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Synergistic Motifs in Gaussian Systems.

Enrico Caprioglio1, Pedro A M Mediano2,3, Luc Berthouze1

  • 1University of Sussex, Department of Informatics, Brighton, United Kingdom.

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Summary
This summary is machine-generated.

High-order interdependencies in complex systems emerge from simple pairwise interactions when correlational structures are antibalanced. This finding explains synergy

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Area of Science:

  • Complex Systems Science
  • Information Theory
  • Network Science

Background:

  • High-order interdependencies are crucial in complex systems but lack mechanistic explanations.
  • Existing models often overlook how these arise solely from pairwise interactions.
  • Synergy quantifies high-order interdependencies using information theory.

Purpose of the Study:

  • To determine conditions under which high-order interdependencies (synergy) emerge from pairwise interactions.
  • To provide precise mathematical conditions for synergy dominance over low-order effects.
  • To validate these conditions across different system types and interaction regimes.

Main Methods:

  • Analytical derivation of sufficient and necessary conditions for synergy in Gaussian systems and Ornstein-Uhlenbeck processes.
  • Focus on antibalanced (highly frustrated) correlational structures and interaction motifs.
  • Validation through simulations and analysis of Ising, oscillatory, and empirical networks.

Main Results:

  • Antibalanced correlational structures in Gaussian systems are sufficient for synergy dominance.
  • Antibalanced interaction motifs in Ornstein-Uhlenbeck processes are necessary for synergy dominance.
  • These findings extend beyond the weak interaction regime and apply to diverse network types.

Conclusions:

  • Pairwise interactions alone can generate synergistic information without explicit high-order mechanisms.
  • Structural balance theory provides a key framework for understanding high-order interdependencies.
  • This work offers a mechanistic explanation for synergy emergence in complex systems.