# Measures of spike train synchrony for data with multiple time-scales

## TL;DR

This paper introduces adaptive, multi-scale measures of spike train synchrony that improve analysis of neural data with diverse time-scales, providing rate-independent and timing-sensitive tools.

## Contribution

It proposes the A-ISI-distance, A-SPIKE-distance, and A-SPIKE-synchronization, generalizing existing measures to handle multiple time-scales adaptively and independently of firing rates.

## Key findings

- A-ISI-distance and A-SPIKE-distance improve analysis of multi-scale spike trains.
- A-SPIKE-synchronization is more efficient in spike matching.
- RIA-SPIKE-distance is rate-ratio independent.

## Abstract

Background: Measures of spike train synchrony are widely used in both experimental and computational neuroscience. Time-scale independent and parameter-free measures, such as the ISI-distance, the SPIKE-distance and SPIKE-synchronization, are preferable to time-scale parametric measures, since by adapting to the local firing rate they take into account all the time-scales of a given dataset. New Method: In data containing multiple time-scales (e.g. regular spiking and bursts) one is typically less interested in the smallest time-scales and a more adaptive approach is needed. Here we propose the A-ISI-distance, the A-SPIKE-distance and A-SPIKE-synchronization, which generalize the original measures by considering the local relative to the global time-scales. For the A-SPIKE-distance we also introduce a rate-independent extension called the RIA-SPIKE-distance, which focuses specifically on spike timing. Results: The adaptive generalizations A-ISI-distance and A-SPIKE-distance allow to disregard spike time differences that are not relevant on a more global scale. A-SPIKE-synchronization does not any longer demand an unreasonably high accuracy for spike doublets and coinciding bursts. Finally, the RIA-SPIKE-distance proves to be independent of rate ratios between spike trains. Comparison with Existing Methods: We find that compared to the original versions the A-ISI-distance and the A-SPIKE-distance yield improvements for spike trains containing different time-scales without exhibiting any unwanted side effects in other examples. A-SPIKE-synchronization matches spikes more efficiently than SPIKE-Synchronization. Conclusions: With these proposals we have completed the picture, since we now provide adaptive generalized measures that are sensitive to rate only (A-ISI-distance), to timing only (ARI-SPIKE-distance), and to both at the same time (A-SPIKE-distance).