Wang-Landau Sampling Research Articles

Exploring transitions in finite-size Potts model: comparative analysis using Wang–Landau sampling and parallel tempering

Abstract This research provides a examination of transitions within the various-state Potts model in two-dimensional finite-size lattices. Leveraging the Wang–Landau sampling and parallel tempering, we systematically obtain the density of states, facilitating a comprehensive comparative analysis of the results. The determination of the third-order transitions location are achieved through a meticulous examination of the density of states using microcanonical inflection-point analysis. The remarkable alignment between canonical and microcanonical results for higher-order transition locations affirms the universality of these transitions. Our results further illustrate the universality of the robust and microcanonical inflection-point analysis of Wang–Landau sampling.

Pseudo-phase transitions of Ising and Baxter–Wu models in two-dimensional finite-size lattices

This article offers a detailed analysis of pseudo-phase transitions of Ising and Baxter–Wu models in two-dimensional finite-size lattices. We carry out Wang–Landau sampling to obtain the density of states. Using microcanonical inflection-point analysis with microcanonical entropy, we obtain the order of the pseudo-phase transitions in the models. The microcanonical analysis results of the second-order transition for the Ising model and the first-order transition for the Baxter–Wu model are consistent with the traditional canonical results. In addition, the third-order transitions are found in both models, implying the universality of higher-order phase transitions.

Universality in the two-dimensional dilute Baxter-Wu model.

We study the question of universality in the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal field Δ. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau sampling at fixed values of Δ and a parallelized variant of the multicanonical approach performed at constant temperature T. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram indicates that the transition belongs to the universality class of the four-state Potts model. Previous controversies with respect to the nature of the transition are discussed and attributed to the presence of strong finite-size effects, especially as one approaches the pentacritical point of the model.

A First Look at Structural Properties of Long HP Model Sequences

The longest sequence in the literature of the HP model of protein folding is studied on a simple cubic lattice using replica-exchange Wang-Landau sampling. We find a lower ground state energy than found in previous studies, and, for the first time, study the structural and thermal behavior of this sequence during the folding process.

Thermodynamic stability of Pd-Ru alloy nanoparticles: combination of density functional theory calculations, supervised learning, and Wang-Landau sampling.

Solid-solution alloy nanoparticles (NPs) comprising Pd and Ru, which are immiscible in the bulk state, have been synthesised and show excellent catalytic performance. To date, most studies have evaluated the stability of alloy NPs at 0 K only. Because the thermodynamic stability of Pd-Ru alloy NPs may differ from that of the alloy in the bulk state, the stable configuration of the NPs must be evaluated under a finite temperature. Such stability evaluations are critical for developing the durable NPs as catalysts. Therefore, the thermodynamic stability of Pd-Ru alloy NPs was analysed using density functional theory (DFT), supervised learning (SL), and Wang-Landau sampling. We calculated the excess energy of Pd-Ru alloy NPs, which depends on their composition, structure, NP size, adatom type, and defects, and applied SL to all models. The excess energies of the Pd-Ru alloy NPs expressed by structural information, such as the surface-to-volume ratio, correlated with those calculated using DFT. Wang-Landau sampling based on the energy estimated by SL gave the thermodynamic stability of Pd-Ru alloy NPs with a stable configuration under a finite temperature. The solid-solution atomic configuration was subdivided into partially mixed configurations in the surface layer or in the core of the NPs, which is different from the bulk state. The partially mixed configuration was determined by the overall composition and surface properties. The findings from the combined method could contribute to a better understanding of the alloy-NP stability and their application in catalysis.

