高阶网络上传染动力学中的跨阶诱导行为
Cross-order induced behaviors in contagion dynamics on higher-order networks
AI总结：
本文研究了高阶网络中传染动力学的跨阶诱导行为，通过信息论度量揭示了高阶机制与结构相关性的关系。
摘要：
最近的研究表明，复杂系统中新型集体行为的出现是由于高阶相互作用。然而，这些相互作用的结构相关性如何塑造此类行为仍然是当前研究中的重大空白。为此，我们利用高阶行为（HOBs）的特征来识别底层的动力学规则，或高阶机制（HOMs）。在本工作中，我们比较了几种从信息论中衍生出的HOB度量方法。利用一个简单SIS传染模型，我们证明了更简单、计算效率更高的度量方法可以作为稳健的HOM指示器。我们揭示了跨阶诱导行为的新现象，其中行为特征在没有直接机制存在的相互作用阶中出现。关键的是，这些跨阶HOBs并非仅仅由结构相关性（如嵌套性和超边重叠）诱导，而是在任何HOM的邻域中出现。在我们测试的信息论度量中，协同性是最可靠的HOM真实阶的指示器。这些发现为网络结构与高阶系统观察到的动力学之间的关系提供了新的见解。
英文摘要：
Recent studies have shown that novel collective behaviors emerge in complex systems due to higher-order interactions. However, the way in which the structural correlations of these interactions shape such behaviors remains a significant gap in current research. To address this, we use signatures of higher-order behaviors (HOBs) to identify the underlying dynamical rules, or higher-order mechanisms (HOMs). In this work, we compare several HOB measures derived from information theory. Utilizing a simplicial SIS contagion model, we demonstrate that simpler, computationally efficient measures can serve as robust indicators of HOMs. We uncover the novel phenomenon of cross-order induced behaviors, where behavioral signatures emerge at interaction orders where no direct mechanism is present. Crucially, these cross-order HOBs are not simply induced by structural correlations -- such as nestedness and hyperedge overlap -- but they appear in the neighborhood of any HOM. Among the information-theoretic measures we tested, synergy is the most reliable indicator of the true order where the underlying mechanism is at play. These findings offer new insights into the relationship between the network structure and observed dynamics of higher-order systems.
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