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Power Laws in Empirical Eigenvalue Spectra.

Benyuan Liu1,2, Yung-Ying Chen1,2, M Shane Li1,2

  • 1School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA.

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Summary
This summary is machine-generated.

This study introduces a robust method for analyzing neural data, improving the assessment of the critical brain hypothesis by focusing on eigenvalue density rather than traditional regression. This enhances the reliability of findings in neuroscience research.

Keywords:
phenomenological renormalization grouppower-law scalingspontaneous neural data

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Area of Science:

  • Neuroscience
  • Complex Systems
  • Statistical Physics

Background:

  • The critical brain hypothesis suggests neural systems optimize information processing near a phase transition.
  • Phenomenological renormalization group (pRG) analysis, using eigenvalue scaling, investigates this hypothesis.
  • Current methods for estimating scaling exponents (μ) rely on biased linear regression of eigenvalues versus rank.

Purpose of the Study:

  • To develop a more robust method for estimating the power-law scaling exponent (μ) in neural data.
  • To improve the interpretation of scale-invariant features in the context of the critical brain hypothesis.
  • To establish standards for data requirements in pRG eigenvalue analysis.

Main Methods:

  • Instead of fitting eigenvalue-vs-rank plots, this study fits the density of eigenvalues.
  • Utilized a synthetic model with controlled exponents to validate the approach.
  • Applied the method to publicly available Neuropixels recordings.

Main Results:

  • The eigenvalue density fitting method provides a more reliable estimation of the scaling exponent (μ).
  • Demonstrated the approach's efficacy on both synthetic and real neural data.
  • Established criteria for minimal data needed for accurate power-law quantification in pRG analysis.

Conclusions:

  • The proposed method offers a more rigorous approach to assessing the neural criticality hypothesis.
  • This tool helps understand experimental data limitations (spatial, temporal) in neural analyses.
  • Contributes to a more reliable evaluation of brain function near critical states.