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The corresponding random effects mean correlation matrix calculated by Eq. (1) (which serves as input for the linear model) can be found in Online Appendix E. The number of citations was collected on January 13 , 2017

The mean correlation matrix

The obtained mean correlation matrix also has a block diagonal structure.

The main insight from the mean correlation matrix is that we observe strong correlations of regulatory parameters with promoter thresholds.

Similar to the full search case, we compute the mean correlation matrix to detect the significant correlations between parameters (see Figure 3.6 in Additional file 1).

Note that the correlations corresponding to the most significant entries in the mean correlation matrix (with absolute values greater than 0.5) are statistically present in all individual correlation matrices because corresponding standard deviations are relatively small (less than 0.2).

For directly comparing the connectivity difference between two groups, two-sample two-tailed t-test was performed on all 4005 potential connections included in the

CPC analysis showed that family-mean correlation matrices were not similar or not proportional across positions (P < 0.01, using either methods), but shared common principal components (P = 0.760 using the step-up method, P = 0.696 using the jump-up method).

So the mean and correlation matrix of the Rice channel matrix can be expressed as (13) (14).

In this case, propagation is Rayleigh [35], and z may also be modeled as zero mean with correlation matrix R z.

Using the same method as for the Rayleigh channel, an adjustment factor can be obtained to maximize (2) when the statistic estimated value of mean and correlation matrix of the Rice channel matrix are known by the receiver side in the BS.