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We study several natural decision problems in braid groups and Artin groups. We classify the Artin groups with decidable submonoid membership problem in terms of the non-existence of certain forbidden induced subgraphs of the defining graph. Furthermore, we also classify the Artin groups for which the following problems are decidable: the rational subset membership problem, semigroup intersection problem, and the fixed-target submonoid membership problem. In the case of braid groups our results show that the submonoid membership problem, and each and every one of these problems, is decidable in the braid group $\mathbf{B}_n$ if and only if $n \leq 3$, which answers an open problem of Potapov (2013). Our results also generalize and extend results of Lohrey & Steinberg (2008) who classified right-angled Artin groups with decidable submonoid (and rational subset) membership problem., Comment: 20 pages. Comments welcome!

The purpose of this paper is to introduce a new family of semigroups - the free projection-generated regular $*$-semigroups - and initiate their systematic study. Such a semigroup $PG(P)$ is constructed from a projection algebra $P$, using the recent groupoid approach to regular $*$-semigroups. The assignment $P\mapsto PG(P)$ is a left adjoint to the forgetful functor that maps a regular $*$-semigroup $S$ to its projection algebra $P(S)$. In fact, the category of projection algebras is coreflective in the category of regular $*$-semigroups. The algebra $P(S)$ uniquely determines the biordered structure of the idempotents $E(S)$, up to isomorphism, and this leads to a category equivalence between projection algebras and regular $*$-biordered sets. As a consequence, $PG(P)$ can be viewed as a quotient of the classical free idempotent-generated (regular) semigroups $IG(E)$ and $RIG(E)$, where $E=E(PG(P))$; this is witnessed by a number of presentations in terms of generators and defining relations. The semigroup $PG(P)$ can also be viewed as the fundamental groupoid of a simplicial complex explicitly constructed from $P$. The theory is then illustrated on a number of examples. In one direction, the free construction applied to the projection algebras of adjacency semigroups yields a new family of graph-based path semigroups. In another, it turns out that, remarkably, the Temperley-Lieb monoid $TL_n$ is the free regular $*$-semigroup over its own projection algebra $P(TL_n)$., Comment: 48 pages, 7 figures, 4 tables

We use 3D computer modelling to investigate the timescales and radiative output from maser flares generated by the impact of shock-waves on astronomical unit-scale clouds in interstellar and star-forming regions, and in circumstellar regions in some circumstances. Physical conditions are derived from simple models of isothermal hydrodynamic (single-fluid) and C-type (ionic and neutral fluid) shock-waves, and based on the ortho-H$_2$O 22-GHz transition. Maser saturation is comprehensively included, and we find that the most saturated maser inversions are found predominantly in the shocked material. We study the effect on the intensity, flux density and duration of flares of the following parameters: the pre-shock level of saturation, the observer's viewpoint, and the shock speed. Our models are able to reproduce observed flare rise times of a few times 10 days, specific intensities of up to 10$^5$ times the saturation intensity and flux densities of order $100(R/d)^2$Jy from a source of radius $R$ astronomical units at a distance of $d$ kiloparsec. We found that flares from C-type shocks are approximately 5 times more likely to be seen by a randomly placed observer than flares from hydrodynamically shocked clouds of similar dimensions. We computed intrinsic beaming patterns of the maser emission, finding substantial extension of the pattern parallel to the shock front in the hydrodynamic models. Beaming solid angles for hydrodynamic models can be as small as $1.3\times 10^{-5}$sr, but are an order of magnitude larger for C-type models., Comment: Accepted for publication in MNRAS - 27 pages, 21 figures, 2 Tables

The water molecule is a key ingredient in the formation of planetary systems, with the water snowline being a favourable location for the growth of massive planetary cores. Here we present Atacama Large Millimeter/ submillimeter Array data of the ringed protoplanetary disk orbiting the young star HL Tauri that show centrally peaked, bright emission arising from three distinct transitions of the main water isotopologue. The spatially and spectrally resolved water content probes gas in a thermal range down to the water sublimation temperature. Our analysis implies a stringent lower limit of 3.7 Earth oceans of water vapour available within the inner 17 astronomical units of the system. We show that our observations are limited to probing the water content in the atmosphere of the disk, due to the high dust column density and absorption, and indicate that the main water isotopologue is the best tracer to spatially resolve water vapour in protoplanetary disks., Comment: Published in Nature Astronomy (2024), arXiv version presents text and figures before proofing

