Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:B1L-B

Session:

Number:304

Graph analysis on simulate hierarchical complex networks dynamic structure

Vincent Buntinx,  Vladyslav Shaposhnyk,  Alessandro E.P. Villa,  

pp.304-307

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.304

PDF download (448KB)

The brain is a complex structure that can contain up to several billion neurons connected to each other. One possible way to study its structure is to design neural computation algorithms for simulating a simplified mathematical modelisation with several features of the brain and its neurons inspired by their biological features. Due to the large number of neurons and brain dynamics, the mathematical object representing the simulated brain can be considered as a complex network and a study of its dynamic structure is possible by using graph theory [1] to calculate a number of relevant measures [2] that evolve over time in order to observe emergent properties associated to network dynamics. In this context, we have provided some simulations of bio-inspired complex neural network modeled by a hierarchically organized circuit of evolvable neural networks [3]. This model is based on the observations that the vertebrate brain possess several specific areas organized and connected by a hierarchical topology. Neurons are simulated by leaky integrate and fire spiking neurons interconnected by modifiable synapses according to Spike Time Dependent Plasticity (STDP). An other study [4] suggest that the introduction of a feedback connection between two networks hierarchicaly organized can modify their dynamic structure with unexpected differences between the two networks. We studied two hierarchical topologies based upon the feedforward topology with and without recurrent loops. The purpose of this paper is to present new datas on geometrical properties of the networks by means of graph analysis. Some basic graph measures are represented with time dependency considerations by using the R software package ”Igraph” [5]. In this simulation, there is no cell death except apoptosis, we chose to present results based on the analysis of different sets of excitatory neurons selected following their level of activity.

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