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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

ON THE RELIABILITY OF POLARIZATION ESTIMATION USING ROTATION MEASURE SYNTHESIS

We benchmark the reliability of the rotation measure (RM) synthesis algorithm using the 1005 Centaurus A field sources of Feain et al. The RM synthesis solutions are compared with estimates of the polarization parameters using traditional methods. This analysis provides verification of the reliability of RM synthesis estimates. We show that estimates of the polarization parameters can be made at lower signal-to-noise ratio (S/N) if the range of RMs is bounded, but reliable estimates of individual sources with unusual RMs require unconstrained solutions and higher S/N. We derive from first principles the statistical properties of the polarization amplitude associated with RM synthesis in the presence of noise. The amplitude distribution depends explicitly on the amplitude of the underlying (intrinsic) polarization signal. Hence, it is necessary to model the underlying polarization signal distribution in order to estimate the reliability and errors in polarization parameter estimates. We introduce a Bayesian method to derive the distribution of intrinsic amplitudes based on the distribution of measured amplitudes. The theoretically derived distribution is compared with the empirical data to provide quantitative estimates of the probability that an RM synthesis solution is correct as a function of S/N. We provide quantitative estimates of the probability that any given RM synthesis solution is correct as a function of measured polarized amplitude and the intrinsic polarization amplitude compared to the noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Formal Experimentation and Analysis of Handheld RFID Readers as a Tool for Nuclear Material Accounting

Commercial, off-the-shelf Radio Frequency Identification (RFID) systems have been successfully deployed for inventory tracking in numerous industries, but their viability in the tracking of complex environments containing nuclear material is less understood. Of primary interest in this setting is a RFID tracking system for nuclear material accounting which can reliably identify as many tags as possible with high accuracy, while also reducing an operator’s exposure to radiation. In this work, we develop a formal statistical approach to identify relevant handheld RFID reader settings which optimize tagging performance. To achieve this goal, we design a full factorial split-plot experiment for a static shelf configuration scene with 50 randomly placed nuclear material containers affixed with RFID tags. We use Bayesian inference to fit a second-order response surface model which expresses the probability of a successful match for each container as a function of the experimental factors. Such effects are allowed to vary across individual containers and the containers’ population in its entirety to estimate overall effects. Uncertainties of estimates and predictions are quantified via their corresponding posterior distributions. Following extensive model checking and validation, the fitted model is used to identify experimental factors which maximize matching probabilities at both the container-level and for the full shelf configuration scene. We also analyze sensitivity of performance to relevant factors.

25 ENERGY STORAGE↗
DOE OSTI2023

Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels

Abstract We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behaviour. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.

Karwa, Vishesh↗
DOE OSTI2016

Network design for quantifying urban CO<sub>2</sub> emissions: assessing trade-offs between precision and network density

The majority of anthropogenic CO 2 emissions are attributable to urban areas. While the emissions from urban electricity generation often occur in locations remote from consumption, many of the other emissions occur within the city limits. Evaluating the effectiveness of strategies for controlling these emissions depends on our ability to observe urban CO 2 emissions and attribute them to specific activities. Cost-effective strategies for doing so have yet to be described. Here we characterize the ability of a prototype measurement network, modeled after the Berkeley Atmospheric CO 2 Observation Network (BEACO 2 N) in California's Bay Area, in combination with an inverse model based on the coupled Weather Research and Forecasting/Stochastic Time-Inverted Lagrangian Transport (WRF-STILT) to improve our understanding of urban emissions. The pseudo-measurement network includes 34 sites at roughly 2 km spacing covering an area of roughly 400 km 2 . The model uses an hourly 1 × 1 km 2 emission inventory and 1 × 1 km 2 meteorological calculations. We perform an ensemble of Bayesian atmospheric inversions to sample the combined effects of uncertainties of the pseudo-measurements and the model. We vary the estimates of the combined uncertainty of the pseudo-observations and model over a range of 20 to 0.005 ppm and vary the number of sites from 1 to 34. We use these inversions to develop statistical models that estimate the efficacy of the combined model–observing system in reducing uncertainty in CO 2 emissions. We examine uncertainty in estimated CO 2 fluxes on the urban scale, as well as for sources embedded within the city such as a line source (e.g., a highway) or a point source (e.g., emissions from the stacks of small industrial facilities). Using our inversion framework, we find that a dense network with moderate precision is the preferred setup for estimating area, line, and point sources from a combined uncertainty and cost perspective. The dense network considered here (modeled after the BEACO 2 N network with an assumed mismatch error of 1 ppm at an hourly temporal resolution) could estimate weekly CO 2 emissions from an urban region with less than 5 % error, given our characterization of the combined observation and model uncertainty.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

