Density functional theory for encapsidated polyelectrolytes: a comparison with Monte Carlo simulation.
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ABSTRACT:
SUBMITTER: Jin Z
PROVIDER: S-EPMC3416876 | biostudies-other | 2012 Jul
REPOSITORIES: biostudies-other
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Project description:BackgroundPlotless density estimators are those that are based on distance measures rather than counts per unit area (quadrats or plots) to estimate the density of some usually stationary event, e.g. burrow openings, damage to plant stems, etc. These estimators typically use distance measures between events and from random points to events to derive an estimate of density. The error and bias of these estimators for the various spatial patterns found in nature have been examined using simulated populations only. In this study we investigated eight plotless density estimators to determine which were robust across a wide range of data sets from fully mapped field sites. They covered a wide range of situations including animal damage to rice and corn, nest locations, active rodent burrows and distribution of plants. Monte Carlo simulations were applied to sample the data sets, and in all cases the error of the estimate (measured as relative root mean square error) was reduced with increasing sample size. The method of calculation and ease of use in the field were also used to judge the usefulness of the estimator. Estimators were evaluated in their original published forms, although the variable area transect (VAT) and ordered distance methods have been the subjects of optimization studies.ResultsAn estimator that was a compound of three basic distance estimators was found to be robust across all spatial patterns for sample sizes of 25 or greater. The same field methodology can be used either with the basic distance formula or the formula used with the Kendall-Moran estimator in which case a reduction in error may be gained for sample sizes less than 25, however, there is no improvement for larger sample sizes. The variable area transect (VAT) method performed moderately well, is easy to use in the field, and its calculations easy to undertake.ConclusionPlotless density estimators can provide an estimate of density in situations where it would not be practical to layout a plot or quadrat and can in many cases reduce the workload in the field.
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Project description:Generalized structured component analysis (GSCA) is a theoretically well-founded approach to component-based structural equation modeling (SEM). This approach utilizes the bootstrap method to estimate the confidence intervals of its parameter estimates without recourse to distributional assumptions, such as multivariate normality. It currently provides the bootstrap percentile confidence intervals only. Recently, the potential usefulness of the bias-corrected and accelerated bootstrap (BCa) confidence intervals (CIs) over the percentile method has attracted attention for another component-based SEM approach-partial least squares path modeling. Thus, in this study, we implemented the BCa CI method into GSCA and conducted a rigorous simulation to evaluate the performance of three bootstrap CI methods, including percentile, BCa, and Student's t methods, in terms of coverage and balance. We found that the percentile method produced CIs closer to the desired level of coverage than the other methods, while the BCa method was less prone to imbalance than the other two methods. Study findings and implications are discussed, as well as limitations and directions for future research.
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Project description:BackgroundMonte Carlo simulation is considered as the most accurate method for dose calculation in radiotherapy. PRIMO is a Monte-Carlo program with a user-friendly graphical interface.Material and methodA VitalBeam with 6MV and 6MV flattening filter free (FFF), equipped with the 120 Millennium multileaf collimator was simulated by PRIMO. We adjusted initial energy, energy full width at half maximum (FWHM), focal spot FWHM, and beam divergence to match the measurements. The water tank and ion-chamber were used in the measurement. Percentage depth dose (PDD) and off axis ratio (OAR) were evaluated with gamma passing rates (GPRs) implemented in PRIMO. PDDs were matched at different widths of standard square fields. OARs were matched at five depths. Transmission factor and dose leaf gap (DLG) were simulated. DLG was measured by electronic portal imaging device using a sweeping gap method.ResultFor the criterion of 2%/2 mm, 1%/2 mm and 1%/1 mm, the GPRs of 6MV PDD were 99.33-100%, 99-100%, and 99-100%, respectively; the GPRs of 6MV FFF PDD were 99.33-100%, 98.99-99.66%, and 97.64-98.99%, respectively; the GPRs of 6MV OAR were 96.4-100%, 90.99-100%, and 85.12-98.62%, respectively; the GPRs of 6MV FFF OAR were 95.15-100%, 89.32-100%, and 87.02-99.74%, respectively. The calculated DLG matched well with the measurement (6MV: 1.36 mm vs. 1.41 mm; 6MV FFF: 1.07 mm vs. 1.03 mm, simulation vs measurement). The transmission factors were similar (6MV: 1.25% vs. 1.32%; 6MV FFF: 0.8% vs. 1.12%, simulation vs measurement).ConclusionThe calculated PDD, OAR, DLG and transmission factor were all in good agreement with measurements. PRIMO is an independent (with respect to analytical dose calculation algorithm) and accurate Monte Carlo tool.
