Long-Range Temporal Correlations in Brain-state Dynamics via a Multivariate One-hot Approach

Temporal sequences of discrete brain states provide a symbolic representation of large-scale neural dynamics. Here, we introduce a one-hot detrended fluctuation analysis (DFA) formulation to quantify long-range temporal correlations in the recurrence dynamics of individual states, independent of the embedding geometry or the symbolic transition encoding. Applied to resting-state Electroencephalographic microstate sequences acquired under eyes-open (EO) and eyes-closed (EC) conditions, the method reveals heterogeneous scaling exponents across states and a global increase of scaling under EC, indicating condition-dependent modulation of multi-timescale organization. Systematic surrogate manipulations disentangle the structural sources of scaling. Disrupting state lifetime statistics through microstate duration equalization or randomization markedly reduces the Hurst exponent, whereas transition-order shuffling alone produces comparatively minor changes in absolute scaling. These findings indicate that long-range dependence is primarily associated with structured state lifetimes rather than with higher-order symbolic syntax. At the same time, transition ordering modulates EO-EC differences, suggesting that symbolic organization contributes to the context-dependent expression of temporal memory. Combined surrogate operations reveal additive effects. The proposed one-hot formulation provides a minimal, representation-invariant characterization of temporal correlations in symbolic sequences and can be generalized to discrete brain-state dynamics obtained from different neuroimaging modalities.