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Mukkamala and Pere\~niguez recently discovered a new master function for even-parity metric perturbations of the Schwarzschild spacetime. Remarkably, this function satisfies the Regge-Wheeler equation (instead of the Zerilli equation), which was previously understood to govern the odd-parity sector of the perturbation only. In this paper I follow up on their work. First, I identify a source term for their Regge-Wheeler equation, constructed from the perturbing energy-momentum tensor. Second, I relate the new master function to the radiation fields at future null infinity and the event horizon. Third, I reconstruct the metric perturbation from the new master function, in the Regge-Wheeler gauge. The main conclusion of this work is that the greater simplicity of the Regge-Wheeler equation (relative to the Zerilli equation) is offset by a greater complexity of obtaining the radiation fields and reconstructing the metric., Comment: 6 pages, no figure

We study the Rellich type theorem (RT) for the Maxwell operator $\hat H^D=\hat D\hat H_0$ on ${\bf Z}^3$ with constant anisotropic medium, i.e. the permittivity and permeability of which are non-scalar constant diagonal matrices. We also study the unique continuation theorem for the perturbed Maxwell operator $\hat H^{D_p}=\hat {D}_p\hat H_0$ on ${\bf Z}^3$ where the permittivity and permeability are locally perturbed from a constant matrix on a compact set in ${\bf Z}^3$. It then implies that, if $\hat H^D- \lambda$ satisfies (RT), then all distributions $\hat u$ in Besov space $\mathcal B_0^{\ast}({\bf Z}^3;{\bf C}^3)$ satisfying the equation $(\hat H^{D_p} - \lambda) \hat u = 0$ outside a compact set vanish near infinity.

We define and calculate the mass multipole moments of a material body of mass $M$ and electric charge $Q$ tidally deformed by a particle of mass $m \ll M$ and charge $q \ll Q$ placed at a distance $r_0$ from the body. Given $Q/M$ and $r_0$, we choose $q/m$ so that the gravitational attraction between body and particle is balanced by the electrostatic repulsion; the system can then be maintained in a static state. The multipole moments are defined in a setting in which the body's self-gravity is allowed to be strong, but the mutual gravity between body and companion is required to be weak. In this setting, the body is described in full general relativity, in terms of a perturbed metric and electromagnetic potential characterized by tidal constants, and the mutual gravity is described within the post-Newtonian approximation to general relativity, in terms of objects with a multipole structure. Matching the different descriptions of the same field delivers a relation between the tidal constants and the multipole moments. In our implementation of this program, the calculation is performed in full Einstein-Maxwell theory (as a linearized perturbation of the unperturbed field), without appeal to a post-Newtonian approximation. After the fact we take $M/r_0$ to be small and carry out an expansion of the metric in powers of $M/r$ to obtain the multipole moments and associated Love numbers. The calculations are performed for a body made up of a perfect fluid with a uniform ratio of charge to mass densities, governed by a polytropic equation of state. We show that the Love numbers of a charged body in a situation of balanced gravitational and electrostatic forces are negative. The statement remains true even when $Q/M$ is very small, and we conclude that the tidal deformability of a charged body is radically different from that of an uncharged object, for which the Love numbers are positive., Comment: 47 pages, 15 figures. A long and technical paper, but the introductory section summarizes the essential points

