{"id":112508,"date":"2018-03-11T10:39:31","date_gmt":"2018-03-11T10:39:31","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/algebraic-tools-in-phylogenomics\/"},"modified":"2018-03-11T10:39:31","modified_gmt":"2018-03-11T10:39:31","slug":"algebraic-tools-in-phylogenomics","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria-algebraica\/algebraic-tools-in-phylogenomics\/","title":{"rendered":"Algebraic tools in phylogenomics."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Anna Magdalena Kedzierska <\/strong><\/h2>\n<p>In this thesis we develop interdisciplinary algebraic tools for genomic and phylogenetic problems.  to study  the molecular evolution of species one often uses stochastic evolutionary models. The evolution is represented in a tree (called phylogenetic tree) whose leaves represent current species  and whose internal nodes correspond to their common ancestors. The length of a branch of the tree represents the number of mutations that have occurred between the two species adjacent to the branch. Then ,the evolution of dna sequences in these species is modeled with a hidden markov  process along the tree. If the markov  process  is assumed to be continuous in  time, it is usually assumed homogeneous as well and, if so, the model parameters are the instantaneous rate of mutation and the lengths of the branches. If  the markov process is discrete in time, then the model parameters are the conditional probabilities of nucleotide substitution along the tree and there is no assumption of homogeneity. The latter are the types of models we consider in this thesis and are therefore more general than the homogeneous continuous ones.  from this perspective we study the basic problems of phylogenetics: given a set of dna sequences, what is the  evolutionary model that best fits the data? How can we efficiently infer the model parameters? Also, as we also checked in this thesis, it is possible that species have not evolved along a single tree but a mixture of trees so that  we need to address these questions in this more general case. For continuous-time, homogeneous, evolutionary models, several solutions to these questions have been proposed during the last decades. In this thesis we solve these two problems for discrete-time evolutionary models, using algebraic techniques from linear algebra, group theory, algebraic geometry and algebraic statistics. In addition, our solution to the first problem is also valid for phylogenetic mixtures.  we have made tests of the methods proposed in this thesis on simulated and real data from encode project (encyclopedia of dna elements). To test our methods, we also provide algorithms to generate sequences evolving under  discrete-time models with a given expected number of mutations. Even more, we have proved that these algorithms generate all possible sequences (for most models). Tests on simulated data show that the methods are very accurate and our results on real data  confirm hypotheses previously formulated. All the methods in this thesis have been implemented for an arbitrary number of species and are publicly available.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Algebraic tools in phylogenomics.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Algebraic tools in phylogenomics. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Anna Magdalena Kedzierska <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de catalunya<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 16\/03\/2012<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Marta Casanellas Rius<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: arcadi Navarro cuartiellas <\/li>\n<li>lior Patcher (vocal)<\/li>\n<li>  (vocal)<\/li>\n<li>  (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Anna Magdalena Kedzierska In this thesis we develop interdisciplinary algebraic tools for genomic and phylogenetic problems. to 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