Nonreversible Markov Chain Monte Carlo Algorithm for Efficient Generation of Self-Avoiding Walks

We introduce an efficient nonreversible Markov chain Monte Carlo algorithm to generate self-avoiding walks with a variable endpoint. In two dimensions, the new algorithm slightly outperforms the two-move nonreversible Berretti-Sokal algorithm introduced by H. Hu, X. Chen, and Y. Deng, while for three-dimensional walks, it is 3–5 times faster. The new algorithm introduces nonreversible Markov chains that obey global balance and allow for three types of elementary moves on the existing self-avoiding walk: shorten, extend or alter conformation without changing the length of the walk.

A Bayesian parametric approach to the retrieval of the atmospheric number size distribution from lidar data

We consider the problem of reconstructing the number size distribution (or particle size distribution) in the atmosphere from lidar measurements of the extinction and backscattering coefficients. We assume that the number size distribution can be modeled as a superposition of log-normal distributions, each one defined by three parameters: mode, width and height. We use a Bayesian model and a Monte Carlo algorithm to estimate these parameters. We test the developed method on synthetic data generated by distributions containing one or two modes and perturbed by Gaussian noise as well as on three datasets obtained from AERONET. We show that the proposed algorithm provides good results when the right number of modes is selected. In general, an overestimate of the number of modes provides better results than an underestimate. In all cases, the PM1, PM2.5 and PM10 concentrations are reconstructed with tolerable deviations.

THEORETICAL AND COMPUTER MODELS OF 3-DIMENSIONAL GRAIN BOUNDARY MIGRATION WITH MOBILE PARTICLES

In this work, the migration of a three-dimensional (3D) spherical crystal in the presence of mobile particles using a Monte Carlo algorithm was studied. Different concentrations of particles (<i>f</i>) and different particle mobility (<i>M_p</i>) were used. It was found that the grain size reaches a critical radius (<i>R_c</i>) which depends exclusively on <i>f</i>. This dependence can be written as: <i>R_c</i>∝<i>f</i>^1/3. The dynamic equation of grain size evolution and its analytical solution were also found. The analytical solution proposed fits successfully the simulation results. The particle fraction in the grain boundary was also found analytically and it fits the computational data.

Prediction of the RNA Tertiary Structure Based on a Random Sampling Strategy and Parallel Mechanism

Background: Macromolecule structure prediction remains a fundamental challenge of bioinformatics. Over the past several decades, the Rosetta framework has provided solutions to diverse challenges in computational biology. However, it is challenging to model RNA tertiary structures effectively when the de novo modeling of RNA involves solving a well-defined small puzzle.Methods: In this study, we introduce a stepwise Monte Carlo parallelization (SMCP) algorithm for RNA tertiary structure prediction. Millions of conformations were randomly searched using the Monte Carlo algorithm and stepwise ansatz hypothesis, and SMCP uses a parallel mechanism for efficient sampling. Moreover, to achieve better prediction accuracy and completeness, we judged and processed the modeling results.Results: A benchmark of nine single-stranded RNA loops drawn from riboswitches establishes the general ability of the algorithm to model RNA with high accuracy and integrity, including six motifs that cannot be solved by knowledge mining–based modeling algorithms. Experimental results show that the modeling accuracy of the SMCP algorithm is up to 0.14 Å, and the modeling integrity on this benchmark is extremely high.Conclusion: SMCP is an ab initio modeling algorithm that substantially outperforms previous algorithms in the Rosetta framework, especially in improving the accuracy and completeness of the model. It is expected that the work will provide new research ideas for macromolecular structure prediction in the future. In addition, this work will provide theoretical basis for the development of the biomedical field.

Bayesian Model Updating Based on Kriging Surrogate Model and Simulated Annealing Algorithm

Aiming at the problem of difficulty in selecting the proposal distribution and low computational efficiency in the traditional Markov chain Monte Carlo algorithm, a Bayesian model updating method using surrogate model technology and simulated annealing algorithm is proposed. Firstly, the Kriging surrogate model is used to mine the implicit relationship between the structural parameters to be updated and the corresponding dynamic responses, and the Kriging model that meets the accuracy requirement is used to replace the complex finite element model to participate in the iterative calculation to improve the model updating efficiency. Then, the simulated annealing algorithm is introduced to reorganize the Markov chains from different proposal distributions to obtain high-quality posterior samples, which are used to estimate the parameters posterior distributions. Finally, a space truss structure is used to verify the effectiveness of the proposed method.

A New Discrete Implicit Monte Carlo Scheme for Simulating Radiative Transfer Problems

We present a new algorithm for radiative transfer—based on a statistical Monte Carlo approach—that does not suffer from teleportation effects, on the one hand, and yields smooth results, on the other hand. Implicit Monte Carlo (IMC) techniques for modeling radiative transfer have existed from the 1970s. When they are used for optically thick problems, however, the basic algorithm suffers from “teleportation” errors, where the photons propagate faster than the exact physical behavior, due to the absorption-blackbody emission processes. One possible solution is to use semianalog Monte Carlo, in its new implicit form (ISMC), which uses two kinds of particles, photons and discrete material particles. This algorithm yields excellent teleportation-free results, but it also produces noisier solutions (relative to classic IMC), due to its discrete nature. Here, we derive a new Monte Carlo algorithm, Discrete Implicit Monte Carlo (DIMC), which also uses the idea of two kinds of discrete particles, and thus does not suffer from teleportation errors. DIMC implements the IMC discretization and creates new radiation photons for each time step, unlike ISMC. Using the continuous absorption technique, DIMC yields smooth results like classic IMC. One of the main elements of the algorithm is the avoidance of the explosion of the particle population, by using particle merging. We test the new algorithm on 1D and 2D cylindrical problems, and show that it yields smooth, teleportation-free results. We finish by demonstrating the power of the new algorithm on a classic radiative hydrodynamic problem—an opaque radiative shock wave. This demonstrates the power of the new algorithm for astrophysical scenarios.

Randomized Local Network Computing: Derandomization Beyond Locally Checkable Labelings

We carry on investigating the line of research questioning the power of randomization for the design of distributed algorithms. In their seminal paper, Naor and Stockmeyer [STOC 1993] established that, in the context of network computing in which all nodes execute the same algorithm in parallel, any construction task that can be solved locally by a randomized Monte-Carlo algorithm can also be solved locally by a deterministic algorithm. This result, however, holds only for distributed tasks such that the correctness of their solutions can be locally checked by a deterministic algorithm. In this article, we extend the result of Naor and Stockmeyer to a wider class of tasks. Specifically, we prove that the same derandomization result holds for every task such that the correctness of their solutions can be locally checked using a 2-sided error randomized Monte-Carlo algorithm.

On the Hierarchical Bernoulli Mixture Model Using Bayesian Hamiltonian Monte Carlo

The model developed considers the uniqueness of a data-driven binary response (indicated by 0 and 1) identified as having a Bernoulli distribution with finite mixture components. In social science applications, Bernoulli’s constructs a hierarchical structure data. This study introduces the Hierarchical Bernoulli mixture model (Hibermimo), a new analytical model that combines the Bernoulli mixture with hierarchical structure data. The proposed approach uses a Hamiltonian Monte Carlo algorithm with a No-U-Turn Sampler (HMC/NUTS). The study has performed a compatible syntax program computation utilizing the HMC/NUTS to analyze the Bayesian Bernoulli mixture aggregate regression model (BBMARM) and Hibermimo. In the model estimation, Hibermimo yielded a result of ~90% compliance with the modeling of each district and a small Widely Applicable Information Criteria (WAIC) value.