Eigenvalue distributions for a class of covariance matrices with application to Bienenstock-Cooper-Munro neurons under noisy conditions.
We analyze the effects of noise correlations in the input to, or among, Bienenstock-Cooper-Munro neurons using the Wigner semicircular law to construct random, positive-definite symmetric correlation matrices and compute their eigenvalue distributions. In the finite dimensional case, we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments. These correlations can be due either to correlations in the noise from the input lateral geniculate nucleus neurons, or correlations in the variability of lateral connections in a network of neurons. In particular, we find that for fixed dimensionality, a large noise variance can give rise to long lifetimes of synaptic strengths. This may be of physiological significance.
Bazzani
Armando
A
Department of Physics and National Institute of Nuclear Physics, University of Bologna, via Irnerio 46 40126, Bologna, Italy. armando.bazzani@bo.infn.it
Castellani
Gastone C
GC
Cooper
Leon N
LN
D000465:Algorithms; D000818:Animals; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D005829:Geniculate Bodies / Q000473:pathology; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D008962:Models, Theoretical; D009415:Nerve Net; D009473:Neuronal Plasticity; D009474:Neurons / Q000473:pathology*; D009435:Synaptic Transmission; D013997:Time Factors