Figure 2

Visualization of the pattern matching definition. Two different illustrations of the notion pattern matching are shown in (A) and (B). For the light gray pattern matching, we have $\mathcal{ℳ}=\{2\sim 2,3\sim 3,9\sim 13,10\sim 14,11\sim 15\}$ and $\mathcal{S}=\left\{\right(2,11\sim 2,15),(3,10\sim 3,14\left)\right\}$. Note that the two separated regions in both sequences are connected through base pairs. Furthermore, the set of structure matches is $\mathcal{ℳ}{|}_{\mathcal{S}}=\{2\sim 2,3\sim 3,10\sim 14,11\sim 15\}$ and the set of sequence matches is $\mathcal{ℳ}\setminus \mathcal{ℳ}{|}_{\mathcal{S}}=\{9\sim 13\}$. The pattern matching can be extended by the base pair match shown in dark gray, i.e., ${\mathcal{ℳ}}^{\prime }=\mathcal{ℳ}\cup \{1\sim 1,12\sim 16\}$ and ${\mathcal{S}}^{\prime }=\mathcal{S}\cup \left\{\right(1,12\sim 1,16\left)\right\}$. $(\mathcal{ℳ},\mathcal{S})$, the EPM shown in light gray, is a strict EPM, whereas $({\mathcal{ℳ}}^{\prime },{\mathcal{S}}^{\prime })$, the EPM extended by the dark gray part, is a relaxed EPM as mismatches in structure matches occur. (C) shows an example of an invalid matching. Separately, both the small and the big matched gray parts are valid EPMs, but together they do not form a valid EPM as the two individual parts are not connected.