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Under the hypotheses that there are two different aspects (linked to subjects and items), acting in a separable manner, RM allows for constructing a single metric scale defining a ranking of Items and Person parameters.
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When a hue was chosen, it was removed from the circle and the selection process was repeated until all the remaining hues were chosen, defining a rank ordering of the "harmonies" of each figural color against all background colors.
This defines a ranking of the edges.
For comparison of different rankings, we defined a rank deviation as significant if the rank order of the same intervention differed by two or more points on the ordinal scale.
Given a set of expression data and a quantitative measure of coexpression, for each gene in the dataset we defined a Ranked Coexpression Group as the gene itself together with the k genes most closely coexpressed with it.
To define a ranked list of genes significantly expressed in cartilage, a supervised analysis [ 13], comparing cartilage versus non-cartilage gene expression, was employed.
That part of the government's case pivots on defining a fair ranking by the I.B.F. as a thing of value and a right due to the boxers the organization served.
In this paper, through applying pairwise constraints between relevant and irrelevant labels, and defining an approximate ranking loss, we generalize binary Lagrangian support vector machine (LSVM) to construct its multi-label form (Rank-LSVM), resulting into a strictly convex QP problem with non-negative constraints only.
It is almost impossible to define a general ranking for estimating a country's overall orientation towards sustainability: the numerous indexes available simply confirm the differences among countries, but it is extremely hard to classify them, because of the differences in index composition and in the trait of sustainability under observation.
In order to examine degree of mental health specialization in the contact adolescents achieved, we defined a hierarchical ranking of level of specialization.
Note that the k th column of Z can be written as Z ( :, k ) = E ( k, : ) ⊗ F ( k, : ) T ∈ C N 1 N 2 × 1, k = 1, …, K. Defining a rank-one matrix Z ~ k ≐ unvec ( Z ( :, k ) ) ∈ C N 2 × N 1, it follows that Z ~ k = F ( k, : ) T E ( k, : ), from which E k,:) and F k,:) can be determined as the unique right and left singular vectors of Z ~ k, k=1,…,K.
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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