Related papers: Reconstructing Trees from Subtree Weights
In this work, we present a neural approach to reconstructing rooted tree graphs describing hierarchical interactions, using a novel representation we term the Lowest Common Ancestor Generations (LCAG) matrix. This compact formulation is…
We consider the problem of constructing an an optimal-weight tree from the 3*(n choose 4) weighted quartet topologies on n objects, where optimality means that the summed weight of the embedded quartet topologiesis optimal (so it can be the…
Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…
Recently it was shown that, if the subtree and chain reduction rules have been applied exhaustively to two unrooted phylogenetic trees, the reduced trees will have at most 15k-9 taxa where k is the TBR (Tree Bisection and Reconnection)…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we…
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…
A \emph{metric tree embedding} of expected \emph{stretch~$\alpha \geq 1$} maps a weighted $n$-node graph $G = (V, E, \omega)$ to a weighted tree $T = (V_T, E_T, \omega_T)$ with $V \subseteq V_T$ such that, for all $v,w \in V$,…
We derive tractable criteria for the consistency of Bayesian tree reconstruction procedures, which constitute a central class of algorithms for inferring common ancestry among DNA sequence samples in phylogenetics. Our results encompass…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
It is proved that the restriction of a $k$ and $(k-1)$-component directed spanning forest of minimal weight to an atom of the subset algebra generated by the sets of vertices of trees of $k$-component minimal spanning forests is a tree. For…
For a weighted digraph without loops $V$, the arc weights of which can be obtained from an undirected graph with loops ${\sf P}$ according to the rule $v_{ij}=p_{ij}-p_{ii}$, the properties are studied. An effective algorithm for…
We prove a new formula for the generating function of multitype Cayley trees counted according to their degree distribution. Using this formula we recover and extend several enumerative results about trees. In particular, we extend some…
We introduce the notion of metric semilattice on the metric space and prove the criterion of $\R$-tree as connected geodesic metric space $X$ admitting the partial order, such that $X$ is semilinear metric semilattice. Also we state the…
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…
We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak…
Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…
A treedepth decomposition of an undirected graph $G$ is a rooted forest $F$ on the vertex set of $G$ such that every edge $uv\in E(G)$ is in ancestor-descendant relationship in $F$. Given a weight function $w\colon V(G)\rightarrow…
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…
The evolution of aligned DNA sequence sites is generally modeled by a Markov process operating along the edges of a phylogenetic tree. It is well known that the probability distribution on the site patterns at the tips of the tree…