Monte Carlo-based Methods Research Articles

Simulating Linear Sweep Voltammetry from First-Principles: Application to Electrochemical Oxidation of Water on Pt(111) and Pt3Ni(111)

Cyclic voltammetry is a fundamental experimental method for characterizing adsorbates on electrochemical surfaces. We present a model for the electrochemical solid–liquid interface, and we simulate the linear sweep voltammogram of the electrochemical oxidation of H2O on Pt(111) and Pt3Ni(111), based on kinetic and thermodynamic parameters computed by Density Functional Theory (DFT) and the dynamics of the system solved through Monte Carlo-based methods. The model predicts onset of OH and O formation in good agreement with voltammetric and ex situ XPS experiments.

Fine-Mapping CASP8 Risk Variants in Breast Cancer

Multiple genome-wide and candidate gene association studies have been conducted in search of common risk variants for breast cancer. Recent large meta analyses, consolidating evidence from these studies, have been consistent in highlighting the caspase-8 (CASP8) gene as important in this regard. To define a risk haplotype and map the CASP8 gene region with respect to underlying susceptibility variant/s, we screened four genes in the CASP8 region on 2q33-q34 for breast cancer risk. Two independent data sets from the United Kingdom and the United States, including 3,888 breast cancer cases and controls, were genotyped for 45 tagging single nucleotide polymorphisms (tSNP) in the expanded CASP8 region. SNP and haplotype association tests were carried out using Monte Carlo-based methods. We identified a three-SNP haplotype across rs3834129, rs6723097, and rs3817578 that was significantly associated with breast cancer (P < 5 × 10(-6)), with a dominant risk ratio and 95% CI of 1.28 (1.21-1.35) and frequency of 0.29 in controls. Evidence for this risk haplotype was extremely consistent across the two study sites and also consistent with previous data. This three-SNP risk haplotype represents the best characterization so far of the chromosome upon which the susceptibility variant resides. Characterization of the risk haplotype provides a strong foundation for resequencing efforts to identify the underlying risk variant, which may prove useful for individual-level risk prediction, and provide novel insights into breast carcinogenesis.

Comparison of Monte Carlo methods for fluorescence molecular tomography-computational efficiency

The Monte Carlo method is an accurate model for time-resolved quantitative fluorescence tomography. However, this method suffers from low computational efficiency due to the large number of photons required for reliable statistics. This paper presents a comparison study on the computational efficiency of three Monte Carlo-based methods for time-domain fluorescence molecular tomography. The methods investigated to generate time-gated Jacobians were the perturbation Monte Carlo (pMC) method, the adjoint Monte Carlo (aMC) method and the mid-way Monte Carlo (mMC) method. The effects of the different parameters that affect the computation time and statistics reliability were evaluated. Also, the methods were applied to a set of experimental data for tomographic application. In silico results establish that, the investigated parameters affect the computational time for the three methods differently (linearly, quadratically, or not significantly). Moreover, the noise level of the Jacobian varies when these parameters change. The experimental results in preclinical settings demonstrates the feasibility of using both aMC and pMC methods for time-resolved whole body studies in small animals within a few hours. Among the three Monte Carlo methods, the mMC method is a computationally prohibitive technique that is not well suited for time-domain fluorescence tomography applications. The pMC method is advantageous over the aMC method when the early gates are employed and large number of detectors is present. Alternatively, the aMC method is the method of choice when a small number of source-detector pairs are used.

Rao-Blackwellization of Particle Markov Chain Monte Carlo Methods Using Forward Filtering Backward Sampling

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distribution. In recent years there has been an increased interest in Monte Carlo-based methods, often involving particle filters, for approximate smoothing in nonlinear and/or non-Gaussian state-space models. One such method is to approximate filter distributions using a particle filter and then to simulate, using backward kernels, a state trajectory backwards on the set of particles. We show that by simulating multiple realizations of the particle filter and adding a Metropolis-Hastings step, one obtains a Markov chain Monte Carlo scheme whose stationary distribution is the exact smoothing distribution. This procedure expands upon a similar one recently proposed by Andrieu, Doucet, Holenstein, and Whiteley. We also show that simulating multiple trajectories from each realization of the particle filter can be beneficial from a perspective of variance versus computation time, and illustrate this idea using two examples.

