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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 11: Networks - From Topology to Dynamics I (joint SOE/DY/BP)
SOE 11.4: Vortrag
Mittwoch, 18. März 2020, 18:15–18:30, GÖR 226
Revealing network size from the dynamics of a single node? — •Georg Börner1, Hauke Haehne2, Jose Casadiego1, and Marc Timme1 — 1Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), TU Dresden — 2Institute for Physics, Carl von Ossietzky University Oldenburg
Networks are ubiquitous in the natural and human-made world and their dynamics fundamentally underlie the function of a variety of systems, from gene regulation in the cell and the activity of neuronal circuits to the distribution of electric power and the transport of people and goods.
Recent work [1] introduced a method to infer the size of a network, its number of dynamical variables, from measuring times series of a fraction of its units only. Here we demonstrate that size inference is possible even from the observed time series of a single unit. We state mathematical conditions required for such inference in principle and show that, in practice, the success depends strongly on numerical constraints as well as on experimental decisions. We illustrate successful size inference for systems of N=18 variables and point to ways for improving the reliability and power of the reconstruction. We briefly comment on how the success of the approach depends on the quality and quantity of collected data and formulate some general rules of thumb on how to approach the measurement of a given system.
[1] H. Haehne et al., Detecting Hidden Units and Network Size from Perceptible Dynamics Phys. Rev. Lett. 122:158301 (2019).