SOA: in this stage, the only computation is to update the probability vectors (Equation 19) S times in one generation.
We adjusted the original representation of the protagonist-interest vectors (Equation 2) in order to mitigate the data bias, which was reflected in that some countries were overly represented, because they produced much more tweets than others (Figure 12(a)).
The discussion of the complexity for each stage is as follows: (1) SOA: in this stage, the only computation is to update the probability vectors (Equation 19) S times in one generation.
To characterize whether the search is sufficient or exhaustive we investigated the convergence for two measures: the parameter-spectrum width (Equation 3) and the variability in the feasible solution space of the parameter vectors (Equation 7). Figure 3 shows the changes in the parameter-spectrum width with respect to the number of solutions.
The unweighted vectors (equation 12) were also computed.
In contrast, the IDW-refined model deviates by only 1.79 Å using the local scheme with c=4 and cut-off distance R set to include the nine closest feature vectors (Equation 6).
Computing column j in matrices EDT α and ED, the algorithm performs O matrix-vector min-plus multiplications (Equations 15 and 16), each taking O n 2 λ 2 log | D | 2 (n ) time using the algorithm in Section "The EDDC algorithm based on efficient D-discrete min-plus matrix-vector multiplication", and computes the entry-wise minimum of | Σ| i-length vectors (Equation 16) in O (| Σ| i) time.
Because the state-vector equations accurately represent most physical systems, which only have small deviations about their steady-state behaviour, it follows that in the natural world small-scale control is almost always possible, at least in principle.
The kinematical model of UHP is identified based on the loop vector equations, while the dynamical model is derived based on the Lagrangian formulation.
Linear algebra, especially vector equations in 3-dimensional (3D) space, was the least performed topic of fundamental mathematics for Japanese engineering students.
