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This paper considers a tracking control problem, in which the dynamic controller is encrypted with an additively homomorphic encryption scheme and the output of a process tracks a dynamic reference asymptotically. Our paper is motivated by the following problem: When dealing with both asymptotic tracking and dynamic reference, we find that the control input is generally subject to overflow issues under a finite modulus, though the dynamic controller consists of only integer coefficients. First, we provide a new controller design method such that the coefficients of the tracking controller can be transformed into integers leveraging the zooming-in factor of dynamic quantization. By the Cayley-Hamilton theorem, we represent the control input as linear combination of the previous control inputs. Leveraging the property above, we design an algorithm on the actuator side such that it can restore the control input from the lower bits under a finite modulus. A lower bound of the modulus is also provided. As an extension of the first result, we further solve the problem of unbounded internal state taking place in the actuator. In particular, the actuator can restore the correct control input under the same modulus. A simulation example is provided to verify the control schemes proposed in our paper.

The radial gradient of gas-phase metallicity is a powerful probe of the chemical and structural evolution of star-forming galaxies, closely tied to disk formation and gas kinematics in the early universe. We present spatially resolved chemical and dynamical properties for a sample of 26 galaxies at $0.5 \lesssim z \lesssim 1.7$ from the MSA-3D survey. These innovative observations provide 3D spectroscopy of galaxies at a spatial resolution approaching JWST's diffraction limit and a high spectral resolution of $R\simeq2700$. The metallicity gradients measured in our galaxy sample range from $-$0.05 to 0.02 dex~kpc$^{-1}$. Most galaxies exhibit negative or flat radial gradients, indicating lower metallicity in the outskirts or uniform metallicity throughout the entire galaxy. We confirm a tight relationship between stellar mass and metallicity gradient at $z\sim1$ with small intrinsic scatter of 0.02 dex~kpc$^{-1}$. Our results indicate that metallicity gradients become increasingly negative as stellar mass increases, likely because the more massive galaxies tend to be more "disky". This relationship is consistent with the predictions from cosmological hydrodynamic zoom-in simulations with strong stellar feedback. This work presents the effort to harness the multiplexing capability of JWST NIRSpec/MSA in slit-stepping mode to map the chemical and kinematic profiles of high-redshift galaxies in large samples and at high spatial and spectral resolution., Comment: 23 pages, 6 figures, 1 table; submitted to ApJL

Narrow emission lines in a galaxy's spectrum that show double peaks indicate the presence of distinct gas components with different velocities, and its physical origin remains uncertain. This study uses galaxies from the final MaNGA data release to detect double-peaked narrow emission-line spaxels (DPSs) by examining the double Gaussian profiles of the H$ \alpha $-[N \uppercase\expandafter{\romannumeral2}] doublets across all MaNGA spaxels. A total of 5,420 DPSs associated with 304 double-peaked narrow emission-line galaxies (DPGs) are identified, each DPG containing a minimum of 5 DPSs and being free from overlap with other galaxies. We find that DPSs can be categorized into three groups according to their central distance $r/R_e$ and the velocity difference $\Delta v$ between their two components: the inner low-$\Delta v$, inner high-$\Delta v$ and outer DPSs. By incorporating the physical characteristics of the DPGs into their DPSs, we demonstrate for the first time the existence of statistical correlations between barred DPGs and inner low-$\Delta v$ DPSs, AGN-hosting DPGs and inner high-$\Delta v$ DPSs, as well as tidal DPGs and outer DPSs., Comment: 15 pages, 10 figures, 2 tables

