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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Tomotherapy treatment plan quality assurance: The impact of applied criteria on passing rate in gamma index method

Purpose: Pretreatment patient plan verification with gamma index (GI) metric analysis is standard procedure for intensity modulated radiation therapy (IMRT) treatment. The aim of this paper is to evaluate the variability of the local and global gamma index obtained during standard pretreatment quality assurance (QA) measurements for plans performed with Tomotherapy unit. The QA measurements were performed with a 3D diode array, using variable passing criteria: 3%/3 mm, 2%/2 mm, 1%/1 mm, each with both local and global normalization.Methods: The authors analyzed the pretreatment QA results for 73 verifications; 37 were prostate cancer plans, 16 were head and neck plans, and 20 were other clinical sites. All plans were treated using the Tomotherapy Hi-Art System. Pretreatment QA plans were performed with the commercially available 3D diode array ArcCHECK™. This device has 1386 diodes arranged in a helical geometry spaced 1 cm apart. The dose measurements were acquired on the ArcCHECK™ and then compared with the calculated dose using the standard gamma analysis method. The gamma passing rate (%GP), defined as the percentage of points satisfying the condition GI < 1, was calculated for different criteria (3%/3 mm, 2%/2 mm, 1%/1 mm) and for both global and local normalization. In the case of local normalization method, the authors set three dose difference threshold (DDT) values of 2, 3, and 5 cGy. Dose difference threshold is defined as the minimum absolute dose error considered in the analysis when using local normalization. Low-dose thresholds (TH) of 5% and 10% were also applied and analyzed.Results: Performing a paired-t-test, the authors determined that the gamma passing rate is independent of the threshold values for all of the adopted criteria (5%TH vs 10%TH, p > 0.1). Our findings showed that mean %GPs for local (or global) normalization for the entire study group were 93% (98%), 84% (92%), and 66% (61%) for 3%/3 mm, 2%/2 mm, and 1%/1 mm criteria, respectively. DDT was equal to 2 cGy for the local normalization analysis cases. The authors observed great variability in the resulting %GP. With 3%/3 mm gamma criteria, the overall passing rate with local normalization was 4.6% less on the average than with global one, as expected. The wide difference between %GP calculated with global or local approach is also confirmed by an unpaired t-test statistical analysis.Conclusions: The variability of %GP obtained confirmed the necessity to establish defined agreement criteria that could be universal and comparable between institutions. In particular, while the gamma passing rate does not depend on the choice of threshold, the choice of DDT strongly influences the gamma passing rate for local calculations. The difference between global and local %GP was statistically significant for prostate and other treatment sites when DDT was changed from 2 to 3 cGy.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

Automatic Extraction of Network Configurations for Realistic Simulation and Validation

Popular HPC network interconnection simulators such as SST Macro provide a variety of configurable parameters to explore the design space of hardware components such as network links and switches. While such knobs provide flexibility to explore design trade-offs for novel hardware, manually configuring simulations for existing hardware to focus on topology exploration can be cumbersome and error-prone, leading to widely inaccurate simulations. This challenge is compounded when specifications of various (proprietary) technologies are not readily available or are intentionally omitted. In this work, we provide a methodology to automatically tune the simulation configuration of the multiple network models running within SST Macro using Bayesian optimization. We perform this optimization in the context of multiple messaging regimes (i.e., small to large and latency to bandwidth-bound messages) and provide a detailed analysis of the simulation error for four systems. With our automated framework, we achieve a 5x improvement in accuracy over best-effort configurations based on available hardware specifications.

Suetterlein, Joshua D.↗
DOE OSTI2014

SU-E-T-192: FMEA Severity Scores - Do We Really Know?

Purpose: Failure modes and effects analysis (FMEA) is a subjective risk mitigation technique that has not been applied to physics-specific quality management practices. There is a need for quantitative FMEA data as called for in the literature. This work focuses specifically on quantifying FMEA severity scores for physics components of IMRT delivery and comparing to subjective scores. Methods: Eleven physical failure modes (FMs) for head and neck IMRT dose calculation and delivery are examined near commonly accepted tolerance criteria levels. Phantom treatment planning studies and dosimetry measurements (requiring decommissioning in several cases) are performed to determine the magnitude of dose delivery errors for the FMs (i.e., severity of the FM). Resultant quantitative severity scores are compared to FMEA scores obtained through an international survey and focus group studies. Results: Physical measurements for six FMs have resulted in significant PTV dose errors up to 4.3% as well as close to 1 mm significant distance-to-agreement error between PTV and OAR. Of the 129 survey responses, the vast majority of the responders used Varian machines with Pinnacle and Eclipse planning systems. The average years of experience was 17, yet familiarity with FMEA less than expected. Survey reports perception of dose delivery error magnitude varies widely, in some cases 50% difference in dose delivery error expected amongst respondents. Substantial variance is also seen for all FMs in occurrence, detectability, and severity scores assigned with average variance values of 5.5, 4.6, and 2.2, respectively. Survey shows for MLC positional FM(2mm) average of 7.6% dose error expected (range 0–50%) compared to 2% error seen in measurement. Analysis of ranking in survey, treatment planning studies, and quantitative value comparison will be presented. Conclusion: Resultant quantitative severity scores will expand the utility of FMEA for radiotherapy and verify accuracy of FMEA results compared to highly variable subjective scores.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