Previous work has shown that time-reversal symmetric Weyl semimetals with a quadrupolar arrangement of first-order Weyl nodes exhibit a mixed crystalline-electromagnetic response. For systems with higher order Weyl nodes, which are attached to both surface and hinge Fermi arcs, additional phenomena appear on surfaces of codimension $n>1$, such as electromagnetic responses of the hinges. Here we construct a model possessing a quadrupole of higher order Weyl nodes to study the interplay between higher order topology and mixed crystalline-electromagnetic responses. We show that the higher order nature of the Weyl nodes yields a dipole of Dirac nodes on certain surfaces, leading to a mixed crystalline-electromagnetic \emph{surface} response that binds charge to dislocations and momentum-density to magnetic fields. In addition, we show that the model possesses a bulk quadrupole moment of crystal-momentum that provides a link between the bulk and surface responses of the system.

We continue the study of the structure of general subgroups (in particular maximal subgroups, also known as group $\mathcal{H}$-classes) of special inverse monoids. Recent research of the authors has established that these can be quite wild, but in this paper we show that if we restrict to special inverse monoids which are $E$-unitary (or have a weaker property we call $\mathcal{R}_1$-injectivity), the maximal subgroups are strongly governed by the group of units. In particular, every maximal subgroup has a finite index subgroup which embeds in the group of units. We give a construction to show that every finite group can arise as a maximal subgroup in an $\mathcal{R}_1$-injective special inverse monoid with trivial group of units. It remains open whether every combination of a group $G$ and finite index subgroup $H$ can arise as maximal subgroup and group of units., Comment: 32 pages, 10 figures. V2: additional example added to Section 6, new result added to the end of Section 7, some additional figures added and some minor corrections made

Motivated by approaches to the word problem for one-relation monoids arising from work of Adian and Oganesian (1987), Guba (1997), and Ivanov, Margolis and Meakin (2001), we study the submonoid and rational subset membership problems in one-relation monoids and in positive one-relator groups. We give the first known examples of positive one-relator groups with undecidable submonoid membership problem, and apply this to give the first known examples of one-relation monoids with undecidable submonoid membership problem. We construct several infinite families of one-relation monoids with undecidable submonoid membership problem, including examples that are defined by relations of the form $w=1$ but which are not groups, and examples defined by relations of the form $u=v$ where both of $u$ and $v$ are non-empty. As a consequence we obtain a classification of the right-angled Artin groups that can arise as subgroups of one-relation monoids. We also give examples of monoids with a single defining relation of the form $aUb = a$, and examples of the form $aUb=aVa$, with undecidable rational subset membership problem. We give a one-relator group defined by a freely reduced word of the form $uv^{-1}$ with $u, v$ positive words, in which the prefix membership problem is undecidable. Finally, we prove the existence of a special two-relator inverse monoid with undecidable word problem, and in which both the relators are positive words. As a corollary, we also find a positive two-relator group with undecidable prefix membership problem. In proving these results, we introduce new methods for proving undecidability of the rational subset membership problem in monoids and groups, including by finding suitable embeddings of certain trace monoids., Comment: 33 pages, 1 figure; incorporates referee's suggestions

