QUANTITATIVE BIOLOGY SEMINAR<br>Reconstructing Connectivity of Oscillator Networks from Observations

We discuss the problem of network inference from data and present an approach for invariant reconstruction of phase dynamics from observations; invariance here means independence of the recovered model on the observables used for the analysis. We start with the simplest case of two interacting oscillators and present an application of the approach to cardio-respiratory interaction in humans. We demonstrate the invariance property of our technique by showing that the coupling functions reconstructed using respiratory flow and either electrocardiogram or arterial pulse are very close.

Next, we present an approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.