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『Science』聚焦：静态网络与时效网络，孰优孰劣？

已有 3378 次阅读 2018-3-23 17:48 |个人分类:好文推荐|系统分类:论文交流

以往，网络科学的研究集中于静态网络。在静态网络中，结点间有着固定的链路(link)且在程序执行期间，链路固定不变。然而，随着研究的不断深入，人们发现大部分的自然和社会系统实际上是一种“时效”网络 ("temporal" networks)，即链路是间歇可变的 (intermittently)，网络结构会随着时间的变化而变化，比如：代谢系统中，链路随着化学反应的变化而变化；社会网络中，友情链路会随着面对面或线上交流而变化。

研究表明，链路的暂时性 (link temporality) 会阻断网络路径，导致信息的传输与获取中断，从而阻碍系统中正在发生的动态过程。对于自然界中随处可见的时效网络，除了上述缺陷，其暂时性就毫无优势可言吗？

表面上看，静态网络确实优于时效网络，更容易控制系统。但在《Science》发表的The Fundamental Advantages of Temporal Networks 一文中，研究者提出了不一样的观点：时效网络易控制、能耗低、紧凑简约，拥有静态网络难以企及的灵活度。

研究者运用分析框架，采用连续时间切换系统的理论方法，将时效网络转化为时空上演化的网络切片(snapshot)，从控制时间、能量、轨迹三个方面系统地探讨了在控制时效网络时，其相较于传统静态网络所具有的潜在优势。

全文链接：

http://science.sciencemag.org/content/358/6366/1042

摘要：

Most networked systems of scientific interest are characterized by temporal links, meaning the network’s structure changes over time. Link temporality has been shown to hinder many dynamical processes, from information spreading to accessibility, by disrupting network paths. Considering the ubiquity of temporal networks in nature, we ask: Are there any advantages of the networks’ temporality? We use an analytical framework to show that temporal networks can, compared to their static counterparts, reach controllability faster, demand orders of magnitude less control energy, and have control trajectories, that are considerably more compact than those characterizing static networks.Thus, temporality ensures a degree of flexibility that would be unattainable in static networks, enhancing our ability to control them.

文章在对系统能控性问题的论述中，引用了2017年IJAC发表的综述Pinning Control and Controllability of Complex Dynamical Networks (Vol.14, No.1, 作者: 陈关荣)：多数系统在进行操作时，控制(control)必不可少。为实现系统的能控性，需要保证其具有连续的路径，可将输入的信号传送到网络中的其他部位。

◇ 引文链接 ◇

复杂动态网络的牵制控制与能控性问题

Pinning Control and Controllability of Complex Dynamical Networks

① SpringerLink:

https://link.springer.com/article/10.1007/s11633-016-1052-9

② IJAC官网：

http://www.ijac.net/EN/abstract/abstract1865.shtml

文中，陈关荣教授首先介绍了复杂网络牵制控制(Pinning Control)的思想和方法，然后介绍由线性时不变系统节点组成的有向加权复杂网络的状态能控性和结构能控性概念、单输入单输出(SISO)系统节点情形的最少牵制控制输入原理和能控性判据，并举例说明了多输入多输出(MIMO)系统节点情形的多样性和复杂性，给出了相应的状态能控性的充分必要条件。最后对复杂网络科学目前研究现状和未来发展趋势进行了总结与分析。

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摘要：

In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output (SISO) or multi-input multi-output (MIMO) dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant (LTI) systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying (LTV) node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.

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