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Updated: Jun 18, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Patchy percolation on a hierarchical network with small-world bonds.

Stefan Boettcher¹, Jessica L Cook, Robert M Ziff

¹Department of Physics, Emory University, Atlanta, Georgia 30322, USA. rziff@umich.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

This summary is machine-generated.

Hanoi networks exhibit unique percolation properties due to hierarchical bonds, creating patchy order. This leads to a finite probability of spanning clusters, differing from typical lattice behaviors.

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Last Updated: Jun 18, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Area of Science:

Statistical Physics
Network Science
Complex Systems

Background:

Scale-free networks lack analytical tractability.
Hanoi networks offer a model between lattice and mean-field limits.
Percolation theory studies connectivity in random systems.

Purpose of the Study:

Analyze bond-percolation properties of Hanoi networks.
Investigate the role of hierarchical small-world bonds.
Understand the phase behavior and critical phenomena.

Main Methods:

Renormalization group analysis.
Study of bond-percolation on Hanoi networks.
Comparison with lattice and mean-field models.

Main Results:

Hanoi networks display "patchy" order from hierarchical bonds.
Percolation transition is not a sharp 0-1 probability.
Finite probability of spanning clusters observed.
Phase behavior depends on long-range bond prevalence.

Conclusions:

Hanoi networks provide an analytically tractable model for percolation.
Hierarchical structure influences phase transitions significantly.
Observed fixed points exhibit nonuniversal behavior.