Monte Carlo Error Analysis Research Articles

In-situ relative calibration of Bragg crystals with Monte Carlo line ratio analysis.

X-ray line emission spectra can thoroughly characterize hot plasmas, especially when line shapes and ratios convey distinct aspects of plasma conditions. However, the high spectral resolution required for observing line shapes is often at odds with the large bandwidth required to observe many line ratios across a wide spectral range. One strategy to obtain high spectral resolution over a wide bandwidth is to use multiple crystals with calibrated reflectivity so that line intensities across different crystals can be compared. Here, we explore the use of a low-resolution, wide-bandwidth mica survey spectrometer to infer relative reflectivity of two high-resolution, narrow-bandwidth quartz crystals. A Monte Carlo error analysis determines comparable x-ray line ratios measured from both spectrometers, resulting in an in situ calibration factor and associated uncertainty for the relative reflectivity of the high-resolution crystals.

Improving safety in complex systems: A review of integration of functional resonance analysis method with semi‐quantitative and quantitative approaches

AbstractFunctional resonance analysis method (FRAM) is extensively employed in analyzing and managing performance variabilities. Additionally, semi‐quantitative and quantitative methods have been increasingly integrated with the FRAM to analyze complex socio‐technical systems to improve safety levels. This review article presents a comprehensive and updated survey of current literature focused on semi‐quantitative and quantitative methods employed for quantifying performance variabilities and exploring aggregation/propagation rules. A total of 1659 studies published between 2012 and March 2024 from various scientific databases were systematically examined using preferred reporting items for systematic review and meta‐analysis, identifying 29 studies that met inclusion criteria. The identified studies were categorized into four groups based on the quantitative methods employed: Monte Carlo simulation, fuzzy logic, cognitive reliability and error analysis method, and miscellaneous approaches. While different methodologies had unique strengths, they commonly relied on expert judgment for data collection, whether for defining probability distributions in Monte Carlo simulations, membership functions, and fuzzy rule bases in fuzzy inference systems, or selecting common performance conditions, determining their interrelationships, and assigning scores. Addressing bias from expert judgment in assessing performance variabilities can be achieved by using suitable experts' opinions integration techniques, and leading safety indicators in the analysis.

A rate-of-rise facility for measuring properties of wick structures

This work details a mass rate-of-rise (mROR) apparatus and analysis method for the accurate and precise determination of capillary wick parameters: permeability, K, effective pore radius, r eff, and porosity, ϵ. Three factors were examined: (a) the accuracy of the theoretical models and their curve-fitting approaches associated with the mROR technique, (b) the influence of the experimental procedure on repeatability, and (c) how the uncertainty of the experimental input parameters propagates through the data analysis procedure and compounds the overall uncertainty of the wick parameters (K and r eff). Four models and fittings methods were investigated: the Lucas–Washburn method, the gravity-based dm/dt method, the gravity-based t–m method, and the gravity-based m–t method. It is demonstrated that the m–t method developed here shows the lowest error and, equally importantly, that it is free of user decisions in the context of ‘data scrubbing’ because the entire mROR data set is used in its raw form. To test accuracy and repeatability, a precision-controlled mROR apparatus is proposed. Experiments were performed for commercially available wicks. A robust Monte Carlo error analysis method was developed and applied to quantify the overall uncertainty in the wick parameters as a function of the input uncertainties of all measured quantities.

An improved mathematical prediction of the time evolution of the Covid-19 pandemic in Italy, with a Monte Carlo simulation and error analyses

