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Design, Surface Treatment, Cellular Plating, and Culturing of Modular Neuronal Networks Composed of Functionally Inter-connected Circuits
Published on: April 15, 2015
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Griffiths phases and localization in hierarchical modular networks.
Géza Ódor1, Ronald Dickman2, Gergely Ódor3
1MTA-MFA-EK Research Institute for Technical Physics and Materials Science, H-1121 Budapest, P.O. Box 49, Hungary.
Scientific Reports
|September 25, 2015
Summary
Hierarchical modular networks exhibit a Griffiths phase with bursty dynamics near the percolation threshold. Link disorder can induce localization even in highly connected small-world brain connectivity models.
Area of Science:
- Computational neuroscience
- Network science
- Complex systems
Background:
- Hierarchical modular network models are used to represent functional brain connectivity.
- Previous models, like small-world networks, often lack sufficient topological heterogeneity to show complex dynamics.
Purpose of the Study:
- To investigate dynamic processes on hierarchical modular networks with exponentially decaying connection probabilities.
- To explore the emergence of complex behaviors like Griffiths phases and localization.
Main Methods:
- Extensive simulations of contact process (CP) and threshold models.
- Quenched mean-field theory (QMF) for analyzing network dynamics.
- Analysis of networks embedded in 2D Euclidean space, including hierarchical trees.
Main Results:
- A Griffiths phase emerges under reduced connection probabilities, leading to bursty, power-law dynamics.
- Localization in the steady state is observed via QMF.
- Link asymmetry and coupling disorder can induce localization, even in highly connected small-world networks.
Conclusions:
- Hierarchical modular networks with specific connection probabilities can display complex emergent dynamics not seen in simpler models.
- Topological heterogeneities are crucial for observing phenomena like Griffiths phases.
- Network disorder plays a significant role in localization phenomena in brain connectivity models.
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