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Students often drift in and out of focus during class. Effective teachers recognize this and re-engage them when necessary. With the shift to remote learning, teachers have lost the visual feedback needed to adapt to varying student engagement. We propose using readily available front-facing video to infer attention levels based on movements of the eyes, head, and face. We train a deep learning model to predict a measure of attention based on overt eye movements. Specifically, we measure Inter-Subject Correlation of eye movements in ten-second intervals while students watch the same educational videos. In 3 different experiments (N=83) we show that the trained model predicts this objective metric of attention on unseen data with $R^2$=0.38, and on unseen subjects with $R^2$=0.26-0.30. The deep network relies mostly on a student's eye movements, but to some extent also on movements of the brows, cheeks, and head. In contrast to Inter-Subject Correlation of the eyes, the model can estimate attentional engagement from individual students' movements without needing reference data from an attentive group. This enables a much broader set of online applications. The solution is lightweight and can operate on the client side, which mitigates some of the privacy concerns associated with online attention monitoring. GitHub implementation is available at https://github.com/asortubay/timeISC, Comment: 10 pages, 3 figures

Studying the orbital motion of stars around Sagittarius A* in the Galactic Center provides a unique opportunity to probe the gravitational potential near the supermassive black hole at the heart of our Galaxy. Interferometric data obtained with the GRAVITY instrument at the Very Large Telescope Interferometer (VLTI) since 2016 has allowed us to achieve unprecedented precision in tracking the orbits of these stars. GRAVITY data have been key to detecting the in-plane, prograde Schwarzschild precession of the orbit of the star S2, as predicted by General Relativity. By combining astrometric and spectroscopic data from multiple stars, including S2, S29, S38, and S55 - for which we have data around their time of pericenter passage with GRAVITY - we can now strengthen the significance of this detection to an approximately $10 \sigma$ confidence level. The prograde precession of S2's orbit provides valuable insights into the potential presence of an extended mass distribution surrounding Sagittarius A*, which could consist of a dynamically relaxed stellar cusp comprised of old stars and stellar remnants, along with a possible dark matter spike. Our analysis, based on two plausible density profiles - a power-law and a Plummer profile - constrains the enclosed mass within the orbit of S2 to be consistent with zero, establishing an upper limit of approximately $1200 \, M_\odot$ with a $1 \sigma$ confidence level. This significantly improves our constraints on the mass distribution in the Galactic Center. Our upper limit is very close to the expected value from numerical simulations for a stellar cusp in the Galactic Center, leaving little room for a significant enhancement of dark matter density near Sagittarius A*., Comment: Submitted to A&A on September 17, 2024

In this paper, a novel approach based on robust stability concepts and tools is introduced to evaluate the unconditional stability of microwave active $\textit{n}$-port devices. An efficient calculation of the Structured Singular Value of the $\textit{n}$x$\textit{n}$ scattering matrix is proposed to obtain the stability characteristics of the device. The presented method is validated in two ways. First, it is applied to a referential 4x4 scattering parameter set for independent verification. Second, the method is applied to a 4-port GaAs FET amplifier fabricated in hybrid technology. The results confirm the validity and computational efficiency of the proposed approach.

In this work we characterize the sets $E\subset X$ for which there is some $\alpha>0$ such that the function $d(\cdot,E)^{-\alpha}$ belongs to the Muckenhoupt class $A_1(X,d,\mu)$, where $(X,d,\mu)$ is a space of homogeneous type, extending a recent result obtained by Carlos Mudarra in metric spaces endowed with doubling measures. In particular, generalizations of the notions of weakly porous sets and doubling of the maximal hole function are given and it is shown that these concepts have a natural connection with the $A_1$ condition of some negative power of its distance function. The proof presented here is based on Whitney-type covering lemmas built on balls of a particular quasi-distance equivalent to the initial quasi-distance $d$ and provided by Roberto Mac\'ias and Carlos Segovia in "A well-behaved quasi-distance for spaces of homogeneous type", Trabajos de Matem\'atica 32, Instituto Argentino de Matem\'atica, 1981, 1-18., Comment: 21 pages

Complex systems, such as brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often challenging. We propose using a Vector Autoregressive model with eXogenous input (VARX) to capture delayed interactions between internal and external variables. While this model aligns with Granger's statistical formalism for testing "causal relations", the connection between the two is not widely understood. Here, we bridge this gap by providing fundamental equations, user-friendly code, and demonstrations using simulated and real-world data from neuroscience, physiology, sociology, and economics. Our examples illustrate how the model avoids spurious correlation by factoring out external influences from internal dynamics, leading to more parsimonious explanations of the systems. We also provide methods for enhancing model efficiency, such as L2 regularization for limited data and basis functions to cope with extended delays. Additionally, we analyze model performance under various scenarios where model assumptions are violated. MATLAB, Python, and R code are provided for easy adoption: https://github.com/lcparra/varx

The small-strain damping ratio plays a crucial role in assessing the response of soil deposits to earthquake-induced ground motions and general dynamic loading. The damping ratio can theoretically be inverted for after extracting frequency-dependent Rayleigh wave attenuation coefficients from wavefields collected during surface wave testing. However, determining reliable estimates of in-situ attenuation coefficients is much more challenging than achieving robust phase velocity dispersion data, which are commonly measured using both active-source and ambient-wavefield surface wave methods. This paper introduces a new methodology for estimating frequency-dependent attenuation coefficients through the analysis of ambient noise wavefield data recorded by two-dimensional (2D) arrays of surface seismic sensors for the subsequent evaluation of the small-strain damping ratio. The approach relies on the application of an attenuation-specific wavefield conversion and frequency-domain beamforming. Numerical simulations are employed to verify the proposed approach and inform best practices for its application. Finally, the practical efficacy of the proposed approach is showcased through its application to field data collected at a deep, soft soil site in Logan, Utah, USA, where phase velocity and attenuation coefficients are extracted from surface wave data and then simultaneously inverted to develop deep shear wave velocity and damping ratio profiles., Comment: 42 pages, 12 figures

