Replica Exchange Monte Carlo Method Research Articles

Data-driven estimation of spatial electrical property of multi-compartment models with neuronal morphology by replica exchange Monte Carlo method

Data-driven estimation of spatial electrical property of multi-compartment models with neuronal morphology by replica exchange Monte Carlo method

Data-analysis software framework 2DMAT and its application to experimental measurements for two-dimensional material structures

An open-source data-analysis framework 2DMAT has been developed for experimental measurements of two-dimensional material structures. 2DMAT offers five analysis methods: (i) Nelder-Mead optimization, (ii) grid search, (iii) Bayesian optimization, (iv) replica exchange Monte Carlo method, and (v) population-annealing Monte Carlo method. Methods (ii) through (v) are implemented by parallel computation, which is efficient not only for personal computers but also for supercomputers. The current version of 2DMAT is applicable to total-reflection high-energy positron diffraction (TRHEPD), surface X-ray diffraction (SXRD), and low-energy electron diffraction (LEED) experiments by installing corresponding forward problem solvers that generate diffraction intensity data from a given dataset of the atomic positions. The analysis methods are general and can be applied also to other experiments and problems. Program summaryProgram Title: 2DMATCPC Library link to program files:https://doi.org/10.17632/c2t3vzbx9f.1Developer's repository link:https://www.pasums.issp.u-tokyo.ac.jp/2dmat/Code Ocean capsule:https://codeocean.com/capsule/7260490Licensing provisions: GNU General Public License v3.0Programming language: Python 3External routines/libraries: Numpy, Scipy, Tomli, mpy4pyNature of problem: Analysis of experimental measurement data.Solution method: Optimization, grid-based global search, Monte Carlo method.

A New Look at the Spin Glass Problem from a Deep Learning Perspective.

Spin glass is the simplest disordered system that preserves the full range of complex collective behavior of interacting frustrating elements. In the paper, we propose a novel approach for calculating the values of thermodynamic averages of the frustrated spin glass model using custom deep neural networks. The spin glass system was considered as a specific weighted graph whose spatial distribution of the edges values determines the fundamental characteristics of the system. Special neural network architectures that mimic the structure of spin lattices have been proposed, which has increased the speed of learning and the accuracy of the predictions compared to the basic solution of fully connected neural networks. At the same time, the use of trained neural networks can reduce simulation time by orders of magnitude compared to other classical methods. The validity of the results is confirmed by comparison with numerical simulation with the replica-exchange Monte Carlo method.

Optimization of basis functions for multiconfiguration mixing using the replica exchange Monte Carlo method and its application to C12

Background: To calculate excited states in quantum many-body systems, multiconfiguration mixing has often been employed. However, it remains unclear how to choose important Slater determinants from a huge model space.Purpose: We propose an efficient method as the replica exchange Monte Carlo (RXMC) method to sample important Slater determinants and optimize and analyze the results obtained. As an application, we investigate the ground and excited states of $^{12}\mathrm{C}$ based on the Bloch-Brink $\ensuremath{\alpha}$ cluster model and show the detailed structure of the obtained states.Methods: The RXMC method enables us to efficiently sample Slater determinants following the Boltzmann distribution on the multidimensional potential-energy surface (PES) under a given model space. To analyze the excited states obtained, we embed sampled basis functions onto the PES calculated with the $\ensuremath{\beta}\text{\ensuremath{-}}\ensuremath{\gamma}$ constraint method and discuss the main component in each state.Results: The RXMC method efficiently performs the samplings with a temperature parameter of ${T}_{L}=2.5$ MeV in $^{12}\mathrm{C}$. We obtain the gas-like state with a wide density distribution in the tail part in the second ${0}^{+}$ state. We also obtain the linear-chain-like states with the bending and stretching vibrational modes in the third and fourth ${0}^{+}$ states, respectively. In the fifth ${0}^{+}$ state, the main component of the basis functions contains expanded equilateral-triangle configurations.Conclusions: The second ${0}^{+}$ gas-like state emerges at the local minimum in the PES, which is the beginning of the valley structure connected to the linear-chain breakup channel. The third and fourth linear-chain-like states emerge in this valley structure. We conclude that the RXMC method is a powerful method to calculate the excited states of nuclei, which would be applied to much more complicated nuclear fission dynamics in heavier nuclei.

Replica-Exchange Monte Carlo Method Incorporating Auto-tuning Algorithm Based on Acceptance Ratios for Effective Bayesian Spectroscopy

To promote the widespread use of Bayesian spectroscopy using a replica-exchange Monte Carlo (RXMC) method, we proposed an auto-tuning algorithm for step widths (magnitude of random numbers). It tun...

