Complex networks have become essential tools for understanding diverse phenomena in social systems, traffic systems, biomolecular systems, and financial systems. Identifying critical nodes is a central theme in contemporary research, serving as a vital bridge between theoretical foundations and practical applications. Nevertheless, the intrinsic complexity and structural heterogeneity characterizing real-world networks, with particular emphasis on dynamic and higher-order networks, present substantial obstacles to the development of universal frameworks for critical node identification. This paper provides a comprehensive review of critical node identification techniques, categorizing them into seven main classes: centrality, critical nodes deletion problem, influence maximization, network control, artificial intelligence, higher-order and dynamic methods. Our review bridges the gaps in existing surveys by systematically classifying methods based on their methodological foundations and practical implications, and by highlighting their strengths, limitations, and applicability across different network types. Our work enhances the understanding of critical node research by identifying key challenges, such as algorithmic universality, real-time evaluation in dynamic networks, analysis of higher-order structures, and computational efficiency in large-scale networks. The structured synthesis consolidates current progress and highlights open questions, particularly in modeling temporal dynamics, advancing efficient algorithms, integrating machine learning approaches, and developing scalable and interpretable metrics for complex systems.

Randerath {\em et al.} [Discrete Math. 251 (2002) 137-153] proved that every $(P_6,C_3)$-free graph $G$ satisfies $\chi(G)\leq4$. Pyatkin [Discrete Math. 313 (2013) 715-720] proved that every $(2P_3,C_3)$-free graph $G$ satisfies $\chi(G)\leq4$. In this paper, we prove that for a connected $(P_2\cup P_4, C_3)$-free graph $G$, either $G$ has two nonadjacent vertices $u,v$ such that $N(u)\subseteq N(v)$, or $G$ is 3-colorable, or $G$ contains Grőtzsch graph as an induced subgraph and is an induced subgraph of Clebsch graph. Consequently, we have determined the chromatic number of $(P_2\cup P_4, C_3)$-free graph is 4. A graph $G$ is {\em perfectly divisible} if, for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and \omega(H[B])<\omega(H). A {\em bull} is a graph consisting of a triangle with two disjoint pendant edges. Deng and Chang [Graphs Combin. (2025) 41: 63] proved that every ($P_2\cup P_3$, bull)-free graph $G$ with $\omega(G)\geq3$ has a partition $(X,Y)$ such that $G[X]$ is perfect and $G[Y]$ has clique number less than $\omega(G)$ if $G$ admits no homogeneous set; Chen and Wang [arXiv:2507.18506v2] proved that such property is also true for ($P_2\cup P_4$, bull)-free graphs. In this paper, we prove that a ($P_2\cup P_4$, bull)-free graph is perfectly divisible if and only if it contains no Grőtzsch graph.

Group-level emotion recognition (GER) aims to identify holistic emotions within a scene involving multiple individuals. Current existed methods underestimate the importance of visual scene contextual information in modeling individual relationships. Furthermore, they overlook the crucial role of semantic information from emotional labels for complete understanding of emotions. To address this limitation, we propose a novel framework that incorporates visual scene context and label-guided semantic information to improve GER performance. It involves the visual context encoding module that leverages multi-scale scene information to diversely encode individual relationships. Complementarily, the emotion semantic encoding module utilizes group-level emotion labels to prompt a large language model to generate nuanced emotion lexicons. These lexicons, in conjunction with the emotion labels, are then subsequently refined into comprehensive semantic representations through the utilization of a structured emotion tree. Finally, similarity-aware interaction is proposed to align and integrate visual and semantic information, thereby generating enhanced group-level emotion representations and subsequently improving the performance of GER. Experiments on three widely adopted GER datasets demonstrate that our proposed method achieves competitive performance compared to state-of-the-art methods.

The development of aerial autonomy has enabled aerial robots to fly agilely in complex environments. However, dodging fast-moving objects in flight remains a challenge, limiting the further application of unmanned aerial vehicles (UAVs). The bottleneck of solving this problem is the accurate perception of rapid dynamic objects. Recently, event cameras have shown great potential in solving this problem. This paper presents a complete perception system including ego-motion compensation, object detection, and trajectory prediction for fast-moving dynamic objects with low latency and high precision. Firstly, we propose an accurate ego-motion compensation algorithm by considering both rotational and translational motion for more robust object detection. Then, for dynamic object detection, an event camera-based efficient regression algorithm is designed. Finally, we propose an optimizationbased approach that asynchronously fuses event and depth cameras for trajectory prediction. Extensive real-world experiments and benchmarks are performed to validate our framework. Moreover, our code will be released to benefit related researches.

Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier transform (GFT) with a fractional-order parameter, enabling flexible spectral analysis while preserving mathematical consistency. The angular graph Fourier transform (AGFT) introduces angular control via GFT eigenvector rotation; however, existing constructions fail to degenerate to the GFT at zero angle, which is a critical flaw that undermines theoretical consistency and interpretability. To resolve these complementary limitations - GFRFT's lack of angular regulation and AGFT's defective degeneracy - this study proposes an angular GFRFT (AGFRFT), a unified framework that integrates fractional-order and angular spectral analyses with theoretical rigor. A degeneracy-friendly rotation matrix family ensures exact GFT degeneration at zero angle, with two AGFRFT variants (I-AGFRFT and II-AGFRFT) defined accordingly. Rigorous theoretical analyses confirm their unitarity, invertibility, and smooth parameter dependence. Both support learnable joint parameterization of the angle and fractional order, enabling adaptive spectral processing for diverse graph signals. Extensive experiments on real-world data denoising, image denoising, and point cloud denoising demonstrate that AGFRFT outperforms GFRFT and AGFT in terms of spectral concentration, reconstruction quality, and controllable spectral manipulation, establishing a robust and flexible tool for integrated angular fractional spectral analysis in graph signal processing.

Ensuring the safety and extended operational life of fighter aircraft necessitates frequent and exhaustive inspections. While surface defect detection is feasible for human inspectors, manual methods face critical limitations in scalability, efficiency, and consistency due to the vast surface area, structural complexity, and operational demands of aircraft maintenance. We propose a smart surface damage detection and localization system for fighter aircraft, termed J-DDL. J-DDL integrates 2D images and 3D point clouds of the entire aircraft surface, captured using a combined system of laser scanners and cameras, to achieve precise damage detection and localization. Central to our system is a novel damage detection network built on the YOLO architecture, specifically optimized for identifying surface defects in 2D aircraft images. Key innovations include lightweight Fasternet blocks for efficient feature extraction, an optimized neck architecture incorporating Efficient Multiscale Attention (EMA) modules for superior feature aggregation, and the introduction of a novel loss function, Inner-CIOU, to enhance detection accuracy. After detecting damage in 2D images, the system maps the identified anomalies onto corresponding 3D point clouds, enabling accurate 3D localization of defects across the aircraft surface. Our J-DDL not only streamlines the inspection process but also ensures more comprehensive and detailed coverage of large and complex aircraft exteriors. To facilitate further advancements in this domain, we have developed the first publicly available dataset specifically focused on aircraft damage. Experimental evaluations validate the effectiveness of our framework, underscoring its potential to significantly advance automated aircraft inspection technologies.

Event-based Action Recognition (EAR) possesses the advantages of high-temporal resolution capturing and privacy preservation compared with traditional action recognition. Current leading EAR solutions typically follow two regimes: project unconstructed event streams into dense constructed event frames and adopt powerful frame-specific networks, or employ lightweight point-specific networks to handle sparse unconstructed event points directly. However, such two regimes are blind to a fundamental issue: failing to accommodate the unique dense temporal and sparse spatial properties of asynchronous event data. In this article, we present a synergy-aware framework, i.e., EventCrab, that adeptly integrates the "lighter" frame-specific networks for dense event frames with the "heavier" point-specific networks for sparse event points, balancing accuracy and efficiency. Furthermore, we establish a joint frame-text-point representation space to bridge distinct event frames and points. In specific, to better exploit the unique spatiotemporal relationships inherent in asynchronous event points, we devise two strategies for the "heavier" point-specific embedding: i) a Spiking-like Context Learner (SCL) that extracts contextualized event points from raw event streams. ii) an Event Point Encoder (EPE) that further explores event-point long spatiotemporal features in a Hilbert-scan way. Experiments on four datasets demonstrate the significant performance of our proposed EventCrab, particularly gaining improvements of 5.17% on SeAct and 7.01% on HARDVS.

