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Digitalization in many economic sectors drove the financial system to adapt to new paradigms of technological transformation. Moreover, the extant regulatory framework forced the financial system to reconsider its business models and its relationship with the market. Such reasons generated also in the banking sector a new model of competition within the ecosystem never seen before in this sector. The new ecosystem of banks and financial institutions lacks a common framework that not only synthesizes the development lines of open innovation in the banking sector, but also regarding the planification of strategic choices and organisation within the new ecosystems. The present study aims to inquire the strategic positioning of European banks toward their digital transformation strategies, by analysing the decision-making processes that occurred between 2015 and 2019. A qualitative analysis on partnerships and the adoption of Application Programming Interfaces (APIs) development in support of new service models was carried out. Results have relevant policy implications for regulators, linked to the business evolution and the risks of outsourcing, and managerial implications for the followers, specifically on the plan of service integration to diversify and boost their activities in the segment of customer relationship management and care, providing a better user experience.

When the cornea becomes hydrated above its physiologic level it begins to significantly scatter light, loosing transparency and thus impairing eyesight. This condition, known as corneal edema, can be associated with different causes, such as corneal scarring, corneal infection, corneal inflammation, and others, making it difficult to diagnose and quantify. Previous works have shown that Second Harmonic Generation Microscopy (SHG) represents a valuable non-linear optical imaging tool to non-invasively identify and monitor changes in the collagen architecture of the cornea, potentially playing a pivotal role in future in-vivo cornea diagnostic methods. However, the interpretation of SHG data can pose significant problems when transferring such approaches to clinical settings, given the low availability of public data sets, and training resources. In this work we explore the use of three Deep Learning models, the highly popular InceptionV3 and ResNet50, alongside FLIMBA, a custom developed architecture, requiring no pre-training, to automatically detect corneal edema in SHG images of porcine cornea. We discuss and evaluate data augmentation strategies tuned to the specifics of the herein addressed application and observe that Deep Learning models building on different architectures provide complementary results. Importantly, we observe that the combined use of such complementary models boosts the overall classification performance in the case of differentiating edematous and healthy corneal tissues, up to an AU-ROC=0.98. These results have potential to be extrapolated to other diagnostics scenarios, such as differentiation of corneal edema in different stages, automated extraction of hydration level of cornea, or automated identification of corneal edema causes, and thus pave the way for novel methods for cornea diagnostics with Deep-Learning assisted non-linear optical imaging., Comment: 19 pages, 7 figures, 1 Table

The LOPES experiment was a radio interferometer built at the existing air shower array KASCADE-Grande in Karlsruhe, Germany. The last configuration of LOPES was called LOPES 3D and consisted of ten tripole antennas. Each of these antennas consisted of three crossed dipoles east-west, north-south, and vertically aligned. With this, LOPES 3D had the unique possibility to study the benefits of measurements with vertically aligned antennas in the environment of the well understood and calibrated particle detector array KASCADE-Grande. The measurements with three spatially coincident antennas allows a redundant reconstruction of the electric field vector. Several methods to exploit the redundancy were developed and tested. Furthermore, for the first time in LOPES, the background noise could be studied polarization- and direction dependent. With LOPES 3D it could be demonstrated that radio detection reaches a higher efficiency for inclined showers when including measurements with vertically aligned antennas and that the vertical component gets more important for the measurement of inclined showers. In this contribution we discuss a weighting scheme for the best combination of three redundant reconstructed electric field vectors. Furthermore, we discuss the influence of these weighting schemes on the ability to reconstruct air showers using the radio method. We show an estimate of the radio efficiency for inclined showers with focus on the benefits of measurements with vertically aligned antennas and we present the direction dependent noise in the different polarizations., Comment: Submission to the proceedings of the ARENA2014 workshop, which unfortunately were never published; thus documented here for reference

