Analytical applications of Monte Carlo techniques

Güell, Oscar A.; Holcombe, James A.

doi:10.1021/ac00208a001

Cited by 35 publications

(8 citation statements)

References 15 publications

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“…Diffusion. Diffusion arises from the random Brownian motion of molecules and is often modeled as a random-walk process with a constant step size in one or three dimensions. ,,,,,, This approach has been extended by varying the step size about a nonzero average value. , Although this extension allows for some statistical variation, it does not provide an accurate distribution of step sizes. Betteridge et al and Wentzell et al .…”

Section: Description and Validation Of Transport Algorithmsmentioning

confidence: 99%

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Three-Dimensional Molecular Simulation of Electrophoretic Separations

Hopkins

McGuffin

1998

Anal. Chem.

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A three-dimensional stochastic simulation has been developed for electrophoretic separations. This simulation follows the trajectories of individual molecules by applying the fundamental equations of motion for diffusion, electroosmotic flow, and electrophoretic migration. The molecular zone profile may then be examined and characterized at any specified time or distance. The stochastic simulation has been validated by comparison with classical transport models, having average relative errors for the mean zone distance and variance of 0.01-0.04% and 2.67-4.36%, respectively. The simulation also shows excellent agreement with experimental results for the electrophoretic separation of the nucleotide monophosphates in phosphate buffer solution, having average relative errors for the mean zone distance and variance of 1.65% and 12.99%, respectively. This stochastic simulation provides an accurate and versatile means to examine and characterize transport processes in complex electrophoretic systems.Electrophoresis is an important analytical technique for the separation of strong and weak electrolytes as well as large polyelectrolytes of biological and industrial importance. Our understanding of the fundamental processes that comprise electrophoresis has been achieved through comparison of experimental results with the predictions of theoretical models. The classical models used to describe mass transport in electrophoretic separations are usually developed to address the conditions of a specific mode of separation, such as zone electrophoresis (ZE), 1-6 moving boundary electrophoresis (MBE), 7 isotachophoresis (ITP), 5,8-12 and isoelectric focusing (IEF). 13-17 However, unified models that can be used to describe all of the electrophoretic separation modes have also been developed. 18-21 Descriptions of these and other electrophoretic models can be found in several reviews. [22][23][24] These classical transport models require the formulation of detailed differential equations of mass and charge balance, together with the associated boundary conditions. The solution of these equations yields the concentration profile as a function of time and/or the steady-state concentration profile in the cases of ITP 10,11 and IEF. 15-17 A comprehensive model must include all of the physical and chemical processes that contribute to the migration and dispersion of the solute zone in the electrophoretic system. In practice, however, these comprehensive differential equations cannot be solved analytically in closed form and are generally solved by numerical methods after simplifying assumptions are invoked. 25 For example, some models may consider electrophoretic migration alone, 6,26 whereas others may include additional processes such as molecular diffusion and electrodiffusion, 27 convection, 4,5,28 chemical equilibria, 12 and various combinations thereof. 1,2,29 As a consequence of these simplifying assumptions, the classical models do not provide a completely general description of transport phenomena in electrophoretic systems...

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Section: Description and Validation Of Transport Algorithmsmentioning

confidence: 99%

“…This problem has been overcome with the routine availability of high-speed, high-memory computers, particularly those with parallel processors . In recent years, three-dimensional molecular simulations have been applied to the study of flow injection analysis, , field-flow fractionation, , gas and liquid chromatography, , and capillary electrophoresis …”

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confidence: 99%

Three-Dimensional Molecular Simulation of Electrophoretic Separations

Hopkins

McGuffin

1998

Anal. Chem.

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“…The variation in the percentage of random patterns rejected was determined to be approximately ±0.5% based on replicate experiments. Of course, with a large number of random patterns ( n = 10 000), the variation would be expected to be quite small …”

Section: Resultsmentioning

confidence: 99%

“…Monte Carlo simulation studies were used in this work to determine outlier rejection threshold levels. Monte Carlo methods comprise a branch of experimental mathematics that is concerned with experiments on random numbers . In this work, random pattern vectors were generated and presented to the PNN.…”

Section: Theorymentioning

confidence: 99%

Improved Probabilistic Neural Network Algorithm for Chemical Sensor Array Pattern Recognition

Shaffer

Rose-Pehrsson

1999

Anal. Chem.

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An improved probabilistic neural network (IPNN) algorithm for use in chemical sensor array pattern recognition applications is described. The IPNN is based on a modified probabilistic neural network (PNN) with three innovations designed to reduce the computational and memory requirements, to speed training, and to decrease the false alarm rate. The utility of this new approach is illustrated with the use of four data sets extracted from simulated and laboratory-collected surface acoustic wave sensor array data. A competitive learning strategy, based on a learning vector quantization neural network, is shown to reduce the storage and computation requirements. The IPNN hidden layer requires only a fraction of the storage space of a conventional PNN. A simple distance-based calculation is reported to approximate the optimal kernel width of a PNN. This calculation is found to decrease the training time and requires no user input. A general procedure for selecting the optimal rejection threshold for a PNN-based algorithm using Monte Carlo simulations is also demonstrated. This outlier rejection strategy is implemented for an IPNN classifier and found to reject ambiguous patterns, thereby decreasing the potential for false alarms.

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“…The simulated data sets, generated by the Monte Carlo method [9,10], were chosen to reproduce usual data set structures found in real analysis data. Applying the technique to two real data sets demonstrated that the probability of b error using OLS and WLS regression techniques can be very different from that from the BLS regression method when errors in both axes are considered.…”

Section: Introductionmentioning

confidence: 99%

Evaluating bias in method comparison studies using linear regression with errors in both axes

Martı́nez

Riu

Rius

2002

Journal of Chemometrics

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This paper presents a theoretical background for estimating the probability of committing a b error when checking the presence of method bias. Results obtained at different concentration levels from the analytical method being tested are compared by linear regression with the results from a reference method. Method bias can be detected by applying the joint confidence interval test to the regression line coefficients from a bivariate least squares (BLS) regression technique. This finds the regression line considering the errors in the two methods. We have validated the estimated probabilities of b error by comparing them with the experimental values from 24 simulated data sets. We also compared the probabilities of b error estimated using the BLS regression method on two real data sets with those estimated using ordinary least squares (OLS) and weighted least squares (WLS) regression techniques for a given level of significance a. We found that there were important differences in the values predicted with WLS and OLS compared to those predicted with the BLS regression method.

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Analytical applications of Monte Carlo techniques

Cited by 35 publications

References 15 publications

Three-Dimensional Molecular Simulation of Electrophoretic Separations

Three-Dimensional Molecular Simulation of Electrophoretic Separations

Improved Probabilistic Neural Network Algorithm for Chemical Sensor Array Pattern Recognition

Evaluating bias in method comparison studies using linear regression with errors in both axes

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