Model-based offline reinforcement Learning (RL) is a promising approach that leverages existing data effectively in many real-world applications, especially those involving high-dimensional inputs like images and videos. To alleviate the distribution shift issue in offline RL, existing model-based methods heavily rely on the uncertainty of learned dynamics. However, the model uncertainty estimation becomes significantly biased when observations contain complex distractors with non-trivial dynamics. To address this challenge, we propose a new approach - \emph{Separated Model-based Offline Policy Optimization} (SeMOPO) - decomposing latent states into endogenous and exogenous parts via conservative sampling and estimating model uncertainty on the endogenous states only. We provide a theoretical guarantee of model uncertainty and performance bound of SeMOPO. To assess the efficacy, we construct the Low-Quality Vision Deep Data-Driven Datasets for RL (LQV-D4RL), where the data are collected by non-expert policy and the observations include moving distractors. Experimental results show that our method substantially outperforms all baseline methods, and further analytical experiments validate the critical designs in our method. The project website is \href{https://sites.google.com/view/semopo}{https://sites.google.com/view/semopo}., Comment: 23 pages, 10 figures

We present a study of the molecular gas in early-mid stage major-mergers, with a sample of 43 major-merger galaxy pairs selected from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey and a control sample of 195 isolated galaxies selected from the xCOLD GASS survey. Adopting kinematic asymmetry as a new effective indicator to describe the merger stage, we aim to study the role of molecular gas in the merger-induced star formation enhancement along the merger sequence of galaxy pairs. We obtain the molecular gas properties from CO observations with the James Clerk Maxwell Telescope (JCMT), Institut de Radioastronomie Milimetrique (IRAM) 30-m telescope, and the MASCOT survey. Using these data, we investigate the differences in molecular gas fraction ($f_{\rm H_{2}}$), star formation rate (SFR), star formation efficiency (SFE), molecular-to-atomic gas ratio ($M_{\rm H_{2}}/M_{\rm HI}$), total gas fraction ($f_{\rm gas}$), and the star formation efficiency of total gas (${\rm SFE_{gas}}$) between the pair and control samples. In the full pair sample, our results suggest the $f_{\rm H_{2}}$ of paired galaxies is significantly enhanced, while the SFE is comparable to that of isolated galaxies. We detect significantly increased $f_{\rm H_{2}}$ and $M_{\rm H_{2}}/M_{\rm HI}$ in paired galaxies at the pericenter stage, indicating an accelerated transition from atomic gas to molecular gas due to interactions. Our results indicate that the elevation of $f_{\rm H_{2}}$ plays a major role in the enhancement of global SFR in paired galaxies at the pericenter stage, while the contribution of enhanced SFE in specific regions requires further explorations through spatially resolved observations of a larger sample spanning a wide range of merger stages., Comment: 25 pages, 12 figures, 5 tables, accepted for publication in ApJS

Quiescent galaxies generally possess denser cores than star-forming galaxies with similar mass. As a measurement of the core density, the central stellar mass surface density within a radius of 1 kpc ($\Sigma_1$) was thus suggested to be closely related to galaxy quenching. Massive star-forming galaxies with high $\Sigma_1$ do not fit into this picture. To understand the origin of such galaxies, we compare the spatially-resolved stellar population and star formation properties of massive ($ > 10^{10.5}{\rm M}_{\odot}$) blue spiral galaxies with high and low $\Sigma_1$, divided by $\Sigma_1 = 10^{9.4} M_\odot \, {\rm kpc}^{-2}$, based on the final release of MaNGA IFU data. We find that both high $\Sigma_1$ and low $\Sigma_1$ blue spirals show large diversities in stellar population and star formation properties. Despite the diversities, high $\Sigma_1$ blue spirals are statistically different from the low $\Sigma_1$ ones. Specifically, the radial profiles of the luminosity-weighted age and Mgb/${\rm \langle Fe \rangle}$ show that high $\Sigma_1$ blue spirals consist of a larger fraction of galaxies with younger and less $\alpha$-element enhanced centers than their low $\Sigma_1$ counterparts, $\sim 55\%$ versus $\sim 30\%$. The galaxies with younger centers mostly have higher central specific star formation rates, which still follow the spaxel-based star formation main sequence relation though. Examinations of the H$\alpha$ velocity field and the optical structures suggest that galactic bars or galaxy interactions should be responsible for the rejuvenation of these galaxies. The remaining $\sim 45\% $ of high $\Sigma_1$ blue spirals are consistent with the inside-out growth scenario., Comment: 22 pages, 14 figures, accepted for publication in ApJ

