论文标题
时间网络中的内存形状
The shape of memory in temporal networks
论文作者
论文摘要
时间网络是广泛使用的模型，用于描述复杂系统的体系结构。网络内存 - 这是时间网络的过去的依赖性 - 已显示出在网络上发生的扩散，流行病和其他过程，甚至改变其社区结构中发挥着重要作用。最近的工作提出了使用高阶Markov模型来估计时间网络中的内存时间。在这里，我们表明网络内存本质上是多维的，不能有意义地减少到单个标量数量。因此，我们引入了一个数学框架，用于定义和有效地估计记忆的显微镜形状，该框架完全表征了每个链接的活动如何与所有其他链接的活动交织在一起。我们在具有可调记忆的时间网络的各种综合模型上验证了我们的方法，然后研究了各种现实世界网络中出现的记忆的异质形状。
Temporal networks are widely used models for describing the architecture of complex systems. Network memory -- that is the dependence of a temporal network's structure on its past -- has been shown to play a prominent role in diffusion, epidemics and other processes occurring over the network, and even to alter its community structure. Recent works have proposed to estimate the length of memory in a temporal network by using high-order Markov models. Here we show that network memory is inherently multidimensional and cannot be meaningfully reduced to a single scalar quantity. Accordingly, we introduce a mathematical framework for defining and efficiently estimating the microscopic shape of memory, which fully characterises how the activity of each link intertwines with the activities of all other links. We validate our methodology on a wide range of synthetic models of temporal networks with tuneable memory, and subsequently study the heterogeneous shapes of memory emerging in various real-world networks.
