Sentence examples for result on quartet from inspiring English sources

Our proof relies on a new result on quartet compatibility we believe is of independent interest.

We now contrast our result on quartet compatibility with a result on triplets.

The next theorem allows us to use our result on quartet compatibility to establish a lower bound on f(r).

We contrast our result on quartet compatibility with a result on the compatibility of rooted triplets: For every n≥3, if R is an incompatible set of triplets over n labels, and | R|> n−1, then some proper subset of R is incompatible.

Our lower bound on f(r) is proven via a result on quartet compatibility that may be of independent interest: For every n≥4, there exists an incompatible set Q of Ω(n) quartets over n labels such that every proper subset of Q is compatible.

We contrast our results on quartets with the case of rooted triplets: For every n≥3, if R is an incompatible set of more than n−1 triplets over n labels, then some proper subset of R is incompatible.

Quartet-based methods QILI (Quartet Inference and Local Inconsistency) [ 58] is based on quartet topologies extracted from unrooted gene trees.

Attempts to reduce these errors include variations on quartet puzzling which limit the quartets that are examined, provide different weights for individual quartets, or modify the puzzling procedure [ 18- 20].

Given a quartet topology set Q on a taxon set S = { s1, s2,..., s n }, Q is complete if Q contains exactly one quartet topology for every quartet of S. In this paper, we assume Q is complete.

We refer the reader to [ 1, 23] for more on quartet rules.

The result finds the quartet at its most magnetic and adventurous.