 Research group
 EGSA  Differential Equations, Geometry, Control and Dynamical Systems, and Applications
 Department
 Department of Applied Mathematics I
 School
 Barcelona School of Industrial Engineering (ETSEIB)
 jesus.fernandez.sanchezupc.edu
 Contact details
 UPC directory
Scientific and technological production


Testing of the three multiplicatively closed (Lie Markov) model heirarchies which respect purine/pyrimidine, WatsonCrick, and amino/keto nucleotide groupings
Woodhams, Michael D.; Fernández Sánchez, Jesús; Sumner, Jeremy
Date: 201403
Report
Read the abstract Access to the full text Share Reference managersWe 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) exceptions, in a third Markov matrix that is still in the model. Additionally, the models in each hierarchy respectively distinguish between (i) purines and pyrimadines (RY), (ii) WatsonCrick pairs (WS), and (iii) amino/keto pairs (MK), but otherwise treat the four nucleotides without distinction. The multiplicative closure property allows mathematically consistent modeling of timeinhomogeneous scenarios, unlike models that are not closed, such as the general timereversible model (GTR) and many of its submodels. We derive the nesting relationships of the three model hierarchies and present software implementing the models. For a diverse range of biological data sets, we perform Bayesian information criterion model comparision analogous to that of the ModelTest framework. We find that our models outperform the GTR model in some (but not all) cases.
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) exceptions, in a third Markov matrix that is still in the model. Additionally, the models in each hierarchy respectively distinguish between (i) purines and pyrimadines (RY), (ii) WatsonCrick pairs (WS), and (iii) amino/keto pairs (MK), but otherwise treat the four nucleotides without distinction. The multiplicative closure property allows mathematically consistent modeling of timeinhomogeneous scenarios, unlike models that are not closed, such as the general timereversible model (GTR) and many of its submodels. We derive the nesting relationships of the three model hierarchies and present software implementing the models. For a diverse range of biological data sets, we perform Bayesian information criterion model comparision analogous to that of the ModelTest framework. We find that our models outperform the GTR model in some (but not all) cases. 
GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONES
Alberich Carramiñana, Maria; Amoros Torrent, Jaume; Barja Yañez, Miguel Angel; Elgueta Montó, Josep; Fernández Sánchez, Jesús; Ventura González Alonso, Daniel; Barbieri Solha, Romero; Miranda Galceran, Eva; Pascual Gainza, Pedro; Roig Marti, Agustin; Roig Maranges, Abdo; Feliu Trijueque, Elsienda; Gálvez Carrillo, Maria Immaculada; Casanellas Rius, Marta
Participation in a competitive project
Share 
Lie Markov models with purine/pyrimidine symmetry
Fernández Sánchez, Jesús; Sumner, Jeremy; Jarvis, Peter; Woodhams, Michael D.
Date: 201306
Report
Read the abstract Access to the full text Share Reference managersContinuoustime Markov chains are a standard tool in phylogenetic inference. If homo geneity is assumed, the chain is formulated by specifying timeindependent rates of substitu tions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to gen eralise it and allow for an inhomogeneous process, with timedependent rates satisfying the same constraints. It is then useful to require that there exists a homogeneous average of this inhomogeneous process within the same model. This leads to the denition of \Lie Markov models", which are precisely the class of models where such an average exists. These models form Lie algebras and hence concepts from Lie group theory are central to their derivation. In this paper, we concentrate on applications to phylogenetics and nucleotide evolution, and derive the complete hierarchy of Lie Markov models that respect the grouping of nucleotides into purines and pyrimidines { that is, models with purine/pyrimidine symmetry. We also discuss how to handle the subtleties of applying Lie group methods, most naturally dened over the complex eld, to the stochastic case of a Markov process, where parameter values are restricted to be real and positive. In particular, we explore the geometric embedding of the cone of stochastic rate matrices within the ambient space of the associated complex Lie algebra.
Continuoustime Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying timeindependent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to generalise it and allow for an inhomogeneous process, with timedependent rates satisfying the same constraints. It is then useful to require that there exists a homogeneous average of this inhomogeneous process within the same model. This leads to the definition of "Lie Markov models", which are precisely the class of models where such an average exists. These models form Lie algebras and hence concepts from Lie group theory are central to their derivation. In this paper, we concentrate on applications to phylogenetics and nucleotide evolution, and derive the complete hierarchy of Lie Markov models that respect the grouping of nucleotides into purines and pyrimidines  that is, models with purine/pyrimidine symmetry. We also discuss how to handle the subtleties of applying Lie group methods, most naturally defined over the complex field, to the stochastic case of a Markov process, where parameter values are restricted to be real and positive. In particular, we explore the geometric embedding of the cone of stochastic rate matrices within the ambient space of the associated complex Lie algebra. 
