Search

Given a finite group G with an irreducible character \chi \in Irr(G), the codegree of \chi is defined by cod(\chi) = |G :\ker \chi|/\chi(1). The set of non-linear irreducible character codegrees of G is denoted by cod(G|G'). In this note, we classify all finite groups G with |cod(G|G')|> 1 and for each pair of distinct elements m, n \in cod(G|G'), m and n are coprime.

A large, faint nebula was unexpectedly discovered near M31 using narrowband [O III] images. Its apparent size and the lack of a clear counterpart at other wavelengths make it unique and challenging to explain. We aim to determine whether the nebula is extragalactic or located within the Milky Way. This will enable us to constrain its physical properties and assess its nature. To do so, we obtained deep narrowband [O II]3727 and H$\alpha$+[NII] observations with the JAST80 telescope at the Observatorio Astrof\'isico de Javalambre, as well as high-spectral-resolution spectroscopy at four locations within the region of interest using MEGARA at the Gran Telescopio Canarias. We found extended [O II] emission along two near-parallel strands to the [O III], offset by six arcmin. The nebular spectra reveals up to 6 emission lines from [O III]4959,5007, H$\beta$, [N II]6583, and [S II]6716,6731. Their receding velocities are above $-$40 km s$^{-1}$, far from the systemic velocity of M31 ($-$300 km s$^{-1}$). The fluxes and velocities are consistent for the same lines across different regions of the nebula. The nebular properties suggest a location within the Milky Way rather than being physically associated with M31. The most likely scenario is a resolved ionization structure in a Galactic nebula with a separation between [O II] and [O III] of a few parsecs. The observed receding velocities would be unprecedented for an object physically linked to M31 but are common for nearby gas filaments. Their consistency across the nebula would also be unusual if it were larger than a kiloparsec. The analysis of the emission-line ratios, line widths, and morphology suggests the possibility of it being an interstellar gas filament with an additional source of ionization to explain the [O III] emission. However, the complex properties of this object call for further observations to confirm its nature., Comment: 13 pages, 6 figures. Submitted to Astronomy & Astrophysics

The HeartBert model is introduced with three primary objectives: reducing the need for labeled data, minimizing computational resources, and simultaneously improving performance in machine learning systems that analyze Electrocardiogram (ECG) signals. Inspired by Bidirectional Encoder Representations from Transformers (BERT) in natural language processing and enhanced with a self-supervised learning approach, the HeartBert model-built on the RoBERTa architecture-generates sophisticated embeddings tailored for ECG-based projects in the medical domain. To demonstrate the versatility, generalizability, and efficiency of the proposed model, two key downstream tasks have been selected: sleep stage detection and heartbeat classification. HeartBERT-based systems, utilizing bidirectional LSTM heads, are designed to address complex challenges. A series of practical experiments have been conducted to demonstrate the superiority and advancements of HeartBERT, particularly in terms of its ability to perform well with smaller training datasets, reduced learning parameters, and effective performance compared to rival models. The code and data are publicly available at https://github.com/ecgResearch/HeartBert., Comment: Second version, 27 pages, 11 Figures, 7 Tables

According to the well established hierarchical framework for galaxy evolution, galaxies grow through mergers with other galaxies and the LambdaCDM cosmological model predicts that the stellar halos of massive galaxies are rich in remnants from minor mergers. The Stellar Streams Legacy Survey (SSLS) has provided a first release of a catalogue with a statistically significant sample of stellar streams in the Local Universe, detected in deep images from DESI Legacy Surveys and the Dark Energy Survey (DES). The main objective is to compare the results of the observations of stellar tidal streams with predictions from state-of-the-art cosmological simulations regarding their abundance, up to a redshift z < 0.02, according to the LambdaCDM model. We use the predictions of the cosmological simulations Copernicus Complexio, TNG50 of the IllustrisTNG project, and Auriga to generate mock-images of nearby halos and search for stellar streams. We compare the stream frequency, characteristics and photometry in these images with DES observations. We find generally good agreement between the real images and the simulated ones regarding frequency, characteristics and photometry of the streams, while the stream morphology is somewhat different between observations and simulations, and between simulations themselves. By varying the sky background of the synthetic images to emulate different surface brightness limit levels, we also obtain predictions for the detection rate of stellar tidal streams up to a surface brightness limit of 35 mag arcsec^-2. The cosmological simulations predict that with an instrument such as the one used in the DES, it would be necessary to reach a surface brightness limit of 32 mag arcsec^-2 in the r-band to achieve a frequency of up to around 70% in the detection of stellar tidal streams around galaxies in the redshift range considered here., Comment: 19 pages, 23 figures

