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Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this reason, many alternative robust techniques have been studied in literature. In these terms, the Least Squares Quantile (LQS), and in particular the Least Squares Median, are among the regression estimators that exhibit better robustness properties. However, the accurate computation of this estimators is computationally demanding, resulting in a difficult estimator to obtain. In this paper, new novel approaches to compute a global optimal solution for the LQS estimator based on single-level and bilevel optimization methods are proposed. An extensive computational study is provided to support the efficiency of the methods considered, and an ad hoc procedure to address the scalability of the problem to larger instances is proposed.

We numerically investigate a crucial parameter for understanding particle acceleration theory via turbulence-induced magnetic reconnection: the particle acceleration time. We examine particles accelerated either during the jet's dynamic evolution or in a post-processing, nearly stationary regime. We derive the particle acceleration time and compare it with theoretical predictions for both the Fermi and drift regimes identified in the simulations. In the Fermi regime, the acceleration time is expected to be independent of the particles' energy, for constant reconnection velocity, as energy increases exponentially with time. Conversely, we expect the reconnection acceleration time to depend on the current sheet's thickness and the reconnection velocity, a dependence recently revisited by xu and lazarian 2023. They identified three conditions for \(t_{acc}\). We tested these relations using statistical distributions of the current sheets' thickness and reconnection velocities in the turbulent jet over time. The resulting average value of \(t_{acc}\) was found to be nearly constant with particle energy. We compared this acceleration time with the average acceleration time derived directly from 50,000 particles accelerated in situ in the same relativistic jet. When considering a longer time interval for particle acceleration in a nearly stationary snapshot of the turbulent jet, we find that the acceleration time during the Fermi regime remains nearly independent of particle energy and aligns with the acceleration time theoretical relations up to the threshold energy, attained when the particles Larmor radius becomes as large as the thickness of the largest current sheets. Beyond this threshold, the acceleration regime shifts to the slower drift regime, showing strong energy dependence, as predicted. The results also indicate a clear dominance of the Fermi regime of acceleration., Comment: Submitted to ApJ

The bright high-mass X-ray binary GX 301-2 exhibits two periodic flare episodes along its orbit which are produced when the neutron star is close to the apastron and periastron passages. Time-resolved spectra were extracted and several models applied to describe all of them. The best description was obtained with a blackbody continuum modified by the Fe K-shell absorption edge, absorbed by a large column density on the order of $10^{23}$ cm$^{-2}$ and, if present, a Fe K$\alpha$ fluorescent emission line. Three of the nine apastron flares were as bright as the pre-periastron flare and two of them coincided with spin-up episodes of the neutron star. This fact points to the presence of a transient disc around the neutron star as it passes through the apastron that increases the accretion process. The size of emitting region on the neutron star surface showed some variability but quite consistent with a hot spot., Comment: 36 pages, 77 figures, accepted for publication in RMxAA. It will appear in Vol. 61, N{\deg}1, April 2025

Cen X-3 is a compact, high-mass X-ray binary (HMXRB), likely powered by Roche lobe overflow. We present a phase-resolved X-ray spectral and timing analysis of a target of opportunity \textit{Chandra} observation made during a low-flux to high-flux transition. The high-resolution spectra allow us to delve into the events that occurred during this episode. The spectrum is described by a single black body absorbed by a local column density of the order of $10^{23-24}$ cm$^{-2}$, which is one to two orders of magnitude higher than found for previous analyses of data taken at similar orbital phases. Such a large column produces a Compton shoulder in the Fe K$\alpha$ line. The transition appears to be caused by the onset of efficient cooling, which cools the plasma by 10 million degrees in just 10 ks, allowing matter to enter the magnetosphere. This happens after a major disturbance, probably the arrival of a train of wind clumps with individual masses in the range $10^{19-20}$ g. This train moves ballistically in an eccentric orbit around the NS, producing a distinctive Doppler modulation in the \ion{Fe}{xxv} line.

