Using nonlinear interdependence measures to detect directional couplings in networks
Early Stage Researcher: Irene Malvestio
Principle Investigators: Ralph G Andrzejak (Barcelona, UPF – major institution), Thomas Kreuz (Florence, Unifi – partner institution)
This project is positioned at the interface between physics, applied mathematics, physiology and medicine. It is focused on the development and application of novel nonlinear signal analysis techniques to study interactions in networks of dynamics, building on existing nonlinear techniques that allow one to study interactions between pairs of dynamics. All novel techniques will be evaluated thoroughly on mathematical model systems and later be applied to experimental cardio-respiratory recordings.
The framework of nonlinear time series analysis allows characterizing dynamical systems in which nonlinearity gives rise to a complex, seemingly irregular temporal evolution. Importantly, these nonlinear techniques can extract information from real-world experimental signals that cannot be resolved by classical linear techniques, such as spectral analysis. In application to single signals from isolated dynamics, nonlinear time series analysis can, for example, help to discriminate nonlinear deterministic and linear stochastic dynamics [1-3]. In our project we will focus on the study of multivariate signals measured from networks of connected dynamics. We will apply nonlinear interdependence measures  to characterize directional couplings between the dynamics. Departing from existing techniques designed to study stationary couplings between flows and point process signals  and time-dependent event-related couplings  in pairs of signals, we will develop novel innovative techniques to study signals measured from networks of dynamics.
All approaches will at first be validated using signals from model dynamics. For this purpose we will resort to the dynamics treated analytically and numerically in a variety of different nodes in the COSMOS project. Finally, our approaches will be applied to experimental cardio-respiratory recordings [7-8]. The application of our nonlinear interdependence measures to these recordings aims to characterize the nonlinear relations between the oscillators driving circulation and respiration. Thereby, we aim to generate information about the vital state of the investigated organism. This approach is relevant to human health. This is a novel medical approach, as usually diseases are measured and differentiated in medicine.
- Andrzejak RG. Nonlinear time series analysis in a nutshell. Tutorial book chapter in Osorio et al. (eds.) Epilepsy: The Intersection of Neurosciences, Biology, Mathematics, Engineering and Physics. 125, 2011
- Andrzejak RG, Mormann F, Kreuz T. Detecting determinism from point processes. PHYSICAL REVIEW E. 90, 062906, 2014.
- Naro D, Rummel C, Schindler K, Andrzejak RG. 2014. Detecting determinism with improved sensitivity in time series: Rank-based nonlinear predictability score. PHYSICAL REVIEW E. 90, 032913, 2014
- Chicharro D, Andrzejak RG. Reliable detection of directional couplings using rank statistics. PHYSICAL REVIEW E. 80, 026217, 2009
- Andrzejak RG, Kreuz T. Characterizing unidirectional couplings between point processes and flows. EPL (Europhysics Letters) 96, 50012, 2011.
- Andrzejak RG, Ledberg A, Deco G. Detecting event-related time-dependent directional couplings. NEW JOURNAL OF PHYSICS. 8, 6, 2006
- Kralemann, B; Frühwirth, M; Pikovsky, A; Rosenblum, M; Kenner, T; Schaefer, J; Moser, M. In vivo cardiac phase response curve elucidates human respiratory heart rate variability. Nature Communication. 4, 2418-2418, 2013
- von Bonin, D; Grote, V; Buri, C; Cysarz, D; Heusser, P; Moser, M; Wolf, U; Laederach, K. Adaption of cardio-respiratory balance during day-rest compared to deep sleep-An indicator for quality of life? Psychiatry Research. 219(3): 638-644, 2014