In many real-world visual Imitation Learning (IL) scenarios, there is a misalignment between the agent's and the expert's perspectives, which might lead to the failure of imitation. Previous methods have generally solved this problem by domain alignment, which incurs extra computation and storage costs, and these methods fail to handle the \textit{hard cases} where the viewpoint gap is too large. To alleviate the above problems, we introduce active sensoring in the visual IL setting and propose a model-based SENSory imitatOR (SENSOR) to automatically change the agent's perspective to match the expert's. SENSOR jointly learns a world model to capture the dynamics of latent states, a sensor policy to control the camera, and a motor policy to control the agent. Experiments on visual locomotion tasks show that SENSOR can efficiently simulate the expert's perspective and strategy, and outperforms most baseline methods.

Imitating skills from low-quality datasets, such as sub-optimal demonstrations and observations with distractors, is common in real-world applications. In this work, we focus on the problem of Learning from Noisy Demonstrations (LND), where the imitator is required to learn from data with noise that often occurs during the processes of data collection or transmission. Previous IL methods improve the robustness of learned policies by injecting an adversarially learned Gaussian noise into pure expert data or utilizing additional ranking information, but they may fail in the LND setting. To alleviate the above problems, we propose Denoised Imitation learning based on Domain Adaptation (DIDA), which designs two discriminators to distinguish the noise level and expertise level of data, facilitating a feature encoder to learn task-related but domain-agnostic representations. Experiment results on MuJoCo demonstrate that DIDA can successfully handle challenging imitation tasks from demonstrations with various types of noise, outperforming most baseline methods.

Model-based methods have significantly contributed to distinguishing task-irrelevant distractors for visual control. However, prior research has primarily focused on heterogeneous distractors like noisy background videos, leaving homogeneous distractors that closely resemble controllable agents largely unexplored, which poses significant challenges to existing methods. To tackle this problem, we propose Implicit Action Generator (IAG) to learn the implicit actions of visual distractors, and present a new algorithm named implicit Action-informed Diverse visual Distractors Distinguisher (AD3), that leverages the action inferred by IAG to train separated world models. Implicit actions effectively capture the behavior of background distractors, aiding in distinguishing the task-irrelevant components, and the agent can optimize the policy within the task-relevant state space. Our method achieves superior performance on various visual control tasks featuring both heterogeneous and homogeneous distractors. The indispensable role of implicit actions learned by IAG is also empirically validated.

We investigate the suppression of star formation in galaxy pairs based on the isolated galaxy pair sample derived from the SDSS survey. By comparing the star formation rate between late-type galaxies in galaxy pairs and those in the isolated environment, we detect the signal of star formation suppression in galaxy pairs at $d_p < 100$kpc and $200$kpc$ < d_p < 350$kpc. The occurrence of star formation suppression in these late-type galaxies requires their companion galaxies to have an early-type morphology ($n_s > 2.5$). Star formation suppression in wide galaxy pairs with $200$kpc$ < d_p < 350$kpc mainly occurs in massive late-type galaxies, while in close galaxy pairs with $d_p < 100$kpc, it only appears in late-type galaxies with a massive companion ( $\log M_\star > 11.0$), nearly independent of their own stellar mass. Based on these findings, we infer that star formation suppression in wide galaxy pairs is actually a result of galaxy conformity, while in close galaxy pairs, it stems from the influence of hot circum-galactic medium surrounding companion galaxies., Comment: 10 pages, 4 figures, accepted for publication in ApJ

