9 citations · 11 across the 6 of their papers we have counts for
8 papers
Phylogenetic invariants: straightforward from the general Markov to equivariant models
Marta Casanellas, Jesús Fernández-Sánchez
In the last decade, some algebraic tools have been successfully applied to phylogenetic reconstruction. These tools are mainly based on the knowledge of equations describing algebr…
Designing weights for quartet-based methods when data is heterogeneous across lineages
Marta Casanellas, Jesús Fernández-Sánchez, Marina Garrote-López +1
Homogeneity across lineages is a common assumption in phylogenetics according to which nucleotide substitution rates remain constant in time and do not depend on lineages. This is…
SAQ: semi-algebraic quartet reconstruction method
Marta Casanellas, Jesús Fernández-Sánchez, Marina Garrote-López
We present the phylogenetic quartet reconstruction method SAQ (Semi-algebraic quartet reconstruction). SAQ is consistent with the most general Markov model of nucleotide substituti…
An open set of embeddable matrices whose principal logarithm is not a Markov generator
Marta Casanellas, Jesús Fernández-Sánchez, Jordi Roca-Lacostena
A Markov matrix is embeddable if it can represent a homogeneous continuous-time Markov process. It is well known that if a Markov matrix has real and pairwise-different eigenvalues…
The embedding problem for Markov matrices
Marta Casanellas, Jesús Fernández-Sánchez, Jordi Roca-Lacostena
Characterizing whether a Markov process of discrete random variables has an homogeneous continuous-time realization is a hard problem. In practice, this problem reduces to deciding…
Rank conditions on phylogenetic networks
Marta Casanellas, Jesús Fernández-Sánchez
Less rigid than phylogenetic trees, phylogenetic networks allow the description of a wider range of evolutionary events. In this note, we explain how to extend the rank invariants…
Distance to the stochastic part of phylogenetic varieties
Marta Casanellas, Jesús Fernández-Sánchez, Marina Garrote-López
Modelling the substitution of nucleotides along a phylogenetic tree is usually done by a hidden Markov process. This allows to define a distribution of characters at the leaves of…
Local description of phylogenetic group-based models
Marta Casanellas, Jesús Fernández-Sánchez, Mateusz Michałek
Motivated by phylogenetics, our aim is to obtain a system of equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this pape…