HPC Network Simulation Tuning via Automatic Extraction of Hardware Parameters

Popular HPC network interconnection simulators such as SST/macro provide a variety of configurable parameters to explore the design space of hardware components such as network interface cards (NIC), switches, and links among them. While such knobs provide flexibility to explore design trade-offs for novel hardware, manually configuring simulations for matching configurations of the existing hardware to focus on topology exploration can be cumbersome and error-prone, leading to widely inaccurate simulations. This challenge is compounded when specifications of various (proprietary) technologies are not readily available or intentionally omitted. In this work, we propose a framework to autotune the multiple network models’ simulation configurations within SST/macro using Tree-structured Parzen Estimator-based Bayesian optimization to observe the effect on simulation accuracy across different message regimes. These regimes consist of small to large message sizes and latency to bandwidth-bound messages. We provide a detailed analysis of the simulation error for four representative HPC systems. Our Bayesian optimization based autotuning framework for network models achieves a maximum of 5x improvement in accuracy over best-effort manual configurations based on available hardware specifications.

Simulation, autotuning↗
DOE OSTI2025

Co-Firing Switchgrass and Waste Coal in A Power Plant: A Techno-Economic and Life Cycle Evaluation for The Ohio River Valley (SWITCH) (Final Technical Report for Ohio State/FE0032204)

Abandoned coal mine lands (AMLs) represent one of the most persistent environmental challenges in the United States. Prior to the enactment of the Surface Mining Control and Reclamation Act (SMCRA) in 1977, coal mining operations were not legally required to reclaim disturbed lands, leaving behind approximately 500,000 AML sites nationwide. These sites pose severe environmental and health risks, including acid mine drainage, soil and water contamination, and spontaneous combustion of waste coal piles. Millions of Americans live within one mile of these AMLs, underscoring the urgency of remediation. Traditional reclamation practices, such as planting cool-season grasses, often fail to fully restore ecological function or leverage the economic potential of these lands. This project addressed these challenges by developing integrated strategies for resource recovery, land reclamation, and sustainable energy production. This project evaluated an integrated strategy to convert this liability into an opportunity by recovering waste coal and co-firing it with switchgrass (Panicum virgatum L.) cultivated on reclaimed or marginal AML areas in existing coal-fired power plants. Switchgrass not only provides a renewable feedstock but also aids in land reclamation and carbon sequestration. 1) Remote Sensing and Machine Learning for Waste Coal Identification Using Sentinel-2 satellite imagery and supervised classification, we applied four machine learning models to detect historical waste coal piles. Random Forest achieved the highest accuracy (precision: 86%, recall: 77%). Time-series analysis revealed gradual vegetation recovery since 1986, indicating natural reclamation processes in historical sites, while active mining areas showed ongoing disturbance. This workflow enables scalable monitoring and prioritization of reclamation efforts. 2) UAS-Based Stockpile Volume Estimation To quantify recoverable waste coal, we evaluated Unmanned Aerial Systems (UAS) equipped with Light Detection and Ranging (LiDAR) and multispectral sensors. Structure-from-Motion (SfM) photogrammetry combined with interpolated Digital Terrain Models (DTMs) achieved strong agreement with LiDAR reference volumes (Root Mean Square Error (RMSE) ≈147 m 3 , Mean Absolute Percentage Error (MAPE) ≈2%). Sensitivity analysis confirmed that spatial resolution significantly influences accuracy, emphasizing the need for high-resolution data for precise volume estimation. This approach offers a scalable, cost-effective, and accurate alternative to conventional ground-based surveys. 3) Switchgrass Cultivation for Bioenergy and Water Quality Improvement We assessed the hydrological and water quality impacts of converting AMLs to switchgrass production areas using the Soil and Water Assessment Tool (SWAT). Results showed that converting 10% of the watershed area into the switchgrass production zone reduced streamflow by 3.1%, total suspended solids by 18.1%, total nitrogen by 7.6%, and total phosphorus by 6.2%, while achieving biomass yields of 8.6–9.2 metric tons per hectare. These findings highlight switchgrass as a dual-benefit strategy for land reclamation and bioenergy feedstock production. 4) Integrated Co-Firing and CCS for Carbon-Negative Power Generation We modeled co-firing scenarios using the Power Plant Flexible Model (PPFM) to evaluate plant efficiency, greenhouse gas (GHG) emissions, and levelized cost of electricity (LCOE). Without carbon capture and storage (CCS), increasing switchgrass co-firing ratios reduced LCOE from $\$$150/MWh at 0% biomass to $\$$110/MWh at full substitution. Under CCS, costs remained higher (~$\$$250/MWh at 0% biomass) but decreased to $\$$200/MWh at 100% biomass, while enabling net-zero or carbon-negative electricity due to switchgrass sequestration benefits. Although CCS introduced efficiency penalties, pairing it with biomass co-firing offset these impacts and maximized climate benefits. Overall, optimizing co-firing ratios between 60-100%, supported by reliable logistics and storage strategies, emerged as a practical pathway to balance affordability, sustainability, and net-zero or negative GHG emissions while promoting productive reuse of AMLs.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2014

