sRQA: AN INTEGRATIVE PIPELINE FOR SYMBOLIC RECURRENCE QUANTIFICATION ANALYSIS

Abstract

Recurrence Quantification Analysis (RQA) is a powerful phenomenological method for characterizing dynamical systems from sequential empirical data, but it is fundamentally limited to continuous signals. Symbolic RQA (sRQA) extends this framework to discrete state sequences, enabling the analysis of both inherently discrete systems and continuous systems where state-based dynamics and motifs are of interest. Despite its promise, accessible and unified software support for sRQA has remained limited. Here we introduce the sRQA package, an open-source R library that consolidates discretization and symbolization, data visualization, and computation of recurrence and cross-recurrence metrics into a single accessible toolset. We validated the method using simulated data with known dynamical properties, confirming that sRQA metrics behaved as theoretically expected. We then demonstrated the utility of sRQA across three real-world applications. First, we applied sRQA to ECG recordings, showing that symbolic recurrence metrics reliably distinguished atrial fibrillation from normal sinus rhythm, with an XGBoost classifier achieving 92% accuracy and an AUC of 0.97. Second, we applied sRQA to fMRI BOLD time series from the dorsal attention network, finding that symbolic and cross-recurrence metrics differentiated movie-viewing from resting-state conditions, revealing greater regularity and inter-subnetwork coordination during task engagement. Third, we applied sRQA to intrinsically symbolized sequences of pauses in speech, identifying valence-specific differences in pause dynamics between truthful and deceptive statements, as well as sex differences in pause structure during negatively-valenced speech. Together, these results demonstrate that sRQA provides a flexible and sensitive framework for characterizing discrete and discretized dynamical systems across biological and behavioral domains. AUTHOR SUMMARYMany biological and behavioral systems are best understood as sequences of discrete states rather than smooth, continuous processes. For example, a heartbeat that shifts between rhythms, a brain that transitions between activity patterns, or a speaker who pauses and resumes in ways that carry meaning. Standard methods for analyzing the dynamics of such systems were not designed with this kind of data in mind. Here, we introduce the sRQA package, an open-source software library that makes it straightforward to apply symbolic recurrence analysis to both discrete and continuous data. We demonstrate the library across four examples: simulated data with known properties, cardiac recordings distinguishing atrial fibrillation from normal heart rhythm, brain imaging data capturing differences between rest and task engagement, and speech recordings where pause patterns differ between truthful and deceptive statements. In each case, sRQA revealed meaningful structure in the data that would be difficult to detect with conventional tools. We hope this library will make symbolic recurrence analysis more accessible to researchers across the biological and behavioral sciences.