Water and the hydroxyl radical are major constituents of the envelope of O-rich late-type stars. Transitions involving energy levels that are highly excited have been observed in both H$_2$O and OH. These and more recently discovered transitions can now be observed at a high sensitivity and angular resolution with the ALMA Array. Spectra and maps of H$_2$O and OH observed with an angular resolution of 20 to $\sim$200 mas were obtained at two epochs with the ALMA array. Observations with the Compact Array were also used to check for time variability of water transitions. Radiative transfer models of water were revisited to characterize masing conditions and up-to-date chemical models were used for comparison with our observations. Ten rotational transitions of H$_2$O with energies up to 9000 K were observed in various vibrational states. All but one are new detections in space, and from these we have derived accurate rest frequencies. Hyperfine split $\Lambda$-doubling transitions in v = 0, J = 27/2 and 29/2 levels of the $^2\Pi_{3/2}$ state and, $J = 33/2$ and 35/2 of the $^2\Pi_{1/2}$ state of OH with excitation energies up to 8900 K were also observed. Four of these transitions are new detections in space. Combining our measurements with earlier observations of OH, the v = 0 and v = 1 $\Lambda$-doubling frequencies have been improved. Our H$_2$O maps show compact emission and extensions up to twelve stellar radii or more. The 268.149 GHz emission line of water in the v$_2$ = 2 state is time variable, tends to be masing with dominant radiative pumping, and is widely excited. The widespread but weaker 262.898 GHz water line in v$_2$ = 1 also shows signs of maser emission. Emission and absorption of both H$_2$O and OH reveal an infall of matter and complex kinematics influenced by binarity. From our observed column densities, we derived OH/H$_2$O abundance ratios in a few stars., Comment: 41 pages with references and 25 figures in main text. 4 Tables in Appendix A. 10 figures in Appendix B. 2 figures in Appendix C. 14 figures in Appendix D. 5 figures in Appendix E. 2 figures in Appendix F

A prefix monoid is a finitely generated submonoid of a finitely presented group generated by the prefixes of its defining relators. Important results of Guba (1997), and of Ivanov, Margolis and Meakin (2001), show how the word problem for certain one-relator monoids, and inverse monoids, can be reduced to solving the membership problem in prefix monoids of certain one-relator groups. Motivated by this, in this paper we study the class of prefix monoids of finitely presented groups. We obtain a complete description of this class of monoids. All monoids in this family are finitely generated, recursively presented and group-embeddable. Our results show that not every finitely generated recursively presented group-embeddable monoid is a prefix monoid, but for every such monoid if we take a free product with a suitably chosen free monoid of finite rank, then we do obtain a prefix monoid. Conversely we prove that every prefix monoid arises in this way. Also, we show that the groups that arise as groups of units of prefix monoids are precisely the finitely generated recursively presented groups, while the groups that arise as Sch\"utzenberger groups of prefix monoids are exactly the recursively enumerable subgroups of finitely presented groups. We obtain an analogous result classifying the Sch\"utzenberger groups of monoids of right units of special inverse monoids. We also give some examples of right cancellative monoids arising as monoids of right units of finitely presented special inverse monoids, and show that not all right cancellative recursively presented monoids belong to this class., Comment: 22 pages

Aims. Through the ATOMIUM project, based on an ALMA large program, we aim to present a consistent view of a sample of 17 nearby cool evolved stars (Aymptotic Giant Branch and red supergiant stars). Methods. Here we present VLT/SPHERE-ZIMPOL polarimetric maps obtained in the visible of 14 out of the 17 ATOMIUM sources. They were obtained contemporaneously with the ALMA high spatial resolution data. To help interpret the polarized signal, we produced synthetic maps of light scattering by dust, through 3D radiative transfer simulations with the RADMC3D code. Results. The degree of linear polarization (DoLP) observed by ZIMPOL spreads across several optical filters. We infer that it primarily probes dust located just outside of the point spread function, and in or near the plane of the sky, with a total optical depth close to unity in the line of sight, representing only a fraction of the total circumstellar dust. The maximum DoLP ranges from 0.03-0.38 depending on the source, fractions that can be reproduced by our 3D pilot models for grains composed of common dust species. The spatial structure of the DoLP shows a diverse set of shapes. Only for three sources do we note a correlation between the ALMA CO and SiO lines, which trace the gas density, and the DoLP, which traces the dust. Conclusion. The clumpiness of the DoLP and the lack of a consistent correlation between the gas and the dust location show that, in the inner circumstellar environment (CSE), dust formation occurs at very specific sites. This has potential consequences for the derived mass-loss rates and dust-to-gas ratio in the inner region of the CSE. Except for $\pi^1$~Gru and perhaps GY Aql, we do not detect interactions between the circumstellar wind and the hypothesized companions that shape the wind at larger scales. This suggests that the orbits of any other companions are tilted out of the plane of the sky., Comment: Accepted for publication in Astronomy & Astrophysics. 22 pages, 15 figures, 5 tables

