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Axiomatic phylogenetics

Vladimir Turaev

TL;DR

This work uses the language of quivers to formulate a mathematical framework for phylogenetics that is compatible with prior work on EMT and phylogenetics.

Abstract

We use the language of quivers to formulate a mathematical framework for phylogenetics.

Axiomatic phylogenetics

TL;DR

This work uses the language of quivers to formulate a mathematical framework for phylogenetics that is compatible with prior work on EMT and phylogenetics.

Abstract

We use the language of quivers to formulate a mathematical framework for phylogenetics.

Paper Structure

This paper contains 45 sections, 23 theorems, 31 equations.

Table of Contents

  1. Introduction
  2. Quivers and evolutions
  3. Quivers
  4. Evolutions
  5. Isotypy
  6. Hereditary and anti-hereditary properties
  7. Examples
  8. Primitivity and the height
  9. Primitive vertices
  10. The height
  11. Examples
  12. Universal evolutions and phylogenetic vertices
  13. Universal evolutions
  14. Phylogenetic vertices
  15. Examples
  16. ...and 30 more sections

Key Result

Lemma 2.1

The relation $\leq$ is reflexive and transitive.

Theorems & Definitions (41)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Theorem 4.1
  • proof
  • ...and 31 more