Stellar tidal streams are a key tracer of galaxy evolution and have the potential to provide an indirect means for tracing dark matter. For the Local Group, many diffuse substructures have been identified and their link to galaxy evolution has been traced. However, an analysis of a larger sample is required to better probe the frequency and characteristics of these streams to verify the predictions of the Lambda-CDM model and its implementation in cosmological simulations. For that purpose, we are carrying out the first systematic survey of faint stellar debris from tidally disrupted dwarf satellites around nearby galaxies up to a distance of 100 Mpc. In this paper, we present a catalogue with the results of the first harvest of stellar tidal streams found by visual inspection in deep images of ~ 700 galaxies from the Dark Energy Survey (DES). We include a photometric characterisation of the streams obtained by measuring their surface brightnesses and colours. We found a total of 63 streams in our sample at distances between 40 and 100 Mpc, including 59 which were not previously reported. We measured their average surface brightness for the grz bands, to be 28.35+/-0.20, 27.81+/-0.13 and 27.62+/-0.09 mag arcsec^-2, respectively. By applying a statistical analysis to our findings, we obtained a stream detection frequency of 9.1% +/- 1.1% , in agreement with previous studies. We identified stream progenitors in 5-14% of our stream sample, depending on the confidence level. The first catalogue of streams in the Local Universe presented here will be complemented by future stream surveys within the Stellar Stream Legacy Survey. In this work we have learnt that the faintest measured stream surface brightness can be significantly brighter than the surface brightness limit of an image measured at pixel level, mainly due to correlated noise present in the images., Comment: 20 pages with 16 figures, plus Appendices: 27 pages in total

When a structure displays dependence on distance and azimuthal angle from a center (for example the spiral arms of galaxies or the diffraction spikes of stars), projecting the pixels to polar coordinates greatly simplifies their study. This projection from one pixel grid to another is known as a "polar plot". For this purpose, a new option has been added to the GNU Astronomy Utilities (Gnuastro) in version 0.23 to "astscript-radial-profile" script, which we describe in this research note. The figures of this research note are reproducible with Maneage, on the Git commit 5d34243., Comment: Supplementary data on Zenodo (http://doi.org/10.5281/zenodo.11403643), project source on Codeberg (https://codeberg.org/gnuastro/papers/src/branch/polar-plot) and archived on Software Heritage (swh:1:dir:4e09bf85f9f87336fa55920bf67e7bcf6d58bbd5; see text for usage)

We present radio observations of the galaxy cluster Abell S1136 at 888 MHz, using the Australian Square Kilometre Array Pathfinder radio telescope, as part of the Evolutionary Map of the Universe Early Science program. We compare these findings with data from the Murchison Widefield Array, XMM-Newton, the Wide-field Infrared Survey Explorer, the Digitised Sky Survey, and the Australia Telescope Compact Array. Our analysis shows the X-ray and radio emission in Abell S1136 are closely aligned and centered on the BCG, while the X-ray temperature profile shows a relaxed cluster with no evidence of a cool core. We find that the diffuse radio emission in the centre of the cluster shows more structure than seen in previous low-resolution observations of this source, which appeared formerly as an amorphous radio blob, similar in appearance to a radio halo; our observations show the diffuse emission in the Abell S1136 galaxy cluster contains three narrow filamentary structures visible at 888 MHz, between$\sim 80$ and 140 kpc in length; however the properties of the diffuse emission do not fully match that of a radio (mini-)halo or (fossil) tailed radio source., Comment: To appear in PASA

