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To compare the connectivity maps, we define 2 measures, the "recurrence strength" as the ratio of the mean within-layer and the mean interlayer connection probabilities and the "loop strength" as the ratio of the mean connection probability of the cortical feed-forward loop (Gilbert 1983, L4 to L2/3 to L5 to L6 to L4) and the mean connection probability of all other interlayer connections.
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For comparison of LDU maps we defined a hotspot as a region of maximum size 5 kb in which there was at least a one LDU change between two encompassed SNPs, as observed in previous studies [ 37].
To objectively analyze the data from these heat maps, we defined a set of criteria to use in classifying motif pairs into three groups; a flow chart of this process is shown in Figure 2. Briefly, in the Class 1 pairs, co-occurrences are found mainly in the vicinity of TSSs [-500 to +500] in both types of heat maps.
Given the low resolution of the sheep, pig, and opossum genetic maps, we defined windows as the regions between pairs of consecutive genetic markers, thus, generating windows with median sizes of 1.7, 4.4, and 18.3 Mb, respectively, but with high variance (supplementary fig. S-2, Supplementary Material online).
Based on the mapping, we define transformation algorithms using Query/View/Transformation (QVT) which is a standard model transformation language by OMG.
For the given mapping we define.
For a given mapping, we define.
For a given mapping, we define (3.3).
For, where is a set-valued map we define (2.12).
To write system (3.5) as a map, we define the map : (3.7). is the map evaluated at the point.
If is a Lefschetz map, we define the Lefschetz set (or ) by (1.5).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com