Research ArticleNONLINEAR DYNAMICS

Revealing physical interaction networks from statistics of collective dynamics

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Science Advances  10 Feb 2017:
Vol. 3, no. 2, e1600396
DOI: 10.1126/sciadv.1600396

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Abstract

Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system’s model or dynamical data at a level of detail often not available. We exploit changes in invariant measures, in particular distributions of sampled states of the system in response to driving signals, and use compressed sensing to reveal physical interaction networks. Dynamical observations following driving suffice to infer physical connectivity even if they are temporally disordered, are acquired at large sampling intervals, and stem from different experiments. Testing various nonlinear dynamic processes emerging on artificial and real network topologies indicates high reconstruction quality for existence as well as type of interactions. These results advance our ability to reveal physical interaction networks in complex synthetic and natural systems.

Keywords
  • nonlinear dynamics
  • network dynamics
  • network reconstruction
  • physical connectivity
  • structural connectivity
  • gene networks

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

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