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Project description:Conventional mammography can suffer from poor contrast between healthy and cancerous tissues due to the small difference in attenuation properties. Coherent scatter slot scan imaging is an imaging technique which provides additional information and is compatible with conventional mammography. A Monte Carlo simulation of coherent scatter slot scan imaging was performed to assess its performance and provide system optimization. Coherent scatter could be exploited using a system similar to conventional slot scan mammography system with antiscatter grids tilted at the characteristic angle of cancerous tissues. System optimization was performed across several parameters, including source voltage, tilt angle, grid distances, grid ratio, and shielding geometry. The simulated carcinomas were detectable for tumors as small as 5 mm in diameter, so coherent scatter analysis using a wide-slot setup could be promising as an enhancement for screening mammography. Employing coherent scatter information simultaneously with conventional mammography could yield a conventional high spatial resolution image with additional coherent scatter information.
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Project description:BackgroundIn the Point-Centred Quarter Method (PCQM), the mean distance of the first nearest plants in each quadrant of a number of random sample points is converted to plant density. It is a quick method for plant density estimation. In recent publications the estimator equations of simple PCQM (PCQM1) and higher order ones (PCQM2 and PCQM3, which uses the distance of the second and third nearest plants, respectively) show discrepancy. This study attempts to review PCQM estimators in order to find the most accurate equation form. We tested the accuracy of different PCQM equations using Monte Carlo Simulations in simulated (having 'random', 'aggregated' and 'regular' spatial patterns) plant populations and empirical ones.Principal findingsPCQM requires at least 50 sample points to ensure a desired level of accuracy. PCQM with a corrected estimator is more accurate than with a previously published estimator. The published PCQM versions (PCQM1, PCQM2 and PCQM3) show significant differences in accuracy of density estimation, i.e. the higher order PCQM provides higher accuracy. However, the corrected PCQM versions show no significant differences among them as tested in various spatial patterns except in plant assemblages with a strong repulsion (plant competition). If N is number of sample points and R is distance, the corrected estimator of PCQM1 is 4(4N - 1)/(π ∑ R2) but not 12N/(π ∑ R2), of PCQM2 is 4(8N - 1)/(π ∑ R2) but not 28N/(π ∑ R2) and of PCQM3 is 4(12N - 1)/(π ∑ R2) but not 44N/(π ∑ R2) as published.SignificanceIf the spatial pattern of a plant association is random, PCQM1 with a corrected equation estimator and over 50 sample points would be sufficient to provide accurate density estimation. PCQM using just the nearest tree in each quadrant is therefore sufficient, which facilitates sampling of trees, particularly in areas with just a few hundred trees per hectare. PCQM3 provides the best density estimations for all types of plant assemblages including the repulsion process. Since in practice, the spatial pattern of a plant association remains unknown before starting a vegetation survey, for field applications the use of PCQM3 along with the corrected estimator is recommended. However, for sparse plant populations, where the use of PCQM3 may pose practical limitations, the PCQM2 or PCQM1 would be applied. During application of PCQM in the field, care should be taken to summarize the distance data based on 'the inverse summation of squared distances' but not 'the summation of inverse squared distances' as erroneously published.
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