## 3 Results and Discussion
### Finding tfbs Using Power Spectra as Fingerprints  
The results of searching for Sp1 tfbs using Sp1 fingerprints in chromosome 21 are given in Table 2. The best performing structural parameter using the cosine distance is minor groove width which finds 2.4 Sp1 tfbs on average in the top 1% of the ranked list of spectra. Decreasing twist flexibility, \(k\)-Twist, is clearly next with 1.6, and then two partition coefficients and roll3 all retrieved approximately 1.4 tfbs. By chance we would expect a retrieval rate of 0.88 tfbs in 1% of the chromosomal blocks. Sequence performs well, retrieving 1.7 tfbs, but is clearly outperformed by minor groove width. Figure 9: Comparison of Sp1 tfbs 76 \(3k\)-Roll spectra with its occurrence spectra. PSD – power spectral density. (a) Summed \(3k\)-Roll spectra for all Sp1 tfbs in chromosome 21; (b) Sp1 tfbs 76 \(3k\)-Roll spectrum alone; (c) summed Sp1 \(3k\)-Roll spectra omitting tfbs 76 (d) Sp1 tfbs 76 occurrence spectrum alone; (e) summed Sp1 occurrence spectra omitting tfbs 76. The next obvious step is to perform data fusion using some combination of parameters, the results being given in Table 3. As might be expected, fusing minor groove width and decreasing twist flexibility gives an improved retrieval rate, to 3 tfbs. In contrast, fusing minor groove with and sequence gives 2.5 tfbs, little improvement over groove width alone, suggesting that minor groove width is capturing most of the information provided by sequence. Adding in more parameters gives more improvement, with the best performance being given by the fusion of groove, \(k\char 100\) Twist, roll3, sequence and 3Q \(\char 100\) Twist. The performance tails off when further parameters are fused. Thus using all structural parameters with individual retrieval rates better than 0.88 gives a an overall retrieval rate of 1.3 Sp1 tfbs, which is an improvement upon some individual parameters, but clearly is not as good as the best single parameter. In Figure 10 we give the retrieval plots for minor groove width, decreasing twist flexibility and sequence, (cyan, red and magenta lines respectively), together with some of the fusion results (blue, black and green lines). It is clear that fusing parameters \begin{table}
\begin{tabular}{|l|l|l|l|l|} \hline
**parameter** & **Sp1** & **Random** & **Shuffled** & **Zscore** \\
**r** & & & & \\ \hline \(k\char 100\) Twist & 1.60 & 1.16 & 1.01 & 2.8 \\ \(k\char 100\) Twist & 0.85 & 0.61 & 1.02 & -1.2 \\ \(k\char 100\) Roll & 0.90 & 0.71 & 0.78 & 0.64 \\ \(k\char 100\) Roll & 0.67 & 0.81 & 0.83 & -1.1 \\ \(3k\char 100\) Twist & 1.15 & 0.94 & 0.97 & 1.1 \\ \(3k\char 100\) Roll & 1.10 & 0.86 & 0.67 & 1.1 \\ \(3k\char 100\) Roll & 1.13 & 0.94 & 0.94 & 1.5 \\ \(3k\char 100\) Roll & 1.14 & 0.86 & 1.09 & 0.48 \\ Q \(\char 100\) Twist & 1.18 & 0.84 & 0.66 & 3.0 \\ Q \(\char 100\) Twist & 0.90 & 0.62 & 0.87 & 0.40 \\ Q \(\char 100\) Roll & 0.88 & 0.69 & 0.74 & 1.1 \\ Q \(\char 100\) Roll & 0.92 & 0.74 & 0.71 & 1.0 \\ \(3\)Q \(\char 100\) Twist & 0.92 & 0.78 & 0.99 & -0.85 \\ \(3\)Q \(\char 100\) Twist & 1.45 & 0.93 & 0.82 & 3.6 \\ \(3\)Q \(\char 100\) Roll & 1.41 & 0.95 & 0.65 & 4.8 \\ \(3\)Q \(\char 100\) Roll & 1.07 & 0.82 & 0.61 & 2.5 \\ twist3 & 1.25 & 0.86 & 0.67 & 2.4 \\ roll3 & 1.35 & 0.83 & 0.82 & 2.6 \\ slide3 & 1.12 & 0.82 & 0.80 & 2.1 \\ shift3 & 0.79 & 0.68 & 0.67 & 1.2 \\ RMSD & 0.97 & 0.78 & 0.79 & 1.7 \\ groove & 2.40 & 1.16 & 0.88 & 5.2 \\ bistability & 0.38 & 0.11 & 0.00 & 2.1 \\ Sequence & 1.67 & 1.05 & 0.67 & 4.4 \\ \hline \end{tabular}
\end{table} 
Table 2: Sp1 tfbs retrieval in chromosome 21.  
together both decreases the number of times that few tfbs are retrieved and increases the maximum number of tfbs retrieved (to 12 whereas the maximum retrieval for a single parameter is 7). Figure 10: Data fusion retrieval. Single parameters : groove (cyan); \(k^{-}_{\mathrm{Twist}}\)(red); sequence, (magenta).