Benchmarking Measures of Network Controllability on Canonical Graph Models
Benchmarking Measures of Network Controllability on Canonical Graph Models
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DOI：
10.1007/s00332-018-9448-z
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发表时间：
2017-06
影响因子：
3
通讯作者：
Elena Wu-Yan;Richard F. Betzel;Evelyn Tang;Shi Gu;F. Pasqualetti;D. Bassett
中科院分区：
文献类型：
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作者：
Elena Wu-Yan;Richard F. Betzel;Evelyn Tang;Shi Gu;F. Pasqualetti;D. Bassett
网络动力系统的控制为系统生物学和神经科学的新发现和新疗法提供了可能性。最近的理论进展提供了候选机制，通过这些机制，系统可以从一个预先指定的状态驱动到另一个状态，计算方法提供了在现实世界系统中测试这些机制的工具。尽管已经应用于生物学和神经科学的网络系统研究，但这些工具和相关措施在具有预先指定结构的简单网络上的实际性能尚未得到评估。在这里，我们研究了四个控制指标（全局、平均、模态和边界可控性）在八个典型图（包括Erdős-Rényi、正则、小世界、随机几何、Barábasi-Albert优先连接和几个模块化网络）上的行为，这些图具有不同的边缘加权方案（高斯分布、幂律分布和两个来自大脑网络的非参数分布，作为现实世界系统的例子）。我们观察到，与正态分布相反，当边缘权重分布是重尾分布时，图模型之间的全局可控性差异更为显著。相反，当边缘权重分布较轻时，图模型之间（以及图中的节点之间）的平均、模态和边界可控性的差异更为显著。在图模型和边加权方案中，平均可控性和模态可控性在节点间呈负相关；然而，在图形实例中，平均可控性和模态可控性之间的关系可以是正的、负的或不显著的。总的来说，这些发现表明，具有不同拓扑的图的可控性统计（及其关系）是不同的，并且这些差异可以通过边缘权重分布的差异来减弱或增强。更一般地说，我们的数值研究激发了未来的分析工作，以更好地理解图拓扑和控制之间关系的数学基础，以及设计具有特定控制配置文件的网络的努力。
The control of networked dynamical systems opens the possibility for new discoveries and therapies in systems biology and neuroscience. Recent theoretical advances provide candidate mechanisms by which a system can be driven from one pre-specified state to another, and computational approaches provide tools to test those mechanisms in real-world systems. Despite already having been applied to study network systems in biology and neuroscience, the practical performance of these tools and associated measures on simple networks with pre-specified structure has yet to be assessed. Here, we study the behavior of four control metrics (global, average, modal, and boundary controllability) on eight canonical graphs (including Erdős–Rényi, regular, small-world, random geometric, Barábasi–Albert preferential attachment, and several modular networks) with different edge weighting schemes (Gaussian, power-law, and two nonparametric distributions from brain networks, as examples of real-world systems). We observe that differences in global controllability across graph models are more salient when edge weight distributions are heavy-tailed as opposed to normal. In contrast, differences in average, modal, and boundary controllability across graph models (as well as across nodes in the graph) are more salient when edge weight distributions are less heavy-tailed. Across graph models and edge weighting schemes, average and modal controllability are negatively correlated with one another across nodes; yet, across graph instances, the relation between average and modal controllability can be positive, negative, or nonsignificant. Collectively, these findings demonstrate that controllability statistics (and their relations) differ across graphs with different topologies and that these differences can be muted or accentuated by differences in the edge weight distributions. More generally, our numerical studies motivate future analytical efforts to better understand the mathematical underpinnings of the relationship between graph topology and control, as well as efforts to design networks with specific control profiles.