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Photonic quantum information processing in metropolitan quantum networks lays the foundation for cloud quantum computing [1, 2], secure communication [3, 4], and the realization of a global quantum internet [5, 6]. This paradigm shift requires on-demand and high-rate generation of flying qubits and their quantum state teleportation over long distances [7]. Despite the last decade has witnessed an impressive progress in the performances of deterministic photon sources [8-11], the exploitation of distinct quantum emitters to implement all-photonic quantum teleportation among distant parties has remained elusive. Here, we overcome this challenge by using dissimilar quantum dots whose electronic and optical properties are engineered by light-matter interaction [12], multi-axial strain [13] and magnetic fields [14] so as to make them suitable for the teleportation of polarization qubits. This is demonstrated in a hybrid quantum network harnessing both fiber connections and 270 m free-space optical link connecting two buildings of the University campus in the center of Rome. The protocol exploits GPS-assisted synchronization, ultra-fast single photon detectors as well as stabilization systems that compensate for atmospheric turbulence. The achieved teleportation state fidelity reaches up to 82+-1%, above the classical limit by more than 10 standard deviations. Our field demonstration of all-photonic quantum teleportation opens a new route to implement solid-state based quantum relays and builds the foundation for practical quantum networks.

RNA molecules exhibit various biological functions intrinsically dependent on their diverse ecosystem of highly flexible structures. This flexibility arises from complex hydrogen-bonding networks defined by canonical and non-canonical base pairs that require protonation events to stabilize or perturb these interactions. Constant pH molecular dynamics (CpHMD) methods provide a reliable framework to explore the conformational and protonation space of dynamic structures and for robust calculations of pH-dependent properties, such as the pK$_\mathrm{a}$ of titrable sites. Despite growing biological evidence concerning pH regulation of certain motifs and in biotechnological applications, pH-sensitive in silico methods have rarely been applied to nucleic acids. In this work, we extended the stochastic titration CpHMD method to include RNA parameters from the standard $\chi$OL3 AMBER force field and highlighted its capability to depict titration events of nucleotides in single-stranded RNAs. We validated the method using trimers and pentamers with a single central titrable site while integrating a well-tempered metadynamics approach into the st-CpHMD methodology (CpH-MetaD) using PLUMED. This approach enhanced the convergence of the conformational landscape and enabled more efficient sampling of protonation-conformation coupling. Our pK$_\mathrm{a}$ estimates agree with experimental data, validating the method's ability to reproduce electrostatic changes around a titrable nucleobase in single-stranded RNA. These findings provided molecular insight into intramolecular phenomena, such as nucleobase stacking and phosphate interactions, that dictate the experimentally observed pK$_\mathrm{a}$ shifts between different strands. Overall, this work validates both the st-CpHMD and the metadynamics integration as reliable tools for studying biologically relevant RNA systems.

This paper presents an innovative framework for analyzing the regularity of solutions to the stochastic Navier-Stokes equations by integrating Sobolev-Besov hybrid spaces with fractional operators and quantum-inspired dynamics. We propose new regularity theorems that address the multiscale and chaotic nature of fluid flows, offering novel insights into energy dissipation mechanisms. The introduction of a Schr\"odinger-like operator into the fluid dynamics model captures quantum-scale turbulence effects, enhancing our understanding of energy redistribution across different scales. The results also include the development of anisotropic stochastic models that account for direction-dependent viscosity, improving the representation of real-world turbulent flows. These advances in stochastic modeling and regularity analysis provide a comprehensive toolset for tackling complex fluid dynamics problems. The findings are applicable to fields such as engineering, quantum turbulence, and environmental sciences. Future directions include the numerical implementation of the proposed models and the use of machine learning techniques to optimize parameters for enhanced simulation accuracy., Comment: 14 pages

