated follow-up spectroscopy, and publicly available optical light curves, we have identified 116 CL-AGNs where (at least) one broad emission line has essentially (dis-)appeared, as well as 88 other extremely variable systems. Our CL-AGN sample, with 107 newly identified cases, is the largest reported to date, and includes $\sim0.4\%$ of the AGNs reobserved in first-year SDSS-V operations. Among our CL-AGNs, 67% exhibit dimming while 33% exhibit brightening. Our sample probes extreme AGN spectral variability on months to decades timescales, including some cases of recurring transitions on surprisingly short timescales ($\lesssim 2$ months in the rest frame). We find that CL events are preferentially found in lower-Eddington-ratio ($f_{Edd}$) systems: Our CL-AGNs have a $f_{Edd}$ distribution that significantly differs from that of a carefully constructed, redshift- and luminosity-matched control sample (Anderson-Darling test yielding $p_{\rm AD}\approx 6\times10^{-5}$; median $f_{Edd}\approx0.025$ vs. $0.043$). This preference for low $f_{Edd}$ strengthens previous findings of higher CL-AGN incidence at lower $f_{Edd}$, found in smaller samples. Finally, we show that the broad MgII emission line in our CL-AGN sample tends to vary significantly less than the broad H$\beta$ emission line. Our large CL-AGN sample demonstrates the advantages and challenges in using multi-epoch spectroscopy from large surveys to study extreme AGN variability and physics., Comment: Submitted to ApJ. Full tables and figure-sets will be published upon acceptance, and can be made available upon request$.$

We investigate a variational method for ill-posed problems, named $\texttt{graphLa+}\Psi$, which embeds a graph Laplacian operator in the regularization term. The novelty of this method lies in constructing the graph Laplacian based on a preliminary approximation of the solution, which is obtained using any existing reconstruction method $\Psi$ from the literature. As a result, the regularization term is both dependent on and adaptive to the observed data and noise. We demonstrate that $\texttt{graphLa+}\Psi$ is a regularization method and rigorously establish both its convergence and stability properties. We present selected numerical experiments in 2D computerized tomography, wherein we integrate the $\texttt{graphLa+}\Psi$ method with various reconstruction techniques $\Psi$, including Filter Back Projection ($\texttt{graphLa+FBP}$), standard Tikhonov ($\texttt{graphLa+Tik}$), Total Variation ($\texttt{graphLa+TV}$), and a trained deep neural network ($\texttt{graphLa+Net}$). The $\texttt{graphLa+}\Psi$ approach significantly enhances the quality of the approximated solutions for each method $\Psi$. Notably, $\texttt{graphLa+Net}$ is outperforming, offering a robust and stable application of deep neural networks in solving inverse problems.

This is a review of preconditioning techniques based on fast-diagonalization methods for space-time isogeometric discretization of the heat equation. Three formulation are considered: the Galerkin approach, a discrete least-square and a continuous least square. For each formulation the heat differential operator is written as a sum of terms that are kronecker products of uni-variate operators. These are used to speed-up the application of the operator in iterative solvers and to construct a suitable preconditioner. Contrary to the fast-diagonalization technique for the Laplace equation where all uni-variate operators acting on the same direction can be simultaneously diagonalized in the case of the heat equation this is not possible. Luckily this can be done up to an additional term that has low rank allowing for the utilization of arrow-head like factorization or inversion by Sherman-Morrison formula. The proposed preconditioners work extremely well on the parametric domain and, when the domain is parametrized or when the equation coefficients are not constant, they can be adapted and retain good performance characteristics., Comment: arXiv admin note: substantial text overlap with arXiv:1909.07309, arXiv:2311.18461

This work proposes a stabilized space--time method for the monodomain equation coupled with the Rogers--McCulloch ionic model, which is widely used to simulate electrophysiological wave propagation in the cardiac tissue. By extending the Spline Upwind method and exploiting low-rank matrix approximations, as well as preconditioned solvers, we achieve both significant computational efficiency and accuracy. In particular, we develop a formulation that is both simple and highly effective, designed to minimize spurious oscillations and ensuring computational efficiency. We rigorously validate the method's performance through a series of numerical experiments, showing its robustness and reliability in diverse scenarios.

