Recent studies have shown that Graph Convolutional Networks (GCNs) are vulnerable to adversarial attacks on the graph structure. Although multiple works have been proposed to improve their robustness against such structural adversarial attacks, the reasons for the success of the attacks remain unclear. In this work, we theoretically and empirically demonstrate that structural adversarial examples can be attributed to the non-robust aggregation scheme (i.e., the weighted mean) of GCNs. Specifically, our analysis takes advantage of the breakdown point which can quantitatively measure the robustness of aggregation schemes. The key insight is that weighted mean, as the basic design of GCNs, has a low breakdown point and its output can be dramatically changed by injecting a single edge. We show that adopting the aggregation scheme with a high breakdown point (e.g., median or trimmed mean) could significantly enhance the robustness of GCNs against structural attacks. Extensive experiments on four real-world datasets demonstrate that such a simple but effective method achieves the best robustness performance compared to state-of-the-art models.

Recent studies have shown that Graph Convolutional Networks (GCNs) are vulnerable to adversarial attacks on the graph structure. Although multiple works have been proposed to improve their robustness against such structural adversarial attacks, the reasons for the success of the attacks remain unclear. In this work, we theoretically and empirically demonstrate that structural adversarial examples can be attributed to the non-robust aggregation scheme (i.e., the weighted mean) of GCNs. Specifically, our analysis takes advantage of the breakdown point which can quantitatively measure the robustness of aggregation schemes. The key insight is that weighted mean, as the basic design of GCNs, has a low breakdown point and its output can be dramatically changed by injecting a single edge. We show that adopting the aggregation scheme with a high breakdown point (e.g., median or trimmed mean) could significantly enhance the robustness of GCNs against structural attacks. Extensive experiments on four real-world datasets demonstrate that such a simple but effective method achieves the best robustness performance compared to state-of-the-art models.

Background: For medium and low speed maglev transportation system, the eddy current will be induced in rail, which is made of solid steel, while the train is running. The levitation force of electromagnets will be weakened by the magnetic field generated by eddy current in the rail, especially at the position of the forefront electromagnets. With the increase of train running speed, the eddy current effect will also increase, which will reach 30 % at 100 km/h, and which will directly affect the levitation stability of the train during high-speed running. Put it another way, it will limit the further improvement of the running speed of the medium and low speed maglev train. Aim: In order to solve the above problem, and compensate the levitation force reduced by the eddy current effect. Methods: The FEA method is used to obtain the magnetic field distribution and levitation force changing with the train speed. And taking the middle and low speed maglev trains and rails of Changsha Maglev Express as the research object, we have adopted two solutions, and the prototypes of airsprings and levitation magnets are manufactured and tested in the train. Results: The test result show that the currents of the windings at the front end of the two forefront electromagnets are reduced obviously. Conclusion: In this paper, the medium and low speed maglev train and rail used by Changsha Maglev Express are studied, the eddy current effect is analyzed, and two solutions are proposed. The results show that the solution methods can alleviate the eddy current effects to some extent.

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Background: The short stator linear induction motor (LIM) is normally used in medium-low speed maglev train. The restriction by mounting space on bogie and motor input voltage from the third power supply rail lead that the maximum speed of medium-low speed maglev train can reach no more than 120 km/h. Aim: In this paper, by means of the LIM design optimization, improvement of the LIM force characteristic in high speed range, the maximum speed of medium-low speed maglev train can reach 160 km/h. Methods: After comparing the LIM theoretical calculation and actual test data, it shows that the new designed LIM is effective. Conclusion: Afterwards, by installing the new designed LIMs, the traditional medium-low speed maglev train becomes a fast-speed maglev train, and it has a bright future in transportation applications.