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Criticality in a multisignal system using principal component analysis.

Miguel Sánchez-Islas1, Juan Claudio Toledo-Roy1,2, Alejandro Frank1,2,3

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Principal Component Analysis (PCA) identifies collective criticality in complex systems by analyzing eigenvalues and eigenvectors. This method reveals "multicriticality" in systems with multiple signals, including brain activity, and aids in distinguishing cognitive states.

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Area of Science:

  • Complex Systems Science
  • Statistical Physics
  • Neuroscience

Background:

  • Criticality in dynamical systems is typically assessed via individual variables.
  • Identifying criticality in systems with multiple, distinct signals presents a challenge.
  • Existing methods struggle when individual signals do not show clear signs of criticality.

Purpose of the Study:

  • To introduce Principal Component Analysis (PCA) as a method for detecting collective criticality.
  • To demonstrate PCA's utility in identifying "multicriticality" in systems with coupled components.
  • To apply PCA to electroencephalographic (EEG) data to support the brain criticality hypothesis.

Main Methods:

  • Constructed a multilayer Ising model with coupled lattices having distinct critical temperatures.
  • Applied PCA to magnetization signals across a range of global temperatures.
  • Analyzed eigenvalue spectra for power-law behavior indicative of collective criticality.
  • Applied PCA to electroencephalographic (EEG) recordings from human subjects.

Main Results:

  • A specific global temperature revealed a power-law eigenvalue spectrum, signifying "multicriticality".
  • EEG data analysis also showed a power-law eigenspectrum, supporting brain criticality.
  • Eigenvectors differentiated between resting and cognitive task states.
  • Information was found in all eigenvectors, not solely dominant ones.

Conclusions:

  • PCA effectively identifies collective criticality and "multicriticality" in complex systems.
  • The findings provide further evidence for the brain criticality hypothesis.
  • PCA offers valuable insights beyond dimensionality reduction for analyzing multi-signal data.