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Area of Science:

  • Theoretical physics
  • Computational neuroscience
  • Complex systems

Background:

  • Biological systems require diverse timescales for stimulus response.
  • Emergence of these timescales without external fine-tuning is a significant puzzle.
  • Discrete Markovian systems offer a framework to study this using random matrix theory.

Purpose of the Study:

  • Investigate how biological systems can generate long timescales without fine-tuning.
  • Explore the role of a dynamic range variable in Markovian systems.
  • Analyze brain activity using these theoretical models.

Main Methods:

  • Analysis of discrete Markovian systems and transition matrices.
  • Application of random matrix theory and concepts of phase transitions.
  • Extension to Hidden Markov Models (HMMs) and analysis of fMRI data.

Main Results:

  • A phase transition is identified, driven by increased dynamic range, which avoids random matrix theory predictions and leads to long relaxation times.
  • This transition is associated with decreased entropy rate and increased complexity (predictive information).
  • fMRI data from human subjects at rest quantitatively align with the random model, near the phase transition point.

Conclusions:

  • Long timescales in biological systems can emerge from intrinsic dynamics rather than external fine-tuning.
  • The identified phase transition provides a mechanism for generating complexity and long timescales.
  • Brain activity during unconstrained cognition operates near this critical transition, supporting the brain criticality hypothesis.