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As a well-known open cluster, NGC 2323 (also called M50) has been widely investigated for over a hundred years and has always been considered a classical single cluster. In this work, with the help of Gaia DR3, we study the binary structure nature of this cluster. Although indistinguishable in the spatial space, the small but undeniable difference in the proper motion indicates that they may be two individual clusters. After investigating the properties of the two clusters, it is found that they have very close positions (three-dimensional $\Delta$pos = 12.3 pc, $\sigma_{\Delta \mathrm{pos}} = 3.4$ pc) and similar tangential velocities (two-dimensional $\Delta$V = 2.2 km s$^{-1}$, $\sigma_{\Delta \mathrm{V}} = 0.02$ km s$^{-1}$), indicating the existence of their physical association. Moreover, the best isochrone fitting ages of the two clusters are the same (158 Myr), further proving their possibly common origin. To comprehensively understand the formation and evolution of this binary cluster, we employ the PETAR $N$-body code to trace back their birthplace and deduce their dynamical evolutionary fate. With observational mean cluster properties, the simulations suggest that they may form together, and then orbit each other as a binary cluster for over 200 Myr. After that, because of their gradual mass loss, the two clusters will eventually separate and evolve into two independent clusters. Meanwhile, the numerical $N$-body simulation suggests that the less massive cluster is unlikely to be the cluster tidal tails created by the differential rotation of the Milky Way., Comment: 14 pages, 8 figures

This study introduces an innovative methodology for mortality forecasting, which integrates signature-based methods within the functional data framework of the Hyndman-Ullah (HU) model. This new approach, termed the Hyndman-Ullah with truncated signatures (HUts) model, aims to enhance the accuracy and robustness of mortality predictions. By utilizing signature regression, the HUts model aims to capture complex, nonlinear dependencies in mortality data which enhances forecasting accuracy across various demographic conditions. The model is applied to mortality data from 12 countries, comparing its forecasting performance against classical models like the Lee-Carter model and variants of the HU models across multiple forecast horizons. Our findings indicate that overall the HUts model not only provides more precise point forecasts but also shows robustness against data irregularities, such as those observed in countries with historical outliers. The integration of signature-based methods enables the HUts model to capture complex patterns in mortality data, making it a powerful tool for actuaries and demographers. Prediction intervals are also constructed using bootstrapping methods., Comment: 46 pages, 24 figures, 9 tables

We investigated the stellar mass function and the binary fraction of 114 nearby open clusters (OCs) using the high-precision photometric data from Gaia Data Release 3 (Gaia DR3). We estimated the mass of member stars by using a ridge line (RL) that is better in line with the observed color-magnitude diagram (CMD), thus obtaining more accurate stellar mass and binary mass ratio ($q$) at the low-mass region. By analyzing the present-day mass function (PDMF) of star clusters, we found that 108 OCs follow a two-stage power-law distribution, whereas 6 OCs present a single power-law PDMF. Subsequently, we fitted the high(low)-mass index of PDMF ($dN/dm \propto m^{-\alpha}$), denoted as $\alpha_{\rm h}$($\alpha_{\rm l}$), and segmentation point $m_{\rm c}$. For our cluster sample, the median values of $\alpha_{\rm h}$ and $\alpha_{\rm l}$ are 2.65 and 0.95, respectively, which are approximately consistent with the initial mass function (IMF) results provided by Kroupa (2001). We utilized the cumulative radial number distribution of stars with different masses to quantify the degree of mass segregation. We found a significant positive correlation between the state of dynamical evolution and mass segregation in OCs. We also estimated the fraction of binary stars with $q \geq 0.5$, ranging from 6% to 34% with a median of 17%. Finally, we provided a catalog of 114 nearby cluster properties, including the total mass, the binary fraction, the PDMF, and the dynamical state., Comment: 20 pages, 15 figures, accepted for publication in ApJ

The study of their morphological coherence allows us to obtain a better understanding of the morphological evolution of open clusters. We employed the ellipsoid fitting method to delineate the 3D spatial structure of the sample clusters while using the morphological dislocation (MD) defined in our previous work and the ellipticity ratio (ER) of the clusters' inner and outer structures to characterize the morphological coherence of the sample clusters. The results show an inverse correlation between the ER of the sample clusters and the number of their members, indicating that sample clusters with a much more elliptical external morphology than internal shape generally tend to host a large number of members. Meanwhile, a slight shrinking of the MD of the sample clusters with their members' number may shed light on the significant role of the gravitational binding of the sample clusters in maintaining their morphological stability. Moreover, there are no correlations between the MD and ER of the sample clusters and their age. They are also not significantly correlated with the X-axis, the Y-axis, their orbital eccentricities, and the radial and vertical forces on them. However, the ER of the sample clusters displays some fluctuations in the distributions between it and the above covariates, implying that the morphologies of the sample clusters are sensitive to the external environment if sample effects are not taken into account. Finally, the analysis of the 3D spatial shapes of sample clusters with a small ER or a large ER demonstrates that the number of members lays an important foundation for forming a dense internal system for sample clusters. At the same time, the MD of the sample clusters can serve well as an indicator of their morphological stability, which is built upon a certain amount of member stars., Comment: 17 pages, 13 figures, 1 table. Accepted by Astronomy & Astrophysics

