High expectations on phase locking: Better quantifying the concentration of circular data.

Andrzejak, Ralph G; Espinoso, Anaïs; García-Portugués, Eduardo; Pewsey, Arthur; Epifanio, Jacopo; Leguia, Marc G; Schindler, Kaspar (2023). High expectations on phase locking: Better quantifying the concentration of circular data. Chaos, 33(9) AIP Publishing 10.1063/5.0166468

Text 091106_1_5.0166468.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (2MB) | Request a copy

The degree to which unimodal circular data are concentrated around the mean direction can be quantified using the mean resultant length, a measure known under many alternative names, such as the phase locking value or the Kuramoto order parameter. For maximal concentration, achieved when all of the data take the same value, the mean resultant length attains its upper bound of one. However, for a random sample drawn from the circular uniform distribution, the expected value of the mean resultant length achieves its lower bound of zero only as the sample size tends to infinity. Moreover, as the expected value of the mean resultant length depends on the sample size, bias is induced when comparing the mean resultant lengths of samples of different sizes. In order to ameliorate this problem, here, we introduce a re-normalized version of the mean resultant length. Regardless of the sample size, the re-normalized measure has an expected value that is essentially zero for a random sample from the circular uniform distribution, takes intermediate values for partially concentrated unimodal data, and attains its upper bound of one for maximal concentration. The re-normalized measure retains the simplicity of the original mean resultant length and is, therefore, easy to implement and compute. We illustrate the relevance and effectiveness of the proposed re-normalized measure for mathematical models and electroencephalographic recordings of an epileptic seizure.

Interest & Impact

Downloads

0 since deposited on 02 Oct 2023
0 in the past 12 months

Citations

5 Citations in Web of Science ®
6 Citations in Scopus

Search

in Google Scholar™

Services

Actions (login required)

Edit item

Actions (login required)

Edit item