Confidence set inference with a prior quadratic bound

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

Backus, George E.↗
DOE OSTI2024

Deep Learning and Likelihood Approaches for Viral Phylogeography Converge on the Same Answers Whether the Inference Model Is Right or Wrong

Abstract Analysis of phylogenetic trees has become an essential tool in epidemiology. Likelihood-based methods fit models to phylogenies to draw inferences about the phylodynamics and history of viral transmission. However, these methods are often computationally expensive, which limits the complexity and realism of phylodynamic models and makes them ill-suited for informing policy decisions in real-time during rapidly developing outbreaks. Likelihood-free methods using deep learning are pushing the boundaries of inference beyond these constraints. In this paper, we extend, compare, and contrast a recently developed deep learning method for likelihood-free inference from trees. We trained multiple deep neural networks using phylogenies from simulated outbreaks that spread among 5 locations and found they achieve close to the same levels of accuracy as Bayesian inference under the true simulation model. We compared robustness to model misspecification of a trained neural network to that of a Bayesian method. We found that both models had comparable performance, converging on similar biases. We also implemented a method of uncertainty quantification called conformalized quantile regression that we demonstrate has similar patterns of sensitivity to model misspecification as Bayesian highest posterior density (HPD) and greatly overlap with HPDs, but have lower precision (more conservative). Finally, we trained and tested a neural network against phylogeographic data from a recent study of the SARS-Cov-2 pandemic in Europe and obtained similar estimates of region-specific epidemiological parameters and the location of the common ancestor in Europe. Along with being as accurate and robust as likelihood-based methods, our trained neural networks are on average over 3 orders of magnitude faster after training. Our results support the notion that neural networks can be trained with simulated data to accurately mimic the good and bad statistical properties of the likelihood functions of generative phylogenetic models.

Evolutionary Biology↗
NASA NTRSDate not supplied

A Framework for the Analysis of Deep Neural Networks in Autonomous Aerospace Applications using Bayesian Statistics

Deep Neural Networks (DNNs) are considered to be key components in many autonomous systems. Applications range from vision-based obstacle avoidance to intelligent/learning control and planning. Safety-critical applications as found in the aerospace domain require that the behavior of the DNN is validated and tested rigorously for safety of the autonomous system (AUS). In this paper, we present a framework to support testing of DNNs and the analysis of the network structure. Our framework employs techniques from statistical modeling and active learning to effectively generate test cases for DNN safety testing and performance analysis. We will present results of a case study on a physics-based Deep recurrent residual neural network (DR-RNN), which has been trained to emulate the aerodynamics behavior of a fixed-wing aircraft.

