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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 OSTI2014

SU-E-T-442: Sensitivity of Quality Assurance Tools to Delivery Errors On a Magnetic Resonance-Imaging Guided Radiation Therapy (MR-IGRT) System

Purpose: To test the sensitivity of the quality assurance (QA) tools actively used on a clinical MR-IGRT system for potential delivery errors. Methods: Patient-specific QA procedures have been implemented for a commercially available Cobalt-60 MR-IGRT system. The QA tools utilized were a MR-compatible cylindrical diode-array detector (ArcCHECK) with a custom insert which positions an ionization chamber (Exradin A18) in the middle of the device, as well as an in-house treatment delivery verification program. These tools were tested to investigate their sensitivity to delivery errors. For the ArcCHECK and ion chamber, a baseline was established with a static field irradiation to a known dose. Variations of the baseline were investigated which included rotated gantry, altered field size, directional shifts, and different delivery time. In addition, similar variations were tested with the automated delivery verification program that compared the treatment parameters in the machine delivery logs to the ones in the plan. To test the software, a 3-field conformal plan was generated as the baseline. Results: ArcCHECK noted at least a 13% decrease in passing rate from baseline in the following scenarios: gantry rotation of 1 degree from plan, 5mm change in field size, 2mm lateral shift, and delivery time decrease. Ion chamber measurements remained consistent for these variations except for the 5 second decrease in delivery time scenario which resulted in an 8% difference from baseline. The delivery verification software was able to detect and report the simulated errors such as when the gantry was rotated by 0.6 degrees, the beam weighting was changed by a percent, a single multileaf collimator was moved by 1cm, and the dose was changed from 2 to 1.8Gy. Conclusion: The results show that the current tools used for patient specific QA are capable of detecting small errors in RT delivery with presence of magnetic field.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-T-642: Safety Procedures for Error Elimination in Cyberknife Stereotactic Radiosurgery (SRS) and Stereotactic Body Radiation Therapy (SBRT)

Purpose: Cyberknife system is used for providing stereotactic radiosurgery (SRS) and stereotactic body radiation therapy (SBRT) hypofractionation scheme. The whole treatment delivery is based on live imaging of the patient. The minor error made at any stage may bring severe radiation injury to the patient or damage to the system itself. Several safety measures were taken to make the system safer. Methods: The radiation treatment provided thru a 6MV linac attached to Kuka robot (Cyberknife G4, Accuray Inc. Sunnyvale, CA, USA). Several possible errors were identified related to patient alignment, treatment planning, dose delivery and physics quality assurance. During dose delivery, manual and visual checks were introduced to confirm pre and intra-treatment imaging to reduce possible errors. One additional step was introduced to confirm that software tracking-tools had worked correctly with highest possible confidence level. Robotic head move in different orientations over and around the patient body, the rigidity of linac-head cover and other accessories was checked periodically. The vender was alerted when a tiny or bigger piece of equipment needed additional interlocked support. Results: As of our experience treating 525 patients on Cyberknife during the last four years, we saw on and off technical issues. During image acquisition, it was made essential to follow the site-specific imaging protocols. Adequate anatomy was contoured to document the respective doses. Followed by auto-segmentation, manual tweaking was performed on every structure. The calculation box was enclosing the whole image during the final calculation. Every plan was evaluated on slice-by slice basis. To review the whole process, a check list was maintained during the physics 2nd-check. Conclusion: The implementation of manual and visual additional checks introduced along with automated checks for confirmation was found promising in terms of reduction in systematic errors and making the system safer than before.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-CAMPUS-I-02: Estimation of the Dosimetric Error Caused by the Voxelization of Hybrid Computational Phantoms Using Triangle Mesh-Based Monte Carlo Transport

