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Hydrodynamical (or 3D) and non-local thermodynamic equilibrium (NLTE) effects are known to affect abundance analyses. However, there are very few observational abundance testsof 3D and NLTE models. We developed a new way of testing the abundance predictions of 3D and NLTE models, taking advantage of large spectroscopic survey data. We use a line-by-line analysis of the Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectra (H band) with the Brussels Automatic Code for Characterizing High accUracy Spectra (BACCHUS). We compute line-by-line abundances of Mg, Si, Ca, and Fe for a large number of globular cluster K giants in the APOGEE survey. We compare this line-by-line analysis against NLTE and 3D predictions. While the 1D-NLTE models provide corrections in the right direction, there are quantitative discrepancies between different models. We observe a better agreement with the data for the models including reliable collisional cross-sections. The agreement between data and models is not always satisfactory when the 3D spectra are computed in LTE. However, we note that for a fair comparison, 3D corrections should be computed with self-consistently derived stellar parameters, and not on 1D models with identical stellar parameters. Finally, we focus on 3D and NLTE effects on Fe lines in the H band, where we observe a systematic difference in abundance relative to the value from the optical. Our results suggest that the metallicities obtained from the H band are more accurate in metal-poor giants. More atomic data and extended self-consistent 3D-NLTE computations need to be made. The method we have developed for testing 3D and NLTE models could be extended to other lines and elements, and is particularly suited for large spectroscopic surveys., Comment: 13 pages, 9 figures, accepted in A&A

Let $\mathcal{C}(n,k)$ be the set of $k$-dimensional simplicial complexes $C$ over a fixed set of $n$ vertices such that: (1) $C$ has a complete $k-1$-skeleton; (2) $C$ has precisely ${{n-1}\choose {k}}$ $k$-faces; (3) the homology group $H_{k-1}(C)$ is finite. Consider the probability measure on $\mathcal{C}(n,k)$ where the probability of a simplicial complex $C$ is proportional to $|H_{k-1}(C)|^2$. For any fixed $k$, we determine the local weak limit of these random simplicial complexes as $n$ tends to infinity. This local weak limit turns out to be the same as the local weak limit of the $1$-out $k$-complexes investigated by Linial and Peled.

The timing-based localization, which utilize the triangulation principle with the different arrival time of gamma-ray photons, with a fleet of Cubesats is a unique and powerful solution for the future all-sky gamma-ray observation, which is a key for identification of the electromagnetic counterpart of the gravitational wave sources. The Cubesats Applied for MEasuring and Localising Transients (CAMELOT) mission is now being promoted by the Hungarian and Japanese collaboration with a basic concept of the nine Cubesats constellations in low earth orbit. The simulation framework for estimation of the localization capability has been developed including orbital parameters, an algorithm to estimate the expected observed profile of gamma-ray photons, finding the peak of the cross-correlation function, and a statistical method to find a best-fit position and its uncertainty. It is revealed that a degree-scale localization uncertainty can be achieved by the CAMELOT mission concept for bright short gamma-ray bursts, which could be covered by future large field of view ground-based telescopes. The new approach utilizing machine-learning approach is also investigated to make the procedure automated for the future large scale constellations. The trained neural network with 10$^6$ simulated light curves generated by the artificial short burst templates successfully predicts the time-delay of the real light curve and achieves a comparable performance to the cross-correlation algorithm with full automated procedures., Comment: 9 pages, 4 figures, Proceedings of SPIE "Astronomical Telescopes and Instrumentation" 2020

As a powerful source of gravitational waves (GW), a supermassive black hole (SMBH) merger may be accompanied by a relativistic jet that leads to detectable electromagnetic (EM) emission. We model the propagation of post-merger jets inside a pre-merger circumnuclear environment formed by disk winds, and calculate multi-wavelength EM spectra from the forward shock region. We show that the non-thermal EM signals from SMBH mergers are detectable up to the detection horizon of future GW facilities such as the Laser Interferometer Space Antenna (LISA). Calculations based on our model predict slowly fading transients with time delays from days to months after the coalescence, leading to implications for EM follow-up observations after the GW detection., Comment: 6 pages, 3 figures, accepted for publication in ApJL. Schematic diagrams added

The dichromatic number $\vec{\chi}(D)$ of a digraph $D$ is the smallest $k$ for which it admits a $k$-coloring where every color class induces an acyclic subgraph. Inspired by Hadwiger's conjecture for undirected graphs, several groups of authors have recently studied the containment of directed graph minors in digraphs with given dichromatic number. In this short note we improve several of the existing bounds and prove almost linear bounds by reducing the problem to a recent result of Postle on Hadwiger's conjecture., Comment: 7 pages, note

The recent detection of TeV photons from two gamma-ray bursts (GRBs), GRB 190114C and GRB 180720B, has opened a new window for multi-messenger and multi-wavelength astrophysics of high-energy transients. We study the origin of very-high-energy (VHE) $\gamma$-rays from the short GRB 160821B, for which the MAGIC Collaboration reported a $\sim 3 \sigma$ statistical significance. Short GRBs are often accompanied by extended and plateau emission, which is attributed to internal dissipation resulting from activities of a long-lasting central engine, and Murase et al. (2018) recently suggested the external inverse-Compton (EIC) scenario for VHE counterparts of short GRBs and neutron star mergers. Applying this scenario to GRB 160821B, we show that the EIC flux can reach $\sim 10^{-12}\rm~erg~cm^{-2}~s^{-1}$ within a time period of $\sim 10^3 - 10^4\rm~s$, which is consistent with the MAGIC observations. EIC $\gamma$-rays expected during the extended and plateau emission will be detectable with greater significance by future detectors such as the Cherenkov Telescope Array (CTA). The resulting light curve has a distinguishable feature, where the VHE emission is predicted to reach the peak around the end of the seed emission., Comment: 6 pages, 2 figures, accepted for publication in ApJL

The detection of TeV gamma-ray bursts (GRBs) brought new opportunities for studying the physics of particle acceleration at relativistic shocks. The \hess telescopes recently observed very-high-energy (VHE) emission from a nearby low-luminosity GRB, GRB 190829A. Follow-up observations with, e.g., Swift-XRT, revealed unusual flare activities at $\sim 10^3\rm~s$, which can be caused by a long-lasting central engine. We show that the VHE emission during the H.E.S.S. observation time is naturally produced in the external inverse-Compton (EIC) scenario, where seed photons supplied by the flares or other late-time dissipation are upscattered to VHE energies by the non-thermal electrons accelerated at the external forward shock. Our calculations show that the EIC flare nearly coincides with the late-prompt flare, but extends $\sim3-4$ times longer than the duration of the late-prompt flare. The preferred kinetic energy and initial Lorentz factor used in our model are $\sim 10^{52}\rm~erg$ and $\sim 20$, respectively. Understanding the mechanisms of the VHE emission from low-luminosity GRBs will help us constrain the properties of the outflow and the central engine activities, as well as the particle acceleration mechanism., Comment: 12 pages, 6 figures, accepted for publication in ApJ. HESS data are added, figures are updated, appendix is extended, main conclusions unchanged

GRBAlpha is a 1U CubeSat mission with an expected launch date in the first half of 2021. It carries a 75 x 75 x 5 mm CsI(Tl) scintillator, read out by a dual-channel multi-pixel photon counter (MPPC) setup, to detect gamma-ray bursts (GRBs). The GRB detector is an in-orbit demonstration for the detector system on the Cubesats Applied for MEasuring and LOcalising Transients (CAMELOT) mission. While GRBAlpha provides 1/8th of the expected effective area of CAMELOT, the comparison of the observed light curves with other existing GRB monitoring satellites will allow us to validate the core idea of CAMELOT, i.e. the feasibility of timing-based localization., Comment: Submitted to the Proceedings of the SPIE for Astronomical Telescopes + Instrumentation 2020

We give a new operator formula for Grothendieck polynomials that generalizes Magyar's Demazure operator formula for Schubert polynomials. Our proofs are purely combinatorial, contrasting with the geometric and representation theoretic tools used by Magyar. We apply our formula to prove a necessary divisibility condition for a monomial to appear in a given Grothendieck polynomial., Comment: 19 pages; Added additional section in v2