Operations optimization of multireservoir systems using storage moments equations

Fletcher–Ponnambalam presented a new model for considering the balance equation of the storage volume of the reservoir using indicator functions. For stochastic inflows, the two storage moments of this balance equation, namely, the mean and variance, calculated using a random release policy were found to be quite accurate unlike any known models. Significantly, this model required no discretization of storage volumes or releases. In this paper, this work has been extended to two new cases: for multireservoir systems which require further consideration of the stochastic releases and for arbitrary distribution of inflows using the Beta-equivalent Kumaraswamy distribution which has a simpler form than Beta. The randomized release policies are easy to use even in a multireservoir problem. The Parambikulm-Aliyar Project from India is used as a case study. Results show accurate predictions of mean of storages in the multireservoir case but show the need for further improvement in the standard deviations of storages. The optimal benefits and the policies obtained are shown to be at least as good as obtained using Monte Carlo-based methods.

Evaluation of fecal mRNA reproducibility via a marginal transformed mixture modeling approach

BackgroundDeveloping and evaluating new technology that enables researchers to recover gene-expression levels of colonic cells from fecal samples could be key to a non-invasive screening tool for early detection of colon cancer. The current study, to the best of our knowledge, is the first to investigate and report the reproducibility of fecal microarray data. Using the intraclass correlation coefficient (ICC) as a measure of reproducibility and the preliminary analysis of fecal and mucosal data, we assessed the reliability of mixture density estimation and the reproducibility of fecal microarray data. Using Monte Carlo-based methods, we explored whether ICC values should be modeled as a beta-mixture or transformed first and fitted with a normal-mixture. We used outcomes from bootstrapped goodness-of-fit tests to determine which approach is less sensitive toward potential violation of distributional assumptions.ResultsThe graphical examination of both the distributions of ICC and probit-transformed ICC (PT-ICC) clearly shows that there are two components in the distributions. For ICC measurements, which are between 0 and 1, the practice in literature has been to assume that the data points are from a beta-mixture distribution. Nevertheless, in our study we show that the use of a normal-mixture modeling approach on PT-ICC could provide superior performance.ConclusionsWhen modeling ICC values of gene expression levels, using mixture of normals in the probit-transformed (PT) scale is less sensitive toward model mis-specification than using mixture of betas. We show that a biased conclusion could be made if we follow the traditional approach and model the two sets of ICC values using the mixture of betas directly. The problematic estimation arises from the sensitivity of beta-mixtures toward model mis-specification, particularly when there are observations in the neighborhood of the the boundary points, 0 or 1. Since beta-mixture modeling is commonly used in approximating the distribution of measurements between 0 and 1, our findings have important implications beyond the findings of the current study. By using the normal-mixture approach on PT-ICC, we observed the quality of reproducible genes in fecal array data to be comparable to those in mucosal arrays.

“A comparison between Gauss-Newton and Markov-chain Monte Carlo-based methods for inverting spectral induced-polarization data for Cole-Cole parameters,” GEOPHYSICS, 73, no. 6, F247–F259

“A comparison between Gauss-Newton and Markov-chain Monte Carlo-based methods for inverting spectral induced-polarization data for Cole-Cole parameters,” G<scp>EOPHYSICS</scp>, <b>73</b>, no. 6, F247–F259

Analytical SIR for Self-Organizing Wireless Networks

The signal to interference ratio (SIR) in the presence of multipath fading, shadowing and path loss is a valuable parameter for studying the capacity of a wireless system. This paper presents a new generalized path loss equation that takes into account the large-scale path loss as well as the small-scale multipath fading. The probability density function (pdf) of the SIR for selforganising wireless networks with Nakagami-m channel model is analytically derived using the new path loss equation. We chose the Nakagami-m channel fading model because it encompasses a large class of fading channels. The results presented show good agreement between the analytical and Monte Carlo-based methods. Furthermore, the pdf of the signal to interference plus noise ratio (SINR) is provided as an extension to the SIR derivation. The analytical derivation of the pdf for a single interferer in this paper lays a solid foundation to calculate the statistics for multiple interferers.

