Fig. 3.

Bernoulli, Hit Integration, and Heaviside models. The Bernoulli (for $p=0.7$), the ${\int }_{0.5}^{1.0}$ Hit Integration, and the ${\sum }_{\frac{1}{2}}^1$ Heaviside probability mass functions of the number of matches, on alignments of length $\ell =64$. Highlighted dots indicate the weights given for each alignment class with a given number of matches m out of $\ell$ alignment symbols, under each of the three models. Note that, since the sum of the weights is always 1 for any model, and since the class of alignments with exactly $m=32$ matches out of $\ell =64$ is fully included in ${\sum }_{\frac{1}{2}}^1$ Heaviside model but only half-included in ${\int }_{0.5}^{1.0}$ Hit Integration model, there is a thin difference between the two resulting lines