Related papers: Nodal distances for rooted phylogenetic trees
We consider distance labeling schemes for trees: given a tree with $n$ nodes, label the nodes with binary strings such that, given the labels of any two nodes, one can determine, by looking only at the labels, the distance in the tree…
In this thesis the properties of two kinds of non-uniform random recursive trees are studied. In the first model weights are assigned to each node, thus altering the attachment probabilities. We will call these trees weighted recursive…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…
The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…
Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the…
There is a unique path from the root of a tree to any other vertex. Every vertex, except the root, has a parent: the adjoining vertex on this unique path. This is the conventional definition of the parent vertex. For complete binary trees,…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
When estimating a phylogeny from a multiple sequence alignment, researchers often assume the absence of recombination. However, if recombination is present, then tree estimation and all downstream analyses will be impacted, because…
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…
We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…
In this paper, we address the question of comparison between populations of trees. We study an statistical test based on the distance between empirical mean trees, as an analog of the two sample z statistic for comparing two means. Despite…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
Neutral macroevolutionary models, such as the Yule model, give rise to a probability distribution on the set of discrete rooted binary trees over a given leaf set. Such models can provide a signal as to the approximate location of the root…
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees ("Otter trees"), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size $n$ is proved to…
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a…
We define a multi-scale metric $d_\rho$ on strings by aggregating angle distances between all $n$-gram count vectors with exponential weights $\rho^n$. We benchmark $d_\rho$ in DBSCAN clustering against edit and $n$-gram baselines, give a…
In 1989 Erd\H{o}s and Sz\'ekely showed that there is a bijection between (i) the set of rooted trees with $n+1$ vertices whose leaves are bijectively labeled with the elements of $[\ell]=\{1,2,\dots,\ell\}$ for some $\ell \leq n$, and (ii)…
It is known from the algebraic graph theory that if $L$ is the Laplacian matrix of some tree $G$ with a vertex degree sequence $\mathbf{d}=(d_1, ..., d_n)^\top$ and $D$ is its distance matrix, then…
Ancestral mixture model, proposed by Chen and Lindsay (2006), is an important model to build a hierarchical tree from high dimensional binary sequences. Mixture trees created from ancestral mixture models involve in the inferred…
Agreement forests continue to play a central role in the comparison of phylogenetic trees since their introduction more than 25 years ago. More specifically, they are used to characterise several distances that are based on tree…