### Inverse-engineering of complex oscillatory networks

Early Stage Researcher: Marc Grau

Principle Investigators: Zoran Levnajic (Novo Mesto, FIS – major institution), Ralph G Andrzejak (Barcelona, UPF – partner institution)

Complex systems, including biological organisms, social networks or infrastructure systems, are composed of many interacting units. Such cooperative systems display emergent behavior that cannot be exhibited by any unit in isolation. The crucial factor determining the properties of the emergent behavior is the topology of inter-unit interactions, i.e., the rules specifying which units interact and how. However, finding these rules for real complex systems is a very challenging problem, which is why the precise topology of most real networks is at best partially known.

This project will both extend the existing, and develop new, methods of detecting the topology of unknown networks from the available synthetic or empirical data. Relying on the previous results (see references), which include novel derivative-variable correlation methods, the aim is to construct a framework of methodologies applicable in a variety of realistic scenarios. The designed methods should be robust to strongly noise-contaminated data or data with considerable observation errors, both ubiquitous in real experiments. Moreover, the method should be applicable to data of varying length, potentially characterizing different dynamical regimes (regular, chaotic etc.). Special emphasis will be given to examining the power of the method in relation to the set of hypotheses assumed about the system. Except for dynamical systems and statistical physics approaches to the problem, the work might involve techniques from machine learning and related fields of computer science. The real data is expected to include time series of gene expression levels for networks of interacting genes, in addition to other biological and non-biological data. The data will include examples where ground-truth is known (verification of the method) and examples where it is not known (actual application of the method).

The findings are expected to significantly advance the state-of-the-art in the field of network reconstruction, possibly inspiring the development of open-source software useful to domain scientists.

References:

- Z. Levnajić, A. Pikovsky, Untangling complex dynamical systems via derivative-variable correlations, Scientific Reports 4, 5030, 2014.
- O. N. Yaveroglu, N. Malod-Dognin, D. Davis, Z. Levnajić, Vuk Janjić, R. Karapandža, A. Stojmirović, N. Pržulj, Revealing the Hidden Language of Complex Networks, Scientific Reports 4, 4547, 2014.
- Z. Levnajić, Derivative-variable correlation reveals the structure of dynamical networks, European Physical Journal B 86, 298, 2013.
- Z. Levnajić, Evolutionary Design of Non-frustrated Networks of Phase-repulsive Oscillators, Scientific Reports 2, 967, 2012.
- Z. Levnajić, A. Pikovsky, Network Reconstruction from Random Phase Resetting, Physical Review Letters 107, 034101, 2011.
- R. G. Andrzejak, T. Kreuz, Characterizing unidirectional couplings between point processes and flows, Europhysics Letters 96, 50012, 2011.