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For the two vertices in the example above, we have R s (vi,j l,r)) = ((0,0),(j,r), 0,0))=R s (v i ′,j(l′,r)) because for both vertices, the corresponding set (mathcal {V}_{1,b}(bullet,bullet)) is not fully included in (mathcal {V}_{s}).
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Starting with these, we built an undirected graph, where vertices are proteins and edges link vertices to the corresponding BLAST hits.
In IPR, the reconstructed residuals associated with sampled vertices are copied and assigned to the vertices in the corresponding local-set, and then the projection procedure is conducted.
In such case, the parameters are obtained by simply solving the linear system in (2) using the four vertices of the quadrilateral and the four vertices of the corresponding square block.
For IPR, the reconstructed residuals associated with the sampled vertices are firstly copied and propagated to the unsampled vertices in the corresponding local-sets, and then the signal is projected onto the low-pass filtering subspace.
For a cooperative network, we write the set of vertices of the corresponding graph as V = V O ∪ V A, where V A is the set of vertices corresponding to the anchors, and V O is the set of vertices associated with ordinary nodes.
Anna Karnenina Network (AKN; (lambda ) (_{mathrm{sp}}) = 2.47) [24]: this a network of 138 characters (vertices) in the novel Anna Karnenina; there exists an edge between two vertices if the corresponding characters have appeared together in at least one scene in the novel.
Korea Family Planning Network (KFP; (lambda ) (_{mathrm{sp}} = 1.69)) [25]: this is a network of 39 women (vertices) at a Mothers Clubb in Korea; there existed an edge between two vertices if the corresponding women were seen discussing family planning methods during an observation period.
There exists an edge between two vertices if the corresponding faculty are friends of each other.
There exists an edge between two vertices if the corresponding residents are friends of each other. 5.
There exists an edge between two vertices if the corresponding two books were co-purchased by the same buyer (at least one buyer).
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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