A subset $C$ of the vertex set of a graph $\Gamma$ is said to be $(\alpha,\beta)$-regular if $C$ induces an $\alpha$-regular subgraph and every vertex outside $C$ is adjacent to exactly $\beta$ vertices in $C$. In particular, if $C$ is an $(\alpha,\beta)$-regular set in some Cayley sum graph of a finite group $G$ with connection set $S$, then $C$ is called an $(\alpha,\beta)$-regular set of $G$ and a $(0,1)$-regular set is called a perfect code of $G$. By Sq$(G)$ and NSq$(G)$ we mean the set of all square elements and non-square elements of $G$. As one of the main results in this note, we show that a subgroup $H$ of a finite abelian group $G$ is an $(\alpha,\beta)$-regular set of $G$, for each $0\leq \alpha \leq |$NSq$(G)\cap H|$ and $0\leq \beta \leq \mathcal{L}(H)$, where $\mathcal{L}(H)=|H|$, if Sq$(G) \subseteq H$ and $\mathcal{L}(H)=|$NSq$(G)\cap H|$, otherwise. As a consequence of our result we give a very brief proof for the main results in \cite{mama, ma}. Also, we consider the dihedral group $G=D_{2n} $ and for each subgroup $H $ of $G$, by giving an appropriate connection set $S$, we determine each possibility for $(\alpha, \beta)$, where $H$ is an $(\alpha,\beta)$-regular set of $G$.

We present an overview of the LIGHTS (LBT Imaging of Galactic Halos and Tidal Structures) survey, which currently includes 25 nearby galaxies that are on average $\sim$ 1 mag fainter than the Milky Way, and a catalog of 54 low central surface brightness (24 $< \mu_{0,g}$/mag arcsec$^{-2} < 28$) satellite galaxy candidates, most of which were previously uncatalogued. The depth of the imaging exceeds the full 10-year depth of the Rubin Observatory's Legacy Survey of Space and Time (LSST). We find, after applying completeness corrections, rising numbers of candidate satellites as we approach the limiting luminosity (M$_r \sim -8$ mag) and central surface brightness ($\mu_{0,g} \sim 28$ mag arcsec$^{-2}$). Over the parameter range we explore, each host galaxy (excluding those that are in overdense regions, apparently groups) has nearly 4 such candidate satellites to a projected radius of $\sim$ 100 kpc. These objects are mostly just at or beyond the reach of spectroscopy unless they are H I rich or have ongoing star formation. We identify 3, possibly 4, ultra-diffuse satellite galaxies (UDGs; effective radius $ > 1.5$ kpc). This incidence rate falls within expectations of the extrapolation of the published relationship between the number of UDGs and host halo mass. Lastly, we visually identify 12 candidate satellites that host a nuclear star cluster (NSC). The NSC occupation fraction for the sample (12/54) matches that published for satellites of early-type galaxies, suggesting that the parent's morphological type plays at most a limited role in determining the NSC occupation fraction., Comment: 26 pages, accepted for publication in AJ

Commercially impactful quantum algorithms such as quantum chemistry and Shor's algorithm require a number of qubits and gates far beyond the capacity of any existing quantum processor. Distributed architectures, which scale horizontally by networking modules, provide a route to commercial utility and will eventually surpass the capability of any single quantum computing module. Such processors consume remote entanglement distributed between modules to realize distributed quantum logic. Networked quantum computers will therefore require the capability to rapidly distribute high fidelity entanglement between modules. Here we present preliminary demonstrations of some key distributed quantum computing protocols on silicon T centres in isotopically-enriched silicon. We demonstrate the distribution of entanglement between modules and consume it to apply a teleported gate sequence, establishing a proof-of-concept for T centres as a distributed quantum computing and networking platform., Comment: 14 pages, 13 figures

The discovery of interstellar comet 2I/Borisov offered the unique opportunity to obtain a detailed analysis of an object coming from another planetary system, and leaving behind material in our interplanetary space. We continuously observed 2I/Borisov between October 3 and December 13, 2019 using the 1.52-m Telescopio Carlos S\'{a}nchez equipped with MuSCAT2 instrument, and the 2.54-m Isaac Newton Telescope with Wide Field Camera. We characterize its morphology and spectro-photometric features using the data gathered during this extended campaign. Simultaneous imaging in four bands ($g$, $r$, $i$, and $z_s$) reveals a homogeneous composition and a reddish hue, resembling Solar System comets, and as well a diffuse profile exhibiting familiar cometary traits. We discern a stationary trend fluctuating around a constant activity level throughout October and November 2019. Subsequently, a reduction in activity is observed in December. Dust production and mass loss calculations indicate approximately an average of 4 kg/s before perihelion, while after perihelion the net mass loss is about 0.6 kg/s. Our simulations indicate the most probable size of coma dust particles should be in the range 200-250 nm, and the terminal speed around 300 m/s. The spectrum acquired with the 4.2-m William Herschel Telescope shows the presence of a strong CN line for which we find a gas production rate of $1.2 \times 10^{24}~s^{-1}$. We also detected NH$_2$ and OI bands. The ratio between NH$_2$ and CN productions is $\log (NH_2/CN) =-0.2$. Overall, this observing campaign provides a new understanding of 2I/Borisov's unique characteristics and activity patterns., Comment: accepted to MNRAS on 12th Feb 2024

