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signal-noise-analysis
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Asymptotic eigenvectors, topological patterns and recurrent networks
, Article Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science ; Volume 14, Issue 2 , 2013 , Pages 95-100 ; 14549069 (ISSN) ; Sharif University of Technology
2013
Abstract
The notions of asymptotic eigenvectors and asymptotic eigenvalues are defined. Based on these notions a special probability rule for pattern selection in a Hopfield type dynamics is introduced. The underlying network is considered to be a d-regular graph, where d is an integer denoting the number of nodes connected to each neuron. It is shown that as far as the degree d is less than a critical value dc, the number of stored patterns with m μ = O(1) can be much larger than that in a standard recurrent network with Bernouill random patterns. As observed in [4] the probability rule we study here turns out to be related to the spontaneous activity of the network. So our result might be an...
Computing all the Floquet eigenfunctions of oscillators using harmonic balance Jacobian matrices
, Article IET Circuits, Devices and Systems ; Volume 5, Issue 4 , July , 2011 , Pages 257-266 ; 1751858X (ISSN) ; Farzaneh, F ; Sharif University of Technology
2011
Abstract
Floquet eigenfunctions and Floquet exponents are encountered in stability and noise analysis of circuits operating at large signal periodic regime. It is analytically verified that the spectrum vectors of the left-hand and right-hand Floquet eigenfunctions and the Floquet exponents (Floquet eigenpairs) are members of the harmonic balance eigenvalues and eigenvectors (HB eigenpairs). The relationships between other HB eigenpairs with the Floquet eigenpairs are discussed. This discussion leads to a practical algorithm for computing the Floquet eigenpairs through HB eigenpairs. Furthermore, it is analytically verified that the main arguments of the study are consistent with the...
Topological pattern selection in recurrent networks
, Article Neural Networks ; Volume 31 , 2012 , Pages 22-32 ; 08936080 (ISSN) ; Abbassian, A ; Sharif University of Technology
2012
Abstract
The impact of adding correlation to a population of neurons on the information and the activity of the population is one of the fundamental questions in recent system neuroscience. In this paper, we would like to introduce topology-based correlation at the level of storing patterns in a recurrent network. We then study the effects of topological patterns on the activity and memory capacity of the network. The general aim of the present work is to show how the repertoire of possible stored patterns is determined by the underlying network topology.Two topological probability rules for pattern selection in recurrent network are introduced. The first one selects patterns according to a...