饱和总种群依赖的分支过程和病毒式市场
Saturated total-population dependent branching process and viral markets
摘要：
有趣的帖子不断被在线社交网络（OSN）的用户转发。这种传播导致将帖子重新转发给一些先前的接收者，这随着帖子到达大量用户而增加。因此，有效转发（在删除重新转发之后）减少，最终导致总副本数饱和。我们模拟这个过程作为一个新的变种的分支过程，“饱和总人口依赖的分支过程”，并分析它使用的随机逼近技术。值得注意的是，我们获得确定性的轨迹近似的总和未读的副本后“渐近，几乎肯定”在任何有限的时间窗口，这个轨迹只取决于四个参数的网络特性。此外，我们还提供了未读副本峰值、最大外展和帖子寿命的表达式。我们观察到已知的指数增长性，但随时间变化的速度。我们还通过对SNAP Twitter数据集的详细模拟来验证我们的理论。
英文摘要：
Interesting posts are continually forwarded by the users of the online social network (OSN). Such propagation leads to re-forwarding of the post to some of the previous recipients, which increases as the post reaches a large number of users. Consequently, the effective forwards (after deleting the re-forwards) reduce, eventually leading to the saturation of the total number of copies. We model this process as a new variant of the branching process, the `saturated total-population-dependent branching process', and analyse it using the stochastic approximation technique. Notably, we obtain deterministic trajectories which approximate the total and unread copies of the post `asymptotically and almost surely' over any finite time window; this trajectory depends only on four parameters related to the network characteristics. Further, we provide expressions for the peak unread copies, maximum outreach and the life span of the post. We observe known exponential growth but with time-varying rates. We also validate our theory through detailed simulations on the SNAP Twitter dataset.
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