Afterglows of gamma-ray bursts (GRBs) are emitted from expanding forward shocks, which are expected to have magnetic field much stronger than the interstellar field, although the origin of the field is a long-standing problem. Two field amplification mechanisms, plasma kinetic instabilities and magnetohydrodynamic instabilities, have been discussed so far. The coherence length scales of the fields amplified by these two processes are different by $7-10$ orders of magnitudes, and the polarimetric observations may distinguish them. We construct a semi-analytic model of the forward shock afterglow polarization under the assumption of hydrodynamic-scale turbulent magnetic field. We perform numerical calculations of synchrotron polarization for the isotropic turbulence and the zero viewing angle. We find that the polarization degrees are $ \sim1~\%$ when the field coherence length scale in the fluid comoving frame is of the order of the thickness of the shocked regions. This range of polarization degree is comparable to that of the observed late-phase optical afterglows. Our model also shows that the radio polarization degrees are comparable to the optical ones on average but can be higher than the optical ones at some time intervals. The polarization angles are shown to vary randomly and continuously. These polarimetric properties are clearly different from the case of plasma kinetic instability. Simultaneous polarimetric observations of GRB afterglows at the radio and optical bands have recently started, which will help us constrain the magnetic field amplification mechanism.

We report measurements of the gravitationally lensed secondary image -- the first in an infinite series of so-called "photon rings" -- around the supermassive black hole M87* via simultaneous modeling and imaging of the 2017 Event Horizon Telescope (EHT) observations. The inferred ring size remains constant across the seven days of the 2017 EHT observing campaign and is consistent with theoretical expectations, providing clear evidence that such measurements probe spacetime and a striking confirmation of the models underlying the first set of EHT results. The residual diffuse emission evolves on timescales comparable to one week. We are able to detect with high significance a southwestern extension consistent with that expected from the base of a jet that is rapidly rotating in the clockwise direction. This result adds further support to the identification of the jet in M87* with a black hole spin-driven outflow, launched via the Blandford-Znajek process. We present three revised estimates for the mass of M87* based on identifying the modeled thin ring component with the bright ringlike features seen in simulated images, one of which is only weakly sensitive to the astrophysics of the emission region. All three estimates agree with each other and previously reported values. Our strongest mass constraint combines information from both the ring and the diffuse emission region, which together imply a mass-to-distance ratio of $4.20^{+0.12}_{-0.06}~\mu{\rm as}$ and a corresponding black hole mass of $(7.13\pm0.39)\times10^9M_\odot$, where the error on the latter is now dominated by the systematic uncertainty arising from the uncertain distance to M87*.

Realizing the full potential of ultrahigh-intensity lasers for particle and radiation generation will require multi-beam arrangements due to technology limitations. Here, we investigate how to optimize their coupling with solid targets. Experimentally, we show that overlapping two intense lasers in a mirror-like configuration onto a solid with a large preplasma can greatly improve the generation of hot electrons at the target front and ion acceleration at the target backside. The underlying mechanisms are analyzed through multidimensional particle-in-cell simulations, revealing that the self-induced magnetic fields driven by the two laser beams at the target front are susceptible to reconnection, which is one possible mechanism to boost electron energization. In addition, the resistive magnetic field generated during the transport of the hot electrons in the target bulk tends to improve their collimation. Our simulations also indicate that such effects can be further enhanced by overlapping more than two laser beams.

Supermassive black holes in active galactic nuclei launch relativistic jets, as indicated by observed superluminal radio blobs. The energy source of these jets is widely discussed in the theoretical framework of Blandford-Znajek process, the electromagnetic energy extraction from rotating black holes (BHs), while formation mechanism of the radio blobs in the electromagnetically-dominated jets has been a long-standing problem. Recent high-resolution magnetohydrodynamic simulations of magnetically arrested disks exhibited magnetic reconnection in a transient magnetically-dominated part of the equatorial disk near the BH horizon, which led to a promising scenario of efficient MeV gamma-ray production and subsequent electron-positron pair loading into BH magnetosphere. We develop this scenario to build a theoretical framework on energetics, timescales and particle number density of the superluminal radio blobs and discuss observable signatures in other wavebands. We analytically show that the non-thermal electrons emit broadband photons from optical to multi-MeV bands. The electron-positron pairs produced in the magnetosphere are optically thick for synchrotron-self absorption, so that the injected energy is stored in the plasma. The stored energy is enough to power the superluminal radio blobs observed in M87. This scenario predicts rather dim radio blobs around Sgr A*, which are consistent with no clear detection by current facilities. In addition, this scenario inevitably produces strong X-ray flares in a short timescale, which will be detectable by future X-ray satellites., Comment: 14 pages, 5 figures, 1 table, accepted for publication in ApJL