We present spot properties on 32 periodic young stellar objects in IC 5070. Long term, $\sim$5 yr, light curves in the $V$, $R$, and $I$-bands are obtained through the HOYS (Hunting Outbursting Young Stars) citizen science project. These are dissected into six months long slices, with 3 months oversampling, to measure 234 sets of amplitudes in all filters. We fit 180 of these with reliable spot solutions. Two thirds of spot solutions are cold spots, the lowest is 2150 K below the stellar temperature. One third are warm spots that are above the stellar temperature by less than $\sim$2000 K. Cold and warm spots have maximum surface coverage values of 40 percent, although only 16 percent of warm spots are above 20 percent surface coverage as opposed to 60 percent of the cold spots. Warm spots are most likely caused by a combination of plages and low density accretion columns, most common on objects without inner disc excess emission in $K-W2$. Five small hot spot solutions have $<3$ percent coverage and are 3000 - 5000 K above the stellar temperature. These are attributed to accretion, and four of them occur on the same object. The majority of our objects are likely to be accreting. However, we observe very few accretion hot spots as either the accretion is not stable on our timescale or the photometry is dominated by other features. We do not identify cyclical spot behaviour on the targets. We additionally identify and discuss a number of objects that have interesting amplitudes, phase changes, or spot properties., Comment: Accepted for publication by MNRAS. 17 + 7 pages, 7 + 23 figures, 1 table

We obtain a necessary and sufficient condition on the Haar coefficients of a real function $f$ defined on $\mathbb{R}^+$ for the Lipschitz $\alpha$ regularity of $f$ with respect to the ultrametric $\delta(x,y)=\inf \{|I|: x, y\in I; I\in\mathcal{D}\}$, where $\mathcal{D}$ is the family of all dyadic intervals in $\mathbb{R}^+$ and $\alpha$ is positive. Precisely, $f\in \textrm{Lip}_\delta(\alpha)$ if and only if $\left\vert\left\right\vert\leq C 2^{-(\alpha + \tfrac{1}{2})j}$, for some constant $C$, every $j\in\mathbb{Z}$ and every $k=0,1,2,\ldots$ Here, as usual $h^j_k(x)= 2^{j/2}h(2^jx-k)$ and $h(x)=\mathcal{X}_{[0,1/2)}(x)-\mathcal{X}_{[1/2,1)}(x)$., Comment: 6 pages. This manuscript has been accepted for publication in the Revista de la Uni\'{o}n Matem\'{a}tica Argentina

In this paper we use the neighborhood topology generated by affinities between pairs of points in a set, in orden to explore the underlying dynamics of connectivity by thresholding of the affinity. We apply the method to the connectivity provided by the public transport system in Buenos Aires., Comment: 10 pages, 11 figures

In this article we aim to obtain the Fisher Riemann geodesics for nonparametric families of probability densities as a weak limit of the parametric case with increasing number of parameters., Comment: 26 pages, 11 figures

This paper reviews the results of existence and uniqueness of the solutions of these equations: the Korteweg-de Vries equation, the Kuramoto-Sivashinsky equation, the generalized Korteweg-de Vries-Kuramoto-Sivashinski equation and the non homogeneous boundary value problem for KdV-KS equation in quarter plane.

We present our optical photometric observations of the 2022 eruption of the recurrent nova U Scorpii (U Sco) using 49,152 data points over 70 d following the optical peak. We have also analyzed its soft X-ray (0.3--1 keV) light curve by the Neil Gehrels Swift Observatory. During the 2022 eruption, the optical plateau stage started 13.8--15.0 d and ended 23.8--25.0 d after the optical peak. The soft X-ray stage started 14.6--15.3 d and ended 38.7--39.5 d after the optical peak. Both stages started later and had shorter durations, and the soft X-ray light curve peaked earlier and was less luminous compared to those during the U Sco 2010 eruption. These points suggest that there were differences in the envelope mass between the different cycles of the nova eruption. Furthermore, we have analyzed the optical eclipses during the 2022 eruption. The primary eclipse was first observed 10.4--11.6 d after the optical peak, earlier than the beginning of the optical plateau stage. This sequence of events can be explained by the receding ejecta photosphere associated with the expanding nova ejecta. We have determined the ingress and egress phases of the primary eclipses and estimated the outer radius of the optical light source centered at the white dwarf (WD). During the optical plateau stage, the source radius remained $\sim$1.2 times larger than the Roche volume radius of the primary WD, being close to the L1 point. When the optical plateau stage ended, the source radius drastically shrank to the tidal truncation radius within a few orbital periods. This previously unresolved phenomenon can be interpreted as a structural change in U Sco where the temporarily expanded accretion disk due to the nova wind returned to a steady state., Comment: 16 pages, 7 figures, 7 tables, accepted for publication in PASJ; doi:10.1093/pasj/psae010