Different brain imaging modalities offer unique insights into brain function and structure. Combining them enhances our understanding of neural mechanisms. Prior multimodal studies fusing functional MRI (fMRI) and structural MRI (sMRI) have shown the benefits of this approach. Since sMRI lacks temporal data, existing fusion methods often compress fMRI temporal information into summary measures, sacrificing rich temporal dynamics. Motivated by the observation that covarying networks are identified in both sMRI and resting-state fMRI, we developed a novel fusion method, by combining deep learning frameworks, copulas and independent component analysis (ICA), named copula linked parallel ICA (CLiP-ICA). This method estimates independent sources for each modality and links the spatial sources of fMRI and sMRI using a copula-based model for more flexible integration of temporal and spatial data. We tested CLiP-ICA using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Our results showed that CLiP-ICA effectively captures both strongly and weakly linked sMRI and fMRI networks, including the cerebellum, sensorimotor, visual, cognitive control, and default mode networks. It revealed more meaningful components and fewer artifacts, addressing the long-standing issue of optimal model order in ICA. CLiP-ICA also detected complex functional connectivity patterns across stages of cognitive decline, with cognitively normal subjects generally showing higher connectivity in sensorimotor and visual networks compared to patients with Alzheimer, along with patterns suggesting potential compensatory mechanisms., Comment: 25 pages, 10 figures, journal article

Phonons in solid-state quantum emitters play a crucial role in their performance as photon sources in quantum technology. For resonant driving, phonons dampen the Rabi oscillations resulting in reduced preparation fidelities. The phonon spectral density, which quantifies the strength of the carrier-phonon interaction, is non-monotonous as a function of energy. As one of the most prominent consequences, this leads to the reappearance of Rabi rotations for increasing pulse power, which was theoretically predicted in Phys. Rev. Lett. 98, 227403 (2007). In this paper we present the experimental demonstration of the reappearance of Rabi rotations.

The generation of single photons using solid-state quantum emitters is pivotal for advancing photonic quantum technologies, particularly in quantum communication. As the field continuously advances towards practical use cases and beyond shielded laboratory environments, specific demands are placed on the robustness of quantum light sources during operation. In this context, the robustness of the quantum light generation process against intrinsic and extrinsic effects is a major challenge. Here, we present a robust scheme for the coherent generation of indistinguishable single-photon states with very low photon number coherence (PNC) using a three-level system in a semiconductor quantum dot. Our novel approach combines the advantages of adiabatic rapid passage (ARP) and stimulated two-photon excitation (sTPE). We demonstrate robust quantum light generation while maintaining the prime quantum-optical quality of the emitted light state. Moreover, we highlight the immediate advantages for the implementation of various quantum cryptographic protocols., Comment: 12 pages, 6 figures

The generation of entangled photons from radiative cascades has enabled milestone experiments in quantum information science with several applications in photonic quantum technologies. Significant efforts are being devoted to pushing the performances of near-deterministic entangled-photon sources based on single quantum emitters often embedded in photonic cavities, so to boost the flux of photon pairs. The general postulate is that the emitter generates photons in a nearly maximally entangled state of polarization, ready for application purposes. Here, we demonstrate that this assumption is unjustified. We show that in radiative cascades there exists an interplay between photon polarization and emission wavevector, strongly affecting quantum correlations when emitters are embedded in micro-cavities. We discuss how the polarization entanglement of photon pairs from a biexciton-exciton cascade in quantum dots strongly depends on their propagation wavevector, and it can even vanish for large emission angles. Our experimental results, backed by theoretical modelling, yield a brand-new understanding of cascaded emission for various quantum emitters. In addition, our model provides quantitative guidelines for designing optical microcavities that retain both a high degree of entanglement and collection efficiency, moving the community one step further towards an ideal source of entangled photons for quantum technologies.

