Sentence examples for underlying trees from inspiring English sources

The weight of a true split in Figure 2 is calculated as summing up the split weights of this split in eight underlying trees by switching off one branch in a reticulate event.

The comparison of the underlying tree has the complexity O(N log N).

Adiga et al. [11] showed that the skew energy of an oriented tree is independent of its orientation, which is equal to the energy of its underlying tree.

For two tree monomials α and β, say that α is divisible by β whenever there exists a subtree of the underlying tree of α for which the corresponding tree monomial α ′ is equal to α.

Moreover, Shader and So showed that S ( G σ ) has the same spectrum as that of its underlying tree for any oriented tree G σ ; see Theorem 2.5 of [12].

More generally, lessons at the high school and undergraduate level should de-emphasize the technical aspects of phylogeny reconstruction in favor of a focus on the concepts underlying tree thinking.

One can find that S ( G σ ) is similar to S ( G v σ ), thus G v σ has the same skew energy as that of G σ. Especially, Adiga et al. [11] showed that the skew energy of a directed tree is independent of its orientation, which is equal to the energy of its underlying tree.

Every α = α ( x 1, …, x n ) ∈ F V ( n ) has a unique expression α = ( path ( 1 ), …, path ( n ), [ i 1 ⋯ i n ] ), where path ( r ) ∈ V ∗ for 1 ≤ r ≤ n is the unique path from the root to the leaf r and the permutation [ i 1 ⋯ i n ] lists the labels of the leaves of the underlying tree in the order determined by the planar structure, from left to right.

The underlying tree was derived from our above RAxML v7.0.4 analysis.

Ideally, the assumptions of systematists should be in agreement with those underlying tree-building algorithms [37].

Second, we performed additional analyses under Model A to investigate whether metabolic rate was dependent on the underlying tree.