Context. Dust in active galactic nuclei is clearly present right outside the broad-line region (BLR) in the form of a dusty molecular torus. However, some models of the BLR predict that dust may also exist within the BLR. Aims. We study the reprocessing of radiation by the BLR with the aim of observing how the presence of dust affects the reprocessed continuum and the line properties. Methods. We calculated a range of models using the CLOUDY photoionisation code for dusty and dustless plasma. We paid particular attention to the well-studied object NGC 5548, and we compared the line equivalent width predictions with the data from observations for this object. Results. We obtained a rough agreement between the expected equivalent widths of the H$\beta$ and Mg II lines and the observed values for NGC 5548 for the line distances implied by the time-delay measurement (for H$\beta)$ and the radius-luminosity relation (for Mg II) when the medium is dusty. We found the incident radiation to be consistent with the radiation seen by the observer, so no shielding between the inner disc and the BLR is required. High ionisation lines such as He II, however, clearly form in the inner dustless region. When the additional absorber is present, the H$\beta$ emitting region moves closer to the dustless part of the accretion disc surface., Comment: 10 pages, 7 figures, 1 table, accepted for publication in the Astronomy and Astrophysics journal

Fe II emission is a well-known contributor to the UV spectra of active galactic nuclei and the modeling of this part may affect the results obtained for the MgII$\lambda2800$ emission, which is one of the lines used for black hole mass measurements and cosmological applications. We use the 11-year monitoring of the selected quasar HE 0413-4031 with the South African Large Telescope (SALT) and we supplement this monitoring with the near-IR spectrum taken with the SOAR telescope. A new redshift determination ($z=1.39117 \pm 0.00017$) using [OIII]$\lambda \lambda 4959,5007$ gave a very different value than the previous determination based only on the UV FeII pseudocontinuum ($z=1.3764$). It favors a different decomposition of the spectrum into Mg II and UV Fe II emissions. The line characteristics and the time delay of the Mg II emission ($224^{+21}_{-23}$ days) are not significantly affected. However, in comparison with the previous analysis, the rest-frame UV FeII time delay ($251^{+9}_{-7}$ days) is consistent with the inferred UV FeII line FWHM of $4200\,{\rm km/s}$ that is only slightly smaller than the MgII line FWHM. Hence the FeII-emitting material is more distant than the MgII-emitting gas in HE 0413-4031 by $\sim 0.023$ pc (4700 AU). The inferred velocity shift of both Mg II and UV Fe II lines with respect to the systemic redshift is now rather low, below 300 km s$^{-1}$. In addition, we construct an updated MgII radius-luminosity ($R-L$) relation from 194 sources, which is more than double the previous sample. The MgII $R-L$ relation is flatter than the UV FeII, optical FeII, and H$\beta$ $R-L$ relations. While the new decomposition of the spectrum is satisfactory, we see a need to create better Fe II templates using the newest version of the code CLOUDY., Comment: 19 pages, 12+8 Figures, 5+1 Tables (Main Text+Appendix); accepted by A&A; minor corrections applied

This work studies the relationship between accretion-disk size and quasar properties, using a sample of 95 quasars from the SDSS-RM project with measured lags between the $g$ and $i$ photometric bands. Our sample includes disk lags that are both longer and shorter than predicted by the \citet{SS73} model, requiring explanations which satisfy both cases. Although our quasars each have one lag measurement, we explore the wavelength-dependent effects of diffuse broad line region (BLR) contamination through our sample's broad redshift range, $0.1

In this letter, we propose the use of a meta-learning based precoder optimization framework to directly optimize the Rate-Splitting Multiple Access (RSMA) precoders with partial Channel State Information at the Transmitter (CSIT). By exploiting the overfitting of the compact neural network to maximize the explicit Average Sum-Rate (ASR) expression, we effectively bypass the need for any other training data while minimizing the total running time. Numerical results reveal that the meta-learning based solution achieves similar ASR performance to conventional precoder optimization in medium-scale scenarios, and significantly outperforms sub-optimal low complexity precoder algorithms in the large-scale regime.

