高阶模型捕捉时间网络可控性的变化
Higher-order models capture changes in controllability of temporal networks
摘要：
在许多复杂系统中，元件通过时变网络拓扑进行交互。最近的研究表明，相互作用的时间顺序的时间相关性至关重要的影响网络的性质和动力学过程。这些相关性如何影响我们控制具有时变相互作用的系统的能力仍不清楚。在这项工作中，我们使用高阶网络模型扩展的结构可控性的时间网络的框架，其中的时间顺序的相互作用产生了尊重时间的路径与非马尔可夫特征。我们研究了六个经验数据集，表明真实系统的非马尔可夫特性可以增加或减少控制整个系统所需的最小时间。与经验数据和合成模型，我们进一步表明，谱特性的概括图拉普拉斯高阶网络可以用来分析捕获的时间相关性的可控性的影响。我们的工作强调了（i）相互作用的时间顺序的相关性是复杂性的重要来源，它显著影响了时间网络的可控性，（ii）高阶网络模型是理解经验系统的时间拓扑特征的有力工具。
英文摘要：
In many complex systems, elements interact via time-varying network topologies. Recent research shows that temporal correlations in the chronological ordering of interactions crucially influence network properties and dynamical processes. How these correlations affect our ability to control systems with time-varying interactions remains unclear. In this work, we use higher-order network models to extend the framework of structural controllability to temporal networks, where the chronological ordering of interactions gives rise to time-respecting paths with non-Markovian characteristics. We study six empirical data sets and show that non-Markovian characteristics of real systems can both increase or decrease the minimum time needed to control the whole system. With both empirical data and synthetic models, we further show that spectral properties of generalisations of graph Laplacians to higher-order networks can be used to analytically capture the effect of temporal correlations on controllability. Our work highlights that (i) correlations in the chronological ordering of interactions are an important source of complexity that significantly influences the controllability of temporal networks, and (ii) higher-order network models are a powerful tool to understand the temporal-topological characteristics of empirical systems.
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