In this work, we investigate the effects of first-order phase transitions on the singlet fermionic dark matter in the scotogenic model. It is known that this dark matter candidate tends to conflict with the relevant constraints such as the neutrino oscillation data and charged lepton flavor violating processes if its thermal production mechanism is assumed. We find that the dark matter production mechanisms are modified by first-order phase transitions at some specific parameter regions, where the phase transitions can be one-step or two-step depending on the parameters. If the phase transition is one-step, a sufficiently low nucleation temperature is required to reproduce the observed relic abundance of dark matter. If the phase transition is two-step, the dark matter should never be thermalized, otherwise the abundance would remain too much and overclose the universe. This is because the nucleation temperature cannot be low as in the one-step case. Therefore we require another way of dark matter production, the freeze-in mechanism for the two-step case. We show that the freeze-in mechanism is modified by the temporary vacuum expectation value of the inert scalar field. In both cases, the first-order phase transitions could produce observable gravitational wave spectra. In particular for the one-step phase transition, the generated gravitational waves with sizable energy density are intrinsically correlated with the dark matter production mechanism, and can be detectable by future space-based interferometers., Comment: 28 pages, 11 figures, version to appear in JHEP

Nanocrystalline Si and Ge are of high interest for integrated Si photonics related to light emission, optical sensors, photodetectors, solar energy harvesting and conversion devices, and also for floating gate non-volatile memories (NVMs). In this review, we have focused on nanocrystalline porous Si (nc-PS) with extension to Si nanodots, and Ge nanocrystals (NCs)/quantum dots (QDs)/nanoparticles (NPs) embedded in oxides (SiO$_2$, TiO$_2$, HfO$_2$, Al$_2$O$_3$). The great asset of nc-PS is its intense photoluminescence in VIS at room temperature (RT), while Ge NCs/NPs embedded in oxides show high photosensitivity in VIS-NIR-SWIR in the spectral photocurrent up to 1325 nm at RT. Ge NCs/NPs/QDs floating gate NVMs present high memory performance, the retention characteristics corresponding to the state of the art for NCs floating gate NVMs. We prove the relevance of controlling the preparation parameters for obtaining films with targeted photoluminescence, photosensitivity and charge storage properties for applications, e.g. VIS-NIR-SWIR optical sensors and photodetectors, and electronic and photoelectric NVMs. We evidence the correlation of preparation conditions, morphology, composition and crystalline structure with optical, electrical, photoelectrical and charge storage properties and also evidence the contribution of quantum confinement effect, localized states and trapping centers.

Although previous infection and vaccination provide protection against SARS-CoV-2 infection, both reinfection and breakthrough infection are possible events whose occurrence would increase with time after first exposure to the antigen and with the emergence of new variants of the virus. Periodic vaccination could counteract this decline in protection. In the present work, our aim was to develop and explore a model of SARS-CoV-2 spread with vaccination, reinfection and breakthrough infection. A modified deterministic SIS (Susceptible-Infected-Susceptible) model represented by a system of differential equations was designed. As in any SIS model, the population was divided into susceptible and infected individuals. But in our design, susceptible individuals were, in turn, grouped into three consecutive categories whose susceptibility increases with time after infection or vaccination. The model was studied by means of computer simulations, which were analysed qualitatively. The results obtained show that the prevalence, after oscillating between peaks and valleys, reaches a plateau phase. Moreover, as might be expected, the magnitude of the peaks and plateaus increases as the infection rate rises, the vaccination rate decreases and the rate of decay of protection conferred by vaccination or previous infection increases. Therefore, the present study suggests that, at least under certain conditions, the spread of SARS-CoV-2, although it could experience fluctuations, would finally evolve into an endemic form, with a more or less stable prevalence that would depend on the levels of infection and vaccination, and on the kinetics of post-infection and post-vaccination protection. However, it should be kept in mind that our development is a theoretical scheme with many limitations. For this reason, its predictions should be considered with great care., Comment: 24 pages with 12 figures

