复杂网络中相互作用信号源的定位
Locating the source of interacting signal in complex networks
摘要：
研究了复杂网络中自交互信号扩频的源定位问题。我们使用一个著名的谣言模型作为一个例子的过程与自我互动。根据这个基于SIR流行动力学的模型，被感染的节点可以以$α$的概率相互作用并阻止彼此八卦。本文比较了三种声源定位算法：有限Pinto-Thiran-Vettarli（LPTV）、梯度极大似然（GMLA）和基于时间和距离的Pearson相关性的算法。数值模拟的结果表明，感染节点之间的额外的相互作用降低了LPTV和皮尔逊的质量。GMLA对自相互作用的有害影响是最有抵抗力的，这对于过程的中等和高水平的随机性尤其明显，当铺展率低于0.5时。其原因可能是GMLA只使用最近的观察者，这些观察者不太可能受到受感染节点之间相互作用的影响，因为随着流行病的发展和感染媒介数量的增加，这些接触变得重要。
英文摘要：
We investigate the problem of locating the source of a self-interacting signal spreading in a complex networks. We use a well-known rumour model as an example of the process with self-interaction. According to this model based on the SIR epidemic dynamics, the infected nodes may interact and discourage each other from gossiping with probability $α$. We compare three algorithms of source localization: Limited Pinto-Thiran-Vettarli (LPTV), Gradient Maximum Likelihood (GMLA) and one based on Pearson correlation between time and distance. The results of numerical simulations show that additional interactions between infected nodes decrease the quality of LPTV and Pearson. GMLA is the most resistant to harmful effects of the self-interactions, which is especially visible for medium and high level of stochasticity of the process, when spreading rate is below 0.5. The reason for this may be the fact that GMLA uses only the nearest observers, which are much less likely affected by the interactions between infected nodes, because these contacts become important as the epidemics develops and the number of infected agents increases.
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