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Our ILP has constraints (described below) to ensure that each value assignment to the F-variables corresponds to a restricted representative selection for P.
Let G be any restricted representative selection for P displayed by R. By Theorem 3, T = Maj+(G) and R is the completion of G.
Each R ∈ ⟨ P⟩ r is called a restricted representative selection for P. Since ⟨ P⟩ r ⊆ ⟨ P⟩, the restricted span represents an intermediate level between the input profile and the original definition of span.
We first describe the variables and constraints that are used to ensure that the settings of the fill-in variables (the F variables) correspond to a restricted representative selection.
To guarantee that the assignment to the F variables corresponds to a restricted representative selection, we require that C pq = 1 for every two column indices p, q that correspond to splits in the same input tree.
A fill-in of matrix M(P) is a matrix representation for a restricted representative selection G for P. Note that M G) has no question marks and that, for every taxon x and split i such that M xi (P) ∈ {0, 1}, we have M xi (G) = M xi (P).
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This table is restricted to representative allele frequencies.
Further, conference committee meetings should be restricted to representatives, senators and their aides, and verbatim transcripts of the proceedings inserted in the Congressional Record.
Until today, an overall number of 11 Hox genes has been identified in seven out of the eight molluscan "class -level taxa [ 24– 38], but expression studies on Hox genes are restriclass -levelesentaxaves of two, probably derived, clades of Mollusca that belong to the conchiferans, namely Gastropoda (snails and slugs) and Cephalopoda (squids and octopuses).
For each gene, a phylogenetic analysis was conducted with the 20 best BLASTP hits of P. acanthamoebae and L. drancourtii that was restricted to one representative species per genus.
After sample size calculation the cohort was restricted to a representative sample of 34,393 migrants according to the spatial distribution and urban/rural proportion who were at least 15 years old when they migrated to Germany.
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