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A detailed study of the Smith-Waterman alignment algorithm is performed in order to find an analytical approach to the problem of assessing the statistical significance of local alignments with gaps. The significance is shown to be given in terms of an eigenvalue equation which captures the dynamics of the much simpler global alignment algorithm. This eigenvalue equation is then explicitly solved for a simple scoring system and the resulting significance estimations are verified by a comparison to extensive numerical simulations

An analytic approach to significance assessment in local sequence alignment with gaps