Monte Carlo search results

Monte Carlo searching becomes more difficult for large molecules. This is because a small change in the middle of the molecule can result in a large displacement of the atoms at the ends of the molecule. One solution to this problem is to hold bond lengths and angles fixed, thus changing conformations only, and to use a small maximum displacement. 

Incorporation of an imine unit into a mPE began with a Monte Carlo search of dodecamer (58e), which indicated that the oligomer adopted a six-turn helical structure [86]. To verify these results solvent denaturation studies were performed on 58e which showed a helix coil transition with a AG(CH3CN) very similar to that of the native oligomers (3.0 0.2 for 58e vs 3.2 0.1 for 15). The small difference in the AG(CH3CN) indicates that the imine bond has a negligible effect on the stability of the folded state of the oligomer. With this... 

In order to characterize the distributions of selective values in the second and the third model, we explored the value landscape by a Monte Carlo search. We created three random samples of 38,000 different sequences each (one repeat with 76,000 sequences gave essentially the same results) with predetermined ratios of probabilities for (0/1) digits, Pi = 0.2857, p2 = 0.5, and p3 = 0.7143, which led to mutant distributions centered at the 20-, 35-, and 50-error mutants of the all-zero sequence Iq. Three different parts of the value landscapes determined by Eqs. (IV.9)-(IV.ll) were explored in that way. The results are shown in Figure 22. 

We further experimented with training NanoCells using another Monte-Carlo search algorithm, simulated annealing. Simulated annealing produced essentially the same results as the GA. It is our opinion that in this case, the particular base search algorithm is not nearly as important as the manner in which it is adapted to the NanoCell problem. 

Fig. 4 Lowest energy conformations resulting from a Monte Carlo conformational search on an unsubstituted phenylene ethynylene dodecamer. The ideal helical conformation is shown in the lower right-hand corner. All of the other conformations are destabilized by the addition of bulky side chains...

The search for local minima in the neighborhood of a given local minimum is usually performed by the excitation of the system from this state followed by the relaxation of the system. If the relaxation of the excited system results in a state different from the initial state (and explored earlier), then a new local minimum is found, otherwise the evolution of the excited system is continued. The ways of moving out of the initial state can be different in temperature accelerated dynamics (TAD) by Sorensen and Voter [78], MD is used at high temperatures in the activation-relaxation technique (ART) by Mousseau and Barkema [79] and the local activated Monte Carlo method (LAMC) [80], the system evolves along the direction opposite to the direction of the force in the long-scale kinetic Monte Carlo... 

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