Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Simple model of spiking neurons
IEEE Transactions on Neural Networks
Persistent activation blobs in spiking neural networks with Mexican hat connectivity
ICAISC'10 Proceedings of the 10th international conference on Artifical intelligence and soft computing: Part II
Theoretical model for mesoscopic-level scale-free self-organization of functional brain networks
IEEE Transactions on Neural Networks
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Power law graphs are an actively studied branch of random graph theory, motivated by a number of recent empirical discoveries which revealed power law degree distributions in a variety of networks. Power laws often coexist with some degree of self-organization either based on growth and preferential attachment (which seems to be the case in sociological/technological networks) or duplication (which seems to be the case for biological/methabolic networks). Quite recently a power law graph with exponent γ ≅ 2 has been observed in fMRI brain studies of correlations of functional centers of activity. We study the model we introduced previously to explore possible mechanisms existing in large neural networks that might lead to power law connectivity. The model (referred to as the spike flow model) resembles a kind of spiking neural network and yields a power law graph with exactly γ ≅ 2 as a byproduct of its dynamical behavior. In this paper we investigate whether the power law is robust under certain changes to the model's dynamics. In particular we study the effect of merging the model with a random Erdös-Rényi graph which can be interpreted as an addition of long range myelinated connections. Our numerical results indicate that as long as the density of Erdös-Rényi fraction is bounded by a constant, the power law is preserved in systems of appropriate size.