The Hunting Outbursting Young Stars (HOYS) project performs long-term, optical, multi-filter, high cadence monitoring of 25 nearby young clusters and star forming regions. Utilising Gaia DR3 data we have identified about 17000 potential young stellar members in 45 coherent astrometric groups in these fields. Twenty one of them are clear young groups or clusters of stars within one kiloparsec and they contain 9143 Gaia selected potential members. The cluster distances, proper motions and membership numbers are determined. We analyse long term (about 7yr) V, R, and I-band light curves from HOYS for 1687 of the potential cluster members. One quarter of the stars are variable in all three optical filters, and two thirds of these have light curves that are symmetric around the mean. Light curves affected by obscuration from circumstellar materials are more common than those affected by accretion bursts, by a factor of 2-4. The variability fraction in the clusters ranges from 10 to almost 100 percent, and correlates positively with the fraction of stars with detectable inner disks, indicating that a lot of variability is driven by the disk. About one in six variables shows detectable periodicity, mostly caused by magnetic spots. Two thirds of the periodic variables with disk excess emission are slow rotators, and amongst the stars without disk excess two thirds are fast rotators - in agreement with rotation being slowed down by the presence of a disk., Comment: accepted for publication in MNRAS, 1 table, 9 figures

The centre of the Milky Way hosts a supermassive black hole of 4 million solar masses called Sagittarius A*. This object has been observed for more than 20 years in the near infrared. This has confirmed some effects of General Relativity. In addition, recurrent observations have made it possible to detect flares, i.e. a much larger flux than the average, with a variability of the order of 30 minutes to 1 hour. In 2018, GRAVITY, using the 4 large telescopes of the VLTI/ESO, observed an orbital motion of the source of these flares. This thesis focuses on the modelling of these flares, using models of varying complexity, including one based on the phenomenon of magnetic reconnection. The latter corresponds to an abrupt change in the magnetic configuration around the black hole, releasing a large amount of energy. We are also looking at the problem of polarisation in General Relativity., Comment: PhD Thesis, 258 pages, written in French

We aim to investigate the origin of the HI Br$\gamma$ emission in young stars by using GRAVITY to image the innermost region of circumstellar disks, where important physical processes such as accretion and winds occur. With high spectral and angular resolution, we focus on studying the continuum and the HI Br$\gamma$-emitting area of the Herbig star HD58647. Using VLTI-GRAVITY, we conducted observations of HD58647 with both high spectral and high angular resolution. Thanks to the extensive $uv$ coverage, we were able to obtain detailed images of the circumstellar environment at a sub-au scale, specifically capturing the continuum and the Br$\gamma$-emitting region. Through the analysis of velocity-dispersed images and photocentre shifts, we were able to investigate the kinematics of the HI Br$\gamma$-emitting region. The recovered continuum images show extended emission where the disk major axis is oriented along a position angle of 14\degr. The size of the continuum emission at 5-sigma levels is $\sim$ 1.5 times more extended than the sizes reported from geometrical fitting (3.69 mas $\pm$ 0.02 mas). This result supports the existence of dust particles close to the stellar surface, screened from the stellar radiation by an optically thick gaseous disk. Moreover, for the first time with GRAVITY, the hot gas component of HD58647 traced by the Br$\gamma$ ,has been imaged. This allowed us to constrain the size of the Br$\gamma$-emitting region and study the kinematics of the hot gas; we find its velocity field to be roughly consistent with gas that obeys Keplerian motion. The velocity-dispersed images show that the size of the hot gas emission is from a more compact region than the continuum (2.3 mas $\pm$ 0.2 mas). Finally, the line phases show that the emission is not entirely consistent with Keplerian rotation, hinting at a more complex structure in the hot gaseous disk., Comment: accepted in A&A on 20/11/2023

The dark compact object at the centre of the Milky Way is well established to be a supermassive black hole with mass $M_{\bullet} \sim 4.3 \cdot 10^6 \, M_{\odot}$, but the nature of its environment is still under debate. In this work, we used astrometric and spectroscopic measurements of the motion of the star S2, one of the closest stars to the massive black hole, to determine an upper limit on an extended mass composed of a massive vector field around Sagittarius A*. For a vector with effective mass $10^{-19} \, \rm eV \lesssim m_s \lesssim 10^{-18} \, \rm eV$, our Markov Chain Monte Carlo analysis shows no evidence for such a cloud, placing an upper bound $M_{\rm cloud} \lesssim 0.1\% M_{\bullet}$ at $3\sigma$ confidence level. We show that dynamical friction exerted by the medium on S2 motion plays no role in the analysis performed in this and previous works, and can be neglected thus., Comment: 9 pages, 5 figures, accepted to MNRAS

Lightcurves of many classical novae deviate from the canonical "fast rise - smooth decline" pattern and display complex variability behavior. We present the first TESS-space-photometry-based investigation of this phenomenon. We use TESS Sector 41 full-frame images to extract a lightcurve of the slow Galactic nova V606 Vul that erupted nine days prior to the start of the TESS observations. The lightcurve covers the first of two major peaks of V606 Vul that was reached 19 days after the start of the eruption. The nova reached its brightest visual magnitude V=9.9 in its second peak 64 days after the eruption onset, following the completion of Sector 41 observations. To increase the confidence level of the extracted lightcurve, we performed the analysis using four different codes implementing the aperture photometry (Lightkurve, VaST) and image subtraction (TESSreduce, tequila_shots) and find good agreement between them. We performed ground-based photometric and spectroscopic monitoring to complement the TESS data. The TESS lightcurve reveals two features: periodic variations (0.12771d, 0.01mag average peak-to-peak amplitude) that disappeared when the source was within 1mag of peak optical brightness and a series of isolated mini-flares (with peak-to-peak amplitudes of up to 0.5mag) appearing at seemingly random times. We interpret the periodic variations as the result of azimuthal asymmetry of the photosphere engulfing the nova-hosting binary that was distorted by and rotating with the binary. Whereas we use spectra to associate the two major peaks in the nova lightcurve with distinct episodes of mass ejection, the origin of mini-flares remains elusive., Comment: 31 pages, 10 figures, submitted to ApJ; comments welcome

