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While significant efforts have been attempted in the design, control, and optimization of complex networks, most existing works assume the network structure is known or readily available. However, the network topology can be radically recast after an adversarial attack and may remain unknown for subsequent analysis. In this work, we propose a novel Bayesian sequential learning approach to reconstruct network connectivity adaptively: A sparse Spike and Slab prior is placed on connectivity for all edges, and the connectivity learned from reconstructed nodes will be used to select the next node and update the prior knowledge. Central to our approach is that most realistic networks are sparse, in that the connectivity degree of each node is much smaller compared to the number of nodes in the network. Sequential selection of the most informative nodes is realized via the between-node expected improvement. We corroborate this sequential Bayesian approach in connectivity recovery for a synthetic ultimatum game network and the IEEE-118 power grid system. Results indicate that only a fraction (∼50%) of the nodes need to be interrogated to reveal the network topology.
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Finding influential nodes in networks using pinning control: Centrality measures confirmed with electrochemical oscillators
The spatiotemporal organization of networks of dynamical units can break down resulting in diseases (e.g., in the brain) or large-scale malfunctions (e.g., power grid blackouts). Re-establishment of function then requires identification of the optimal intervention site from which the network behavior is most efficiently re-stabilized. Here, we consider one such scenario with a network of units with oscillatory dynamics, which can be suppressed by sufficiently strong coupling and stabilizing a single unit, i.e., pinning control. We analyze the stability of the network with hyperbolas in the control gain vs coupling strength state space and identify the most influential node (MIN) as the node that requires the weakest coupling to stabilize the network in the limit of very strong control gain. A computationally efficient method, based on the Moore–Penrose pseudoinverse of the network Laplacian matrix, was found to be efficient in identifying the MIN. In addition, we have found that in some networks, the MIN relocates when the control gain is changed, and thus, different nodes are the most influential ones for weakly and strongly coupled networks. A control theoretic measure is proposed to identify networks with unique or relocating MINs. We have identified real-world networks with relocating MINs, such as social and power grid networks. The results were confirmed in experiments with networks of chemical reactions, where oscillations in the networks were effectively suppressed through the pinning of a single reaction site determined by the computational method.
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- Award ID(s):
- 1900011
- PAR ID:
- 10557367
- Publisher / Repository:
- AIP
- Date Published:
- Journal Name:
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Volume:
- 33
- Issue:
- 9
- ISSN:
- 1054-1500
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1063/5.0163899
