Related papers: Lassoing and corraling rooted phylogenetic trees
We consider extremal problems related to decks and multidecks of rooted binary trees (a.k.a. rooted phylogenetic tree shapes). Here, the deck (resp. multideck) of a tree $T$ refers to the set (resp. multiset) of leaf induced binary subtrees…
Given a distance matrix consisting of pairwise distances between species, a distance-based phylogenetic reconstruction method returns a tree metric or equidistant tree metric (ultrametric) that best fits the data. We investigate…
The inference of the evolutionary history of a collection of organisms is a problem of fundamental importance in evolutionary biology. The abundance of DNA sequence data arising from genome sequencing projects has led to significant…
Phylogenetic trees elucidate evolutionary relationships among species, but phylogenetic inference remains challenging due to the complexity of combining continuous (branch lengths) and discrete parameters (tree topology). Traditional Markov…
We prove that finding a rooted subtree with at least $k$ leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family $\cal L$ that…
Tanglegrams are formed by taking two rooted binary trees $T$ and $S$ with the same number of leaves and uniquely matching each leaf in $T$ with a leaf in $S$. They are usually represented using layouts, which embed the trees and the…
Mutations of genetic sequences are often accompanied by their recombinations, known as phylogenetic networks. These networks are typically reconstructed from coalescent processes that may arise from optimal merging or fitting together a…
Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…
We present a new way to summarize and select mixture models via the hierarchical clustering tree (dendrogram) constructed from an overfitted latent mixing measure. Our proposed method bridges agglomerative hierarchical clustering and…
We present a novel metric for generative modeling evaluation, focusing primarily on generative networks. The method uses dendrograms to represent real and fake data, allowing for the divergence between training and generated samples to be…
Computing a Single-Linkage Dendrogram (SLD) is a key step in the classic single-linkage hierarchical clustering algorithm. Given an input edge-weighted tree $T$, the SLD of $T$ is a binary dendrogram that summarizes the $n-1$ clusterings…
Given natural limitations on the length DNA sequences, designing phylogenetic reconstruction methods which are reliable under limited information is a crucial endeavor. There have been two approaches to this problem: reconstructing partial…
We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by the input alignments, instead of comparing…
How a single fertilized cell gives rise to a complex array of specialized cell types in development is a central question in biology. The cells grow, divide, and acquire differentiated characteristics through poorly understood molecular…
Topological phylogenetic trees can be assigned edge weights in several natural ways, highlighting different aspects of the tree. Here the rooted triple and quartet metrizations are introduced, and applied to formulate novel fast methods of…
The relative importance of the intrinsic and extrinsic factors determining the variety of geometric shapes exhibited by dendritic trees remains unclear. This question was addressed by developing a model of the growth of dendritic trees…
Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable…
We consider the problem of estimating the evolutionary history of a set of species (phylogeny or species tree) from several genes. It is known that the evolutionary history of individual genes (gene trees) might be topologically distinct…
Understanding how the human brain progresses from processing simple linguistic inputs to performing high-level reasoning is a fundamental challenge in neuroscience. While modern large language models (LLMs) are increasingly used to model…
Phylogenetic reconstruction aims at finding plausible hypotheses of the evolutionary history of genes or species based on genomic sequence information. The distinction of orthologous genes (genes that having a common ancestry and diverged…