Hidden Topological Structure of Flow Network Functionality

Jason W. Rocks, Andrea J. Liu, and Eleni Katifori
Phys. Rev. Lett. 126, 028102 – Published 13 January 2021
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Abstract

The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges, organisms robustly control the propagation of inputs to perform specific tasks. However, a fundamental disconnect exists between the structure and function: networks with different local architectures can perform the same functions. Here, we answer the question of how changes at the level of individual edges collectively create functionality at the scale of an entire network. Using persistent homology, we analyze networks tuned to perform complex tasks. We find that the responses of such networks encode a hidden topological structure composed of sectors of nearly uniform pressure. Although these sectors are not apparent in the underlying network structure, they correlate strongly with the tuned function. The connectivity of these sectors, rather than that of individual nodes, provides a quantitative relationship between structure and function in flow networks.

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  • Received 13 December 2019
  • Revised 1 July 2020
  • Accepted 29 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.126.028102

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsCondensed Matter, Materials & Applied PhysicsInterdisciplinary PhysicsPolymers & Soft MatterNetworks

Authors & Affiliations

Jason W. Rocks, Andrea J. Liu*, and Eleni Katifori

  • Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

  • *Corresponding author. ajliu@upenn.edu

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Issue

Vol. 126, Iss. 2 — 15 January 2021

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