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<meta content="Sumner, Jeremy G." name="eprints.creators_name" />
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<meta content="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." name="eprints.abstract" />
<meta content="2006-12" name="eprints.date" />
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phylogenetics
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<meta content="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." name="DC.description" />
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<h1 class="ep_tm_pagetitle">Entanglement, invariants, and phylogenetics</h1>
<p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Sumner, Jeremy G.</span> (2006) <xhtml:em>Entanglement, invariants, and phylogenetics.</xhtml:em> PhD thesis, University of Tasmania.</p><p style="margin-bottom: 1em" class="not_ep_block"></p><table style="margin-bottom: 1em" class="not_ep_block"><tr><td valign="top" style="text-align:center"><a onmouseover="EPJS_ShowPreview( event, 'doc_preview_721' );" href="http://eprints.utas.edu.au/709/1/01front.pdf" onmouseout="EPJS_HidePreview( event, 'doc_preview_721' );"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" class="ep_doc_icon" border="0" /></a><div class="ep_preview" id="doc_preview_721"><table><tr><td><img alt="" src="http://eprints.utas.edu.au/709/thumbnails/1/preview.png" class="ep_preview_image" border="0" /><div class="ep_preview_title">Preview</div></td></tr></table></div></td><td valign="top"><a href="http://eprints.utas.edu.au/709/1/01front.pdf"><span class="ep_document_citation">PDF (01: Front Matter)</span></a> - Requires a PDF viewer<br />89Kb</td></tr><tr><td valign="top" style="text-align:center"><a onmouseover="EPJS_ShowPreview( event, 'doc_preview_722' );" href="http://eprints.utas.edu.au/709/2/02whole.pdf" onmouseout="EPJS_HidePreview( event, 'doc_preview_722' );"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" class="ep_doc_icon" border="0" /></a><div class="ep_preview" id="doc_preview_722"><table><tr><td><img alt="" src="http://eprints.utas.edu.au/709/thumbnails/2/preview.png" class="ep_preview_image" border="0" /><div class="ep_preview_title">Preview</div></td></tr></table></div></td><td valign="top"><a href="http://eprints.utas.edu.au/709/2/02whole.pdf"><span class="ep_document_citation">PDF (02: Whole Thesis)</span></a> - Requires a PDF viewer<br />602Kb</td></tr></table><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">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.</p></div><table style="margin-bottom: 1em" cellpadding="3" class="not_ep_block" border="0"><tr><th valign="top" class="ep_row">Item Type:</th><td valign="top" class="ep_row">Thesis (PhD)</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">mathematical physics, markov model, phylogenetics, biology</td></tr><tr><th valign="top" class="ep_row">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/230100.html">230000 Mathematical Sciences > 230100 Mathematics</a></td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">709</td></tr><tr><th valign="top" class="ep_row">Deposited By:</th><td valign="top" class="ep_row"><span class="ep_name_citation"><span class="person_name">UTas Digital Archives Librarian</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">07 Feb 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">09 Jan 2008 02:30</td></tr><tr><th valign="top" class="ep_row">ePrint Statistics:</th><td valign="top" class="ep_row"><a target="ePrintStats" href="/es/index.php?action=show_detail_eprint;id=709;">View statistics for this ePrint</a></td></tr></table><p align="right">Repository Staff Only: <a href="http://eprints.utas.edu.au/cgi/users/home?screen=EPrint::View&eprintid=709">item control page</a></p>
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