No abstract

In this paper, we investigate the characteristics of collective motion of Stokesian swimmers with impulsive acceleration (SSIA). We consider two types of intensity function, namely, the displacement-based intensity function and elapsed-time-based intensity function. The stationary velocity distribution function (VDF) of the SSIA obtained by the direct simulation Monte Carlo method is compared with the analytical approximation, which is obtained by the kinetic (mean-field) equation of the SSIA. Finally, the collective motion of the SSIA confined by 2D box is analyzed by considering Vicsek-like effects to consider the effects of binary collision on the VDF of the SSIA.

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We propose a method for the modelling of the propagation of text data in web site space among some groups by using a multivariate Hawkes process with a sparse structure. For estimation, we introduced a hybrid method using a quasi-maximum likelihood estimator (QMLE) and a $L^1$-penalized QMLE. As a real example, we investigated posts on a Japanese web service about uncomfortable gender experiences, which we classified into 12 groups by age and sex, and we calculated the magnitude of the correlation between each group. In addition, we visualized the propagation structure of posts in each group by summarizing the results in a directed Hawkes graph and a heat map of time integrals of kernel functions.