To exploit the full potential of the transverse spatial structure of light using the Laguerre-Gaussian basis, it is necessary to control the azimuthal and radial components of the photons. Vortex phase elements are commonly used to generate these modes of light, offering precise control over the azimuthal index but neglect the radially dependent amplitude term which defines their associated corresponding transverse profile. Here we experimentally demonstrate the generation of high purity Laguerre-Gaussian beams with a single step on-axis transformation implemented with a dielectric phase-amplitude metasurface. By vectorially structuring the input beam and projecting it onto an orthogonal polarisation basis, we can sculpt any vortex beam in phase and amplitude. We characterize the azimuthal and radial purity of the generated vortex beams, reaching a purity of 98% for a vortex beam with $\ell=50$ and $p=0$. Furthermore, we comparatively show that the purity of the generated vortex beams outperform those generated with other well-established phase-only metasurface approaches. In addition, we highlight the formation of 'ghost' orbital angular momentum orders from azimuthal gratings (analogous to ghost orders in ruled gratings), which have not been widely studied to date. Our work brings higher-order vortex beams and their unlimited potential within reach of wide adoption., Comment: article (19 pages, 5 figures) and supplemental (7 pages, 8 figures)

The origins of the GeV gamma-rays from nearby radio galaxies are unknown. Hadronic emission from magnetically arrested disks (MADs) around central black holes (BHs) is proposed as a possible scenario. Particles are accelerated in the MAD by magnetic reconnection and stochastic turbulence acceleration. We pick out the fifteen brightest radio galaxies in the GeV band from the Fermi 4LAC-DR2 catalog and apply the MAD model. We find that we can explain the data in the GeV bands by the MAD model if the accretion rate is lower than 0.1% of the Eddington rate. For a higher accretion rate, GeV gamma-rays are absorbed by two-photon interaction due to copious low-energy photons. If we assume another proposed prescription of the electron heating rate by magnetic reconnection, the MAD model fails to reproduce the GeV data for the majority of our sample. This indicates that the electron heating rate is crucial. We also apply the MAD model to Sgr A* and find that GeV gamma-rays observed at the Galactic center do not come from the MAD of Sgr A*. We estimate the cosmic ray intensity from Sgr A*, but it is too low to explain the high-energy cosmic ray intensity on Earth., Comment: 15 pages, 10 figures, accepted for publication in ApJ

The interactions between a relativistic magnetized collisionless shock and dense clumps have been expected to play a crucial role on the magnetic field amplification and cosmic-ray acceleration. We investigate this process by two-dimensional Particle-In-Cell (PIC) simulations for the first time, where the clump size is much larger than the gyroradius of downstream particles. We also perform relativistic magnetohydrodynamic (MHD) simulations for the same condition to see the kinetic effects. We find that particles escape from the shocked clump along magnetic field lines in the PIC simulations, so that the vorticity is lower than that in the MHD simulations. Moreover, in both the PIC and MHD simulations, the shocked clump quickly decelerates because of relativistic effects. Owing to the escape and the deceleration, the shocked clump cannot amplify the downstream magnetic field in relativistic collisionless shocks. This large-scale PIC simulation opens a new window to understand large-scale behaviors in collisionless plasma systems., Comment: Accepted for publication in The Astrophysical Journal Letters

In this paper, we obtain mean square values of the double zeta-functions of the Apostol-Vu type and the Mordell-Tornheim type., Comment: 33 pages, minor revisons. To appear in European Journal of Mathematics

Using light curves with $\sim$3 min cadence and a duration of 2 hrs made using the OmegaWhite survey, we present the results of a search for short-period variable stars in the field of 20 open clusters. We identified 92 variable stars in these fields. Using a range of cluster member catalogues and Gaia EDR3 data, we have determined that 10 are cluster members and 2 more are probable members. Based on their position on the Gaia HRD and their photometric periods, we find that most of these are $\delta$ Sct stars. We obtained low-resolution optical spectroscopy of some of these cluster members and field stars. We discuss the cluster variable stars in the context of $\delta$ Sct stars in other open clusters., Comment: Accepted for publication in MNRAS. 20 pages, 14 figures

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community., Comment: 356 pages, Large pdf file (40 MB) submitted to Snowmass 2021; v2 references to Snowmass contributions added, additional authors; v3 references added, some updates, additional authors