In this paper, we investigate tracking control of heterogeneous multi-agent systems under Denial-of-Service (DoS) attacks and state quantization. Dynamic quantized mechanisms are designed for inter-follower communication and leader-follower communication. Zooming-in and out factors, and data rates of both mechanisms for preventing quantizer saturation are provided. Our results show that by tuning the inter-follower quantized controller, one cannot improve the resilience beyond a level determined by the data rate of leader-follower quantized communication, i.e., the ceiling effect. Otherwise, overflow of followers' state quantizer can occur. On the other hand, if one selects a "large" data rate for leader-follower quantized communication, then the inter-follower quantized communication determines the resilience, and further increasing the data rate for leader-follower quantized communication cannot improve the resilience, i.e., the bottleneck effect. Simulation examples are provided to justify the results of our paper.

In single-cloud storage, ciphertext-policy attribute-based encryption (CP-ABE) allows one to encrypt any data under an access structure to a cloud server, specifying what attributes are required to decrypt. In multi-cloud storage, a secret sharing scheme (SSS) allows one to split any data into multiple shares, one to a single server, and specify which subset of the servers are able to recover the data. It is an interesting problem to remove some attributes/servers but still enable the remaining attributes/servers in every authorized set to recover the data. The problem is related to the contraction problem of access structures for SSSs. In this paper, we propose a method that can efficiently transform a given SSS for an access structure to SSSs for contractions of the access structure. We show its applications in solving the attribute removal problem in the CP-ABE based single-cloud storage and the data relocating problem in multi-cloud storage. Our method results in solutions that require either less server storage or even no additional server storage., Comment: IEEE Transactions on Services Computing

This paper studies distributed Nash equilibrium (NE) seeking under Denial-of-Service (DoS) attacks and quantization. The players can only exchange information with their own direct neighbors. The transmitted information is subject to quantization and packet losses induced by malicious DoS attacks. We propose a quantized distributed NE seeking strategy based on the approach of dynamic quantized consensus. To solve the quantizer saturation problem caused by DoS attacks, the quantization mechanism is equipped to have zooming-in and holding capabilities, in which the holding capability is consistent with the results in quantized consensus under DoS. A sufficient condition on the number of quantizer levels is provided, under which the quantizers are free from saturation under DoS attacks. The proposed distributed quantized NE seeking strategy is shown to have the so-called maximum resilience to DoS attacks. Namely, if the bound characterizing the maximum resilience is violated, an attacker can deny all the transmissions and hence distributed NE seeking is impossible.

It is believed that gravity can be considered as a quantum coherent mediator. In this study, we propose a plan to test the existence of extra dimensions using the Quantum Gravity Induced Entanglement of Masses (QGEM) experiment. This experiment involves two freely falling test masses passing through a Stern-Gerlach-like device. We investigate the entanglement witness between these masses within the framework of the Randall-Sundrum II model (RS-II). Our findings indicate that the system reaches entanglement more rapidly in the presence of extra dimensions, particularly when the radius of the extra dimension is large.

This paper deals with dynamic quantized consensus of dynamical agents in a general form under packet losses induced by Denial-of-Service (DoS) attacks. The communication channel has limited bandwidth and hence the transmitted signals over the network are subject to quantization. To deal with agent's output, an observer is implemented at each node. The state of the observer is quantized by a finite-level quantizer and then transmitted over the network. To solve the problem of quantizer overflow under malicious packet losses, a zooming-in and out dynamic quantization mechanism is designed. By the new quantized controller proposed in the paper, the zooming-out factor is lower bounded by the spectral radius of the agent's dynamic matrix. A sufficient condition of quantization range is provided under which the finite-level quantizer is free of overflow. A sufficient condition of tolerable DoS attacks for achieving consensus is also provided. At last, we study scalar dynamical agents as a special case and further tighten the zooming-out factor to a value smaller than the agent's dynamic parameter. Under such a zooming-out factor, it is possible to recover the level of tolerable DoS attacks to that of unquantized consensus, and the quantizer is free of overflow.

