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The surface brightness -- colour relation (SBCR) is a basic tool in establishing precise and accurate distances within the Local Group. Detached eclipsing binary stars with accurately determined radii and trigonometric parallaxes allow for a calibration of the SBCRs with unprecedented accuracy. We analysed four nearby eclipsing binary stars containing late F-type main sequence components: AL Ari, AL Dor, FM Leo and BN Scl. We determined very precise spectroscopic orbits and combined them with high precision ground- and space-based photometry. We derived the astrophysical parameters of their components with mean errors of 0.1% for mass and 0.4% for radius. We combined those four systems with another 24 nearby eclipsing binaries with accurately known radii from the literature for which $Gaia$ EDR3 parallaxes are available, in order to derive the SBCRs. The resulting SBCRs cover stellar spectral types from B9 V to G7 V. For calibrations we used Johnson optical $B$ and $V$, $Gaia$ $G_{\rm BP}$ and $G$ and 2MASS $JHK$ bands. The most precise relations are calibrated using the infrared $K$ band and allow to predict angular diameters of A-, F-, and G-type dwarf and subgiant stars with a precision of 1%., Comment: Accepted for publication in Astronomy & Astrophysics, 17 pages

Satellites, are both crucial and, despite common misbelieve, very fragile parts our civilian and military critical infrastructure. While, many efforts are focused on securing ground and space segments, especially when national security or large businesses interests are affected, the small-sat, newspace revolution democratizes access to, and exploitation of the near earth orbits. This brings new players to the market, typically in the form of small to medium sized companies, offering new or more affordable services. Despite the necessity and inevitability of this process, it also opens potential new venues for targeted attacks against space-related infrastructure. Since sources of satellite ephemerides are very often centralized, they are subject to classical Man-in-the-Middle attacks which open venues for TLE spoofing attack, which may result in unnecessary collision avoidance maneuvers, in best case and orchestrated crashes, in worst case. In this work, we propose a countermeasure to the presented problem that include distributed solution, which will have no central authority responsible for storing and disseminating TLE information. Instead, each of the peers participating to the system, have full access to all of the records stored in the system, and distribute the data in a consensual manner,ensuring information replication at each peer node. This way, single point of failure syndromes of classic systems, which currently exist due to the direct ephemerids distribution mechanism, are removed. Our proposed solution is to build data dissemination systems using permissioned, private ledgers where peers have strong and verifiable identities, which allow also for redundancy in SST data sourcing.

In this work we study 35 stellar clusters in the Small Magellanic Cloud (SMC) in order to provide their mean metallicities and ages. We also provide mean metallicities of the fields surrounding the clusters. We used Str\"omgren photometry obtained with the 4.1 m SOAR telescope and take advantage of $(b - y)$ and $m1$ colors for which there is a metallicity calibration presented in the literature. The spatial metallicity and age distributions of clusters across the SMC are investigated using the results obtained by Str\"omgren photometry. We confirm earlier observations that younger, more metal-rich star clusters are concentrated in the central regions of the galaxy, while older, more metal-poor clusters are located farther from the SMC center. We construct the age-metallicity relation for the studied clusters and find good agreement with theoretical models of chemical enrichment, and with other literature age and metallicity values for those clusters. We also provide the mean metallicities for old and young populations of the field stars surrounding the clusters, and find the latter to be in good agreement with recent studies of the SMC Cepheid population. Finally, the Str\"omgren photometry obtained for this study is made publicly available., Comment: 22 pages, 12 figures, 6 tables, Published in A&A

Deep near-infrared $J$- and $K$-band photometry of three Local Group dwarf spheroidal galaxies: Fornax, Carina, and Sculptor, is made available for the community. Until now, these data have only been used by the Araucaria Project to determine distances using the tip of the red giant and RR Lyrae stars. Now, we present the entire data collection in a form of a database, consisting of accurate $J$- and $K$-band magnitudes, sky coordinates, ellipticity measurements, and timestamps of observations, complemented by stars' loci in their reference images. Depth of our photometry reaches about 22 mag at 5$\sigma$ level, and is comparable to NIR surveys, like the UKIRT Infrared Deep Sky Survey (UKIDSS) or the VISTA Hemisphere Survey (VHS). Small overlap with VHS and no overlap with UKIDSS makes our database a unique source of quality photometry., Comment: 15 pages, 7 figures, accepted to The Astrophysical Journal Supplement