We consider a recently introduced extension of General Relativity dubbed as Cotton gravity (CG), based on the use of the Cotton tensor, to estimate the size of a new constant $\gamma$ appearing within a spherically symmetric, vacuum solution of the theory. Taking into account its non-asymptotically flat character, we use the inferred size of the central brightness depression of the supermassive object at the heart of the Milky Way galaxy (Sgr A*) by the Event Horizon Telescope to constrain at $2\sigma$ the CG parameter as $\gamma M \approx 3.5 \times 10^{-12}$. We study the potential observational consequences from the smallness of such a value using exact and numerical expressions for the deflection angle, optical images from optically and geometrically thin accretion disks, isoradials, and instability scales (Lyapunov index) of nearly bound geodesics associated to photon rings. Our results point towards the impossibility to distinguish between these two geometries using current and foreseeable techniques in the field of interferometric detection of optical sources., Comment: 13 pages, 8 figures

Recently, J. Harada proposed a theory relating gravity to the Cotton tensor, dubbed as ''Cotton gravity'' (CG). This is an extension of General Relativity such that every solution of the latter turns out to be a solution of the former (but the converse is not true) and, furthermore, it is possible to derive the cosmological constant as an integration constant within it. In this work we investigate CG by coupling it to both non-linear electrodynamics (NLED) and scalar fields. We study static and spherically symmetric solutions implementing a bouncing behaviour in the radial function so as to avoid the development of singularities, inspired by the Simpson-Visser black bounce and the Bardeen model, both interpreted as magnetic monopoles. We identify the NLED Lagrangian density and the scalar field potential generating such solutions, and investigate the corresponding gravitational configurations in terms of horizons, behaviour of the metric functions, and regularity of the Kretchsman curvature scalar. Our analysis extends the class of non-singular geometries found in the literature and paves the ground for further analysis of black holes in CG., Comment: 14 pages, 6 figures. V2: 16 pages, 6 figures. Discussion and references added; matches published version

The sequential resonant excitation of a 2-level quantum system results in the emission of a state of light showing time-entanglement encoded in the photon-number-basis - notions that can be extended to 3-level quantum systems as discussed in a recent proposal. Here, we report the experimental implementation of a sequential two-photon resonant excitation process of a solid-state 3-level system, constituted by the biexciton-, exciton-, and ground-state of a semiconductor quantum dot. The resulting light state exhibits entanglement in time and energy, encoded in the photon-number basis, which could be used in quantum information applications, e.g., dense information encoding or quantum communication protocols. Performing energy- and time-resolved correlation experiments in combination with extensive theoretical modelling, we are able to partially retrieve the entanglement structure of the generated state., Comment: 14 pages (including 5 figures, 56 citations)

One-class learning (OCL) comprises a set of techniques applied when real-world problems have a single class of interest. The usual procedure for OCL is learning a hypersphere that comprises instances of this class and, ideally, repels unseen instances from any other classes. Besides, several OCL algorithms for graphs have been proposed since graph representation learning has succeeded in various fields. These methods may use a two-step strategy, initially representing the graph and, in a second step, classifying its nodes. On the other hand, end-to-end methods learn the node representations while classifying the nodes in one learning process. We highlight three main gaps in the literature on OCL for graphs: (i) non-customized representations for OCL; (ii) the lack of constraints on hypersphere parameters learning; and (iii) the methods' lack of interpretability and visualization. We propose One-cLass Graph Autoencoder (OLGA). OLGA is end-to-end and learns the representations for the graph nodes while encapsulating the interest instances by combining two loss functions. We propose a new hypersphere loss function to encapsulate the interest instances. OLGA combines this new hypersphere loss with the graph autoencoder reconstruction loss to improve model learning. OLGA achieved state-of-the-art results and outperformed six other methods with a statistically significant difference from five methods. Moreover, OLGA learns low-dimensional representations maintaining the classification performance with an interpretable model representation learning and results.

We present new results to model and understand the role of encoder-decoder design in machine learning (ML) from an information-theoretic angle. We use two main information concepts, information sufficiency (IS) and mutual information loss (MIL), to represent predictive structures in machine learning. Our first main result provides a functional expression that characterizes the class of probabilistic models consistent with an IS encoder-decoder latent predictive structure. This result formally justifies the encoder-decoder forward stages many modern ML architectures adopt to learn latent (compressed) representations for classification. To illustrate IS as a realistic and relevant model assumption, we revisit some known ML concepts and present some interesting new examples: invariant, robust, sparse, and digital models. Furthermore, our IS characterization allows us to tackle the fundamental question of how much performance (predictive expressiveness) could be lost, using the cross entropy risk, when a given encoder-decoder architecture is adopted in a learning setting. Here, our second main result shows that a mutual information loss quantifies the lack of expressiveness attributed to the choice of a (biased) encoder-decoder ML design. Finally, we address the problem of universal cross-entropy learning with an encoder-decoder design where necessary and sufficiency conditions are established to meet this requirement. In all these results, Shannon's information measures offer new interpretations and explanations for representation learning.