Path planning is an essential component of mobile robotics. Classical path planning algorithms, such as wavefront and rapidly-exploring random tree (RRT) are used heavily in autonomous robots. With the recent advances in machine learning, development of learning-based path planning algorithms has been experiencing rapid growth. An unified path planning interface that facilitates the development and benchmarking of existing and new algorithms is needed. This paper presents PathBench, a platform for developing, visualizing, training, testing, and benchmarking of existing and future, classical and learning-based path planning algorithms in 2D and 3D grid world environments. Many existing path planning algorithms are supported; e.g. A*, Dijkstra, waypoint planning networks, value iteration networks, gated path planning networks; and integrating new algorithms is easy and clearly specified. The benchmarking ability of PathBench is explored in this paper by comparing algorithms across five different hardware systems and three different map types, including built-in PathBench maps, video game maps, and maps from real world databases. Metrics, such as path length, success rate, and computational time, were used to evaluate algorithms. Algorithmic analysis was also performed on a real world robot to demonstrate PathBench's support for Robot Operating System (ROS). PathBench is open source., Comment: Accepted to Advanced Robotics Journal; 23 pages, 9 figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:2105.01777

We prove a version of the Hodge-Riemann bilinear relations for Schur polynomials of K\"ahler forms and for Schur polynomials of positive forms on a complex vector space., Comment: 25 pages. v2 minor typos fixed

Although surface diffusion is critical for many physical and chemical processes, including the epitaxial growth of crystals and heterogeneous catalysis, it is particularly challenging to directly study. Here, we estimate the carbon adatom migration barrier on freestanding monolayer graphene by quantifying its temperature-dependent electron knock-on damage. Due to the fast healing of vacancies by diffusing adatoms, the damage rate decreases with increasing temperature. By analyzing the observed damage rates at 300-1073 K using a model describing our finite scanning probe, we find a barrier of (0.33 \pm 0.03) eV., Comment: 6 pages, 3 figures. Additionally, some supplemental material has been uploaded: 1 PDF, 1 Jupyter Notebook, 1 Python module, 3 data files in tabular form)

The thermal production mechanism of dark matter is attractive and well-motivated by predictivity. A representative of this type of dark matter candidate is the canonical, weakly interacting massive particles. An alternative is semi-annihilating dark matter, which exhibits different phenomenological aspects from the former example. In this study, we constructed a model of dark matter semi-annihilating into a pair of anti-dark matter and a Majoron based on a global $U(1)_{B-L}$ symmetry, and show that semi-annihilation induces the core formation of dark matter halos, which can alleviate the so-called small-scale problems. In addition, the box-shaped spectrum of neutrinos was produced by the subsequent decay of the Majoron. This can be a distinctive signature of the dark matter in the model. We find a parameter space where the produced neutrinos can be detected by the future large-volume neutrino detector Hyper-Kamiokande. We also compared the dark matter scenario with the case of halo core formation by the strongly self-interacting dark matter., Comment: 19 pages, 5 figures

Doping of the graphene lattice with transition metal atoms resulting in high magnetic anisotropy energy (MAE) is an important goal of materials research owing to its potential application in spintronics. In this article, by using spin-polarized density functional theory including spin-orbit coupling, we examined magnetic properties of graphene with vacancy defects, both bare and nitrogen-decorated, and doped by Cr, Mn and Fe transition metal single atom (TM-SA) and two different TM atoms simultaneously. [...] The computational findings are supplemented by an atomic-resolution characterization of an incidental Mn impurity bonded to four carbon atoms, whose localized spin matches expectations as measured using core-level electron energy-loss spectroscopy. Conducting TM-doped graphene with robust magnetic features offers prospects for the design of graphene-based spintronic devices., Comment: 31 + 61 pages, 5 + 81 figures

Optical metasurfaces have come into the spotlight as a promising platform for light manipulation at the nanoscale, including ultrafast all-optical control via excitation with femtosecond laser pulses. Recently, dichroic metasurfaces have been exploited to modulate the polarization state of light with unprecedented speed. Here, we theoretically predict and experimentally demonstrate by pump-probe spectroscopy the capability to reconfigure the ultrafast dichroic signal of a gold metasurface by simply acting on the polarization of the pump pulse, which is shown to reshape the spatio-temporal distribution of the optical perturbation. The photoinduced anisotropic response, driven by out-of-equilibrium carriers and extinguished in a sub-picosecond temporal window, is readily controlled in intensity by tuning the polarization direction of the excitation up to a full sign reversal. This work proves that nonlinear metasurfaces offer the flexibility to tailor their ultrafast optical response in a fully all-optically reconfigurable platform.

