Large‐scale asynchronous and distributed multidimensional replica exchange molecular simulations and efficiency analysis

We describe methods to perform replica exchange molecular dynamics (REMD) simulations asynchronously (ASyncRE). The methods are designed to facilitate large scale REMD simulations on grid computing networks consisting of heterogeneous and distributed computing environments as well as on homogeneous high‐performance clusters. We have implemented these methods on NSF (National Science Foundation) XSEDE (Extreme Science and Engineering Discovery Environment) clusters and BOINC (Berkeley Open Infrastructure for Network Computing) distributed computing networks at Temple University and Brooklyn College at CUNY (the City University of New York). They are also being implemented on the IBM World Community Grid. To illustrate the methods, we have performed extensive (more than 60 ms in aggregate) simulations for the beta‐cyclodextrin‐heptanoate host‐guest system in the context of one‐ and two‐dimensional ASyncRE, and we used the results to estimate absolute binding free energies using the binding energy distribution analysis method. We propose ways to improve the efficiency of REMD simulations: these include increasing the number of exchanges attempted after a specified molecular dynamics (MD) period up to the fast exchange limit and/or adjusting the MD period to allow sufficient internal relaxation within each thermodynamic state. Although ASyncRE simulations generally require long MD periods (>picoseconds) per replica exchange cycle to minimize the overhead imposed by heterogeneous computing networks, we found that it is possible to reach an efficiency similar to conventional synchronous REMD, by optimizing the combination of the MD period and the number of exchanges attempted per cycle. © 2015 Wiley Periodicals, Inc.     

Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis–Hastings Method

Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.     

Experimental analysis of propagation of fatigue crack on gears

Gears of different sizes and with different systems of loading are indispensable components of machines and devices. When optimizing such gear assemblies, on of the most important parameters is their required service life. To calculate the service life as precisely and reliably as possible, researchers need to use the required mathematical models for describing loading, the geometry, properties of materials and fracture mechanics parameters. The accuracy and reliability of the gear model assemblies can be compared only with appropriate experimental results. To this end, the authors have used and developed a series of methods and test pieces. A comparison of results has shown that the models and approaches are adequate.     

The temperature intervals with global exchange of replicas empirical accelerated sampling method: parameter sensitivity and extension to a complex molecular system

The recently developed "temperature intervals with global exchange of replicas" (TIGER2) algorithm is an efficient replica-exchange sampling algorithm that provides the freedom to specify the number of replicas and temperature levels independently of the size of the system and temperature range to be spanned, thus making it particularly well suited for sampling molecular systems that are considered to be too large to be sampled using conventional replica exchange methods. Although the TIGER2 method is empirical in nature, when appropriately applied it is able to provide sampling that satisfies the balance condition and closely approximates a Boltzmann-weighted ensemble of states. In this work, we evaluated the influence of factors such as temperature range, temperature spacing, replica number, and sampling cycle design on the accuracy of a TIGER2 simulation based on molecular dynamics simulations of alanine dipeptide in implicit solvent. The influence of these factors is further examined by calculating the properties of a complex system composed of the B1 immunoglobulin-binding domain of streptococcal protein G (protein G) in aqueous solution. The accuracy of a TIGER2 simulation is particularly sensitive to the maximum temperature level selected for the simulation. A method to determine the appropriate maximum temperature level to be used in a TIGER2 simulation is presented.     

Hierarchical neural networks for the storage of correlated memories

A class of hierarchical neural network models introduced by Dotsenko for the storage and associative recall of strongly correlated memories is studied analytically and numerically. In these models, patterns stored in higher levels of the hierarchy represent generalized categories and those stored in lower levels describe finer details. We first show that the models originally proposed by Dotsenko have a serious flaw: they are not able to detect or correct errors in categorization which may be present in the input. We then describe three different models which attempt to overcome this shortcoming of the original models. In the first model, the interaction between different levels of the hierarchy has the form of an external field conjugate to memories stored in the lower level. In the second model, a three-spin interaction term is included in addition to the usual binary interactions of the Hopfield type. The third model makes use of a time delay mechanism to induce, if necessary, transitions between memory states and their complements. Detailed analytical and numerical studies of the performance of these models are presented. Our analysis shows that all three models are able to detect and also to correct in varying degrees any error in categorization that may be present in the input pattern.     