Let $h(0),h(1),\dots,h(k)$ be a symmetric concave sequence. For a $(d,k)$-biregular factor graph $G$ and $x\in \{0,1\}^V$, we define the Hamiltonian \[H_G(x)=\sum_{f\in F} h\left(\sum_{v\in \partial f} x_v\right),\] where $V$ is the set of variable nodes, $F$ is the set of factor nodes. We prove that if $(G_n)$ is a large girth sequence of $(d,k)$-biregular factor graphs, then the free energy density of $G_n$ converges. The limiting free energy density is given by the Bethe-approximation.

Let $G$ be a finite tree. For any matching $M$ of $G$, let $U(M)$ be the set of vertices uncovered by $M$. Let $\mathcal{M}_G$ be a uniform random maximum size matching of $G$. In this paper, we analyze the structure of $U(\mathcal{M}_G)$. We first show that $U(\mathcal{M}_G)$ is a determinantal process. We also show that for most vertices of $G$, the process $U(\mathcal{M}_G)$ in a small neighborhood of that vertex can be well approximated based on a somewhat larger neighborhood of the same vertex. Then we show that the normalized Shannon entropy of $U(\mathcal{M}_G)$ can be also well approximated using the local structure of $G$. In other words, in the realm of trees, the normalized Shannon entropy of $U(\mathcal{M}_G)$ -- that is, the normalized logarithm of the number of maximum size matchings of $G$ -- is a Benjamini-Schramm continuous parameter. We show that $U(\mathcal{M}_G)$ is a determinantal process through establishing a new connection between $U(\mathcal{M}_G)$ and the adjacency matrix of $G$. This result sheds a new light on the well-known fact that on a tree, the number of vertices uncovered by a maximum size matching is equal to the nullity of the adjacency matrix. Some of the proofs are based on the well established method of introducing a new perturbative parameter, which we call temperature, and then define the positive temperature analogue of $\mathcal{M}_G$, the so called monomer-dimer model, and let the temperature go to zero.

We present a generic theoretical model for the structuring of a relativistic jet propagating through the ejecta of a binary neutron star merger event, introducing the effects of the neutron conversion-diffusion, which provides a baryon flux propagating transversely from the ejecta towards the jet axis. This results naturally in an increased baryon load structure of the outer jet with the approximate isotropic energy distribution $E_{iso}(\theta) \propto \theta^{-4}$, which is compatible with the first gravitational wave and short gamma-ray burst event GW170817/GRB 170817A observed at an off-axis angle of the jet., Comment: 17 pages, 10 figures, Accepted for publication in MNRAS

In this paper we investigate properties of metric projections onto specific closed and geodesically convex proper subsets of Wasserstein spaces $(\mathcal{P}_p(\mathbf{R}^d),W_p).$ When $d=1$, as $(\mathcal{P}_2(\mathbf{R}),W_2)$ is isometrically isomorphic to a flat space with a Hilbertian structure, the corresponding projection operators are expected to be nonexpansive. We give a direct proof of this fact, relying on intrinsic analysis, which also implies nonexpansiveness in certain special cases in higher dimensions. When $d>1$, we show the failure of this property in two regimes: when $p>1$ is either small enough or large enough. Finally, we prove some positive curvature properties of Wasserstein spaces $(\mathcal{P}_p(\mathbf{R}^d),W_p)$ when $d\ge 2$ and $p\in(1,+\infty)$ are arbitrary: we show that Wasserstein spaces are nowhere locally Busemann NPC spaces, and they nowhere locally satisfy the so-called projection criterion. As a corollary of the former, they have nonnegative upper Alexandrov curvature, in a precise sense that we define here. In our analysis a particular subset of probability measures having densities uniformly bounded above by a given constant plays a special role., Comment: 16 pages