Dynamic wavefront aberrations negatively impact a wide range of optical applications including astronomy, optical free-space telecommunications and bio-imaging. Wavefront errors can be compensated by an adaptive optics system comprised of a deformable mirror and wavefront sensor connected by a control loop. For satellite optical communications (SatCom), wavefront sensing is particularly challenging due to the rapid wavefront fluctuations induced by strong turbulence and movement of the transmitting satellite across the sky. Existing wavefront sensing techniques require fast cameras (>kHz) that are not widely available at wavelengths suitable for SatCom (e.g., 1550nm and mid-to-long wave infrared). Here, we propose a new wavefront sensing technique that uses a single photodiode and a fast mirror to make phase-diverse intensity measurements of the incoming wavefront. We train neural networks to accurately estimate the input phase given this phase-diverse sub-millisecond intensity trace. Our simulations show that our technique is robust in cases of strong turbulence where previous modal wavefront sensors fail due to modal crosstalk, achieving 99% of the optimal Strehl ratio from a 50-mode correction at a sensing rate of 2kHz. We explore typical cases of turbulence magnitude, sensing speed and noise that might be encountered by such a system., Comment: We discovered issues with the training data that biased the results in this manuscript. This work is being updated and a revised manuscript will be posted at a later date

Radial profiles play a crucial role in the analysis and interpretation of astronomical data, facilitating the extraction of spatial information. However, highly customizable (for different scenarios) measurements over each elliptical annulus can be challenging. In response, we present 'astscript-radial-profile', which is part of Gnuastro from version 0.15 and has an extensive documentation. A convenient feature of this program is its capability to make the measurements with different operators (mean, median, sigma-clipping, and many more) over ellipses, very quickly and directly on the command-line with minimal dependencies. This research note is reproducible with Maneage, on the Git commit 104aad5., Comment: Accepted RNAAS. Supplementary data on Zenodo (https://doi.org/10.5281/zenodo.10124582), project source on Codeberg (https://codeberg.org/gnuastro/papers/src/branch/radial-profile) and archived on Software Heritage (swh:1:dir:d5029e066916cb64f0d95d20eb88294acc78b2b1)

Color plays a crucial role in the visualization, interpretation, and analysis of multi-wavelength astronomical images. However, generating color images that accurately represent the full dynamic range of astronomical sources is challenging. In response, Gnuastro v0.22 introduces the program 'astscript-color-faint-gray', which is extensively documented in the Gnuastro manual. It employs a non-linear transformation to assign an 8-bit RGB (Red-Green-Blue) value to brighter pixels, while the fainter ones are shown in an inverse grayscale. This approach enables the simultaneous visualization of low surface brightness features within the same image. This research note is reproducible with Maneage, on the Git commit 48f5408., Comment: Accepted RNAAS. Supplementary data on Zenodo (https://doi.org/10.5281/zenodo.10058165), project source on Codeberg (https://codeberg.org/gnuastro/papers/src/branch/color-faint-gray) and archived on Software Heritage (swh:1:dir:1064a48d4bb58d6684c3df33c6633a04d4141d2d)

Gcharacter tables of a finite group G were defined before. These tables can be very useful to obtain certain structural information of a normal subgroup from the character table of G. We analyze certain structural properties of normal subgroups which can be determined using their Gcharacter tables. For instance, we prove an extension of the Thompsons theorem from minimal Ginvariant characters of a normal subgroup. We also obtain a variation of Taketas theorem for hypercentral normal subgroups considering their minimal G-invariant characters. This generalization allows us to introduce a new class of nilpotent groups, the class of nMIgroups, whose members verify that its nilpotency class is bounded by the number of irreducible character degrees of the group.

