1,123 research outputs found

    Ensemble of expanded ensembles: A generalized ensemble approach with enhanced flexibility and parallelizability

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    Over the past decade, alchemical free energy methods like Hamiltonian replica exchange (HREX) and expanded ensemble (EXE) have gained popularity for the computation of solvation free energies and binding free energies. These methods connect the end states of interest via nonphysical pathways defined by states with different modified Hamiltonians. However, there exist systems where traversing all alchemical intermediate states is challenging, even if alchemical biases (e.g., in EXE) or coordinate exchanges (e.g., in HREX) are applied. This issue is exacerbated when the state space is multidimensional, which can require extensive communications between hundreds of cores that current parallelization schemes do not fully support. To address this challenge, we present the method of ensemble of expanded ensembles (EEXE), which integrates the principles of EXE and HREX. Specifically, the EEXE method periodically exchanges coordinates of EXE replicas sampling different ranges of states and allows combining weights across replicas. With the solvation free energy calculation of anthracene, we show that the EEXE method achieves accuracy akin to the EXE and HREX methods in free energy calculations, while offering higher flexibility in parameter specification. Additionally, its parallelizability opens the door to wider applications, such as estimating free energy profiles of serial mutations. Importantly, extensions to the EEXE approach can be done asynchronously, allowing looser communications between larger numbers of loosely coupled processors, such as when using cloud computing, than methods such as replica exchange. They also allow adaptive changes to the parameters of ensembles in response to data collected. All algorithms for the EEXE method are available in the Python package ensemble_md, which offers an interface for EEXE simulation management without modifying the source code in GROMACS

    Bayesian Estimation of Regression Quantiles in the Presence of Autocorrelated Errors

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    This is a study of Bayesian quantile regression that broadly considered the estimation of regression quantiles in the presence of autocorrelated error. Regression models are based on several important statistical assumptions upon which their inferences rely. Autocorrelation of the error terms violates the ordinary least squares regression assumption that error terms are uncorrelated which invalidate Gauss Markov theorem. This study designed schemes for estimation and making inference of regression quantiles in the presence of autocorrelated errors using Bayesian approach. Bayesian method to quantile regression models regards unknown parameters as random variables and the parameter uncertainty was taken into account without relying on asymptotic approximations.The empirical analysis used the data set from Central Bank of Nigeria bulletin which comprised of Nigeria GDP growth, export rate, import rate, inflation rate and exchange rate from the period of 1985–2018. Bayesian inferences with autocorrelated error in the framework of quantile regression accounted better for the variability in the distribution of autocorrelation and gave robust and less biased estimates in dealing with non normality and non constant variance assumptions, the results of the research reported minimal Mean Square Errors in Bayesian approach than classical approach across the entire distribution. Keywords: Bayesian Estimation; Regression Quantiles; Autocorrelated Errors; Regression Analysis

    Improved Distributed Algorithms for Random Colorings

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    Markov Chain Monte Carlo (MCMC) algorithms are a widely-used algorithmic tool for sampling from high-dimensional distributions, a notable example is the equilibirum distribution of graphical models. The Glauber dynamics, also known as the Gibbs sampler, is the simplest example of an MCMC algorithm; the transitions of the chain update the configuration at a randomly chosen coordinate at each step. Several works have studied distributed versions of the Glauber dynamics and we extend these efforts to a more general family of Markov chains. An important combinatorial problem in the study of MCMC algorithms is random colorings. Given a graph GG of maximum degree Δ\Delta and an integer kΔ+1k\geq\Delta+1, the goal is to generate a random proper vertex kk-coloring of GG. Jerrum (1995) proved that the Glauber dynamics has O(nlogn)O(n\log{n}) mixing time when k>2Δk>2\Delta. Fischer and Ghaffari (2018), and independently Feng, Hayes, and Yin (2018), presented a parallel and distributed version of the Glauber dynamics which converges in O(logn)O(\log{n}) rounds for k>(2+ε)Δk>(2+\varepsilon)\Delta for any ε>0\varepsilon>0. We improve this result to k>(11/6δ)Δk>(11/6-\delta)\Delta for a fixed δ>0\delta>0. This matches the state of the art for randomly sampling colorings of general graphs in the sequential setting. Whereas previous works focused on distributed variants of the Glauber dynamics, our work presents a parallel and distributed version of the more general flip dynamics presented by Vigoda (2000) (and refined by Chen, Delcourt, Moitra, Perarnau, and Postle (2019)), which recolors local maximal two-colored components in each step.Comment: 25 pages, 2 figure
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