Replica Exchange Monte Carlo Method for Proton and X-Ray Induced DNA Damage and Repair

Replica Exchange Monte Carlo Method for Proton and X-Ray Induced DNA Damage and Repair

Calculation of Order Parameter and Critical Exponents of the Spin Glass in the Frame of Edwards-Anderson Model

It is well known that critical phenomena occur in condensed matter under certain conditions, when an abrupt change in its properties occurs. In the vicinity of critical points, various phenomena may arise. The critical region can be described by a set of state parameters (order parameters), which allow one to obtain information about the anomalous behavior of thermodynamic averages, internal processes, and the nature of the objects of study. The abnormal nonlinear behavior of state parameters is described by critical exponents. In this article, we considered spin glass on the example of the Edwards-Anderson model. For the simulation, the replica-exchange Monte-Carlo method was used. Critical exponents were obtained to describe the behavior of the model in the critical region.

Application of a Distance-Dependent Sigmoidal Dielectric Constant to the REMC/SAAP3D Simulations of Chignolin, Trp-Cage, and the G10q Mutant.

The replica-exchange Monte Carlo method based on the single amino acid potential (SAAP) force field, i.e., REMC/SAAP3D, was recently developed by our group for the molecular simulation of short peptides. In this study, the method has been improved by applying a distance-dependent dielectric (DDD) constant and extended to the peptides containing D-amino acid (AA) residues. For chignolin (10 AAs), a sigmoidal DDD model reasonably allocated the native-like β-hairpin structure with all-atom root mean square deviation (RMSD) = 2.0Å as a global energy minimum. The optimal DDD condition was subsequently applied for Trp-cage (20 AAs) and its G10q mutant. The native-like α-rich folded structures with main-chain RMSD = 3.7 and 3.8Å were obtained as global energy minima for Trp-cage and G10q, respectively. The results suggested that the REMC/SAAP3D method with the sigmoidal DDD model is useful for structural prediction for the short peptides comprised of up to 20 AAs. In addition, the relative contributions of SAAP to the total energy (%SAAP) were evaluated by energetic component analysis. The ratios of %SAAP were about 40 and 20% for chignolin and Trp-cage (or G10q), respectively. It was proposed that SAAP is more important for the secondary structure formation than for the assembly to a higher-order folded structure, in which the attractive van der Waals interaction may play a more important role.

A universal Bayesian inference framework for complicated creep constitutive equations

Evaluating the creep deformation process of heat-resistant steels is important for improving the energy efficiency of power plants by increasing the operating temperature. There is an analysis framework that estimates the rupture time of this process by regressing the strain–time relationship of the creep process using a regression model called the creep constitutive equation. Because many creep constitutive equations have been proposed, it is important to construct a framework to determine which one is best for the creep processes of different steel types at various temperatures and stresses. A Bayesian model selection framework is one of the best frameworks for evaluating the constitutive equations. In previous studies, approximate-expression methods such as the Laplace approximation were used to develop the Bayesian model selection frameworks for creep. Such frameworks are not applicable to creep constitutive equations or data that violate the assumption of the approximation. In this study, we propose a universal Bayesian model selection framework for creep that is applicable to the evaluation of various types of creep constitutive equations. Using the replica exchange Monte Carlo method, we develop a Bayesian model selection framework for creep without an approximate-expression method. To assess the effectiveness of the proposed framework, we applied it to the evaluation of a creep constitutive equation called the Kimura model, which is difficult to evaluate by existing frameworks. Through a model evaluation using the creep measurement data of Grade 91 steel, we confirmed that our proposed framework gives a more reasonable evaluation of the Kimura model than existing frameworks. Investigating the posterior distribution obtained by the proposed framework, we also found a model candidate that could improve the Kimura model.

Analysis of liquids, gases, and supercritical fluids by a two-dimensional replica-exchange Monte Carlo method in temperature and chemical potential space.

We investigate the liquid, gas, and supercritical fluid phases of a Lennard-Jones 12-6 potential system by a two-dimensional replica-exchange method in which not only temperature but also chemical potential is exchanged. The method is referred to as the grand canonical replica-exchange method (GCREM). While one-dimensional replica exchange, which exchanges only temperature, cannot cross first-order phase transition points, GCREM can avoid this problem by making a detour in the two-dimensional parameter space. From only one simulation run, we can obtain probability distributions in the grand canonical ensemble for wide temperature and chemical potential values using the multiple-histogram reweighting techniques. We define a phase diagram near the critical point using thermodynamic quantities. Moreover, we discuss structures in each defined phase and at phase transition points.