In this article, we consider the radial Dunkl geometric case $k=1$ corresponding to flat Riemannian symmetric spaces in the complex case and we prove exact estimates for the positive valued Dunkl kernel and for the radial heat kernel. Dans cet article, nous consid\'erons le cas g\'eom\'etrique radial de Dunkl $ k = 1 $ correspondant aux espaces sym\'etriques riemanniens plats dans le cas complexe et nous prouvons des estimations exactes pour le noyau de Dunkl \`a valeur positive et pour le noyau de chaleur radial

In this article, we consider flat and curved Riemannian symmetric spaces in the complex case and we study their basic integral kernels, in potential and spherical analysis: heat, Newton, Poisson kernels and spherical functions, i.e. the kernel of the spherical Fourier transform. We introduce and exploit a simple new method of construction of these $W$-invariant kernels by alternating sum formulas. We then use the alternating sum representation of these kernels to obtain their asymptotic behavior. We apply our results to the Dyson Brownian Motion on $R^d$.

VARCLUST algorithm is proposed for clustering variables under the assumption that variables in a given cluster are linear combinations of a small number of hidden latent variables, corrupted by the random noise. The entire clustering task is viewed as the problem of selection of the statistical model, which is defined by the number of clusters, the partition of variables into these clusters and the 'cluster dimensions', i.e. the vector of dimensions of linear subspaces spanning each of the clusters. The optimal model is selected using the approximate Bayesian criterion based on the Laplace approximations and using a non-informative uniform prior on the number of clusters. To solve the problem of the search over a huge space of possible models we propose an extension of the ClustOfVar algorithm which was dedicated to subspaces of dimension only 1, and which is similar in structure to the $K$-centroid algorithm. We provide a complete methodology with theoretical guarantees, extensive numerical experimentations, complete data analyses and implementation. Our algorithm assigns variables to appropriate clusterse based on the consistent Bayesian Information Criterion (BIC), and estimates the dimensionality of each cluster by the PEnalized SEmi-integrated Likelihood Criterion (PESEL), whose consistency we prove. Additionally, we prove that each iteration of our algorithm leads to an increase of the Laplace approximation to the model posterior probability and provide the criterion for the estimation of the number of clusters. Numerical comparisons with other algorithms show that VARCLUST may outperform some popular machine learning tools for sparse subspace clustering. We also report the results of real data analysis including TCGA breast cancer data and meteorological data. The proposed method is implemented in the publicly available R package varclust., Comment: 24 pages, 34 figures

In this paper, we study the Lambert-Tsallis function, which is a generalization of the Lambert function with two real parameters. We give a condition on the parameters such that there exists a complex domain touching zero on boundary which is mapped bijectively to the upper half plane by the Lambert-Tsallis function., Comment: 24 pages. arXiv admin note: text overlap with arXiv:2008.10446

We present a new study of late-type eclipsing binary stars in the Small Magellanic Cloud (SMC) undertaken with the aim of improving the distance determination to this important galaxy. A sample of 10 new detached, double-lined eclipsing binaries indentified from the OGLE variable star catalogues and consisting of F- and G-type giant components has been analysed. The absolute physical parameters of the individual components have been measured with a typical accuracy of better than 3%. All but one of the systems consist of young and intermediate population stars with masses in the range of 1.4 to 3.8 M_Sun. This new sample has been combined with five SMC eclipsing binaries previously published by our team. Distances to the binary systems were calculated using a surface brightness - color calibration. The targets form an elongated structure, highly inclined to the plane of the sky. The distance difference between the nearest and most-distant system amounts to 10 kpc with the line of sight depth reaching 7 kpc. We find tentative evidence of the existence of a spherical stellar sub-structure (core) in the SMC coinciding with its stellar center, containing about 40% of the young and intermediate age stars in the galaxy. The radial extension of this sub-structure is ~1.5 kpc. We derive a distance to the SMC center of D_SMC=62.44 +/- 0.47 (stat.) +/- 0.81 (syst.) kpc corresponding to a distance modulus (m-M)_SMC=18.977 +/- 0.016 +/- 0.028 mag, representing an accuracy of better than 2%., Comment: 18 pages, accepted to the Astrophysical Journal

Vinberg cones and the ambient vector spaces are important in modern statistics of sparse models and of graphical models. The aim of this paper is to study eigenvalue distributions of Gaussian, Wigner and covariance matrices related to growing Vinberg matrices, corresponding to growing daisy graphs. For Gaussian or Wigner ensembles, we give an explicit formula for the limiting distribution. For Wishart ensembles defined naturally on Vinberg cones, their limiting Stieltjes transforms, support and atom at 0 are described explicitly in terms of the Lambert-Tsallis functions, which are defined by using the Tsallis $q$-exponential functions., Comment: 27 pages, supplemental material 53 pages

