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In the situation of the multiplicity of the eigenvalue being 1, there exists a unique real eigenfunction up to sign, and for double eigenvalues, there exist a pair of normalized linearly independent eigenfunctions, and for a multiplicity (l (l=3, 4, ldots, 2m)) eigenvalue, the number of the normalized linearly independent eigenfunctions is l.
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Formally, the flat-sim score between a pair of -normalized feature vectors and is given by their dot product flat-sim.
The dependence between any pair of normalized sources can be characterized, for example, by the conditional expectations E[ S i |S j ] and E[ S j |S i ] (i ≠ j).
The following theorem provides us the values of the constants a and b. ( [[19]], Theorem 3):Given a pair of dependent normalized sources S i, S j, if the conditional expectation E[ S i |S j ] is linear in S j, that is E[ S i |S j ] = a S j + b, then a = E[ S i S j ] and b = 0.
If BLASTN did not return a score for a pair of IGR sequences, the normalized sequence identity for the pair was set to 0. We calculated the median of the normalized sequence identity scores for all pairs in an ortholog set as a single metric of IGR sequence identity within the set.
Markers are presented along these curves, indicating each evaluated pair of normalized misalignment and number of operations per sample.
We must construct a pair of circular genomes AF and BF, a normalized similarity measure σ for genes in AF and BF, and a positive integer k′≤| AF| such that the family-free DCJ similarity of AF and BF is at least k′ if and only if the exemplar DCJ distance of genomes A and B is at most k.
Any CompariMotif hits matching at least two positions with a MatchIC ≥ 1.5 (approximately equivalent to one fixed and one 3-fold degenerate position, or a pair of 2-fold degenerate positions) and a normalized IC ≥ 0.5 (i.e. at least half the smallest motif is matched) were classed as motif matches.
It is simply the normalized version of the number of shared neighbors between a pair of nodes in a graph.
A pair of friends.
A pair of shoes?
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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