@article{oai:nagoya.repo.nii.ac.jp:00026960,
 author = {Mitsutake, Ayori and Mori, Yoshiharu and Okamoto, Yuko},
 journal = {Physics Procedia},
 month = {Aug},
 note = {We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function E0 by adding any physical quantity V of interest as a new energy term with a coupling constant λ. We then perform a multi-dimensional multicanonical simulation where a random walk in E0 and V space is realized. We can alternately perform a multi-dimensional simulated-tempering simulation where a random walk in temperature T and parameter λ is realized. The results of the multi-dimensional replica-exchange simulations can be used to determine the weight factors for these multi-dimensional multicanonical and simulated tempering simulations. Two examples of the above methods are presented for biomoleculr systems where the parameter λ corresponds to the solvation parameter and the pressure. In the former, a random walk in the conformational energy and solvation free energy is performed, and in the latter, a random walk in the potential energy and volume is realized.},
 pages = {89--105},
 title = {Multi-dimensional multicanonical algorithm, simulated tempering, replica-exchange method, and all that},
 volume = {4},
 year = {2010}
}