Effects of small variations of speed of sound in optoacoustic tomographic imaging

Purpose: Speed of sound difference in the imaged object and surrounding coupling medium may reduce the resolution and overall quality of optoacoustic tomographic reconstructions obtained by assuming a uniform acoustic medium. In this work, the authors investigate the effects of acoustic heterogeneities and discuss potential benefits of accounting for those during the reconstruction procedure. Methods: The time shift of optoacoustic signals in an acoustically heterogeneous medium is studied theoretically by comparing different continuous and discrete wave propagation models. A modification of filtered back-projection reconstruction is subsequently implemented by considering a straight acoustic rays model for ultrasound propagation. The results obtained with this reconstruction procedure are compared numerically and experimentally to those obtained assuming a heuristically fitted uniform speed of sound in both full-view and limited-view optoacoustic tomography scenarios. Results: The theoretical analysis showcases that the errors in the time-of-flight of the signals predicted by considering the straight acoustic rays model tend to be generally small. When using this model for reconstructing simulated data, the resulting images accurately represent the theoretical ones. On the other hand, significant deviations in the location of the absorbing structures are found when using a uniform speed of sound assumption. The experimental results obtained with tissue-mimicking phantoms and a mouse postmortem are found to be consistent with the numerical simulations. Conclusions: Accurate analysis of effects of small speed of sound variations demonstrates that accounting for differences in the speed of sound allows improving optoacoustic reconstruction results in realistic imaging scenarios involving acoustic heterogeneities in tissues and surrounding media.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Accurate contrast determination for X-ray speckle visibility spectroscopy

X-ray speckle visibility spectroscopy using X-ray free-electron lasers has long been proposed as a probe of fast dynamics in noncrystalline materials. In this paper, numerical modeling is presented to show how the data interpretation of visibility spectroscopy can be impacted by the nonidealities of real-life X-ray detectors. Using simulated detector data, this work provides a detailed analysis of the systematic errors of several contrast extraction algorithms in the context of low-count-rate X-ray speckle visibility spectroscopy and their origins are discussed. Here, it was found that the finite detector charge cloud and pixel size lead to an unavoidable `degeneracy' in photon position determination, and that the contrasts extracted using different algorithms can all be corrected by a simple linear model. The results suggest that experimental calibration of the correction coefficient at the count rate of interest is possible and essential. This allows computationally lightweight algorithms to be implemented for on-the-fly analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

On the Correspondence between Mean Forecast Errors and Climate Errors in CMIP5 Models

The present study examines the correspondence between short- and long-term systematic errors in five atmospheric models by comparing the 16 five-day hindcast ensembles from the Transpose Atmospheric Model Intercomparison Project II (Transpose-AMIP II) for July–August 2009 (short term) to the climate simulations from phase 5 of the Coupled Model Intercomparison Project (CMIP5) and AMIP for the June–August mean conditions of the years of 1979–2008 (long term). Because the short-term hindcasts were conducted with identical climate models used in the CMIP5/AMIP simulations, one can diagnose over what time scale systematic errors in these climate simulations develop, thus yielding insights into their origin through a seamless modeling approach. The analysis suggests that most systematic errors of precipitation, clouds, and radiation processes in the long-term climate runs are present by day 5 in ensemble average hindcasts in all models. Errors typically saturate after few days of hindcasts with amplitudes comparable to the climate errors, and the impacts of initial conditions on the simulated ensemble mean errors are relatively small. This robust bias correspondence suggests that these systematic errors across different models likely are initiated by model parameterizations since the atmospheric large-scale states remain close to observations in the first 2–3 days. However, biases associated with model physics can have impacts on the large-scale states by day 5, such as zonal winds, 2-m temperature, and sea level pressure, and the analysis further indicates a good correspondence between short- and long-term biases for these large-scale states. Therefore, improving individual model parameterizations in the hindcast mode could lead to the improvement of most climate models in simulating their climate mean state and potentially their future projections.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Fluorescent amplification for next generation sequencing (FA-NGS) library preparation