A closed interval and circle are the only smooth Julia sets in polynomial dynamics. D. Ruelle proved that the Hausdorff dimension of unicritical Julia sets close to the circle depends analytically on the parameter. Near the tip of the Mandelbrot set M, the Hausdorff dimension is generally discontinuous. Answering a question of J-C. Yoccoz in the conformal setting, we observe that the Hausdorff dimension of quadratic Julia sets depends continuously on $c$ and find explicit bounds at the tip of M for most real parameters in the the sense of 1-dimensional Lebesgue measure., Comment: The upper bound in the main theorem is improved. In the prior version, the logarithmic term was raised to the power 3/2. The lower bound and its proof remain largely unchanged

Convolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($\varphi$), permeability $k$, and tortuosity ($T$). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. It is demonstrated that the CNNs are able to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between $T$ and $\varphi$ has been reproduced and compared with the empirical estimate. The analysis has been performed for the systems with $\varphi \in (0.37,0.99)$ which covers five orders of magnitude span for permeability $k \in (0.78, 2.1\times 10^5)$ and tortuosity $T \in (1.03,2.74)$., Comment: 12 pages, 9 figures

The surface brightness - color relationship (SBCR) is a poweful tool for determining the angular diameter of stars from photometry. It was for instance used to derive the distance of eclipsing binaries in the Large Magellanic Cloud (LMC), which led to its distance determination with an accuracy of 1%. We calibrate the SBCR for red giant stars in the 2.1 < V-K < 2.5 color range using homogeneous VEGA/CHARA interferometric data secured in the visible domain, and compare it to the relation based on infrared interferometric observations, which were used to derive the distance to the LMC. Observations of eight G-K giants were obtained with the VEGA/CHARA instrument. The derived limb-darkened angular diameters were combined with a homogeneous set of infrared magnitudes in order to constrain the SBCR. The average precision we obtain on the limb-darkened angular diameters of the eight stars in our sample is 2.4%. For the four stars in common observed by both VEGA/CHARA and PIONIER/VLTI, we find a 1 sigma agreement for the angular diameters. The SBCR we obtain in the visible has a dispersion of 0.04 magnitude and is consistent with the one derived in the infrared (0.018 magnitude). The consistency of the infrared and visible angular diameters and SBCR reinforces the result of 1% precision and accuracy recently achieved on the distance of the LMC using the eclipsing-binary technique. It also indicates that it is possible to combine interferometric observations at different wavelengths when the SBCR is calibrated., Comment: 9 pages, in press in A&A revue

Contact tracing is an important instrument for national health services to fight epidemics. As part of the COVID-19 situation, many proposals have been made for scaling up contract tracing capacities with the help of smartphone applications, an important but highly critical endeavor due to the privacy risks involved in such solutions. Extending our previously expressed concern, we clearly articulate in this article, the functional and non-functional requirements that any solution has to meet, when striving to serve, not mere collections of individuals, but the whole of a nation, as required in face of such potentially dangerous epidemics. We present a critical information infrastructure, PriLock, a fully-open preliminary architecture proposal and design draft for privacy preserving contact tracing, which we believe can be constructed in a way to fulfill the former requirements. Our architecture leverages the existing regulated mobile communication infrastructure and builds upon the concept of "checks and balances", requiring a majority of independent players to agree to effect any operation on it, thus preventing abuse of the highly sensitive information that must be collected and processed for efficient contact tracing. This is enforced with a largely decentralised layout and highly resilient state-of-the-art technology, which we explain in the paper, finishing by giving a security, dependability and resilience analysis, showing how it meets the defined requirements, even while the infrastructure is under attack.

We consider multivariate centered Gaussian models for the random variable $Z=(Z_1,\ldots, Z_p)$, invariant under the action of a subgroup of the group of permutations on $\{1,\ldots, p\}$. Using the representation theory of the symmetric group on the field of reals, we derive the distribution of the maximum likelihood estimate of the covariance parameter $\Sigma$ and also the analytic expression of the normalizing constant of the Diaconis-Ylvisaker conjugate prior for the precision parameter $K=\Sigma^{-1}$. We can thus perform Bayesian model selection in the class of complete Gaussian models invariant by the action of a subgroup of the symmetric group, which we could also call complete RCOP models. We illustrate our results with a toy example of dimension $4$ and several examples for selection within cyclic groups, including a high dimensional example with $p=100$., Comment: 28 pages of the main text, 15 pages of the Supplementary material, 6 figures, 5 tables. Accepted to Annals of Statistics

