The sum of Pi from the expanded diagram should be equal to that of the states (pi) obtained from the original diagram, which was indeed confirmed by the algebraic results.
In this case, whatever the number of creases, all alternate angles must sum to pi.
The tracked object is localized by the estimation of mean state, which is calculated at each time step by begin{aligned} tilde{S} = sum _{n=1}^N pi _n s_n.
Third, we compute the normed sum of PIs over the entire fast subspace in order to justify QEA.
Thus, if the normed sum of PIs over all fast modes exceeds 0.7, the reaction is defined as fast.
When comparing the normed sum of PIs for the three different regimes, four different categories of reactions can be identified depending on their respective PIs, e.g. the reaction can always be classified as fast or it changes its role between regimes.
Intriguingly, plant available P contents (sum of resin-Pi, NaHCO3-Pi and NaOH-Pi) in the prehistoric topsoils and the recent topsoils were similar (23% and 20% of extractable P, respectively), suggesting that even plant available P was maintained in the prehistoric topsoil relicts.
The last term in the likelihood corresponds to the constraint that (sum _{i=1}^{n} pi _{i} = 1).
The constraint that (sum _{i=1}^{n} pi _{i} = 1) yields n−1 score equations given by s j =∂ logL/∂ π j.
Maximum likelihood estimation is now carried forth under the constraint that (sum _{i=1}^{n} pi _{i} = 1) similar to classic maximum likelihood based empirical density estimation.