The unprecedented success of image reconstruction approaches based on deep neural networks has revolutionised both the processing and the analysis paradigms in several applied disciplines. In the field of digital humanities, the task of digital reconstruction of ancient frescoes is particularly challenging due to the scarce amount of available training data caused by ageing, wear, tear and retouching over time. To overcome these difficulties, we consider the Deep Image Prior (DIP) inpainting approach which computes appropriate reconstructions by relying on the progressive updating of an untrained convolutional neural network so as to match the reliable piece of information in the image at hand while promoting regularisation elsewhere. In comparison with state-of-the-art approaches (based on variational/PDEs and patch-based methods), DIP-based inpainting reduces artefacts and better adapts to contextual/non-local information, thus providing a valuable and effective tool for art historians. As a case study, we apply such approach to reconstruct missing image contents in a dataset of highly damaged digital images of medieval paintings located into several chapels in the Mediterranean Alpine Arc and provide a detailed description on how visible and invisible (e.g., infrared) information can be integrated for identifying and reconstructing damaged image regions., Comment: 26 pages

In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an ill-posed inverse problem and its solution is difficult to approximate when noise affects the data. Really, one limitation of neural networks for deblurring is their sensitivity to noise and other perturbations, which can lead to instability and produce poor reconstructions. In addition, networks do not necessarily take into account the numerical formulation of the underlying imaging problem, when trained end-to-end. In this paper, we propose some strategies to improve stability without losing to much accuracy to deblur images with deep-learning based methods. First, we suggest a very small neural architecture, which reduces the execution time for training, satisfying a green AI need, and does not extremely amplify noise in the computed image. Second, we introduce a unified framework where a pre-processing step balances the lack of stability of the following, neural network-based, step. Two different pre-processors are presented: the former implements a strong parameter-free denoiser, and the latter is a variational model-based regularized formulation of the latent imaging problem. This framework is also formally characterized by mathematical analysis. Numerical experiments are performed to verify the accuracy and stability of the proposed approaches for image deblurring when unknown or not-quantified noise is present; the results confirm that they improve the network stability with respect to noise. In particular, the model-based framework represents the most reliable trade-off between visual precision and robustness.

In Khadka et al. (2023), a sample of X-ray-detected reverberation-mapped quasars was presented and applied for the comparison of cosmological constraints inferred using two well-established relations in AGN -- the X-ray/UV luminosity ($L_{X}-L_{UV}$) relation and the broad-line region radius-luminosity ($R-L$) relation. $L_{X}-L_{UV}$ and $R-L$ luminosity distances to the same quasars exhibit a distribution of their differences that is generally asymmetric and positively shifted for the six cosmological models we consider. We demonstrate that this behaviour can be interpreted qualitatively to arise as a result of the dust extinction of UV/X-ray quasar emission. We show that the extinction always contributes to the non-zero difference between $L_{X}-L_{UV}$-based and $R-L$-based luminosity distances and we derive a linear relationship between the X-ray/UV colour index $E_{X-UV}$ and the luminosity-distance difference, which also depends on the value of the $L_{X}-L_{UV}$ relation slope. Taking into account the median and the peak values of the luminosity-distance difference distributions, the average X-ray/UV colour index falls in the range of $\overline{E}_{X-UV}=0.03-0.28$ mag for the current sample of 58 sources. This amount of extinction is typical for the majority of quasars and it can be attributed to the circumnuclear and interstellar media of host galaxies. After applying the standard hard X-ray and far-UV extinction cuts, heavily extincted sources are removed but overall the shift towards positive values persists. The effect of extinction on luminosity distances is more pronounced for the $L_{X}-L_{UV}$ relation since the extinction of UV and X-ray emissions both contribute., Comment: 22 pages, 11 figures, 4 tables; accepted by AAS journals

This work investigates the design of Hybrid Automatic Repeat Request (HARQ) strategies for downlink Rate-Splitting Multiple Access (RSMA). The existence of private and common stream as well as their conditioning for Successive Interference Cancellation (SIC), gives rise to an expanded set of opportunities for retransmission of failed packets. Specifically, we devise a scheme in which the retransmissions are scheduled through the common stream, which offers a higher success probability. With this, the common stream needs to carry both new and retransmitted bits, which leads to a layered HARQ (L-HARQ) strategy which is capable of trading off throughput and reliability. Simulation results demonstrate that the devised HARQ scheme outperforms RSMA with conventional HARQ, where each retransmission is handled independently through its own stream. It also helps in closing the throughput gap between HARQ and Adaptive Modulation and Coding (AMC) in the high Signal-to-Noise Ratio (SNR) regime while also achieving a decreased Packet Error Rate (PER) and a lower latency.

