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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Practical and reliable error bars for quantum process tomography

Current techniques in quantum process tomography typically return a single point estimate of an unknown process based on a finite albeit large amount of measurement data. Due to statistical fluctuations, however, other processes close to the point estimate can also produce the observed data with near certainty. Unless appropriate error bars can be constructed, the point estimate does not carry any sound operational interpretation. Here, we provide a solution to this problem by constructing a confidence region estimator for quantum processes. Our method enables reliable estimation of essentially any figure of merit for quantum processes on few qubits, including the diamond distance to a specific noise model, the entanglement fidelity, and the worst-case entanglement fidelity, by identifying error regions which contain the true state with high probability. We also provide a software package, QPtomographer, implementing our estimator for the diamond norm and the worst-case entanglement fidelity. We illustrate its usage and performance with several simulated examples. Furthermore, our tools can be used to reliably certify the performance of, e.g., error correction codes, implementations of unitary gates, or more generally any noise process affecting a quantum system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

SU-F-T-252: An Investigation of Gamma Knife Frame Definition Error When Using a Pre-Planning Workflow

Purpose: To determine causal factors related to high frame definition error when treating GK patients using a pre-planning workflow. Methods: 160 cases were retrospectively reviewed. All patients received treatment using a pre-planning workflow whereby stereotactic coordinates are determined from a CT scan acquired after framing using a fiducial box. The planning software automatically detects the fiducials and compares their location to expected values based on the rigid design of the fiducial system. Any difference is reported as mean and maximum frame definition error. The manufacturer recommends these values be less than 1.0 mm and 1.5 mm. In this study, frame definition error was analyzed in comparison with a variety of factors including which neurosurgeon/oncologist/physicist was involved with the procedure, number of post used during framing (3 or 4), type of lesion, and which CT scanner was utilized for acquisition. An analysis of variance (ANOVA) approach was used to statistically evaluate the data and determine causal factors related to instances of high frame definition error. Results: Two factors were identified as significant: number of post (p=0.0003) and CT scanner (p=0.0001). Further analysis showed that one of the four scanners was significantly different than the others. This diagnostic scanner was identified as an older model with localization lasers not tightly calibrated. The average value for maximum frame definition error using this scanner was 1.48 mm (4 posts) and 1.75 mm (3 posts). For the other scanners this value was 1.13 mm (4 posts) and 1.40 mm (3 posts). Conclusion: In utilizing a pre-planning workflow the choice of CT scanner matters. Any scanner utilized for GK should undergo routine QA at a level appropriate for radiation oncology. In terms of 3 vs 4 post, it is hypothesized that three posts provide less stability during CT acquisition. This will be tested in future work.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Monte Carlo MP2-F12 for Noncovalent Interactions: The C 60 Dimer

A scalable stochastic algorithm is presented that can evaluate explicitly correlated (F12) second-order many-body perturbation (MP2) energies of weak, noncovalent, intermolecular interactions. It first transforms the formulas of the MP2 and F12 energy differences into a short sum of high-dimensional integrals of Green’s functions in real space and imaginary time. Furthermore, these integrals are then evaluated by the Monte Carlo method augmented by parallel execution, redundant-walker convergence acceleration, direct-sampling autocorrelation elimination, and control-variate error reduction. By sharing electron-pair walkers across the supermolecule and its subsystems spanned by the joint basis set, the statistical uncertainty is reduced by one to 2 orders of magnitude in the MP2 binding energy corrected for the basis-set incompleteness and superposition errors. The method predicts the MP2-F12/aug-cc-pVDZ binding energy of 19.1 ± 4.0 kcal mol –1 for the C 60 dimer at the center distance of 9.748 Å.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Balancing aggregation and smoothing errors in inverse models

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.

Turner, A. J.↗
DOE OSTI2016

Tracking Climate Change through the Spatiotemporal Dynamics of the Teletherms, the Statistically Hottest and Coldest Days of the Year

Instabilities and long term shifts in seasons, whether induced by natural drivers or human activities, pose great disruptive threats to ecological, agricultural, and social systems. Here, we propose, measure, and explore two fundamental markers of location-sensitive seasonal variations: the Summer and Winter Teletherms—the on-average annual dates of the hottest and coldest days of the year. We analyze daily temperature extremes recorded at 1218 stations across the contiguous United States from 1853–2012, and observe large regional variation with the Summer Teletherm falling up to 90 days after the Summer Solstice, and 50 days for the Winter Teletherm after the Winter Solstice. We show that Teletherm temporal dynamics are substantive with clear and in some cases dramatic shifts reflective of system bifurcations. We also compare recorded daily temperature extremes with output from two regional climate models finding considerable though relatively unbiased error. In conclusion, our work demonstrates that Teletherms are an intuitive, powerful, and statistically sound measure of local climate change, and that they pose detailed, stringent challenges for future theoretical and computational models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Uncertainty quantification for nuclear density functional theory and information content of new measurements

