Rotation distances measure the difference in shape in rooted binary trees. We construct sharp bounds on maximal right-arm rotation distance and restricted right-arm rotation distance for trees of size n. These bounds sharpen the results of Cleary and Taback and incorporate the lengths of the right side of the trees to improve the bounds. c © 2007 Elsevier B.V. All rights reserved.

Reconstructing the evolutionary tree for a set of n species based on pairwise distances between the species is a fundamental problem in bioinformatics. Neighbor joining is a popular distance based tree reconstruction method. It always proposes fully resolved binary trees despite missing evidence in the underlying distance data. Distance based methods based on the theory of Buneman trees and ref...

The approximation of stochastic processes by trees is an important topic in multistage stochastic programming. In this paper we focus on improving the approximation of large trees by smaller (tractable) trees. The quality of the approximation is measured by the nested distance, recently introduced in [Pflug, Pfl09]. The nested distance is derived from the Wasserstein distance. It additionally t...

The string correction problem looks at minimal ways to modify one string into another using fixed operations, such as for example inserting a symbol, deleting a symbol and interchanging the positions of two symbols (a “swap”). This has been generalized to trees in various ways, but unfortunately having operations to insert/delete nodes in the tree and operations that move subtrees, such as a “s...

Today we’re going to use PAUP* to generate trees using distance methods. We’ve discussed distance methods in class, and you have learned that they are not the most theoretically justified of methods for finding trees. However, it is important that you learn how to utilize them. First you should use them as one of the analyses in your paper. Also some people do feel that they are a good way to f...

MOTIVATION Subtree prune and regraft (SPR) is one kind of tree rearrangements that has seen applications in solving several computational biology problems. The minimum number of rooted SPR ((r)SPR) operations needed to transform one rooted binary tree to another is called the (r)SPR distance between the two trees. Computing the (r)SPR distance has been actively studied in recent years. Currentl...

Approximate distance estimation can be used to determine fundamental landscape properties including complexity and openness. We show that variations in the skyline of photos estimate distances trees on horizon. A methodology based has been developed investigate potential relationships with objects. The signal, defined by height expressed pixels, was extracted for a set 148 Land Use/Cover Area f...