## 3 Results
### Results for DREAM3 Challenge Network  
To test the prediction effect of the DCNTC algorithm on simulated data, DREAM challenge data, which were widely used, will be used as test data to reconstruct the GRNs [32]. DREAM3 is one of many DREAM Challenge subprojects that provide users with baseline data and control networks to test and evaluate the regulatory network model's effectiveness. We validated our approach on the DREAM3 dataset, where the sizes of the yeast knockout gene expression data were 10, 50, and 100, respectively. In the first, we tested the DCNTC algorithm on the yeast gene expression data of network size 10 and a sample size of 10. Figure 2 indicates the network extrapolated from gene expression data in different ways. Figure 2A is the real GRN with 10 nodes and 10 edges chosen from an experimentally validated network in yeast genomes. Figure 2B is the network derived from gene expression data with the LDCNET algorithm. The edges of solid dotted black lines are correctly deduced, and the edges of red dotted lines are incorrect. On the edge of false inferences, G2-G9 is a redundant edge, whereas edge G3-G5 is unfound. Figure 2C shows the network deduced from the gene expression data, which is the network inferred from us. Clearly, in our network, the inexistent regulations of G2-G9 were successfully removed. The performance data for each of the seven algorithms is shown in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Method** & **TP** & **FP** & **TN** & **FN** & **TPR** & **FPR** & **PPV** & **ACC** & **MCC** \\ \hline CLR & 6 & 10 & 25 & 4 & 0.600 & 0.286 & 0.375 & 0.689 & 0.273 \\ ARACNE & 6 & 6 & 29 & 4 & 0.600 & 0.171 & 0.500 & 0.778 & 0.403 \\ MRNET & 6 & 12 & 23 & 4 & 0.600 & 0.343 & 0.333 & 0.644 & 0.218 \\ REL-DC & 10 & 4 & 31 & 0 & 1 & 0.114 & 0.714 & 0.911 & 0.795 \\ MRNET- & 10 & 13 & 22 & 0 & 1 & 0.371 & 0.435 & 0.711 & 0.523 \\ DC & 8 & 1 & 34 & 2 & 0.8 & 0.029 & 0.889 & 0.933 & 0.802 \\ DCNTC & **9** & **0** & **35** & **1** & **0.9** & **0** & **1** & **0.978** & **0.936** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the performance of different methods for inferring a 10-gene network in DREAM3. Figure 2: Comparison of a 10-gene network inferred from a DREAM3 dataset. (**A**) The true network with 10 nodes and 10 edges. (**B**) The network inferred by LDCNET from gene expression data. The edge with red dotted lines G3–G5 is false-positive, while the edge G2–G9 is false-negative. (**C**) The network inferred from gene expression data. The false-negative edge G2–G9 in LDCNET was successfully removed by DCNTC. In the second, we tested the DCNTC algorithm on the yeast gene expression data of network size 50 and a sample size of 50. The real network consists of 50 nodes and 77 edges. In Table 2, we can find that the REL algorithm predicts more accurate edges, but this algorithm also expects a lot of wrong edges. The MRNET algorithm can only predict a tiny number of edges among the four algorithms. In comparison, among the four algorithms, the DCNTC algorithm has higher accuracy (ACC) and lower FPR. In the third, we tested the DCNTC algorithm on yeast gene expression data with a network size of 100 and a sample size of 100. The whole network consists of 100 nodes and 166 edges. In Table 3, we can find that the MRNET algorithm predicts more accurate boundaries, but this algorithm also expects a lot of unfair advantages. In comparison, among the four algorithms, the DCNTC algorithm has higher accuracy (ACC) and lower FPR. On the simulated dataset, the algorithm in this paper performed better in all aspects, mainly because only genes with the greatest distance correlation to the target gene were selected when picking regulatory genes for the target gene. This controls the introduction of false-positive edges to a certain extent.