Relativistic jets are collimated outflows with speeds close to light speed, which are associated with gamma-ray bursts (GRBs), active galactic nuclei (AGNs), and so on. This article mainly overviews recent developments of polarimetric studies of GRBs and their afterglows in the gamma-ray and optical wavebands as well as the first detections of their radio polarization. Polarimetric observations and theoretical modelings can address the emission mechanism, magnetic field structure, and energetics of GRB jets and related collisionless plasma physics. Some of the discussed key physics are common with AGN jets. Furthermore, we mention that polarimetry of AGN jets and protoplanetary disks may be a novel approach to search for ultra-light axion dark matter., Comment: 8 pages, 5 figures, to appear in proceedings of IAU symposium 360 "Astronomical Polarimetry -- New Era of Multi-Wavelength Polarimetry", held at Mar 22-26, 2021

We present a quantitatively accurate machine-learning (ML) model for the computational prediction of core-electron binding energies, from which x-ray photoelectron spectroscopy (XPS) spectra can be readily obtained. Our model combines density functional theory (DFT) with $GW$ and uses kernel ridge regression for the ML predictions. We apply the new approach to materials and molecules containing carbon, hydrogen and oxygen, and obtain qualitative and quantitative agreement with experiment, resolving spectral features within 0.1 eV of reference experimental spectra. The method only requires the user to provide a structural model for the material under study to obtain an XPS prediction within seconds. Our new tool is freely available online through the XPS Prediction Server.

Elastic knock-on is the main electron irradiation damage mechanism in metals including graphene. Atomic vibrations influence its cross-section, but only the out-of-plane direction has been considered so far in the literature. Here, we present a full three-dimensional theory of knock-on damage including the effect of temperature and vibrations to describe ejection into arbitrary directions. We thus establish a general quantitative description of electron irradiation effects through elastic scattering. Applying our methodology to in-plane jumps of pyridinic nitrogen atoms, we show their observed rates imply much stronger inelastic effects than in pristine graphene., Comment: 5 pages, 2 figures, 1 table (+ supplement)

Let $A$ be a central division algebra of prime degree $p$ over $\mathbb{Q}$. We obtain subconvex hybrid bounds, uniform in both the eigenvalue and the discriminant, for the sup-norm of Hecke-Maass forms on the compact quotients of $\operatorname{SL}_p(\mathbb{R})/\operatorname{SO}(p)$ by unit groups of orders in $A$. The exponents in the bounds are explicit and polynomial in $p$. We also prove subconvex hybrid bounds in the case of certain Eichler-type orders in division algebras of arbitrary odd degree., Comment: 29 pages. Minor improvements, implemented suggestions from referee. To appear in Trans. AMS. Comments are welcome!

The black-hole images obtained with the Event Horizon Telescope (EHT) are expected to be variable at the dynamical timescale near their horizons. For the black hole at the center of the M87 galaxy, this timescale (5-61 days) is comparable to the 6-day extent of the 2017 EHT observations. Closure phases along baseline triangles are robust interferometric observables that are sensitive to the expected structural changes of the images but are free of station-based atmospheric and instrumental errors. We explored the day-to-day variability in closure phase measurements on all six linearly independent non-trivial baseline triangles that can be formed from the 2017 observations. We showed that three triangles exhibit very low day-to-day variability, with a dispersion of $\sim3-5^\circ$. The only triangles that exhibit substantially higher variability ($\sim90-180^\circ$) are the ones with baselines that cross visibility amplitude minima on the $u-v$ plane, as expected from theoretical modeling. We used two sets of General Relativistic magnetohydrodynamic simulations to explore the dependence of the predicted variability on various black-hole and accretion-flow parameters. We found that changing the magnetic field configuration, electron temperature model, or black-hole spin has a marginal effect on the model consistency with the observed level of variability. On the other hand, the most discriminating image characteristic of models is the fractional width of the bright ring of emission. Models that best reproduce the observed small level of variability are characterized by thin ring-like images with structures dominated by gravitational lensing effects and thus least affected by turbulence in the accreting plasmas., Comment: Accepted for Publication in ApJ