Synergistic Motifs in Gaussian Systems

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.