The goal of this work is to characterize the polarization effects of the VLTI and GRAVITY. This is needed to calibrate polarimetric observations with GRAVITY for instrumental effects and to understand the systematic error introduced to the astrometry due to birefringence when observing targets with a significant intrinsic polarization. By combining a model of the VLTI light path and its mirrors and dedicated experimental data, we construct a full polarization model of the VLTI UTs and the GRAVITY instrument. We first characterize all telescopes together to construct a UT calibration model for polarized targets. We then expand the model to include the differential birefringence. With this, we can constrain the systematic errors for highly polarized targets. Together with this paper, we publish a standalone Python package to calibrate the instrumental effects on polarimetric observations. This enables the community to use GRAVITY to observe targets in a polarimetric observing mode. We demonstrate the calibration model with the galactic center star IRS 16C. For this source, we can constrain the polarization degree to within 0.4 % and the polarization angle within 5 deg while being consistent with the literature. Furthermore, we show that there is no significant contrast loss, even if the science and fringe-tracker targets have significantly different polarization, and we determine that the phase error in such an observation is smaller than 1 deg, corresponding to an astrometric error of 10 {\mu}as. With this work, we enable the use of the polarimetric mode with GRAVITY/UTs and outline the steps necessary to observe and calibrate polarized targets. We demonstrate that it is possible to measure the intrinsic polarization of astrophysical sources with high precision and that polarization effects do not limit astrometric observations of polarized targets., Comment: Accepted by A&A

[Abridged] Context. The Galactic Center supermassive black hole is well known to exhibit transient peaks of flux density on a daily basis across the spectrum. Recent infrared and millimeter observations have strengthened the case for the association between these flares and circular orbital motion in the vicinity of the event horizon. The strongly polarized synchrotron radiation associated with these events leads to specific observables called QU loops, that is, looping motion in the Stokes QU plane of linear polarization. Aims. We want to deepen the understanding of the QU loops associated with orbiting hot spots. We compute such loops in Minkowski and Schwarzschild spacetimes in order to determine which aspects of the observed patterns are due to special- or general-relativistic phenomena. Results. We show that QU loops in Minkowski spacetime at low or moderate inclination i < 45 deg share all qualitative features of Schwarzschild QU loops: there exist QU loops for all setups considered (including face-on view and vertical magnetic field), there may be one or two QU loops per orbital period for a vertical magnetic field configuration, there are always two QU loops in case of a toroidal magnetic field. We provide analytical formulas in Minkowski spacetime to explain the details of this behavior. Moreover, we analyze the flux variation of the hot spot and show that it is dictated either by the angular dependence of the radiative transfer coefficients, or by relativistic beaming. In the former case, this can lead to extreme flux ratios even at moderate inclination. Finally, we highlight the increasing mirror asymmetry of the Schwarzschild QU track with increasing inclination and show that this behavior is a specific Schwarzschild feature caused by light bending., Comment: 20 pages, 14 figures, submitted to A&A

We present new astrometric and polarimetric observations of flares from Sgr A* obtained with GRAVITY, the near-infrared interferometer at ESO's Very Large Telescope Interferometer (VLTI), bringing the total sample of well-covered astrometric flares to four and polarimetric ones to six, where we have for two flares good coverage in both domains. All astrometric flares show clockwise motion in the plane of the sky with a period of around an hour, and the polarization vector rotates by one full loop in the same time. Given the apparent similarities of the flares, we present a common fit, taking into account the absence of strong Doppler boosting peaks in the light curves and the EHT-measured geometry. Our results are consistent with and significantly strengthen our model from 2018: We find that a) the combination of polarization period and measured flare radius of around nine gravitational radii ($9 R_g \approx 1.5 R_{ISCO}$, innermost stable circular orbit) is consistent with Keplerian orbital motion of hot spots in the innermost accretion zone. The mass inside the flares' radius is consistent with the $4.297 \times 10^6 \; \text{M}_\odot$ measured from stellar orbits at several thousand $R_g$. This finding and the diameter of the millimeter shadow of Sgr A* thus support a single black hole model. Further, b) the magnetic field configuration is predominantly poloidal (vertical), and the flares' orbital plane has a moderate inclination with respect to the plane of the sky, as shown by the non-detection of Doppler-boosting and the fact that we observe one polarization loop per astrometric loop. Moreover, c) both the position angle on sky and the required magnetic field strength suggest that the accretion flow is fueled and controlled by the winds of the massive, young stars of the clockwise stellar disk 1-5 arcsec from Sgr A*, in agreement with recent simulations., Comment: 10 pages, 12 figures. Accepted for publication in A&A

The motion of S2, one of the stars closest to the Galactic Centre, has been measured accurately and used to study the compact object at the centre of the Milky Way. It is commonly accepted that this object is a supermassive black hole but the nature of its environment is open to discussion. Here, we investigate the possibility that dark matter in the form of an ultralight scalar field ``cloud'' clusters around Sgr~A*. We use the available data for S2 to perform a Markov Chain Monte Carlo analysis and find the best-fit estimates for a scalar cloud structure. Our results show no substantial evidence for such structures. When the cloud size is of the order of the size of the orbit of S2, we are able to constrain its mass to be smaller than $0.1\%$ of the central mass, setting a strong bound on the presence of new fields in the galactic centre., Comment: Published on MNRAS. References added

