论文标题
非马克维亚随机步行将网络鲁棒性与非本地级联
Non-Markovian random walks characterize network robustness to nonlocal cascades
论文作者
论文摘要
现实世界网络中的局部扰动有可能在整个系统级别触发级联反应，从而阻碍其操作和功能。通过分析解决此问题的标准方法主要基于静态描述，例如渗透，或者是通过在首次邻接连接中演变而来的模型，至关重要地未能捕获真实级联的典型的非局部性行为。我们介绍了一个动力学模型，该模型将整个网络的失败传播映射到一个自我避免的随机行走，在每个步骤中，都有可能对操作系统单位进行非局部跳跃的可能性。尽管该过程的固有非马克维亚性质，但我们还是能够以平衡状态表征系统的临界行为，以及级联反应的停止时间分布。我们关于合成和经验生物学和运输网络的数值实验与理论期望非常吻合，这表明了我们框架量化具有互连结构的复杂系统非局部级联失败的脆弱性的能力。
Localized perturbations in a real-world network have the potential to trigger cascade failures at the whole system level, hindering its operations and functions. Standard approaches analytically tackling this problem are mostly based either on static descriptions, such as percolation, or on models where the failure evolves through first-neighbor connections, crucially failing to capture the nonlocal behavior typical of real cascades. We introduce a dynamical model that maps the failure propagation across the network to a self-avoiding random walk that, at each step, has a probability to perform nonlocal jumps toward operational systems' units. Despite the inherent non-Markovian nature of the process, we are able to characterize the critical behavior of the system out of equilibrium, as well as the stopping time distribution of the cascades. Our numerical experiments on synthetic and empirical biological and transportation networks are in excellent agreement with theoretical expectation, demonstrating the ability of our framework to quantify the vulnerability to nonlocal cascade failures of complex systems with interconnected structure.