On the Thermodynamic Stability of Alloys: Combination of Neural Network Potential and Wang-Landau Sampling

On the Thermodynamic Stability of Alloys: Combination of Neural Network Potential and Wang-Landau Sampling

Thermodynamic Stabilities of PdRuM (M = Cu, Rh, Ir, Au) Alloy Nanoparticles Assessed by Wang–Landau Sampling Combined with DFT Calculations and Multiple Regression Analysis

Abstract Unique features of alloy nanoparticles (NPs) originate from the configuration of elements within NPs; solid solution and segregated configurations show different properties even with the same overall composition of elements. The configuration space of an alloy NP is exponentially expanded by an increase of the constituent elements. Besides, the configurational entropy in an alloy NP cannot be analytically estimated due to the heterogeneous surface. Revealing the stable configuration and the corresponding entropy in the extensive configuration space is difficult. Herein, Wang–Landau sampling, combined with density functional theory (DFT) calculations and multiple regression analysis, was used to assess the thermodynamic stabilities of PdRuM (M = Cu, Rh, Ir, Au) ternary alloy NPs. Specifically, the excess energies calculated by DFT were subjected to multiple regression analysis, and the obtained regression equations were used for Wang–Landau sampling. The thus-obtained configurational densities of states allowed us to estimate thermodynamic quantities, and hence, to predict stable configurations at a finite temperature. We conclude that the developed method is well suited to probing the stable configurations of multinary alloy NPs at a finite temperature.

A Deep Graph Network-Enhanced Sampling Approach to Efficiently Explore the Space of Reduced Representations of Proteins.

The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless development of computer architectures and algorithms. The consequent explosion in the number and extent of MD trajectories induces the need for automated methods to rationalize the raw data and make quantitative sense of them. Recently, an algorithmic approach was introduced by some of us to identify the subset of a protein’s atoms, or mapping, that enables the most informative description of the system. This method relies on the computation, for a given reduced representation, of the associated mapping entropy, that is, a measure of the information loss due to such simplification; albeit relatively straightforward, this calculation can be time-consuming. Here, we describe the implementation of a deep learning approach aimed at accelerating the calculation of the mapping entropy. We rely on Deep Graph Networks, which provide extreme flexibility in handling structured input data and whose predictions prove to be accurate and-remarkably efficient. The trained network produces a speedup factor as large as 105 with respect to the algorithmic computation of the mapping entropy, enabling the reconstruction of its landscape by means of the Wang–Landau sampling scheme. Applications of this method reach much further than this, as the proposed pipeline is easily transferable to the computation of arbitrary properties of a molecular structure.

Effects of lattice constraints in coarse-grained protein models.

We compare and contrast folding behavior in several coarse-grained protein models, both on- and off-lattice, in an attempt to uncover the effect of lattice constraints in these kinds of models. Using modern, extended ensemble Monte Carlo methods-Wang-Landau sampling, multicanonical sampling, replica-exchange Wang-Landau sampling, and replica-exchange multicanonical sampling, we investigate the thermodynamic and structural behavior of the protein Crambin within the context of the hydrophobic-polar, hydrophobic-"neutral"-polar (H0P), and semi-flexible H0P model frameworks. We uncover the folding process in all cases; all models undergo, at least, the two major structural transitions observed in nature-the coil-globule collapse and the folding transition. As the complexity of the model increases, these two major transitions begin to split into multi-step processes, wherein the lattice coarse-graining has a significant impact on the details of these processes. The results show that the level of structural coarse-graining is coupled to the level of interaction coarse-graining.

Replica exchange Wang–Landau sampling of long HP model sequences

Long sequences of the HP model of protein folding are studied using replica exchange Wang–Landau sampling. We find lower ground state energies than found from earlier simulations using PERM and replica exchange Monte Carlo and, for the first time, extract specific heat curves.

Wang–Landau sampling for estimation of the reliability of physical networks

Modern physical networks, for example in communication and transportation, can be interpreted as directed graphs. Network models are used to identify the probability that given nodes are connected, and therefore the effect of a failure at a given link. This is essential for network design, optimization, and reliability. In this study, we investigated three alternative ensembles for estimating network reliability using the Wang–Landau algorithm. The first performed random walks on a structure function having two possible states: connected and disconnected. The second used random walks on a reliability polynomial. The third combined random walks with the average of connecting probabilities. The accuracy and limitations of the three ensembles were compared by estimating the reliability of three network models: a bridge network, a ladder-type network, and a dodecahedron network. The simulation results showed that the use of a random walk on a structure function failed to produce estimates when applied to highly reliable networks in any of the three network types. The other two approaches performed efficiently for bridge or ladder-type networks at any level of network reliability. The random walk on a probability space using the 1∕t algorithm was the only ensemble that was able to yield accurate estimates for a dodecahedron network, though even this failed at the highest level of network reliability. The other two methods failed to converge within 108 Monte Carlo trials. The use of the average of connecting probabilities required a shorter computation time when applied to a large network. Methods that can reduce variance for large, highly reliable networks require further investigation.