We study space--time isogeometric discretizations of the linear acoustic wave equation that use splines of arbitrary degree p, both in space and time. We propose a space--time variational formulation that is obtained by adding a non-consistent penalty term of order 2p+2 to the bilinear form coming from integration by parts. This formulation, when discretized with tensor-product spline spaces with maximal regularity in time, is unconditionally stable: the mesh size in time is not constrained by the mesh size in space. We give extensive numerical evidence for the good stability, approximation, dissipation and dispersion properties of the stabilized isogeometric formulation, comparing against stabilized finite element schemes, for a range of wave propagation problems with constant and variable wave speed.

We propose an isogeometric mortar method to fourth order elliptic problems. In particular we are interested in the discretization of the biharmonic equation on $C^0$-conforming multi-patch domains and we exploit the mortar technique to weakly enforce $C^1$-continuity across interfaces. In order to obtain discrete inf-sup stability, a particular choice for the Lagrange multiplier space is needed. Actually, we use as multipliers splines of degree reduced by two, w.r.t. the primal spline space, and with merged elements in the neighbourhood of the corners. In this framework, we are able to show optimal a priori error estimates. We also perform numerical tests that reflect theoretical results.

We present a high-cadence multi-epoch analysis of dramatic variability of three broad emission lines (MgII, H$\beta$, and H$\alpha$) in the spectra of the luminous quasar ($\lambda L_{\lambda}$(5100\r{A}) = $4.7 \times 10^{44}$ erg s$^{-1}$) SDSS J141041.25+531849.0 at $z = 0.359$ with 127 spectroscopic epochs over 9 years of monitoring (2013-2022). We observe anti-correlations between the broad emission-line widths and flux in all three emission lines, indicating that all three broad emission lines "breathe" in response to stochastic continuum variations. We also observe dramatic radial velocity shifts in all three broad emission lines, ranging from $\Delta{v}$ $\sim$400 km s$^{-1}$ to $\sim$800 km s$^{-1}$, that vary over the course of the monitoring period. Our preferred explanation for the broad-line variability is complex kinematics in the broad-line region gas. We suggest a model for the broad-line variability that includes a combination of gas inflow with a radial gradient, an azimuthal asymmetry (e.g., a hot spot), superimposed on the stochastic flux-driven changes to the optimal emission region ("line breathing"). Similar instances of line-profile variability due to complex gas kinematics around quasars are likely to represent an important source of false positives in radial velocity searches for binary black holes, which typically lack the kind of high-cadence data we analyze here. The long-duration, wide-field, and many-epoch spectroscopic monitoring of SDSS-V BHM-RM provides an excellent opportunity for identifying and characterizing broad emission-line variability, and the inferred nature of the inner gas environment, of luminous quasars.

The Vera Rubin Observatory will provide an unprecedented set of time-dependent observations of the sky. The planned Legacy Survey of Space and Time (LSST) operating for 10 years will provide dense lightcurves for thousands of active galactic nuclei (AGN) in Deep Drilling Fields (DDFs) and less dense lightcurves for millions of AGN. We model the prospects for measuring time delays for emission lines with respect to the continuum, using these data. We model the artificial lightcurves using Timmer-Koenig algorithm, we use the exemplary cadence to sample them, we supplement lightcurves with the expected contamination by the strong emission lines (Hbeta, Mg II and CIV as well as with Fe II pseudo-continuum and the starlight). We choose the suitable photometric bands appropriate for the redshift and compare the assumed line time delay with the recovered time delay for 100 statistical realizations of the light curves. We show that time delays for emission lines can be well measured from the Main Survey for the bright tail of the quasar distribution (about 15% of all sources) with the accuracy within 1 sigma error, for DDFs results for fainter quasars are also reliable when all 10 years of data are used. There are also some prospects to measure the time delays for the faintest quasars at the smallest redshifts from the first two years of data, and eventually even from the first season. The entire quasar population will allow obtaining results of apparently high accuracy but in our simulations, we see a systematic offset between the assumed and recovered time delay depending on the redshift and source luminosity which will not disappear even in the case of large statistics. Such a problem might affect the slope of the radius-luminosity relation and cosmological applications of quasars if simulations correcting for such effects are not performed., Comment: Astronomy & Astrophysics in press