We study the maximal subgroups (also known as group $\mathcal{H}$-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and moreover every such maximal subgroup can also arise in the $E$-unitary case. We also prove that the possible groups of units are exactly the finitely generated recursively presented groups; this improves upon a result of, and answers a question of, the first author and Ru\v{s}kuc. These results give the first significant insight into the maximal subgroups of such monoids beyond the group of units, and the results together demonstrate that it is possible for the subgroup structure to have a complexity which significantly exceeds that of the group of units. We also observe that a finitely presented special inverse monoid (even an $E$-unitary one) may have infinitely many pairwise non-isomorphic maximal subgroups., Comment: 25 pages, 2 figures; incorporates referee's suggestions including minor changes to the title and abstract

We discuss studies of polarization in astrophysical masers with particular emphasis on the case where the Zeeman splitting is small compared to the Doppler profile, resulting in a blend of the transitions between magnetic substates. A semi-classical theory of the molecular response is derived, and coupled to radiative transfer solutions for 1 and 2-beam linear masers, resulting in a set of non-linear, algebraic equations for elements of the molecular density matrix. The new code, PRISM, implements numerical methods to compute these solutions. Using PRISM, we demonstrate a smooth transfer between this case and that of wider splitting. For a J=1-0 system, with parameters based on the $v=1, J=1-0$ transition of SiO, we investigate the behaviour of linear and circular polarization as a function of the angle between the propagation axis and the magnetic field, and with the optical depth, or saturation state, of the model. We demonstrate how solutions are modified by the presence of Faraday rotation, generated by various abundances of free electrons, and that strong Faraday rotation leads to additional angles where Stokes-Q changes sign. We compare our results to a number of previous models, from the analytical limits derived by Goldreich, Keeley and Kwan in 1973, through computational results by W. Watson and co-authors, to the recent work by Lankhaar and Vlemmings in 2019. We find that our results are generally consistent with those of other authors given the differences of approach and the approximations made., Comment: 36 pages, 15 figures. Accepted for publication in ApJ

This White Paper summarises potential key science topics to be achieved with Thai National Radio Telescope (TNRT). The commissioning phase has started in mid 2022. The key science topics consist of "Pulsars and Fast Radio Bursts (FRBs)", "Star Forming Regions (SFRs)", "Galaxy and Active Galactic Nuclei (AGNs)", "Evolved Stars", "Radio Emission of Chemically Peculiar (CP) Stars", and "Geodesy", covering a wide range of observing frequencies in L/C/X/Ku/K/Q/W-bands (1-115 GHz). As a single-dish instrument, TNRT is a perfect tool to explore time domain astronomy with its agile observing systems and flexible operation. Due to its ideal geographical location, TNRT will significantly enhance Very Long Baseline Interferometry (VLBI) arrays, such as East Asian VLBI Network (EAVN), Australia Long Baseline Array (LBA), European VLBI Network (EVN), in particular via providing a unique coverage of the sky resulting in a better complete "uv" coverage, improving synthesized-beam and imaging quality with reducing side-lobes. This document highlights key science topics achievable with TNRT in single-dish mode and in collaboration with VLBI arrays., Comment: 75 pages, 16 figures, 15 tables. White Paper for Potential Key Sciences to be Achieved with Thai National Radio Telescope (TNRT)

Learning to detect objects, such as humans, in imagery captured by an unmanned aerial vehicle (UAV) usually suffers from tremendous variations caused by the UAV's position towards the objects. In addition, existing UAV-based benchmark datasets do not provide adequate dataset metadata, which is essential for precise model diagnosis and learning features invariant to those variations. In this paper, we introduce Archangel, the first UAV-based object detection dataset composed of real and synthetic subsets captured with similar imagining conditions and UAV position and object pose metadata. A series of experiments are carefully designed with a state-of-the-art object detector to demonstrate the benefits of leveraging the metadata during model evaluation. Moreover, several crucial insights involving both real and synthetic data during model optimization are presented. In the end, we discuss the advantages, limitations, and future directions regarding Archangel to highlight its distinct value for the broader machine learning community., Comment: IEEE Access

