Related papers: A Fast Algorithm for Computing Geodesic Distances …
A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these…
Phylogenomics is a new field which applies to tools in phylogenetics to genome data. Due to a new technology and increasing amount of data, we face new challenges to analyze them over a space of phylogenetic trees. Because a space of…
Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…
Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies…
In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point $s$ on a polyhedral surface…
We study the statistical properties of geodesics, i.e. paths of minimal length, in large random planar quadrangulations. We extend Schaeffer's well-labeled tree bijection to the case of quadrangulations with a marked geodesic, leading to…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
Temporal sequences of terrains arise in various application areas. To analyze them efficiently, one generally needs a suitable abstraction of the data as well as a method to compare and match them over time. In this paper we consider merge…
In this paper we introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity $d_{nav}$ counts the steps along a "combing" of the Nearest Neighbor Interchange (NNI)…
We study the behavior of phylogenetic tree shapes in the tropical geometric interpretation of tree space. Tree shapes are formally referred to as tree topologies; a tree topology can also be thought of as a tree combinatorial type, which is…
In graph theory, a tree is one of the more popular families of graphs with a wide range of applications in computer science as well as many other related fields. While there are several distance measures over the set of all trees, we…
Kondo et al. (DS 2014) proposed methods for computing distances between unordered rooted trees by transforming an instance of the distance computing problem into an instance of the integer programming problem. They showed that the tree edit…
It is known that for a variety of choices of metrics, including the standard bottleneck distance, the space of persistence diagrams admits geodesics. Typically these existence results produce geodesics that have the form of a convex…
Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf…
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…
We study distorted metrics on binary trees in the context of phylogenetic reconstruction. Given a binary tree $T$ on $n$ leaves with a path metric $d$, consider the pairwise distances $\{d(u,v)\}$ between leaves. It is well known that these…
An important application of distance geometry to biochemistry studies the embeddings of the vertices of a weighted graph in the three-dimensional Euclidean space such that the edge weights are equal to the Euclidean distances between…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
Distance based algorithms are a common technique in the construction of phylogenetic trees from taxonomic sequence data. The first step in the implementation of these algorithms is the calculation of a pairwise distance matrix to give a…
Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…