The spread of microbial infections is governed by the self-organization of bacteria on surfaces. Limitations of live imaging techniques make collective behaviors in clinically relevant systems challenging to quantify. Here, novel experimental and image analysis techniques for high-fidelity single-cell segmentation of bacterial colonies are developed. Machine learning-based segmentation models are trained solely using synthetic microscopy images that are processed to look realistic using state-of-the-art image-to-image translation methods, requiring no biophysical modeling. Accurate single-cell segmentation is achieved for densely packed single-species colonies and multi-species colonies of common pathogenic bacteria, even under suboptimal imaging conditions and for both brightfield and confocal laser scanning microscopy. The resulting data provide quantitative insights into the self-organization of bacteria on soft surfaces. Thanks to their high adaptability and relatively simple implementation, these methods promise to greatly facilitate quantitative descriptions of bacterial infections in varied environments., Comment: 12 pages, 5 figures

This study provides accurate results for the electronic stopping cross-sections of H, He, N, and Ne in silicon in low to intermediate energy ranges using various non-perturbative theoretical methods, including real-time time-dependent density functional theory, transport cross-section, and induced-density approach. Recent experimental findings [Ntemou \textit{et al.}, Phys. Rev. B {\bf 107}, 155145 (2023)] revealed discrepancies between the estimates of density functional theory and observed values. We show that these discrepancies vanish by considering the nonuniform electron density of the silicon deeper bands for ion velocities approaching zero ($v \to 0$). This indicates that mechanisms such as ``elevator'' and ``promotion,'' which can dynamically excite deeper-band electrons, are active, enabling a localized free electron gas to emulate ion energy loss, as pointed out by [Lim \textit{et al.}, Phys. Rev. Lett. {\bf 116}, 043201 (2016)]. The observation and the description of a velocity-proportionality breakdown in electronic stopping cross-sections at very low velocities are considered to be a signature of the deeper-band electrons' contributions.

The ability to detect when a system undergoes an incipient fault is of paramount importance in preventing a critical failure. In this work, we propose an information-driven fault detection method based on a novel concept drift detector. The method is tailored to identifying drifts in input-output relationships of additive noise models (i.e., model drifts) and is based on a distribution-free mutual information (MI) estimator. Our scheme does not require prior faulty examples and can be applied distribution-free over a large class of system models. Our core contributions are twofold. First, we demonstrate the connection between fault detection, model drift detection, and testing independence between two random variables. Second, we prove several theoretical properties of the proposed MI-based fault detection scheme: (i) strong consistency, (ii) exponentially fast detection of the non-faulty case, and (iii) control of both significance levels and power of the test. To conclude, we validate our theory with synthetic data and the benchmark dataset N-CMAPSS of aircraft turbofan engines. These empirical results support the usefulness of our methodology in many practical and realistic settings, and the theoretical results show performance guarantees that other methods cannot offer., Comment: 28 pages, 11 figures