Purpose: Computational voxel phantom provides realistic anatomy but the voxel structure may result in dosimetric error compared to real anatomy composed of perfect surface. We analyzed the dosimetric error caused from the voxel structure in hybrid computational phantoms by comparing the voxel-based doses at different resolutions with triangle mesh-based doses. Methods: We incorporated the existing adult male UF/NCI hybrid phantom in mesh format into a Monte Carlo transport code, penMesh that supports triangle meshes. We calculated energy deposition to selected organs of interest for parallel photon beams with three mono energies (0.1, 1, and 10 MeV) in antero-posterior geometry. We also calculated organ energy deposition using three voxel phantoms with different voxel resolutions (1, 5, and 10 mm) using MCNPX2.7. Results: Comparison of organ energy deposition between the two methods showed that agreement overall improved for higher voxel resolution, but for many organs the differences were small. Difference in the energy deposition for 1 MeV, for example, decreased from 11.5% to 1.7% in muscle but only from 0.6% to 0.3% in liver as voxel resolution increased from 10 mm to 1 mm. The differences were smaller at higher energies. The number of photon histories processed per second in voxels were 6.4×10{sup 4}, 3.3×10{sup 4}, and 1.3×10{sup 4}, for 10, 5, and 1 mm resolutions at 10 MeV, respectively, while meshes ran at 4.0×10{sup 4} histories/sec. Conclusion: The combination of hybrid mesh phantom and penMesh was proved to be accurate and of similar speed compared to the voxel phantom and MCNPX. The lowest voxel resolution caused a maximum dosimetric error of 12.6% at 0.1 MeV and 6.8% at 10 MeV but the error was insignificant in some organs. We will apply the tool to calculate dose to very thin layer tissues (e.g., radiosensitive layer in gastro intestines) which cannot be modeled by voxel phantoms.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

TH-A-9A-03: Dosimetric Effect of Rotational Errors for Lung Stereotactic Body Radiotherapy

Purpose: To evaluate the dosimetric effects on target volume and organs at risk (OARs) due to roll rotational errors in treatment setup of stereotactic body radiation therapy (SBRT) for lung cancer. Methods: There were a total of 23 volumetric modulated arc therapy (VMAT) plans for lung SBRT examined in this retrospective study. Each CT image of VMAT plans was intentionally rotated by ±1°, ±2°, and ±3° to simulate roll rotational setup errors. The axis of rotation was set at the center of T-spine. The target volume and OARs in the rotated CT images were re-defined by deformable registration of original contours. The dose distributions on each set of rotated images were re-calculated to cover the planning target volume (PTV) with the prescription dose before and after the couch translational correction. The dose-volumetric changes of PTVs and spinal cords were analyzed. Results: The differences in D95% of PTVs by −3°, −2°, −1°, 1°, 2°, and 3° roll rotations before the couch translational correction were on average −11.3±11.4%, −5.46±7.24%, −1.11±1.38% −3.34±3.97%, −9.64±10.3%, and −16.3±14.7%, respectively. After the couch translational correction, those values were −0.195±0.544%, −0.159±0.391%, −0.188±0.262%, −0.310±0.270%, −0.407±0.331%, and −0.433±0.401%, respectively. The maximum dose difference of spinal cord among the 23 plans even after the couch translational correction was 25.9% at −3° rotation. Conclusions: Roll rotational setup errors in lung SBRT significantly influenced the coverage of target volume using VMAT technique. This could be in part compensated by the translational couch correction. However, in spite of the translational correction, the delivered doses to the spinal cord could be more than the calculated doses. Therefore if rotational setup errors exist during lung SBRT using VMAT technique, the rotational correction would rather be considered to prevent over-irradiation of normal tissues than the translational correction.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Using computer-extracted image features for modeling of error-making patterns in detection of mammographic masses among radiology residents

Purpose: Mammography is the most widely accepted and utilized screening modality for early breast cancer detection. Providing high quality mammography education to radiology trainees is essential, since excellent interpretation skills are needed to ensure the highest benefit of screening mammography for patients. The authors have previously proposed a computer-aided education system based on trainee models. Those models relate human-assessed image characteristics to trainee error. In this study, the authors propose to build trainee models that utilize features automatically extracted from images using computer vision algorithms to predict likelihood of missing each mass by the trainee. This computer vision-based approach to trainee modeling will allow for automatically searching large databases of mammograms in order to identify challenging cases for each trainee. Methods: The authors’ algorithm for predicting the likelihood of missing a mass consists of three steps. First, a mammogram is segmented into air, pectoral muscle, fatty tissue, dense tissue, and mass using automated segmentation algorithms. Second, 43 features are extracted using computer vision algorithms for each abnormality identified by experts. Third, error-making models (classifiers) are applied to predict the likelihood of trainees missing the abnormality based on the extracted features. The models are developed individually for each trainee using his/her previous reading data. The authors evaluated the predictive performance of the proposed algorithm using data from a reader study in which 10 subjects (7 residents and 3 novices) and 3 experts read 100 mammographic cases. Receiver operating characteristic (ROC) methodology was applied for the evaluation. Results: The average area under the ROC curve (AUC) of the error-making models for the task of predicting which masses will be detected and which will be missed was 0.607 (95% CI,0.564-0.650). This value was statistically significantly different from 0.5 (p < 0.0001). For the 7 residents only, the AUC performance of the models was 0.590 (95% CI,0.537-0.642) and was also significantly higher than 0.5 (p = 0.0009). Therefore, generally the authors’ models were able to predict which masses were detected and which were missed better than chance. Conclusions: The authors proposed an algorithm that was able to predict which masses will be detected and which will be missed by each individual trainee. This confirms existence of error-making patterns in the detection of masses among radiology trainees. Furthermore, the proposed methodology will allow for the optimized selection of difficult cases for the trainees in an automatic and efficient manner.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Characterization of XR-RV3 GafChromic{sup ®} films in standard laboratory and in clinical conditions and means to evaluate uncertainties and reduce errors

