The effect of the density of states on the Metropolis algorithm
Information Processing Letters
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Protein Folding, the Levinthal Paradox and Rapidly Mixing Markov Chains
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Necessary and sufficient conditions for success of the metropolis algorithm for optimization
Proceedings of the 12th annual conference on Genetic and evolutionary computation
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In order to understand what makes natural proteins fold rapidly, Sali, Shakhnovich and Karplus (1994) [6,7] had used the Metropolis algorithm to search for the minimum energy conformations of chains of beads in the lattice model of protein folding. Based on their computational experiments, they concluded that the Metropolis algorithm would find the minimum energy conformation of a chain of beads within an acceptable time scale if and only if there is a large gap between the energies of the minimum energy conformation and that of the second minimum. Clote (1999) [1] attempted to support this conclusion by a proof that the mixing time of the underlying Markov chain would decrease as the gap in energies of the minimum energy conformation and that of the second minimum increased. He was able to show that an upper bound on the mixing time does indeed decrease as the energy gap increases. We show in this paper that the mixing time itself, however, is a non-decreasing function of the value of the energy gap. Therefore, our result contradicts what Clote had attempted to prove.