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We found that, from these particular phase synchrony matrices, the mean number of edges required to guarantee that all graphs were weakly connected was d ≥ 11, whilst d ≥ 13 was required to ensure strong connectivity.
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When Φ = I (I is the identity matrix), the mean square deviation (MSD) and when Φ = R (R is the autocorrelation matrix of the input signal), the excess mean square error (EMSE) expressions are derived.
Because male and female samples are independent within each species, covariance matrices for SShD were computed as the sum of the covariance matrices for the mean shapes of the males and females.
We define the cross-coexpression matrix as the mean of the individual matrices, and pairs of genes in this matrix with values close to 1 are highly correlated in both datasets.
The data matrix is optionally double-centered by subtracting from each matrix entry the mean value calculated over the corresponding matrix row and the mean value calculated over the matrix column, followed by adding the global mean value computed over all matrix entries.
The correlation matrix, the means, and the standard deviations for the measured variables are shown in Table 3.
There was no correlation between the similarity matrix of the mean species assemblage per fallow and the matrix of fallow coordinates (rho = −0.145, p = 0.76).
The same procedure was performed for the similarity matrix of the mean species assemblage per fallow and the distance matrix of geographic positions of the fallows.
So, it is an effective method to avoid singularity matrix that the mean component in every band is added in the covariance matrix.
By applying the M-matrix technique, the mean square exponential stability is studied.
which is very close to the original matrix, P. The mean vectors and the variances were also very close to the real values.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com