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grahamknockillaree authored Jan 14, 2024
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12 changes: 10 additions & 2 deletions tutorial/tutorialTDA.xml
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Expand Up @@ -244,17 +244,25 @@ can be computed and the persistent homology can be derived from these homology h
</Example>

<P/>
<Alt Only="HTML">&lt;img src="images/1v2x.gif" align="center" height="500" alt="a protein backbone"/></Alt>
<Alt Only="HTML">&lt;img src="images/1v2x.gif" align="center" height="500" alt="a protein backbone"/></Alt>

<!--
<Alt Only="HTML">&lt;img src="images/1v2x.png" align="center" height="500" alt="a protein backbone"/></Alt>
-->
<P/>The next command reads in the pdb file for the T.thermophilus 1V2X protein and represents it as a <M>3</M>-dimensional pure cubical complex <M>K</M>. A resolution of <M>r=5</M> is chosen and this results in a representation as a subcomplex <M>K</M> of an ambient rectangular box of volume equal to <M>184\times 186\times 294</M> unit cubes. The complex <M>K</M> should have the homotopy type of a circle and the protein backbone is a 1-dimenional curve that should lie in <M>K</M>. The final command displays <M>K</M>.

<Example>
<#Include SYSTEM "tutex/4.11.txt">
</Example>

<P/>
<P/>
<Alt Only="HTML">&lt;img src="images/1v2xcubical.gif" align="center" height="500" alt="pure cubical complex representing a protein backbone"/></Alt>

<!--
<Alt Only="HTML">&lt;img src="images/1v2xcubical.png" align="center" height="500" alt="pure cubical complex representing a protein backbone"/></Alt>
-->


<P/>Next we create a filtered pure cubical complex by repeatedly
thickening <M>K</M>. We perform <M>15</M> thickenings, each thickening being a term in the filtration. The <M>\beta_1</M> barcode for the filtration is displayed. This barcode is a descriptor for the geometry of the protein. For current purposes it suffices to note that the first few terms of the filtration have first
homology equal to that of a circle. This indicates that the Euclidean coordinates in the pdb file robustly determine some knot.
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