论文标题
饱和的总人口依赖的分支过程和病毒市场
Saturated total-population dependent branching process and viral markets
论文作者
论文摘要
在线社交网络（OSN）的用户不断转发有趣的帖子。这种传播导致将帖子重新转换为以前的一些收件人，随着帖子到达大量用户，该帖子会增加。因此，有效的前向（删除重新汇票后）减少了，最终导致副本总数的饱和。我们将此过程建模为分支过程的新变体，即“饱和的总人口相关的分支过程”，并使用随机近似技术对其进行分析。值得注意的是，我们获得了确定性的轨迹，这些轨迹近似于任何有限的时间窗口，近似“渐近和几乎肯定”的帖子的总副本；该轨迹仅取决于与网络特征相关的四个参数。此外，我们为未读的峰值副本，最大外展和帖子的寿命提供表达方式。我们观察到已知的指数增长，但随着时变的速度。我们还通过在Snap Twitter数据集中的详细模拟来验证我们的理论。
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.