Long-tailed semi-supervised learning (LTSSL) represents a practical scenario for semi-supervised applications, challenged by skewed labeled distributions that bias classifiers. This problem is often aggravated by discrepancies between labeled and unlabeled class distributions, leading to biased pseudo-labels, neglect of rare classes, and poorly calibrated probabilities. To address these issues, we introduce Flexible Distribution Alignment (FlexDA), a novel adaptive logit-adjusted loss framework designed to dynamically estimate and align predictions with the actual distribution of unlabeled data and achieve a balanced classifier by the end of training. FlexDA is further enhanced by a distillation-based consistency loss, promoting fair data usage across classes and effectively leveraging underconfident samples. This method, encapsulated in ADELLO (Align and Distill Everything All at Once), proves robust against label shift, significantly improves model calibration in LTSSL contexts, and surpasses previous state-of-of-art approaches across multiple benchmarks, including CIFAR100-LT, STL10-LT, and ImageNet127, addressing class imbalance challenges in semi-supervised learning. Our code is available at https://github.com/emasa/ADELLO-LTSSL., Comment: Accepted at ECCV2024, 25 pages, 6 figures

In this brief note we aim to provide, through a well known class of singular densities in harmonic analysis, a simple approach to the fact that the homogeneity of the universe on scales of the order of a hundred millions light years is completely compatible with the fine-scale condensation of matter and energy. We give precise and quantitative definitions of homogeneity and isotropy on large scales. Then we show that Muckenhoupt densities have the ingredients required to a model for the large-scale homogeneity and the fine-scale condensation of the universe. In particular, these densities can take locally infinitely large values (black holes) and at once, in the large scales they are independent of the location. We also show some locally singular densities satisfying the large scale isotropy property., Comment: 9 pages, 1 figure. We add a comment on page 5 and two references. The article has been accepted for publication in the Revista de la Union Matematica Argentina

In this note we explore the structure of the diffusion metric of Coifman-Lafon determined by fractional dyadic Laplacians. The main result is that, for each ${t>0}$, the diffusion metric is a function of the dyadic distance, given in $\mathbb{R}^+$ by $\delta(x,y) = \inf\{|I|: I \text{ is a dyadic interval containing } x \text{ and } y\}$. Even if these functions of $\delta$ are not equivalent to $\delta$, the families of balls are the same, to wit, the dyadic intervals., Comment: 8 pages

In the Milky Way the central massive black hole, SgrA*, coexists with a compact nuclear star cluster that contains a sub-parsec concentration of fast-moving young stars called S-stars. Their location and age are not easily explained by current star formation models, and in several scenarios the presence of an intermediate-mass black hole (IMBH) has been invoked. We use GRAVITY astrometric and SINFONI, KECK, and GNIRS spectroscopic data of S2 to investigate whether a second massive object could be present deep in the Galactic Centre (GC) in the form of an IMBH binary companion to SgrA*. To solve the three-body problem, we used a post-Newtonian framework and consider two types of settings: (i) a hierarchical set-up where the star S2 orbits the SgrA* - IMBH binary and (ii) a non-hierarchical set-up where the IMBH trajectory lies outside the S2 orbit. In both cases we explore the full 20-dimensional parameter space by employing a Bayesian dynamic nested sampling method. For the hierarchical case we find: IMBH masses > 2000 Msun on orbits with smaller semi-major axes than S2 are largely excluded. For the non-hierarchical case the parameter space contains several pockets of valid IMBH solutions. However, a closer analysis of their impact on the resident stars reveals that IMBHs on semi-major axes larger than S2 tend to disrupt the S-star cluster in less than a million years. This makes the existence of an IMBH among the S-stars highly unlikely. The current S2 data do not formally require the presence of an IMBH. If an IMBH hides in the GC, it has to be either a low-mass IMBH inside the S2 orbit that moves on a short and significantly inclined trajectory or an IMBH with a semi-major axis >1". We provide the parameter maps of valid IMBH solutions in the GC and discuss the general structure of our results. (abridged), Comment: 11 pages, 6 figures, published in A $\&$ A

This paper is one in a series reporting results from small telescope observations of variable young stars. Here, we study the repeating outbursts of three likely Be stars based on long-term optical, near-infrared, and mid-infrared photometry for all three objects, along with follow-up spectra for two of the three. The sources are characterised as rare, truly regularly outbursting Be stars. We interpret the photometric data within a framework for modelling light curve morphology, and find that the models correctly predict the burst shapes, including their larger amplitudes and later peaks towards longer wavelengths. We are thus able to infer the start and end times of mass loading into the circumstellar disks of these stars. The disk sizes are typically 3-6 times the areas of the central star. The disk temperatures are ~40%, and the disk luminosities are ~10% of those of the central Be star, respectively. The available spectroscopy is consistent with inside-out evolution of the disk. Higher excitation lines have larger velocity widths in their double-horned shaped emission profiles. Our observations and analysis support the decretion disk model for outbursting Be stars., Comment: Accepted for publication by MNRAS. 20 pages, 11 figures, 2 tables

Sagittarius A*, the supermassive black hole at the center of our galaxy, exhibits episodic near-infrared flares. The recent monitoring of three such events by the GRAVITY instrument has shown that some flares are associated with orbital motions in the close environment of the black hole with super Keplerian velocity. We develop a semi-analytic model of Sagittarius~A* flares based on an ejected large plasmoid, inspired by recent particle-in-cell global simulations of black hole magnetospheres. We model the infrared astrometric and photometric signatures associated to this model. We consider a spherical large plasmoid ejected along a conical orbit around the black hole. This plasmoid is assumed to be formed by successive mergers of smaller plasmoids produced through magnetic reconnection. Non-thermal electrons are injected in the plasmoid. We compute the evolution of the electron-distribution under the influence of synchrotron cooling. We solve the radiative transfer problem and transport the radiation along null geodesics of the Schwarzschild spacetime. We also take into account the quiescent radiation of the accretion flow, on top of which the flare evolves. For the first time, we successfully account for the astrometric and flux variations of the GRAVITY data with a flare model that incorporates an explicit modeling of the emission mechanism. We find good agreement between the prediction of our model and the recent data. In particular, the azimuthal velocity is set by the magnetic field line it belongs to, which is anchored in the inner parts of the accretion flow, hence the super-Keplerian motion. The astrometric track is also shifted with respect to the center of mass due to the quiescent radiation, in agreement with the difference measured with the GRAVITY data. These results support the picture of magnetic reconnection as a viable model for Sagittarius~A* infrared flares., Comment: 20 pages, 14 figures, accepted in A&A