Multiscale molecular modeling in nanostructured material design and process system engineering

Atomistic-based simulations such as molecular mechanics, molecular dynamics, and Monte Carlo-based methods have come into wide use for material design. Using these atomistic simulation tools, we can analyze molecular structure on the scale of 0.1–10 nm. However, difficulty arises concerning limitations of the time and length scale involved in the simulation. Although a possible molecular structure can be simulated by the atom-based simulations, it is less realistic to predict the mesoscopic structure defined on the scale of 100–1000 nm, for example the morphology of polymer blends and composites, which often dominates actual material properties. For the morphology on these scales, mesoscopic simulations such as the dynamic mean field density functional theory and dissipative particle dynamics are available as alternatives to atomistic simulations. It is therefore inevitable to adopt a mesoscopic simulation technique and bridge the gap between atomistic and mesoscopic simulations for an effective material design. Furthermore, it is possible to transfer the simulated mesoscopic structure to finite elements modeling tools for calculating macroscopic properties for the systems of interest. In this contribution, a hierarchical procedure for bridging the gap between atomistic and macroscopic modeling passing through mesoscopic simulations will be presented and discussed. The concept of multiscale (or many scale) modeling will be outlined, and examples of applications of single scale and multiscale procedures for nanostructured systems of industrial interest will be presented. In particular the following industrial applications will be considered: (i) polymer-organoclay nanocomposites of a montmorillonite–polymer–surface modifier system; (ii) mesoscale simulation for diblock copolymers with dispersion of nanoparticels; (iii) polymer–carbon nanotubes system and (iv) applications of multiscale modeling for process systems engineering.

Monte Carlo-based filtering for fatigue crack growth estimation

The lifetime prediction of industrial and structural components is a recognized valuable task for operating safely and managing with profit the production of industrial plants. One way to address this prognostic challenge is by implementing model-based estimation methods for inferring the life evolution of a component on the basis of a sequence of noisy measurements related to its state. In practice, the non-linearity of the state evolution and/or the non-Gaussianity of the associated noise may lead to inaccurate prognostic estimations even with advanced approaches, such as the Kalman, Gaussian-sum and grid-based filters. An alternative approach which seems to offer significant potential of successful application is one which makes use of Monte Carlo-based estimation methods, also called particle filters. The present paper demonstrates such potential on a problem of crack propagation under uncertain monitoring conditions. The crack growth process, taken from literature, is described by a non-linear model affected by non-additive noises. To the authors’ best knowledge, this is the first time that (i) a particle filtering technique is applied to a structural prognostic problem and (ii) the filter is modified so as to estimate the distribution of the component’s remaining lifetime on the basis of observations taken at predefined inspection times.

Identification of Time-Varying Autoregressive Systems Using Maximuma PosterioriEstimation

Time-varying systems and nonstationary signals arise naturally in many engineering applications, such as speech, biomedical, and seismic signal processing. Thus, identification of the time-varying parameters is of crucial importance in the analysis and synthesis of these systems. The present time-varying system identification techniques require either demanding computation power to draw a large amount of samples (Monte Carlo-based methods) or a wise selection of basis functions (basis expansion methods). In this paper, the identification of time-varying autoregressive systems is investigated. It is formulated as a Bayesian inference problem with constraints on the conditional and prior probabilities of the time-varying parameters. These constraints can be set without further knowledge about the physical system. In addition, only a few hyper parameters need tuning for better performance. Based on these probabilistic constraints, an iterative algorithm is proposed to evaluate the maximum a posteriori estimates of the parameters. The proposed method is computationally efficient since random sampling is no longer required. Simulation results show that it is able to estimate the time-varying parameters reasonably well and a balance between the bias and variance of the estimation is achieved by adjusting the hyperparameters. Moreover, simulation results indicate that the proposed method outperforms the particle filter in terms of estimation errors and computational efficiency.

