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Area of Science:

  • Complex Systems Analysis
  • Causal Inference
  • Information Theory

Background:

  • Information flow quantifies causal interactions in dynamical systems.
  • Previous work established componentwise information flow.
  • Analyzing interactions between complex subsystems remains challenging.

Purpose of the Study:

  • Extend information flow formalism to bulk interactions between complex subsystems.
  • Develop analytical formulas and estimators for bulk information flow.
  • Validate the new method and compare it with existing proxies.

Main Methods:

  • Developed closed-form analytical formulas for bulk information flow.
  • Derived maximum likelihood estimators under a Gaussian assumption.
  • Validated formulas using subsystems with known relationships.

Main Results:

  • The bulk information flow formulas accurately capture causal interactions.
  • Traditional proxies like averages and principal components show limitations.
  • The new method successfully identifies expected causalities.

Conclusions:

  • Bulk information flow provides a robust measure for subsystem interactions.
  • This formalism offers a superior alternative to common proxies.
  • Applications span climate science, neuroscience, finance, and more.