Deep Neural networks↗
DOE OSTI2021

Effects of a nuclear disturbed environment on a quantum free space optical link

This manuscript investigates the potential effect of a nuclear-disturbed atmospheric environment on the signal attenuation of a ground/satellite transmitter/receiver system for both classical optical and quantum communications applications. Attenuation of a signal transmitted through the rising nuclear cloud and the subsequently transported debris is modeled climatologically for surface-level detonations of 10 kt, 100 kt, and 1 Mt. Attenuation statistics were collected as a function of time after detonation. These loss terms were compared to normal loss sources such as clouds, smoke from fires, and clear sky operation. Finally, the loss was related to the degradation of transmitted entanglement derived from Bayesian mean estimation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Quantifying Uncertainties of Microscopic Nuclear Theories

The goal of this project was to produce modernized nuclear data libraries of light ion fusion reactions and actinide fission product yields. Such libraries are essential input in both stockpile science but also fundamental science (nucleosynthesis, superheavy nuclei). When such libraries are used to model complex processes involving exotic, very short-lived nuclei that have not been measured experimentally, the underlying nuclear data come from theoretical models, the predictive power of which needs to be quantified, together with its uncertainties. By teaming up nuclear theorists and statisticians, we built comprehensive theoretical frameworks based on the most fundamental theories of fusion and fission that we coupled for the first time with a Bayesian framework with machine learning techniques for uncertainty quantification. Our results include: (1) statistical emulators for neutron-alpha scattering, and the fission product mass yields of neutron-induced fission of 239 Pu, which will enable developers to generate random realizations of the corresponding data for uncertainty quantification (UQ) in applications; (2) the first complete and most accurate ab initio prediction of the S-factor for proton capture on 7 Be, which – combined with UQ – may become the recommended value at solar energies in the next review of solar fusion cross sections; (3) statistical emulators for fission mass yields in the neutron-induced fission of 239 Pu; (4) the first quantification of how uncertainties in nuclear forces impact fission properties that are relevant in nucleosynthesis simulations to explain how heavy elements are formed in the Cosmos.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2004

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Neural Networks (Computer)↗
DOE OSTI2017

Gaussian process-based surrogate modeling framework for process planning in laser powder-bed fusion additive manufacturing of 316L stainless steel

Here, Laser Powder-Bed Fusion (L-PBF) metal-based additive manufacturing (AM) is complex and not fully understood. Successful processing for one material, might not necessarily apply to a different material. This paper describes a workflow process that aims at creating a material data sheet standard that describes regimes where the process can be expected to be robust. The procedure consists of building a Gaussian process-based surrogate model of the L-PBF process that predicts melt pool depth in single-track experiments given a laser power, scan speed, and laser beam size combination. The predictions are then mapped onto a power versus scan speed diagram delimiting the conduction from the keyhole melting controlled regimes. This statistical framework is shown to be robust even for cases where experimental training data might be suboptimal in quality, if appropriate physics-based filters are applied. Additionally, it is demonstrated that a high-fidelity simulation model of L-PBF can equally be successfully used for building a surrogate model, which is beneficial since simulations are getting more efficient and are more practical to study the response of different materials, than to re-tool an AM machine for new material powder.

316L stainless steel↗
NASA NTRS2020

Chrono-Validation of Near-Real-Time Landslide Susceptibility Models via Plugin Statistical Simulations

The idea behind any validation scheme in landslide susceptibility studies is to test whether a model calibrated on a certain data can predict an unknown dataset of the same nature (landslide presences/absences and covariates). Almost the entirety of landslide susceptibility studies are validated by subsetting a single dataset into a training and test sets. This dataset usually corresponds either to event-specific or to historical inventories. Very rarely, a multi-temporal inventory is available and, in the few cases where this condition is met, the validation practices involve training a model on a specific landslide inventory, deriving a single predictive equation and validating it on a subsequent landslide inventory. This commonly leads landslide predictive studies, even those with a strong statistical rigor, to neglect the uncertainty estimation in their modeling scheme. In statistics, validation can also be performed via statistical simulations. This means that after fitting a given model, one can generate any number of predictive functions and test their predictive skills on any type and number of unknown datasets. In this work, we take a similar direction and we apply it to model and validate three separate co-seismic inventories, including an uncertainty estimation phase. We mapped these inventories within the same area in Indonesia, for three earthquakes occurred in 2012, 2017 and 2018. Specifically, we build three event-specific Bayesian Generalize Additive Models of the binomial family. From each model we then simulate 1000 predictive realizations over the remaining two inventories, by using a plug-in scheme where all the morphometric covariates are kept fixed and only the ground motion is replaced according to the prediction target. By doing so, we introduce a new analytical tool for near-real-time landslide predictive purposes, which is able to produce a probabilistic model which stands in between the definitions of susceptibility and hazard. In fact, our model is able to accurately estimate “where” and “when” - although not “how frequently” - landslide have occurred by featuring the multitemporal information of the trigger. In our findings, the simulations are quite similar to the fitted models; and the nine combinations we analyse produce excellent performance. This result confirms the assumption that “the past is the key to the future”, as we show that the relative contribution of each variable and their interactions in each probabilistic model remains practically the same across temporal replicates. This information is not trivial because it supports the routines implemented in global near-real-time applications.

