Math of DNA 2009 Project Suggestions
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1. Implement the transvection algorithm for virtual trackball controlled
three-dimensional rotations in Labview, Java, Matlab, C++.
You may base your implementation on my Flash/Actionscript version
for Platonic Solids.

<BR> <A HREF="http://www.math.utah.edu/~palais/mst/platonic_transvection.html">Transvection Demo</A>

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/transvection.txt">Algorithm code</A>

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/perspective.html">Perspective figures</A>

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/perspective.txt">Perspective code</A>

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2. Generate data for three-dimensional visualization of strands
of DNA winding into double helices and unwinding to random coils
from time varying curvature and torsion. You might include sequence
dependent features.

<BR> <A HREF="http://www.math.uiowa.edu/~seaman/DGImage53100.htm#PrscribedCrvTor1">Space curves</A>

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/04gm_curves.pdf">Curvature and torsion</A>

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3. Convert a set of related computer programs (or any other
evolving information) into DNA sequences of ACGTs and perform 
hierarchical clustering on them without multiple alignment,  
and with some different forms of multiple alignment first. 
You may use the Clustal programs to do this.

<BR> <A HREF="http://www-igbmc.u-strasbg.fr/BioInfo/ClustalW/">Clustal W homepage</A>

<BR> <A HREF="http://www-igbmc.u-strasbg.fr/BioInfo/ClustalX/">Clustal X homepage</A>


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4. Solve the DNA Melting Curve Model ODE with prescribed thermodynamic
parameters calculated from a given sequence in Labview using the built 
in Runge-Kutta solver .vi and the thermodynamic parameter calculator.

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/melt.pdf">Melting curves</A>

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/melt.txt">Melting curve ODEs</A>

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/SantaLuciaJr">SantaLucia papers</A>

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5. Obtain the genomic data for the SNPs on a chromosome, and find
examples of every SNP type having frequencies within a desired
range for homozygous, heterozygous, and wild-type forms.

<BR> <A HREF="http://www.ncbi.nlm.nih.gov/">NCBI Homepage</A>

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6. Investigate the dependence of the background fluorescence vs. temperature
amplitude and decay behavior on the properties of the single-stranded
oligonucleotides present (e.g. their length, GC content, sequence, etc.)

<BR> <A HREF="http://www.math.utah.edu/~palais/pcr/exp/HiR1xw6c.exe">Melting curves program</A>

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7. How many classes does a dendrogram represent?

<BR> <A HREF="http://www.egg.isu.edu/biocourses/bios599/projects/Quinn_html">Clustering</A>

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8. Systematic organization of tetrads with mismatchs for DNA with one mismatch,
DNA-RNA, dangling ends, etc.

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/SantaLuciaJr">SantaLucia papers</A>

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9. Investigate simulate the advantages/disadvantages of different
thermodynamic parameter inversion methods - Fit vs. Local, Which linear
system, etc., and different molecules (sequences) for determining parameters.

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/SantaLuciaJr">SantaLucia papers</A>

<BR> <A HREF="http://www.proteinscience.org/cgi/content/abstract/9/7/1416">Melting curve theory</A>

<BR> <A HREF="http://www.math.utah.edu/~palais/dnamath/DNAPapers/Sugimoto.pdf">Melting curve theory</A>