In recent years, machine learning-based anomaly detection (AD) has become an important measure against security threats from Internet of Things (IoT) networks. Machine learning (ML) models for network traffic AD require datasets to be trained, evaluated and compared. Due to the necessity of realistic and up-to-date representation of IoT security threats, new datasets need to be constantly generated to train relevant AD models. Since most traffic generation setups are developed considering only the author's use, replication of traffic generation becomes an additional challenge to the creation and maintenance of useful datasets. In this work, we propose GothX, a flexible traffic generator to create both legitimate and malicious traffic for IoT datasets. As a fork of Gotham Testbed, GothX is developed with five requirements: 1)easy configuration of network topology, 2) customization of traffic parameters, 3) automatic execution of legitimate and attack scenarios, 4) IoT network heterogeneity (the current iteration supports MQTT, Kafka and SINETStream services), and 5) automatic labeling of generated datasets. GothX is validated by two use cases: a) re-generation and enrichment of traffic from the IoT dataset MQTTset,and b) automatic execution of a new realistic scenario including the exploitation of a CVE specific to the Kafka-MQTT network topology and leading to a DDoS attack. We also contribute with two datasets containing mixed traffic, one made from the enriched MQTTset traffic and another from the attack scenario. We evaluated the scalability of GothX (450 IoT sensors in a single machine), the replication of the use cases and the validity of the generated datasets, confirming the ability of GothX to improve the current state-of-the-art of network traffic generation.

This is the third and final entry in a sequence of papers devoted to the formulation of a theory of self-gravitating anisotropic fluids in Newtonian gravity and general relativity. In this third paper we elevate the Newtonian theory of the second paper to general relativity, and apply it to the construction of relativistic stellar models. The relativistic theory is crafted by promoting the fluid variables to a curved spacetime, and promoting the gravitational potential to the spacetime metric. The Newtonian action is then generalized in a direct and natural way, and dynamical equations for all the relevant variables are once more obtained through a variational principle. We specialize our relativistic theory of a self-gravitating anisotropic fluid to static and spherically symmetric configurations, and thus obtain models of anisotropic stars in general relativity. As in the Newtonian setting, the models feature a transition from an anisotropic phase at high density to an isotropic phase at low density. Our survey of stellar models reveals that for the same equations of state and the same central density, anisotropic stars are always less compact than isotropic stars., Comment: 21 pages, 7 figures

This paper is the second in a sequence of three devoted to the formulation of a theory of self-gravitating anisotropic fluids in both Newtonian gravity and general relativity. In this second paper we develop the Newtonian theory, inspired by a real-life example of an anisotropic fluid, the (nematic) liquid crystal. We apply the theory to the construction of static and spherical stellar models. In addition to the usual fluid variables (mass density, velocity field), the Newtonian theory features a director vector field, whose length provides a local measure of the size of the anisotropy, and whose direction gives the local direction of anisotropy. The theory is defined in terms of a Lagrangian which implicates all the relevant forms of energy: kinetic energy (with contributions from the velocity field and the time derivative of the director vector), internal energy (with isotropic and anisotropic contributions), gravitational interaction energy, and gravitational-field energy. This Lagrangian is easy to motivate, and it provides an excellent starting point for a relativistic generalization in the third paper. The equations of motion for the fluid, and Poisson's equation for the gravitational potential, follow from a variation of the action functional, given by the time integral of the Lagrangian. Because our stellar models feature a transition from an anisotropic phase at high density to an isotropic phase at low density, a substantial part of the paper is devoted to the development of a mechanics for the interface fluid, which mediates the phase transition., Comment: 40 pages, 7 figures

This paper is the first in a sequence of three devoted to the formulation of a theory of self-gravitating anisotropic fluids in both Newtonian and relativistic gravity. In this first paper we set the stage, place our work in the context of a vast literature on anisotropic stars in general relativity, and provide an overview of the results obtained in the remaining two papers. In both cases, Newtonian and relativistic, the state of the fluid is described by the familiar variables of an isotropic fluid (such as mass density and velocity field), to which we adjoin a director vector, which defines a locally preferred direction within the fluid. Both the Newtonian and relativistic theories are defined in terms of an action functional. While each theory is formulated in complete generality, in these papers we apply them to the construction of stellar models by restricting the fluid configurations to be static and spherically symmetric. We find that the equations of anisotropic stellar structure are generically singular at the stellar surface. To avoid a singularity, we postulate the existence of a phase transition at a critical value of the mass density; the fluid is anisotropic at high densities, and goes to an isotropic phase at low densities. In the case of Newtonian stars, we find that sequences of equilibrium configurations terminate at a maximum value of the central density; beyond this maximum the density profile becomes multi-valued within the star, and the model therefore becomes unphysical. In the case of relativistic stars, this phenomenon typically occurs beyond the point at which the stellar mass achieves a maximum. Also in the case of relativistic stars, we find that for a given equation of state and a given assignment of central density, anisotropic stellar models are always less compact than isotropic models., Comment: 13 pages, 5 figures

