Hard water
Water's hardness is determined by the concentration of multivalent cations in the water. Multivalent cations are positively charged metal complexes with a charge greater than 1+. Usually, the cations have the charge of 2+. Common cations found in hard water include Ca and Mg. These ions enter a water supply by leaching from minerals within an aquifer. Common calcium-containing minerals are calcite and gypsum. A common magnesium mineral is dolomite (which also contains calcium). Rainwater and distilled water are soft, because they contain few ions.
Weighted correlation network analysis
Next, an adjacency matrix (network), formula_11, is used to quantify how strongly genes are connected to one another. formula_12 is defined by thresholding the co-expression similarity matrix formula_13 . 'Hard' thresholding (dichotomizing) the similarity measure formula_14 results in an unweighted gene co-expression network. Specifically an unweighted network adjacency is defined to be 1 if formula_15 and 0 otherwise.
Because hard thresholding encodes gene connections in a binary fashion, it can be sensitive to the choice of the threshold and result in the loss of co-expression information. The continuous nature of the co-expression information can be preserved by employing soft thresholding, which results in a weighted network. Specifically, WGCNA uses the following power function assess their connection strength: