To quantitatively describe the interplay of surface roughness and film thickness, we introduced two roughness characteristics: the ratio of film thickness to the surface's root-mean-square roughness (h/σ), and a surface-pattern parameter, defined as the ratio of correlation lengths in two orthogonal directions.
The ratio of correlation is denoted as T, and calculated as T = X/ Y.
We use the ratio of correlation of one stage relative to the other stage for measuring the co-expression change of a gene pair.
The analytical distribution of the ratio of correlation is described as follows: (8) where t is the value of variant T, f XY (x, y) is the joint probability density of X and Y.
This analysis also showed that as TFs have more TGs the ratio of correlation of the expression of the TFs with its TGs compared to all genes converges to one.
Our analyses also revealed that as TFs have more TGs the ratio of correlation of the expression of the TFs with its TGs compared to all genes converges to one.
The joint probability in Equation (9) is computed as: (11) Note that x = ty, then by combining Equations (8) and (11), the analytical distribution function for the ratio of correlation of stage 2 relative to stage 1 is presented as: (12) where,,,, and K is a normalization constant.
For a given gene, its analytical distribution of the ratio of correlations formed by all other genes pairing this gene, is treated as a background to assess the significance of the observed values of the ratio of correlations.
This conservation pattern is more obvious when we use a heatmap to show the ratios of TSS correlations to TTS correlations for all pairs of organisms.
No remarkable spectral peaks of vortex shedding appeared in the NPSD, and the ratios of the correlation lengths to the tube diameter for the cross-shaped tube bundle were much shorter than that of the random excitation force acting on circular tube bundles.
