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Duality between predictability and reconstructability in complex systems.

Charles Murphy1,2, Vincent Thibeault3,4, Antoine Allard3,4

  • 1Département de physique, de génie physique et d'optique, Université Laval, Québec, QC, G1V 0A6, Canada. charles.murphy.1@ulaval.ca.

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This study explores the link between predicting complex system evolution and reconstructing their interaction structures. Researchers found predictability and reconstructability can surprisingly behave in dual, opposite ways.

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Area of Science:

  • Complex systems theory
  • Information theory
  • Network science

Background:

  • Predicting system evolution from interaction structure is key in complex systems.
  • Reconstructing interaction structures from temporal data is also a fundamental challenge.

Purpose of the Study:

  • To investigate the relationship between predictability and reconstructability in complex systems.
  • To quantify this relationship using information-theoretic measures.

Main Methods:

  • Utilized mutual information to measure codependence between random graphs and stochastic processes.
  • Employed uncertainty coefficients, derived from mutual information, to quantify predictability and reconstructability.
  • Performed analytical calculations for various systems and developed numerical procedures for intractable cases.

Main Results:

  • Demonstrated that uncertainty coefficients quantify the ability to reconstruct graphs and predict process evolution.
  • Found that predictability and reconstructability, despite being linked by mutual information, can exhibit distinct, even dual, behaviors.
  • Showed this duality universally emerges with changes in the number of process steps.

Conclusions:

  • Established a theoretical framework linking predictability and reconstructability via information theory.
  • Highlighted the potential for "predictability-reconstruction dualities" in dynamical processes.
  • Provided evidence for such dualities in real-world networks near criticality.