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In particular, the diagonal entries of the matrix raised to the n th power give information about the periodic orbits with period n.
The network adjacency matrix is the gene pair-wise correlation matrix raised to the power of 6, chosen based on the scale-free topology criteria [ 77].
For reaction i this is given by [ M n ] ii, the diagonal value of the matrix raised to the nth power.
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We also show with the help of matrix geometric means and a Riemannian metric over the set of positive definite matrices that for a rational exponent p in the interval (0,1], the matrix X raised to p is the largest element of a set represented by linear matrix inequalities.
Second, this correlation matrix was raised to power β = 6 to calculate a adjacency matrix.
Next the matrix is raised to a soft-thresholding power (β = 8 in this study) to obtain an adjacency matrix.
The correlations matrix was raised to the power 6, thus producing a weighted network.
This adjacency matrix is raised to the power γ (soft thresholding).
Thus, the computed similarity matrix was raised to different values of β spanning a range from 1 to 30 and their corresponding Rs were calculated.
The A matrix was raised to the power 5. Based on the connectivity of individual SNP with all the other SNPs in the network, the top 1500 highest connected SNPs were selected for the network construction.
This matrix was then raised to a power (beta = 8 in this study) to achieve an adjacency matrix holding connection strengths.
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