In this work, we study timelike and lightlike geodesics in Kalb-Ramond (KR) gravity around a black hole with the goal of constraining the Lorentz symmetry-breaking parameter $l$. The analysis involves studying the precession of the S2 star periastron orbiting Sgr A* and geodesic precession around the Earth. The ratio of precession frequencies for General Relativity (GR) and KR gravity is computed, with Event Horizon Telescope (EHT) results providing a parameter range for the spontaneous symmetry-breaking of $-0.185022 \leq l \leq 0.060938$. Utilizing the geodesic precession frequency from the Gravity Probe B (GP-B), the $l$ parameter is further constrained to $-6.30714 \times 10^{-12} \leq l \leq 3.90708 \times 10^{-12}$, which is consistent with the Schwarzschild limits. Moreover, for timelike geodesics, the innermost circular orbit (ICO) and innermost stable circular orbit (ISCO) are determined and analyzed to illustrate the impact of the symmetry breaking term. Zoom-whirl obstructions are compared with the Schwarzschild solution. Lower and upper limits of the photon sphere for lightlike geodesics are established to demonstrate the influence of KR gravity on the photon sphere. Additionally, the shadow radius is determined for two observers, one situated at a finite distance from the KR black hole, and the other located at an infinite distance, to constrain the symmetry-breaking parameter $l$, with comparisons made to EHT results. The bounds for $l$ derived from constraints on the photon sphere radius for lightlike geodesics yield $-0.0700225 \leq l \leq 0.189785$ using EHT data. The findings of this paper align with experimental results in the $l \rightarrow 0$ limit., Comment: 11 pages, 4 figures

In this paper, we investigate the gravitational lensing effect for the Schwarzschild-like black hole spacetime in the background of a Kalb-Ramond (KR) field proposed in [K. Yang et. al., Phys. Rev. D 108 (2023) 124004]. The solution is characterized by a single extra parameter $l$, which is associated to the Lorentz symmetry breaking induced by the KR field. First, we calculate the exact deflection angle of massive and massless particles for finite distances using elliptic integrals. Then we study this effect in the weak and strong field regimes, discussing the correction of the KR parameter on the coefficients of the expansions in both limits. We also find that increasing $l$ decreases the deflection angle. Furthermore, we use the available data from the Sagittarius $A^{\star}$ object, which is believed to be a supermassive black hole at the center of our galaxy, to calculate relevant observables, such as, the image position, luminosity, and delay time. The values found could be potentially measured in the weak field regime, though for strong fields one would have to wait for the next generation of interferometers., Comment: 16 pages, 8 figures. V2: references added. arXiv admin note: text overlap with arXiv:2309.02658

The life course perspective in criminology has become prominent last years, offering valuable insights into various patterns of criminal offending and pathways. The study of criminal trajectories aims to understand the beginning, persistence and desistence in crime, providing intriguing explanations about these moments in life. Central to this analysis is the identification of patterns in the frequency of criminal victimization and recidivism, along with the factors that contribute to them. Specifically, this work introduces a new class of models that overcome limitations in traditional methods used to analyze criminal recidivism. These models are designed for recurrent events data characterized by excess of zeros and spatial correlation. They extend the Non-Homogeneous Poisson Process, incorporating spatial dependence in the model through random effects, enabling the analysis of associations among individuals within the same spatial stratum. To deal with the excess of zeros in the data, a zero-inflated Poisson mixed model was incorporated. In addition to parametric models following the Power Law process for baseline intensity functions, we propose flexible semi-parametric versions approximating the intensity function using Bernstein Polynomials. The Bayesian approach offers advantages such as incorporating external evidence and modeling specific correlations between random effects and observed data. The performance of these models was evaluated in a simulation study with various scenarios, and we applied them to analyze criminal recidivism data in the Metropolitan Region of Belo Horizonte, Brazil. The results provide a detailed analysis of high-risk areas for recurrent crimes and the behavior of recidivism rates over time. This research significantly enhances our understanding of criminal trajectories, paving the way for more effective strategies in combating criminal recidivism., Comment: 23 pages, 9 figuras and 5 tables

Research on aging processes of Gas Electron Multipliers (GEMs) is important to obtain insights on how to increase the detector's longevity, stability, and performance, as highlighted in the latest developments roadmap by the European Council of Future Accelerators (ECFA). One key aspect of the aging process is the deposit formation on the electrodes surfaces. In this work, through the analysis of the molecular content on the surface of a used GEM, we provide evidence for polyimide redeposition as a source of organic material contributing to the formation of insulating layers on the electrodes, which eventually lead to sparks and detector failure. Furthermore, we show that chromium, used to promote adhesion between copper and polyimide, in the device undergoes a diffusion process, effectively blurring the layered structure. We demonstrate the significance of surface-sensitive chemical analysis to investigate the surface deposits on electrodes of gaseous detectors and our results reveal the necessity of standardization and more stringent study protocols., Comment: 19 pages and 10 figures