The near-infrared (NIR) and X-ray emission of Sagittarius A* shows occasional bright flares that are assumed to originate from the innermost region of the accretion flow. We identified $25$ $4.5 \mu m$ and $24$ X-ray flares in archival data obtained with the \textit{Spitzer} and \textit{Chandra} observatories. With the help of general relativistic ray-tracing code, we modeled trajectories of ``hot spots'' and studied the light curves of the flares for signs of the effects of general relativity. Despite their apparent diversity in shape, all flares share a common, exponential impulse response, a characteristic shape that is the building block of the variability. This shape is symmetric, that is, the rise and fall times are the same. Furthermore, the impulse responses in the NIR and X-ray are identical within uncertainties, with an exponential time constant $\tau\sim 15$ minute. The observed characteristic flare shape is inconsistent with hot-spot orbits viewed edge-on. Individually modeling the light curves of the flares, we derived constraints on the inclination of the orbital plane of the hot spots with respect to the observer ($i \sim 30^{\circ} , < 75^{\circ} $) and on the characteristic timescale of the intrinsic variability (tens of minutes).

In this paper we aim to use different metrics in the Euclidean space and Sobolev type metrics in function spaces in order to produce reliable parameters for the differentiation of point distributions and dynamical systems. The main tool is the analysis of the geometrical evolution of the hypergraphs generated by the growth of the radial parameters for a choice of an appropriate metric in the space containing the data points. Once this geometric dynamics is obtained we use Lebesque and Sobolev type norms in order to compare the basic geometric signals obtained., Comment: 11 pages, 5 figures, 6 tables

The ExoClock project has been created with the aim of increasing the efficiency of the Ariel mission. It will achieve this by continuously monitoring and updating the ephemerides of Ariel candidates over an extended period, in order to produce a consistent catalogue of reliable and precise ephemerides. This work presents a homogenous catalogue of updated ephemerides for 450 planets, generated by the integration of $\sim$18000 data points from multiple sources. These sources include observations from ground-based telescopes (ExoClock network and ETD), mid-time values from the literature and light-curves from space telescopes (Kepler/K2 and TESS). With all the above, we manage to collect observations for half of the post-discovery years (median), with data that have a median uncertainty less than one minute. In comparison with literature, the ephemerides generated by the project are more precise and less biased. More than 40\% of the initial literature ephemerides had to be updated to reach the goals of the project, as they were either of low precision or drifting. Moreover, the integrated approach of the project enables both the monitoring of the majority of the Ariel candidates (95\%), and also the identification of missing data. The dedicated ExoClock network effectively supports this task by contributing additional observations when a gap in the data is identified. These results highlight the need for continuous monitoring to increase the observing coverage of the candidate planets. Finally, the extended observing coverage of planets allows us to detect trends (TTVs - Transit Timing Variations) for a sample of 19 planets. All products, data, and codes used in this work are open and accessible to the wider scientific community., Comment: Recommended for publication to ApJS (reviewer's comments implemented). Main body: 13 pages, total: 77 pages, 7 figures, 7 tables. Data available at http://doi.org/10.17605/OSF.IO/P298N

Many real-world recognition problems are characterized by long-tailed label distributions. These distributions make representation learning highly challenging due to limited generalization over the tail classes. If the test distribution differs from the training distribution, e.g. uniform versus long-tailed, the problem of the distribution shift needs to be addressed. A recent line of work proposes learning multiple diverse experts to tackle this issue. Ensemble diversity is encouraged by various techniques, e.g. by specializing different experts in the head and the tail classes. In this work, we take an analytical approach and extend the notion of logit adjustment to ensembles to form a Balanced Product of Experts (BalPoE). BalPoE combines a family of experts with different test-time target distributions, generalizing several previous approaches. We show how to properly define these distributions and combine the experts in order to achieve unbiased predictions, by proving that the ensemble is Fisher-consistent for minimizing the balanced error. Our theoretical analysis shows that our balanced ensemble requires calibrated experts, which we achieve in practice using mixup. We conduct extensive experiments and our method obtains new state-of-the-art results on three long-tailed datasets: CIFAR-100-LT, ImageNet-LT, and iNaturalist-2018. Our code is available at https://github.com/emasa/BalPoE-CalibratedLT., Comment: Accepted at CVPR 2023, 19 pages

V392 Persei is a known dwarf nova (DN) that underwent a classical nova eruption in 2018. Here we report ground-based optical, Swift UV and X-ray, and Fermi-LAT \gamma-ray observations following the eruption for almost three years. V392 Per is one of the fastest evolving novae yet observed, with a $t_2$ decline time of 2 days. Early spectra present evidence for multiple and interacting mass ejections, with the associated shocks driving both the \gamma-ray and early optical luminosity. V392 Per entered Sun-constraint within days of eruption. Upon exit, the nova had evolved to the nebular phase, and we saw the tail of the super-soft X-ray phase. Subsequent optical emission captured the fading ejecta alongside a persistent narrow line emission spectrum from the accretion disk. Ongoing hard X-ray emission is characteristic of a standing accretion shock in an intermediate polar. Analysis of the optical data reveals an orbital period of 3.230 \pm 0.003 days, but we see no evidence for a white dwarf (WD) spin period. The optical and X-ray data suggest a high mass WD, the pre-nova spectral energy distribution (SED) indicates an evolved donor, and the post-nova SED points to a high mass accretion rate. Following eruption, the system has remained in a nova-like high mass transfer state, rather than returning to the pre-nova DN low mass transfer configuration. We suggest that this high state is driven by irradiation of the donor by the nova eruption. In many ways, V392 Per shows similarity to the well-studied nova and DN GK Persei., Comment: Accepted by MNRAS. 20 pages including references, with 37 pages of supplementary material