Supermassive black hole (SMBH) coalescences are ubiquitous in the history of the Universe and often exhibit strong accretion activities and powerful jets. These SMBH mergers are also promising candidates for future gravitational wave detectors such as Laser Space Inteferometric Antenna (LISA). In this work, we consider neutrino counterpart emission originating from the jet-induced shocks. The physical picture is that relativistic jets launched after the merger will push forward inside the premerger disk wind material, and then they subsequently get collimated, leading to the formation of internal shocks, collimation shocks, forward shocks and reverse shocks. Cosmic rays can be accelerated in these sites and neutrinos are expected via the photomeson production process. We formulate the jet structures and relevant interactions therein, and then evaluate neutrino emission from each shock site. We find that month-to-year high-energy neutrino emission from the postmerger jet after the gravitational wave event is detectable by IceCube-Gen2 within approximately five to ten years of operation in optimistic cases where the cosmic-ray loading is sufficiently high and a mildly super-Eddington accretion is achieved. We also estimate the contribution of SMBH mergers to the diffuse neutrino intensity, and find that a significant fraction of the observed very high-energy ($E_\nu\gtrsim1$ PeV) IceCube neutrinos could originate from them in the optimistic cases. In the future, such neutrino counterparts together with gravitational wave observations can be used in a multimessenger approach to elucidate in greater detail the evolution and the physical mechanism of SMBH mergers., Comment: 17 pages, 9 figures, 1 table. Accepted for publication in PRD

We investigate hadronic and leptonic scenarios for the GeV--TeV gamma-ray emission from jets of the microquasar SS 433. The emission region of the TeV photons coincides with the X-ray knots, where electrons are efficiently accelerated. On the other hand, the optical high-density filaments are also located close to the X-ray knots, which may support a hadronic scenario. We calculate multi-wavelength photon spectra of the extended jet region by solving the transport equations for the electrons and protons. We find that both hadronic and leptonic models can account for the observational data, including the latest {\it Fermi} LAT result. The hadronic scenarios predict higher-energy photons than the leptonic scenarios, and future observations such as with the Cherenkov Telescope Array (CTA), the Large High-Altitude Air Shower Observatory (LHAASO), and the Southern Wide-field Gamma-ray Observatory (SWGO) may distinguish between these scenarios and unravel the emission mechanism of GeV--TeV gamma-rays. Based on our hadronic scenario, the analogy between microquasars and radio galaxies implies that the X-ray knot region of the radio-galaxy jets may accelerate heavy nuclei up to ultrahigh energies., Comment: 9 pages, 2 figures, 2 tables, accepted for publication in ApJ, discussion added, conclusions unchanged

High-energy neutrinos are a promising tool for identifying astrophysical sources of high and ultra-high energy cosmic rays (UHECR). Prospects of detecting neutrinos at high energies ($\gtrsim$TeV) from blazars have been boosted after the recent association of IceCube-170922A and TXS 0506+056. We investigate the high-energy neutrino, IceCube-190331A, a high-energy starting event (HESE) with a high likelihood of being astrophysical in origin. We initiated a Swift/XRT and UVOT tiling mosaic of the neutrino localisation, and followed up with ATCA radio observations, compiling a multiwavelength SED for the most likely source of origin. NuSTAR observations of the neutrino location and a nearby X-ray source were also performed. We find two promising counterpart in the 90% confidence localisation region and identify the brightest as the most likely counterpart. However, no Fermi/LAT $\gamma$-ray source and no prompt Swift/BAT source is consistent with the neutrino event. At this point it is unclear whether any of the counterparts produced IceCube-190331A. We note that the Helix Nebula is also consistent with the position of the neutrino event, and we calculate that associated particle acceleration processes cannot produce the required energies to generate a high-energy HESE neutrino., Comment: 10 pages, 8 figures. Accepted for publication by MNRAS

