Scale factor Φ and largest eigenvalue λ<sub>max</sub> for spatially-irregular inputs.

Abstract

<p>(A) The scale factor Φ for <i>M</i> > 1 superimposed fields (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005782#pcbi.1005782.e152" target="_blank">Eq 70</a>). The black dots are obtained by estimating the power spectrum at frequency |<b>k</b>| = 1 m<sup>−1</sup> for 3600 input realizations. The red line is the theoretical curve in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005782#pcbi.1005782.e169" target="_blank">Eq 82</a>. (B) The largest eigenvalue λ<sub>max</sub> as a function of the number of superimposed fields <i>M</i>. The black dots are obtained by computing the eigenvalues of the correlation matrix <i>C<sub>ij</sub></i> − <i>aδ<sub>ij</sub></i> for <i>N</i> = 3600 inputs, where <i>δ<sub>ij</sub></i> is the Kronecker delta (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005782#pcbi.1005782.e048" target="_blank">Eq 21</a>). The red line is obtained from Eqs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005782#pcbi.1005782.e156" target="_blank">71</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005782#pcbi.1005782.e169" target="_blank">82</a>. Note that, according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005782#pcbi.1005782.e156" target="_blank">Eq 71</a>, the largest eigenvalue is always at the critical frequency <i>k</i><sub>max</sub> = 3 m<sup>−1</sup> for any value of <i>M</i>. Parameter values as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005782#pcbi.1005782.g009" target="_blank">Fig 9</a> (see Sec Numerical simulations).</p

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