Over-smoothing is a persistent challenge in Graph Neural Networks (GNNs), where node embeddings become indistinguishable as network depth increases, fundamentally limiting their effectiveness on tasks requiring fine-grained distinctions. This issue arises from the reliance on diffusion-based propagation mechanisms, which suppress high-frequency information essential for preserving feature diversity. To mitigate this, we propose a wave-driven GNN framework that redefines feature propagation through the wave equation. Unlike diffusion, the wave equation incorporates second-order dynamics, balancing smoothing with oscillatory behavior to retain high-frequency components while ensuring effective information flow. To enhance the stability and convergence of wave equation discretization on graphs, an energy-based mechanism inspired by kinetic and potential energy dynamics is introduced, balancing temporal evolution and structural alignment to stabilize propagation. Extensive experiments on benchmark datasets, including Cora, Citeseer, and PubMed, as well as real-world graphs, demonstrate that the proposed framework achieves state-of-the-art performance, effectively mitigating over-smoothing and enabling deeper, more expressive architectures. The code is available at https://github.com/rene0329/EWGNN/.

The security of Graph Neural Networks (GNNs) is crucial for ensuring the reliability and protection of the systems they are integrated within real-world applications. However, current approaches lack the ability to prevent GNNs from learning high-risk information, including edges, nodes, convolutions, etc. In this paper, we propose a secure GNN learning framework called Reinforcement Learning-based Secure Training Algorithm . We first introduce a model conversion technique that transforms the training process of GNNs into a verifiable Markov Decision Process model. To maintain the security of model we employ Deep Q-Learning algorithm to prevent high-risk information messages. Additionally, to verify whether the strategy derived from Deep Q-Learning algorithm meets safety requirements, we design a model transformation algorithm that converts MDPs into probabilistic verification models, thereby ensuring our method’s security through formal verification tools. The effectiveness and feasibility of our proposed method are demonstrated by achieving a 6.4% improvement in average accuracy on open-source datasets under adversarial attack graphs.

Social relationships offer crucial supplementary information for recommendations by leveraging users' social connections to gain insights into their preferences. However, prevalent social recommendation methods often grapple with the issues of sparsity and noise, which curtail their effectiveness. In addition, these methods overlook the intricacies of user interactions within social networks, which could provide invaluable information. Addressing their deficiencies, this article introduces a novel sociological-theory-based multitopic self-supervised recommendation method (SMSR). This method integrates user attitude information into the construction of social relationships and utilizes dynamic routing to identify and categorize topics, thereby mitigating the impact of social noise on recommendation accuracy. Furthermore, we reveal sophisticated higher order user relations within these topics by using motifs. By combining the light graph convolutional network with balance theory, SMSR efficiently aggregates information from diverse social relations to gain its outstanding performance. Moreover, we have devised and integrated four self-supervised signals, inspired by social theory and derived from heterogeneous graph analysis, to more effectively exploit the rich structural and semantic information inherent in social relationship graphs. Empirical results from extensive experiments on publicly available datasets underscore SMSR's superiority over the state of the art.

The Traveling Salesman Problem is a combinatorial optimization problem that seeks to find the shortest path visiting a set of locations, where each location is visited exactly once, and the path returns to the starting point. Using traditional computing model to solve Traveling Salesman Problem would face the issue of state explosion. This paper proposes a solving method based on the probe machine model, greatly accelerating the solving speed. By iteratively adding probes and performing probe operations in sequence, both optimal and feasible solutions for this problem can be obtained. We developed a solver PROBE4TSP and presented its framework and execution process. Through comparative experiments, we demonstrate that this method is faster than some classical solvers for small-scale Traveling Salesman Problems, especially fewer than thirty nodes.

Specifying spatio-temporal aspects is one of the important areas in cyber-physical systems.Spatio-temporal logic with changes of truth value in discrete time and dense time has been researched, but a combination of spatial and temporal components with changes of spatial entities in dense time hasn't been well-done.The major problem is dense time and real-valued variables of the spatio-temporal properties of cyber-physical systems.In this paper, we propose a spatio-temporal specification language, named STSL, which integrates Signal Temporal Logic (STL) with a spatial logic S4u to deal with the changes of realvalues spatial entities in dense time.The combined language is divided into two formalisms, ST SLP C and ST SLOC , which is applied to interpret the Boolean semantics and quantitative semantics, respectively.The syntax of the two formalism and the corresponding semantics are provided.Besides, we present a Hilbert-style axiomatization for the proposed STSL and provide the soundness and completeness result by the spatio-temporal extension of maximal consistent set and canonical model.

Human-centric design is based on the psychological and physical needs of the human users. Model-driven engineering provides formal model to be analyzed. How to combine formal model with human-centric design methodology is a crucial issue and yet it has not been settled. In fact, the difficulty of this problem is lacking of formal representations of the human-centric property. The intention of our research is to provide some new approaches to effectively model and analyze the human-centric system. So we proposed model-based methodologies for modeling and analyzing the human-centric system, which aim to use hierarchical model framework to effectively build systems. This paper mainly addresses two issues. The first one is the modeling of human-centric system by the hierarchical model framework. Then we selected the automatic train control braking system as the application to build hierarchical model based on five corresponding sub-models and provide the new braking modes and new braking strategies.