Local description of phylogenetic groupbased models
Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz
Date: 201312
Report
Read the abstract Access to the full text Share Reference managersMotivated by phylogenetics, our aim is to obtain a system of equations that dene a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties dened via groupbased models. For any nite abelian group G, we provide an explicit construction of codimX phylogenetic invariants (polynomial equations) of degree at most jGj that dene the variety X on a Zariski open set U. The set U contains all biologically meaningful points when G is the group of the Kimura 3parameter model. In particular, our main result conrms [Mic12, Conjecture 7.9] and, on the set U, Conjectures 29 and 30 of [SS05].
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 ned via groupbased models. For any nite abelian group G, we provide an explicit construction of codimX phylogenetic invariants (polynomial equations) of degree at most jGj that de ne the variety X on a Zariski open set U. The set U contains all biologically meaningful points when G is the group of the Kimura 3parameter model. In particular, our main result con rms [Mic12, Conjecture 7.9] and, on the set U, Conjectures 29 and 30 of [SS05]. 
Modelos de Lie Markov con simetría fijada
Fernández Sánchez, Jesús
Congreso de Jóvenes Investigadores Real Sociedad Matemática Española
Presentation's date: 20130916
Presentation of work at congresses
Share Reference managers 
Lie Markov models with prescribed symmetry
Fernández Sánchez, Jesús
Applied Algebraic Geometry
Presentation's date: 20130803
Presentation of work at congresses
Share Reference managers 
The space of phylogenetic mixtures for equivariant models
Casanellas Rius, Marta; Fernández Sánchez, Jesús; Kedzierska, A.M.
Algorithms for Molecular Biology
Date of publication: 20121128
Journal article
Read the abstract Access to the full text Share Reference managersThe selection of the most suitable evolutionary model to analyze the given molecular data is usually left to biologist's choice. In his famous book, J Felsenstein suggested that certain linear equations satisfied by the expected probabilities of patterns observed at the leaves of a phylogenetic tree could be used for model selection. It remained open the question regarding whether these equations were enough for characterizing the evolutionary model. Here we prove that, for equivariant models of evolution, the space of distributions satisfying these linear equations coincides with the space of distributions arising from mixtures of trees on a set of taxa. In other words, we prove that an alignment is produced from a mixture of phylogenetic trees under an equivariant evolutionary model if and only if its distribution of column patterns satisfies the linear equations mentioned above. Moreover, for each equivariant model and for any number of taxa, we provide a set of linearly independent equations defining this space of phylogenetic mixtures. This is a powerful tool that has already been successfully used in model selection. We also use the results obtained to study identifiability issues for phylogenetic mixtures. 
Is the general timereversible model bad for molecular phylogenetics?
Sumner, Jeremy; Jarvis, Peter; Fernández Sánchez, Jesús; Kaine, Bodie; Woodhams, Michael; Holland, Barbara
Systematic biology
Date of publication: 20120322
Journal article
View Share Reference managers 
Lie Markov models
Sumner, Jeremy; Fernández Sánchez, Jesús; Jarvis, Peter
Journal of theoretical biology
Date of publication: 20120407
Journal article
Read the abstract View Share Reference managersRecent work has discussed the importance of multiplicative closure for the Markov models used in phylogenetics. For continuoustime Markov chains, a sufficient condition for multiplicative closure of a model class is ensured by demanding that the set of ratematrices belonging to the model class form a Lie algebra. It is the case that some wellknown Markov models do form Lie algebras and we refer to such models as “Lie Markov models”. However it is also the case that some other wellknown Markov models unequivocally do not form Lie algebras (GTR being the most conspicuous example). In this paper, we will discuss how to generate Lie Markov models by demanding that the models have certain symmetries under nucleotide permutations. We show that the Lie Markov models include, and hence provide a unifying concept for, “groupbased” and “equivariant” models. For each of two and four character states, the full list of Lie Markov models with maximal symmetry is presented and shown to include interesting examples that are neither groupbased nor equivariant. We also argue that our scheme is pleasing in the context of applied phylogenetics, as, for a given symmetry of nucleotide substitution, it provides a natural hierarchy of models with increasing number of parameters. We also note that our methods are applicable to any application of continuoustime Markov chains beyond the initial motivations we take from phylogenetics. 