Ultra-luminous X-ray sources (ULXs) are high-mass X-ray binaries with an X-ray luminosity above $10^{39}$ erg s$^{-1}$. These ULXs can be powered by black holes that are more massive than $20M_\odot$, accreting in a standard regime, or lighter compact objects accreting supercritically. There are only a few ULXs with known optical or UV counterparts, and their nature is debated. Determining whether optical/UV radiation is produced by the donor star or by the accretion disc is crucial for understanding ULX physics and testing massive binary evolution. We conduct, for the first time, a fully consistent multi-wavelength spectral analysis of a ULX and its circumstellar nebula. We aim to establish the donor star type and test the presence of strong disc winds in the prototypical ULX Holmberg II X-1 (Ho II X-1). We intent to obtain a realistic spectral energy distribution of the ionising source, which is needed for robust nebula analysis. We acquired new UV spectra of Ho II X-1 with the HST and complemented them with archival optical and X-ray data. We explored the spectral energy distribution of the source and analysed the spectra using the stellar atmosphere code PoWR and the photoionisation code Cloudy. Our analysis of the X-ray, UV, and optical spectra of Ho II X-1 and its nebula consistently explains the observations. We do not find traces of disc wind signatures in the UV and the optical, rejecting previous claims of the ULX being a supercritical accretor. The optical/UV counterpart of HoII X-1 is explained by a B-type supergiant donor star. Thus, the observations are fully compatible with Ho II X-1 being a close binary consisting of an $\gtrsim 66\,M_\odot$ black hole accreting matter from an $\simeq 22 M_\odot$ B-supergiant companion. Also, we propose a possible evolution scenario for the system, suggesting that Ho II X-1 is a potential gravitational wave source progenitor., Comment: Accepted in A&A. 14 pages (12 main body + 2 appendix), 6 figures, 6 tables

The topics of interest are location analysis and related problems. This includes location models, networks, transportation, logistics, exact and heuristic solution methods, and computational geometry, among many others., Comment: The proceedings book of the previous editions can be found at arXiv:2002.08287 arXiv:2002.08293 arXiv:2002.08300 arXiv:2002.01702 arXiv:2202.13878 . arXiv:2309.08337 . The XIII International Workshop on Locational Analysis and Related Problems will take place during September 4--6, 2024 in Granada (Spain). It is organized by the Spanish Location Network, REDLOCA, and the Location Group, GELOCA, from the Spanish Society of Statistics and Operations Research (SEIO). The Spanish Location Network is a group of 100+ researchers from several Spanish universities organized into 7 thematic groups. The Network has been funded by the Spanish Government since 2003

In this work, we determine the dissociation line of the nitrogen (N$_2$) hydrate by computer simulation using the TIP4P/Ice model for water and the TraPPE force field for N$_2$. We use the solubility method proposed recently by some of us to evaluate the dissociation temperature of the hydrate at different pressures, from 500 to 1500 bar. Particularly, we calculate the solubility of N$_2$ in the aqueous solution when it is in contact with a N$_2$-rich liquid phase and when in contact with the hydrate phase via planar interfaces as functions of temperature. Since the solubility of N$_2$ decreases with temperature in the first case and increases with temperature in the second case, both curves intersect at a certain temperature that determines the dissociation temperature at a given pressure. We find a good agreement between the predictions obtained in this work and the experimental data taken from the literature in the range of pressures considered in this work. From our knowledge of the solubility curves of N$_2$ in the aqueous solution, we also determine the driving force for nucleation of the hydrate, as a function of temperature, at different pressures. In particular, we use two different thermodynamic routes to evaluate the change in chemical potential for hydrate formation. Although the driving force for nucleation slightly decreases (in absolute value) when the pressure is increased, our results indicate that the effect of pressure can be considered negligible in the range of pressures studied in this work. To the best of our knowledge, this is the first time the driving force for nucleation of a hydrate that exhibits crystallographic structure sII, along its dissociation line, is studied from computer simulation., Comment: 15 pages, 9 figures. arXiv admin note: text overlap with arXiv:2408.03257

