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Surface optimization governs the local design of physical networks
Meng, Xiangyi Piazza, Benjamin Both, Csaba Barzel, Baruch Barabási, Albert László
Meng, Xiangyi
Piazza, Benjamin
Both, Csaba
Barzel, Baruch
Barabási, Albert László
Title / Series / Name
Nature
Publication Volume
649
Publication Issue
8096
Pages
Editors
Keywords
Animals
Brain/cytology
Connectome
Humans
Models, Neurological
Nerve Net/physiology
Synapses/physiology
Brain/cytology
Connectome
Humans
Models, Neurological
Nerve Net/physiology
Synapses/physiology
Files
URI
https://hdl.handle.net/20.500.14018/28800
Abstract
The brain’s connectome1, 2–3 and the vascular system4 are examples of physical networks whose tangible nature influences their structure, layout and, ultimately, their function. The material resources required to build and maintain these networks have inspired decades of research into wiring economy, offering testable predictions about their expected architecture and organization. Here we empirically explore the local branching geometry of a wide range of physical networks, uncovering systematic violations of the long-standing predictions of wiring minimization. This leads to the hypothesis that predicting the true material cost of physical networks requires us to account for their full three-dimensional geometry, resulting in a largely intractable optimization problem. We discover, however, an exact mapping of surface minimization onto high-dimensional Feynman diagrams in string theory5, 6–7, predicting that, with increasing link thickness, a locally tree-like network undergoes a transition into configurations that can no longer be explained by length minimization. Specifically, surface minimization predicts the emergence of trifurcations and branching angles in excellent agreement with the local tree organization of physical networks across a wide range of application domains. Finally, we predict the existence of stable orthogonal sprouts, which are not only prevalent in real networks but also play a key functional role, improving synapse formation in the brain and nutrient access in plants and fungi.
Topic
Publisher
Place of Publication
Type
Journal article
Date
2026-01-07
Language
ISBN
Identifiers
10.1038/s41586-025-09784-4