样条领带衰减时空网络

Chanon Thongprayoon, Naoki Masuda
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引用次数: 0

摘要

有关时态网络或时变网络的数据越来越多。时态网络数据有多种表示方法,每种方法对于下游任务(如数学分析、可视化、基于代理的时态网络动态模拟和其他动态模拟)和发现有用的结构都有不同的优势。领带衰减网络是时态网络的一种表现形式,其优点包括能够从离散的时间戳接触事件数据生成连续时间网络,具有数学上的可操作性和较低的计算成本。然而,目前的领带衰减网络框架在每个离散接触事件如何影响随时间变化的领带强度(我们称之为内核)方面受到了限制。在这里,我们从内核的角度扩展了领带衰减网络模型。具体来说,我们使用三次样条函数来模拟内核的短期行为,使用指数衰减函数来模拟长期行为,并将它们嫁接在一起。这种样条曲线版本的领带衰减网络可以实现两个节点之间的延迟和 $C^1$ 连续交互率,而相对于传统的领带衰减网络,它只稍微增加了计算和内存负担。我们展示了平分线领带衰减网络的数学特性,并通过三个任务对其进行了数值展示:网络嵌入、确定性舆论动力学模型和随机流行病传播模型。
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Spline tie-decay temporal networks
Increasing amounts of data are available on temporal, or time-varying, networks. There have been various representations of temporal network data each of which has different advantages for downstream tasks such as mathematical analysis, visualizations, agent-based and other dynamical simulations on the temporal network, and discovery of useful structure. The tie-decay network is a representation of temporal networks whose advantages include the capability of generating continuous-time networks from discrete time-stamped contact event data with mathematical tractability and a low computational cost. However, the current framework of tie-decay networks is limited in terms of how each discrete contact event can affect the time-dependent tie strength (which we call the kernel). Here we extend the tie-decay network model in terms of the kernel. Specifically, we use a cubic spline function for modeling short-term behavior of the kernel and an exponential decay function for long-term behavior, and graft them together. This spline version of tie-decay network enables delayed and $C^1$-continuous interaction rates between two nodes while it only marginally increases the computational and memory burden relative to the conventional tie-decay network. We show mathematical properties of the spline tie-decay network and numerically showcase it with three tasks: network embedding, a deterministic opinion dynamics model, and a stochastic epidemic spreading model.
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