The spectral analysis and data products in Data Release 16 (DR16; December 2019) from the high-resolution near-infrared APOGEE-2/SDSS-IV survey are described. Compared to the previous APOGEE data release (DR14; July 2017), APOGEE DR16 includes about 200000 new stellar spectra, of which 100000 are from a new southern APOGEE instrument mounted on the 2.5 m du Pont telescope at Las Campanas Observatory in Chile. DR16 includes all data taken up to August 2018, including data released in previous data releases. All of the data have been re-reduced and re-analyzed using the latest pipelines, resulting in a total of 473307 spectra of 437445 stars. Changes to the analysis methods for this release include, but are not limited to, the use of MARCS model atmospheres for calculation of the entire main grid of synthetic spectra used in the analysis, a new method for filling "holes" in the grids due to unconverged model atmospheres, and a new scheme for continuum normalization. Abundances of the neutron capture element Ce are included for the first time. A new scheme for estimating uncertainties of the derived quantities using stars with multiple observations has been applied, and calibrated values of surface gravities for dwarf stars are now supplied. Compared to DR14, the radial velocities derived for this release more closely match those in the Gaia DR2 data base, and a clear improvement in the spectral analysis of the coolest giants can be seen. The reduced spectra as well as the result of the analysis can be downloaded using links provided in the SDSS DR16 web page.

Let $G=(S,T,E)$ be a bipartite graph. For a matching $M$ of $G$, let $V(M)$ be the set of vertices covered by $M$, and let $B(M)$ be the symmetric difference of $V(M)$ and $S$. We prove that if $M$ is a uniform random matching of $G$, then $B(M)$ satisfies the BK inequality for increasing events.

We prove that the matching measure of an infinite vertex-transitive connected graph has no atoms. Generalizing the results of Salez, we show that for an ergodic non-amenable unimodular random rooted graph with uniformly bounded degrees, the matching measure has only finitely many atoms. Ku and Chen proved the analogue of the Gallai-Edmonds structure theorem for non-zero roots of the matching polynomial for finite graphs. We extend their results for infinite graphs. We also show that the corresponding Gallai-Edmonds decomposition is compatible with the zero temperature monomer-dimer model., Comment: 38 pages

We present optical-infrared photometric and spectroscopic observations of Gaia18dvy, located in the Cygnus OB3 association at a distance of 1.88 kpc. The object was noted by the Gaia alerts system when its lightcurve exhibited a $\gtrsim$4 mag rise in 2018-2019. The brightening was also observable at mid-infared wavelengths. The infrared colors of Gaia18dvy became bluer as the outburst progressed. Its optical and near-infrared spectroscopic characteristics in the outburst phase are consistent with those of bona fide FU Orionis-type young eruptive stars. The progenitor of the outburst is probably a low-mass K-type star with an optical extinction of $\sim$3 mag. A radiative transfer modeling of the circumstellar structure, based on the quiescent spectral energy distribution, indicates a disk with a mass of $4{\times}10^{-3}\,M_{\odot}$. Our simple accretion disk modeling implies that the accretion rate had been exponentially increasing for more than 3 years until mid-2019, when it reached a peak value of $6.9 \times 10^{-6}\,M_{\odot}$yr$^{-1}$. In many respects, Gaia18dvy is similar to the FU Ori-type object HBC 722, Comment: 11 pages, 7 figures, accepted for publication in ApJ

The Universe is filled with a diffuse background of MeV gamma-rays and PeV neutrinos, whose origins are unknown. Here, we propose a scenario that can account for both backgrounds simultaneously. Low-luminosity active galactic nuclei have hot accretion flows where thermal electrons naturally emit soft gamma rays via Comptonization of their synchrotron photons. Protons there can be accelerated via turbulence or reconnection, producing high-energy neutrinos via hadronic interactions. We demonstrate that our model can reproduce the gamma-ray and neutrino data. Combined with a contribution by hot coronae in luminous active galactic nuclei, these accretion flows can explain the keV -- MeV photon and TeV -- PeV neutrino backgrounds. This scenario can account for the MeV background without non-thermal electrons, suggesting a higher transition energy from the thermal to non-thermal Universe than expected. Our model is consistent with X-ray data of nearby objects, and testable by future MeV gamma-ray and high-energy neutrino detectors., Comment: Published in Nature Communications. Conclusions unchanged. Calculation methods and presentations are improved. Discussions are extended

