ArticleScientific reports2015
Griffiths phases and localization in hierarchical modular networks.
Article in Scientific reports, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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15 citing papers in PubMed, 45 citations in OpenAlex.
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- Emergence of metastability in frustrated oscillatory networks: the key role of hierarchical modularity.Frontiers in network physiology · 2024Article
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- An Integrated World Modeling Theory (IWMT) of Consciousness: Combining Integrated Information and Global Neuronal Workspace Theories With the Free Energy Principle and Active Inference Framework; Toward Solving the Hard Problem and Characterizing Agentic Causation.Frontiers in artificial intelligence · 2020Article
- Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs.Scientific reports · 2019Article
- Spike-Timing-Dependent Plasticity With Axonal Delay Tunes Networks of Izhikevich Neurons to the Edge of Synchronization Transition With Scale-Free Avalanches.Frontiers in systems neuroscience · 2019Article
- Avalanche precursors of failure in hierarchical fuse networks.Scientific reports · 2018Article
- Griffiths phases in infinite-dimensional, non-hierarchical modular networks.Scientific reports · 2018Article
- Spontaneous cortical activity is transiently poised close to criticality.PLoS computational biology · 2017Article
- Griffiths phase on hierarchical modular networks with small-world edges.Physical review. E · 2017Article
- The exact Laplacian spectrum for the Dyson hierarchical network.Scientific reports · 2017Article
- The topology of large Open Connectome networks for the human brain.Scientific reports · 2016Article
Corrections and comments
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Authors and funding
3 authors at 1 institution in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
We study variants of hierarchical modular network models suggested by Kaiser and Hilgetag [ Front. in Neuroinform., 4 (2010) 8] to model functional brain connectivity, using extensive simulations and quenched mean-field theory (QMF), focusing on structures with a connection probability that decays exponentially with the level index. Such networks can be embedded in two-dimensional Euclidean space. We explore the dynamic behavior of the contact process (CP) and threshold models on networks of this kind, including hierarchical trees. While in the small-world networks originally proposed to model brain connectivity, the topological heterogeneities are not strong enough to induce deviations from mean-field behavior, we show that a Griffiths phase can emerge under reduced connection probabilities, approaching the percolation threshold. In this case the topological dimension of the networks is finite, and extended regions of bursty, power-law dynamics are observed. Localization in the steady state is also shown via QMF. We investigate the effects of link asymmetry and coupling disorder, and show that localization can occur even in small-world networks with high connectivity in case of link disorder.
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