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. In addition, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A digital twin for rapid qualification of 3D printed metallic components

The customized production of complex components by 3D printing has been hailed as a potentially transformative tool in manufacturing with important applications in health care, automotive and aerospace industries. However, after about a quarter of a century of research and development, only a handful of commercial alloys can be printed and the market value of all 3D printed products now amounts to a negligible portion of the manufacturing economy. This difficulty is attributable to a remarkable diversity in structure and properties of the printed components and susceptibility to defects. In addition, the current practice of qualifying components by prolonged trial and error with expensive printing equipment and feed stock material confine the printed products to a niche market where the high product cost and the delay in the qualification are not critical factors. In this report we explain how a digital twin or a digital replica of the printing machine will reduce the number of trial and error tests to obtain desired product attributes and reduce the time required for part qualification to make the printed components cost effective. It is shown that a comprehensive digital twin of 3D printing machine consisting of mechanistic, control and statistical models of 3D printing, machine learning and big data can reduce the volume of trial and error testing, reduce defects and shorten time between the design and production.

36 MATERIALS SCIENCE↗
DOE OSTI2015

On the accuracy of Hipparcos using binary stars as a calibration tool

Stellar binary systems, specifically those that present the most accurate available orbital elements, are a reliable tool to test the accuracy of astrometric observations. We selected all 35 binaries with these characteristics. Our objective is to provide standard uncertainties for the positions and parallaxes measured by Hipparcos relative to this trustworthy set, as well as to check supposed correlations between several parameters (measurement residuals, positions, magnitudes, and parallaxes). In addition, using the high-confidence subset of visual–spectroscopic binaries, we implemented a validation test of the Hipparcos trigonometric parallaxes of binary systems that allowed the evaluation of their reliability. Standard and non-standard statistical analysis techniques were applied in order to achieve well-founded conclusions. In particular, errors-in-variables models such as the total least-squares method were used to validate Hipparcos parallaxes by comparison with those obtained directly from the orbital elements. Previously, we executed Thompson's τ technique in order to detect suspected outliers in the data. Furthermore, several statistical hypothesis tests were carried out to verify if our results were statistically significant. A statistically significant trend indicating larger Hipparcos angular separations with respect to the reference values in 5.2 ± 1.4 mas was found at the 10{sup −8} significance level. Uncertainties in the polar coordinates θ and ρ of 1.°8 and 6.3 mas, respectively, were estimated for the Hipparcos observations of binary systems. We also verified that the parallaxes of binary systems measured in this mission are absolutely compatible with the set of orbital parallaxes obtained from the most accurate orbits at least at the 95% confidence level. This methodology allows us to better estimate the accuracy of Hipparcos observations of binary systems. Indeed, further application to the data collected by Gaia should yield a standard procedure to compare both data sets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Ensuring statistical reproducibility of ocean model simulations in the age of hybrid computing

Novel high performance computing systems that feature hybrid architectures require large scale code refactoring to unravel underlying exploitable parallelism. Such redesign can often be accompanied with machine-precision changes as the order of computation cannot always be maintained. For chaotic systems like climate models, these round-off level differences can grow rapidly. Systematic errors may also manifest initially as machine-precision differences. Isolating genuine round off level differences from such errors remains a challenge. Here, we apply two-sample equality of distribution tests to evaluate statistical reproducibility of the ocean model component of US Department of Energy's Energy Exascale Earth System Model (E3SM). A 2-year control simulation ensemble is compared to a modified ensemble as a test case - after a known non-bit-for-bit change in a model component is introduced - to evaluate the null hypothesis that the two ensembles are statistically indistinguishable. To quantify the false negative rates of these tests, we conduct a formal power analysis using a targeted suite of short simulation ensembles. The ensemble suite contains several perturbed ensembles, each with a progressively different climate than the baseline ensemble - obtained by perturbing the magnitude of a single model tuning parameter, the Gent and McWilliams κ, in a controlled manner. The null hypothesis is evaluated for each of perturbed ensembles using these tests. The power analysis informs on the detection limits of the tests for given ensemble size allowing model developers to evaluate the impact of an introduced non-bit-for-bit change to the model.