We have investigated the properties (e.g., age, metallicity) of the stellar populations of a ring-like tidal stellar stream (or streams) around the edge-on galaxy SPRC047 (z = 0.031) using spectral energy distribution (SED) fits to integrated broad-band aperture flux densities. We used visual images in six different bands and Spitzer/IRAC 3.6 micron data. We have attempted to derive best-fit stellar population parameters (metallicity, age) in three non-contiguous segments of the stream. Due to the very low surface brightness of the stream, we have performed a deconvolution with a Richardson-Lucy type algorithm of the low spatial resolution 3.6 micron IRAC image, thereby reducing the effect of the point-spread-function (PSF) aliased "emission" from the bright edge-on central galaxy at the locations of our three stream segments. Our SED fits that used several different star formation history priors, from an exponentially decaying star formation burst to continuous star formation, indicate that the age-metallicity-dust degeneracy is not resolved, most likely because of inadequate wavelength coverage and low signal-to-noise ratios of the low surface brightness features. We also discuss how future deep visual-near-infrared observations, combined with absolute flux calibration uncertainties at or below the 1 per cent level, complemented by equally well absolute flux calibrated observations in ultraviolet and mid-infrared bands, would improve the accuracy of broad-band SED fitting results for low surface brightness targets, such as stellar streams around nearby galaxies that are not resolved into stars., Comment: Accepted for publication in the Astrophysical Journal

Calibration of pixel values is a fundamental step for accurate measurements in astronomical imaging. In astronomical jargon this is known as estimating zero point magnitude. Here, we introduce a newly added script in GNU Astronomy Utilities (Gnuastro) version 0.20 for the zero point magnitude estimation, named: astscript-zeropoint. The script offers numerous features, such as the flexibility to use either image(s) or a catalog as the reference dataset. Additionally, steps are parallelized to enhance efficiency for big data. Thanks to Gnuastro's minimal dependencies, the script is both flexible and portable. The figures of this research note are reproducible with Maneage, on the Git commit c89275e., Comment: Supplementary data on Zenodo (https://doi.org/10.5281/zenodo.10256845), project source on Codeberg (https://codeberg.org/gnuastro/papers/src/branch/zeropoint) and archived on Software Heritage (swh:1:dir:8b2d1f63be96de3de03aa3e2bb68fa7fa52df56f; see text for usage)

We present a new method for obtaining photometric redshifts (photo-z) for sources observed by multiple photometric surveys using a combination (conflation) of the redshift probability distributions (PDZs) obtained independently from each survey. The conflation of the PDZs has several advantages over the usual method of modelling all the photometry together, including modularity, speed, and accuracy of the results. Using a sample of galaxies with narrow-band photometry in 56 bands from J-PAS and deeper grizy photometry from the Hyper-SuprimeCam Subaru Strategic program (HSC-SSP), we show that PDZ conflation significantly improves photo-z accuracy compared to fitting all the photometry or using a weighted average of point estimates. The improvement over J-PAS alone is particularly strong for i>22 sources, which have low signal-to-noise ratio in the J-PAS bands. For the entire i<22.5 sample, we obtain a 64% (45%) increase in the number of sources with redshift errors |Dz|<0.003, a factor 3.3 (1.9) decrease in the normalised median absolute deviation of the errors (sigma_NMAD), and a factor 3.2 (1.3) decrease in the outlier rate compared to J-PAS (HSC-SSP) alone. The photo-z accuracy gains from combining the PDZs of J-PAS with a deeper broadband survey such as HSC-SSP are equivalent to increasing the depth of J-PAS observations by ~1.2--1.5 magnitudes. These results demonstrate the potential of PDZ conflation and highlight the importance of including the full PDZs in photo-z catalogues., Comment: 15 pages, 16 figures, 1 table. Accepted for publication in A&A

The pointing pattern is an integral part of designing one's observation strategy for a certain scientific goal. But accounting for the particular science case or instrument artifacts (like distortion, vignetting or large areas of bad pixels) can make it hard to predict how the exposure map of the final stack will be. To help address this problem, Gnuastro 0.21 includes a new executable program called astscript-pointing-simulate that is fully described in the Gnuastro manual and comes with a complete tutorial. The figures of this research note are reproducible with Maneage, on the Git commit 4176d29.