Fractal MapReduce decomposition of sequence alignment

Table 3 Detailed calculation of length of similar segment, d_USM, from USM coordinates of individual homologous units.

Encoding
ubase = new usm('acggctgctatctgcgtacggtcgac')
uprobe = new usm('aaagctatctgaaaggtcaaa',ubase.abc)
u = new usm(null, 'acgt')
Reviewing coordinates of positions highlighted in Table 1 and 2
ubase.cgrForward[7]	uprobe.cgrForward[4]
[0.4225834224013004, 0.6976523056276487]	[0.2517343767806896, 0.502943755599859]
ubase.cgrBackward[7]	uprobe.cgrBackward[4]
[0.3390888473255761, 0.8645502159677478]	[0.33679262961989864, 0.8595585153381897]
Calculating one step at a time, $d_{C G R}^{f o r w a r d}$ and $d_{C G R}^{b a c k w a r d}$
u.distCGR([0.4225834224013004, 0.6976523056276487],[0.2517343767806896, 0.502943755599859]) 2
u.distCGR([0.3390888473255761, 0.8645502159677478],[0.33679262961989864, 0.8595585153381897]) 7
Applying Equation 5 directly to find length of similar segment = 2+7-1 = 8
u.dist(ubase.usm[7],uprobe.usm[4])8

In this illustrative example, the coordinates for base and probe sequences for nucleotide "c" in position 8 and 5 respectively: acggctg[c]tatctg cgtacggtcgac, and aaag[c]tatctg aaaggtcaaa will be compared using Equation 5. Note array indexes in JavaScript start with 0 (zero), so this corresponds to comparing coordinate indexes 7 and 4. This distance result is also highlighted in Figure 3.

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