Purpose: To investigate the optimal use of XR-RV3 GafChromic{sup ®} films to assess patient skin dose in interventional radiology while addressing the means to reduce uncertainties in dose assessment. Methods: XR-Type R GafChromic films have been shown to represent the most efficient and suitable solution to determine patient skin dose in interventional procedures. As film dosimetry can be associated with high uncertainty, this paper presents the EURADOS WG 12 initiative to carry out a comprehensive study of film characteristics with a multisite approach. The considered sources of uncertainties include scanner, film, and fitting-related errors. The work focused on studying film behavior with clinical high-dose-rate pulsed beams (previously unavailable in the literature) together with reference standard laboratory beams. Results: First, the performance analysis of six different scanner models has shown that scan uniformity perpendicular to the lamp motion axis and that long term stability are the main sources of scanner-related uncertainties. These could induce errors of up to 7% on the film readings unless regularly checked and corrected. Typically, scan uniformity correction matrices and reading normalization to the scanner-specific and daily background reading should be done. In addition, the analysis on multiple film batches has shown that XR-RV3 films have generally good uniformity within one batch (<1.5%), require 24 h to stabilize after the irradiation and their response is roughly independent of dose rate (<5%). However, XR-RV3 films showed large variations (up to 15%) with radiation quality both in standard laboratory and in clinical conditions. As such, and prior to conducting patient skin dose measurements, it is mandatory to choose the appropriate calibration beam quality depending on the characteristics of the x-ray systems that will be used clinically. In addition, yellow side film irradiations should be preferentially used since they showed a lower dependence on beam parameters compared to white side film irradiations. Finally, among the six different fit equations tested in this work, typically used third order polynomials and more rational and simplistic equations, of the form dose inversely proportional to pixel value, were both found to provide satisfactory results. Fitting-related uncertainty was clearly identified as a major contributor to the overall film dosimetry uncertainty with up to 40% error on the dose estimate. Conclusions: The overall uncertainty associated with the use of XR-RV3 films to determine skin dose in the interventional environment can realistically be estimated to be around 20% (k = 1). This uncertainty can be reduced to within 5% if carefully monitoring scanner, film, and fitting-related errors or it can easily increase to over 40% if minimal care is not taken. This work demonstrates the importance of appropriate calibration, reading, fitting, and other film-related and scan-related processes, which will help improve the accuracy of skin dose measurements in interventional procedures.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TU-AB-202-03: Prediction of PET Transfer Uncertainty by DIR Error Estimating Software, AUTODIRECT

