Related papers: Geometric comparison of phylogenetic trees with di…
In this work, we answer an open problem in the study of phylogenetic networks. Phylogenetic trees are rooted binary trees in which all edges are directed away from the root, whereas phylogenetic networks are rooted acyclic digraphs. For the…
Phylogenetics begins with reconstructing biological family trees from genetic data. Since Nature is not limited to tree-like histories, we use networks to organize our data, and have discovered new polytopes, metric spaces, and simplicial…
Tree rearrangement operations typically induce a metric on the space of phylogenetic trees. One important property of these metrics is the size of the neighbourhood, that is, the number of trees exactly one operation from a given tree. We…
Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…
Bayesian inference for phylogenetics is a gold standard for computing distributions of phylogenies. It faces the challenging problem of. moving throughout the high-dimensional space of trees. However, hyperbolic space offers a low…
We present an algorithm for classification tasks on big data. Experiments conducted as part of this study indicate that the algorithm can be as accurate as ensemble methods such as random forests or gradient boosted trees. Unlike ensemble…
The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…
Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…
Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric…
Construction of phylogenetic trees has traditionally focused on binary trees where all species appear on leaves, a problem for which numerous efficient solutions have been developed. Certain application domains though, such as viral…
Phylogenetic trees are widely used to understand the evolutionary history of organisms. Tree shapes provide information about macroevolutionary processes. However, macroevolutionary models are unreliable for inferring the true processes…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
As researchers collect increasingly large molecular data sets to reconstruct the Tree of Life, the heterogeneity of signals in the genomes of diverse organisms poses challenges for traditional phylogenetic analysis. A class of phylogenetic…
We present a novel representation of compressed data structure for simultaneous bounding volume hierarchy (BVH) traversals like they appear for instance in collision detection & proximity query. The main idea is to compress bounding volume…
In this paper, we will analyze the behavior of the Neighbor Joining algorithm on five taxa and we will show that the partition of the sample (data) space for estimation of a tree topology with five taxa into subspaces, within each of which…
We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…
We compare three basic kinds of discrete mathematical models used to portray phylogenetic relationships among species and higher taxa: phylogenetic trees, Hennig trees and Nelson cladograms. All three models are trees, as that term is…
The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms…
We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…
Phylogenetically decisive collections of taxon sets have the property that if trees are chosen for each of their elements, as long as these trees are compatible, the resulting supertree is unique. This means that as long as the trees…