Accurate masses and radii for normal stars derived from observations of detached eclipsing binary stars are of fundamental importance for testing stellar models and may be useful for calibrating free parameters in these model if the masses and radii are sufficiently precise and accurate. We aim to measure precise masses and radii for the stars in the bright eclipsing binary AI Phe, and to quantify the level of systematic error in these estimates. We use several different methods to model the TESS light curve of AI Phe combined with spectroscopic orbits from multiple sources to estimate precisely the stellar masses and radii together with robust error estimates. We find that the agreement between different methods for the light curve analysis is very good but some methods underestimate the errors on the model parameters. The semi-amplitudes of the spectroscopic orbits derived from spectra obtained with modern echelle spectrographs are consistent to within 0.1%. The masses of the stars in AI Phe are $M_1 = 1.1938 \pm 0.0008 M_{\odot}$ and $M_2 = 1.2438 \pm 0.0008M_{\odot}$, and the radii are $R_1 = 1.8050 \pm 0.0022 R_{\odot}$ and $R_2 = 2.9332 \pm 0.0023 R_{\odot}$. We conclude that it is possible to measure accurate masses and radii for stars in bright eclipsing binary stars to a precision of 0.2% or better using photometry from TESS and spectroscopy obtained with modern echelle spectrographs. We provide recommendations for publishing masses and radii of eclipsing binary stars at this level of precision., Comment: Accepted for publication in MNRAS. 12 pages, 4 tables and 8 figures

In magnonics, an emerging branch of wave physics characterized by low-energy consumption, it is highly desirable to realize circuit elements within the scope of spin-wave computing. Here, based on numerical simulations, we demonstrate the functionality of the spin-wave diode and the circulator to steer and manipulate spin waves over a wide range of frequency in the GHz regime. They take advantage of the unidirectional coupling induced by the interfacial Dzyaloshinskii-Moriya interaction to transfer the spin wave between thin ferromagnetic layers in only one direction of propagation. Using the multilayered structure consisting of Py and Co in direct contact with Pt, we obtain sub-micrometer-size devices of high efficiency. In the diode, the power loss ratio between forward and reverse direction reaches 22 dB, while in the four-port circulator, the efficiency exceeds 13 dB. Thus, our work contributes to the emerging branch of energy-efficient magnonic logic devices, where, thanks to short wavelength of spin waves, it is possible to realize nanoscale devices.

We present reddening maps of the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC), based on color measurements of the red clump. Reddening values of our maps were obtained by calculating the difference of the observed and intrinsic color of the red clump in both galaxies. To obtain the intrinsic color of the red clump, we used reddenings obtained from late-type eclipsing binary systems, measurements for blue supergiants and reddenings derived from Str\"{o}mgren photometry of B-type stars. We obtained intrinsic color of the red clump $(V-I)_0$ = 0.838 $\pm$ 0.034 mag in the LMC, and $(V-I)_{0}$ = 0.814 $\pm$ 0.034 mag in the SMC. We prepared our map with 3 arcmin resolution, covering the central part of the LMC and SMC. The mean value of the reddening is E$(B-V)_{\mathrm{LMC}}$=0.127 mag and E$(B-V)_{\mathrm{SMC}}$=0.084 mag for the LMC and SMC, respectively. The systematic uncertainty of the average reddening value assigned to each field of our maps is 0.013 mag for both Magellanic Clouds. Our reddening values are on average higher by 0.061 mag for the LMC and 0.054 mag for the SMC, compared with the maps of Haschke et al. (2011). We also compared our values with different types of reddening tracers. Cepheids, RR Lyrae stars, early-type eclipsing binaries and other reddening estimations based on the red clump color on average show reddenings consistent with our map to within a few hundredths of magnitude., Comment: Accepted for Publication in the Astrophysical Journal

We present new mechanism for manipulation of the spin-wave amplitude through the use of the dynamic charge-mediated magnetoelectric effect in ultrathin multilayers composed of dielectric thin-film capacitors separated by a ferromagnetic bilayer. Propagating spin waves can be amplified and attenuated with rising and decreasing slopes of the oscillating voltage, respectively, locally applied to the sample. The way the spin accumulation is generated makes the interaction of the spin-transfer torque with the magnetization dynamics mode-selective and restricted to some range of spin-wave frequencies, which is in contrary to known types of the spin-transfer torque effects. The interfacial nature of spin-dependent screening allows to reduce the thickness of the fixed magnetization layer to a few nanometers, thus the proposed effect significantly contributes toward realization of the magnonic devices and also miniaturization of the spintronic devices.