In recent years, complexity compression of neural network (NN)-based speech enhancement (SE) models has gradually attracted the attention of researchers, especially in scenarios with limited hardware resources or strict latency requirements. The main difficulties and challenges lie in achieving a balance between complexity and performance according to the characteristics of the task. In this paper, we propose an intra-inter set knowledge distillation (KD) framework with time-frequency calibration (I$^2$S-TFCKD) for SE. Different from previous distillation strategies for SE, the proposed framework fully utilizes the time-frequency differential information of speech while promoting global knowledge flow. Firstly, we propose a multi-layer interactive distillation based on dual-stream time-frequency cross-calibration, which calculates the teacher-student similarity calibration weights in the time and frequency domains respectively and performs cross-weighting, thus enabling refined allocation of distillation contributions across different layers according to speech characteristics. Secondly, we construct a collaborative distillation paradigm for intra-set and inter-set correlations. Within a correlated set, multi-layer teacher-student features are pairwise matched for calibrated distillation. Subsequently, we generate representative features from each correlated set through residual fusion to form the fused feature set that enables inter-set knowledge interaction. The proposed distillation strategy is applied to the dual-path dilated convolutional recurrent network (DPDCRN) that ranked first in the SE track of the L3DAS23 challenge. Objective evaluations demonstrate that the proposed KD strategy consistently and effectively improves the performance of the low-complexity student model and outperforms other distillation schemes.

This paper devotes to combine the chirp basis function transformation and symplectic coordinates transformation to yield a novel Wigner distribution (WD) associated with the linear canonical transform (LCT), named as the symplectic WD in the LCT domain (SWDL). It incorporates the merits of the symplectic WD (SWD) and the WD in the LCT domain (WDL), achieving stronger capability in the linear frequency-modulated (LFM) signal frequency rate feature extraction while maintaining the same level of computational complexity. Some essential properties of the SWDL are derived, including marginal distributions, energy conservations, unique reconstruction, Moyal formula, complex conjugate symmetry, time reversal symmetry, scaling property, time translation property, frequency modulation property, and time translation and frequency modulation property. Heisenberg's uncertainty principles of the SWDL are formulated, giving rise to three kinds of lower bounds attainable respectively by Gaussian enveloped complex exponential signal, Gaussian signal and Gaussian enveloped chirp signal. The optimal symplectic matrices corresponding to the highest time-frequency resolution are generated by solving the lower bound optimization (minimization) problem. The time-frequency resolution of the SWDL is compared with those of the SWD and WDL to demonstrate its superiority in LFM signals time-frequency energy concentration. A synthesis example is also carried out to verify the feasibility and reliability of the theoretical analysis.

The security of spatial modulation (SM) aided networks can always be improved by reducing the desired link's power at the cost of degrading its bit error ratio performance and assuming the power consumed to artificial noise (AN) projection (ANP). We formulate the joint optimization problem of maximizing the secrecy rate (Max-SR) over the transmit antenna selection and ANP in the context of secure SM-aided networks, which is mathematically a non-linear mixed integer programming problem. In order to solve this problem, we provide a pair of solutions, namely joint and separate solutions. Specifically, an accurate approximation of the SR is used for reducing the computational complexity, and the optimal AN covariance matrix (ANCM) is found by convex optimization for any given active antenna group (AAG). Then, given a large set of AAGs, simulated annealing mechanism is invoked for optimizing the choice of AAG, where the corresponding ANCM is recomputed by this optimization method as well when the AAG changes. To further reduce the complexity of the above-mentioned joint optimization, a low-complexity two-stage separate optimization method is also proposed. Furthermore, when the number of transmit antennas tends to infinity, the Max-SR problem becomes equivalent to that of maximizing the ratio of the desired user's signal-to-interference-plus-noise ratio to the eavesdropper's. Thus our original problem reduces to a fractional programming problem, hence a significant computational complexity reduction can be achieved for the optimization problem. Our simulation results show that the proposed algorithms outperform the existing leakage-based null-space projection scheme in terms of the SR performance attained, and drastically reduces the complexity at a slight SR performance reduction.

