Kim Jason Z, Soffer Jonathan M, Kahn Ari E, Vettel Jean M, Pasqualetti Fabio, Bassett Danielle S
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, 19104.
Department of Neuroscience, University of Pennsylvania, Philadelphia, PA, 19104 and U.S. Army Research Laboratory, Aberdeen, MD 21001.
Nat Phys. 2018;14:91-98. doi: 10.1038/nphys4268. Epub 2017 Sep 25.
Networked systems display complex patterns of interactions between components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology, supporting a variety of system-wide dynamical behaviors such as synchronization. While descriptions of these behaviors are important, they are only a first step towards understanding and harnessing the relationship between network topology and system behavior. Here, we use linear network control theory to derive accurate closed-form expressions that relate the connectivity of a subset of structural connections (those linking driver nodes to non-driver nodes) to the minimum energy required to control networked systems. To illustrate the utility of the mathematics, we apply this approach to high-resolution connectomes recently reconstructed from Drosophila, mouse, and human brains. We use these principles to suggest an advantage of the human brain in supporting diverse network dynamics with small energetic costs while remaining robust to perturbations, and to perform clinically accessible targeted manipulation of the brain's control performance by removing single edges in the network. Generally, our results ground the expectation of a control system's behavior in its network architecture, and directly inspire new directions in network analysis and design via distributed control.
网络系统展示了组件之间复杂的相互作用模式。在物理网络中，这些相互作用通常沿着结构连接发生，这些结构连接在硬连线连接拓扑中链接组件，支持各种全系统范围的动态行为，如同步。虽然对这些行为的描述很重要，但它们只是理解和利用网络拓扑与系统行为之间关系的第一步。在这里，我们使用线性网络控制理论来推导精确的闭式表达式，这些表达式将结构连接的一个子集（那些将驱动节点连接到非驱动节点的连接）的连通性与控制网络系统所需的最小能量联系起来。为了说明数学方法的实用性，我们将这种方法应用于最近从果蝇、小鼠和人类大脑重建的高分辨率连接组。我们利用这些原理来揭示人类大脑在以小能量成本支持多样化网络动态同时对扰动保持稳健性方面的优势，并通过去除网络中的单个边来对大脑的控制性能进行临床上可及的靶向操纵。一般来说，我们的结果将控制系统行为的期望建立在其网络架构之上，并通过分布式控制直接激发网络分析和设计的新方向。
