Now showing items 1-20 of 21

    • 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 ...
    • 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)
      External 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)
      External 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 ...
    • 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 ...
    • Relevant phylogenetic invariants of evolutionary models 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús (2010-01)
      External research report
      Open Access
      Recently there have been several attempts to provide a whole set of generators of the ideal of the algebraic variety associated to a phylogenetic tree evolving under an algebraic model. These algebraic varieties have been ...
    • Testing of the three multiplicatively closed (Lie Markov) model heirarchies which respect purine/pyrimidine, Watson-Crick, and amino/keto nucleotide groupings 

      Woodhams, Michael D.; Fernández Sánchez, Jesús; Sumner, Jeremy (2014-03)
      External research report
      Restricted access - confidentiality agreement
      We present three hierarchies of Lie Markov models of DNA sequence evolution. These models are (locally) “multiplicatively closed,” meaning that the composition of two Markov matrices in the model results, with some (rare) ...
    • The inertia of the symmetric approximation for low-rank matrices 

      Casanellas Rius, Marta; Fernández Sánchez, Jesús; Garrote López, Marina (Taylor & Francis, 2017-11-10)
      Article
      Open Access
      © 2017 Informa UK Limited, trading as Taylor & Francis Group In many areas of applied linear algebra, it is necessary to work with matrix approximations. A usual situation occurs when a matrix obtained from experimental ...