Temporal validation↗
DOE OSTI2014

Bayesian model aggregation for ensemble-based estimates of protein pKa values

This paper investigates an ensemble-based technique called Bayesian Model Averaging (BMA) to improve the performance of protein amino acid p$K_a$ predictions. Structure-based p$K_a$ calculations play an important role in the mechanistic interpretation of protein structure and are also used to determine a wide range of protein properties. A diverse set of methods currently exist for p$K_a$ prediction, ranging from empirical statistical models to {\it ab initio} quantum mechanical approaches. However, each of these methods are based on a set of assumptions that have inherent bias and sensitivities that can effect a model's accuracy and generalizability for p$K_a$ prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pKa values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pKa Cooperative and the pKa measurements are based on experimental work conducted by the Garc{\'i}a-Moreno lab. Our study demonstrates that the aggregated estimate obtained from BMA outperforms all individual prediction methods in our cross-validation study with improvements from 40-70\% over other method classes. This work illustrates a new possible mechanism for improving the accuracy of p$K_a$ prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy.

electrostatics↗
DOE OSTI2022

Density reconstruction in convergent high-energy-density systems using x-ray radiography and Bayesian inference

X-ray radiography is a technique frequently used to diagnose convergent high-energy-density (HED) systems, such as inertial confinement fusion implosion, and provides unique information that is not available through self-emission measurements. In this work, we investigate the scope and limits of that information using a radiography simulation combined with the Bayesian inference workflow. The accuracy of density reconstruction from simulated radiographs of spherical implosions driven with 27 kJ laser energy is assessed, including the increase or decrease in accuracy due to the addition of Lagrangian marker layers, Poisson noise, and improved prior information. This work is the first to present the full uncertainty distributions inferred from radiography analysis in HED systems and demonstrates the importance of constructing the full posterior probability density, as opposed to a point estimate, due to the modal structure of the likelihood surface introduced by typical experimental noise sources. This general methodology can be used both for robust analysis of radiographic data and for an improved design of radiography experiments by modeling the full experimental system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2021

Spatiotemporal Associations Between Social Vulnerability, Environmental Measurements, and COVID-19 in the Conterminous United States

This study summarizes the results from fitting a Bayesian hierarchical spatiotemporal model to coronavirus disease 2019 (COVID-19) cases and deaths at the county level in the United States for the year 2020. Two models were created, one for cases and one for deaths, utilizing a scaled Besag, York, Mollié model with Type I spatial-temporal interaction. Each model accounts for 16 social vulnerability and 7 environmental variables as fixed effects. The spatial pattern between COVID-19 cases and deaths is significantly different in many ways. The spatiotemporal trend of the pandemic in the United States illustrates a shift out of many of the major metropolitan areas into the United States Southeast and Southwest during the summer months and into the upper Midwest beginning in autumn. Analysis of the major social vulnerability predictors of COVID-19 infection and death found that counties with higher percentages of those not having a high school diploma, having non-White status and being Age 65 and over to be significant. Among the environmental variables, above ground level temperature had the strongest effect on relative risk to both cases and deaths. Hot and cold spots, areas of statistically significant high and low COVID-19 cases and deaths respectively, derived from the convolutional spatial effect show that areas with a high probability of above average relative risk have significantly higher Social Vulnerability Index composite scores. The same analysis utilizing the spatiotemporal interaction term exemplifies a more complex relationship between social vulnerability, environmental measurements, COVID-19 cases, and COVID-19 deaths.