An {\em odd hole} in a graph is an induced subgraph which is a cycle of odd length at least five. An {\em odd parachute} is a graph obtained from an odd hole $H$ by adding a new edge $uv$ such that $x$ is adjacent to $u$ but not to $v$ for each $x\in V(H)$. A graph $G$ is perfectly divisible if for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and \omega(H[B])<\omega(H). A vertex of a graph is {\em trisimplicial} if its neighbourhood is the union of three cliques. In this paper, we prove that $\chi(G)\leq \binom{\omega(G)+1}{2}$ if $G$ is a (fork, odd parachute)-free graph by showing that $G$ contains a trisimplicial vertex when $G$ is nonperfectly divisible. This generalizes some results of Karthick, Kaufmann and Sivaraman [{\em Electron. J. Combin.} \textbf{29} (2022) \#P3.19], and Wu and Xu [{\em Discrete Math.} \textbf{347} (2024) 114121]. As a corollary, every nonperfectly divisible claw-free graph contains a trisimplicial vertex.

The off-shell characteristics of pion generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) are examined within the framework of the Nambu-Jona-Lasinio model. In our previous papers, we separately investigated the properties of on-shell pion GPDs and light-front wave functions. It is particularly intriguing to compare the differences between on-shell and off-shell pion GPDs, which allows us to explore the effects associated with off-shellness. Due to the absence of crossing symmetry, the moments of GPDs also incorporate odd powers of the skewness parameter, resulting in new off-shell form factors. Through our calculations, we derived correction functions that account for modifications in pion GPDs due to off-shell effects. Unlike their on-shell counterparts, certain properties break down in the off-shell scenario; for instance, symmetry properties and polynomiality conditions may no longer hold. Additionally, we evaluate off-shell TMDs and compare them with their on-shell equivalents while also investigating their dependence on $\bm{k}_{\perp}$.

Gaze is an intuitive and direct way to represent the intentions of an individual. However, when it comes to assistive aerial teleoperation which aims to perform operators' intention, rare attention has been paid to gaze. Existing methods obtain intention directly from the remote controller (RC) input, which is inaccurate, unstable, and unfriendly to non-professional operators. Further, most teleoperation works do not consider environment perception which is vital to guarantee safety. In this paper, we present GPA-Teleoperation, a gaze enhanced perception-aware assistive teleoperation framework, which addresses the above issues systematically. We capture the intention utilizing gaze information, and generate a topological path matching it. Then we refine the path into a safe and feasible trajectory which simultaneously enhances the perception awareness to the environment operators are interested in. Additionally, the proposed method is integrated into a customized quadrotor system. Extensive challenging indoor and outdoor real-world experiments and benchmark comparisons verify that the proposed system is reliable, robust and applicable to even unskilled users. We will release the source code of our system to benefit related researches.

As an effective method to deliver external materials into biological cells, microinjection has been widely applied in the biomedical field. However, the cognition of cell mechanical property is still inadequate, which greatly limits the efficiency and success rate of injection. Thus, a new rate-dependent mechanical model based on membrane theory is proposed for the first time. In this model, an analytical equilibrium equation between the injection force and cell deformation is established by considering the speed effect of microinjection. Different from the traditional membrane-theory-based model, the elastic coefficient of the constitutive material in the proposed model is modified as a function of the injection velocity and acceleration, effectively simulating the influence of speeds on the mechanical responses and providing a more generalized and practical model. Using this model, other mechanical responses at different speeds can be also accurately predicted, including the distribution of membrane tension and stress and the deformed shape. To verify the validity of the model, numerical simulations and experiments are carried out. The results show that the proposed model can match the real mechanical responses well at different injection speeds.

Micro-expression recognition (MER) draws intensive research interest as micro-expressions (MEs) can infer genuine emotions. Prior information can guide the model to learn discriminative ME features effectively. However, most works focus on researching the general models with a stronger representation ability to adaptively aggregate ME movement information in a holistic way, which may ignore the prior information and properties of MEs. To solve this issue, driven by the prior information that the category of ME can be inferred by the relationship between the actions of facial different components, this work designs a novel model that can conform to this prior information and learn ME movement features in an interpretable way. Specifically, this paper proposes a Decomposition and Reconstruction-based Graph Representation Learning (DeRe-GRL) model to effectively learn high-level ME features. DeRe-GRL includes two modules: Action Decomposition Module (ADM) and Relation Reconstruction Module (RRM), where ADM learns action features of facial key components and RRM explores the relationship between these action features. Based on facial key components, ADM divides the geometric movement features extracted by the graph model-based backbone into several sub-features, and learns the map matrix to map these sub-features into multiple action features; then, RRM learns weights to weight all action features to build the relationship between action features. The experimental results demonstrate the effectiveness of the proposed modules, and the proposed method achieves competitive performance.

