测量单个单元在产生复杂网络集体行为中的重要性
Measuring the importance of individual units in producing the collective behavior of a complex network
AI总结：
本文在连续时间动力系统框架下严格推导单元到网络其余部分的累积信息流，并以线性最大似然估计识别 Stuart-Landau 振子网络中的关键低度数节点。
摘要：
对单个单元在产生复杂网络集体行为中所做贡献进行定量评估，可使我们理解由于局部节点失效而对结构完整性造成的潜在损害。给定这些单元的时间序列，一种自然的方法是寻找从所关注单元流向网络其余部分的信息。在本研究中，我们表明这种信息流可以在连续时间动力系统的设定下被严格推导出来。在线性假设下，可以得到一个最大似然估计量，使我们能够以简便的方式对其进行估计。正如预期的那样，这种“累积信息流”并不等于流向其他单个单元的信息流之和，这反映了集体并非个体成员简单相加的集体现象。为了演示和验证，我们考察了一个由 Stuart-Landau 振子构成的网络。根据拓扑结构的不同，计算得到的信息流可能有所差异。在某些情况下，对网络而言最关键的节点并非枢纽；它们可能具有较低的度，而一旦受到抑制或攻击，将导致整个网络失效。
英文摘要：
A quantitative evaluation of the contribution of individual units in producing the collective behavior of a complex network can allow us to understand the potential damage to the structure integrity due to the failure of local nodes. Given time series for the units, a natural way to do this is to find the information flowing from the unit of concern to the rest of the network. In this study, we show that this flow can be rigorously derived in the setting of a continuous-time dynamical system. With a linear assumption, a maximum likelihood estimator can be obtained, allowing us to estimate it in an easy way. As expected, this "cumulative information flow" does not equal to the sum of the information flows to other individual units, reflecting the collective phenomenon that a group is not the addition of the individual members. For the purpose of demonstration and validation, we have examined a network made of Stuart-Landau oscillators. Depending on the topology, the computed information flow may differ. In some situations, the most crucial nodes for the network are not the hubs; they may have low degrees, and, if depressed or attacked, will cause the failure of the entire network.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
