Related papers: Maximum Likelihood Jukes-Cantor Triplets: Analytic…
We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph $G= (A \cup P, E)$ with weights on the edges in $E$, and with lower and upper quotas on the vertices in $P$. We…
A phylogenetic network is a directed acyclic graph that visualises an evolutionary history containing so-called reticulations such as recombinations, hybridisations or lateral gene transfers. Here we consider the construction of a simplest…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
Phylogenetic Diversity (PD) is a measure of the overall biodiversity of a set of present-day species (taxa) within a phylogenetic tree. In Maximize Phylogenetic Diversity (MPD) one is asked to find a set of taxa (of bounded size/cost) for…
When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a…
Several computational problems in phylogenetic reconstruction can be formulated as restrictions of the following general problem: given a formula in conjunctive normal form where the literals are rooted triples, is there a rooted binary…
Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We…
It has recently been shown that the NP-hard problem of calculating the minimum number of hybridization events that is needed to explain a set of rooted binary phylogenetic trees by means of a hybridization network is fixed-parameter…
Solving arithmetic word problems is a cornerstone task in assessing language understanding and reasoning capabilities in NLP systems. Recent works use automatic extraction and ranking of candidate solution equations providing the answer to…
Here we show that deciding whether two rooted binary phylogenetic trees on the same set of taxa permit a cherry-picking sequence, a special type of elimination order on the taxa, is NP-complete. This improves on an earlier result which…
Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in…
We present a polynomial-time algorithm that discovers all maximal patterns in a point set, $D\subset\mathbb{R}^k$, that are related by transformations in a user-specified class, $F$, of bijections over $\mathbb{R}^k$. We also present a…
The Dollo model for reconstructing evolutionary trees from binary characters has been proposed as a generalization of the infinite sites model, also known as the Perfect Phylogeny. In particular, the Dollo model is considered more realistic…
We address phylogenetic reconstruction when the data is generated from a mixture distribution. Such topics have gained considerable attention in the biological community with the clear evidence of heterogeneity of mutation rates. In our…
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…
Phylogenetic networks are a generalization of phylogenetic trees that are used in biology to represent reticulate or non-treelike evolution. Recently, several algorithms have been developed which aim to construct phylogenetic networks from…
Phylogenetic networks are a flexible model of evolution that can represent reticulate evolution and handle complex data. Tree-based networks, which are phylogenetic networks that have a spanning tree with the same root and leaf-set as the…
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many…
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
The PHASE software package allows phylogenetic tree construction with a number of evolutionary models designed specifically for use with RNA sequences that have conserved secondary structure. Evolution in the paired regions of RNAs occurs…