How the human brain processes information during different cognitive tasks is one of the greatest questions in contemporary neuroscience. Understanding the statistical properties of brain signals during specific activities is one promising way to address this question. Here we analyze freely available data from implanted electrocorticography (ECoG) in five human subjects during two different cognitive tasks in the light of information theory quantifiers ideas. We employ a symbolic information approach to determine the probability distribution function associated with the time series from different cortical areas. Then we utilize these probabilities to calculate the associated Shannon entropy and a statistical complexity measure based on the disequilibrium between the actual time series and one with a uniform probability distribution function. We show that an Euclidian distance in the complexity-entropy plane and an asymmetry index for complexity are useful for comparing the two conditions. We show that our method can distinguish visual search epochs from blank screen intervals in different electrodes and patients. By using a multi-scale approach and embedding time delays to downsample the data, we find important time scales in which the relevant information is being processed. We also determine cortical regions and time intervals along the 2-second-long trials that present more pronounced differences between the two cognitive tasks. Finally, we show that the method is useful to distinguish cognitive processes using brain activity on a trial-by-trial basis.

Machine Learning and Deep Learning are computational tools that fall within the domain of artificial intelligence. In recent years, numerous research works have advanced the application of machine and deep learning in various fields, including optics and photonics. In this article, we employ machine learning algorithms to investigate the feasibility of predicting a stochastic phenomena: random laser emissions. Our results indicate that machine and deep learning have the capacity to accurately reproduce fluctuations characteristic of random lasers. By employing simple supervised learning algorithms, we demonstrate that the random laser intensity fluctuations can be predicted using spontaneous emission and pump intensity as input parameters in the models. Applications based on the demonstrated results are discussed. Keywords: Machine Learning, Deep Learning, Random Laser.

The total mean curvature functional for submanifolds into the Riemannian product space $\mathbb{S}^n\times\mathbb{R}$ is considered and its first variational formula is presented. Later on, two second order differential operators are defined and a nice integral inequality relating both of them is proved. Finally we prove our main result: an integral inequality for closed stationary $\mathcal{H}$-surfaces in $\mathbb{S}^n\times\mathbb{R}$, characterizing the cases where the equality is attained., Comment: 17 pages

The Weyl-Wigner formalism for evaluating the intrinsic information of Dirac bispinors as correlated qubits (localized) in a magnetic field is investigated in the extension to statistical ensembles. The confining external field quantizes the quantum correlation measures implied by the spin-parity qubit structure of the Dirac equation in 3+1 dimensions, which simplifies the computation of the entanglement quantifier for mixed states in relativistic Landau levels. This allows for the evaluation of quantum and classical correlations in terms of entropy measures for Dirac structures that are eventually mixed. Our results are twofold. First, a family of mixed Gaussian states is obtained in phase space, and its intrinsic correlation structure is computed in closed form. Second, the partition function for the low-dimensional Dirac equation in a magnetic field is derived through complex integration techniques. It describes the low-temperature regime in terms of analytically continued Zeta functions and the high temperature limit as a polynomial on the temperature variable. The connection with lower dimensional systems is further elicited by mapping the spin-parity qubits to valley-sublattice bispinors of the low-energy effective Hamiltonian of graphene., Comment: 48 pages, 6 figures

