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Due to the longitudinal nature of these data (2 to 78 lipid data points per individual; mean = 14.4±10.1 data points), we defined two phenotypes to be used in the analyses below: (1) median HDL and (2) modeled HDL as previously described [17].
To quantify epidermal deterioration pictures of epidermal samples of different genotypes and time points, we defined four classes I to IV reflecting distinct stages of epidermal membrane labeling loss.
For every pair of parameter points, we defined a straight line connecting them, and identified a set of three points that subdivide the line into four equally long segments (we also subdivided the line into 5, 6, 7, and 8 equally long segments, obtaining qualitatively identical results).
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Because all glycemic indices reached their lowest level between 15 and 27 months (arbitrarily defined nadir point), we defined ΔGA/HbA1c as the difference in GA/HbA1c between the end point (39 to 51 months) and nadir point (15 to 27 months).
Then, using the median cutoff point, we defined a group with 'low TYRP1' and a group with 'high TYRP1' and showed the corresponding Kaplan Meier curves in Figure 2 (top panel).
For an arbitrary initial point, we define the iterative scheme by (1.23).
Using such a point, we define the metric projection by for every.
At this point, we define d(i) as the position facing i diagonally.
At this point, we define two terms certain and uncertain state for a code (C) using Eq. 8. C = left {begin{array}{ll} text{certain}, textrm{state,} & {if},, mid delta mid ge T text{uncertain}, textrm{state,} & {otherwise} end{array} right.
We define non-uniform birth rates of multiple marks based on the data energy for each marked point; we define death rates based on both the data energy and the current configuration of the marked points.
For each point, we define { x i, y i}, i = 1, …, n, the moving M-regression inclusion function, as Thus, the moving M-regression line can be found by minimizing the following expression: Function F is not differentiable at all points (x i, y i) such that y i = ax i + b − d1 and y i = ax i + b + d2.
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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