时间网络中链接形成的记忆效应：分数阶微积分方法
Memory effects on link formation in temporal networks: A fractional calculus approach
摘要：
记忆在复杂系统相互作用的时间演化中起着至关重要的作用。为了解决记忆对网络时间模式的影响，我们提出了一个简单的优先连接模型，在该模型中，节点有优先倾向于与最活跃的节点建立链接。节点活动是通过节点在给定时间间隔内观察到的链路数量来衡量的。记忆研究使用时间分数阶导数方程，这已被证明是一个强大的方法来理解现象的长期记忆。无记忆的情况下，揭示了一个特征时间，节点活动的行为不同，低于和高于它。我们还观察到，密集的时间网络（大量的事件）显示出更清晰的特征时间比稀疏的。有趣的是，我们还发现记忆会导致节点活动的衰减;因此，节点接收新连接的机会随着节点的年龄而减少。最后，我们讨论了不同记忆长度的网络的统计特性。
英文摘要：
Memory plays a vital role in the temporal evolution of interactions of complex systems. To address the impact of memory on the temporal pattern of networks, we propose a simple preferential connection model, in which nodes have a preferential tendency to establish links with most active nodes. Node activity is measured by the number of links a node observes in a given time interval. Memory is investigated using a time-fractional order derivative equation, which has proven to be a powerful method to understand phenomena with long-term memory. The memoryless case reveals a characteristic time where node activity behaves differently below and above it. We also observe that dense temporal networks (high number of events) show a clearer characteristic time than sparse ones. Interestingly, we also find that memory leads to decay of the node activity; thus, the chances of a node to receive new connections reduce with the node's age. Finally, we discuss the statistical properties of the networks for various memory-length.
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