Visual Tracking Using Wang–Landau Reinforcement Sampler

In this study, we present a novel tracking system, in which the tracking accuracy can be considerably enhanced by state prediction. Accordingly, we present a new Q-learning-based reinforcement method, augmented by Wang–Landau sampling. In the proposed method, reinforcement learning is used to predict a target configuration for the subsequent frame, while Wang–Landau sampler balances the exploitation and exploration degrees of the prediction. Our method can adapt to control the randomness of policy, using statistics on the number of visits in a particular state. Thus, our method considerably enhances conventional Q-learning algorithm performance, which also enhances visual tracking performance. Numerical results demonstrate that our method substantially outperforms other state-of-the-art visual trackers and runs in realtime because our method contains no complicated deep neural network architectures.

Tricritical point in the mixed-spin Blume-Capel model on three-dimensional lattices: Metropolis and Wang-Landau sampling approaches.

We investigate the mixed-spin Blume-Capel model with spin-1/2 and spin-S (S=1, 2, and 3) on the simple cubic and body-centered cubic lattices with single-ion-splitting crystal field (Δ) by using the Metropolis and the Wang-Landau Monte Carlo methods. We show that the two methods are complementary: The Wang-Landau algorithm is efficient to construct phase diagrams and the Metropolis algorithm allows access to large-sized lattices. By numerical simulations, we prove that the tricritical point is independent of S for both lattices. The positions of the tricritical point in the phase diagram are determined as [Δ_{t}/J=2.978(1); k_{B}T_{t}/J=0.439(1)] and [Δ_{t}/J=3.949(1); k_{B}T_{t}/J=0.854(1)] for the simple cubic and the body-centered cubic lattices, respectively. A very strong supercritical slowing down and hysteresis were observed in the Metropolis update close to first-order transitions for Δ>Δ_{t} in the body-centered cubic lattice. In addition, for both lattices we found a line of compensation points, where the two sublattice magnetizations have the same magnitude. We show that the compensation lines are also S independent.

An Adaptive Image Watermarking Method Combining SVD and Wang-Landau Sampling in DWT Domain

To keep a better trade-off between robustness and imperceptibility is difficult for traditional digital watermarks. Therefore, an adaptive image watermarking method combining singular value decomposition (SVD) and the Wang–Landau (WL) sampling method is proposed to solve the problem. In this method, the third-level approximate sub-band obtained by applying the three-level wavelet transform is decomposed by SVD to obtain the principal component, which is firstly selected as the embedded position. Then, the information is finally embedded into the host image by the scaling factor. The Wang–Landau sampling method is devoted to finding the best embedding coefficient through the proposed objective evaluation function, which is a global optimization algorithm. The embedding strength is adaptively adjusted by utilizing the historical experience, which overcomes the problem of falling into local optimization easily in many traditional optimization algorithms. To affirm the reliability of the proposed method, several image processing attacks are applied and the experimental results are given in detail. Compared with other existing related watermarking techniques based on both qualitative and quantitative evaluation parameters, such as peak signal to noise ratio (PSNR) and normalized cross-correlation (NC), this method has been proven to achieve a trade-off between robustness and invisibility.

Multicanonical Monte Carlo ensemble growth algorithm.

We present an ensemble Monte Carlo growth method to sample the equilibrium thermodynamic properties of random chains. The method is based on the multicanonical technique of computing the density of states in the energy space. Such a quantity is temperature independent, and therefore microcanonical and canonical thermodynamic quantities, including the free energy, entropy, and thermal averages, can be obtained by reweighting with a Boltzmann factor. The algorithm we present combines two approaches: The first is the Monte Carlo ensemble growth method, where a "population" of samples in the state space is considered, as opposed to traditional sampling by long random walks, or iterative single-chain growth. The second is the flat-histogram Monte Carlo, similar to the popular Wang-Landau sampling, or to multicanonical chain-growth sampling. We discuss the performance and relative simplicity of the proposed algorithm, and we apply it to known test cases.