Active regions (ARs) appear in the solar atmosphere as a consequence of the emergence of magnetic flux-ropes (FR). In this study, we use Bayesian methods to analyze line-of-sight magnetograms of emerging ARs. We employ a FR model consisting of a half-torus field structure based on eight parameters. The goal is to derive constrained physical parameters of the originating FR which are consistent with the observations. Specifically, we aim to obtain a precise estimation of the AR tilt angle and magnetic twist at different stages of the emergence process. To achieve this, we propose four temporal methods that correlate the field parameter evolutions with a single coherent FR. These methods differ from each other in the size of the explored parameter space. We test the methods on four bipolar ARs observed with the Michelson Doppler Imager on board the Solar and Heliospheric Observatory. We find that tilt angles are typically consistent between the temporal methods, improving previous estimations at all stages of the emergence. The twist sign derived from the temporal methods is consistent with previous estimations. The standard errors of all the methods used are similar, indicating that they model the observations equally well. These results indicate that the proposed methods can be used to obtain global magnetic parameters of ARs during their early evolution. The derived parameters contribute to a better understanding of the formation of FRs, and the role of ARs in the magnetic recycling process along the solar cycle.

We analyze the magnetic evolution of solar active region (AR) NOAA 11476 that, between 9 and 10 May 2012, produced a series of surge-type eruptions accompanied by GOES X-ray class M flares. Using force-free models of the AR coronal structure and observations in several wavelengths, in previous works we studied the detailed evolution of those eruptions, relating them to the characteristic magnetic topology of the AR and reconstructing the involved reconnection scheme. We found that the eruptions were due to the ejection of minifilaments, which were recurrently ejected and reformed at the polarity inversion line of a bipole that emerged in the middle of the positive main AR magnetic polarity. The bipole was observed to rotate for several tens of hours before the events. In this article we analyze, for the full AR and the rotating bipole, the evolution of a series of magnetic parameters computed using the Helioseismic and Magnetic Imager (HMI) vector magnetograms. We combine this analysis with estimations of the injection of magnetic energy and helicity obtained using the Differential Affine Velocity Estimator for Vector Magnetograms (DAVE4VM) method that determines, from vector magnetograms, the affine velocity field constrained by the induction equation. From our results, we conclude that the bipole rotation was the main driver that provided the magnetic energy and helicity involved in the minifilament destabilizations and ejections. The results also suggest that the observed rotation is probably due to the emergence of a kinked magnetic flux rope with negative writhe helicity., Comment: Accepted for publication in Solar Physics

Active regions (ARs) appear in the solar atmosphere as a consequence of the emergence of magnetic flux ropes (FRs). Due to the presence of twist, the photospheric line-of-sight (LOS) magnetograms of emerging ARs show an elongation of the polarities known as magnetic tongues. These tongues can affect the estimation of tilt angles during their emergence phase. In this work, we propose a Bayesian method to model LOS magnetograms of emerging ARs using a half-torus twisted FR model. We apply this model to 21 emerging ARs observed during Solar Cycle 23. We find that the Bayesian method corrects the tilt when compared to other methods, removing the spurious rotation of the polarities produced by the retraction of the tongues during the emergence. We find a variation in Joy's law with the stage of the AR emergence and the method used for its estimation.