Bayesian Spectroscopy with a Replica Exchange Monte Carlo Method on an Excitonic Absorption Spectrum of a Cu2O Thin Crystal

To study a bi-axial stress effect in a Cu2O thin crystal sandwiched by paired MgO substrates, we have applied Bayesian spectroscopy to decompose an absorption spectrum with employing a replica exchange Monte Carlo (RXMC) method. The absorption spectrum includes broad bands of an inter-band transition and an exciton continuous state simultaneously with excitonic resonance transitions. However, it had been difficult to decompose correctly because of a bottleneck in optimal solution search efficiency. To relieve the bottleneck, we introduced the RXMC method and succeeded in decomposing all spectral components. Posterior probabilities of the band-gap energy and the exciton binding energy distribute at lower energy side than those in stress-free bulk crystals, which provides statistical evidence to show that the bi-axial stress remains in the Cu2O thin crystal sandwiched by MgO substrates.

Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field

We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the “kagome-ice” problem. We discuss the similarity and dissimilarity of the magnetization curves of the “kagome-ice” state and the two-dimensional kagome lattice.

Direct coupling of first-principles calculations with replica exchange Monte Carlo sampling of ion disorder in solids

We demonstrate the feasibility of performing sufficient configurational sampling of disordered oxides directly from first-principles without resorting to the use of fitted models such as cluster expansion. This is achieved by harnessing the power of modern-day cluster supercomputers using the replica exchange Monte Carlo method coupled directly with structural relaxation and energy calculation performed by density functional codes. The idea is applied successfully to the calculation of the temperature-dependence of the degree of inversion in the cation sublattice of MgAl2O4 spinel oxide. The possibility of bypassing fitting models will lead to investigation of disordered systems where cluster expansion is known to perform badly, for example, systems with large lattice deformation due to defects, or systems where long-range interactions dominate such as electrochemical interfaces.

Composition-related structural transition of random peptides: insight into the boundary between intrinsically disordered proteins and folded proteins

Previous studies based on bioinformatics showed that there is a sharp distinction of structural features and residue composition between the intrinsically disordered proteins and the folded proteins. What induces such a composition-related structural transition? How do various kinds of interactions work in such processes? In this work, we investigate these problems based on a survey on peptides randomly composed of charged residues (including glutamic acids and lysines) and the residues with different hydrophobicity, such as alanines, glycines, or phenylalanines. Based on simulations using all-atom model and replica-exchange Monte Carlo method, a coil-globule transition is observed for each peptide. The corresponding transition temperature is found to be dependent on the contents of the hydrophobic and charged residues. For several cases, when the mean hydrophobicity is larger than a certain threshold, the transition temperature is higher than the room temperature, and vise versa. These thresholds of hydrophobicity and net charge are quantitatively consistent with the border line observed from the study of bioinformatics. These results outline the basic physical reasons for the compositional distinction between the intrinsically disordered proteins and the folded proteins. Furthermore, the contributions of various interactions to the structural variation of peptides are analyzed based on the contact statistics and the charge-pattern dependence of the gyration radii of the peptides. Our observations imply that the hydrophobicity contributes essentially to such composition-related transitions. Thus, we achieve a better understanding on composition–structure relation of the natural proteins and the underlying physics.

Exhaustive Search for Sparse Variable Selection in Linear Regression

We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By collecting the results of exhaustively computing ES-K, various approximate methods for selecting sparse variables can be summarized as density of states. With this density of states, we can compare different methods for selecting sparse variables such as relaxation and sampling. For large problems where the combinatorial explosion of explanatory variables is crucial, the AES-K method enables density of states to be effectively reconstructed by using the replica-exchange Monte Carlo method and the multiple histogram method. Applying the ES-K and AES-K methods to type Ia supernova data, we confirmed the conventional understanding in astronomy when an appropriate K is given beforehand. However, we found the difficulty to determine K from the data. Using virtual measurement and analysis, we argue that this is caused by data shortage.

Bayesian Spectroscopy of Admixed Photoluminescence Spectra with Exciton, Biexciton and Electron Hole Droplet States in a GaAs/AlAs Type-II Superlattice

We have analyzed a photoluminescence (PL) spectrum in a GaAs/AlAs type-II superlattice and have statistically confirmed stable existence of an electron-hole droplet (EHD) state. Although the PL spectrum consists of spectral components of the EHD, exciton and biexciton states, we have succeeded in decomposing the admixed spectrum into the respective components. In addition, posterior probability distributions of spectral parameters have been obtained in all spectral components from 30,000 times samplings through a replica exchange Monte Carlo method. By using mean values of their posterior probabilities, the PL spectrum can be completely reproduced by the sum of these spectral components. The stability energy of the EHD state has a sharp distribution in its posterior probability and has been confirmed to be enough larger than the ambient thermal energy. This fact is a strong evidence for the stable formation of the EHD state in the GaAs/AlAs type-II superlattice.