We present an improved mathematical analysis of the time evolution of the Covid-19 pandemic in Italy and a statistical error analyses of its evolution, including a Monte Carlo simulation with a very large number of runs to evaluate the uncertainties in its evolution. A previous analysis was based on the assumption that the number of nasopharyngeal swabs would be constant. However, the number of daily swabs is now more than five times what it was when we did our previous analysis. Therefore, here we consider the time evolution of the ratio of the new daily cases to number of swabs, which is more representative of the evolution of the pandemic when the number of swabs is increasing or changing in time. We consider a number of possible distributions representing the evolution of the pandemic in Italy, and we test their prediction capability over a period of up to 6 weeks. The results show that a distribution of the type of Planck black body radiation law provides very good forecasting. The use of different distributions provides an independent possible estimate of the uncertainty. We then consider five possible trajectories for the number of daily swabs and we estimate the potential dates of a substantial reduction in the number of new daily cases. We then estimate the spread in a substantial reduction, below a certain threshold, of the daily cases per swab among the Italian regions. We finally perform a Monte Carlo simulation with 25,000 runs to evaluate a random uncertainty in the prediction of the date of a substantial reduction in the number of diagnosed daily cases per swab.

Stepwise joint inversion of surface wave dispersion, Rayleigh wave ZH ratio, and receiver function data for 1D crustal shear wave velocity structure

Accurate determination of seismic velocity of the crust is important for understanding regional tectonics and crustal evolution of the Earth. We propose a stepwise joint linearized inversion method using surface wave dispersion, Rayleigh wave ZH ratio (i.e., ellipticity), and receiver function data to better resolve 1D crustal shear wave velocity (vS) structure. Surface wave dispersion and Rayleigh wave ZH ratio data are more sensitive to absolute variations of shear wave speed at depths, but their sensitivity kernels to shear wave speeds are different and complimentary. However, receiver function data are more sensitive to sharp velocity contrast (e.g., due to the existence of crustal interfaces) and vP/vS ratios. The stepwise inversion method takes advantages of the complementary sensitivities of each dataset to better constrain the vS model in the crust. We firstly invert surface wave dispersion and ZH ratio data to obtain a 1D smooth absolute vS model and then incorporate receiver function data in the joint inversion to obtain a finer vS model with better constraints on interface structures. Through synthetic tests, Monte Carlo error analyses, and application to real data, we demonstrate that the proposed joint inversion method can resolve robust crustal vS structures and with little initial model dependency.

Mantle upwelling beneath Madagascar: evidence from receiver function analysis and shear wave splitting

Crustal receiver functions have been calculated from 128 events for two three-component broadband seismomenters located on the south coast (FOMA) and in the central High Plateaux (ABPO) of Madagascar. For each station, crustal thickness and Vp/Vs ratio were estimated from H- κ plots. Self-consistent receiver functions from a smaller back-azimuthal range were then selected, stacked and inverted to determine shear wave velocity structure as a function of depth. These results were corroborated by guided forward modeling and by Monte Carlo error analysis. The crust is found to be thinner (39 ± 0.7 km) beneath the highland center of Madagascar compared to the coast (44 ± 1.6 km), which is the opposite of what would be expected for crustal isostasy, suggesting that present-day long wavelength topography is maintained, at least in part, dynamically. This inference of dynamic support is corroborated by shear wave splitting analyses at the same stations, which produce an overwhelming majority of null results (>96 %), as expected for vertical mantle flow or asthenospheric upwelling beneath the island. These findings suggest a sub-plate origin for dynamic support.

Програмне забезпечення SERC для аналізу похибки оцінки надійності відмовостійких реконфігуровних багатопроцесорних ситем

The article devoted to reliability estimation of fault-tolerant reconfigurable multiprocessor systems. The paper briefly describes implementation of software SERC (Statistical Experiments for Reliability Calculation) which contains known and proposed by author statistical methods for fault tolerant reconfigurable multiprocessor systems reliability estimation and tools for Monte Carlo Error analysis of the estimation.