Purpose: Deformable image registration (DIR) is a powerful tool, but DIR errors can adversely affect its clinical applications. To estimate voxel-specific DIR uncertainty, a software tool, called AUTODIRECT (automated DIR evaluation of confidence tool), has been developed and validated. This work tests the ability of this software to predict uncertainty for the transfer of standard uptake values (SUV) from positron-emission tomography (PET) with DIR. Methods: Virtual phantoms are used for this study. Each phantom has a planning computed tomography (CT) image and a diagnostic PET-CT image set. A deformation was digitally applied to the diagnostic CT to create the planning CT image and establish a known deformation between the images. One lung and three rectum patient datasets were employed to create the virtual phantoms. Both of these sites have difficult deformation scenarios associated with them, which can affect DIR accuracy (lung tissue sliding and changes in rectal filling). The virtual phantoms were created to simulate these scenarios by introducing discontinuities in the deformation field at the lung rectum border. The DIR algorithm from Plastimatch software was applied to these phantoms. The SUV mapping errors from the DIR were then compared to that predicted by AUTODIRECT. Results: The SUV error distributions closely followed the AUTODIRECT predicted error distribution for the 4 test cases. The minimum and maximum PET SUVs were produced from AUTODIRECT at 95% confidence interval before applying gradient-based SUV segmentation for each of these volumes. Notably, 93.5% of the target volume warped by the true deformation was included within the AUTODIRECT-predicted maximum SUV volume after the segmentation, while 78.9% of the target volume was within the target volume warped by Plastimatch. Conclusion: The AUTODIRECT framework is able to predict PET transfer uncertainty caused by DIR, which enables an understanding of the associated target volume uncertainty.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Estimating the Contributions to Human Error Probability from the Convolution of the Distribution of Time Available and Time Required

As part of their duties, Human Reliability Analysis must often evaluate if crews in nuclear power plants (NPPs) can complete tasks associated with a human-failure event within time limits. For example, the time required in NPP scenarios is determined by systematic and structured walkthroughs, feasibility studies, recorded times from training exercises, and interviews with experienced operators and experts. Typically, a point estimate is derived for the estimate (mean, maximum, or 95th percentile of time required). Using point-estimate values can mask the risk associated with variability among crews, plant conditions and set-up, environmental conditions, and other impact factors under which these actions are executed. While point estimates for time required and time available have served the industry well, without considering the uncertainty they could lead to biased understanding about the risk. The Integrated Human Event Analysis System - General Methodology (IDHEAS-G) model (developed by the US Nuclear Regulatory Commission, NRC) for human error probability calculates human error probability by summing two probabilities: insufficient time and cognitive error. As such, the model takes a more holistic approach by considering the full distributions for time required and time available to calculate the human error probability because the time available to complete the task is insufficient. In this study, we expand on the work of the NRC and discuss methods for estimating these time considerations. For example, for the time required, the impact of Performance Influencing Factors (PIFs) on the distribution was divided into impacts that are aleatory in nature, such as crew-to-crew variability, and those that are epistemic (i.e., the PIFs). Starting with the factors that introduce aleatory uncertainty, a first-order distribution was developed from a large set of time required (i.e., NPP task completion times) data for the range of operator actions that occur in the NPP control room under simulated accident conditions. The first-order distribution can then be adjusted to account for epistemic uncertainty using research associated with the impact of applicable PIFs on the time required. We also develop guidance for analysts to address the probability distributions for the time available. The guidance we developed on how to estimate time required and time available distributions is based on the identification of pertinent research and data, data analyses, and expert knowledge elicitation.

human error probability, human performance, time e↗
DOE OSTI2014

Effects of Spectral Error in Efficiency Measurements of GaInAs-Based Concentrator Solar Cells

This technical report documents a particular error in efficiency measurements of triple-absorber concentrator solar cells caused by incorrect spectral irradiance -- specifically, one that occurs when the irradiance from unfiltered, pulsed xenon solar simulators into the GaInAs bottom subcell is too high. For cells designed so that the light-generated photocurrents in the three subcells are nearly equal, this condition can cause a large increase in the measured fill factor, which, in turn, causes a significant artificial increase in the efficiency. The error is readily apparent when the data under concentration are compared to measurements with correctly balanced photocurrents, and manifests itself as discontinuities in plots of fill factor and efficiency versus concentration ratio. In this work, we simulate the magnitudes and effects of this error with a device-level model of two concentrator cell designs, and demonstrate how a new Spectrolab, Inc., Model 460 Tunable-High Intensity Pulsed Solar Simulator (T-HIPSS) can mitigate the error.