In this work, the tetrahydrofuran (THF) hydrate-water interfacial free energy is determined at $500\,\text{bar}$, at one point of the univariant two-phase coexistence line of the THF hydrate, by molecular dynamics simulation. The Mold Integration-Host methodology, an extension of the original Mold Integration technique to deal with hydrate-fluid interfaces, is used to calculate the interfacial energy. Water is described using the well-known TIP4P/Ice model and THF is described using a rigid version of the TraPPE model. We have recently used the combination of these two models to accurately describe the univariant two-phase dissociation line of the THF hydrate, in a wide range of pressures, from computer simulation [J. Chem. Phys. 160, 164718 (2024)]. The THF hydrate-water interfacial free energy predicted in this work is compared with the only experimental data available in the literature. The value obtained, $27(2)\,\text{mJ/m}^{2}$, is in excellent agreement with the experimental data taken from the literature, $24(8)\,\text{mJ/m}^{2}$. To the best of our knowledge, this is the first time that the THF hydrate-water interfacial free energy is predicted from computer simulation. This work confirms that the Mold Integration technique can be used with confidence to predict solid-fluid interfaces of complex structures, including hydrates that exhibit sI and sII crystallographic structures., Comment: 11 pages, 6 figures

In this work, we determine the dissociation line of the nitrogen (N$_{2}$) hydrate by computer simulation using the TIP4P/Ice model for water and the TraPPE force field for N$_{2}$. This work is the natural extension of our previous paper in which the dissociation temperature of the N$_2$ hydrate has been obtained at $500$, $1000$, and $1500\,\text{bar}$ [\emph{J. Chem. Phys.} \textbf{159}, 224707 (2023)] using the solubility method and assuming single occupancy. We extend our previous study and determine the dissociation temperature of the N$_2$ hydrate at different pressures, from $500$ to $4500\,\text{bar}$, taking into account single and double occupancy of the N$_{2}$ molecules in the hydrate structure. We calculate the solubility of N$_2$ in the aqueous solution, as a function of temperature, when it is in contact with a N$_{2}$-rich liquid phase and when in contact with the hydrate phase with single and double occupancy via planar interfaces. Both curves intersect at a certain temperature that determines the dissociation temperature at a given pressure. We observe a negligible effect of the occupancy on the dissociation temperature. Our findings are in very good agreement with the experimental data taken from the literature. We have also obtained the driving force for nucleation of the hydrate as a function of the temperature and occupancy at several pressures. As in the case of the dissociation line, the effect of the occupancy on the driving force for nucleation is negligible. To the best of our knowledge, this is the first time that the effect of the occupancy on the driving force for nucleation of a hydrate that exhibits sII crystallographic structure is studied from computer simulation., Comment: 15 pages, 13 figures

[Abridged] The relation between nuclear star clusters (NSCs) and the growth of the central SMBHs, as well as their connection to the properties of the host galaxies, is crucial for understanding the evolution of galaxies. Recent observations have revealed that about 10 per cent of nucleated galaxies host hybrid nuclei, consisting of both NSCs and accreting SMBHs that power active galactic nuclei (AGN). Motivated by the potential of the recently published multi-wavelength data sets from LeMMINGs survey, here we present the most thorough investigation to date of the incidence of hybrid nuclei in a large sample of 100 nearby nucleated galaxies (10 E, 25 S0, 63 S, and 2 Irr), covering a wide range in stellar mass ($M_{*,\rm gal} \sim 10^{8.7}-10^{12}~\rm M_{sun}$). We identify the nuclei and derive their properties by performing detailed 1D and 2D multi-component decompositions of the optical and near-infrared $HST$ stellar light distributions of the galaxies using S\'ersic and core-S\'ersic models. Our AGN diagnostics are based on homogeneously derived nuclear 1.5 GHz $e$-MERLIN radio, $Chandra$ X-ray (0.3--10 keV) and optical emission-line data. We determine the nucleation fraction ($f_{\rm nuc} $) as the relative incidence of nuclei across the LeMMINGs $HST$ sample and find $f_{\rm nuc} =~ $100/149 (= 67 $\pm$ 7 per cent), confirming previous work, with a peak value of 49/56~(= $88 \pm 13$ per cent) at bulge masses $M_{*,\rm bulge} \sim 10^{9.4}$- $10^{10.8}~\rm M_{sun}$. We identify 30 nucleated LeMMINGs galaxies that are optically active, radio-detected and X-ray luminous ($L_{X} > 10^{39}$ erg s$^{-1}$). This indicates that our nucleated sample has a lower limit $\sim$ 30 per cent occupancy of hybrid nuclei, which is a function of $M_{*,\rm bulge}$ and $M_{*,\rm gal}$. We find that hybrid nuclei have a number density of $(1.5 \pm 0.4) \times 10^{-5}$ Mpc$^{-3}$., Comment: Accepted for publication in MNRAS (21 pages, 10 figures, 9 tables)

Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent reports suggest that certain types of damage can be modeled as a diffusion process and that the accumulation effects of this process must be kept low in order to reduce damage. We therefore develop an explicit mathematical formulation of spatiotemporal diffusion processes in STEM that take into account both instrument and sample parameters. Furthermore, our framework can aid the design of Diffusion Controlled Sampling (DCS) strategies using optimally selected probe positions in STEM, that constrain the cumulative diffusion distribution. Numerical simulations highlight the variability of the cumulative diffusion distribution for different experimental STEM configurations. These analytical and numerical frameworks can subsequently be used for careful design of 2- and 4-dimensional STEM experiments where beam damage is minimised., Comment: Main document: 29 pages, 12 figures; Supplementary document: 18 pages, 5 figures

In this work, the univariant two-phase coexistence line of the hydrate of tetrahydrofuran (THF) is determined from 100 to 1000 bar by molecular dynamics simulations. The study is carried out by putting in contact a THF hydrate phase with a stoichiometric aqueous solution phase. Following the direct coexistence technique, the pressure has been fixed, and the coexistence line has been determined by analyzing if the hydrate phase grows or melts at different values of temperature. The model of water used is the well-known TIP4P/Ice model. We have used two different models of THF based on the transferable parameters for phase equilibria-united atom approach (TraPPE-UA), the original (flexible) TraPPe-UA model as well as a rigid and planar version of it. Overall, at high pressures, small differences have been observed in the results obtained by both models. Also, large differences have been observed in the computational efforts required by the simulations performed using both models, being the rigid and planar version much faster than the original one. The effect of the unlike dispersive interactions between the water and THF molecules has been also analyzed at 250 bar using the rigid and planar THF model. In particular, we have modified the Berthelot combining rule by adding a factor ({\xi}O-THF) that modifies the unlike water-THF dispersive interactions and we have analyzed the effect on the dissociation temperature when {\xi}O-THF is modified from 1.0 (original Berthelot combining rule) to 1.4 (modified Berthelot combining rule). We have extended the study using {\xi}O-THF = 1.4 and the rigid THF model to the rest of the pressures considered in this work, finding an excellent agreement with the scarce experimental data taken from the literature., Comment: 10 pages, 5 figures

High-resolution X-ray spectra of $\pi\,$Aqr, a $\gamma\,$Cas-type star, obtained with the Chandra/HETG grating spectrometer, revealed emission lines of H-like ions of Mg, Si, S, and Fe, a strong, hard continuum, and a lack of He-like ions, indicating the presence of very hot thermal plasma. The X-ray light curve showed significant fluctuations, with coherent variability at period of about 3400 seconds in one observation. The hardness ratio was relatively constant except for one observation in which the spectrum was much harder and more absorbed. We interpret the X-ray emission as arising from accretion onto the secondary, which is likely a magnetic white dwarf, an intermediate polar system., Comment: 7 pages, 3 figures, 3 tables

