Optimal structure of signal networks for efficient information aggregation
Scientific Reports, vol. 15, pp. 40692
Abstract
This paper develops a mathematical framework to study signal networks, in which nodes can be active or inactive, and their activation or deactivation is driven by external signals and the states of the nodes to which they are connected via links. The focus is on determining the optimal number of key nodes (= highly connected and structurally important nodes) required to represent the global activation state of the network accurately. Motivated by neuroscience, medical science, and social science examples, we describe the node dynamics as a continuous-time inhomogeneous Markov process. Under mean-field and homogeneity assumptions, appropriate for large scale-free and disassortative signal networks, we derive differential equations characterising the global activation behaviour and compute the expected hitting time to network triggering. Analytical and numerical results show that two or three key nodes are typically sufficient to approximate the overall network state well, balancing sensitivity and robustness. Our findings provide insight into how natural systems can efficiently aggregate information by exploiting minimal structural components.
Authors 4
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Affiliation as printed
Department of Operations Analytics, VU University Amsterdam, De Boelelaan 1105, 1081 HV, Amsterdam, The Netherlands
Vrije Universiteit Amsterdam
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Affiliation as printed
Mathematical Institute, Leiden University, Einsteinweg 55, 2333 CC, Leiden, The Netherlands
Leiden University
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Ines Lindner corresponding
Affiliation as printed
Department of Economics, VU University Amsterdam, De Boelelaan 1105, 1081 HV, Amsterdam, The Netherlands. i.d.lindner@vu.nl
Vrije Universiteit Amsterdam
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Affiliation as printed
Mathematical Institute, Leiden University, Einsteinweg 55, 2333 CC, Leiden, The Netherlands
Leiden University
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