相关论文: Identifiability of 3-Class Jukes-Cantor Mixtures
This paper explores unsupervised learning of parsing models along two directions. First, which models are identifiable from infinite data? We use a general technique for numerically checking identifiability based on the rank of a Jacobian…
We investigated testing the likelihood of a phylogenetic tree by comparison to its subtree pruning and regrafting (SPR) neighbors, with or without re-optimizing branch lengths. This is inspired by aspects of Bayesian significance tests, and…
Identification of tree species plays a key role in forestry related tasks like forest conservation, disease diagnosis and plant production. There had been a debate regarding the part of the tree to be used for differentiation, whether it…
Diversification models describe the random growth of evolutionary trees, modeling the historical relationships of species through speciation and extinction events. One class of such models allows for independently changing traits, or types,…
Following Poupard's study of strictly ordered binary trees with respect to two parameters, namely, "end of minimal chain" and "parent of maximum leaf" a true Tree Calculus is being developed to solve a partial difference equation system and…
Phylogenetic trees represent evolutionary relationships and can be uniquely defined by sets of finite-state biological characteristics. Despite prior work showing that sufficiently large trees can be determined by $r$-state character sets,…
The invariant polytope algorithm was a breakthrough in the joint spectral radius computation, allowing to find the exact value of the joint spectral radius for most matrix families~\cite{GP2013,GP2016}. This algorithm found many…
Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site…
Quantum simulations constructing probability tensors of biological multi-taxa in phylogenetic trees are proposed, in terms of positive trace preserving maps, describing evolving systems of quantum walks with multiple walkers. Basic…
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…
Buczy\'{n}ska and Wi\'{s}niewski showed that for the Jukes Cantor binary model of a 3-valent tree the Hilbert polynomial depends only on the number of leaves of the tree and not on its shape. We ask if this can be generalized to other…
A Profile Mixture Model is a model of protein evolution, describing sequence data in which sites are assumed to follow many related substitution processes on a single evolutionary tree. The processes depend in part on different amino acid…
In this paper we apply new geometric and combinatorial methods to the study of phylogenetic mixtures. The focus of the geometric approach is to describe the geometry of phylogenetic mixture distributions for the two state random cluster…
Galled trees are studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into tree-child, galled and reticulation-visible network classes by relaxing a structural condition imposed on…
Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. They are also objects of interest in pure mathematics, such as algebraic geometry and combinatorics, due to their discrete geometry.…
In this paper we study group-based Markov models of evolution and their mixtures. In the algebreo-geometric setting, group-based phylogenetic tree models correspond to toric varieties, while their mixtures correspond to secant and join…
We investigate the use of additional 3D and phylogenetic non-3D tree balance indices for analyzing and monitoring forests using an exemplary "virtual forest" dataset from the Wytham Woods, Oxford, UK. This study assesses 3D model quality,…
In evolutionary biology, phylogenetic trees are commonly inferred from a set of characters (partitions) of a collection of biological entities (e.g., species or individuals in a population). Such characters naturally arise from molecular…
Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network…
The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic…