# Warped phase coherence: an empirical synchronization measure combining phase and amplitude information

## TL;DR

This paper introduces a modified coherence measure that combines phase and amplitude information, improving the detection of synchronization in nonlinear oscillators and physiological signals, with applications in brain-computer interfaces.

## Contribution

It proposes a warped phase coherence measure that enhances sensitivity to amplitude fluctuations and phase relationships, improving inference of structural couplings in complex signals.

## Key findings

- Enhanced synchronization detection in oscillator simulations.
- Improved classification accuracy in EEG movement tasks.
- Potential applications in brain-machine interfaces.

## Abstract

The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the instantaneous phases extracted from the measured or simulated time-series via the analytic signal. Here, we demonstrate that adding a possibly complex constant value to this normally null-mean signal has a non-trivial warping effect. Among other consequences, this introduces a level of sensitivity to the amplitude fluctuations and average relative phase. By means of simulations of Roessler systems and experiments on single-transistor oscillator networks, it is shown that the resulting coherence measure may have an empirical value in improving the inference of the structural couplings from the dynamics. When tentatively applied to the electroencephalogram recorded while performing imaginary and real movements, this straightforward modification of the phase locking value substantially improved the classification accuracy. Hence, its possible practical relevance in brain-computer and brain-machine interfaces deserves consideration.