We have studied multi-Dirac/Weyl systems with arbitrary topological charge n in the presence of a lattice of local magnetic moments. To do so, we propose a multi-Dirac/Weyl Kondo lattice model which is analyzed through a mean-field approach appropriate to the paramagnetic phase. We study both the broken time-reversal and the broken inversion-symmetry Weyl cases. The multi- Dirac and broken-time reversal multi-Weyl cases have similar behavior, which is in contrast to the broken-parity case. For the former, low-energy particle-hole symmetry leads to the emergence of a critical coupling constant below which there is no Kondo quenching, reminiscent of the pseudogap Kondo impurity problem. Away from particle-hole symmetry, there is always Kondo quenching. For the broken inversion symmetry, there is no critical coupling. Depending on the conduction electron filling, Kondo insulator, heavy fermion metal or semimetal phases can be realized. In the last two cases, quasiparticle renormalizations can differ widely between opposite chirality sectors, with characteristic dependences on microscopic parameters that could in principle be detected experimentally., Comment: 15 pages, 12 figures

This comprehensive study delves into the intricate interplay between protons and organic polymers, offering insights into proton therapy in cancer treatment. Focusing on the influence of the spatial electron density distribution on stopping power estimates, we employed time-dependent density functional theory (TDDFT), coupled with the Penn method. Surprisingly, the assumption of electron density homogeneity in polymers is fundamentally flawed, resulting in an overestimation of stopping power values at energies below 2 MeV, approximately. Moreover, Bragg's rule application in specific compounds exhibited significant deviations from experimental data in the Bragg peak region, challenging established norms., Comment: 8 pages, 7 figures, research article

The geodesic method has played a crucial role in understanding the circular orbits generated by compact objects, culminating in the definition of the photon sphere, which was later generalized to a photon surface in arbitrary spacetimes. This new formulation extends the concept of the photon sphere in a broader sense, including dynamical spacetimes, as shown by the Vaidya solution. The photon surface essentially defines the null geodesics, which are originally tangent to the temporal surface, and keeps them confined to this surface. However, this formalism does not cover all classes of particles, and to overcome this limitation, a more comprehensive approach, denoted as the "massive particle surface", has been proposed that also accounts for charged massive particles. Indeed, the photon surface concept is recovered when the charge and mass of the particles are zero. In this work, we use these three formalisms to check the consistency of the results for the values of the radius of the photon sphere ($r_{ps}$) and the radius of the "innermost stable circular orbit" (ISCO) ($r_{\rm ISCO}$) for some gravitational models. In our results, the first model is described by conformal gravity, with the peculiarity that $g_{00}\neq-g_{11}^{-1}$. The second model, i.e. the Culetu solution, is developed by coupling General Relativity with nonlinear electrodynamics, which requires the consideration of the effective metric ($g_{\rm eff}^{\mu\nu}$) for geodesic approaches. Furthermore, we have also analysed the expressions for $r_{ps}$ and $r_{\rm ISCO}$ in a general static and spherically symmetric metric. Under these circumstances, we have found a discrepancy of $r_{ps}$ and $r_{\rm ISCO}$ obtained by the massive particle surface formalism as compared to the geodesic and photon surface formalisms., Comment: 15 pages, 1 figure; comments are welcome

Along the lines of the Einstein-Rosen wave equation of General Relativity (GR), we derive a gravitational wave equation with cylindrical symmetry in the Einstein-aether (EA) theory. We show that the gravitational wave in the EA is periodic in time for both the metric functions $\Psi(r,t)$ and $H(r,t)$. However, in GR, $\Psi(r,t)$ is periodic in time, but $H(r,t)$ is semi-periodic in time, having a secular drifting in the wave frequency. The evolution of wave pulses of a given width is entirely different in both theories in the $H(r,t)$ metric function due to this frequency drifting. Another fundamental difference between the two theories is the gravitational wave velocity. While in GR, the waves propagate with the speed of light, in EA, there is no upper limit to the wave velocity, reaching infinity if $c_{13} \rightarrow 1$ and zero if $c_{13} \rightarrow -\infty$. We also show that energy-momentum pseudotensor and superpotential get contributions from aether in addition to the usual gravitational field part. All these characteristics are observational signatures that differentiate GR and EA., Comment: 26 pages, 10 figures. We have corrected the initial conditions for $H(r,t)$ in order to have $\Psi(r,t)$ not equal to $H(r,t)$