We use measurements of 59/58 quasars (QSOs), over a redshift range $0.0041\leq z \leq 1.686$, to do a comparative study of the radius--luminosity ($R-L$) and X-ray$-$UV luminosity ($L_X-L_{UV}$) relations and the implication of these relations for cosmological parameter estimation. By simultaneously determining $R-L$ or $L_X-L_{UV}$ relation parameters and cosmological parameters in six different cosmological models, we find that both $R-L$ and $L_X-L_{UV}$ relations are standardizable but provide only weak cosmological parameter constraints, with $L_X-L_{UV}$ relation data favoring larger current non-relativistic matter density parameter $\Omega_{m0}$ values than $R-L$ relation data and most other available data. We derive $L_X-L_{UV}$ and $R-L$ luminosity distances for each of the sources in the six cosmological models and find that $L_X-L_{UV}$ relation luminosity distances are shorter than $R-L$ relation luminosity distances as well as standard flat $\Lambda$CDM model luminosity distances. This explains why $L_X-L_{UV}$ relation QSO data favor larger $\Omega_{m0}$ values than do $R-L$ relation QSO data or most other cosmological measurements. While our sample size is small and only spans a small $z$ range, these results indicate that more work is needed to determine whether the $L_X-L_{UV}$ relation can be used as a cosmological probe., Comment: 20 pages, 10 figures, MNRAS in press

We test a scenario claiming that the broad absorption line (BAL) phenomenon in quasars (QSOs) is not a temporary stage of their life. In this scenario, we see the BAL effect only if the line of sight is within a spatially limited and collimated massive outflow cone covering only a fraction of sky from the point of view of the nucleus. The aim is to understand the theoretical mechanism behind the massive outflow in BAL QSOs which is important for modelling the impact of quasars onto the star formation rate in the host galaxy, and, subsequently, onto the galaxy evolution. We apply the specific theoretical model of dust-driven wind. The model has considerable predictive power. The 2.5D version of FRADO model of Czerny & Hryniewicz gives rise to the formation of fast funnel-shaped outflow from the disk for a certain range of black hole masses, Eddington ratios and metallicities. We now interpret BAL QSO as sources viewed along the outflowing stream and we calculate the probabilities of seeing the BAL phenomenon as functions of these global parameters, and we compare these probabilities to those seen in the observational data. We include considerations on the presence/absence of obscuring torus. Comparing our theoretical results with observational data for a sample consisting of two sub-populations of BAL and non-BAL QSOs we found that both in the model and in the data the BAL phenomenon mostly happens for sources with black hole masses larger than 10^{8} solar mass, the effect get stronger with accretion rate, and also high metallicities are more likely in QSOs showing BAL features if the presence of torus is taken into account. The consistency of the model with the data provides support for the interpretation of the BAL phenomenon as the result of the orientation of the source. It also supports the underlying theoretical model although more consistency checks should be done in the future., Comment: 15 pages, 13 figures, 3 tables, Accepted for publication in the Journal of Astronomy and Astrophysics (A&A)

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based on deep learning overwhelm the more traditional model-based approaches in performance, but they typically suffer from instability with respect to data perturbation. In this paper, we theoretically analyze the trade-off between stability and accuracy of neural networks, when used to solve linear imaging inverse problems for not under-determined cases. Moreover, we propose different supervised and unsupervised solutions to increase the network stability and maintain a good accuracy, by means of regularization properties inherited from a model-based iterative scheme during the network training and pre-processing stabilizing operator in the neural networks. Extensive numerical experiments on image deblurring confirm the theoretical results and the effectiveness of the proposed deep learning-based approaches to handle noise on the data., Comment: 21 pages, 6 figure. Paper will be sent for publication on a journal soon. This is a preliminary version, updated versions will be uploaded on ArXiv

