Now showing items 1-20 of 25

    • A new phylogenetic reconstruction method based on invariants 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús (2005)
      Article
      Open Access
      An attempt to use phylogenetic invariants for tree reconstruction was made at the end of the 80s and the beginning of the 90s by several authors (the initial idea due to Lake [Lake, 1987] and Cavender and Felsenstein [Cavender ...
    • An open set of 4×4 embeddable matrices whose principal logarithm is not a Markov generator 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús; Roca Lacostena, Jordi (Taylor & Francis, 2020-12-17)
      Article
      Open Access
      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, then the embeddability can be determined ...
    • Distance to the stochastic part of phylogenetic varieties 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús; Garrote López, Marina (2021-05)
      Article
      Restricted access - publisher's policy
      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 the trees and one might be able to obtain ...
    • Embeddability and rate identifiability of Kimura 2-parameter matrices 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús; Roca Lacostena, Jordi (2020-03-01)
      Article
      Open Access
      Deciding whether a substitution matrix is embeddable (i.e. the corresponding Markov process has a continuous-time realization) is an open problem even for 4×4 matrices. We study the embedding problem and rate identifiability ...
    • Embeddability of Kimura 3ST Markov matrices 

      Roca Lacostena, Jordi; Fernández Sánchez, Jesús (2018-05-14)
      Article
      Open Access
      In this note, we characterize the embeddability of generic Kimura 3ST Markov matrices in terms of their eigenvalues. As a consequence, we are able to compute the volume of such matrices relative to the volume of all Markov ...
    • EXPRESSIO GRAFICA I DISENY ASSISTIT PER ORDINADOR (Examen 1r Quadr.) 

      Fernández Sánchez, Jesús (Universitat Politècnica de Catalunya, 2004-01-14)
      Exam
      Restricted access to the UPC academic community
    • EXPRESSIO GRAFICA I DISENY ASSISTIT PER ORDINADOR (Examen 2n Quadr.) 

      Fernández Sánchez, Jesús (Universitat Politècnica de Catalunya, 2003-04-03)
      Exam
      Restricted access to the UPC academic community
    • EXPRESSIO GRAFICA I DISENY ASSISTIT PER ORDINADOR (Examen 2n Quadr.) 

      Fernández Sánchez, Jesús (Universitat Politècnica de Catalunya, 2002-06-17)
      Exam
      Restricted access to the UPC academic community
    • Invariant versus classical quartet inference when evolution is heterogeneous across sites and lineages 

      Fernández Sánchez, Jesús; Casanellas Rius, Marta (2016)
      Article
      Open Access
      One reason why classical phylogenetic reconstruction methods fail to correctly infer the underlying topology is because they assume oversimplified models. In this article, we propose a quartet reconstruction method consistent ...
    • Invariants, una aproximació a la filogenètica des de l'àlgebra 

      Fernández Sánchez, Jesús (2010)
      Article
      Open Access
      En els darrers anys, una nova aproximació a la reconstrucció filogenètica basada en tècniques provinents de l’àlgebra s’ha estat consolidant. Fixat un model evolutiu per a un conjunt donat d’espècies, els invariants són ...
    • Lie Markov model 

      Sumner, Jeremy; Fernández Sánchez, Jesús; Jarvis, Peter (2012)
      Article
      Open Access
      Recent work has discussed the importance of multiplicative closure for the Markov mod- els used in phylogenetics. For continuous-time Markov chains, a sufficient condition for multiplicative closure of a model class is ...
    • Lie Markov models 

      Sumner, Jeremy; Fernández Sánchez, Jesús; Jarvis, Peter (2012-04-07)
      Article
      Restricted access - publisher's policy
      Recent work has discussed the importance of multiplicative closure for the Markov models used in phylogenetics. For continuous-time Markov chains, a sufficient condition for multiplicative closure of a model class is ensured ...
    • Lie Markov models with purine/pyrimidine symmetry 

      Fernández Sánchez, Jesús; Sumner, Jeremy; Jarvis, Peter; Woodhams, Michael D. (2015-03-01)
      Article
      Open Access
      Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, ...
    • Lie Markov models with purine/pyrimidine symmetry 

      Fernández Sánchez, Jesús; Sumner, Jeremy; Jarvis, Peter; Woodhams, Michael D. (2013-06)
      Research report
      Open Access
      Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, ...
    • Local description of phylogenetic group-based models 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz (2013-12)
      Research report
      Open Access
      Motivated by phylogenetics, our aim is to obtain a system of equations that de ne a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties de ...
    • Local equations for equivariant evolutionary models 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz (2017-07-31)
      Article
      Open Access
      Phylogenetic varieties related to equivariant substitution models have been studied largely in the last years. One of the main objectives has been finding a set of generators of the ideal of these varieties, but this has ...
    • Low degree equations for phylogenetic group-based models 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz (2015)
      Article
      Open Access
      Motivated by phylogenetics, our aim is to obtain a system of low degree equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic ...
    • Phylogenetic reconstruction using algebraic geometry 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús (2010-12-31)
      Article
      Restricted access - publisher's policy
      A new approach to phylogenetic reconstruction has been emerging in the last years. Given an evolutionary model, the joint probability distribution of the nucleotides for these species satisfy some algebraic constraints ...
    • Rank conditions on phylogenetic networks 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús (Birkhäuser, 2021)
      Part of book or chapter of book
      Restricted access - publisher's policy
      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 from phylogenetic trees to phylogenetic ...
    • Reconstrucción filogenética usando Geometría Algebraica 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús (2010)
      Article
      Open Access
      Una nueva aproximación a la reconstrucción filogenética basada en la geometría algebraica está ganando fuerza en los últimos años. Fijado un modelo evolutivo para un conjunto de especies, las distribuciones teóricas de ...