分支过程与攻击：病毒式竞争市场
Branching Process with Attack: Viral Competing Markets
摘要：
在线社交网络（OSN）上广告的显著增加使得内容传播的研究成为必要。我们分析了病毒式市场与内容提供方竞争的传播类似的职位在OSN。为此，我们需要一个新的分支过程（BP）的变体，我们将其命名为“攻击分支过程”;唤醒后的实体试图攻击并获取相反的种群;此外，每个实体都会产生其后代，正如通常在BP中所考虑的那样。除了为个别员额的增长率、二分法等提供表述外，我们探讨了帖子的共存;竞争性内容能否在网络上同时传播和爆炸（两个帖子的未读/实时副本数量随时间显著增长）？我们证明了一个或两个人口/职位灭绝或人口解决到一个唯一的共存平衡，并得出相应的渐近比的两个人口/职位。我们的分析适用于大型人口网络，专注于大众行为，而不是微观细节。我们的研究提供了两个关键设计方面的见解，种子用户的数量和帖子的质量。
英文摘要：
The marked increase in advertisements over online social networks (OSNs) necessitates the study of content propagation. We analyse the viral markets with content providers competing for the propagation of similar posts over OSNs. Towards this, we required a new variant of the branching process (BP), which we named as "Branching process with attack"; the entities upon wake up attempt to attack and acquire the opposite population; furthermore, each entity produces its offsprings as is usually considered in BPs. In addition to providing expressions for the growth rates of individual posts, dichotomy etc., we explore the co-existence of posts; can the competing content spread and explode (number of unread/live copies of both posts grow significantly with time) simultaneously over the network? We prove that either one or both populations/posts get extinct or the populations settle to a unique co-existence equilibrium and derive the corresponding asymptotic ratios of the two populations/posts. Our analysis applies to large population networks focusing on mass behaviour, rather than micro details. Our study provides insights into two crucial design aspects, the number of seed users and the quality of the post.
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