Lie Markov models
Fernández Sánchez, Jesús
Algebraic Statistics
Presentation's date: 20120612
Presentation of work at congresses
Share Reference managers 
Phylogenetic mixtures for equivariant models
Fernández Sánchez, Jesús
Algebraic Statistics
Presentation's date: 20120612
Presentation of work at congresses
Share Reference managers 
An approach to phylogenetic inference by means of group representation theory
Fernández Sánchez, Jesús
Congreso de Jóvenes Investigadores Real Sociedad Matemática Española
Presentation's date: 20110906
Presentation of work at congresses
Share Reference managers 
On adjacent complete ideals above a given complete ideal
Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Proceedings of the Royal Society of Edinburgh. Section A, mathematics
Date of publication: 2010
Journal article
View Share Reference managers 
Relevant phylogenetic invariants of evolutionary models
Casanellas Rius, Marta; Fernández Sánchez, Jesús
Journal de mathématiques pures et appliquées
Date of publication: 20101119
Journal article
View Share Reference managers 
Phylogenetic reconstruction using algebraic geometry
Casanellas Rius, Marta; Fernández Sánchez, Jesús
Arbor (Madrid)
Date of publication: 20101231
Journal article
Read the abstract View Share Reference managersA 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 called invariants. These invariants have theoretical and practical interest, since they can be used to infer phylogenies. In this paper, we explain how to use these invariants to design algorithms for phylogenetic reconstruction and we show how the application of tools and theoretical results coming from commutative algebra and algebraic geometry can improve the performance and the efficiency of these algorithms. 
Invariants, una aproximació a la filogenètica des de l'àlgebra
Fernández Sánchez, Jesús
Butlletí de la Societat Catalana de Matemàtiques
Date of publication: 2010
Journal article
Read the abstract Access to the full text Share Reference managersEn 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 relacions algebraiques satisfetes per les distribucions teòriques de nucleòtids d’aquestes espècies. En aquest article s’exposa com es poden fer servir els invariants per implementar algoritmes de reconstrucció filogenètica i s’explica com l’eficiència d’aquests algoritmes es veu beneficiada per resultats teòrics provinents de la geometria algebraica i la representació de grups. 
Principality of curves on sandwiched singularities
Fernández Sánchez, Jesús
Mathematical research letters
Date of publication: 2010
Journal article
Share Reference managers 
GEOMETRÍA DE VARIEDADES ALGEBRAICAS Y APLICACIONES
Amoros Torrent, Jaume; Barja Yañez, Miguel Angel; Alberich Carramiñana, Maria; Elgueta Montó, Josep; Fernández Sánchez, Jesús; Gonzalez Alonso, Victor; Berna Sepulveda, Isabel Silvana; Ferragut Amengual, Antoni Manel; Casanellas Rius, Marta
Participation in a competitive project
Share 
Relevant phylogenetic invariants of evolutionary models
Casanellas Rius, Marta; Fernández Sánchez, Jesús
Date: 201001
Report
Read the abstract Access to the full text Share Reference managersRecently 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 proven to be useful in phylogenetics. In this paper we prove that, for phylogenetic reconstruction purposes, it is enough to consider generators coming from the edges of the tree, the socalled edge invariants. This is the algebraic analogous to Buneman's Splits Equivalence Theorem. The interest of this result relies on its potential applications in phylogenetics for the widely used evolutionary models such as JukesCantor, Kimura 2 and 3 parameters, and General Markov models. 
On the exceptional locus of the birational projections of a normal surface singularity into a plane
Fernández Sánchez, Jesús
Journal of algebra
Date of publication: 200901
Journal article
Share Reference managers 
GEOMETRIA DE VARIETATS I APLICACIONS
Casanellas Rius, Marta; Berna Sepulveda, Isabel Silvana; Barja Yañez, Miguel Angel; Gonzalez Alonso, Victor; Amoros Torrent, Jaume; Elgueta Montó, Josep; Abío Roig, Ignasi; Plans Berenguer, Bernat; Alvarez Montaner, Josep; Fernández Sánchez, Jesús; Alberich Carramiñana, Maria
Participation in a competitive project
Share 
Clases de equisingularidad de proyecciones birracionales de singularidades normales de superficie en el plano
Fernández Sánchez, Jesús
Date of publication: 200801
Book chapter
Share Reference managers 
Classication of the birational projections of a sandwiched surface singularity to a plane
Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Date: 200809
Report
View Share Reference managers 
Classification of the birational projections of a sandwiched surface singularity to a plane
Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Seminar on Singularities: algebraic methods
Presentation of work at congresses
Share Reference managers 
Performance of a new invariants method for phylogenetic reconstruction
Fernández Sánchez, Jesús
Society for Molecular Biology and Evolution. Meeting
Presentation's date: 20080101
Presentation of work at congresses
Share Reference managers 
Geometry of the Kimura 3parameter model