Since many years we know that dust in the form of the dusty-molecular torus is responsible for the obscuration in active galactic nuclei (AGN) at large viewing angles and thus for the classification of AGN. Recently, we gained some observational and theoretical insight into geometry of the region and the role of the dust in the dynamics of the outflow and failed winds. We will briefly touch on all these aspects, including our dust-based model (FRADO - Failed Radiatively Accelerated Dusty Outflow) of the formation of the Balmer lines in AGN., Comment: Partially based on talk at 31st Symposium on the Physics of Ionized Gases in Belgrade, accepted for European Physical Journal D Topical Issue: "Physics of Ionized Gases and Spectroscopy of Isolated Complex Systems: Fundamentals and Applications"

We propose an innovative isogeometric space-time method for the heat equation, with smooth splines approximation in both space and time. To enhance the stability of the method we add a stabilizing term, based on a linear combination of high-order artificial diffusions. This term is designed in order to make the linear system lower block-triangular, that is, lower triangular with respect to time. In order to keep optimal accuracy, the stabilization terms are further weighted in terms of the residual. Through a series of numerical experiments, we validate the method's capability, showcasing its stability and accuracy.

We report the discovery of a new ``changing-look'' active galactic nucleus (CLAGN) event, in the quasar SDSS J162829.17+432948.5 at z=0.2603, identified through repeat spectroscopy from the fifth Sloan Digital Sky Survey (SDSS-V). Optical photometry taken during 2020--2021 shows a dramatic dimming of ${\Delta}$g${\approx}$1 mag, followed by a rapid recovery on a timescale of several months, with the ${\lesssim}$2 month period of rebrightening captured in new SDSS-V and Las Cumbres Observatory spectroscopy. This is one of the fastest CLAGN transitions observed to date. Archival observations suggest that the object experienced a much more gradual dimming over the period of 2011--2013. Our spectroscopy shows that the photometric changes were accompanied by dramatic variations in the quasar-like continuum and broad-line emission. The excellent agreement between the pre- and postdip photometric and spectroscopic appearances of the source, as well as the fact that the dimmest spectra can be reproduced by applying a single extinction law to the brighter spectral states, favor a variable line-of-sight obscuration as the driver of the observed transitions. Such an interpretation faces several theoretical challenges, and thus an alternative accretion-driven scenario cannot be excluded. The recent events observed in this quasar highlight the importance of spectroscopic monitoring of large active galactic nucleus samples on weeks-to-months timescales, which the SDSS-V is designed to achieve., Comment: Published in ApJL

As Setti & Woltjer noted back in 1973, quasars could be used to construct the Hubble diagram but the actual application was not that straightforward. It took years to implement the idea successfully. Most of the ways to use quasars for cosmology now require an advanced understanding of their structure, step by step. We briefly review this progress, with unavoidable personal bias, and concentrate on bright unobscured sources. We will mention the problem of the gas flow character close to the innermost stable circular orbit close to the black hole, discussed 50 years ago, which later led to the development of the slim disk scenario, but was recently revived in the context of Magnetically Arrested Disks (MAD) and Standard and Normal Evolution (SANE) disk models. We also discuss the hot/warm corona issue, which is still under discussion and complicates the analysis of the X-ray reflection. We present the scenario of the formation of the low ionization part of the Broad Line Region as a mostly failed wind powered by radiation pressure acting on dust (FRADO - Failed Radiatively Driven Dusty Outflow model). Next, we discuss the cosmological constraints that are currently achievable with quasars, mostly concentrating on light echo methods (continuum time delays and spectral line time delays with respect to the continuum) which are (or should be) incorporating the progress mentioned above. Finally, we briefly mention future prospects in this direction., Comment: Astrophysics and Space Science (in press)

We use 38 C IV quasar (QSO) reverberation-mapped (RM) observations, which span eight orders of magnitude in luminosity and the redshift range $0.001064 \leq z \leq 3.368$, to simultaneously constrain cosmological-model and QSO radius-luminosity ($R-L$) relation parameters in six cosmological models, using an improved technique that more correctly accounts for the asymmetric errors bars of the time-lag measurements. We find that $R-L$ relation parameters are independent of the cosmological models used in the analysis and so the $R-L$ relation can be used to standardize the C IV QSOs. The C IV QSO cosmological constraints are consistent with those from Mg II QSOs, allowing us to derive joint C IV + Mg II QSO cosmological constraints which are consistent with currently accelerated cosmological expansion, as well as consistent with cosmological constraints derived using better-established baryon acoustic oscillation (BAO) and Hubble parameter [$H(z)$] measurements. When jointly analyzed with $H(z)$ + BAO data, current C IV + Mg II QSO data mildly tighten current $H(z)$ + BAO data cosmological constraints., Comment: 19 pages, 11 figures, MNRAS accepted version

