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# Table 6 Results on stable L0-structures

ID E* $PERM t e x p MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabdwgaLjabdIha4jabdchaWbqabaaaleqaaaaa@373A@$ REMC pm REMC m
L0-1 -4 -4 (< 1 sec) -4 (< 1 sec) -4 (< 1 sec)
L0-2 -8 -8 (< 1 sec) -8 (< 1 sec) -8 (< 1 sec)
L0-3 -12 -12 (< 1 sec) -12 (< 1 sec) -12 (< 1 sec)
L0-4 -16 -16 (32 sec) -16 (7 sec) -16 (5 sec)
L0-5 -20 -20 (3 hrs†) -20 (1.1 min) -20 (55 sec)
L0-6 -24 -23 -24 (16 min) -24 (13 min)
L0-7 -28 -26 (33 sec) -28 (3.2 hrs) -28 (2.5 hrs)
L0-8 -32 -30 (3 min) -32 (50 hrs) -32 (16 hrs)
L0-9 -36 -34 (22 min) -35 (99 hrs) -35 (100 hrs)
L0-10 -40 -38 (40 min) -38 (9.6 hrs) -39 (100 hrs)
1. The L0-structures proposed in [52] are hard for both REMC and PERM to fold. After L0-5, PERM is unable to find the unique optimal conformation in any of the 100 independent runs conducted. REMC is unable to find the ground-state conformation for L0-9 and L0-10, however, REMC m finds better sub-optimal conformations than PERM in both instances. When only one folding direction of PERM finds the optimal conformation, we report the mean run-time of that direction, denoting this in the table with a †. When best energies found by $PERM t 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabigdaXaqabaaaleqaaaaa@33F5@$ and $PERM t 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabikdaYaqabaaaleqaaaaa@33F7@$ differed (and neither find the optimal solution), the best energy by either is reported and the run-time is omitted. For every instance, 100 independent runs were conducted of 1 CPU hour each. In cases where not every run reached the same energy value after 1 hour, the expected run-time to reach the energy value shown in the table was calculated using the equation detailed by Parkes and Walser [54].