WE-B-351-02: Patient Dose Estimates From CT Examinations

Radiation dose from computed tomography has been an important issue for medical physicists for some time. This issue has increased in significance in the past several years due to advances in multidetector CT, which have resulted in increased utilization in areas such as pediatric CT, cardiac CT and even screening applications. Some of the key issues currently facing the medical physics community are assessing dose to patients from these various exams. One of the key building blocks to these assessments is the estimation of organ dose. The purpose of this presentation is to describe an approach to estimating organ doses to patients using Monte Carlo-based simulation methods. In this approach, both the scanner and patient are modeled in some detail and a CT exam may be simulated. The detailed modeled of the CT scanner is created by including information such as the source spectra and filtration, its geometry, beam collimation and the path that the source travels around the patient (such as the path during a helical CT exam). The development, testing and validation of these models will be discussed. Patient models generally fall into two categories. The first consists of geometric descriptions of organs (based on cones, cylinders, etc.) such as the MIRD phantom. The second consists of voxelized descriptions of patient anatomy that are created based on actual patient scans. In these, radiosensitive organs are identified in the image data to create a voxelized model of the patient geometry. For both types of models, there are challenges to create models representing patients of different sizes, ages and genders. Once both the scanner and patient are modeled, then different scan protocols can be simulated using a Monte Carlo based software package (such as MCNP or EGS). This involves selecting a scanner model, a patient model and then selecting a set of technical parameters, such as one would do for an actual scan — including body region being examined, etc. The Monte Carlo software then simulates the specified scan and tallies absorbed dose in each voxel or geometric unit of the patient model, which then allows the calculation of either mean organ dose or the distribution of dose within an organ. In this presentation, the results of this approach in several applications will be described, including: (a) dose to the fetus in pregnant women of early, middle and late gestational ages, (b) comparing dose to glandular breast tissue from thoracic CT scans both with and without tube current modulation. Educational Objectives: 1. Understand the Monte Carlo simulation based approach to estimating radiation dose to radiosensitive organs from CT scans. 2. Understand the current limitations of the Monte Carlo based approach. 3. Describe the results of some current applications of this approach to estimating fetal dose as well as breast dose reduction from tube current modulation.

Application of Particle Filtering for Estimating the Dynamics of Nuclear Systems

System dynamics estimation is a crucial issue for the safe operation and control of nuclear power plants. Typically, the estimation is based on a model of the plant dynamics and related measurements. In practice, the non-linearity of the dynamics and non-Gaussianity of the noise associated to the process and measurements lead to inaccurate results even with advanced approaches, such as the Kalman, Gaussian-sum and grid-based filters. On the contrary, accurate results may be obtained with Monte Carlo-based estimation methods, also called particle filters. The present paper illustrates the developments of a previous work by the same authors with regards to the comparison of the so called sampling importance resampling filter method with the standard and extended Kalman filtering techniques. Two case studies are analyzed to separately highlight the effect of non-linearity and non-Gaussianity in the process noise.

Multiscale modeling for polymer systems of industrial interest

Atomistic-based simulations such as molecular mechanics (MM), molecular dynamics (MD), and Monte Carlo-based methods (MC) have come into wide use for materials design. Using these atomistic simulation tools, one can analyze molecular structure on the scale of 0.1–10 nm. Although molecular structures can be studied easily and extensively by these atom-based simulations, it is less realistic to predict structures defined on the scale of 100–1000 nm with these methods. For the morphology on these scales, mesoscopic modeling techniques such as the dynamic mean field density functional theory (Mesodyn) and dissipative particle dynamics (DPD) are now available as effective simulation tools. Furthermore, it is possible to transfer the simulated mesoscopic structure to finite element modeling tools (FEM) for calculating macroscopic properties for a given system of interest. In this paper, we present a hierarchical procedure for bridging the gap between atomistic and macroscopic modeling passing through mesoscopic simulations. In particular, we will discuss the concept of multiscale modeling, and present examples of applications of multiscale procedures to polymer–organoclay nanocomposites. Examples of application of multiscale modeling to immiscible polymer blends and polymer–carbon nanotubes systems will also be presented.

Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants

This work studies the effects of sampling variability in Monte Carlo-based methods to estimate very high-dimensional systems. Recent focus in the geosciences has been on representing the atmospheric state using a probability density function, and, for extremely high-dimensional systems, various sample-based Kalman filter techniques have been developed to address the problem of real-time assimilation of system information and observations. As the employed sample sizes are typically several orders of magnitude smaller than the system dimension, such sampling techniques inevitably induce considerable variability into the state estimate, primarily through prior and posterior sample covariance matrices. In this article, we quantify this variability with mean squared error measures for two Monte Carlo-based Kalman filter variants: the ensemble Kalman filter and the ensemble square-root Kalman filter. Expressions of the error measures are derived under weak assumptions and show that sample sizes need to grow proportionally to the square of the system dimension for bounded error growth. To reduce necessary ensemble size requirements and to address rank-deficient sample covariances, covariance-shrinking (tapering) based on the Schur product of the prior sample covariance and a positive definite function is demonstrated to be a simple, computationally feasible, and very effective technique. Rules for obtaining optimal taper functions for both stationary as well as non-stationary covariances are given, and optimal taper lengths are given in terms of the ensemble size and practical range of the forecast covariance. Results are also presented for optimal covariance inflation. The theory is verified and illustrated with extensive simulations.

Molecular docking study on the “back door” hypothesis for product clearance in acetylcholinesterase

Acetylcholinesterase (AChE) is one of the fastest enzymes known, even though the active site is buried inside the protein at the end of a 20-A deep narrow gorge. Among the great variety of crystal structures of this enzyme, both in the absence and presence of various ligands and proteins, the structure of a complex of AChE with the pseudo-irreversible inhibitor Mf268 is of particular interest, as it assists in the proposal of a back door for product clearance from the active site. Binding of Mf268 to AChE results in the carbamoylation of Ser200 and liberation of an eseroline-fragment as the leaving group. The crystal structure of the AChE-Mf268 complex, however, proves that eseroline has escaped from the enzyme, despite the fact that the Ser-bound inhibitor fragment blocks the gorge entrance. The existence of alternative routes other than through the gorge for product clearance has been postulated but is still controversially discussed in the literature, as an experimental proof for such a back door is still missing. We have used Monte Carlo-based molecular docking methods in order to examine possible alternative pathways that could allow eseroline to be released from the protein after being cleaved from the substrate by Ser200. Based on our results, a short channel at the bottom of the gorge seems to be the most probable back-door site, which begins at amino acid Trp84 and ends at the enzyme surface in a cavity close to amino acid Glu445. [Figure: see text].

Sensitivity analysis of a catchment-scale nitrogen model

There are now considerable expectations that semi-distributed models are useful tools for supporting catchment water quality management. However, insufficient attention has been given to evaluating the uncertainties inherent to this type of model, especially those associated with the spatial disaggregation of the catchment. The Integrated Nitrogen in Catchments model (INCA) is subjected to an extensive regionalised sensitivity analysis in application to the River Kennet, part of the groundwater-dominated upper Thames catchment, UK The main results are: (1) model output was generally insensitive to land-phase parameters, very sensitive to groundwater parameters, including initial conditions, and significantly sensitive to in-river parameters; (2) INCA was able to produce good fits simultaneously to the available flow, nitrate and ammonium in-river data sets; (3) representing parameters as heterogeneous over the catchment (206 calibrated parameters) rather than homogeneous (24 calibrated parameters) produced a significant improvement in fit to nitrate but no significant improvement to flow and caused a deterioration in ammonium performance; (4) the analysis indicated that calibrating the flow-related parameters first, then calibrating the remaining parameters (as opposed to calibrating all parameters together) was not a sensible strategy in this case; (5) even the parameters to which the model output was most sensitive suffered from high uncertainty due to spatial inconsistencies in the estimated optimum values, parameter equifinality and the sampling error associated with the calibration method; (6) soil and groundwater nutrient and flow data are needed to reduce uncertainty in initial conditions, residence times and nitrogen transformation parameters, and long-term historic data are needed so that key responses to changes in land-use management can be assimilated. The results indicate the general difficulty of reconciling the questions which catchment nutrient models are expected to answer with typically limited data sets and limited knowledge about suitable model structures. The results demonstrate the importance of analysing semi-distributed model uncertainties prior to model application, and illustrate the value and limitations of using Monte Carlo-based methods for doing so.

