Emergent criticality through adaptive information processing in boolean networks.

Area of Science:

• Computational neuroscience
• Complex systems theory
• Network science

Background:

• Boolean networks are models for studying complex systems.
• Understanding how network properties influence information processing is crucial.
• The relationship between network connectivity, learning, and robustness remains an open question.

Purpose of the Study:

• To investigate the interplay between learning capability, robustness, network topology, and task complexity in evolving boolean networks.
• To determine the critical connectivity value for adaptive information processing in large systems.
• To explore how network properties optimize learning and generalization.

Main Methods:

• Computational analysis of boolean networks with evolving connectivity.
• Systematic exploration of network behavior across varying system sizes and task complexities.
• Analysis of network topology, learning metrics, and fitness variance near critical points.

Main Results:

• Adaptive information processing drives large boolean networks to a critical connectivity of K(c)=2.
• For finite networks, connectivity approaches K(c) via a power law with system size N.
• Network learning and generalization are optimized near criticality, contingent on task complexity and information thresholds.
• Maximal topological diversity and fitness variance are observed in critical network populations.

Conclusions:

• The critical connectivity K(c)=2 is a key feature for optimal information processing in adaptive boolean networks.
• Network topology near criticality supports efficient exploration and robustness of solutions.
• Findings provide insights for designing optimal adaptive dynamical networks for computational tasks.