A three-dimensional breakdown behavior of the magnetic Bloch-point domain wall (BP-DW) propagation was investigated in a ferromagnetic nanowire with the variation of the external magnetic field by means of micromagnetic simulation. As magnetic field strength increases up to a threshold value, the BP-DW velocity approaches a critical phase velocity of the spontaneously emitting spin wave (SW), where a Cherenkov-type DW breakdown phenomenon is observed originating from an interaction between the spontaneously emitting SW and the BP-DW. It is found that the velocity of the BP-DW approaches a maximum value ($2000 m/s) due to the intrinsic reversal time of a BP spin texture. This suggests that although cylindrical ferromagnetic nanowires might be free from the two-dimensional Walker breakdown phenomenon, there exists a Cherenkov-type three-dimensional breakdown behavior.

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In view of the exponential growth of information generated by social networks, social network analysis and recommendation have become important for many web applications. This paper examines the problem of social collaborative filtering to recommend items of interest to users in a social network setting. Many social networks capture the relationships among the nodes by using trust scores to label the edges. The bias of a node denotes its propensity to trust/mistrust its neighbors and is closely related to truthfulness. It is based on the idea that the recommendation of a highly biased node should be removed. In this paper, we propose a model-based approach for recommendation employing matrix factorization after removing the bias nodes from each link, which naturally fuses the users’ tastes and their trusted friends’ favors together. The empirical analysis on real large datasets demonstrate that our approaches outperform other state-of-the-art methods.

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