There are indications that the third known eruption of the recurrent nova T CrB is imminent, and multi-wavelength observations prior to the eruption are important to characterise the system before it erupts. T CrB is known to display the SiO fundamental vibrational feature at 8$\,\mu$m. When the anticipated eruption occurs, it is possible that the shock produced when the ejected material runs into the wind of the red giant in the system may be traced using SiO maser emission. We have used the 100m Effelsberg Radio Telescope to search for $^{28}$SiO emission in the $\upsilon=1$, $\upsilon=2$, $J=1\rightarrow0$ transitions, at 43.122 GHz and 42.820~GHz respectively, while the system is in quiescence. We find no evidence for such emission., Comment: Published in MNRAS, 514, 4894 - 4897 (2022)

The Galactic interstellar medium hosts a significant magnetic field, which can be probed through the synchrotron emission produced from its interaction with relativistic electrons. Linearly polarized synchrotron emission is generated throughout the Galaxy, and at longer wavelengths, modified along nearly every path by Faraday rotation in the intervening magneto-ionic medium. Full characterization of the polarized emission requires wideband observations with many frequency channels. We have surveyed polarized radio emission from the Northern sky over the the range 1280-1750 MHz, with channel width 236.8 kHz, using the John A. Galt Telescope (diameter 25.6 m) at the Dominion Radio Astrophysical Observatory, as part of the Global Magneto-Ionic Medium Survey. The survey covered 72% of the sky, declinations -30 to +87 degrees at all right ascensions. The intensity scale was absolutely calibrated, based on the flux density and spectral index of Cygnus A. Polarization angle was calibrated using the extended polarized emission of the Fan Region. Data are presented as brightness temperatures with angular resolution 40'. Sensitivity in Stokes Q and U is 45 mK rms in a 1.18 MHz band. We have applied rotation measure synthesis to the data to obtain a Faraday depth cube of resolution 150 radians per square metre and sensitivity 3 mK rms of polarized intensity. Features in Faraday depth up to a width of 110 radians per square metre are represented. The maximum detectable Faraday depth is +/- 20,000 radians per square metre. The survey data are available at the Canadian Astronomy Data Centre., Comment: Accepted for publication in the Astronomical Journal

Evolved low- to intermediate-mass stars are known to shed their gaseous envelope into a large, dusty, molecule-rich circumstellar nebula which typically develops a high degree of structural complexity. Most of the large-scale, spatially correlated structures in the nebula are thought to originate from the interaction of the stellar wind with a companion. As part of the Atomium large programme, we observed the M-type asymptotic giant branch (AGB) star R Hydrae with ALMA. The morphology of the inner wind of R Hya, which has a known companion at ~3500 au, was determined from maps of CO and SiO obtained at high angular resolution. A map of the CO emission reveals a multi-layered structure consisting of a large elliptical feature at an angular scale of ~10'' that is oriented along the north-south axis. The wind morphology within the elliptical feature is dominated by two hollow bubbles. The bubbles are on opposite sides of the AGB star and lie along an axis with a position angle of ~115 deg. Both bubbles are offset from the central star, and their appearance in the SiO channel maps indicates that they might be shock waves travelling through the AGB wind. An estimate of the dynamical age of the bubbles yields an age of the order of 100 yr, which is in agreement with the previously proposed elapsed time since the star last underwent a thermal pulse. When the CO and SiO emission is examined on subarcsecond angular scales, there is evidence for an inclined, differentially rotating equatorial density enhancement, strongly suggesting the presence of a second nearby companion. The position angle of the major axis of this disc is ~70 deg in the plane of the sky. We tentatively estimate that a lower limit on the mass of the nearby companion is ~0.65 Msol on the basis of the highest measured speeds in the disc and the location of its inner rim at ~6 au from the AGB star., Comment: 21 pages, 23 figures

We investigate the groups of units of one-relator and special inverse monoids. These are inverse monoids which are defined by presentations where all the defining relations are of the form $r=1$. We develop new approaches for finding presentations for the group of units of a special inverse monoid, and apply these methods to give conditions under which the group admits a presentation with the same number of defining relations as the monoid. In particular our results give sufficient conditions for the group of units of a one-relator inverse monoid to be a one-relator group. When these conditions are satisfied these results give inverse semigroup theoretic analogues of classical results of Adjan for one-relator monoids, and Makanin for special monoids. In contrast, we show that in general these classical results do not hold for one-relator and special inverse monoids. In particular, we show that there exists a one-relator special inverse monoid whose group of units is not a one-relator group (with respect to any generating set), and we show that there exists a finitely presented special inverse monoid whose group of units is not finitely presented., Comment: 40 pages, 1 figure

