# Dynamic Pathway Selection Mechanisms of Brain Networks
## 3 Results
### Regulation of Path Selection by Different Phases of Stimulus Signal
pathways in \((n_{1},n_{5})\) for a given node, and the path selectivity index \(PPS\) is given to explore the phase dependence properties under a specific pathway. The blue curve in Figure 14 indicates the path with the strongest \(PA\) between two node pairs, and the orange color indicates the second strongest path. For Figure 14a, the results show that both the strongest path \(PA\) value and the second strongest path \(PA\) value between a pair of nodes \(P_{15}\) are relatively stable and do not change significantly with the phase shift of the stimulus information. Figure 14b indicates that the strongest path \(PA\) value between node pair \(PA\) changes with the stimulus phase offset, indicating that the phase information carried by the stimulus information will have some influence on the \(PA\) value; that is, the phase information can be used to modulate the network and thus find the optimal path. Figure 14c shows that the strongest path and the second strongest path \(PA\) values between the nodes to \(P_{15}\) change almost together, i.e., it shows that the \(PA\) values will be modulated by the role of phase information, and the selection of the path by the information flow can be either of the two paths, indicating that both paths can characterize the information. Figure 14d shows that the phase information carried by the stimulus information in the node pair \(P_{15}\) has obvious modulation on the \(PA\) values of the strongest path and the second strongest path (blue in the figure indicates \(\Delta\varphi\approx 1.5\pi\), orange indicates \(\Delta\varphi\approx 0.5\pi\)), which mainly shows that the strongest path and the second strongest path have a preferential choice of phase between them under different phase offsets, i.e., under different phase offsets of the stimulus information. When studying the path activation index \(PA\), Figure 14 analyzes the relationship between the strongest path and the second strong path with respect to the stimulus phase in the node \((n_{1},n_{5})\) path set \(P_{15}\). Based on this, it adopts the \(PPS\) to analyze any pathway in the path set \(P_{15}\), and then explore the phase dependence of the specific pathway. Through the statistics of the data results, the \(PPS\) values of all node pairs in the network composed of five nodes are drawn, and the phase selectivity histogram is shown in Figure 15.  
Figure 14: Path activation index PA under different phase shifts of stimulus information (**a**) Both the strongest and the second strongest paths are insensitive to phase. (**b**) Only the strongest path is phase sensitive. (**c**) The strongest and second strongest paths are sensitive to the same phase offset. (**d**) The strongest and second strongest paths are sensitive to different phase offsets. Figure 15 analyzes all paths between node pairs \(P_{15}\). Statistical analysis of the data results is performed to plot the values of all node pairs between \(P_{15}\). The results displayed are consistent with the conclusions of the theoretical analysis; that is, the larger value of \(PPS\) indicates that the path activation index is unstable and vulnerable to the modulation and influence of the phase information of the stimulus information. Figure 15 shows that the value of \(PPS\) is between 0 and 1, and the larger the value of \(PPS\), the more the path between nodes are affected by the phase shift of the stimulus information. After counting the path values between 180 node pairs, \(A\), \(B\), \(C\) and \(D\) correspond to the subplots in Figure 14. It can be seen that when the change of \(PA\) value is small, the value of \(PPS\) is closer to 0, and when the change of \(PA\) value is larger, the value of \(PPS\) converges to 1.