BACKGROUND: Next generation sequencing (NGS) has become a universal practice in modern molecular biology. As the throughput of sequencing experiments increases, the preparation of conventional multiplexed libraries becomes more labor intensive. Conventional library preparation typically requires quality control (QC) testing for individual libraries such as amplification success evaluation and quantification, none of which occur until the end of the library preparation process. RESULTS: In this study, we address the need for a more streamlined high-throughput NGS workflow by tethering real-time quantitative PCR (qPCR) to conventional workflows to save time and implement single tube and single reagent QC. We modified two distinct library preparation workflows by replacing PCR and quantification with qPCR using SYBR Green I. qPCR enabled individual library quantification for pooling in a single tube without the need for additional reagents. Additionally, a melting curve analysis was implemented as an intermediate QC test to confirm successful amplification. Sequencing analysis showed comparable percent reads for each indexed library, demonstrating that pooling calculations based on qPCR allow for an even representation of sequencing reads. To aid the modified workflow, a software toolkit was developed and used to generate pooling instructions and analyze qPCR and melting curve data. CONCLUSIONS: We successfully applied fluorescent amplification for next generation sequencing (FA-NGS) library preparation to both plasmids and bacterial genomes. As a result of using qPCR for quantification and proceeding directly to library pooling, the modified library preparation workflow has fewer overall steps. Therefore, we speculate that the FA-NGS workflow has less risk of user error. The melting curve analysis provides the necessary QC test to identify and troubleshoot library failures prior to sequencing. While this study demonstrates the value of FA-NGS for plasmid or gDNA libraries, we speculate that its versatility could lead to successful application across other library types.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

Restricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter (β) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Comparison of Human Performance between Operators and Students Using Rancor Microworld Simulator: A Preliminary Result

This paper describes an experiment using the Rancor Microworld simulator to probe into differences in human performance between students and actual operators. Six human performance measures – 1) time, 2) error, 3) workload, 4) situational awareness, 5) attention patterns, and 6) number of manipulations – are measured from experiments. The experiment has been conducted for 11 operators and 20 students so far. More experiments and analyses will be continued. Further experimental studies using Rancor Microworld are expected to be able to collect additional data that may be missing from full-scope studies and contribute to items that can support human reliability data.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Human Performance Analysis Depending on Operator Expertise (Student vs. Operator) and Simulator Complexity (Rancor Microworld vs. Compact Nuclear Simulator)

Human reliability analysis (HRA) evaluates human errors and provides human error probabilities (HEPs) for application in probabilistic safety assessment (PSA), which is a comprehensive safety assessment method for nuclear power plants (NPPs). Generally, HRA methods estimate HEPs based on human reliability data collected from actual historical measurement, simulator experiments, or expert judgement. Most recent HRA data collection studies focus on collecting data via full-scope main control room (MCR) simulators with actual licensed reactor operators. Contrary to this, Idaho National Laboratory (INL) has adopted a different approach, which attempts to collect HRA data based on experiment using simplified simulators and student participants by following the Simplified Human Error Experimental Program (SHEEP). This approach has a couple of advantages compared to full-scope data collection. Representatively, it has relatively low entry point for collecting HRA data, and secures large sample sizes with reasonable cost and labor. In the previous studies, we developed the SHEEP framework, then verified whether the data collected through the framework could support a representative full-scope data collection study, i.e., the Human Reliability Data Extraction (HuREX) study. Also, we analyzed human performance measurements depending on participant type (i.e., student vs. operator). In this paper, we analyze human performance data collected from an experiment comparing operator expertise and simulator complexity when using the more simplified simulator developed by INL, i.e., Rancor Microworld and the less simplified simulator, i.e., Compact Nuclear Simulator (CNS) developed by Korea Atomic Energy Research Institute (KAERI). Analysis of variance (ANOVA) tests and correlation analysis are used for analyzing the experimental data.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