Pointcatcher software: analysis of glacial time-lapse photography and integration with multitemporal digital elevation models

ABSTRACTTerrestrial time-lapse photography offers insight into glacial processes through high spatial and temporal resolution imagery. However, oblique camera views complicate measurement in geographic coordinates, and lead to reliance on specific imaging geometries or simplifying assumptions for calculating parameters such as ice velocity. We develop a novel approach that integrates time-lapse imagery with multitemporal DEMs to derive full three-dimensional coordinates for natural features tracked throughout a monoscopic image sequence. This enables daily independent measurement of horizontal (ice flow) and vertical (ice melt) velocities. By combining two terrestrial laser scanner surveys with a 73 days sequence from Sólheimajökull, Iceland, variations in horizontal ice velocity of ~10% were identified over timescales of ~25 days. An overall decrease of ~3.0 m surface elevation showed asynchronous rate changes with the horizontal velocity variations, demonstrating a temporal disconnect between the processes of ice surface lowering and mechanisms of glacier movement. Our software, ‘Pointcatcher’, is freely available for user-friendly interactive processing of general time-lapse sequences and includes Monte Carlo error analysis and uncertainty in projection onto DEM surfaces. It is particularly suited for analysis of challenging oblique glacial imagery, and we discuss good features to track, both for correction of camera motion and for deriving ice velocities.

A biofilm microreactor system for simultaneous electrochemical and nuclear magnetic resonance techniques

Nuclear magnetic resonance (NMR) techniques are ideally suited for the study of biofilms and for probing their microenvironments because these techniques allow for noninvasive interrogation and in situ monitoring with high resolution. By combining NMR with simultaneous electrochemical techniques, it is possible to sustain and study live biofilms respiring on electrodes. Here, we describe a biofilm microreactor system, including a reusable and a disposable reactor, that allows for simultaneous electrochemical and NMR techniques (EC-NMR) at the microscale. Microreactors were designed with custom radio frequency resonator coils, which allowed for NMR measurements of biofilms growing on polarized gold electrodes. For an example application of this system we grew Geobacter sulfurreducens biofilms on electrodes. EC-NMR was used to investigate growth medium flow velocities and depth-resolved acetate concentration inside the biofilm. As a novel contribution we used Monte Carlo error analysis to estimate the standard deviations of the acetate concentration measurements. Overall, we found that the disposable EC-NMR microreactor provided a 9.7 times better signal-to-noise ratio over the reusable reactor. The EC-NMR biofilm microreactor system can ultimately be used to correlate extracellular electron transfer rates with metabolic reactions and explore extracellular electron transfer mechanisms.

Application of XPS imaging analysis in understanding interfacial delamination and X‐ray radiation degradation of PMMA

The recent development of X‐ray Photoelectron Spectroscopy (XPS) instrumentation with spatial resolution down to several microns has advanced the capability of elemental and chemical state imaging. XPS imaging analysis has been applied in understanding the delamination problems of siloxane coatings on polymethyl‐methacrylate (PMMA) polymer. It was found that delamination occurred by interfacial failure, and the coating suffered complete delamination from a PMMA substrate. This example offered an opportunity for the investigation of X‐ray damage on polymers encountered in XPS imaging analysis. This paper also demonstrated how to construct a constrained peak model with the aid of chemical knowledge and supporting evidence of the sample. Monte Carlo error analysis was used to determine the validity of the peak fit models used. Copyright © 2013 John Wiley & Sons, Ltd.

Crustal structure of the British Isles and its epeirogenic consequences

Crustal receiver functions have been calculated for a network of 51 three-component broadband seismometers distributed across the British Isles and NW Europe. Over 3200 receiver functions were assembled for 1055 events. For each station, preliminary estimates of crustal thickness and Vp/Vs ratio were obtained from H−κ plots. Stacked receiver functions were then inverted to determine shear wave velocity as a function of depth. Each result was checked by guided forward modelling and by Monte Carlo error analysis. In this way, the robustness of our final calculated velocity profiles was carefully tested. A set of depth migrated profiles was also constructed using an average of 50 events for each station over a range of backazimuths. These profiles agree well with legacy wide-angle crustal models. Our results show that crustal thickness varies between 24 and 36 km across the British Isles. Thicker crust is found beneath north Wales and beneath central Scotland. Thinner crust occurs beneath northwest Scotland and northwest Ireland. By combining our database with the results of controlled source, wide-angle experiments and with depth-converted reflection profiles, we have produced a detailed crustal thickness map for a region encompassing the British Isles. Our synthesis of crustal thickness and structure has important implications for the tectonic and magmatic histories of this region. Complex Moho structure with lower crustal P-wave velocities of >7 km s−1 occurs beneath regions of Cenozoic magmatism, which may be consistent with magmatic underplating. Thin crust beneath northern Britain suggests that present-day long wavelength topography is maintained by regional dynamic support, originating beneath the lithospheric plate.

