We present a data-driven framework to characterize large-scale brain dynamical states directly from correlation matrices at the single-subject level. By treating correlation thresholding as a percolation-like probe of connectivity, the approach tracks multiple cluster- and network-level observables and identifies a characteristic percolation threshold, rc, at which these signatures converge. We use rc as an operational and physically interpretable descriptor of large-scale brain dynamical state. Applied to resting-state fMRI data from a large cohort of healthy individuals (N = 996), the method yields stable, subject-specific estimates that covary systematically with established dynamical indicators such as temporal autocorrelations. Numerical simulations of a whole-brain model with a known critical regime further show that rc tracks changes in collective dynamics under controlled variations of excitability. By replacing arbitrary threshold selection with a criterion intrinsic to correlation structure, the r-spectra provides a physically grounded approach for comparing brain dynamical states across individuals.
@article{arxiv.2601.03796,
title = {Data-driven inference of brain dynamical states from the r-spectrum of correlation matrices},
author = {Christopher Gabaldon and Adria Mulero and Rong Wang and Daniel A. Martin and Sabrina Camargo and Qian-Yuan Tang and Ignacio Cifre and Changsong Zhou and Dante R. Chialvo},
journal= {arXiv preprint arXiv:2601.03796},
year = {2026}
}