Edits listed in Issue #24

bibook/msa/progressive.md

@@ -10,7 +10,7 @@ In principle, one can use dynamic programming to form MSAs. We can archive such
 
 ### Iterative Approaches as a Practical Alternative
 
-Given the inefficiencies of dynamic programming for MSAs, bioinformaticians have turned to heuristics that mimic the behaviour of full dynamic programming. Particularly iterative approaches, such as progressive alignment . These methods simplify the alignment process by breaking it down into manageable steps. Progressive alignment, for instance, first generates a guide tree based on pairwise similarities, then iteratively aligns sequences according to the tree's order. This reduces the computational burden and allows for the processing of large datasets in a reasonable time frame.
+Given the inefficiencies of dynamic programming for MSAs, bioinformaticians have turned to heuristics that mimic the behaviour of full dynamic programming. Particularly iterative approaches, such as progressive alignment. These methods simplify the alignment process by breaking it down into manageable steps. Progressive alignment, for instance, first generates a guide tree based on pairwise similarities, then iteratively aligns sequences according to the tree's order. This reduces the computational burden and allows for the processing of large datasets in a reasonable time frame.
 
 ## Progressive Alignments
 
@@ -26,7 +26,7 @@ In this chapter, we delve into the mechanics of progressive alignment, exploring
 
 ### Progressive Alignment Steps
 
-The process builds alignments in a stepwise manner, starting with the most similar sequences and gradually incorporating others. Here's a detailed look at how to create a progressive alignment. Lests assume you start with $T$ sequences, $C=\{A_1, \ldots, A_T\}$.
+The process builds alignments in a stepwise manner, starting with the most similar sequences and gradually incorporating others. Here's a detailed look at how to create a progressive alignment. Lets assume you start with $T$ sequences, $C=\{A_1, \ldots, A_T\}$.
 
 1. Compute Pairwise Alignments: Initially, calculate all pairwise alignments between each pair of sequences in $C$ using a suitable algorithm such as Needleman-Wunsch or Smith-Waterman. This provides a matrix of scores or distances that indicate how similar or different each pair of sequences is.