Quantitative comparison of experimental impurity transport with nonlinear gyrokinetic simulation in an Alcator C-Mod L-mode plasma

Nonlinear gyrokinetic simulations of impurity transport are compared to experimental impurity transport for the first time. The GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) was used to perform global, nonlinear gyrokinetic simulations of impurity transport for a standard Alcator C-Mod, L-mode discharge. The laser blow-off technique was combined with soft x-ray measurements of a single charge state of calcium to provide time-evolving profiles of this non-intrinsic, non-recycling impurity over a radial range of 0.0 ⩽ r/a ⩽ 0.6. Experimental transport coefficient profiles and their uncertainties were extracted from the measurements using the impurity transport code STRAHL and rigorous Monte Carlo error analysis. To best assess the agreement of gyrokinetic simulations with the experimental profiles, the sensitivity of the GYRO predicted impurity transport to a wide range of turbulence-relevant plasma parameters was investigated. A direct comparison of nonlinear gyrokinetic simulation and experiment is presented with an in depth discussion of error sources and a new data analysis methodology.

Impact of Landmark Parametrization on Monocular EKF-SLAM with Points and Lines

This paper explores the impact that landmark parametrization has in the performance of monocular, EKF-based, 6-DOF simultaneous localization and mapping (SLAM) in the context of undelayed landmark initialization. Undelayed initialization in monocular SLAM challenges EKF because of the combination of non-linearity with the large uncertainty associated with the unmeasured degrees of freedom. In the EKF context, the goal of a good landmark parametrization is to improve the model’s linearity as much as possible, improving the filter consistency, achieving robuster and more accurate localization and mapping. This work compares the performances of eight different landmark parametrizations: three for points and five for straight lines. It highlights and justifies the keys for satisfactory operation: the use of parameters behaving proportionally to inverse-distance, and landmark anchoring. A unified EKF-SLAM framework is formulated as a benchmark for points and lines that is independent of the parametrization used. The paper also defines a generalized linearity index suited for the EKF, and uses it to compute and compare the degrees of linearity of each parametrization. Finally, all eight parametrizations are benchmarked employing analytical tools (the linearity index) and statistical tools (based on Monte Carlo error and consistency analyses), with simulations and real imagery data, using the standard and the robocentric EKF-SLAM formulations.

Lysine Nζ-Decarboxylation Switch and Activation of the β-Lactam Sensor Domain of BlaR1 Protein of Methicillin-resistant Staphylococcus aureus

The integral membrane protein BlaR1 of methicillin-resistant Staphylococcus aureus senses the presence of β-lactam antibiotics in the milieu and transduces the information to the cytoplasm, where the biochemical events that unleash induction of antibiotic resistance mechanisms take place. We report herein by two-dimensional and three-dimensional NMR experiments of the sensor domain of BlaR1 in solution and by determination of an x-ray structure for the apo protein that Lys-392 of the antibiotic-binding site is posttranslationally modified by N(ζ)-carboxylation. Additional crystallographic and NMR data reveal that on acylation of Ser-389 by antibiotics, Lys-392 experiences N(ζ)-decarboxylation. This unique process, termed the lysine N(ζ)-decarboxylation switch, arrests the sensor domain in the activated ("on") state, necessary for signal transduction and all the subsequent biochemical processes. We present structural information on how this receptor activation process takes place, imparting longevity to the antibiotic-receptor complex that is needed for the induction of the antibiotic-resistant phenotype in methicillin-resistant S. aureus.

