Stringology-based motif discovery for electrophysiological time series: A framework for temporal pattern analysis with an ADHD case study

Recurrent temporal patterns in time series data encode functionally meaningful structure, yet most existing analytical frameworks summarize sequential data through global statistics, i.e., spectral power, entropy indices, or averaged waveforms, without identifying the specific patterns underlying these summaries. We introduce a computational framework that adapts two algorithmic paradigms from stringology, the study of efficient string processing and pattern matching, to the systematic discovery and characterization of temporal motifs in numerical time series. Specifically, order preserving matching (OPM) and Cartesian tree matching (CTM) are employed to identify recurrent subsequences based on relative ordering and hierarchical structure, respectively, rendering the framework invariant to amplitude scaling and robust to inter-sequence variability. To demonstrate the framework's utility on real-world data, we apply it to multichannel electroencephalography (EEG) recordings from 121 children, namely, 61 with attention-deficit/hyperactivity disorder (ADHD) and 60 typically developing controls, using a publicly available dataset. Motifs with support ≥0.9 were discovered and quantified across 19 EEG channels using both OPM and CTM. ADHD participants exhibited significantly higher motif frequencies, shorter OPM motif lengths and greater gradient instability, reflected in larger mean and maximal inter-sample amplitude jumps. CTM analysis further revealed reduced hierarchical complexity in ADHD, characterized by shallower Cartesian tree structures, fewer hierarchical levels, and altered tree balance, despite comparable motif lengths. These group differences were statistically validated using the Mann-Whitney U test with false discovery rate (FDR) correction (q<0.05) across all channels. These results demonstrate that stringology-based motif analysis can capture systematic differences in the structure, stability, and hierarchical organization of recurrent temporal patterns that are not accessible through conventional signal processing approaches. The proposed framework provides a generalizable computational tool for temporal pattern analysis in sequential biomedical data, with potential applications extending beyond EEG to any domain requiring precise characterization of recurrent structure in numerical time series.