We use observations of 66 reverberation-measured \Mgii\ quasars (QSOs) in the redshift range $0.36 \leq z \leq 1.686$ -- a subset of the 78 QSOs we previously studied that also have \rfe\ (flux ratio parameter of UV \Feii\ to \Mgii\ that is used as an accretion-rate proxy) measurements -- to simultaneously constrain cosmological model parameters and QSO 2-parameter and 3-parameter radius-luminosity ($R-L$) relation parameters in six different cosmological models. We find that these QSO $R-L$ relation parameters are independent of the assumed cosmological model and so these QSOs are standardizable through the $R-L$ relations. Also: (1) With the 2-parameter $R-L$ relation, we find that the low-\rfe\ and high-\rfe\ data subsets obey the same $R-L$ relation within the error bars. (2) Extending the 2-parameter $R-L$ relation to a 3-parameter one does not result in the hoped-for reduction in the intrinsic dispersion of the $R-L$ relation. (3) Neither of the 3-parameter $R-L$ relations provide a significantly better fit to the measurements than does the 2-parameter $R-L$ relation. These are promising results for the on-going development of \Mgii\ cosmological probes. The first and third of these results differ significantly from those we found elsewhere from analyses of reverberation-measured \hb\ QSOs., Comment: 9 figures, 21 pages. arXiv admin note: text overlap with arXiv:2112.00052

Effective and adaptive interference management is required in next generation wireless communication systems. To address this challenge, Rate-Splitting Multiple Access (RSMA), relying on multi-antenna rate-splitting (RS) at the transmitter and successive interference cancellation (SIC) at the receivers, has been intensively studied in recent years, albeit mostly under the assumption of perfect Channel State Information at the Receiver (CSIR) and ideal capacity-achieving modulation and coding schemes. To assess its practical performance, benefits, and limits under more realistic conditions, this work proposes a novel design for a practical RSMA receiver based on model-based deep learning (MBDL) methods, which aims to unite the simple structure of the conventional SIC receiver and the robustness and model agnosticism of deep learning techniques. The MBDL receiver is evaluated in terms of uncoded Symbol Error Rate (SER), throughput performance through Link-Level Simulations (LLS), and average training overhead. Also, a comparison with the SIC receiver, with perfect and imperfect CSIR, is given. Results reveal that the MBDL receiver outperforms by a significant margin the SIC receiver with imperfect CSIR, due to its ability to generate on demand non-linear symbol detection boundaries in a pure data-driven manner.

Narrow Line Seyfert 1 (NLSy1) galaxies have been shown to have high Eddington ratios and relatively small black hole masses. The measurement of the black hole masses is based on the virial relation which is dependent on the distribution of the line-emitting gas and the viewing angle to the source. Spectropolarimetry enables us to probe the geometry of this line-emitting gas and allows us to estimate independently the viewing angle of the source by comparing the spectrum viewed under natural light and in the polarized light. We performed spectropolarimetric observations of three NLSy1 - Mrk 1044, SDSS J080101.41+184840.7, and IRAS 04416+1215 using the European Southern Observatory's Very Large Telescope. We use ESO Reflex workflow to perform standard data reduction and extract the natural and polarized spectra. We estimate the Stokes parameters and the viewing angles of the three sources. We model the Stokes parameters and infer the properties of the scattering media - located in the equatorial and polar regions, and simulate the spectra observed both in natural light and in polarized light using the polarization radiative transfer code STOKES. We confirm that all three sources are high Eddington ratio objects. We are successful in recovering the observed H$\alpha$ line profile both in the natural and polarized light using the STOKES modelling. We recover the polarization fractions of the order of 0.2-0.5% for the three sources. Our principal component analysis shows that the sample of the 25 sources including our sources, Fairall 9 from Jiang et al. (2021), and sources from Capetti et al. (2021) are mainly driven by the black hole mass and Eddington ratio. We re-affirm the connection of the strength of the optical FeII emission with the Eddington ratio, but the dependence on the viewing angle is moderate, more like a secondary effect., Comment: 25 pages, 21 figures, 11 tables, to be published in Astronomy & Astrophysics, version after proofs

