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We use Gaia DR3 data to study the Collinder 132-Gulliver 21 region via the machine learning algorithm StarGO, and find eight subgroups of stars (ASCC 32, Collinder 132 gp 1--6, Gulliver 21) located in close proximity. Three co-moving populations were identified among these eight subgroups: (i) a coeval 25 Myr-old moving group (Collinder 132); (ii) an intermediate-age (50--100 Myr) group; and (iii) the 275 Myr-old dissolving cluster Gulliver 21. These three populations form parallel diagonal stripe-shape over-densities in the U--V distribution, which differ from open clusters and stellar groups in the solar neighborhood. We name this kinematic structure the Collinder 132-Gulliver 21 stream, as it extends over 270 pc in the 3D space. The oldest population Gulliver21 is spatially surrounded by the Collinder 132 moving group and the intermediate-age group. Stars in the Collinder 132-Gulliver 21 stream have an age difference up to 250 Myr. Metallicity information shows a variation of 0.3 dex between the youngest and oldest populations. The formation of the Collinder132-Gulliver 21 stream involves both star formation and dynamical heating. The youngest population (Collinder 132 moving group) with homogeneous metallicity is probably formed through filamentary star formation. The intermediate-age and the oldest population were then scatted by the Galactic bar or spiral structure resonance to intercept Collinder 132's orbit. Without mutual interaction between each population, the three populations are flying by each other currently and will become distinct three groups again in approximately ~50Myr., Comment: Accepted to ApJL, 15 pages, 7 figures

We identify members of 65 open clusters in the solar neighborhood using the machine-learning algorithm StarGO based on Gaia EDR3 data. After adding members of twenty clusters from previous studies (Pang et al. 2021a,b; Li et al. 2021) we obtain 85 clusters, and study their morphology and kinematics. We classify the substructures outside the tidal radius into four categories: filamentary (f1) and fractal (f2) for clusters $<100$ Myr, and halo (h) and tidal-tail (t) for clusters $>100$ Myr. The kinematical substructures of f1-type clusters are elongated; these resemble the disrupted cluster Group X. Kinematic tails are distinct in t-type clusters, especially Pleiades. We identify 29 hierarchical groups in four young regions (Alessi 20, IC 348, LP 2373, LP 2442); ten among these are new. The hierarchical groups form filament networks. Two regions (Alessi 20, LP 2373) exhibit global "orthogonal" expansion (stellar motion perpendicular to the filament), which might cause complete dispersal. Infalling-like flows (stellar motion along the filament) are found in UBC 31 and related hierarchical groups in the IC 348 region. Stellar groups in the LP 2442 region (LP 2442 gp 1-5) are spatially well-mixed but kinematically coherent. A merging process might be ongoing in the LP 2442 subgroups. For younger systems ($\lesssim30$ Myr), the mean axis ratio, cluster mass and half-mass radius tend to increase with age values. These correlations between structural parameters may imply two dynamical processes occurring in the hierarchical formation scenario in young stellar groups: (1) filament dissolution and (2) sub-group mergers., Comment: Accepted to ApJ, 33 pages, 14 figures. OC 3D interactive visualization included on http://3doc-morphology.lowell.edu

We analyze the 3D morphology and kinematics of 13 open clusters (OCs) located within 500 pc of the Sun, using Gaia EDR3 and kinematic data from literature. Members of OCs are identified using the unsupervised machine learning method StarGO, using 5D parameters (X, Y, Z, $\mu_\alpha \cos\delta, \mu_\delta$). The OC sample covers an age range of 25Myr--2.65Gyr. We correct the asymmetric distance distribution due to the parallax error using Bayesian inversion. The uncertainty in the corrected distance for a cluster at 500~pc is 3.0--6.3~pc, depending on the intrinsic spatial distribution of its members. We determine the 3D morphology of the OCs in our sample and fit the spatial distribution of stars within the tidal radius in each cluster with an ellipsoid model. The shapes of the OCs are well-described with oblate spheroids (NGC2547, NGC2516, NGC2451A, NGC2451B, NGC2232), prolate spheroids (IC2602, IC4665, NGC2422, Blanco1, Coma Berenices), or triaxial ellipsoids (IC2391, NGC6633, NGC6774). The semi-major axis of the fitted ellipsoid is parallel to the Galactic plane for most clusters. Elongated filament-like substructures are detected in three young clusters (NGC2232, NGC2547, NGC2451B), while tidal-tail-like substructures (tidal tails) are found in older clusters (NGC2516, NGC6633, NGC6774, Blanco1, Coma Berenices). Most clusters may be super-virial and expanding. $N$-body models of rapid gas expulsion with an SFE of $\approx 1/3$ are consistent with clusters more massive than $250\rm M_\odot$, while clusters less massive than 250$\rm M_\odot$ tend to agree with adiabatic gas expulsion models. Only six OCs (NGC2422, NGC6633, and NGC6774, NGC2232, Blanco1, Coma Berenices) show clear signs of mass segregation., Comment: 35 pages, 17 figures, accepted by ApJ

We identify structures of the young star cluster NGC 2232 in the solar neighborhood (323.0 pc), and a newly discovered star cluster LP 2439 (289.1 pc). Member candidates are identified using the Gaia DR2 sky position, parallax and proper motion data, by an unsupervised machine learning method, \textsc{StarGO}. Member contamination from the Galactic disk is further removed using the color magnitude diagram. The four identified groups (NGC 2232, LP 2439 and two filamentary structures) of stars are coeval with an age of 25 Myr and were likely formed in the same giant molecular cloud. We correct the distance asymmetry from the parallax error with a Bayesian method. The 3D morphology shows the two spherical distributions of clusters NGC 2232 and LP 2439. Two filamentary structures are spatially and kinematically connected to NGC 2232. Both NGC 2232 and LP 2439 are expanding. The expansion is more significant in LP 2439, generating a loose spatial distribution with shallow volume number and mass density profiles. The expansion is suggested to be mainly driven by gas expulsion. NGC 2232, with 73~percent of the cluster mass bound, is currently experiencing a process of re-virialization, However, LP 2439, with 52 percent cluster mass being unbound, may fully dissolve in the near future. The different survivability traces different dynamical states of NGC 2232 and LP 2439 prior to the onset of gas expulsion. NGC 2232 may have been substructured and subvirial, while LP 2439 may either have been virial/supervirial, or it has experienced a much faster rate of gas removal., Comment: 14 pages, 6 figures, Accepted by ApJL

Algorithms for computing game-theoretic solutions have recently been applied to a number of security domains. However, many of the techniques developed for compact representations of security games do not extend to {\em Bayesian} security games, which allow us to model uncertainty about the attacker's type. In this paper, we introduce a general framework of {\em catcher-evader} games that can capture Bayesian security games as well as other game families of interest. We show that computing Stackelberg strategies is NP-hard, but give an algorithm for computing a Nash equilibrium that performs well in experiments. We also prove that the Nash equilibria of these games satisfy the {\em interchangeability} property, so that equilibrium selection is not an issue.