Hence, Tj+1 is the smallest subtree of T j containing center(R1),…,center(R k ).
For each S l, let R l be the smallest subtree of T j containing every vertex in S l.
Let Rm′ be the smallest subtree of T j containing the first m centers, center(R1),…,center(R m ) (thus Rk′=Tj+1).
For j=1,…,2⌈logdiam(T ⌉, let (v^{j}_{i}) be the value of v i at the beginning of the j-th iteration, and let T j be the smallest subtree of T containing (v^{j}_{1}, hdots, v^{j}_{n}).
A 'local parse tree' π gh (equivalent to what we have called just π until now) is defined as the minimal (smallest) subtree of a complete parse tree that contains s g and s h.
In addition, for any subset Y ⊆ X, P D T (Y ) denotes the total length of the smallest subtree of T containing the taxa in Y, also known as the phylogenetic diversity of Y with respect to T (see e.g. [ 6]).
For these reasons, the data were split into small groups of 3 8 related species, and branch lengths estimated separately for these small subtrees.
We classified the cases as dual infection if the phylogenetic tree incorporated at least two strongly supported clusters that each contained at least one sequence from the patient under investigation and control sequences; furthermore, we required a threshold number of control sequences interspersed within the smallest subtree that included all sequences of a patient.
In processing a query, the cloud server first locates the smallest subtree covering all the query results.
"Given a rooted gene tree with duplication or speciation assigned to each of its internal nodes, two sequences are ultra-paralogous if and only if the smallest subtree containing them both contains only internal nodes representing duplications".
