Social media rumors have the capacity to harm the public perception and the social progress. The news propagation pattern is a key clue for detecting rumors. Existing propagation-based rumor detection methods represent propagation patterns as a static graph structure. They simply consider the structure information of news distribution in social networks and disregard the temporal information. The dynamic graph is an effective modeling tool for both the structural and temporal information involved in the process of news dissemination. Existing dynamic graph representation learning approaches struggle to capture the long-range dependence of the structure and temporal sequence as well as the rich semantic association between full graph features and individual parts. We build a transformer-based dynamic graph representation learning approach for rumor identification DGTR to address the aforementioned challenges. We design a position embedding format for the graph data such that the original transformer model can be utilized for learning dynamic graph representations. The model can describe the structural long-range reliance between the dynamic graph nodes and the temporal long-range dependence between the temporal snapshots by employing a self-attention mechanism. In addition, the CLS token in transformer may model the rich semantic relationships between the complete graph and each subpart. Extensive experiments demonstrate the superiority of our model when compared to the state of the art.

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In this paper, we will investigate the design of discounted-cost linear quadratic regulator for switched linear systems. The distinguishing feature of the proposed method is that the designed discounted-cost linear quadratic regulator will achieve not only the desired optimization index, but also the exponentially convergent of the state trajectory of the closed-loop switched linear systems. First, we adopt the embedding transformation to transform the studied problem into a quadratic-programming problem. Then, the bang-bang-type solution of the embedded optimal control problem on a finite time horizon is the optimal solution to the original problems. The bang-bang-type solutions of the embedded optimal control problem is to be shown the optimization solution of the studied problem. Then, the computable sufficient conditions on discounted-cost linear quadratic regulator are proposed for finite-time and infinite-time horizon case, respectively. Finally, an example is provided to demonstrate the effectiveness of the proposed method.

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