Mahajan, Salil↗
DOE OSTI2013

IS QUASAR OPTICAL VARIABILITY A DAMPED RANDOM WALK?

The damped random walk (DRW) model is increasingly used to model the variability in quasar optical light curves, but it is still uncertain whether the DRW model provides an adequate description of quasar optical variability across all timescales. Using a sample of OGLE quasar light curves, we consider four modifications to the DRW model by introducing additional parameters into the covariance function to search for deviations from the DRW model on both short and long timescales. We find good agreement with the DRW model on timescales that are well sampled by the data (from a month to a few years), possibly with some intrinsic scatter in the additional parameters, but this conclusion depends on the statistical test employed and is sensitive to whether the estimates of the photometric errors are correct to within {approx}10%. On very short timescales (below a few months), we see some evidence of the existence of a cutoff below which the correlation is stronger than the DRW model, echoing the recent finding of Mushotzky et al. using quasar light curves from Kepler. On very long timescales (>a few years), the light curves do not constrain models well, but are consistent with the DRW model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

A CRITICAL ASSESSMENT OF PHOTOMETRIC REDSHIFT METHODS: A CANDELS INVESTIGATION

We present results from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) photometric redshift methods investigation. In this investigation, the results from 11 participants, each using a different combination of photometric redshift code, template spectral energy distributions (SEDs), and priors, are used to examine the properties of photometric redshifts applied to deep fields with broadband multi-wavelength coverage. The photometry used includes U-band through mid-infrared filters and was derived using the TFIT method. Comparing the results, we find that there is no particular code or set of template SEDs that results in significantly better photometric redshifts compared to others. However, we find that codes producing the lowest scatter and outlier fraction utilize a training sample to optimize photometric redshifts by adding zero-point offsets, template adjusting, or adding extra smoothing errors. These results therefore stress the importance of the training procedure. We find a strong dependence of the photometric redshift accuracy on the signal-to-noise ratio of the photometry. On the other hand, we find a weak dependence of the photometric redshift scatter with redshift and galaxy color. We find that most photometric redshift codes quote redshift errors (e.g., 68% confidence intervals) that are too small compared to that expected from the spectroscopic control sample. We find that all codes show a statistically significant bias in the photometric redshifts. However, the bias is in all cases smaller than the scatter; the latter therefore dominates the errors. Finally, we find that combining results from multiple codes significantly decreases the photometric redshift scatter and outlier fraction. We discuss different ways of combining data to produce accurate photometric redshifts and error estimates.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Impact of genotype‐calling methodologies on genome‐wide association and genomic prediction in polyploids

Abstract Discovery and analysis of genetic variants underlying agriculturally important traits are key to molecular breeding of crops. Reduced representation approaches have provided cost‐efficient genotyping using next‐generation sequencing. However, accurate genotype calling from next‐generation sequencing data is challenging, particularly in polyploid species due to their genome complexity. Recently developed Bayesian statistical methods implemented in available software packages, polyRAD, EBG, and updog, incorporate error rates and population parameters to accurately estimate allelic dosage across any ploidy. We used empirical and simulated data to evaluate the three Bayesian algorithms and demonstrated their impact on the power of genome‐wide association study (GWAS) analysis and the accuracy of genomic prediction. We further incorporated uncertainty in allelic dosage estimation by testing continuous genotype calls and comparing their performance to discrete genotypes in GWAS and genomic prediction. We tested the genotype‐calling methods using data from two autotetraploid species, Miscanthus sacchariflorus and Vaccinium corymbosum , and performed GWAS and genomic prediction. In the empirical study, the tested Bayesian genotype‐calling algorithms differed in their downstream effects on GWAS and genomic prediction, with some showing advantages over others. Through subsequent simulation studies, we observed that at low read depth, polyRAD was advantageous in its effect on GWAS power and limit of false positives. Additionally, we found that continuous genotypes increased the accuracy of genomic prediction, by reducing genotyping error, particularly at low sequencing depth. Our results indicate that by using the Bayesian algorithm implemented in polyRAD and continuous genotypes, we can accurately and cost‐efficiently implement GWAS and genomic prediction in polyploid crops.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

