Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions
TLDR
The role of non-local (axonal) connections in generating and modulating phase transitions of collective activity in the neuropil is investigated and a relationship between critical values of the noise level and non-locality parameter to control the onset of phase transitions is derived.Abstract:
We model the dynamical behavior of the neuropil, the densely interconnected neural tissue in the cortex, using neuropercolation approach. Neuropercolation generalizes phase transitions modeled by percolation theory of random graphs, motivated by properties of neurons and neural populations. The generalization includes (1) a noisy component in the percolation rule, (2) a novel depression function in addition to the usual arousal function, (3) non-local interactions among nodes arranged on a multi-dimensional lattice. This paper investigates the role of non-local (axonal) connections in generating and modulating phase transitions of collective activity in the neuropil. We derived a relationship between critical values of the noise level and non-locality parameter to control the onset of phase transitions. Finally, we propose a potential interpretation of ontogenetic development of the neuropil maintaining a dynamical state at the edge of criticality.read more
Citations
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Graph theoretical analysis of complex networks in the brain
TL;DR: These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity, and increasing evidence that various types of brain disease may be associated with deviations of the functional network topology from the optimal small- world pattern.
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The metastable brain.
TL;DR: Theories and experiments are discussed, suggesting that metastable dynamics underlie the real-time coordination necessary for the brain's dynamic cognitive, behavioral, and social functions.
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The application of graph theoretical analysis to complex networks in the brain
TL;DR: It is demonstrated through evidence from computational studies, in vivo experiments, and functional MRI, EEG and MEG studies in humans, that both the functional and anatomical connectivity of the healthy brain have many features of a small world network, but only to a limited extent of a scale free network.
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Being Critical of Criticality in the Brain
John M. Beggs,Nicholas M. Timme +1 more
TL;DR: The concept of criticality is explained and substantial objections to the criticality hypothesis raised by skeptics are reviewed, and counter points are presented in dialog form.
Invited review The application of graph theoretical analysis to complex networks in the brain
TL;DR: In this paper, the authors focus on the correlation between the structural properties of networks and the dynamics of these networks and demonstrate through evidence from computational studies, in vivo experiments, and functional MRI, EEG and MEG studies in humans, that both the functional and anatomical connectivity of the healthy brain have many features of a small world network, but only to a limited extent of a scale free network.
References
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Journal ArticleDOI
Collective dynamics of small-world networks
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Journal ArticleDOI
Statistical mechanics of complex networks
TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Journal ArticleDOI
Neural networks and physical systems with emergent collective computational abilities
TL;DR: A model of a system having a large number of simple equivalent components, based on aspects of neurobiology but readily adapted to integrated circuits, produces a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size.
Book
Introduction to percolation theory
Dietrich Stauffer,Amnon Aharony +1 more
TL;DR: In this paper, a scaling solution for the Bethe lattice is proposed for cluster numbers and a scaling assumption for cluster number scaling assumptions for cluster radius and fractal dimension is proposed.