14 SOLAR ENERGY↗
DOE OSTI2018

Conceptual Interpretation of First and Second Kinds of Errors at Management Mode Selection under Conditions of Its Possible Crisis State

Errors in the selection of management practices at an enterprise confronting the prospect of crisis are considered: specifically, the adoption of standard management during a crisis; or crisis management when no crisis exists. By analogy with classical approaches in probability theory and operational research, such errors are interpreted as errors of the first and second kind. The basic problems arising from such errors are identified, and some measures are proposed for reducing their likelihood. The results should prove useful to managers at industrial enterprises, consulting firms, developers of management systems, and the faculty at universities and staff-training centers.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Utilizing physics-based input features within a machine learning model to predict wind speed forecasting error

Machine learning is quickly becoming a commonly used technique for wind speed and power forecasting. Many machine learning methods utilize exogenous variables as input features, but there remains the question of which atmospheric variables are most beneficial for forecasting, especially in handling non-linearities that lead to forecasting error. This question is addressed via creation of a hybrid model that utilizes an autoregressive integrated moving-average (ARIMA) model to make an initial wind speed forecast followed by a random forest model that attempts to predict the ARIMA forecasting error using knowledge of exogenous atmospheric variables. Variables conveying information about atmospheric stability and turbulence as well as inertial forcing are found to be useful in dealing with non-linear error prediction. Streamwise wind speed, time of day, turbulence intensity, turbulent heat flux, vertical velocity, and wind direction are found to be particularly useful when used in unison for hourly and 3 h timescales. The prediction accuracy of the developed ARIMA–random forest hybrid model is compared to that of the persistence and bias-corrected ARIMA models. The ARIMA–random forest model is shown to improve upon the latter commonly employed modeling methods, reducing hourly forecasting error by up to 5 % below that of the bias-corrected ARIMA model and achieving an R 2 value of 0.84 with true wind speed.

17 WIND ENERGY↗
NASA NTRS1986

Preliminary estimates of radiosonde thermistor errors

It has been long realized that radiosonde temperature measurements are subject to errors, not the least of which is the effect of long- and short-wave radiation. Methods of adjusting the daytime temperatures to a nighttime equivalent temperature were developed a number of years ago, and are used by some analysis centers. Other than providing consistent observations for analysis this procedure does not provide a true correction. The literature discusses the problem of radiosonde temperature errors but it is not apparent what effort, if any, has been taken to quantify these errors. In order to quantify this radiation error, radiosondes containing multiple thermistors with different coatings were flown at Goddard Space Flight Center/Wallops Flight Facility. The coatings employed had different spectral characteristics and, therefore, different absorption and emissivity properties. Discrimination of the recorded temperatures enabled day and night correction values to be determined for the US standard white-coated rod thermistor. The correction magnitudes are given and a comparison of US measured temperatures before and after correction are compared with temperatures measured with the Vaisala radiosonde. The US and Vaisala radiosonde data are from the recently completed WMO International Radiosonde Intercomparison held at Wallops. The corrections are in the proper direction, day and night, and reduce day-night temperature differences to less than 0,5°C between surface and 30 hPa. The present uncorrected temperatures used with the Viz radiosonde have day-night differences that exceed 1°C at levels below 90 hPa. Additional measurements are planned to confirm these preliminary results and determine the solar elevation angle effect on the corrections. The technique used to obtain the corrections may also be used to recover a true 'absolute' value and might be considered a valuable contribution to the meteorological community for use as a reference instrument.

Temperature measurement↗
NASA NTRS2008

Model Error Budgets

An error budget is a commonly used tool in design of complex aerospace systems. It represents system performance requirements in terms of allowable errors and flows these down through a hierarchical structure to lower assemblies and components. The requirements may simply be 'allocated' based upon heuristics or experience, or they may be designed through use of physics-based models. This paper presents a basis for developing an error budget for models of the system, as opposed to the system itself. The need for model error budgets arises when system models are a principle design agent as is increasingly more common for poorly testable high performance space systems.

error budgets↗
NASA NTRS2011

A Starshade Petal Error Budget for Exo-Earth Detection and Characterization

We present a starshade error budget with engineering requirements that are well within the current manufacturing and metrology capabilities. The error budget is based on an observational scenario in which the starshade spins about its axis on timescales short relative to the zodi-limited integration time, typically several hours. The scatter from localized petal errors is smoothed into annuli around the center of the image plane, resulting in a large reduction in the background flux variation while reducing thermal gradients caused by structural shadowing. Having identified the performance sensitivity to petal shape errors with spatial periods of 3-4 cycles/petal as the most challenging aspect of the design, we have adopted and modeled a manufacturing approach that mitigates these perturbations with 1-meter-long precision edge segments positioned using commercial metrology that readily meets assembly requirements. We have performed detailed thermal modeling and show that the expected thermal deformations are well within the requirements as well. We compare the requirements for four cases: a 32 meter diameter starshade with a 1.5 meter telescope, analyzed at 75 and 90 milliarcseconds, and a 40 meter diameter starshade with a 4 meter telescope, analyzed at 60 and 75 milliarcseconds.

