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• W2077883651 abstract "In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolation-like emergence of a macroscopic observable component in graphs in which the state of a fraction of the nodes, and of their first neighbors, is monitored. We show how their concept of depth-L percolation---where the state of nodes up to a distance L of monitored nodes is known---can be mapped unto multitype random graphs, and use this mapping to exactly solve the observability problem for arbitrary L. We then demonstrate a non-trivial coexistence of an observable and of a non-observable extensive component. This coexistence suggests that monitoring a macroscopic portion of a graph does not prevent a macroscopic event to occur unbeknown to the observer. We also show that real complex systems behave quite differently with regard to observability depending on whether they are geographically-constrained or not." @default.
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• W2077883651 date "2014-02-06" @default.
• W2077883651 modified "2023-10-16" @default.
• W2077883651 title "Coexistence of phases and the observability of random graphs" @default.
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• W2077883651 doi "https://doi.org/10.1103/physreve.89.022801" @default.
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