NGC 752 is a famous Galactic open cluster of intermediate age. In recent works, a very long and asymmetric tail was newly revealed. A blue straggler star (BSS) at the periphery of the tidal tail of the cluster has been identified subsequently. We aim to perform a detailed analysis of the newly detected BSS based on the available comprehensive spectroscopic and photometric data. We also explored this BSS's possible formation pathway and age limitation based on the collected spectroscopic and photometric data. We estimated the projected rotational velocity $v\ \mathrm{sin}i$ and the mass of the BSS from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope low-resolution spectra and multiband photometric data from various catalogs, respectively. The newly discovered BSS is confirmed as a genuine member of NGC 752. The lack of ultraviolet excess in the SED and no significant variations in the light curve imply that this BSS is likely a single star ($mass=1.86^{+3.62}_{-0.94}\ M_{\odot}$) formed through stellar mergers. The fast rotation velocity ($v\ \mathrm{sin}i=206.9\pm4.9$~km $\rm s^{-1}$) of the BSS may provide constraints on its age (less than a hundred million years), but more formation details require further investigation., Comment: 7 pages, 6 figures. Accepted by A&A

Globular clusters (GCs), as old as our Galaxy, constantly lose their members to the field as they cross through the Milky Way (MW). These GC escaped stars (or escapees) are suggested to contribute significantly to the MW halo. If a star has left the host GC a long time ago, chemical finger prints, e.g., N enrichment, may reveal its origin. In this work, we aim to establish dynamical connections between N-rich field stars recently identified by LAMOST and the existing MW GCs. By constructing the full action distribution, and combining with metallicity, we found 29 potential GC progenitors for 15 N-rich field stars. Particularly, some of them may be related to MW accretion events. On the other hand, if a star recently left its host GC via tidal evaporation, it still maintain the kinematic properties of the cluster. Here we identify extra-tidal candidates based on their spatial locations, proper motions (PMs), and their position on color-magnitude-diagrams (CMDs). We successfully identified more than 1600 extra-tidal candidates in the vicinity of six Gaia-Enceladus (GE)-related GCs (i.e., NGC 1851, NGC 1904, NGC 6205, NGC 6341, NGC 6779, NGC 7089). The density map of the extra-tidal candidates is confirmed to be an efficient way to find extra-tidal structures. The possible two density peaks at opposite directions of the inner boundary is a good indicator for long stellar stream. Among 95 extra-tidal candidates with spectroscopic radial velocities and metallicity, 54 of them are confirmed to be GC escaped stars, as they share similar properties as host GCs. These extra-tidal candidates are ideal targets for follow-up spectroscopic observation, as it greatly improves the scientific outcome. Once statistically significant number of spectroscopic radial velocities and metallicities are available, the GC dynamical evolution (e.g., mass loss, rotation) can be carefully investigated., Comment: 14 pages, 12 figures. Accepted by A&A

The split main sequences found in the colour-magnitude diagrams of star clusters younger than ~600 Myr are suggested to be caused by the dichotomy of stellar rotation rates of upper main-sequence stars. Tidal interactions have been suggested as a possible explanation of the dichotomy of the stellar rotation rates. This hypothesis proposes that the slow rotation rates of stars along the split main sequences are caused by tidal interactions in binaries. To test this scenario, we measured the variations in the radial velocities of slowly rotating stars along the split main sequence of the young Galactic cluster NGC 2422 (~90 Myr) using spectra obtained at multiple epochs with the Canada-France-Hawai'i Telescope. Our results show that most slowly rotating stars are not radial-velocity variables. Using the theory of dynamical tides, we find that the binary separations necessary to fully or partially synchronise our spectroscopic targets, on time-scales shorter than the cluster age, predict much larger radial velocity variations across multiple-epoch observations, or a much larger radial velocity dispersion at a single epoch, than the observed values. This indicates that tidal interactions are not the dominant mechanism to form slowly rotating stars along the split main sequences. As the observations of the rotation velocity distribution among B- and A-type stars in binaries of larger separations hint at a much stronger effect of braking with age, we discuss the consequences of relaxing the constraints of the dynamical tides theory., Comment: 14 pages, 10 figures, 2 tables, accepted for publication in MNRAS

