Source-linked AI summary
Remote synchronization reveals network symmetries and functional modules
Vincenzo Nicosia, Miguel Valencia, Mario Chavez, Albert Díaz-Guilera, Vito Latora
TL;DR
The paper examines phase organization and functional synchrony in networked oscillators and brain data. It derives reference behavior for incoherent oscillators, analyzes phase dispersion, and estimates statistically significant functional correlations while accounting for autocorrelation and multiple testing.
Problem
Independent time series and autocorrelated time series require different correlation-significance treatments because standard tests produce greater Type I error for autocorrelated data.
Method
The study combines analytical phase calculations, numerical Lyapunov-exponent computations, anatomical brain connectivity, hierarchical phase clustering, and corrected functional-correlation analysis.
Results
The phase dispersion for seven oscillators approaches 1.39 as α →π/2, while functional-correlation significance is assessed using autocorrelation-corrected degrees of freedom and FDR control at q ≤0.05.
Takeaways & Limitations
Anatomical connectivity and phase similarity can be combined to identify brain areas related by topological symmetry and to compare their functional synchrony.
Abstract
from arXiv · showhide
We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.
APPENDIX
The appendix details how phase dispersion, incoherent baselines, Lyapunov exponents, brain connectivity, functional synchrony, and phase clustering were computed. It also specifies statistical correction procedures for correlations and the brain-data preprocessing pipeline.
- Phase dispersion: The expected phase dispersion for seven incoherent oscillators was estimated as 1.394 ± 0.248 from 10^7 independent realizations.The estimate averages σθ over uniformly sampled phase sets.
- Lyapunov exponent: The maximum Lyapunov exponent was computed across α values from 0 to 1.57 using 500 initial phase configurations per value.Trajectories were perturbed by ε = 10^-4 and evolved with a fourth-order Runge–Kutta step.
- Brain data: Anatomical connectivity was derived from DW-MRI data from 20 healthy participants across 90 atlas-defined brain regions.Matrix elements represent connection probabilities proportional to fiber density.
- Brain data: Functional connectivity used five-minute resting-state BOLD fMRI recordings from 15 healthy subjects, regionally averaged and registered to anatomical data.The scans were co-registered, normalized to the MNI template, and sampled according to the anatomical atlas.
- Functional synchrony: Functional links were defined using zero-lag linear cross-correlation, with Fisher’s Z transformation and degrees-of-freedom correction for autocorrelation.The effective degrees of freedom accounts for autocorrelated time series, which otherwise increase Type I error.
- Functional synchrony: False Discovery Rate correction set the significance threshold so the expected fraction of false positives was q ≤ 0.05.The correction was applied to each matrix of Zij values.
- Phase clustering: Hierarchical agglomerative clustering identified brain areas with similar phases produced by integrating the model on the anatomical connectivity matrix.The resulting dendrogram is shown in Fig. S-1, where similar and dissimilar phase groups are color-coded on anatomical images.