The International Workshop on Locational Analysis and Related Problems will take place during September 7-8, 2023 in Edinburgh (United Kingdom). It is organized by the Spanish Location Network and the Location Group GELOCA from the Spanish Society of Statistics and Operations Research (SEIO). The Spanish Location Network is a group of more than 140 researchers from several Spanish universities organized into 7 thematic groups. The Network has been funded by the Spanish Government since 2003. The current project is RED2022-134149-T. One of the main activities of the Network is a yearly meeting aimed at promoting the communication among its members and between them and other researchers, and to contribute to the development of the location field and related problems. As a proof of the internationalization of this research group, this will be the first time that the meeting is held out of Spain. The topics of interest are location analysis and related problems. This includes location models, networks, transportation, logistics, exact and heuristic solution methods, and computational geometry, among others., Comment: The proceedings book of the previous editions can be found at arXiv:2002.08287 arXiv:2002.08293 arXiv:2002.08300 arXiv:2002.01702 arXiv:2202.13878

Several MHD works and, in particular, the recent one by Medina-Torrejon et al. (2021) based on three-dimensional MHD simulations of relativistic jets, have evidenced that particle acceleration by magnetic reconnection driven by the turbulence in the flow occurs from the resistive up to the large injection scale of the turbulence. Particles experience Fermi-type acceleration up to ultra-high-energies, predominantly of the parallel velocity component to the local magnetic field, in the reconnection layers in all scales due to the ideal electric fields of the background fluctuations ($V\times B$, where $V$ and $B$ are the velocity and magnetic field of the fluctuations, respectively). In this work, we show MHD-particle-in-cell (MHD-PIC) simulations following the early stages of the particle acceleration in the relativistic jet which confirm these previous results, demonstrating the strong potential of magnetic reconnection driven by turbulence to accelerate relativistic particles to extreme energies in magnetically dominated flows. Our results also show that the dynamical time variations of the background magnetic fields do not influence the acceleration of the particles in this process., Comment: Accepted for publication in ApJ

The Athena X-ray Integral Unit (X-IFU) is the high resolution X-ray spectrometer, studied since 2015 for flying in the mid-30s on the Athena space X-ray Observatory, a versatile observatory designed to address the Hot and Energetic Universe science theme, selected in November 2013 by the Survey Science Committee. Based on a large format array of Transition Edge Sensors (TES), it aims to provide spatially resolved X-ray spectroscopy, with a spectral resolution of 2.5 eV (up to 7 keV) over an hexagonal field of view of 5 arc minutes (equivalent diameter). The X-IFU entered its System Requirement Review (SRR) in June 2022, at about the same time when ESA called for an overall X-IFU redesign (including the X-IFU cryostat and the cooling chain), due to an unanticipated cost overrun of Athena. In this paper, after illustrating the breakthrough capabilities of the X-IFU, we describe the instrument as presented at its SRR, browsing through all the subsystems and associated requirements. We then show the instrument budgets, with a particular emphasis on the anticipated budgets of some of its key performance parameters. Finally we briefly discuss on the ongoing key technology demonstration activities, the calibration and the activities foreseen in the X-IFU Instrument Science Center, and touch on communication and outreach activities, the consortium organisation, and finally on the life cycle assessment of X-IFU aiming at minimising the environmental footprint, associated with the development of the instrument. Thanks to the studies conducted so far on X-IFU, it is expected that along the design-to-cost exercise requested by ESA, the X-IFU will maintain flagship capabilities in spatially resolved high resolution X-ray spectroscopy, enabling most of the original X-IFU related scientific objectives of the Athena mission to be retained. (abridged)., Comment: 48 pages, 29 figures, Accepted for publication in Experimental Astronomy with minor editing

