论文标题
在动态网络中，中尺度组件和本地时间尺度的可严重性
Severability of mesoscale components and local time scales in dynamical networks
论文作者
论文摘要
动态系统理论的一个主要目标是搜索对大量相互作用状态的动态的简化描述。对于绝大多数复杂的动态系统，在整个动力学上的降低描述的推导在计算上是不可行的。其他复杂的系统是如此广泛，尽管不断遭到新数据的猛烈攻击，但只能提供部分信息。为了应对这一挑战，我们为局部质量函数的可严重性定义和优化，以测量一组状态随着时间的推移的动态相干性。可断开性的理论基础在于我们对Simon-Ando-Fisher时间尺度分离定理的局部适应，该定理将当地井的直觉形式化了动力学过程的马尔可夫景观或显微镜和宏观动力学之间的分离。最后，我们通过将其应用于来自电力网络，图像分割，社交网络，代谢网络和单词关联的示例来证明可泄计的实际相关性。
A major goal of dynamical systems theory is the search for simplified descriptions of the dynamics of a large number of interacting states. For overwhelmingly complex dynamical systems, the derivation of a reduced description on the entire dynamics at once is computationally infeasible. Other complex systems are so expansive that despite the continual onslaught of new data only partial information is available. To address this challenge, we define and optimise for a local quality function severability for measuring the dynamical coherency of a set of states over time. The theoretical underpinnings of severability lie in our local adaptation of the Simon-Ando-Fisher time-scale separation theorem, which formalises the intuition of local wells in the Markov landscape of a dynamical process, or the separation between a microscopic and a macroscopic dynamics. Finally, we demonstrate the practical relevance of severability by applying it to examples drawn from power networks, image segmentation, social networks, metabolic networks, and word association.