The emerging Internet of Things (IoTs) invokes increasing security demands that require robust encryption or anti-counterfeiting technologies. Albeit being acknowledged as efficacious solutions in processing elaborate graphical information via multiple degrees of freedom, optical data encryption and anti-counterfeiting techniques are typically inept in delivering satisfactory performance without compromising the desired ease-of-processibility or compatibility, thus leading to the exploration of novel materials and devices that are competent. Here, a robust optical data encryption technique is demonstrated utilizing polymer-stabilized-liquid-crystals (PSLCs) combined with projection photoalignment and photopatterning methods. The PSLCs possess implicit optical patterns encoded via photoalignment, as well as explicit geometries produced via photopatterning. Furthermore, the PSLCs demonstrate improved robustness against harsh chemical environments and thermal stability, and can be directly deployed onto various rigid and flexible substrates. Based on this, it is demonstrated that single PSLC is apt to carry intricate information, or serve as exclusive watermark with both implicit features and explicit geometries. Moreover, a novel, generalized design strategy is developed, for the first time, to encode intricate and exclusive information with enhanced security by spatially programming the photoalignment patterns of a pair of cascade PSLCs, which further illustrates the promising capabilies of PSLCs in optical data encryption and anti-counterfeiting.

High-resolution X-ray observations offer a unique tool for probing the still elusive connection between galaxy mergers and active galactic nuclei (AGNs). We present an analysis of nuclear X-ray emission in an optically selected sample of 92 close galaxy pairs (with projected separations $\lesssim 20$ kpc and line-of-sight velocity offsets $<$ 500 km s$^{-1}$) at low redshift ($\bar{z} \sim 0.07$), based on archival Chandra observations. The parent sample of galaxy pairs is constructed without imposing an optical classification of nuclear activity, thus is largely free of selection effect for or against the presence of an AGN. Nor is this sample biased for or against gas-rich mergers. An X-ray source is detected in 70 of the 184 nuclei, giving a detection rate of $38\%^{+5\%}_{-5\%}$, down to a 0.5-8 keV limiting luminosity of $\lesssim 10^{40}\rm~erg~s^{-1}$. The detected and undetected nuclei show no systematic difference in their host galaxy properties such as galaxy morphology, stellar mass and stellar velocity dispersion. When potential contamination from star formation is avoided (i.e., $L_{\rm 2-10~keV} > 10^{41}\rm~erg~s^{-1}$), the detection rate becomes $18\%^{+3\%}_{-3\%}$ (32/184), which shows no excess compared to the X-ray detection rate of a comparison sample of optically classified single AGNs. The fraction of pairs containing dual AGN is only $2\%^{+2\%}_{-2\%}$. Moreover, most nuclei at the smallest projected separations probed by our sample (a few kpc) have an unexpectedly low apparent X-ray luminosity and Eddington ratio, which cannot be solely explained by circumnuclear obscuration. These findings suggest that close galaxy interaction is not a sufficient condition for triggering a high level of AGN activity., Comment: 28 pages, 9 figures. Accepted for publication in ApJ

Gas accretion is an important process in the evolution of galaxies, but it has limited direct observational evidences. In this paper, we report the detection of a possible ongoing gas accretion event in a Blue Compact Dwarf (BCD) galaxy, MaNGA 8313-1901, observed by the Mapping Nearby Galaxies and Apache Point Observatory (MaNGA) program. This galaxy has a distinct off-centered blue clump to the northeast (the NE clump) that shows low metallicity and enhanced star-formation. The kinematics of the gas in the NE clump also seems to be detached from the host BCD galaxy. Together with the metallicity drop of the NE clump, it suggests that the NE clump likely has an external origin, such as the gas accretion or galaxy interaction, rather than an internal origin, such as an \hii~complex in the disk. After removing the underlying host component, we find that the spectrum of the "pure" clump can match very well with a modeled spectrum containing a stellar population of the young stars ($\le 7$ Myr) only. This may imply that the galaxy is experiencing an accretion of cold gas, instead of a merger event involving galaxies with significant pre-existing old stars. We also find signs of another clump (the SW clump) at the south-west corner of the host galaxy, and the two clumps may share the same origin of gas accretion., Comment: 17 pages, 10 figures, accepted for publication in ApJ

