Surface optimization governs the local design of physical networks
TL;DR
Imagine you're building a city's plumbing system. The old idea was to use the least amount of pipe possible to connect every house. This paper argues that nature is smarter than that. Instead of just minimizing the length of the pipes, it also considers their thickness and tries to minimize the total surface area of all the pipes. This different goal explains why we see weird but efficient designs in nature, like three branches sprouting from one point or a tiny branch shooting off at a perfect right angle. It's a more realistic model for how to build things in the physical world, where thickness and maintenance matter just as much as length.
The brain’s connectome and the vascular system 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 theory, 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.
- 1Systematic violations of wiring minimization predictions in physical networks.
- 2Mapping of surface minimization onto high-dimensional Feynman diagrams in string theory.
- 3Prediction of trifurcations and branching angles in physical networks.
- 4Existence of stable orthogonal sprouts improving synapse formation and nutrient access.
Baby chicks pass the bouba-kiki test challenging a theory of language
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Single-minus gluon tree amplitudes are nonzero
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Sub-part-per-trillion test of the Standard Model with atomic hydrogen
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