Related papers: Classifying Tree Topologies along Tropical Line Se…
The number of the non-shared edges of two phylogenies is a basic measure of the dissimilarity between the phylogenies. The non-shared edges are also the building block for approximating a more sophisticated metric called the nearest…
Much evidence from biological theory and empirical data indicates that, gene tree, phylogenetic trees reconstructed from different genes (loci), do not have to have exactly the same tree topologies. Such incongruence between gene trees…
Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of non-treelike evolutionary events, like recombination, hybridization, or lateral gene transfer. In this paper, we present and study a new…
Estimating phylogenetic trees, which depict the relationships between different species, from aligned sequence data (such as DNA, RNA, or proteins) is one of the main aims of evolutionary biology. However, tree reconstruction criteria like…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
We apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the Cavender-Farris-Neyman model of evolution on trees, where all the inner…
A phylogenetic tree is an acyclic graph with distinctly labeled leaves, whose internal edges have a positive weight. Given a set of n leaves, the collection of all phylogenetic trees with this leaf set can be assembled into a metric cube…
We study tropical line arrangements associated to a three-regular graph $G$ that we refer to as \emph{tropical graph curves}. Roughly speaking, the tropical graph curve associated to $G$, whose genus is $g$, is an arrangement of $2g-2$…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
Phylogenetic networks are a special type of graph which generalize phylogenetic trees and that are used to model non-treelike evolutionary processes such as recombination and hybridization. In this paper, we consider {\em unrooted}…
We propose a novel method for the inference of phylogenetic trees that utilises point configurations on hyperbolic space as its optimisation landscape. Each taxon corresponds to a point of the point configuration, while the evolutionary…
In this paper, we investigate random walks in a family of small-world trees having an exponential degree distribution. First, we address a trapping problem, that is, a particular case of random walks with an immobile trap located at the…
Phylogenetic trees are frequently used to model evolution. Such trees are typically reconstructed from data like DNA, RNA, or protein alignments using methods based on criteria like maximum parsimony (amongst others). Maximum parsimony has…
There is a close connection between intersections of Brownian motion paths and percolation on trees. Recently, ideas from probability on trees were an important component of the multifractal analysis of Brownian occupation measure, in joint…
In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network $N$ consists of a phylogenetic…
In this paper, we lay the groundwork on the comparison of phylogenetic networks based on edge contractions and expansions as edit operations, as originally proposed by Robinson and Foulds to compare trees. We prove that these operations…
Tropical rainforests exhibit a rich repertoire of spatial patterns emerging from the intricate relationship between the microscopic interaction between species. In particular, the distribution of vegetation clusters can shed much light on…
We define tropical analogues of the notions of linear space and Plucker coordinate and study their combinatorics. We introduce tropical analogues of intersection and dualization and define a tropical linear space built by repeated…
Deep neural networks show great success when input vectors are in an Euclidean space. However, those classical neural networks show a poor performance when inputs are phylogenetic trees, which can be written as vectors in the tropical…
The tropical Grassmannian parameterizes tropicalizations of linear spaces, while the Dressian parameterizes all planes in $\TP^{n-1}$. We study these parameter spaces and we compute them explicitly for $n \leq 7$. Planes are identified with…