SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics

. 2015 Apr 2;31(15):2489–2496. doi: 10.1093/bioinformatics/btv185

$(C 1)$	$Pr [a \| A] \geq θ_{1}$ and $Pr [b \| B] \geq θ_{1}$	for all base pairs $a \in S$ and $b \in T$
$(C 2)$	$\Pr [i \in loop (\hat{a}) A] \geq θ_{2}$ and $\Pr [k \in loop (\hat{b}) B] \geq θ_{2}$	for all $(i, k) \in A$ , i unpaired and internal in $S$ , k unpaired and internal in $T$ , where $\hat{a}$ denotes the parent of i in $S$ and $\hat{b}$ , the parent of k in $T$
$(C 3)$	$\Pr [a \in loop (\hat{a}) A] \geq θ_{3}$ and $\Pr [b \in loop (\hat{b}) B] \geq θ_{3}$	for all internal base pairs a in S and b in T, where $\hat{a}$ denotes the parent of a in S; $\hat{b}$ , the parent of b in T.