ExploreNEOs. II. THE ACCURACY OF THE WARMSPITZERNEAR-EARTH OBJECT SURVEY

We report on results of observations of near-Earth objects (NEOs) performed with the NASA Spitzer Space Telescope as part of our ongoing (2009–2011) Warm Spitzer NEO survey ("ExploreNEOs"), the primary aim of which is to provide sizes and albedos of some 700 NEOs. The emphasis of the work described here is an assessment of the overall accuracy of our survey results, which are based on a semi-empirical generalized model of asteroid thermal emission. The NASA Spitzer Space Telescope has been operated in the so-called Warm Spitzer mission phase since the cryogen was depleted in 2009 May, with the two shortest-wavelength channels, centered at 3.6 μm and 4.5 μm, of the Infrared Array Camera continuing to provide valuable data. The set of some 170 NEOs in our current Warm Spitzer results catalog contains 28 for which published taxonomic classifications are available, and 14 for which relatively reliable published diameters and albedos are available. A comparison of the Warm Spitzer results with previously published results ("ground truth"), complemented by a Monte Carlo error analysis, indicates that the rms Warm Spitzer diameter and albedo errors are ±20% and ±50%, respectively. Cases in which agreement with results from the literature is worse than expected are highlighted and discussed; these include the potential spacecraft target 138911 2001 AE2. We confirm that 1.4 appears to be an appropriate overall default value for the relative reflectance between the V band and the Warm Spitzer wavelengths, for use in correction of the Warm Spitzer fluxes for reflected solar radiation.

Robust photometric redshift determinations of gamma-ray burst afterglows at z ≳ 2

Theory suggests that about 10% of Swift-detected gamma-ray bursts (GRBs) will originate at redshifts greater than 5 yet a number of high redshift candidates may be left unconfirmed due to the lack of measured redshifts. Here we introduce our code, GRBz, a method of simultaneous multi-parameter fitting of GRB afterglow optical and near infrared, spectral energy distributions. It allows for early determinations of the photometric redshift, spectral index and host extinction to be made. We assume that GRB afterglow spectra are well represented by a power-law decay and model the effects of absorption due to the Lyman forest and host extinction. We use a genetic algorithm-based routine to simultaneously fit the parameters of interest, and a Monte Carlo error analysis. We use GRBs of previously determined spectroscopic redshifts to prove our method, while also introducing new near infrared data of GRB 990510 which further constrains the value of the host extinction. Our method is effective in estimating the photometric redshift of GRBs, relatively unbiased by assumptions of the afterglow spectral index or the host galaxy extinction. Monte Carlo error analysis is required as the method of error estimate based on the optimum population of the genetic algorithm underestimates errors significantly.

A Robust Measure of Tidal Circularization in Coeval Binary Populations: The Solar‐Type Spectroscopic Binary Population in the Open Cluster M35

We present a new homogeneous sample of 32 spectroscopic binary orbits in the young (~150 Myr) main-sequence open cluster M35. The distribution of orbital eccentricity versus orbital period (e- log P) displays a distinct transition from eccentric to circular orbits at an orbital period of ~10 days. The transition is due to tidal circularization of the closest binaries. The population of binary orbits in M35 provide a significantly improved constraint on the rate of tidal circularization at an age of 150 Myr. We propose a new and more robust diagnostic of the degree of tidal circularization in a binary population based on a functional fit to the e- log P distribution. We call this new measure the tidal circularization period. The tidal circularization period of a binary population represents the orbital period at which a binary orbit with the most frequent initial orbital eccentricity circularizes (defined as e = 0.01) at the age of the population. We determine the tidal circularization period for M35, as well as for seven additional binary populations spanning ages from the pre-main sequence (~3 Myr) to the late main sequence (~10 Gyr), and use Monte Carlo error analysis to determine the uncertainties on the derived circularization periods. We conclude that current theories of tidal circularization cannot account for the distribution of tidal circularization periods with population age.

