Identifying Controlling Nodes in Neuronal Networks in Different Scales

Tang, Yang; Gao, Huijun; Zou, Wei; Kurths, Jürgen

doi:10.1371/journal.pone.0041375

Cited by 64 publications

(64 citation statements)

References 56 publications

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“…It is also shown that the minimum number of driver nodes is determined mainly by the degree distribution of the network. Many other studies of controllability in complex networks have followed, including [20], [19], [23], [24], [21].One issue with the approach taken by [16] and much of the follow up work is that the quantitative notion of controllability discussed in [16] (namely, the number/fraction of required driver nodes) is rather crude in some settings. This was noted, for example, by [18] in response to the surprising result in [16] that genetic regulatory networks seem to require many…”

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confidence: 99%

Optimal Sensor and Actuator Placement in Complex Dynamical Networks

Summers

Lygeros

2014

IFAC Proceedings Volumes

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Abstract-Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and actuator placement: choose a subset from a finite set of possible placements to optimize some real-valued controllability and observability metrics of the network. Surprisingly little is known about the structure of such combinatorial optimization problems. In this paper, we show that an important class of metrics based on the controllability and observability Gramians has a strong structural property that allows efficient global optimization: the mapping from possible placements to the trace of the associated Gramian is a modular set function. We illustrate the results via placement of power electronic actuators in a model of the European power grid.I. INTRODUCTION Controllability and observability have been recognized as fundamental structural properties of dynamical systems since the seminal work of Kalman in 1960 [13], but have recently seen renewed interest in the context of large, complex networks, such as power grids, the Internet, transportation networks, and social networks. A prominent example of this recent interest is [16], which, based on Kalman's rank condition and the idea of structural controllability, presents a graph theoretic maximum matching method to efficiently identify a minimal set of so-called driver nodes through which time-varying control inputs can move the system around the entire state space (i.e., render the system controllable). The method of [16] is applied across a range of technological and social systems, leading to several interesting and surprising conclusions. Using a metric of controllability given by the fraction of driver nodes in the minimal set required for complete controllability, it is shown that sparse inhomogeneous networks are difficult to control while dense homogeneous networks are easier. It is also shown that the minimum number of driver nodes is determined mainly by the degree distribution of the network. Many other studies of controllability in complex networks have followed, including [20], [19], [23], [24], [21].One issue with the approach taken by [16] and much of the follow up work is that the quantitative notion of controllability discussed in [16] (namely, the number/fraction of required driver nodes) is rather crude in some settings. This was noted, for example, by [18] in response to the surprising result in [16] that genetic regulatory networks seem to require many

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confidence: 99%

Optimal Sensor and Actuator Placement in Complex Dynamical Networks

Summers

Lygeros

2014

IFAC Proceedings Volumes

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“…Studying the effects of mixed time-delayed coupling on other collective behaviors of coupled nonlinear oscillators is certainly an interesting subject for future investigations. Finally, our findings in this work should attract general interest from researchers in the fields of nonlinear dynamics and have great potential for applications in systems biology, ecology, signal processing, and neuroscience [66].…”

Section: Conclusion and Discussionmentioning

confidence: 78%

Amplitude death in nonlinear oscillators with mixed time-delayed coupling

et al. 2013

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Amplitude death (AD) is an emergent phenomenon whereby two or more autonomously oscillating systems completely lose their oscillations due to coupling. In this work, we study AD in nonlinear oscillators with mixed time-delayed coupling, which is a combination of instantaneous and time-delayed couplings. We find that the mixed time-delayed coupling favors the onset of AD for a larger set of parameters than in the limiting cases of purely instantaneous or completely time-delayed coupling. Coupled identical oscillators experience AD under instantaneous coupling mixed with a small proportion of time-delayed coupling. Our work gives a deeper understanding of delay-induced AD in coupled nonlinear oscillators.

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“…Although (Tang et al, 2012a) investigated the controllability problem of complex networks, unfortunately, the network considered is undirected. Therefore, Tang, Gao, Zou, and Kurths (2012b) concentrates on the identification of controlling regions in neuronal networks of cats' brain, based on singleobjective evolutionary computation methods, in which the network is directed. Then, one simple way to treat the controllability of directed networks is to consider the two measures of controllability P and r, separately.…”

Section: Local Controllabilitymentioning

confidence: 99%

“…Evidently, the way regarding the objectives P and r separately is unavoidable to induce conservativeness (Tang et al, 2012b).…”

Section: Local Controllabilitymentioning

confidence: 99%