Stability of random brain networks with excitatory and inhibitory connections

Gray, Richard T.; Robinson, P. A.

doi:10.1016/j.neucom.2008.06.001

Cited by 11 publications

(25 citation statements)

References 40 publications

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“…We investigate randomly connected brain networks with n neural populations and probability of connection p. Previously (Gray and Robinson 2008b), we investigated the spectrum and stability of networks where the excitatory and inhibitory connections are randomly distributed, we call these random connection networks (RCNs). Here, for comparison, we investigate networks where the connections leaving a given population are all excitatory or all inhibitory, which we call random population networks (RPNs).…”

Section: Random Network With Excitatory and Inhibitory Populationsmentioning

confidence: 99%

“…RPNs are therefore parametrized by n, p, p i , μ e , σ e , μ i , and σ i . These parameters were also used in (Gray and Robinson 2008b) to study RCNs. In that work each parameter represented the same quantity as described here except p i was the probability that a connection is inhibitory rather than the probability that a population is inhibitory, as in the present case.…”

Section: Random Network With Excitatory and Inhibitory Populationsmentioning

confidence: 99%

“…Therefore, we can use the same parameter values for both types of networks and directly compare their stability. In (Gray and Robinson 2008b) we determined the spectra and stability of RCNs showing that the spectrum of these networks can be accurately approximated using the standard results of random matrix theory. The theoretical results derived in that work are summarized in Appendix B so that comparisons can be made with the RPNs studied here.…”

Section: Random Network With Excitatory and Inhibitory Populationsmentioning

confidence: 99%

“…Previously we used standard results from random matrix theory to determine the spectral distribution Robinson 2007, 2008a, b). The standard theory cannot be used here because there are correlations between the entries in each column of G, hence, G does not satisfy the conditions of the standard results (Füredi and Komlós 1981;Gray and Robinson 2008b;Sommers et al 1988). However, the spectral distribution of large fully connected networks with inhibitory populations has been investigated recently by Rajan and Abbott (Rajan and Abbott 2006).…”

Section: Spectrum Of Random Population Networkmentioning

confidence: 99%

“…Previously we studied the stability of randomly connected brain networks with excitatory connections (Gray and Robinson 2007), a distribution of connection strengths that allowed the existence of inhibitory connections (Gray and Robinson 2008a), and with connections randomly assigned to be excitatory or inhibitory and having different probability distributions for the strengths of excitatory and inhibitory connections (Gray and Robinson 2008b). We used the results of random matrix theory to analytically determine the eigenvalue spectrum and stability of brain networks, showing that stability restricts the size of the network, the probability of connection, and the overall mean and variance of the network gains.…”

Section: Introductionmentioning

confidence: 99%

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Stability and structural constraints of random brain networks with excitatory and inhibitory neural populations

Gray

Robinson

2008

J Comput Neurosci

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The stability of brain networks with randomly connected excitatory and inhibitory neural populations is investigated using a simplified physiological model of brain electrical activity. Neural populations are randomly assigned to be excitatory or inhibitory and the stability of a brain network is determined by the spectrum of the network's matrix of connection strengths. The probability that a network is stable is determined from its spectral density which is numerically determined and is approximated by a spectral distribution recently derived by Rajan and Abbott. The probability that a brain network is stable is maximum when the total connection strength into a population is approximately zero and is shown to depend on the arrangement of the excitatory and inhibitory connections and the parameters of the network. The maximum excitatory and inhibitory input into a structure allowed by stability occurs when the net input equals zero and, in contrast to networks with randomly distributed excitatory and inhibitory connections, substantially increases as the number of connections increases. Networks with the largest excitatory and inhibitory input allowed by stability have multiple marginally stable modes, are highly responsive and adaptable to external stimuli, have the same total input into each structure with minimal variance in the excitatory and inhibitory connection strengths, and have a wide range of flexible, adaptable, and complex behavior.

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Section: Random Network With Excitatory and Inhibitory Populationsmentioning

confidence: 99%

Section: Random Network With Excitatory and Inhibitory Populationsmentioning

confidence: 99%

Section: Random Network With Excitatory and Inhibitory Populationsmentioning

confidence: 99%