A guide to time-resolved and parameter-free measures of spike train synchrony

TL;DR

This paper provides a detailed mathematical analysis of three time-resolved, parameter-free measures of spike train synchrony, including their expectations for random spike trains, aiding interpretation in neuroscience research.

Contribution

It offers new analytical expressions and empirical formulas for the expectation values of ISI-distance, SPIKE-distance, and SPIKE-Synchronization measures, enhancing their interpretability.

Findings

Analytic expressions for ISI-distance and SPIKE-Synchronization expectations for Poisson spike trains.

Empirical formula for SPIKE-distance expectation derived from numerical evaluations.

Clarification of these measures' baseline values for randomized spike trains.

Abstract

Measures of spike train synchrony have proven a valuable tool in both experimental and computational neuroscience. Particularly useful are time-resolved methods such as the ISI- and the SPIKE-distance, which have already been applied in various bivariate and multivariate contexts. Recently, SPIKE-Synchronization was proposed as another time-resolved synchronization measure. It is based on Event-Synchronization and has a very intuitive interpretation. Here, we present a detailed analysis of the mathematical properties of these three synchronization measures. For example, we were able to obtain analytic expressions for the expectation values of the ISI-distance and SPIKE-Synchronization for Poisson spike trains. For the SPIKE-distance we present an empirical formula deduced from numerical evaluations. These expectation values are crucial for interpreting the synchronization of spike trains measured in experiments or numerical simulations, as they represent the point of reference for fully randomized spike trains.