Compare transcript-based interaction complexity with related complexity estimators

Compare transcript-based estimators for interaction complexity—specifically (i) the coupling complexity defined from the entropies of the ordinal-pattern sequences of two time series and the entropy of their transcript sequence, and (ii) the complexity characterization based on the probability distributions of transcript order classes C_n—with other related complexity estimators proposed in the literature, including partially ordered permutation complexity and ordinal persistent homology-based coupling complexity, to assess their relationships, relative strengths, and applicability across datasets and dynamical regimes.

Background

The paper revisits transcript-based analysis, which leverages algebraic relations between ordinal patterns (transcripts) derived from pairs of time series to characterize properties of interactions. It introduces and applies estimators for strength, direction, and complexity of interactions. Two distinct complexity perspectives are considered: (i) a coupling complexity derived from entropies of the two ordinal-pattern sequences and the transcript sequence, and (ii) an order-class-based view that uses the distribution over transcript orders C_n to characterize relational complexity.

While transcript-based measures are demonstrated on coupled model systems and multi-day EEG recordings, the authors note that a systematic comparison between these transcript-based complexity estimators and other related approaches in the literature remains to be done. Candidate comparators include measures such as partially ordered permutation complexity and ordinal persistent homology-based coupling complexity (e.g., Haruna 2019; Haruna 2023). Establishing such a comparison would clarify when transcript-based complexity provides distinct advantages or complementary insights relative to these alternatives.