Surface optimization governs the local design of physical networks

Area of Science:

• Network science
• Theoretical physics
• Biology

Background:

• Physical networks, such as the brain's connectome and vascular system, are shaped by material constraints.
• Wiring economy principles predict network architecture based on minimizing material costs.
• Existing models often overlook the full 3D geometry and material costs.

Purpose of the Study:

• To investigate the local branching geometry of physical networks.
• To test the predictions of wiring minimization.
• To develop a more accurate model for network material costs.

Main Methods:

• Empirical exploration of branching geometry in diverse physical networks.
• Mapping surface minimization to high-dimensional Feynman diagrams in string theory.
• Analyzing network configurations beyond length minimization.

Main Results:

• Observed systematic violations of wiring minimization predictions in physical networks.
• Discovered an exact mapping between surface minimization and Feynman diagrams.
• Surface minimization accurately predicts trifurcations and branching angles in networks.
• Predicted and confirmed the existence of stable orthogonal sprouts.

Conclusions:

• Network material costs are better predicted by considering full 3D geometry and surface minimization.
• String theory provides a framework for understanding network structure.
• Orthogonal sprouts play a crucial functional role in biological and physical networks.