Dual-Functional Radar-Communication (DFRC) systems have been investigated to manage the inter-system interference between radar and communication systems. However, the studies in literature often assume that the DFRC possesses perfect Channel State Information at the Transmitter (CSIT), which is an unrealistic assumption due to the inevitable CSIT errors in practical deployments. In this work, we aim to design a DFRC system under the practical assumption of partial CSIT. To achieve this, the proposed DFRC marries the capabilities of a Multiple-Input Multiple-Output (MIMO) radar with Rate-Splitting Multiple Access (RSMA). RSMA is a powerful downlink communication scheme based on linearly precoded Rate-Splitting (RS) that partially decodes multi-user interference (MUI) and partially treats it as noise and is inherently robust to partial CSIT. Using RSMA, the DFRC precoders are optimized in the presence of partial CSIT to simultaneously maximize the Average Weighted Sum-Rate (AWSR) under Quality-of-Service (QoS) constraints and minimize the DFRC beampattern Mean Squared Error (MSE) against an ideal MIMO radar beampattern. Simulation results demonstrate that the RSMA-based DFRC largely outperforms DFRCs based on other commonly used strategies such as Space Division Multiple Access (SDMA) and Non-Orthogonal Multiple Access (NOMA). Specifically, the common stream unique in the RSMA-based DFRC allows for flexible rate partitioning to guarantee user rate fairness with partial CSIT while also being the main contributor to generating a directional beampattern for effective radar sensing. The practical performance of the DFRC is then further assessed through Link-Level simulations (LLS) to take into account the effects of coding and modulation in the finite length regime as well as the channel aging due to mobility and latency, where the superiority of RSMA is again corroborated.

This paper proposes a new two-step procedure for sparse-view tomographic image reconstruction. It is called RISING, since it combines an early-stopped Rapid Iterative Solver with a subsequent Iteration Network-based Gaining step. So far, regularized iterative methods have widely been used for X-ray computed tomography image reconstruction from low-sampled data, since they converge to a sparse solution in a suitable domain, as upheld by the Compressed Sensing theory. Unfortunately, their use is practically limited by their high computational cost which imposes to perform only a few iterations in the available time for clinical exams. Data-driven methods, using neural networks to post-process a coarse and noisy image obtained from geometrical algorithms, have been recently studied and appreciated for both their computational speed and accurate reconstructions. However, there is no evidence, neither theoretically nor numerically, that neural networks based algorithms solve the mathematical inverse problem modeling the tomographic reconstruction process. In our two-step approach, the first phase executes very few iterations of a regularized model-based algorithm whereas the second step completes the missing iterations by means of a neural network. The resulting hybrid deep-variational framework preserves the convergence properties of the iterative method and, at the same time, it exploits the computational speed and flexibility of a data-driven approach. Experiments performed on a simulated and a real data set confirm the numerical and visual accuracy of the reconstructed RISING images in short computational times.

Introduction: This study analyzes the scientific production in business administration in scientific articles based on modeling partial least squares structural equations (Partial Least Squares Structural Equation Modeling PLS-SEM) in the 2011-2020 period. Methodology: The study is exploratory - descriptive and has three phases: a) Selection of keywords and search criteria; (b) Search and refinement of information; c) information analysis. A method of bibliometric review of the specific literature has been used based on the analysis of predefined indicators and completed with a qualitative content synthesis. Results: A total of 167 publications were analyzed, making correlations from the year, search criteria, authors, impact factor by quartile, and by citation variables. More outstanding scientific production comes from Scopus under the search criteria ((pls AND sem) OR "partial least squares") AND (business OR management), being the figure of 4,870 scientific articles, while Web of Science accumulates 3,946 articles Conclusion: There has been a progressive growth in scientific articles with the PLS-SEM technique from 2011 to 2020. Scopus, compared to WoS, presents a more significant number of scientific productions with this statistical approach. The authors who register scientific articles demonstrate a high H index; in addition, there is an important number of scientific articles with a PLS-SEM approach in universities in Malaysia that could be related to the expansion of higher education in that country, as well as in Singapore, Taiwan, and Indonesia. Finally, business administration, accounting, and economics are outstanding scientific production., Comment: 11 pages