M33 X-7 is the only known eclipsing black hole high mass X-ray binary. The system is reported to contain a very massive O supergiant donor and a massive black hole in a short orbit. The high X-ray luminosity and its location in the metal-poor galaxy M33 make it a unique laboratory for studying the winds of metal-poor donor stars with black hole companions and it helps us to understand the potential progenitors of black hole mergers. Using phase-resolved simultaneous HST- and XMM-Newton-observations, we traced the interaction of the stellar wind with the black hole. Our comprehensive spectroscopic investigation of the donor star (X-ray+UV+optical) yields new stellar and wind parameters for the system that differs significantly from previous estimates. In particular, the masses of the components are considerably reduced to 38 for the O-star donor and 11.4 for the black hole. The O giant is overfilling its Roche lobe and shows surface He enrichment. The donor shows a densely clumped wind with a mass-loss rate that matches theoretical predictions. We investigated the wind-driving contributions from different ions and the changes in the ionization structure due to X-ray illumination. Toward the black hole, the wind is strongly quenched due to strong X-ray illumination. For this system, the standard wind-fed accretion scenario alone cannot explain the observed X-ray luminosity, pointing toward an additional mass overflow, which is in line with our acceleration calculations. The X-ray photoionization creates an He II emission region emitting $10^{47}$ ph/s. We computed binary evolutionary tracks for the system using MESA. Currently, the system is transitioning toward an unstable mass transfer phase, resulting in a common envelope of the black hole and donor. Since the mass ratio is q~3.3 and the period is short, the system is unlikely to survive the common envelope, but will rather merge., Comment: Accepted for publication in Astronomy & Astrophysics

The aim of this work is to study both light curve and orbital phase spectroscopy of this source taking advantage of the MAXI/GSC observation strategy. We have investigated the spectral and light curve properties of the X-ray emission from Cen X-3 along the binary orbit. These studies allow delimiting the stellar wind properties and its interactions with the compact object. A timing analysis of light curves in different energy bands was carried out. From the analysis of the light curve, we have estimated the orbital period of the binary system and also found possible QPOs around a superorbital period of $P_\mathrm{superorb} = 220\pm 5$ days. Both orbital phase-averaged and phase-resolved spectra were extracted and analysed in the 2.0-20.0 keV energy range. We have defined and compared the high and low states spectra with the averaged spectrum. Two models have described spectra satisfactorily, a partial absorbed Comptonization of cool photons on hot electrons plus a power law and a partial absorbed blackbody plus a power law, both modified by adding Gaussian lines. The radius of the blackbody emitting area has been determined and the high value of the X-ray luminosity in the averaged spectrum indicates that the accretion mode is not only due to the stellar wind., Comment: 41 pages (draft version), 21 figures. Accepted for publication in Revista Mexicana de Astronom\'ia y Astrof\'isica (RMxAA). This paper will appear in Vol. 58, No 2, October 2022

In this paper, we propose the Ordered Median Tree Location Problem (OMT). The OMT is a single-allocation facility location problem where p facilities must be placed on a network connected by a non-directed tree. The objective is to minimize the sum of the ordered weighted averaged allocation costs plus the sum of the costs of connecting the facilities in the tree. We present different MILP formulations for the OMT based on properties of the minimum spanning tree problem and the ordered median optimization. Given that ordered median hub location problems are rather difficult to solve we have improved the OMT solution performance by introducing covering variables in a valid reformulation plus developing two pre-processing phases to reduce the size of this formulations. In addition, we propose a Benders decomposition algorithm to approach the OMT. We establish an empirical comparison between these new formulations and we also provide enhancements that together with a proper formulation allow to solve medium size instances on general random graphs., Comment: 112 pages, 4 figures, extended version of 'The Ordered Median Location Problem'