Magnetic particle spectroscopy (MPS) is one of the most versatile methods to characterize the magnetic properties of magnetic nanoparticles (MNPs). The excitation magnetic field is one of the most crucial factors that affects the MPS signal of the MNPs. In this study, a multi-frequency MPS system is developed to investigate the MPS signal of MNPs in different ac magnetic fields. The MPS system consists of a multi-channel excitation module for the generation of different-frequency ac magnetic fields and a detection module for the measurement of the magnetic response of the MNPs. The MPS system allows to generate ac magnetic fields with a frequency up to 32.6 kHz and amplitude up to 25 mT. The MPS signals of the MNPs in different ac magnetic fields are measured to systematically evaluate the performance of the multi-frequency MPS system, including the MNP spectra and its dynamic magnetization curve. In addition, the signal-to-noise ratio (SNR) of the MPS system is quantitively assessed with measured MPS signals of a given MNP sample and DI water. Furthermore, a series of MNP samples with different iron concentrations are prepared and measured to evaluate the limit-of-detection (LOD) in terms of iron concentration. The influence of the excitation magnetic field, including frequency and amplitude, is discussed based on the SNRs of the measured harmonics. Experimental results show that the LOD is 2.3 ng in terms of iron., Comment: 7 pages, 12 figures

The particularly abundant presence of blue straggler stars (BSS) in Galactic open clusters offers favorable conditions for detailed studies on the statistical properties and the origin of the blue straggler population. With the help of Gaia DR3, the number of identified open clusters continuously increases, and the determination of star cluster members is more reliable. We performed a more thorough search for BSS in newly found open clusters based on Gaia data. We implemented a uniform membership determination for over one thousand newly identified open clusters with larger sky coverage based on the astrometric and photometric data from Gaia DR3. The membership probabilities of stars were assigned by the pyUPMASK algorithm. Then we estimated the physical parameters of these clusters by isochrone fitting on their CMDs and picked out BSS in the specific region of these CMDs. We identified 138 BSS that had not been reported before in 50 open clusters. Compared with recent catalogs that present more than 1500 BSS in 339 open clusters, our new catalog increased the number of BSS in Galactic open clusters by about 10%, and the number of open clusters with BSS by nearly 17%. In the future, more accurate abundance measurements are anticipated to better probe the origin of BSS in open clusters., Comment: 9 pages, 10 figures, 2 tables. Published in A&A

In this work, we update the catalog of M-giant stars from the low-resolution spectra of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Data Release 9. There are 58,076 M giants identified from the classification pipeline with seven temperature subtypes from M0 to M6. The 2471 misclassified non-M-giant stars are white dwarf binaries, early types, and M dwarfs. And the contamination rate is 4.2$\%$ in the M-giants sample. A total of 372 carbon stars were identified by CaH spectral indices, and were further confirmed by the LAMOST spectra. We update the correlation between the $(W1-W2)_0$ color and [M/H] from APOGEE DR17. We calculate the radial velocities of all M giants by applying cross-correlation to the spectra between 8000 and 8950 \AA with synthetic spectra from ATLAS9. Taking star distances less than 4 kpc from Gaia EDR3 as the standard, we refitted the photometric distance relation of M giants. And based on our M-giant stars, we select a group of Sagittarius stream members, whose sky and 3D velocity distributions are well consistent with K-giant Saggitarius stream members found in Yang et al. With our M giants, we find that the disk is asymmetric out to R = 25 kpc, which is 5 kpc further out than detected using K giants., Comment: 23 pages, 10 figures. arXiv admin note: text overlap with arXiv:1908.01128

We systematically searched for open clusters in the solar neighborhood within 500 pc using pyUPMASK and HDBSCAN clustering algorithms based on {\it Gaia} DR3. Taking into consideration that the physical size for most open clusters is less than 50 pc, we adopted a slicing approach for different distance shells and identified 324 neighboring open clusters, including 223 reported open clusters and 101 newly discovered open clusters (named as OCSN, Open Cluster of Solar Neighborhood). Our discovery has increased the number of open clusters in the solar neighborhood by about 45\%. In this work, larger spatial extents and more member stars were attained for our cluster sample. We provided the member stars and the membership probabilities through the pyUPMASK algorithm for each cluster and derived their astrophysical, age, and structural parameters., Comment: 32 pages, 10 figures

