AI 中文总结
研究时变网络中动态中心性问题，通过将其转化为常微分方程的最优控制问题，利用庞特里亚金极大值原理及 Krylov 型技术求解，能在规定控制约束下有效引导接收中心性。
AI 中文摘要
时变网络在多个领域建模动态交互中起关键作用，与静态网络不同，其拓扑和边权重不断变化。理解和控制这些网络对预测未来行为和优化动态过程至关重要。本文聚焦动态中心性问题，即如何通过对网络结构进行最小修改将网络中心性引导至期望状态。该问题被表述为常微分方程的最优控制问题，利用庞特里亚金极大值原理求解。对于大规模问题，用 Krylov 型技术近似所需矩阵函数操作。数值实验表明该框架能在规定控制约束下有效引导接收中心性。
英文摘要
Time-evolving networks, or temporal networks, play a crucial role in modeling dynamic interactions across various domains, including biology, social sciences, and information technology. Unlike static networks, these systems undergo continuous changes in topology and edge weights, influencing processes such as information flow, transportation efficiency, and neural activity. Understanding and controlling these networks are essential for predicting future behavior and optimizing dynamic processes. This work focuses on the problem of dynamic centrality, a measure of node importance in time-dependent networks. Specifically, we address how to steer network centrality to a desired state by making minimal modifications to the network structure. This problem is formulated as an optimal control problem for an ordinary differential equation, either matrix- or vector-based, where the control acts on network edges. The proposed framework generalizes centrality control problems studied in static networks and leverages the Pontryagin Maximum Principle for efficient solutions. For large-scale problems, the required matrix-function actions are approximated by Krylov-type techniques, avoiding the explicit formation of dense matrix functions. Numerical experiments on synthetic and real temporal networks show that the proposed framework can effectively steer receive centrality under prescribed control constraints.