The primary cell surface receptor for SARS-CoV-2 is the angiotensin-converting enzyme 2 (ACE2). Recently it has been noticed that the viral Spike protein has an RGD motif, suggesting that cell surface integrins may be co-receptors. We examined the sequences of ACE2 and integrins with the Eukaryotic Linear Motif resource, ELM, and were presented with candidate short linear motifs (SLiMs) in their short, unstructured, cytosolic tails with potential roles in endocytosis, membrane dynamics, autophagy, cytoskeleton and cell signalling. These SLiM candidates are highly conserved in vertebrates. They suggest potential interactions with the AP2 mu2 subunit as well as I-BAR, LC3, PDZ, PTB and SH2 domains found in signalling and regulatory proteins present in epithelial lung cells. Several motifs overlap in the tail sequences, suggesting that they may act as molecular switches, often involving tyrosine phosphorylation status. Candidate LIR motifs are present in the tails of ACE2 and integrin beta3, suggesting that these proteins can directly recruit autophagy components. We also noticed that the extracellular part of ACE2 has a conserved MIDAS structural motif, which are commonly used by beta integrins for ligand binding, potentially supporting the proposal that integrins and ACE2 share common ligands. The findings presented here identify several molecular links and testable hypotheses that might help uncover the mechanisms of SARS-CoV-2 attachment, entry and replication, and strengthen the possibility that it might be possible to develop host-directed therapies to dampen the efficiency of viral entry and hamper disease progression. The strong sequence conservation means that these putative SLiMs are good candidates: Nevertheless, SLiMs must always be validated by experimentation before they can be stated to be functional., Comment: 38 pages, 7 figures, 2 tables. Corresponding authors are Luc\'ia B. Chemes, Toby J. Gibson

This manuscript constructs global in time solutions to the $master\ equations$ for potential Mean Field Games. The study concerns a class of Lagrangians and initial data functions, which are $displacement\ convex$ and so, it may be in dichotomy with the class of so--called $monotone$ functions, widely considered in the literature. We construct solutions to both the scalar and vectorial master equations in potential Mean Field Games, when the underlying space is the whole space $\mathbb{R}^d$ and so, it is not compact., Comment: some sections rearranged, presentation improved, references updated; to appear in Comm. Pure Appl. Math

The new version of TLUSTY allows for the calculation of restricted NLTE in cool stars using pre-calculated opacity tables. We demonstrate that TLUSTY gives consistent results with MULTI, a well-tested code for NLTE in cool stars. We use TLUSTY to perform LTE and a series of NLTE calculations of Na, Mg, K and Ca using all combinations of 1, 2, 3 and the 4 elements mentioned above simultaneously in NLTE. In this work we take into account how departures from LTE in one element can affect others through changes in the opacities due to NLTE. We find that atomic Mg, which provides strong UV opacity, and shows departures from LTE in the low-energy states, can impact the NLTE populations of Ca, leading to abundance corrections as large as 0.07 dex. The differences in the derived abundances between the single-element and the multi-element cases can exceed those between the single-element NLTE and an LTE analysis, warning that this is not always a second-order effect. By means of detailed tests for three stars with reliable atmospheric parameters (Arcturus, Procyon and the Sun) we conclude that our NLTE calculations provide abundance corrections in the optical up to 0.1, 0.2 and 0.7 dex for Ca, Na and K, but LTE is a good approximation for Mg. In the H-band, NLTE corrections are much smaller, under 0.1 dex. The derived NLTE abundances in the optical and in the IR are consistent. For all four elements, in all three stars, NLTE line profiles fit better the observations than the LTE counterparts. For elements where over-ionisation is an important NLTE mechanism are likely affected by departures from LTE in Mg . Special care must be taken with the collisions adopted for high-lying levels when calculating NLTE profiles of lines in the H-band. The derived NLTE corrections in the optical and in the H-band differ, but the derived NLTE abundances are consistent between the two spectral regions.