Free‐energy calculations of residue mutations in a tripeptide using various methods to overcome inefficient sampling

Previous free‐energy calculations have shown that the seemingly simple transformation of the tripeptide KXK to KGK in water holds some unobvious challenges concerning the convergence of the forward and backward thermodynamic integration processes (i.e., hysteresis). In the current study, the central residue X was either alanine, serine, glutamic acid, lysine, phenylalanine, or tyrosine. Interestingly, the transformation from alanine to glycine yielded the highest hysteresis in relation to the extent of the chemical change of the side chain. The reason for that could be attributed to poor sampling of φ₂/ψ₂ dihedral angles along the transformation. Altering the nature of alanine's C_β atom drastically improved the sampling and at the same time led to the identification of high energy barriers as cause for it. Consequently, simple strategies to overcome these barriers are to increase simulation time (computationally expensive) or to use enhanced sampling techniques such as Hamiltonian replica exchange molecular dynamics and one‐step perturbation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Characterization of conformational equilibria through Hamiltonian and temperature replica-exchange simulations: assessing entropic and environmental effects

Molecular dynamics simulations based on the replica-exchange framework (REMD) are emerging as a useful tool to characterize the conformational variability that is intrinsic to most chemical and biological systems. In this work, it is shown that a simple extension of the replica-exchange method, known as Hamiltonian REMD, greatly facilitates the characterization of conformational equilibria across large energetic barriers, or in the presence of substantial entropic effects, overcoming some of the difficulties of REMD based on temperature alone. In particular, a comparative assessment of the HREMD and TREMD approaches was made, through computation of the gas-phase free-energy difference between the so-called D(2d) and S(4) states of tetrabutylammonium (TBA), an ionic compound of frequently used in biophysical studies of ion channels. Taking advantage of the greater efficiency of the HREMD scheme, the conformational equilibrium of TBA was characterized in a variety of conditions. Simulation of the gas-phase equilibrium in the 100-300 K range allowed us to compute the entropy difference between these states as well as to describe its temperature dependence. Through HREMD simulations of TBA in a water droplet, the effect of solvation on the conformational equilibrium was determined. Finally, the equilibrium of TBA in the context of a simplified model of the binding cavity of the KcsA potassium channel was simulated, and density maps for D(2d) and S(4) states analogous to those derived from X-ray crystallography were constructed. Overall, this work illustrates the potential of the HREMD approach in the context of computational drug design, ligand-receptor structural prediction and more generally, molecular recognition, where one of the most challenging issues remains to account for conformational flexibility as well for the solvation and entropic effects thereon.     

Replica Symmetry Breaking in FRET‐Assisted Random Laser Based on Electrospun Polymer Fiber

Spin‐glass theory has been widely introduced to describe the statistical behaviors in complex physical systems. By analogy between disorder photonics and other complex systems, the glassy behavior, especially the replica symmetry breaking (RSB) phenomenon, has been observed in random lasers. However, previous studies only analyzed the statistical properties of the random laser systems with single gain material. Here, the first experimental evidence of the glassy behavior in a random laser with complex energy level structure is reported. This novel random laser is demonstrated based on the electrospun polymer fibers with the assistance of Förster resonance energy transfer (FRET). The electrospinning technology employed in the experiment herein promises high‐volume production of random laser devices with multiple energy levels, enabling the comprehensive investigation of lasing properties in multi‐energy level random laser system. Clear paramagnetic phase and spin‐glass phase are observed in the FRET‐assisted random laser under different pump energies. The RSB phase transition is verified to occur at the laser threshold, which is robust among the random lasers with different donor–acceptor ratio. The finding of RSB in FRET‐assisted random laser provides a new statistical analysis method toward the laser system with complex energy level, for example, quantum cascade laser.     

不确定海洋环境中的模态子空间重构稳健定位方法

实际的海洋是一个不确定的声传播环境,常规的匹配场方法在进行目标定位时会遇到环境失配的问题,导致定位性能下降.在不确定的海洋环境中,声场传播中的一部分简正波模态受到声场不确定性的影响较小.基于此,本文提出了一种模态子空间重构的稳健定位方法.该方法使用稳定的模态来重构拷贝场向量,相比于常规匹配场定位方法中使用全阶模态来构造拷贝场向量,其定位结果更加稳健.利用计算机仿真数据和海试数据进行了定位性能分析,并给出了常规匹配场定位方法和稳健最大似然定位方法作为对比.研究结果表明:1)不确定海洋环境中,常规匹配场定位方法即使在较高的信噪比条件下其定位性能也较差.2)模态子空间重构定位方法的性能优于常规匹配场定位方法和稳健最大似然方法.     

Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.