Using $(2712.4\pm14.3)\times10^{6}$ $\psi(3686)$ events collected with the BESIII detector at the BEPCII collider, the decay $\eta_c\to\gamma\gamma$ in $J/\psi\to\gamma\eta_c$ is observed. We determine the product branching fraction $\mathcal{B}(J/\psi\to\gamma\eta_c)\times\mathcal{B}(\eta_c\to\gamma\gamma)=(5.23\pm0.26_{\rm{stat.}}\pm0.30_{\rm{syst.}})\times10^{-6}$. This result is consistent with the LQCD calculation $(5.34\pm0.16)\times10^{-6}$ from HPQCD in 2023. By using the world-average values of $\mathcal{B}(J/\psi\to\gamma\eta_c)$ and the total decay width of $\eta_c$, the partial decay width $\Gamma(\eta_c\to\gamma\gamma)$ is determined to be $(11.30\pm0.56_{\rm{stat.}}\pm0.66_{\rm{syst.}}\pm1.14_{\rm{ref.}})~\rm{keV}$, which deviates from the corresponding world-average value by $3.4\sigma$.

In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat such error patterns in the quantum regime. Our contributions are as follows. Firstly, we derive an upper bound for the correctable burst errors of QBECCs, the quantum Reiger bound (QRB). This bound generalizes the quantum Singleton bound for standard quantum error correction codes (QECCs). Secondly, we propose two constructions of QBECCs: one by heuristic computer search and the other by concatenating two quantum tensor product codes (QTPCs). We obtain several new QBECCs with better parameters than existing codes with the same coding length. Moreover, some of the constructed codes can saturate the quantum Reiger bounds. Finally, we perform numerical experiments for our constructed codes over Markovian correlated depolarizing quantum memory channels, and show that QBECCs indeed outperform standard QECCs in this scenario.

In this paper we prove a sharp global existence result for semilinear wave equations with time-dependent scale-invariant damping terms if the initial data is small. More specifically, we consider Cauchy problem of $\partial_t^2u-\Delta u+\frac{\mu}{t}\partial_tu=|u|^p$, where $n\ge 3$, $t\ge 1$ and $\mu\in(0,1)\cup(1,2)$. For critical exponent $p_{crit}(n,\mu)$ which is the positive root of $(n+\mu-1)p^2-(n+\mu+1)p-2=0$ and conformal exponent $p_{conf}(n,\mu)=\frac{n+\mu+3}{n+\mu-1}$, we establish global existence for $n\geq3$ and $p_{crit}(n,\mu)0$ and $\alpha(m)\in\Bbb R$ are two suitable constants, then we investigate more general semilinear Tricomi equation $\partial_t^2v-t^m\Delta v=t^{\alpha}|v|^p$ and establish related weighted Strichartz estimates. Returning to the original wave equation, the corresponding global existence results on the small data solution $u$ can be obtained.

As vehicles playing an increasingly important role in people's daily life, requirements on safer and more comfortable driving experience have arisen. Connected vehicles (CVs) can provide enabling technologies to realize these requirements and have attracted widespread attentions from both academia and industry. These requirements ask for a well-designed computing architecture to support the Quality-of-Service (QoS) of CV applications. Computation offloading techniques, such as cloud, edge, and fog computing, can help CVs process computation-intensive and large-scale computing tasks. Additionally, different cloud/edge/fog computing architectures are suitable for supporting different types of CV applications with highly different QoS requirements, which demonstrates the importance of the computing architecture design. However, most of the existing surveys on cloud/edge/fog computing for CVs overlook the computing architecture design, where they (i) only focus on one specific computing architecture and (ii) lack discussions on benefits, research challenges, and system requirements of different architectural alternatives. In this paper, we provide a comprehensive survey on different architectural design alternatives based on cloud/edge/fog computing for CVs. The contributions of this paper are: (i) providing a comprehensive literature survey on existing proposed architectural design alternatives based on cloud/edge/fog computing for CVs, (ii) proposing a new classification of computing architectures based on cloud/edge/fog computing for CVs: computation-aided and computation-enabled architectures, (iii) presenting a holistic comparison among different cloud/edge/fog computing architectures for CVs based on functional requirements of CV systems, including advantages, disadvantages, and research challenges.