Table 3 Dynamic programming matrix with distributions of the number of adjacent UMIs
\( \frac{S_g}{K} \) | 1 | 2 | 3 | … | S g |
0 | 1 | 1 − p Neighb | (1 − p Neighb )2 | ... | \( {\left(1-{p}_{Neighb}\right)}^{S_g-1} \) |
1 | 0 | p Neighb | \( \left(1-{p}_{Neighb}\right)\ast {p}_{Neighb}++{p}_{Neighb}\ast \left(1-{p}_{Neighb}\frac{K-1}{K}\right) \) | … | \( {t}_{0,S-1}\ast {p}_{Neighb}++{t}_{1,S-1}\ast \left(1-{p}_{Neighb}\frac{K-1}{K}\right) \) |
2 | 0 | 0 | \( {p}_{Neighb}^2\frac{K-1}{K} \) | … | \( {t}_{1,S-1}\ast {p}_{Neighb}\frac{K-1}{K}++{t}_{2,S-1}\ast \left(1-{p}_{Neighb}\frac{K-2}{K}\right) \) |
… | … | … | … | … | … |
k | 0 | 0 | 0 | … | \( {t}_{k-1,S-1}\ast {p}_{Neighb}\frac{K-k+1}{K}++{t}_{k,S-1}\ast \left(1-{p}_{Neighb}\frac{K-k}{K}\right) \) |
… | … | … | … | … | … |
K | 0 | 0 | 0 | … | \( {t}_{K-1,S-1}\frac{p_{Neighb}}{K}+{t}_{K,S-1} \) |