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An arbitrary function of this sort can be thought of (as can functions in general) as an infinite class of pairs of correlated values of an independent variable and of the function, like the coordinate pairs (x, y) of points on a graph.
This is particularly attractive, because if these linearly dependent coordinate pairs are not deleted in the coupling process, the accuracy of the substructure synthesis can deteriorate.
More specifically, the PUCE program outputs Cartesian coordinate pairs for the two extracted direct space lattice parameters as 32-bit floating point values.
Space is also crisscrossed with continuum fluxes, coordinate pairs that allow instantaneous travel between them without consuming fuel.
On each independent database, we first filtered duplicates out and then concatenated overlapping segments in order to form a list of unique and excluding coordinate pairs representing regions with SDs and/or CNVs.
New coordinate pairs are drawn until a specified number of coordinates have been accepted.
Based on the coordinate pairs and the UCSC alignments, the 2 nt sequences compared are extracted from the corresponding genomes and the alignable sequences are displayed.
To compute p-value the ratio was compared to that of 10,000 triangles whose vertices coordinate pairs were generated randomly from a uniform distribution on a rectangle.
The vector of 500 numbers (250 coordinate pairs) representing each outline can be represented as a point in a 500-dimensional space (approximately 25,000 points in total for this dataset).
Inferior genu (IG) and inferior splenium (IS) were then identified by finding the coordinate pairs with the minimum y values in the anterior and posterior halves of the CC.
Starting at an arbitrary point, (x 0), y(0)), coordinate pairs (x 1, y 1), (x 2, y 2), …, (x(K − 1), y(K − 1)) are encountered when traversing the boundary in a preselected direction.
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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