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For every T ∈ P, let V x, T consist of all the vertices of the minimal subtree of T connecting the labels in ℒ (T ) ∩ L x.
Let S′ be the tree obtained by suppressing any degree-two vertices in the minimal subtree of S connecting the labels in ℒ (T ).
Let ℓ be any multiply-occurring label in T and let T′ be the minimal subtree of T that spans all the leaves labeled by ℓ.
Then, S| Y denotes the tree obtained by suppressing any degree-two vertices in the minimal subtree of S connecting the labels in Y. Now, let T be a phylogenetic tree such that ℒ (T ) ⊆ ℒ (S ).
Let f={ x, y} and let x be the vertex of f where L x ⊆ L v. Let S p be the minimal subtree of S connecting the labels in L x.
Given a tree T with L= L(T) and a state s of χ, we denote by T s the minimal subtree of T connecting all leaves with labels having state s for χ.
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Out of these, 107 were suspected for superinfection and in 94 cases the sequences of the patient belonged to a closely related transmission cluster (size of minimal subtree ≤ 50, see Methods).
An agreement subtree (AST) for a collection of phylogenetic trees on a common leaf set is a minimal subtree connecting a fixed set of leaves that is homeomorphically included in all of the input trees.
Second, the minimal subtree that contained all sequences of the patient had to include at least 50 unrelated control sequences.
An f-frequent subtree, or a frequent subtree (FST) for short, in a collection of m leaf-labeled trees on a common leaf set, is a minimal subtree connecting a fixed set of leaves that is homeomorphically included in at least f· m of the input trees.
In such a tree, if the minimal subtree that includes all sequences of an individual includes also one or more control sequences, then either i) the most recent common ancestor of the sequences was not located in the patient, which indicates superinfection with a distinct lineage or ii) the control sequences are derived from a transmission cluster that originated from the patient.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com