揭示多尺度网络纠缠对经验系统解体的影响
Unraveling the effects of multiscale network entanglement on disintegration of empirical systems
摘要：
复杂系统是实体的大集合，这些实体将自己组织成可以由网络表示的非平凡结构。这类系统的一个关键特性是对随机故障或有针对性的攻击的鲁棒性，即网络在删除节点或链路的情况下保持其完整性的能力。在这里，我们引入网络纠缠，通过多尺度透镜来研究网络的鲁棒性，通过系统传播信息所需的时间进行编码。我们的措施的基础在于最近提出的框架，显然是受量子统计物理学的启发，网络被解释为纠缠单元的集合，可以用类似吉布斯的密度矩阵来表征。我们发现，在最小的时间尺度纠缠减少到节点的程度，而在大规模的，我们表明它的能力来衡量每个节点在网络的完整性所发挥的作用。在介观尺度上，纠缠包含了结构之外的信息，如系统的输运性质。作为一个应用程序，我们表明，网络拆除经验的社会，生物和交通系统揭示了存在一个最佳的时间尺度驱动网络解体。我们的研究结果为网络收缩过程及其对动力学过程的影响的新的多尺度分析打开了大门。
英文摘要：
Complex systems are large collections of entities that organize themselves into non-trivial structures that can be represented by networks. A key emergent property of such systems is robustness against random failures or targeted attacks ---i.e. the capacity of a network to maintain its integrity under removal of nodes or links. Here, we introduce network entanglement to study network robustness through a multi-scale lens, encoded by the time required to diffuse information through the system. Our measure's foundation lies upon a recently proposed framework, manifestly inspired by quantum statistical physics, where networks are interpreted as collections of entangled units and can be characterized by Gibbsian-like density matrices. We show that at the smallest temporal scales entanglement reduces to node degree, whereas at the large scale we show its ability to measure the role played by each node in network integrity. At the meso-scale, entanglement incorporates information beyond the structure, such as system's transport properties. As an application, we show that network dismantling of empirical social, biological and transportation systems unveils the existence of a optimal temporal scale driving the network to disintegration. Our results open the door for novel multi-scale analysis of network contraction process and its impact on dynamical processes.
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