Relativistic jets are believed to be born magnetically dominated. Very and ultra-high energy cosmic rays can be efficiently accelerated by magnetic reconnection in these sources. We here demonstrate this directly, with no extrapolations to large scales, by means of three-dimensional relativistic magnetohydrodynamical (3D-RMHD) simulations of a Poyinting flux dominated jet. We inject thousands of low-energy protons in the region of a relativistic jet that corresponds to the transition from magnetically to kinetically dominated, where its magnetization parameter is $\sigma \sim 1$. In this region, there is efficient fast magnetic reconnection which is naturally driven by current-driven-kink instability (CDKI) turbulence in the helical magnetic fields of the jet. We find that the particles are accelerated by Fermi process in the reconnection regions (and by drift in the final stages) up to energies $E \sim 10^{18}$ eV for background magnetic fields $B \sim 0.1$ G, and $E \sim 10^{20}$ eV for $B \sim 10$ G. We have also derived from the simulations the acceleration rate due to magnetic reconnection which has a weak dependence on the particles energy $ r_{acc} \propto E^{-0.1}$, characteristic of exponential growth. The energy spectrum of the accelerated particles develops a power-law tail with spectral index $p \sim -1.2$. This hardness of the spectrum must decrease when particle losses and feedback into the background plasma are included. Our results can explain observed flux variability in the emission of blazars at the very high energy band as well as the associated neutrino emission. Successful applications of our results to the blazars MRK 421 and TXS 0506+056 are also discussed., Comment: Paper submitted to the Proceedings of 37th International Cosmic Ray Conference (ICRC2021), July 12th - 23rd, 2021. Online - Berlin, Germany

We present the first {\it XMM-Newton} observation of the classical supergiant high-mass X-ray binary XTE J1855$-$026 taken entirely during the eclipse of the neutron star (NS), covering the orbital phases $\phi= 0.00-0.11$. The analysis of the data allows us to a) compare with the parameters obtained during the existing pre eclipse observation and b) explore the back illuminated stellar wind of the B0I type donor. The black body component, used to describe the soft excess during pre eclipse, is not observed during eclipse. It must be then produced near the NS or along the donor-NS line. The $0.3-10$ keV luminosity during eclipse ($\sim 10^{34}$ erg s$^{-1}$) is 70 times lower than pre eclipse. The intensity of the Fe K$\alpha$ line, in the average eclipse spectrum, is $\sim 7.4$ times lower than the one measured during pre eclipse. Since K$\alpha$ photons can not be resonantly scattered in the wind, the vast majority of Fe K$\alpha$ emission must come from distances within $1R_{*}$ from the NS. The eclipse spectrum is successfully modelled through the addition of two photoionized plasmas, one with low ionization ($\log\xi_{\rm 1,cold}=0.36$) and high emission measure ($EM_{\rm 1,cold}\approx 3\times 10^{59}$ cm$^{-3}$) and another with high ionization ($\log\xi_{\rm 2,hot}=3.7$) and low emission measure ($EM_{\rm hot}\approx 2\times 10^{56}$ cm$^{-3}$). Assuming that the cold and hot gas phases are the clumps and the interclump medium of the stellar wind, respectively, and a clump volume filling factor of $\approx [0.04-0.05]$, typical for massive stars, a density contrast between clumps and the interclump medium of $n_{\rm c}/n_{\rm i}\approx 180$ is deduced, in agreement with theoretical expectations and optical-UV observations of massive star winds.

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation of an experimental physical system. Here we show that a dynamical neural network, trained on a minimal amount of data, can predict the behavior of spintronic devices with high accuracy and an extremely efficient simulation time, compared to the micromagnetic simulations that are usually employed to model them. For this purpose, we re-frame the formalism of Neural Ordinary Differential Equations (ODEs) to the constraints of spintronics: few measured outputs, multiple inputs and internal parameters. We demonstrate with Spin-Neural ODEs an acceleration factor over 200 compared to micromagnetic simulations for a complex problem -- the simulation of a reservoir computer made of magnetic skyrmions (20 minutes compared to three days). In a second realization, we show that we can predict the noisy response of experimental spintronic nano-oscillators to varying inputs after training Spin-Neural ODEs on five milliseconds of their measured response to different excitations. Spin-Neural ODE is a disruptive tool for developing spintronic applications in complement to micromagnetic simulations, which are time-consuming and cannot fit experiments when noise or imperfections are present. Spin-Neural ODE can also be generalized to other electronic devices involving dynamics., Comment: 16 pages, 4 figures