Related papers: Root location in random trees: A polarity property…

We study the influence of the seed graph in the preferential attachment model, focusing on the case of trees. We first show that the seed has no effect from a weak local limit point of view. On the other hand, we conjecture that different…

We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…

Deciding whether there is a single tree -a supertree- that summarizes the evolutionary information in a collection of unrooted trees is a fundamental problem in phylogenetics. We consider two versions of this question: agreement and…

Consider a genetic locus carrying a strongly beneficial allele which has recently fixed in a large population. As strongly beneficial alleles fix quickly, sequence diversity at partially linked neutral loci is reduced. This phenomenon is…

A rooted phylogenetic network is a directed acyclic graph with a single root, whose sinks correspond to a set of species. As such networks are useful for representing the evolution of species that have undergone reticulate evolution, there…

We investigate the behaviour of five classical centrality measures--Jordan, rumor, betweenness, degree, and closeness centralities--in the setting of uniform random recursive trees. Motivated by applications in network archaeology, we focus…

A tree-based network $N$ on $X$ is called universal if every phylogenetic tree on $X$ is a base tree for $N$. Recently, binary universal tree-based networks have attracted great attention in the literature and their existence has been…

There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of pairwise distances between leaves. Such…

The path-difference metric is one of the oldest and most popular distances for the comparison of phylogenetic trees, but its statistical properties are still quite unknown. In this paper we compute the expected value under the Yule model of…

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…

The reconstruction of large phylogenetic trees from data that violates clocklike evolution (or as a supertree constructed from any m input trees) raises a difficult question for biologists - how can one assign relative dates to the vertices…

Rooted phylogenetic networks are used by biologists to infer and represent complex evolutionary relationships between species that cannot be accurately explained by a phylogenetic tree. Tree-child networks are a particular class of rooted…

Random forests are a very effective and commonly used statistical method, but their full theoretical analysis is still an open problem. As a first step, simplified models such as purely random forests have been introduced, in order to shed…

The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…

We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…

A normal network is uniquely determined by the set of phylogenetic trees that it displays. Given a set $\mathcal{P}$ of rooted binary phylogenetic trees, this paper presents a polynomial-time algorithm that reconstructs the unique binary…

This paper considers the problem of invoking auxiliary, unobservable variables to facilitate the structuring of causal tree models for a given set of continuous variables. Paralleling the treatment of bi-valued variables in [Pearl 1986], we…

When using machine learning for imbalanced binary classification problems, it is common to subsample the majority class to create a (more) balanced training dataset. This biases the model's predictions because the model learns from data…

We study the detection error probability associated with a balanced binary relay tree, where the leaves of the tree correspond to $N$ identical and independent detectors. The root of the tree represents a fusion center that makes the…

We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…