Regionalization of methane emissions in the Amazon Basin with microwave remote sensing

AbstractWetlands of the Amazon River basin are globally significant sources of atmospheric methane. Satellite remote sensing (passive and active microwave) of the temporally varying extent of inundation and vegetation was combined with field measurements to calculate regional rates of methane emission for Amazonian wetlands. Monthly inundation areas for the fringing floodplains of the mainstem Solimões/Amazon River were derived from analysis of the 37 GHz polarization difference observed by the Scanning Multichannel Microwave Radiometer from 1979 to 1987. L‐band synthetic aperture radar data (Japanese Earth Resources Satellite‐1) were used to determine inundation and wetland vegetation for the Amazon basin (<500 m elevation) at high (May–June 1996) and low water (October 1995). An extensive set of measurements of methane emission is available from the literature for the fringing floodplains of the central Amazon, segregated into open water, flooded forest and floating macrophyte habitats. Uncertainties in the regional emission rates were determined by Monte Carlo error analyses that combined error estimates for the measurements of emission and for calculations of inundation and habitat areas. The mainstem Solimões/Amazon floodplain (54–70°W) emitted methane at a mean annual rate of 1.3 Tg C yr−1, with a standard deviation (SD) of the mean of 0.3 Tg C yr−1; 67% of this range in uncertainty is owed to the range in rates of methane emission and 33% is owed to uncertainty in the areal estimates of inundation and vegetative cover. Methane emission from a 1.77 million square kilometers area in the central basin had a mean of 6.8 Tg C yr−1 with a SD of 1.3 Tg C yr−1. If extrapolated to the whole basin below the 500 m contour, approximately 22 Tg C yr−1 is emitted; this mean flux has a greenhouse warming potential of about 0.5 Pg C as CO2. Improvement of these regional estimates will require many more field measurements of methane emission, further examination of remotely sensed data for types of wetlands not represented in the central basin, and process‐based models of methane production and emission.

Comparison of alpha/beta estimates from homogeneous (individual) and heterogeneous (population) tumor control models for early stage prostate cancer.

Radiobiological parameter estimates for prostate cancer are obtained from both a homogeneous (individual) and heterogeneous (population) tumor control model based on Poisson statistics and the linear quadratic model of cell survival. Parameter estimates for both models are highly correlated: statistically equivalent fits are achievable using either (1) linear quadratic (LQ) parameters with low numbers of radioresistant tumor stem cells, or (2) LQ parameters with corresponding larger number of radiosensitive tumor stem cells. A theoretical framework is developed to explain this correlation. A Monte Carlo error analysis based on binomial statistics is used to estimate confidence intervals for all parameter estimates. It was found that both the homogeneous and heterogeneous models produce approximately equivalent estimates of radiobiological parameters, including the alpha/beta ratio. However, the 95% confidence interval for the alpha/beta ratio derived from the heterogeneous model are considerably larger than those derived from the homogeneous model, which indicate the homogeneous model overestimates the statistical significance of the alpha/beta estimate.

Error in unsaturated stochastic models parameterized with field data

We use Monte Carlo error analysis to illustrate the impact of measurement errors in field‐estimated hydraulic properties on predictions made with 1D and 3D unconditional stochastic models of unsaturated flow and transport. Monte Carlo simulations are conducted across a series of simplified artificial realities completely described by the Gardner–Russo parametric model. The mean values of properties are varied between simulations to elucidate the relationship between true properties and prediction errors. Hydraulic properties are reestimated by simulating tension infiltrometer measurements in the presence of small simple errors. Two types of observation error are considered, along with one inversion‐model error resulting from poor contact between the instrument and the medium. Errors in the spatial statistics of hydraulic properties cause critical stochastic model assumptions to be violated, limiting the usable parameter space for model predictions. Even where critical assumptions are valid, stochastic model predictions show significant error, and the magnitude and pattern of error changes with the true property means, the flow conditions, and the type of measurement error. Mean velocities may show errors up to an order of magnitude. The velocity variance is overestimated by up to three orders of magnitude during 3D flow and eight orders of magnitude during 1D flow. The 1D velocity integral scale is underestimated by as much as five orders of magnitude. The estimates for 1D longitudinal macrodispersivity are surprisingly robust and show relatively small error across most of the parameter space.