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The Geometric Signatures of Brain State Transitions: Recursive Informational Curvature Reveals Hidden Dynamics in

Mahsa Asadi Anar1, Seyed Kiarash Sadat Rafiei1, Soroosh Najafi2

  • 1School of Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran.

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Summary

Recursive Informational Curvature (RIC) effectively describes neural dynamics. Its curvature term, K, accurately distinguishes brain states in macaque electrocorticography (ECoG) data, showing promise for neural analysis.

Keywords:
biomarkerelectrocorticography (ECoG)information geometrymicrostate mappingneural dynamicsnonlinear signal analysisrecursive informational curvature

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Area of Science:

  • Neuroscience
  • Information Theory
  • Dynamical Systems

Background:

  • Recursive Informational Curvature (RIC) offers an information-geometric framework for analyzing dynamical systems.
  • RIC quantifies the balance between system recursion and entropy change.
  • The scalar curvature term (K) of RIC has not been empirically validated in neural data.

Purpose of the Study:

  • To empirically implement and evaluate the scalar curvature term (K) of RIC.
  • To assess the performance of RIC curvature in high-density macaque electrocorticography (ECoG) data.
  • To benchmark RIC curvature against other neural features for state discrimination.

Main Methods:

  • Analysis of two open-access ECoG datasets (eyes-open/closed, food-tracking).
  • Extraction of Shannon entropy, recursive gain, and empirical curvature after symbolic discretization.
  • Evaluation using single-feature, multichannel, and combined-feature models with sensitivity analyses.

Main Results:

  • Multichannel curvature features achieved near-perfect discrimination in the eyes-open/closed benchmark.
  • Combined curvature and amplitude features yielded the best performance in the food-tracking task.
  • Entropy was a weak descriptor; recursive gain and curvature showed similar performance, highlighting the recursive component's importance.

Conclusions:

  • The empirical RIC curvature term is an interpretable and state-sensitive descriptor of neural dynamics in ECoG.
  • This study provides a reproducible benchmark for refining the RIC framework.
  • The findings clarify the potential and limitations of curvature-based neural analysis.