“…(10) and (12) are directly related to the detailed balance condition, 17 which must be satisfied for correct estimation of T ∞ (I, J) elements and the density of states. Equation (12) coincides exactly with the broad histogram equations, initially proposed by Oliveira et al 15 for calculating the density of states.…”
Section: The Transition Matrixsupporting
confidence: 75%
“…Equation (19) corresponds to the broad histogram equation by Oliveira et al 15 and gives only relative values of the density of states. The density of states may be found if the degeneracy of the ground state is known a priori (as for the Ising model) or one of the quantities n(I), (S(I)) is fixed to some value.…”
Section: Calculation Of the Density Of Statesmentioning
confidence: 99%
“…It would be a difficult task to list all methods, so here we mention just some of them. Among these algorithms are the cluster algorithm 9 for the simulation of clusters for the lattice spin models, 10,11 parallel tempering, [12][13][14] broad histogram (BH) method, 15,16 transition matrix Monte Carlo (TMMC), 17 entropy sampling (ES), 18 multicanonical (MUCA) algorithm, [19][20][21][22] and the more recently proposed Wang-Landau (WL) algorithm. 23,24 In general, the ES, MUCA methods, and WL algorithm are based on the idea of sampling the microstates of the system uniformly in the space of some macroscopic observable, i.e.…”
Section: Introductionmentioning
confidence: 99%
“…Currently, the dynamics of WL algorithm and search for optimal schedule for updating γ in order to achieve fast convergence to the true density of states with small statistical errors are under intensive studies. [31][32][33][34][35] Alternative methods for calculating the density of states are the broad histogram 15 and the transition matrix Monte Carlo (TMMC) methods. 17 It can be shown that the broad histogram method may be considered as a particular case of infinite temperature TMMC method 17 (see further in the text).…”
An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical errors. This combination allows to achieve fast convergence to the correct values of density of states. We propose that the violation of TTT identities may serve as a qualitative criterion to check the convergence of density of states. The simulation process can be parallelized by cutting the entire interval of simulation into subintervals. The violation of ergodicity in this case is discussed. We test the algorithm on a set of peptides of different lengths and observe good statistical convergent properties for the density of states. We believe that the method is of general nature and can be used for simulations of other systems with either discrete or continuous energy spectrum.
“…(10) and (12) are directly related to the detailed balance condition, 17 which must be satisfied for correct estimation of T ∞ (I, J) elements and the density of states. Equation (12) coincides exactly with the broad histogram equations, initially proposed by Oliveira et al 15 for calculating the density of states.…”
Section: The Transition Matrixsupporting
confidence: 75%
“…Equation (19) corresponds to the broad histogram equation by Oliveira et al 15 and gives only relative values of the density of states. The density of states may be found if the degeneracy of the ground state is known a priori (as for the Ising model) or one of the quantities n(I), (S(I)) is fixed to some value.…”
Section: Calculation Of the Density Of Statesmentioning
confidence: 99%
“…It would be a difficult task to list all methods, so here we mention just some of them. Among these algorithms are the cluster algorithm 9 for the simulation of clusters for the lattice spin models, 10,11 parallel tempering, [12][13][14] broad histogram (BH) method, 15,16 transition matrix Monte Carlo (TMMC), 17 entropy sampling (ES), 18 multicanonical (MUCA) algorithm, [19][20][21][22] and the more recently proposed Wang-Landau (WL) algorithm. 23,24 In general, the ES, MUCA methods, and WL algorithm are based on the idea of sampling the microstates of the system uniformly in the space of some macroscopic observable, i.e.…”
Section: Introductionmentioning
confidence: 99%
“…Currently, the dynamics of WL algorithm and search for optimal schedule for updating γ in order to achieve fast convergence to the true density of states with small statistical errors are under intensive studies. [31][32][33][34][35] Alternative methods for calculating the density of states are the broad histogram 15 and the transition matrix Monte Carlo (TMMC) methods. 17 It can be shown that the broad histogram method may be considered as a particular case of infinite temperature TMMC method 17 (see further in the text).…”
An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical errors. This combination allows to achieve fast convergence to the correct values of density of states. We propose that the violation of TTT identities may serve as a qualitative criterion to check the convergence of density of states. The simulation process can be parallelized by cutting the entire interval of simulation into subintervals. The violation of ergodicity in this case is discussed. We test the algorithm on a set of peptides of different lengths and observe good statistical convergent properties for the density of states. We believe that the method is of general nature and can be used for simulations of other systems with either discrete or continuous energy spectrum.
“…We also discuss the accuracy and efficiency of our method.PACS numbers: 02.70.Lq, 05.50.+q, 75.10.HkThe search for new and more efficient methods for computer simulations is always an intensive task in science. Multispin coding techniques (see [1] and references therein), cluster algorithms [2,3,4], reweighting procedures [5,6,7] and methods which calculate directly the spectral degeneracy [8,9,10,11] are a few remarkable examples (see [12,13,14] for reviews). An efficient implementation of these methods can lead to an enormous increase in speed and accuracy of computer simulations.…”
We extended the Broad Histogram Method in order to obtain spectral degeneracies for systems with multiparametric Hamiltonians. As examples we obtained the critical lines for the square lattice Ising model with nearest and next-nearest neighbor interactions and the antiferromagnetic Ising model in an external field. For each system, the entire critical line is obtained using data from a single computer run. We also discuss the accuracy and efficiency of our method.PACS numbers: 02.70.Lq, 05.50.+q, 75.10.HkThe search for new and more efficient methods for computer simulations is always an intensive task in science. Multispin coding techniques (see [1] and references therein), cluster algorithms [2,3,4], reweighting procedures [5,6,7] and methods which calculate directly the spectral degeneracy [8, 9, 10, 11] are a few remarkable examples (see [12,13,14] for reviews). An efficient implementation of these methods can lead to an enormous increase in speed and accuracy of computer simulations. Multiparametric simulation is another way to further improve the efficiency.Multiparametric simulations allow, from a single computer run, to explore the whole space of parameters defining a given system, instead of repeating the whole process every time some parameter is changed.
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