Data-driven inference of brain dynamical states from the r-spectrum of correlation matrices
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arXiv
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| Format: | Preprint |
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2026
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| author | Gabaldon, Christopher Mulero, Adria Wang, Rong Martin, Daniel A. Camargo, Sabrina Tang, Qian-Yuan Cifre, Ignacio Zhou, Changsong Chialvo, Dante R. |
| author_facet | Gabaldon, Christopher Mulero, Adria Wang, Rong Martin, Daniel A. Camargo, Sabrina Tang, Qian-Yuan Cifre, Ignacio Zhou, Changsong Chialvo, Dante R. |
| contents | 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 $r_c$ 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 $r_c$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03796 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-driven inference of brain dynamical states from the r-spectrum of correlation matrices Gabaldon, Christopher Mulero, Adria Wang, Rong Martin, Daniel A. Camargo, Sabrina Tang, Qian-Yuan Cifre, Ignacio Zhou, Changsong Chialvo, Dante R. Neurons and Cognition 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 $r_c$ 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 $r_c$ 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. |
| title | Data-driven inference of brain dynamical states from the r-spectrum of correlation matrices |
| topic | Neurons and Cognition |
| url | https://arxiv.org/abs/2601.03796 |