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Table 4:
Summary statistics of the putative CK2 ground states and local minima as identified by CMA-ES. The number of particles, energy, and the BOP values Q4, Q6, and are reported for all instances. For , multiple minima were identified. The putative ground states are labeled “A”.
VEnergyQ4Q6
−0.0931 
0.0939 0.3750 0.7408 −0.0463 
4A 0.7901 0.5092 0.6285 0.0132 
4B 3.0958 0.5312 0.5040 0.0048 
6.0977 0.6250 0.4556 0.0466 
12.0076 0.7638 0.3536 0.0132 
29.2253 0.5536 0.0625 −0.0931 
49.3528 0.3736 0.2502 −0.0931 
75.8984 0.1502 0.3391 −0.0436 
10 108.7305 0.1702 0.1579 −0.0931 
11 149.0286 0.1043 0.3329 −0.0515 
12 192.0350 0.0415 −0.1698 
13A 243.5499 0.0780 0.2679 0.0066 
13B 243.5531 0.1199 0.2714 0.0115 
14 298.9590 0.2813 0.5036 0.0132 
15 360.5035 0.0875 0.2977 0.0076 
16A 426.8723 0.0225 0.2791 −0.0219 
16B 426.8726 0.0352 0.2890 −0.0258 
17 499.0473 0.1055 0.1994 0.0019 
18 576.1469 0.1608 0.3495 0.0566 
19A 658.8684 0.1027 0.2900 0.1166 
19B 658.8689 0.0929 0.2822 0.1205 
20 746.6667 0.2718 0.1698 
21A 840.1743 0.0389 0.1921 0.1141 
21B 840.1976 0.0372 0.1824 0.0835 
21C 840.2036 0.0364 0.1575 0.0922 
22A 938.8178 0.0353 0.1494 0.1517 
22B 938.8197 0.0326 0.1782 0.1098 
23A 1,042.8819 0.0335 0.0571 −0.0206 
23B 1,042.8846 0.0193 0.0592 −0.0507 
23C 1,042.8900 0.0185 0.1077 −0.0846 
23D 1,042.9105 0.0181 0.1098 0.0301 
24A 1,152.1594 0.0058 0.0153 0.0132 
24B 1,152.1789 0.0037 0.0050 −0.0931 
25A 1,266.8947 0.0130 0.0852 0.0706 
25B 1,266.9774 0.0186 0.0201 0.0931 
VEnergyQ4Q6
−0.0931 
0.0939 0.3750 0.7408 −0.0463 
4A 0.7901 0.5092 0.6285 0.0132 
4B 3.0958 0.5312 0.5040 0.0048 
6.0977 0.6250 0.4556 0.0466 
12.0076 0.7638 0.3536 0.0132 
29.2253 0.5536 0.0625 −0.0931 
49.3528 0.3736 0.2502 −0.0931 
75.8984 0.1502 0.3391 −0.0436 
10 108.7305 0.1702 0.1579 −0.0931 
11 149.0286 0.1043 0.3329 −0.0515 
12 192.0350 0.0415 −0.1698 
13A 243.5499 0.0780 0.2679 0.0066 
13B 243.5531 0.1199 0.2714 0.0115 
14 298.9590 0.2813 0.5036 0.0132 
15 360.5035 0.0875 0.2977 0.0076 
16A 426.8723 0.0225 0.2791 −0.0219 
16B 426.8726 0.0352 0.2890 −0.0258 
17 499.0473 0.1055 0.1994 0.0019 
18 576.1469 0.1608 0.3495 0.0566 
19A 658.8684 0.1027 0.2900 0.1166 
19B 658.8689 0.0929 0.2822 0.1205 
20 746.6667 0.2718 0.1698 
21A 840.1743 0.0389 0.1921 0.1141 
21B 840.1976 0.0372 0.1824 0.0835 
21C 840.2036 0.0364 0.1575 0.0922 
22A 938.8178 0.0353 0.1494 0.1517 
22B 938.8197 0.0326 0.1782 0.1098 
23A 1,042.8819 0.0335 0.0571 −0.0206 
23B 1,042.8846 0.0193 0.0592 −0.0507 
23C 1,042.8900 0.0185 0.1077 −0.0846 
23D 1,042.9105 0.0181 0.1098 0.0301 
24A 1,152.1594 0.0058 0.0153 0.0132 
24B 1,152.1789 0.0037 0.0050 −0.0931 
25A 1,266.8947 0.0130 0.0852 0.0706 
25B 1,266.9774 0.0186 0.0201 0.0931 
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