Faraday rotation provides a valuable tracer of magnetic fields in the interstellar medium; catalogs of Faraday rotation measures provide key observations for studies of the Galactic magnetic field. We present a new catalog of rotation measures derived from the Canadian Galactic Plane Survey, covering a large region of the Galactic plane spanning 52 deg < l < 192 deg, -3 deg < b < 5 deg, along with northern and southern latitude extensions around l ~ 105 deg. We have derived rotation measures for 2234 sources (4 of which are known pulsars), 75% of which have no previous measurements, over an area of approximately 1300 square degrees. These new rotation measures increase the measurement density for this region of the Galactic plane by a factor of two., Comment: 16 pages, 6 figures and 3 tables. Accepted by ApJS. Catalog available as ancillary data

This article concerns Ehresmann structures in the partition monoid $P_X$. Since $P_X$ contains the symmetric and dual symmetric inverse monoids on the same base set $X$, it naturally contains the semilattices of idempotents of both submonoids. We show that one of these semilattices leads to an Ehresmann structure on $P_X$ while the other does not. We explore some consequences of this (structural/combinatorial and representation theoretic), and in particular characterise the largest left-, right- and two-sided restriction submonoids. The new results are contrasted with known results concerning relation monoids, and a number of interesting dualities arise, stemming from the traditional philosophies of inverse semigroups as models of partial symmetries (Vagner and Preston) or block symmetries (FitzGerald and Leech): "surjections between subsets" for relations become "injections between quotients" for partitions. We also consider some related diagram monoids, including rook partition monoids, and state several open problems., Comment: v2: 27 pages, 8 figures; incorporates referee's report; to appear in J Algebra. v1: 23 pages, 7 figures

We present new molecular modelling for 14NO and 15NO and a deep, blind molecular line survey at low radio frequencies (99-129 MHz). This survey is the third in a series completed with the Murchison Widefield Array (MWA), but in comparison with the previous surveys, uses four times more data (17 hours vs. 4 hours) and is three times better in angular resolution (1' vs. 3'). The new molecular modelling for nitric oxide and its main isotopologue has seven transitions within the MWA frequency band (although we also present the higher frequency transitions). Although we did not detect any new molecular lines at a limit of 0.21 Jy beam^-1, this work is an important step in understanding the data processing challenges for the future Square Kilometre Array (SKA) and places solid limits on what is expected in the future of low-frequency surveys. The modelling can be utilised for future searches of nitric oxide., Comment: 13 pages, 5 figures, 1 table, accepted by Astrophysical Journals (ApJ)

A 3D maser model has been used to perform an inverse problem on the light curves from three high-amplitude maser flares, selected on the basis of contemporaneous infra-red observations. Plots derived from the model recover the size of the maser cloud, and two parameters linked to saturation, from three observational properties of the light curve. Recovered sizes are consistent with independent interferometric measurements. Maser objects transition between weak and moderate saturation during a flare., Comment: 5 pages, 5 figures, accepted for publication in MNRAS

We give a topological proof that a free inverse monoid on one or more generators is neither of type left-$FP_2$ nor right-$FP_2$. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids., Comment: 5 pages, 1 figure, This article was originally part of our paper arXiv:1805.03413, and has now been extracted as this short note

We simulate maser flares by varying either the pump rate or the background level of radiation in a 3D model of a maser cloud. We investigate the effect of different cloud shapes, saturation levels and viewpoints. Results are considered for clouds with both uniform and internally variable unsaturated inversion. Pumping and background variations are represented by several different driving functions, some of which are light curves drawn from observations. We summarise the pumping variability results in terms of three observable parameters, the maximum flux density achieved, a variability index and duty cycle. We demonstrate typical ranges of the flux density that may result from viewing an aspherical object from random viewpoints. The best object for a flare is a prolate cloud, viewed close to its long axis and driven from unsaturated conditions to at least modest saturation. Results for variation of the background level are qualitatively different from the variable pumping results in that they tend to produce short intervals of low flux density under conditions of moderate saturation and sufficient variability to be consistent with strong flaring. Variable background models typically have a significantly higher duty cycle than those with variable pumping., Comment: 19 pages, 15 figures, accepted for publication in MNRAS