The stars orbiting the compact radio source Sgr A* in the Galactic Centre are precision probes of the gravitational field around the closest massive black hole. In addition to adaptive optics assisted astrometry (with NACO / VLT) and spectroscopy (with SINFONI / VLT, NIRC2 / Keck and GNIRS / Gemini) over three decades, since 2016/2017 we have obtained 30-100 mu-as astrometry with the four-telescope interferometric beam combiner GRAVITY / VLTI reaching a sensitivity of mK = 20 when combining data from one night. We present the simultaneous detection of several stars within the diffraction limit of a single telescope, illustrating the power of interferometry. The new data for the stars S2, S29, S38 and S55 yield significant accelerations between March and July 2021, as these stars pass the pericenters of their orbits between 2018 and 2023. This allows for a high-precision determination of the gravitational potential around Sgr A*. Our data are in excellent agreement with general relativity orbits around a single central point mass, M = 4.30 x 10^6 M_sun with a precision of about +-0.25%. We improve the significance of our detection of the Schwarzschild precession in the S2 orbit to 7 sigma. Assuming plausible density profiles, an extended mass component inside S2's apocentre (= 0.23" or 2.4 x 10^4 R_S) must be 3000 M_sun (1 sigma), or 0.1% of M. Adding the enclosed mass determinations from 13 stars orbiting Sgr A* at larger radii, the innermost radius at which the excess mass beyond Sgr A* tentatively is seen is r = 2.5" >= 10x the apocentre of S2. This is in full harmony with the stellar mass distribution (including stellar-mass black holes) obtained from the spatially resolved luminosity function., Comment: published in A&A

Stellar orbits at the Galactic Center provide a very clean probe of the gravitational potential of the supermassive black hole. They can be studied with unique precision, beyond the confusion limit of a single telescope, with the near-infrared interferometer GRAVITY. Imaging is essential to search the field for faint, unknown stars on short orbits which potentially could constrain the black hole spin. Furthermore, it provides the starting point for astrometric fitting to derive highly accurate stellar positions. Here, we present $\mathrm{G^R}$, a new imaging tool specifically designed for Galactic Center observations with GRAVITY. The algorithm is based on a Bayesian interpretation of the imaging problem, formulated in the framework of information field theory and building upon existing works in radio-interferometric imaging. Its application to GRAVITY observations from 2021 yields the deepest images to date of the Galactic Center on scales of a few milliarcseconds. The images reveal the complicated source structure within the central $100\,\mathrm{mas}$ around Sgr A*, where we detected the stars S29 and S55 and confirm S62 on its trajectory, slowly approaching Sgr A*. Furthermore, we were able to detect S38, S42, S60, and S63 in a series of exposures for which we offset the fiber from Sgr A*. We provide an update on the orbits of all aforementioned stars. In addition to these known sources, the images also reveal a faint star moving to the west at a high angular velocity. We cannot find any coincidence with any known source and, thus, we refer to the new star as S300. From the flux ratio with S29, we estimate its K-band magnitude as $m_\mathrm{K}\left(\mathrm{S300}\right)\simeq 19.0 - 19.3$. Images obtained with CLEAN confirm the detection., Comment: 24 pages, 14 figures

In this work we introduce a concept of complexity for undirected graphs in terms of the spectral analysis of the Laplacian operator defined by the incidence matrix of the graph. Precisely, we compute the norm of the vector of eigenvalues of both the graph and its complement and take their product. Doing so, we obtain a quantity that satisfies two basic properties that are the expected for a measure of complexity. First,complexity of fully connected and fully disconnected graphs vanish. Second, complexity of complementary graphs coincide. This notion of complexity allows us to distinguish different kinds of graphs by placing them in a "croissant-shaped" region of the plane link density - complexity, highlighting some features like connectivity,concentration, uniformity or regularity and existence of clique-like clusters. Indeed, considering graphs with a fixed number of nodes, by plotting the link density versus the complexity we find that graphs generated by different methods take place at different regions of the plane. We consider some generated graphs, in particular the Erd\"os-R\'enyi, the Watts-Strogatz and the Barab\'asi-Albert models. Also, we place some particular, let us say deterministic, to wit, lattices, stars, hyper-concentrated and cliques-containing graphs. It is worthy noticing that these deterministic classical models of graphs depict the boundary of the croissant-shaped region. Finally, as an application to graphs generated by real measurements, we consider the brain connectivity graphs from two epileptic patients obtained from magnetoencephalography (MEG) recording, both in a baseline period and in ictal periods .In this case, our definition of complexity could be used as a tool for discerning between states, by the analysis of differences at distinct frequencies of the MEG recording., Comment: 11 pages , 7 figures