In cybersecurity, CVEs (Common Vulnerabilities and Exposures) are publicly disclosed hardware or software vulnerabilities. These vulnerabilities are documented and listed in the NVD database maintained by the NIST. Knowledge of the CVEs impacting an information system provides a measure of its level of security. This article points out that these vulnerabilities should be described in greater detail to understand how they could be chained together in a complete attack scenario. This article presents the first proposal for the CAPG format, which is a method for representing a CVE vulnerability, a corresponding exploit, and associated attack positions.

A neutron star in an inspiraling binary system is tidally deformed by its companion, and the effect leaves a measurable imprint on the emitted gravitational waves. While the tidal interaction falls within the regime of static tides during the early stages of inspiral, a regime of dynamical tides takes over in the later stages. The description of dynamical tides found in the literature makes integral use of a spectral representation of the tidal deformation, in which it is expressed as a sum over the star's normal modes of vibration. This description is deeply rooted in Newtonian fluid mechanics and gravitation, and we point out that considerable obstacles manifest themselves in an extension to general relativity. To remedy this we propose an alternative, mode-less description of dynamical tides that can be formulated in both Newtonian and relativistic mechanics. Our description is based on a time-derivative expansion of the tidal dynamics. The tidal deformation is characterized by two sets of Love numbers: the static Love numbers $k_\ell$ and the dynamic Love numbers $\ddot{k}_\ell$. These are computed here for polytropic stellar models in both Newtonian gravity and general relativity. The time-derivative expansion of the tidal dynamics seems to preclude any attempt to capture an approach to resonance, which occurs when the frequency of the tidal field becomes equal to a normal-mode frequency. To overcome this limitation we propose a pragmatic extension of the time-derivative expansion which does capture an approach to resonance. We demonstrate that with this extension, our formulation of dynamical tides should be just as accurate as the $f$-mode truncation of the mode representation, in which the sum over modes is truncated to a single term involving the star's fundamental mode of vibration., Comment: 33 pages, 4 figures, 4 tables, matches published version

We are interested by the spectral analysis of the anisotropic discrete Maxwell operator $\hat H^D$ defined on the square lattice $\rm Z\!\!\! Z^3$. In aim to prove that the limiting absorption principle holds we construct a conjugate operator to the Fourier series of $\hat H^D$ at any not-zero real value. In addition we show that at some particular thresholds the conjugate operator is essentially self-adjoint.

The gravitational waves emitted by a perturbed black hole ringing down are well described by damped sinusoids, whose frequencies are those of quasinormal modes. Typically, first-order black hole perturbation theory is used to calculate these frequencies. Recently, it was shown that second-order effects are necessary in binary black hole merger simulations to model the gravitational-wave signal observed by a distant observer. Here, we show that the horizon of a newly formed black hole after the head-on collision of two black holes also shows evidence of non-linear modes. Specifically, we identify one quadratic mode for the $l=2$ shear data, and two quadratic ones for the $l=4,6$ data in simulations with varying mass ratio and boost parameter. The quadratic mode amplitudes display a quadratic relationship with the amplitudes of the linear modes that generate them., Comment: Version appeared in PRL. 14 pages, 15 figures

We investigate inflation driven by the Higgs boson in the Palatini formulation of General Relativity. Our analysis primarily focuses on a small non-minimal coupling of the Higgs field to gravity in the range $0<\xi\lesssim 1$. We incorporate the renormalization group running of the relevant parameters as computed within the Standard Model and allow for small corrections. In addition to $\xi$, our model features two tunable parameters: the low-energy value of the top Yukawa coupling and an effective jump of the Higgs self-interaction. Our results indicate that critical points leading to a large enhancement of the power spectrum can be produced. However, the observed amplitude of perturbations in the CMB cannot be matched within this setting. On the one hand, this makes it difficult to generate a sizable abundance of primordial black holes. On the other hand, our finding can be viewed as further evidence that Palatini Higgs inflation has favourable high-energy properties due to robustness against quantum corrections., Comment: 42 pages, 11 figures, 1 appendix

In the last few decades, reading the literature, we realized that we Astronomers have a strong preference to undertake very ambitious projects, and search for answers to the most fundamental questions in the history of the entire Universe. After running multiple times into such cardinal quest, the curiosity became no more sustainable and we had to find out. To our greater surprise, in the last few decades we had been restlessly participating to this superhuman endevour. Therefore we hereby explore the roots and grounds of this fundamental search, through the past decades, centuries and millennia., Comment: April fools!