This paper is concerned with the quantized consensus problem for uncertain nonlinear multi-agent systems under data-rate constraints and Denial-of-Service (DoS) attacks. The agents are modeled in strict-feedback form with unknown nonlinear dynamics and external disturbance. Extended state observers (ESOs) are leveraged to estimate agents' total uncertainties along with their states. To mitigate the effects of DoS attacks, a novel dynamic quantization with zooming-in and holding capabilities is proposed. The idea is to zoom-in and hold the variable to be quantized if the system is in the absence and presence of DoS attacks, respectively. The control protocol is given in terms of the outputs of the ESOs and the dynamic-quantization-based encoders and decoders. We show that, for a connected undirected network, the developed control protocol is capable of handling any DoS attacks inducing bounded consecutive packet losses with merely 3-level quantization. The application of the zooming-in and holding approach to known linear multi-agent systems is also discussed., Comment: 16 pages, 8 figures

The SDSS-IV MaNGA survey has measured two-dimensional maps of emission line velocities for a statistically powerful sample of nearby galaxies. The asymmetric features of these kinematics maps reflect the non-rotational component of a galaxy's internal motion of ionized gas. In this study, we present a catalog of kinematic asymmetry measurement of $H\alpha$ velocity map of a sample of 5353 MaNGA galaxies. Based on this catalog, we find that `special' galaxies (e.g. merging galaxies, barred galaxies, and AGN host galaxies) contain more galaxies with highly asymmetric velocity maps. However, we notice that more than half of galaxies with high kinematic asymmetry in our sample are quite `regular'. For those `regular' galaxies, kinematic asymmetry shows a significant anti-correlation with stellar mass at $\log M_\star < 9.7$, while such a trend becomes very weak at $\log M_\star>9.7$. Moreover, at a given stellar mass, the kinematic asymmetry shows weak correlations with photometric morphology, star formation rate, and environment, while it is independent of HI gas content. We also have quantified the observational effects in the kinematic asymmetry measurement. We find that both the signal-to-noise ratio of $H\alpha$ flux and disk inclination angle contribute to the measures of kinematic asymmetry, while the physical spatial resolution is an irrelevant factor inside the MaNGA redshift coverage., Comment: 19 pages, 12 figures, 3 tables. Accepted for publication in ApJS

Motivated by current sharing in power networks, we consider a class of output consensus (also called agreement) problems for nonlinear systems, where the consensus value is determined by external disturbances, e.g., power demand. This output consensus problem is solved by a simple distributed output feedback controller if a system is either Krasovskii or shifted passive, which is the only essential requirement. The effectiveness of the proposed controller is shown in simulation on an islanded DC power network.

Detecting out-of-distribution (OOD) samples is crucial to the safe deployment of a classifier in the real world. However, deep neural networks are known to be overconfident for abnormal data. Existing works directly design score function by mining the inconsistency from classifier for in-distribution (ID) and OOD. In this paper, we further complement this inconsistency with reconstruction error, based on the assumption that an autoencoder trained on ID data can not reconstruct OOD as well as ID. We propose a novel method, READ (Reconstruction Error Aggregated Detector), to unify inconsistencies from classifier and autoencoder. Specifically, the reconstruction error of raw pixels is transformed to latent space of classifier. We show that the transformed reconstruction error bridges the semantic gap and inherits detection performance from the original. Moreover, we propose an adjustment strategy to alleviate the overconfidence problem of autoencoder according to a fine-grained characterization of OOD data. Under two scenarios of pre-training and retraining, we respectively present two variants of our method, namely READ-MD (Mahalanobis Distance) only based on pre-trained classifier and READ-ED (Euclidean Distance) which retrains the classifier. Our methods do not require access to test time OOD data for fine-tuning hyperparameters. Finally, we demonstrate the effectiveness of the proposed methods through extensive comparisons with state-of-the-art OOD detection algorithms. On a CIFAR-10 pre-trained WideResNet, our method reduces the average FPR@95TPR by up to 9.8% compared with previous state-of-the-art., Comment: Accepted to AAAI 2023