Improving protein structure prediction with model-based search

De novo protein structure prediction can be formulated as search in a high-dimensional space. One of the most frequently used computational tools to solve such search problems is the Monte Carlo method. We present a novel search technique, called model-based search. This method samples the high-dimensional search space to build an approximate model of the underlying function. This model is incrementally refined in areas of interest, whereas areas that are not of interest are excluded from further exploration. Model-based search derives its efficiency from the fact that the information obtained during the exploration of the search space is used to guide further exploration. In contrast, Monte Carlo-based techniques lack memory and exploration is performed based on random walks, ignoring the information obtained in previous steps. Model-based search is applied to protein structure prediction, where search is employed to find the global minimum of the protein's energy landscape. We show that model-based search uses computational resources more efficiently to find lower-energy conformations of proteins than one of the leading protein structure prediction methods, which relies on a tailored Monte Carlo method to perform a search. The performance improvements become more pronounced as the dimensionality of the search problem increases. We argue that model-based search will enable more accurate protein structure prediction than was previously possible. Furthermore, we believe that similar performance improvements can be expected in other problems that are currently solved using Monte Carlo-based search methods. An implementation of model-based search can be obtained by contacting the authors.

Automated use of mutagenesis data in structure prediction

In the absence of experimental structural determination, numerous methods are available to indirectly predict or probe the structure of a target molecule. Genetic modification of a protein sequence is a powerful tool for identifying key residues involved in binding reactions or protein stability. Mutagenesis data is usually incorporated into the modeling process either through manual inspection of model compatibility with empirical data, or through the generation of geometric constraints linking sensitive residues to a binding interface. We present an approach derived from statistical studies of lattice models for introducing mutation information directly into the fitness score. The approach takes into account the phenotype of mutation (neutral or disruptive) and calculates the energy for a given structure over an ensemble of sequences. The structure prediction procedure searches for the optimal conformation where neutral sequences either have no impact or improve stability and disruptive sequences reduce stability relative to wild type. We examine three types of sequence ensembles: information from saturation mutagenesis, scanning mutagenesis, and homologous proteins. Incorporating multiple sequences into a statistical ensemble serves to energetically separate the native state and misfolded structures. As a result, the prediction of structure with a poor force field is sufficiently enhanced by mutational information to improve accuracy. Furthermore, by separating misfolded conformations from the target score, the ensemble energy serves to speed up conformational search algorithms such as Monte Carlo-based methods.

Area fill synthesis for uniform layout density

Chemical-mechanical polishing (CMP) and other manufacturing steps in very deep submicron very large scale integration have varying effects on device and interconnect features, depending on local characteristics of the layout. To improve manufacturability and performance predictability, the authors seek to make a layout uniform with respect to prescribed density criteria, by inserting area fill geometries into the layout. In this paper, they make the following contributions. First, the authors define the flat, hierarchical, and multiple-layer filling problems, along with a unified density model description. Secondly, for the flat filling problem, they summarize current linear programming approaches with two different objectives, i.e., the Min-Var and Min-Fill objectives. They then propose several new Monte Carlo-based filling methods with fast dynamic data structures. Thirdly, they give practical iterated methods for layout density control for CMP uniformity based on linear programming, Monte Carlo, and greedy algorithms. Fourthly, to address the large data volume and inherent lack of scalability of flat layout density control, the authors propose practical methods for hierarchical layout density control. These methods smoothly trade off runtime, solution quality, and output data volume. Finally, they extend the linear programming approaches and present new Monte Carlo-based methods for the multiple-layer filling problem. Comparisons with previous filling methods show the advantages of the new iterated Monte Carlo and iterated greedy methods for both flat and hierarchical layouts and for both density models (spatial density and effective density). The authors achieve near-optimal filling for flat layouts with respect to each of these objectives. Their experiments indicate that the hybrid hierarchical filling approach is efficient, scalable, accurate, and highly competitive with existing methods (e.g., linear programming-based techniques) for hierarchical layouts.