Studying rotational variability of young stars is enabling us to investigate a multitude of properties of young star-disk systems. We utilise high cadence, multi-wavelength optical time series data from the Hunting Outbursting Young Stars citizen science project to identify periodic variables in the Pelican Nebula (IC5070). A double blind study using nine different period-finding algorithms was conducted and a sample of 59 periodic variables was identified. We find that a combination of four period finding algorithms can achieve a completeness of 85% and a contamination of 30% in identifying periods in inhomogeneous data sets. The best performing methods are periodograms that rely on fitting a sine curve. Utilising GaiaEDR3 data, we have identified an unbiased sample of 40 periodic YSOs, without using any colour or magnitude selections. With a 98.9% probability we can exclude a homogeneous YSO period distribution. Instead we find a bi-modal distribution with peaks at three and eight days. The sample has a disk fraction of 50%, and its statistical properties are in agreement with other similarly aged YSOs populations. In particular, we confirm that the presence of the disk is linked to predominantly slow rotation and find a probability of 4.8$\times$10$^{-3}$ that the observed relation between period and presence of a disk has occurred by chance. In our sample of periodic variables, we also find pulsating giants, an eclipsing binary, and potential YSOs in the foreground of IC5070., Comment: 25 pages, 14 figures, 5 tables, accepted for publication in MNRAS

In this work, we introduce our submission to the 2nd Affective Behavior Analysis in-the-wild (ABAW) 2021 competition. We train a unified deep learning model on multi-databases to perform two tasks: seven basic facial expressions prediction and valence-arousal estimation. Since these databases do not contains labels for all the two tasks, we have applied the distillation knowledge technique to train two networks: one teacher and one student model. The student model will be trained using both ground truth labels and soft labels derived from the pretrained teacher model. During the training, we add one more task, which is the combination of the two mentioned tasks, for better exploiting inter-task correlations. We also exploit the sharing videos between the two tasks of the AffWild2 database that is used in the competition, to further improve the performance of the network. Experiment results shows that the network have achieved promising results on the validation set of the AffWild2 database. Code and pretrained model are publicly available at https://github.com/glmanhtu/multitask-abaw-2021

O-stars are known to experience a wide range of variability mechanisms originating at both their surface and their near-core regions. Characterization and understanding of this variability and its potential causes are integral for evolutionary calculations. We use a new extensive high-resolution spectroscopic data set to characterize the variability observed in both the spectroscopic and space-based photometric observations of the O+B eclipsing binary HD~165246. We present an updated atmospheric and binary solution for the primary component, involving a high level of microturbulence ($13_{-1.3}^{+1.0}\,$km\,s$^{-1}$) and a mass of $M_1=23.7_{-1.4}^{+1.1}$~M$_{\odot}$, placing it in a sparsely explored region of the Hertzsprung-Russell diagram. Furthermore, we deduce a rotational frequency of $0.690\pm 0.003\,$d$^{-1}$ from the combined photometric and line-profile variability, implying that the primary rotates at 40\% of its critical Keplerian rotation rate. We discuss the potential explanations for the overall variability observed in this massive binary, and discuss its evolutionary context., Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society, 14 pages, 10 figures, 6 tables, 1 appendix (4 additional figures)

In this paper we explore conditions on variable symbols with respect to Haar systems, defining Calder\'on-Zygmund type operators with respect to the dyadic metrics associated to the Haar bases.We show that Petermichl's dyadic kernel can be seen as a variable kernel singular integral and we extend it to dyadic systems built on spaces of homogeneous type., Comment: 17 pages

We present our photometric and spectroscopic observations on the peculiar transient AT2018cow. The multi-band photometry covers from peak to $\sim$70 days and the spectroscopy ranges from 5 to $\sim$50 days. The rapid rise ($t_{\mathrm{r}}$$\lesssim$2.9 days), high luminosity ($M_{V,\mathrm{peak}}\sim-$20.8 mag) and fast decline after peak make AT2018cow stand out of any other optical transients. While we find that its light curves show high resemblance to those of type Ibn supernovae. Moreover, the spectral energy distribution remains high temperature of $\sim$14,000 K after $\sim$15 days since discovery. The spectra are featureless in the first 10 days, while some broad emission lines due to H, He, C and O emerge later, with velocity declining from $\sim$14,000 km s$^{-1}$ to $\sim$3000 km s$^{-1}$ at the end of our observations. Narrow and weak He I emission lines emerge in the spectra at $t>$20 days since discovery. These emission lines are reminiscent of the features seen in interacting supernovae like type Ibn and IIn subclasses. We fit the bolometric light curves with a model of circumstellar interaction (CSI) and radioactive decay (RD) of \Ni and find a good fit with ejecta mass $M_{\mathrm{ej}}\sim$3.16 M$_{\odot}$, circumstellar material mass $M_{\mathrm{CSM}}\sim$0.04 M$_{\odot}$, and ejected \Ni mass $M_{^{56}\mathrm{Ni}}\sim$0.23 M$_{\odot}$. The CSM shell might be formed in an eruptive mass ejection of the progenitor star. Furthermore, host environment of AT2018cow implies connection of AT2018cow with massive stars. Combining observational properties and the light curve fitting results, we conclude that AT2018cow might be a peculiar interacting supernova originated from a massive star., Comment: Accepted for publication in ApJ

We provide sufficient conditions on the profile $\varphi$, on the sequence of random variables $\varepsilon_j>0$ and on the sequence of random vectors $y_j\in\mathbb{R}^n$ such that $\mathscr{E}\left(\frac{1}{\varepsilon_j^n(\omega)}\int_{z\in\mathbb{R}^n}\varphi\left(\frac{|x-z-y_j(\omega)|}{\varepsilon_j(\omega)}\right)f(z) dz\right)\longrightarrow f(x)$ when $j\to\infty$ for almost every $x\in\mathbb{R}^n$, $f\in L^p(\mathbb{R}^n)$, $1\leq p\leq\infty$, where $\mathscr{E}$ denotes the expectation, $\varepsilon_j$ tends to $0\in\mathbb{R}$ in law and $y_j$ tends to $\mathbf{0}\in\mathbb{R}^n$ in law., Comment: 12 pages