The role of HI content in galaxy interactions is still under debate. To study the HI content of galaxy pairs at different merging stages, we compile a sample of 66 major-merger galaxy pairs and 433 control galaxies from the SDSS-IV MaNGA IFU survey. In this study, we adopt kinematic asymmetry as a new effective indicator to describe the merging stage of galaxy pairs. With archival data from the HI-MaNGA survey and new observations from the Five-hundred-meter Aperture Spherical Radio Telescope (FAST), we investigate the differences in HI gas fraction ($f_{\text{HI}}$), star formation rate (SFR), and HI star formation efficiency ($\rm SFE_{\text{HI}}$) between the pair and control samples. Our results suggest that the HI gas fraction of major-merger pairs on average is marginally decreased by $\sim 15\%$ relative to isolated galaxies, implying mild HI depletion during galaxy interactions. Compared to isolated galaxies, pre-passage paired galaxies have similar $f_{\text{HI}}$, SFR and $\rm SFE_{\text{HI}}$, while pairs during pericentric passage have weakly decreased $f_{\text{HI}}$ ($-0.10\pm0.05$ dex), significantly enhanced SFR ($0.42\pm0.11$ dex) and $\rm SFE_{\text{HI}}$ ($0.48\pm0.12$ dex). When approaching the apocenter, paired galaxies show marginally decreased $f_{\text{HI}}$ ($-0.05\pm0.04$ dex), comparable SFR ($0.04\pm0.06$ dex) and $\rm SFE_{\text{HI}}$ ($0.08\pm0.08$ dex). We propose the marginally detected HI depletion may originate from the gas consumption in fuelling the enhanced $\rm H_2$ reservoir of galaxy pairs. In addition, new FAST observations also reveal an HI absorber ($N_{\text{HI}}\sim 4.7 \times 10^{21} \text{ cm}^{-2}$), which may suggest gas infalling and the triggering of AGN activity., Comment: 17 pages, 5 figures, accepted for publication in ApJ

We use an updated version of the halo-based galaxy group catalog of Yang et al., and take the surface brightness of the galaxy group ($\mu_{\rm lim}$) based on projected positions and luminosities of galaxy members as a compactness proxy to divide groups into sub-systems with different compactness. By comparing various properties, including galaxy conditional luminosity function, stellar population, active galactic nuclei (AGN) activity, and X-ray luminosity of the intra-cluster medium of carefully controlled high (HC) and low compactness (LC) group samples, we find that the group compactness plays an essential role in characterizing the detailed physical properties of the group themselves and their group members, especially for low mass groups with $M_h \lesssim 10^{13.5}h^{-1}M_{\odot}$. We find that the low-mass HC groups have a systematically lower magnitude gap $\Delta m_{12}$ and X-ray luminosity than their LC counterparts, indicating that the HC groups are probably in the early stage of group merging. On the other hand, a higher fraction of passive galaxies is found in the HC group, which however is a result of systematically smaller halo-centric distance distribution of their satellite population. After controlling of both $M_h$ and halo-centric distance, we do not find any differences for both the quenching faction and AGN activity of the member galaxies between the HC and LC groups. Therefore, we conclude that the halo quenching effect, which result in the halo-centric dependence of galaxy population, is a faster process compared to the dynamical relaxed time-scale of galaxy groups., Comment: 19 pages, 10 figures, ApJ accepted