相关论文: Distorted metrics on trees and phylogenetic forest…

This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…

We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…

Rooted phylogenetic networks are often constructed by combining trees, clusters, triplets or characters into a single network that in some well-defined sense simultaneously represents them all. We review these four models and investigate…

Evolutionary histories for species that cross with one another or exchange genetic material can be represented by leaf-labelled, directed graphs called phylogenetic networks. A major challenge in the burgeoning area of phylogenetic networks…

Let $n>1$ be an integer, and let $T$ be a tree with $n+1$ vertices $v_1,\ldots,v_{n+1}$, where $v_1$ and $v_{n+1}$ are two leaves of $T$. For each edge $e$ of $T$, assign a complex number $w(e)$ as its weight. We obtain that…

How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…

Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…

Phylogenetic tree reconstruction is traditionally based on multiple sequence alignments (MSAs) and heavily depends on the validity of this information bottleneck. With increasing sequence divergence, the quality of MSAs decays quickly.…

A fringe subtree of a rooted tree is a subtree induced by one of the vertices and all its descendants. We consider the problem of estimating the number of distinct fringe subtrees in two types of random trees: simply generated trees and…

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…

Given a set of species whose evolution is represented by a species tree, a gene family is a group of genes having evolved from a single ancestral gene. A gene family evolves along the branches of a species tree through various mechanisms,…

Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…

A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treats…

In this article we study the treewidth of the \emph{display graph}, an auxiliary graph structure obtained from the fusion of phylogenetic (i.e., evolutionary) trees at their leaves. Earlier work has shown that the treewidth of the display…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

In distance query reconstruction, we wish to reconstruct the edge set of a hidden graph by asking as few distance queries as possible to an oracle. Given two vertices $u$ and $v$, the oracle returns the shortest path distance between $u$…

Recent years have witnessed a surge of biological interest in the minimum spanning tree (MST) problem for its relevance to automatic model construction using the distances between data points. Despite the increasing use of MST algorithms…

We prove that there is a randomized polynomial-time algorithm that given an edge-weighted graph $G$ excluding a fixed-minor $Q$ on $n$ vertices and an accuracy parameter $\varepsilon>0$, constructs an edge-weighted graph~$H$ and an…

Motivation: The construction of statistics for summarizing posterior samples returned by a Bayesian phylogenetic study has so far been hindered by the poor geometric insights available into the space of phylogenetic trees, and ad hoc…

The modular decomposition of a symmetric map $\delta\colon X\times X \to \Upsilon$ (or, equivalently, a set of symmetric binary relations, a 2-structure, or an edge-colored undirected graph) is a natural construction to capture key features…