deletions | additions       diff --git a/SmithWaterman.tex b/SmithWaterman.tex  index f5c7c10..d95e756 100644  --- a/SmithWaterman.tex  +++ b/SmithWaterman.tex 
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The Smith-Waterman algorithm is used to find optimal local alignments between two sequences based on a cost matrix for symbols of the alphabet being used and defined gap costs.  A matrix $H$ is constructed in the following manner:  \[\cases{1 & 2 & 3} \]  % \[  H(i,0) = 0, 0 \leq i \leq m \]%  \[ H(0,j) = 0, 0 \leq j \leq n \] % \[ H(i,j) = \hbox{Max} \hbox{max}  \begin{cases} 0 & H(i-1,j-1)+s(a_i,b_j) & max_{k \hbox{max}_{k  \geq 1}\left{ H(i-k,j)+W_k \right} & max_{l \hbox{max}_{l  \geq 1}\left{ H(i, j-l)+W_l) \right} \end{cases}$ \]