Markup | Genome Research

Table 2.

Computation of Derivatives for Fig. 1a

Step	Node	Action
1	7	$U_{7} (i) = π_{i}$
2	7	$\frac{\partial}{\partial θ} P_{7} = \sum_{i} \frac{\partial}{\partial θ} π_{i} D_{7} (i)$
3	5	$U_{5} (j) = \sum_{i} U_{7} (i) R_{7} (j) T_{7 \to 5} (i, j)$
4	5	$\frac{\partial}{\partial θ} P_{7 \to 5} = \sum_{i} \sum_{j} U_{7} (i) R_{7} (i) \frac{\partial}{\partial θ} T_{7 \to 5} (i, j) D_{5} (j)$
5	1	$\frac{\partial}{\partial θ} P_{5 \to 1} = \sum_{i} U_{5} (i) R_{5} (i) \frac{\partial}{\partial θ} T_{5 \to 1} (i, s_{1})$
6	2	$\frac{\partial}{\partial θ} P_{5 \to 2} = \sum_{i} U_{5} (i) L_{5} (i) \frac{\partial}{\partial θ} T_{5 \to 2} (i, s_{2})$
7	6	$U_{6} (j) = \sum_{i} U_{7} (i) L_{7} (j) T_{7 \to 6} (i, j)$
8	6	$\frac{\partial}{\partial θ} P_{7 \to 6} = \sum_{i} \sum_{j} U_{7} (i) L_{7} (i) \frac{\partial}{\partial θ} T_{7 \to 6} (i, j) D_{6} (j)$
9	3	$\frac{\partial}{\partial θ} P_{6 \to 3} = \sum_{i} U_{6} (i) R_{6} (i) \frac{\partial}{\partial θ} T_{6 \to 3} (i, s_{3})$
10	4	$\frac{\partial}{\partial θ} P_{6 \to 4} = \sum_{i} U_{6} (i) L_{6} (i) \frac{\partial}{\partial θ} T_{6 \to 4} (i, s_{4})$