Crambin Homologues in the H0P Lattice Model

To compare folding behavior among lattice proteins which have similar corresponding structures in nature, Crambin homologues are tested in the semi-flexible H0P lattice model using replica-exchange Wang-Landau sampling. Our simulation shows that, at low temperature, these lattice homologues have two common signals in their specific heat curves, implying similarity in the thermodynamic behaviors; while the structural behaviors are more diverse, showing the different stability of their ground state structures at very low temperature. The ground state structures of different homologues can also vary dramatically.

A First Look at Lattice Effects in Coarse-Grained Protein Models via Wang-Landau Simulations

In order to study the effects of lattice constraints on coarse-grained protein models, we apply Wang-Landau sampling to the continuum analogue of the hydrophobic-polar (HP) lattice protein model. The continuum version is inspired by the AB polymer model but incorporates potentials chosen specifically to mimic those of the lattice case. Because of their relative simplicity, both the lattice and continuum models offer significant computational advantage over all-atom simulations, but the impact of the additional lattice constraint on generic folding behavior is unknown. In this preliminary study, we compare and contrast thermodynamics during the folding process of the continuum model to the original HP lattice protein model for sequences mapped from Crambin, a 46 amino acid plant protein. We find that the folding process for both of these coarse-grained models is quite similar, with major structural transitions occurring at almost exactly the same temperatures.

Schottky-Anormaly of the Ising Model on Kagomé Lattice in an External Magnetic Field

The Schottky anomaly is one of the most universal phenomena in physical science and materials engineering. The Schottky anomaly is a prominent finite peak in the specific heat of materials at a low temperature, and it is the most important tool in understanding the unknown properties of new materials by using experimental techniques. Because kagome lattice has inherent frustration, the properties of materials on a kagome lattice are very profound, and it plays vital roles in studying new phenomena in science and engineering. Although both the Schottky anomaly and kagome lattice are important, the properties of the Schottky anomaly on a kagome lattice are not known. Here, we investigate the properties of the Schottky anomaly on a kagome lattice for the first time by using the Wang-Landau sampling method.

Advanced wang–landau monte carlo‐based tracker for abrupt motions

Conventional tracking methods rarely consider abrupt motions and easily fail to track the abrupt motion of an object because they are based on the assumption of smooth motion. To assuage this problem, we propose a novel tracking algorithm combining the background subtraction method with the Wang–Landau Monte Carlo (WLMC) sampling method for dealing with abrupt motions effectively. First, the visual background extractor (ViBe), a background subtraction technique, is introduced to detect the object roughly. Second, we integrate the density‐of‐states term and ViBe information into a WLMC‐based tracking framework. By employing the density‐of states term and ViBe information, the Wang–Landau sampling scheme efficiently tracks the target in the whole state space in a short time. Third, in order to obtain good performance in terms of scalability, an independent fast scale estimation method is applied. Experimental results in both quantitative and qualitative measures demonstrate that our algorithm efficiently samples and tracks the target not only in position but also in scale variance accurately and robustly. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Statistical physics meets biochemistry: Wang-Landau sampling of the HP model of protein folding

We describe a minimalistic model of a protein undergoing folding into its native (ground) state. This HP protein model is composed of a lattice polymer with two types of monomers: hydrophobic (H) and polar (P). The specific sequence of the two types of monomers is often chosen to mimic real proteins. We explain how these kinds of minimalistic models are well suited to study fundamental phenomena of complex biological processes such as protein folding. We then show how Monte Carlo simulations and, in particular, Wang-Landau sampling, together with a properly chosen trial move set, provide a powerful computational means to investigate the rough energy landscape and native state(s) of this intriguingly simple system. We include the computer code which can be used to reproduce the results we discuss or as a template for further research.