error budget↗
NASA NTRS2023

Software Error Incident Categorizations in Aerospace

Since the first use of computers in space and aircraft, software errors have occurred. These errors can manifest as loss-of-life or less catastrophically. As the demand for automation increases, software in safety-critical systems should be designed to be tolerant to the most likely software faults. This paper categorizes historic aerospace software errors to determine trends of how and where automation is most likely to fail. A distinction between software producing wrong (erroneous) output versus no output (fail-silent) is introduced. Of the historical incidents analyzed, 87% were from software acting unexpectedly rather than simply stopping. Rebooting was found to be ineffective to clear erroneous behavior, and only partially effective for silent software. Errors were traced back to the software logic itself in 62% of cases, 13% within configurable data, and 25% introduced through input. Thirty percent (30%) of unexpected software behavior was caused by the absence of software and 20% was due to “unknown-unknowns”. These findings indicate that to achieve fault tolerance in safety-critical systems, backup strategies must be employed to detect and respond to erroneous software behavior beyond only fail-silent cases, and robust off-nominal testing should be performed to uncover unanticipated situations.

Software↗
DOE OSTI2019

Simulating wind power forecast error distributions for spatially aggregated wind power plants

Dispersion and aggregation of wind power plants lower the uncertainty of wind power by reducing wind power forecasting errors. Using quantitative methods, this paper studies the dispersion's impact on the uncertainty of the aggregated wind power production. A method to simulate day-ahead forecast error distributions at different dispersion and forecasting skill scenarios is presented. The proposed method models the uncertainty of wind power forecasting on an annual basis and at different levels of production. As a result, the uncertainty in the forecasting of spatially dispersed wind power plants is modelled using two continuous distributions: Laplace and beta distribution. The analysis shows that even the production level uncertainty can be modelled in various dispersion and forecasting skill scenarios. The model for aggregated forecast error distributions requires only four variables: capacity-weighted distance of the total wind power plant fleet, mean of the site-specific mean absolute errors (MAEs), number of aggregated wind power plants, and the mean variability of the elevations from the proximities of the aggregated wind power plants. Here, the results are especially promising when the number of aggregated wind power plants exceeds five, the terrain complexity is low or moderate, and the aggregation region is large. This is demonstrated through a case study for Texas, United States.

17 WIND ENERGY↗
DOE OSTI2023

Quantum error correction in the black hole interior

We study the quantum error correction properties of the black hole interior in a toy model for an evaporating black hole: Jackiw-Teitelboim gravity entangled with a non-gravitational bath. After the Page time, the black hole interior degrees of freedom in this system are encoded in the bath Hilbert space. We use the gravitational path integral to show that the interior density matrix is correctable against the action of quantum operations on the bath which (i) do not have prior access to details of the black hole microstates, and (ii) do not have a large, negative coherent information with respect to the maximally mixed state on the bath, with the lower bound controlled by the black hole entropy and code subspace dimension. Thus, the encoding of the black hole interior in the radiation is robust against generic, low-rank quantum operations. For erasure errors, gravity comes within an O (1) distance of saturating the Singleton bound on the tolerance of error correcting codes. For typical errors in the bath to corrupt the interior, they must have a rank that is a large multiple of the bath Hilbert space dimension, with the precise coefficient set by the black hole entropy and code subspace dimension.

2D gravity↗
DOE OSTI2019

A posteriori error estimation and adaptivity in hp virtual elements

An explicit and computable error estimator for the hp version of the virtual element method (VEM), together with lower and upper bounds with respect to the exact energy error, is presented. Such error estimator is employed to provide, following the approach of Melenk and Wohlmuth (Adv Comput Math 15(1–4):311–331, 2001), hp adaptive mesh refinements for very general polygonal meshes. In addition, a novel VEM hp Clément quasi-interpolant, instrumental for the a posteriori error analysis, is introduced. The performances of the adaptive method are validated by a number of numerical experiments.

97 MATHEMATICS AND COMPUTING↗