In addition to the extended main-sequence turnoffs widely found in young and intermediate-age (~ 600 Myr-2 Gyr-old) star clusters, some younger clusters even exhibit split main sequences (MSs). Different stellar rotation rates are proposed to account for the bifurcated MS pattern, with red and blue MSs (rMS and bMS) populated by fast and slowly rotating stars, respectively. Using photometry from Gaia Early Data Release 3, we report a Galactic open cluster with a bifurcated MS, NGC 2422 ( ~ 90 Myr). We exclude the possibilities that the bifurcated MS pattern is caused by photometric noise or differential reddening. We aim to examine if stellar rotation can account for the split MSs. We use spectra observed with the Canada-France-Hawaii Telescope and the Southern African Large Telescope, and directly measured v sin i, the projected rotational velocities, for stars populating the bMS and rMS. We find that their v sin i values are weakly correlated with their loci in the color-magnitude diagram because of contamination caused by a large fraction of rMS stars with low projected rotational velocities. Based on the spectral energy distribution fitting method, we suggest that these slowly rotating stars at the rMS may hide a binary companion, which breaks the expected v sin i-color correlation. Future time-domain studies focusing on whether these slowly rotating stars are radial velocity variables are crucial to test the roles of stellar rotation and binarity in generating the split MSs., Comment: 20 pages, 12 figures, 1 table; Accepted for publication in The Astrophysical Journal (ApJ)

Open Clusters are born and evolve along the Milky Way plane, on them is imprinted the history of the Galactic disc, including the chemical and dynamical evolution. Chemical and dynamical properties of open clusters can be derived from photometric, spectroscopic, and astrometric data of their member stars. Based on the photometric and astrometric data from the Gaia mission, the membership of stars in more than 2000 Galactic clusters has been identified in the literature. The chemical and kinematical properties, however, are still poorly known for many of these clusters. In synergy with the large spectroscopic survey LAMOST (data release 8) and Gaia (data release 2), we report a new comprehensive catalogue of 386 open clusters. This catalogue has homogeneous parameter determinations of radial velocity, metallicity, and dynamical properties, such as orbit, eccentricity, angular momenta, total energy, and 3D Galactic velocity. These parameters allow the first radial velocity determination and the first spectroscopic [Fe/H] determination for 44 and 137 clusters, respectively. The metallicity distribution of majority clusters shows falling trends in the parameter space of the Galactocentric radius, the total energy, and the Z component of angular momentum -- except for two old groups that show flat tails in their own parameter planes. Cluster populations of ages younger and older than 500 Myrs distribute diversely on the disc. The latter has a spatial consistency with the Galactic disc flare. The 3-D spatial comparison between very young clusters (< 100 Myr) and nearby molecular clouds revealed a wide range of metallicity distribution along the Radcliffe gas cloud wave, indicating a possible inhomogeneous mixing or fast star formation along the wave. This catalogue would serve the community as a useful tool to trace the chemical and dynamical evolution of the Milky Way., Comment: accepted for publication on A&A

With the help of Gaia data, it is noted that in addition to the core components, there are low-density outer halo components in the extended region of open clusters. To study the extended structure beyond the core radius of the cluster ($\sim$ 10 pc), based on Gaia EDR3 data, taking up to 50 pc as the searching radius, we use the pyUPMASK algorithm to re-determine the member stars of the open cluster within 1-2 kpc. We obtain the member stars of 256 open clusters, especially those located in the outer halo region of open clusters. Furthermore, we find that most open clusters' radial density profile in the outer region deviates from the King's profile. To better describe the internal and external structural characteristics of open clusters, we propose a double components model for description: core components with King model distribution and outer halo components with logarithmic Gaussian distribution, and then suggest using four radii ( $r_c$, $r_t$, $r_o$, $r_e$) for describing the structure and distribution profile of star clusters, where $r_t$ and $r_e$ represent the boundaries of core components and outer halo components respectively. Finally, we provide a catalog of 256 clusters with structural parameters. In addition, our study shows the sizes of these radii are statistically linear related, which indicates that the inner and outer regions of the cluster are interrelated and follow similar evolutionary processes. Further, we show that the structure of two components can be used to better trace the cluster evolution properties in different stages., Comment: 17 pages, 6 figures. Accepted for publication in AJ