Casanellas Rius, Marta; Fernández Sánchez, Jesús
Advances in applied mathematics
Date of publication: 200803
Journal article
View Share Reference managers 
Factorization of adjacent complete ideals in dimension 2
Fernández Sánchez, Jesús
Proceedings of the Royal Society of Edinburgh. Section A, mathematics
Date of publication: 200710
Journal article
Share Reference managers 
Geometry of the Kimura 3parameter model
Casanellas Rius, Marta; Fernández Sánchez, Jesús
Future Directions in Phylogenetic Methods and Models
Presentation of work at congresses
Share Reference managers 
Equisingularity classes of birational projections of normal singularities to a plane
Fernández Sánchez, Jesús
I Congreso HispanoFrancés de Matemàticas
Presentation's date: 20070709
Presentation of work at congresses
Share Reference managers 
Equisingularity classes of birational projections of normal singularities to a plane
Fernández Sánchez, Jesús
Approaching Mathematics through Algebra
Presentation of work at congresses
Share Reference managers 
Performance of a new invariants method for phylogenetic reconstruction
Fernández Sánchez, Jesús
Future Directions in Phylogenetic Methods and Models
Presentation of work at congresses
Share Reference managers 
Equisingularity classes of birational projections of normal singularities to a plane
Fernández Sánchez, Jesús; Alberich Carramiñana, Maria
I Congreso HispanoFrancés de Matemàticas
Presentation of work at congresses
Share Reference managers 
Clases de equisingularidad de proyecciones birracionales de singularidades normales de superficie
Fernández Sánchez, Jesús
Approaching Mathematics through Algebra
Presentation's date: 20070625
Presentation of work at congresses
Share Reference managers 
Performance of a new invariants method on homogeneous and nonhomogeneous quartet trees
Casanellas Rius, Marta; Fernández Sánchez, Jesús
Molecular biology and evolution
Date of publication: 200701
Journal article
View Share Reference managers 
Factorization of complete ideals in normal birational extensions in dimension two
Fernández Sánchez, Jesús
Journal of algebra
Date of publication: 200703
Journal article
View Share Reference managers 
Equisingularity classes of birational projections of normal singularities to a plane
Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Advances in mathematics
Date of publication: 200712
Journal article
Share Reference managers 
Some results relating to adjacent ideals in dimension two
Fernández Sánchez, Jesús
Journal of pure and applied algebra
Date of publication: 200608
Journal article
View Share Reference managers 
Geometría y Topología de Variedades Algebraicas y Simplécticas
Casanellas Rius, Marta; Barja Yañez, Miguel Angel; Fernández Sánchez, Jesús
Participation in a competitive project
Share 
Singularidades de morfismos y variedades II
Alberich Carramiñana, Maria; Casas ., E.; Fernández Sánchez, Jesús
Participation in a competitive project
Share 
Ingenio Mathematica (iMATH)
Zuazua ., Enrique; Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Participation in a competitive project
Share 
Factoritación de ideales completos y singularidades sandwiched
Fernández Sánchez, Jesús
Congreso Conjunto de Matemáticas RSMESCMSEIOSEMA
Presentation's date: 20050202
Presentation of work at congresses
Share Reference managers 
RTACA  Red Temática de Álgebra Conmutativa y Aplicaciones
Elias ., Joan; Casanellas Rius, Marta; Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Participation in a competitive project
Share 
Equivalence of the Nash conjecture for primitive and sandwiched singularities
Fernández Sánchez, Jesús
Proceedings of the American Mathematical Society
Date of publication: 200503
Journal article
Share Reference managers 
Nash families of smooth arcs on a sandwiched singularity
Fernández Sánchez, Jesús
Mathematical proceedings of the Cambridge Philosophical Society
Date of publication: 200501
Journal article
Share Reference managers 
Geometría y topología de las variedades algebraicas
Barja Yañez, Miguel Angel; Roig Marti, Agustin; Pascual Gainza, Pedro; Elgueta Montó, Josep; Abío Roig, Ignasi; Amoros Torrent, Jaume; Casanellas Rius, Marta; Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Participation in a competitive project
Share 
On sandwiched singularities and complete ideals
Fernández Sánchez, Jesús
Journal of pure and applied algebra
Date of publication: 200312
Journal article
Share Reference managers 
Singularidades de morfismos y variedades
Casas ., E.; Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Participation in a competitive project
Share 
Geometria Algebraica.
Casanellas Rius, Marta; Casas ., E.; Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Participation in a competitive project
Share 
On polar germs of planet curves and related in variants
Fernández Sánchez, Jesús
Géométrie algébrique en Liberté VIII
Presentation's date: 20000328
Presentation of work at congresses
Share Reference managers 
EAGEREuropean Algebraic Geometry Research training network
Amoros Torrent, Jaume; Conte ., Alberto; Casanellas Rius, Marta; Alberich Carramiñana, Maria; Fernández Sánchez, Jesús
Participation in a competitive project
Share
Reference managers
Continue