Enhanced replica exchange reactive Monte Carlo simulations for constructing zeolite frameworks

We investigate the ability of a reactive model of silica to build crystalline zeolite frameworks with an enhanced sampling approach based on replica exchange Monte Carlo (REMC) simulations. In our implementation of REMC, the silica hydrolysis/condensation equilibrium constant controlling network formation is chosen as the index parameter characterising each replica. We show that improving the performance of the REMC method by increasing its efficiency in producing zeolite crystals allows zeolites with larger unit cells to be constructed. In particular, we perform an efficiency case study on the sodalite structure, containing 12 tetrahedra per unit cell and then apply the resulting enhancements to construct a significantly larger zeolite. We have improved our simulations in two ways; first, we have analysed the roles of the Monte Carlo parameters on the efficiency of this REMC method. Second, we have implemented an adaptive protocol that resets the values of the hydrolysis/condensation equilibrium constants among the replicas, ‘on the fly’ of each simulation, to optimise replica exchange for the purpose of constructing zeolite crystals. Finally, we show that by applying these enhancements, the REMC method can produce the crystal structure of zeolite AWW, a nanoporous material with 24 tetrahedra per unit cell.

Seismic wavefield imaging of long‐period ground motion in the Tokyo metropolitan area, Japan

AbstractLong‐period ground motions due to large earthquakes can cause devastating disasters, especially in urbanized areas located on sedimentary basins. To assess and mitigate such damage, it is essential to rapidly evaluate seismic hazards for infrastructures, which can be simulated by seismic response analyses that use waveforms at the base of each infrastructure as an input ground motion. The present study reconstructs the seismic wavefield in the Tokyo metropolitan area located on the Kanto sedimentary basin, Japan, from seismograms of the Metropolitan Seismic Observation network. The obtained wavefield fully explains the observed waveforms in the frequency band of 0.10–0.20 Hz. This is attributed to the seismic wavefield imaging technique proposed by Kano et al. (2017), which implements the replica exchange Monte Carlo method to simultaneously estimate model parameters related to the subsurface structure and source information. Further investigation shows that the reconstructed seismic wavefield lower than 0.30 Hz is of high quality in terms of variance reduction, which quantifies a misfit in waveforms but that the variance reduction rapidly worsens in higher frequencies. Meanwhile, the velocity response spectra show good agreement with observations up to 0.90 Hz in terms of the combined goodness of fit, which is a measure of misfit in the velocity response spectra. Inputting the reconstructed wavefield into seismic response analyses, we can rapidly assess the overall damage to infrastructures immediately after a large earthquake.

Subphase transitions in first-order aggregation processes.

In this paper, we investigate the properties of aggregation transitions in the context of generic coarse-grained homopolymer systems. By means of parallel replica-exchange Monte Carlo methods, we perform extensive simulations of systems consisting of up to 20 individual oligomer chains with five monomers each. Using the tools of the versatile microcanonical inflection-point analysis, we show that the aggregation transition is a first-order process consisting of a sequence of subtransitions between intermediate structural phases. We unravel the properties of these intermediate phases by collecting and analyzing their individual contributions towards the density of states of the system. The central theme of this systematic study revolves around translational entropy and its role in the striking phenomena of missing intermediate phases. We conclude with a brief discussion of the scaling properties of the transition temperature and the latent heat.

Optimal Temperature Set for Replica Exchange Sampling

Replica Exchange Monte Carlo method has been introduced to improve sampling of a rugged energy landscape for such systems as polymers, biopolymers and spin glasses. Efficiency of the method however critically depends on the set of replica temperatures used for simulations. A novel method selecting these parameters has been recently proposed1, which numerically evaluates the probability of replica swap between temperatures based on estimated density of states for a system under study. Here we extend this method and prove it provides the optimal set of temperatures i.e. temperatures that guarantee the fastest flow of replicas from the lowest to the highest temperature.During an initial phase of the protocol, energy distributions are collected at different temperatures. Based on these observations, the density of states for the system is computed by the multihistogram method. Knowing the density, improved temperature set is established by minimizing the mean first passage time of replicas in the temperature space. The procedure has been illustrated with a coarse-grained protein folding simulation and all-atom dynamics in AMBER force field. The method has been implemented in BioShell package.2,31 D. Gront and A. Kolinski “Efficient scheme for optimization of parallel tempering Monte Carlo method” Journal of Physics: Condensed Matter 2007 19(3) 036225 http://dx.doi.org/10.1088/0953-8984/19/3/0362252 D. Gront and A. Kolinski “BioShell - a package of tools for structural biology computations” Bioinformatics 2006 22(5):621-6223D. Gront and A. Kolinski “Utility library for structural bioinformatics” Bioinformatics 2008 24(4):584-585