相关论文: A height-based metaconcept for rooted tree balance…

Measures of tree balance play an important role in many different research areas such as mathematical phylogenetics or theoretical computer science. Typically, tree balance is quantified by a single number which is assigned to the tree by a…

Although the analysis of rooted tree shape has wide-ranging applications, notions of tree balance have developed independently in different domains. In computer science, a balanced tree is one that enables efficient updating and retrieval…

Tree balance plays an important role in phylogenetics and other research areas, which is why several indices to measure tree balance have been introduced over the years. Nevertheless, a formal definition of what a balance index actually is…

Tree balance plays an important role in various research areas in phylogenetics and computer science. Typically, it is measured with the help of a balance index or imbalance index. There are more than 25 such indices available, recently…

Measures of tree balance play an important role in different research areas such as mathematical phylogenetics or theoretical computer science. The balance of a tree is usually quantified in a single number, called a balance or imbalance…

Tree shape statistics, particularly measures of tree (im)balance, play an important role in the analysis of the shape of phylogenetic trees. With applications ranging from testing evolutionary models to studying the impact of fertility…

We investigate the use of additional 3D and phylogenetic non-3D tree balance indices for analyzing and monitoring forests using an exemplary "virtual forest" dataset from the Wytham Woods, Oxford, UK. This study assesses 3D model quality,…

Binary rooted trees, both in the ordered and in the un-ordered case, are well studied structures in the field of combinatorics. The aim of this work is to study particular patterns in these classes of trees. We consider completely…

We define a new balance index for rooted phylogenetic trees based on the symmetry of the evolutive history of every set of 4 leaves. This index makes sense for multifurcating trees and it can be computed in time linear in the number of…

(Im)balance indices can be used to quantify the (im)balance of trees by assigning numerical scores to them. An easy way to generate a new index is to construct a compound index, e.g., a linear combination of established indices. Two of the…

Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…

Most real-world classification problems deal with imbalanced datasets, posing a challenge for Artificial Intelligence (AI), i.e., machine learning algorithms, because the minority class, which is of extreme interest, often proves difficult…

The Colless index is one of the most popular and natural balance indices for bifurcating phylogenetic trees, but it makes no sense for multifurcating trees. In this paper we propose a family of Colless-like balance indices…

In a rooted tree, we call a vertex {\em balanced} if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a…

Effects like selection in evolution as well as fertility inheritance in the development of populations can lead to a higher degree of asymmetry in evolutionary trees than expected under a null hypothesis. To identify and quantify such…

Imbalance in the 3D structure of plants can be an important indicator of insufficient light or nutrient supply, as well as excessive wind, (formerly present) physical barriers, neighbor or storm damage. It can also be a simple means to…

Tree balance plays an important role in different research areas like theoretical computer science and mathematical phylogenetics. For example, it has long been known that under the Yule model, a pure birth process, imbalanced trees are…

Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…

We solve a class of optimization problems for (phylogenetic) $X$-trees or their shapes. These problems have recently appeared in different contexts, e.g. in the context of the impact of tree shapes on the size of TBR neighborhoods, but so…

In recent years, there has been an effort to extend the classical notion of phylogenetic balance, originally defined in the context of trees, to networks. One of the most natural ways to do this is with the so-called $B_2$ index. In this…