Multiple circular-circular correlation coefficients for the quantification of phase synchronization processes in the...

Phase synchronization is discussed as a potential mechanism for large-scale integration in the brain. Therefore, the quantification of such synchrony is a crucial topic in brain science research. Furthermore, these cerebral integration processes are likely to involve entire brain areas; therefore, the analysis of multiple couplings is of particular interest. Because phase values are circular variables, it is possible to use circular statistical methods for their examination. In particular, circular-circular correlation coefficients form a suitable measurement to estimate the extent of phase synchronization between different signals. As a multiple circular-circular correlation concept is still pending, two new multiple circular-circular correlation coefficients are presented in this article that can be used to quantify phase couplings between one dependent and an arbitrary number of predictor signals.