COIN-Gaia 13 is a newly discovered open cluster revealed by Gaia DR2 data. It is a nearby open cluster with a distance of about 513 pc. Combined with the five-dimensional astrometric data of Gaia EDR3 with higher accuracy, we use the membership assignment algorithm (pyUPMASK) to determine the membership of COIN-Gaia 13 in a large extended spatial region. The cluster has found 478 candidate members. After obtaining reliable cluster members, we further study its basic properties and spatial distribution. Our results show that there is an obvious extended structure of the cluster in the X-Y plane. This elongated structure is distributed along the spiral arm, and the whole length is about 270 pc. The cluster age is 250 Myr, the total mass is about 439 M$_\odot$, and the tidal radius of the cluster is about 11 pc. Since more than half of the member stars (352 stars) are located outside twice the tidal radius, it is suspected that this cluster is undergoing the dynamic dissolution process. Furthermore, the spatial distribution and kinematic analysis indicate that the extended structure in COIN-Gaia 13 is more likely to be caused by the differential rotation of the Galaxy., Comment: 12 pages, 9 figures, accepted for publication in Research in Astronomy and Astrophysics

This paper introduces CO3 -- an algorithm for communication-efficient federated Deep Neural Network (DNN) training. CO3 takes its name from three processing applied which reduce the communication load when transmitting the local DNN gradients from the remote users to the Parameter Server. Namely: (i) gradient quantization through floating-point conversion, (ii) lossless compression of the quantized gradient, and (iii) quantization error correction. We carefully design each of the steps above to assure good training performance under a constraint on the communication rate. In particular, in steps (i) and (ii), we adopt the assumption that DNN gradients are distributed according to a generalized normal distribution, which is validated numerically in the paper. For step (iii), we utilize an error feedback with memory decay mechanism to correct the quantization error introduced in step (i). We argue that the memory decay coefficient, similarly to the learning rate, can be optimally tuned to improve convergence. A rigorous convergence analysis of the proposed CO3 with SGD is provided. Moreover, with extensive simulations, we show that CO3 offers improved performance when compared with existing gradient compression schemes in the literature which employ sketching and non-uniform quantization of the local gradients., Comment: arXiv admin note: substantial text overlap with arXiv:2203.09044

Water splitting through efficient catalysts represents an ultimate solution for carbon neutrality within 40 years. To achieve this goal, amorphous photocatalysts are noted for their promising performances. Among them, the best known is black titania (amorphous TiOx, x < 2). However, despite the large number of studies on black titania, its color origin, structure-property relationship, and photocatalytic mechanism remain a topic of hot debate, largely due to the difficulty to calculate its precise electronic structure. Here, using ab initio molecular dynamics simulations, we report the precise electronic structures of black titania and further reveal the generic evolution pattern of the electronic structures of covalent compounds upon amorphization and reduction. Moreover, surface adsorption of the co-catalyst atoms (e.g., Pt) on amorphous substances is simulated for the first time: the disordered surface enables easy accommodation of the co-catalyst atoms, while the extended electronic states facilitate the separation of photo-induced electrons and holes, beneficial for hydrogen evolution. This study elucidates the workings of amorphous catalysts and offers practical guidance for enhancing their performances.

In this paper, we introduce a novel algorithm, $\mathsf{CO}_3$, for communication-efficiency distributed Deep Neural Network (DNN) training. $\mathsf{CO}_3$ is a joint training/communication protocol, which encompasses three processing steps for the network gradients: (i) quantization through floating-point conversion, (ii) lossless compression, and (iii) error correction. These three components are crucial in the implementation of distributed DNN training over rate-constrained links. The interplay of these three steps in processing the DNN gradients is carefully balanced to yield a robust and high-performance scheme. The performance of the proposed scheme is investigated through numerical evaluations over CIFAR-10.

We report 541 new open cluster candidates in Gaia EDR3 through revisiting the cluster results from an earlier analysis of the Gaia DR2, which revealed nearly a thousand open cluster candidates in the solar neighborhood (mostly d < 3 kpc) resideing at Galactic latitudes |b| < 20 degrees. A subsequent comparison with lists of known clusters shows a large increases of the cluster samples within 2 kpc from the Sun. We assign membership probabilities to the stars through the open source pyUPMASK algorithm, and also estimate the physical parameters through isochrone fitting for each candidate. Most of the new candidates show small total proper motion dispersions and clear features in the color-magnitude diagrams. Besides, the metallicity gradient of the new candidates is consistent with those found in the literature. The cluster parameters and member stars are available at CDS via anonymous ftp to cdsarc.u-strasbg.fr(130.79.128.5) or via https://cdsarc.unistra.fr/viz-bin/cat/J/ApJS. The discovery of these new objects shows that the open cluster samples in Gaia data is still not complete, and more discoveries are expected in the future researches., Comment: 13 pages, 8 figures, 3 tables, accepted for publication in ApJS; online data submitted to CDS (see link int the paper)