When presented with a data stream of two statistically dependent variables, predicting the future of one of the variables (the target stream) can benefit from information about both its history and the history of the other variable (the source stream). For example, fluctuations in temperature at a weather station can be predicted using both temperatures and barometric readings. However, a challenge when modelling such data is that it is easy for a neural network to rely on the greatest joint correlations within the target stream, which may ignore a crucial but small information transfer from the source to the target stream. As well, there are often situations where the target stream may have previously been modelled independently and it would be useful to use that model to inform a new joint model. Here, we develop an information bottleneck approach for conditional learning on two dependent streams of data. Our method, which we call Transfer Entropy Bottleneck (TEB), allows one to learn a model that bottlenecks the directed information transferred from the source variable to the target variable, while quantifying this information transfer within the model. As such, TEB provides a useful new information bottleneck approach for modelling two statistically dependent streams of data in order to make predictions about one of them., Comment: 41 pages, 26 figures

Context. Active regions (ARs) appear in the solar atmosphere as a consequence of the emergence of magnetic flux tubes. The presence of elongated magnetic polarities in line-of-sight (LOS) magnetograms indicates the existence of twist in the flux tubes forming them. These polarity elongations, called magnetic tongues, bias the measurement of AR characteristics obtained during their emergence phase (e.g. their tilt angle and magnetic flux, among others). In particular, obtaining a good estimation of the tilt angle evolution plays a key role in constraining flux-transport dynamo models. Aims. In this work we aim to estimate the intrinsic properties of the twisted flux tubes, or flux ropes, that form ARs by quantitatively comparing observed LOS magnetograms with synthetic ones derived from a toroidal magnetic flux tube model. Methods. For this reason, we develop a Bayesian inference method to obtain the statistical distributions of the inferred model parameters. As an example, we apply the method to NOAA AR 10268. Next, we test the results using a synthetic-AR generator to quantify the effect of small scale perturbations over the inferred parameter distributions. Results. We conclude that this method can significantly remove the effects of magnetic tongues on the derived AR global characteristics, providing a better knowledge of the intrinsic properties of the emerging flux rope. Conclusions. These results provide a framework for future analysis of the physical properties of emerging ARs using Bayesian statistics.

We study a series of relations between physical parameters in coronal loops of the quiet Sun reconstructed by combining tomographic techniques and modeling of the coronal magnetic field. We use differential emission measure tomography (DEMT) to determine the three-dimensional distribution of the electron density and temperature in the corona, and we model the magnetic field with a potential-field source-surface (PFSS) extrapolation of a synoptic magnetogram. By tracing the DEMT products along the extrapolated magnetic field lines, we obtain loop-averaged electron density and temperature. Also, loop-integrated energy-related quantities are computed for each closed magnetic field line. We apply the procedure to Carrington rotation 2082, during the activity minimum between Solar Cycles 23 and 24. We find a scaling law between the loop-average density $N$ and loop length $L$, $N_m \sim L^{-0.35}$, but we do not find a significant relation between loop-average temperature and loop length. We confirm though the previously found result that loop-average temperatures at the equatorial latitudes are lower than at higher latitudes. We associate this behavior with the presence at the equatorial latitudes of loops with decreasing temperatures along their length (``down'' loops), which are in general colder than loops with increasing temperatures (``up'' loops). We find that the obtained scalings for quiet-Sun loops do not generally agree with those found in the case of AR loops from previous observational and theoretical studies. We suggest that to better understand the relations found, it is necessary to forward model the reconstructed loops using hydrodynamic codes working under the physical conditions of the quiet-Sun corona.