Some short gamma-ray bursts (SGRBs) show a longer lasting emission phase, called extended emission (EE) lasting $\sim 10^{2-3}\,\rm s$, as well as a plateau emission (PE) lasting $\sim10^{4-5}\,\rm s$. While a long-lasting activity of the central engines is a promising explanation for powering both emissions, their physical origin and their emission mechanisms are still uncertain. In this work, we study the properties of the EEs and their connection with the PEs. First, we constrain the minimal Lorentz factor $\Gamma$ of the outflows powering EEs, using compactness arguments and find that the outflows should be relativistic, $\Gamma\gtrsim10$. We propose a consistent scenario for the PEs, where the outflow eventually catches up with the jet responsible for the prompt emission, injecting energy into the forward shock formed by the prior jet, which naturally results in a PE. We also derive the radiation efficiency of EEs and the Lorentz factor of the outflow within our scenario for 10 well-observed SGRBs accompanied by both EE and PE. The efficiency has an average value of $\sim3\,\%$ but shows a broad distribution ranging from $\sim0.01$ to $\sim100\%$. The Lorentz factor is $\sim20-30$, consistent with the compactness arguments. These results suggest that EEs are produced by a slower outflow via more inefficient emission than the faster outflow which causes the prompt emission with a high radiation efficiency., Comment: 10 pages, 4 figures, 3 tables, accepted for publication in MNRAS

Studies of the kinematics and chemical compositions of Galactic globular clusters (GCs) enable the reconstruction of the history of star formation, chemical evolution, and mass assembly of the Galaxy. Using the latest data release (DR16) of the SDSS/APOGEE survey, we identify 3,090 stars associated with 46 GCs. Using a previously defined kinematic association, we break the sample down into eight separate groups and examine how the kinematics-based classification maps into chemical composition space, considering only $\alpha$ (mostly Si and Mg) elements and Fe. Our results show that: (i) The loci of both in situ and accreted subgroups in chemical space match those of their field counterparts; (ii) GCs from different individual accreted subgroups occupy the same locus in chemical space. This could either mean that they share a similar origin or that they are associated with distinct satellites which underwent similar chemical enrichment histories; (iii) The chemical compositions of the GCs associated with the low orbital energy subgroup defined by Massari and collaborators is broadly consistent with an in situ origin. However, at the low metallicity end, the distinction between accreted and in situ populations is blurred; (iv) Regarding the status of GCs whose origin is ambiguous, we conclude the following: the position in Si-Fe plane suggests an in situ}origin for Liller 1 and a likely accreted origin for NGC 5904 and NGC 6388. The case of NGC 288 is unclear, as its orbital properties suggest an accretion origin, its chemical composition suggests it may have formed in situ., Comment: 18 pages, 10 figures, 3 tables. Accepted for publication in MNRAS

The separation of the gamma-ray bursts (GRBs) into short/hard and long/soft subclasses, respectively, is well supported both theoretically and observationally. The long ones are coupled to supernovae type Ib/Ic - the short ones are connected to the merging of two neutron stars, where one or even both neutron stars can be substituted by black holes. These short GRBs - as merging binaries - can also serve as the sources of gravitation waves, and are observable as the recently detected macronovae. Since 1998 there are several statistical studies suggesting the existence of more than two subgroups. There can be a subgroup having an intermediate durations; there can be a subgroup with ultra-long durations; the long/soft subgroup itself can be divided into two subclasses with respect to the luminosity of GRBs. The authors with other collaborators provided several statistical studies in this topic. This field of the GRB-diversity is briefly surveyed in this contribution., Comment: 5 pages, 2 figures, published in Proceedings of the International Astronomical Union

It is well-known that there are two types of gamma-ray bursts (GRBs): short/hard and long/soft ones, respectively. The long GRBs are coupled to supernovae, but the short ones are associated with the so called macronovae (also known as kilonovae), which can serve as the sources of gravitational waves as well. The kilonovae can arise from the merging of two neutron-stars. The neutron stars can be substituded by more massive black holes as well. Hence, the topic of gamma-ray bursts (mainly the topic of short ones) and the topic of massive binaries, are strongly connected. In this contribution, the redshifts of GRBs are studied. The surprising result - namely that the apparently fainter GRBs can be in average at smaller distances - is discussed again. In essence, the results of M\'esz\'aros et al. (2011) are studied again using newer samples of GRBs. The former result is confirmed by the newer data., Comment: 3 pages, 2 figures, published in Proceedings of the International Astronomical Union