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Entanglement, invariants, and phylogenetics


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Sumner, JG 2006 , 'Entanglement, invariants, and phylogenetics', PhD thesis, University of Tasmania.

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This thesis develops and expands upon known techniques of mathematical
physics relevant to the analysis of the popular Markov model of phylogenetic
trees required in biology to reconstruct the evolutionary relationships of taxonomic units from biomolecular sequence data.
The techniques of mathematical physics are plethora and have been developed
for some time. The Markov model of phylogenetics and its analysis is a rela-
tively new technique where most progress to date has been achieved by using
discrete mathematics. This thesis takes a group theoretical approach to the
problem by beginning with a remarkable mathematical parallel to the process
of scattering in particle physics. This is shown to equate to branching events
in the evolutionary history of molecular units. The major technical result of
this thesis is the derivation of existence proofs and computational techniques
for calculating polynomial group invariant functions on a multi-linear space
where the group action is that relevant to a Markovian time evolution. The
practical results of this thesis are an extended analysis of the use of invariant
functions in distance based methods and the presentation of a new recon-
struction technique for quartet trees which is consistent with the most general
Markov model of sequence evolution.

Item Type: Thesis - PhD
Authors/Creators:Sumner, JG
Keywords: mathematical physics, markov model, phylogenetics, biology
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