Scale-freeness and small-world phenomenon in information-flow graphs of geometrical neural networks
Year: 2013
Type: review
Abstract: In this dissertation we set out to study a simplied model of activation ow in articial neural networks with geometrical embedding.The model provides a mathematical description of abstract neural activation transfer in terms, which bear resemblances to multi-value Boltzmann-like evolution.The activation-preserving constraint mimics a critical regime of the dynamics and, along with accounting for geometrical location of the neurons, makes the system more feasible for modelling of real-world networks.We focus on scale invariance or scale-freeness and small-world phenomena in the said networks.Our results clearly conrm presence of both features at the functional level of the activity-ow graph.We show that the degree distribution preserves a power-law shape with the exponent value approximately equal to γ -2.In addition, we present our results concerning characteristic path length in the said graphs, which grows roughly logarithmically with the size of the network, while the clustering coecient turns out to be relatively high.Taken together, the clustering and path length ratios are surprisingly high, and thus conrm large both local and global eciency of the network.Finally, we compare the properties of activation-ow model to those reported in neurobiological analyses of brain networks recorded with functional magnetic resonance imagining (fMRI).There is a strong agreement between the shape and exponent value of degree distribution also the clustering and characteristic path lengths are comparable in both the model and medical data.
Source: ReIn UW (University of Warsaw)
Author: Jarosław Piersa
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1834868316