# Predicting and Modeling Wildfire Propagation Areas with BAT and Maximum-State PageRank
## 4 Experimental Results  
The scale-free network illustrated in Figure 1 is used to validate the proposed algorithm in estimating the occurrence probability of the wildfire propagation areas, i.e., Pr(\(i\), N\({}_{\text{area}}\)) for \(i\) = 0, 1,..., (\(n\)\(-\)1) and N\({}_{\text{area}}\) = 1, 2,..., \(|V|\) = \(n\) without loss generality. In the experiment, we consider all occurrence probabilities for N\({}_{\text{area}}\) = 1, 2,..., 8 by assuming that the ignition area begins in nodes 0, 1,..., 7, respectively. Hence, there are 64 tests included.  
The proposed algorithm was coded in Python, and all 64 tests were run on Spyder, and performed on the Notebook on Windows 10 with an Intel Core i7-8650U CPU at 1.90 GHz and 2.11 GHz with 16 GB RAM.  
Let R\({}_{1}\) = R\({}_{0.85}\) and R\({}_{2}\) = R\({}_{0.15}\) be the related probability for d = 0.85 and 0.15, respectively. The experimental results are listed in Tables 9 and  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(i\) & \(\mathbf{N_{area}}\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **PR** & **1-PR** \\ \hline
**0** & 1 & 7 & 7 & 7 & 7 & 7 & 7 & 1 & 8 & 1 \\
**1** & 1 & 4 & 4 & 4 & 4 & 4 & 2 & 3 & 4 & 3 \\
**2** & 1 & 8 & 8 & 8 & 8 & 8 & 2 & 7 & 1 \\
**3** & 1 & 4 & 4 & 4 & 4 & 4 & 2 & 3 & 4 & 3 \\
**4** & 1 & 4 & 4 & 4 & 4 & 2 & 3 & 4 & 3 \\
**5** & 1 & 2 & 2 & 2 & 3 & 6 & 8 & 2 & 7 \\
**6** & **1** & **1** & **1** & **1** & **1** & **1** & 6 & **1** & 8 \\
**7** & 1 & 3 & 3 & 3 & 2 & 5 & 7 & 3 & 6 \\ \hline \end{tabular}
\end{table}
Table 10: Node ranks based on Table 9 and PageRank values.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(i\) & \(\mathbf{N_{area}}\) & **Vector Number** & **Runtime** & \(\mathbf{R_{1}=R_{0.85}}\) & \(\mathbf{R_{2}=R_{0.15}}\) & \(\mathbf{R_{1}-R_{2}}\) \\ \hline
5 & 1 & 1 & 0.000 & 1.0000 & 1.0000 & 0.0000 \\  & 2 & 252 & 0.003 & 0.9949 & 0.9963 & \(-\)0.0014 \\  & 3 & 594 & 0.006 & 0.9865 & 0.9892 & \(-\)0.0027 \\  & 4 & 8664 & 0.075 & 0.9798 & 0.9834 & \(-\)0.0036 \\  & 5 & 119914 & 1.082 & 0.9696 & 0.9753 & \(-\)0.0057 \\  & 6 & 2050424 & 18.796 & 0.9426 & 0.9540 & \(-\)0.0113 \\  & 7 & 26321044 & 339.085 & 0.8306 & 0.8604 & \(-\)0.0298 \\  & 8 & 183961358 & 2505.281 & 0.4628 & 0.5074 & \(-\)0.0446 \\ \hline
6 & 1 & 1 & 0.000 & 1.0000 & 1.0000 & 0.0000 \\  & 2 & 125 & 0.002 & 0.9984 & 0.9976 & 0.0008 \\  & 3 & 355 & 0.005 & 0.9956 & 0.9942 & 0.0014 \\  & 4 & 5216 & 0.077 & 0.9916 & 0.9904 & 0.0012 \\  & 5 & 70006 & 1.172 & 0.9815 & 0.9811 & 0.0004 \\  & 6 & 1153321 & 18.114 & 0.9573 & 0.9596 & \(-\)0.0023 \\  & 7 & 14700763 & 178.070 & 0.8552 & 0.8706 & \(-\)0.0154 \\  & 8 & 120803944 & 1547.187 & 0.4911 & 0.5204 & \(-\)0.0292 \\ \hline
7 & 1 & 1 & 0.000 & 1.0000 & 1.0000 & 0.0000 \\  & 2 & 124 & 0.002 & 0.9900 & 0.9918 & \(-\)0.0018 \\  & 3 & 456 & 0.007 & 0.9787 & 0.9810 & \(-\)0.0022 \\  & 4 & 7998 & 0.160 & 0.9725 & 0.9753 & \(-\)0.0028 \\  & 5 & 130986 & 1.845 & 0.9650 & 0.9689 & \(-\)0.0039 \\  & 6 & 2571160 & 35.229 & 0.9452 & 0.9528 & \(-\)0.0077 \\  & 7 & 29212442 & 461.061 & 0.8386 & 0.8641 & \(-\)0.0255 \\  & 8 & 179307046 & 2957.642 & 0.4680 & 0.5105 & \(-\)0.0425 \\ \hline \end{tabular}
\end{table}
Table 9: _Cont._Figure 5: Maximum-state PageRank values.  
Figure 3: The probability of R\({}_{2}\) for N\({}_{\text{area}}\) = 1, 2,..., 8 in nodes 0, 1,..., 7.