spatial epidemiology↗
DOE OSTI2021

Energy dependent calculations of fission product, prompt, and delayed neutron yields for neutron induced fission on 235 U, 238 U, and 239 Pu

In this article, we perform energy-dependent calculations of independent and cumulative fission product yields for 235 U, 238 U, and 239 Pu in the first chance fission region. Starting with the primary fission fragment distributions taken from available experimental data and analytical functions based on assumptions for the excitation energy and spin-parity distributions, the Hauser-Feshbach statistical decay treatment for fission fragment de-excitation is applied to more than 1,000 fission fragments for the incident neutron energies up to 5 MeV. The calculated independent yields are then used as an input of β-decay calculations to produce the cumulative yield, and summation calculations are performed. Model parameters in these procedures are adjusted by applying the Bayesian technique at the thermal energy for 235 U and 239 Pu and in the fast energy range for 238 U. The calculated fission observable quantities, such as the energy-dependent cumulative yields, and prompt and delayed neutron yields, are compared with available experimental data. We also study the possible impact of the second chance fission opening on the energy dependence of the delayed neutron yield by on the opening of second chance fission on the energy dependence calculation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Adoption of perennial energy crops in the US Midwest: Causal and heterogeneous determinants

The success of a bioenergy policy relies largely on the wide adoption of perennial energy crops at the farm-scale. This study uses survey data to examine potential adoption decisions by farmers in the US Midwest and the causal effects of various direct and indirect influencing factors, especially heterogeneous preferences of farmers. A Bayesian network (BN) model is developed to delineate the causal-relationship between farmers adoption decisions and the influencing factors. Here, we find a dominating role of economic factors and a non-negligible impact of non-economic factors, such as the perceived environmental benefits and the extent of familiarity with perennial energy crops. To examine the effect of heterogeneity in farmer preferences, we classify the surveyed farmers into four categories based on their attitudes toward the economic, social, and environmental dimensions of perennial energy crops. We identify statistically significant between-group differences in the responses of the four types of farmers to the various influencing factors. Our findings contribute to disentangling the complicated motivations that will influence perennial energy crop adoption decisions and provide implications for more targeted policy development that need to consider the heterogeneous drivers of farmer decisions about land use.

09 BIOMASS FUELS↗
DOE OSTI2013

ESTIMATING THE PROPERTIES OF HARD X-RAY SOLAR FLARES BY CONSTRAINING MODEL PARAMETERS

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23. We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non-Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, E{sub c} , a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that E{sub c} lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 {+-} 4 keV with 68% probability. Using the Bayesian/MCMC approach, we also estimate for the first time probability density functions for the total number of flare-accelerated electrons and the energy they carry for each flare studied. For the 2002 July 23 event, these probability density functions are asymmetric with long tails orders of magnitude higher than the most probable value, caused by the poorly constrained value of the low-energy cutoff. The most probable electron power is estimated at 10{sup 28.1} erg s{sup -1}, with a 68% credible interval estimated at 10{sup 28.1}-10{sup 29.0} erg s{sup -1}, and a 95% credible interval estimated at 10{sup 28.0}-10{sup 30.2} erg s{sup -1}. For the 2005 January 19 flare spectrum, the probability density functions for the total number of flare-accelerated electrons and their energy are much more symmetric and narrow: the most probable electron power is estimated at 10{sup 27.66{+-}0.01} erg s{sup -1} (68% credible intervals). However, in this case the uncertainty due to systematic sources of error is estimated to dominate the uncertainty due to statistical sources of error.

79 ASTRONOMY AND ASTROPHYSICS↗