SpotSDC: Revealing the Silent Data Corruption Propagation in High-Performance Computing Systems

We report the trend of rapid technology scaling is expected to make the hardware of high-performance computing (HPC) systems more susceptible to computational errors due to random bit flips. Some bit flips may cause a program to crash or have a minimal effect on the output, but others may lead to silent data corruption (SDC), i.e., undetected yet significant output errors. Classical fault injection analysis methods employ uniform sampling of random bit flips during program execution to derive a statistical resiliency profile. However, summarizing such fault injection result with sufficient detail is difficult, and understanding the behavior of the fault-corrupted program is still a challenge. In this article, we introduce SpotSDC, a visualization system to facilitate the analysis of a program's resilience to SDC. SpotSDC provides multiple perspectives at various levels of detail of the impact on the output relative to where in the source code the flipped bit occurs, which bit is flipped, and when during the execution it happens. SpotSDC also enables users to study the code protection and provide new insights to understand the behavior of a fault-injected program. Based on lessons learned, we demonstrate how what we found can improve the fault injection campaign method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Solving Drift-flux Model Using High-Resolution Spatial Discretization Scheme

Accurate modeling and simulation of the two-phase flow phenomena are critical to the system and safety analysis of light water reactors. Compared to the more complex two-fluid model, the drift-flux model treats the two phases as a mixture, and thus the models are formulated to consider the conservation laws of the mixture. The relative motion between the two phases is realized by constitutive correlations. Although the drift flux models have limitations in certain applications, they are widely used in many applications due to their simplicity and applicability to a wide range of two-phase flow problems. First-order numerical schemes are widely used in existing codes, which introduces excessive numerical diffusions. The objective of this work is to investigate a high-resolution spatial scheme in the application to solve drift-flux two-phase flow problems. In this study, a high-resolution spatial discretization scheme has been investigated in the application of solving drift-flux two-phase flow problem. The scheme is validated using existing experimental results. Compared to the first order scheme, it demonstrated excellent capability in reducing numerical error. Extended work will focus on the comparison of numerical errors from discretization schemes and model uncertainties. (authors)

42 ENGINEERING↗
DOE OSTI2013

SYSTEMATIC EFFECTS IN INTERFEROMETRIC OBSERVATIONS OF THE COSMIC MICROWAVE BACKGROUND POLARIZATION

The detection of the primordial B-mode spectrum of the polarized cosmic microwave background (CMB) signal may provide a probe of inflation. However, observation of such a faint signal requires excellent control of systematic errors. Interferometry proves to be a promising approach for overcoming such a challenge. In this paper we present a complete simulation pipeline of interferometric observations of CMB polarization, including systematic errors. We employ two different methods for obtaining the power spectra from mock data produced by simulated observations: the maximum likelihood method and the method of Gibbs sampling. We show that the results from both methods are consistent with each other as well as, within a factor of six, with analytical estimates. Several categories of systematic errors are considered: instrumental errors, consisting of antenna gain and antenna coupling errors; and beam errors, consisting of antenna pointing errors, beam cross-polarization, and beam shape (and size) errors. In order to recover the tensor-to-scalar ratio, r, within a 10% tolerance level, which ensures the experiment is sensitive enough to detect the B-signal at r = 0.01 in the multipole range 28 < l < 384, we find that, for a QUBIC-like experiment, Gaussian-distributed systematic errors must be controlled with precisions of |g{sub rms}| = 0.1 for antenna gain, |{epsilon}{sub rms}| = 5 Multiplication-Sign 10{sup -4} for antenna coupling, {delta}{sub rms} Almost-Equal-To 0. Degree-Sign 7 for pointing, {zeta}{sub rms} Almost-Equal-To 0. Degree-Sign 7 for beam shape, and {mu}{sub rms} = 5 Multiplication-Sign 10{sup -4} for beam cross-polarization. Although the combined systematic effects produce a tolerance level on r twice as large for an experiment with linear polarizers, the resulting bias in r for a circular experiment is 15% which is still on the level of desirable sensitivity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, ( x ) u - d , helicity moment, ( x ) Δ u - Δ d , and the transversity moment, ( x ) δu - δd , of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass M π . The final results are obtained using a simultaneous fit in the lattice spacing a , pion mass M π and the finite volume parameter M π L keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the $ \overline{\mathrm{MS}} $ scheme at 2 GeV, are ( x ) u - d = 0 . 155(17)(20), ( x ) Δ u - Δ d = 0 . 183(14)(20) and ( x ) δu - δd = 0 . 220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