A priori mesh quality metrics for three-dimensional hybrid grids

Use of general hybrid grids to attain complex-geometry field simulations poses a challenge on estimation of their quality. Apart from the typical problems of non-uniformity and non-orthogonality, the change in element topology is an extra issue to address. The present work derives and evaluates an a priori mesh quality indicator for structured, unstructured, as well as hybrid grids consisting of hexahedra, prisms, tetrahedra, and pyramids. Emphasis is placed on deriving a direct relation between the quality measure and mesh distortion. The work is based on use of the Finite Volume discretization for evaluation of first order spatial derivatives. The analytic form of the truncation error is derived and applied to elementary types of mesh distortion including typical hybrid grid interfaces. The corresponding analytic expressions provide relations between the truncation error and the degree of stretching, skewness, shearing, torsion, expansion, as well as the type of grid interface.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

STUDIES IN ASTRONOMICAL TIME SERIES ANALYSIS. VI. BAYESIAN BLOCK REPRESENTATIONS

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it-an improved and generalized version of Bayesian Blocks-that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multivariate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by Arias-Castro et al. In the spirit of Reproducible Research all of the code and data necessary to reproduce all of the figures in this paper are included as supplementary material.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

THE ABSOLUTE MAGNITUDE OF RRc VARIABLES FROM STATISTICAL PARALLAX

We present the first definitive measurement of the absolute magnitude of RR Lyrae c-type variable stars (RRc) determined purely from statistical parallax. We use a sample of 242 RRc variables selected from the All Sky Automated Survey for which high-quality light curves, photometry, and proper motions are available. We obtain high-resolution echelle spectra for these objects to determine radial velocities and abundances as part of the Carnegie RR Lyrae Survey. We find that M{sub V,RRc} = 0.59 ± 0.10 at a mean metallicity of [Fe/H] = –1.59. This is to be compared with previous estimates for RRab stars (M{sub V,RRab} = 0.76 ± 0.12) and the only direct measurement of an RRc absolute magnitude (RZ Cephei, M{sub V,RRc} = 0.27 ± 0.17). We find the bulk velocity of the halo relative to the Sun to be (W{sub π}, W{sub θ}, W{sub z} ) = (12.0, –209.9, 3.0) km s{sup –1} in the radial, rotational, and vertical directions with dispersions (σ{sub W{sub π}},σ{sub W{sub θ}},σ{sub W{sub z}}) = (150.4, 106.1, 96.0) km s{sup -1}. For the disk, we find (W{sub π}, W{sub θ}, W{sub z} ) = (13.0, –42.0, –27.3) km s{sup –1} relative to the Sun with dispersions (σ{sub W{sub π}},σ{sub W{sub θ}},σ{sub W{sub z}}) = (67.7,59.2,54.9) km s{sup -1}. Finally, as a byproduct of our statistical framework, we are able to demonstrate that UCAC2 proper-motion errors are significantly overestimated as verified by UCAC4.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Cyber-Attack Detection for Active Neutral Point Clamped (ANPC) Photovoltaic (PV) Converter using Kalman Filter

With the upgrading of communication technology, cyber threats to power converters are increasing. In this paper, a model-based cyber-attack detection methodology is proposed for the interleaved Active neutral point clamped (ANPC) Photovoltaic (PV) converter. The proposed methodology identifies cyber-attacks using two estimations based on the Kalman filter and the state-space model of the ANPC PV converter. The residual between the two estimations is analyzed from a statistical perspective. Based on the Cumulative Sum (CUSUM) Control Chart, the standard errors shift of the residual is used to identify cyber-attacks. Besides, to validate the feasibility of the proposed methodology, several conditions are considered in the simulation, including white noise in the sensor, irradiance variation, and cyber-attacks in the PV converter. Furthermore, the simulation result demonstrates the proposed method can identify cyber-attacks in the ANPC PV converter.

14 SOLAR ENERGY↗
DOE OSTI2013

Real-time catheter tracking for high-dose-rate prostate brachytherapy using an electromagnetic 3D-guidance device: A preliminary performance study

Purpose: In order to increase the accuracy and speed of catheter reconstruction in a high-dose-rate (HDR) prostate implant procedure, an automatic tracking system has been developed using an electromagnetic (EM) device (trakSTAR, Ascension Technology, VT). The performance of the system, including the accuracy and noise level with various tracking parameters and conditions, were investigated. Methods: A direct current (dc) EM transmitter (midrange model) and a sensor with diameter of 1.3 mm (Model 130) were used in the trakSTAR system for tracking catheter position during HDR prostate brachytherapy. Localization accuracy was assessed under both static and dynamic analyses conditions. For the static analysis, a calibration phantom was used to investigate error dependency on operating room (OR) table height (bottom vs midposition vs top), sensor position (distal tip of catheter vs connector end of catheter), direction [left-right (LR) vs anterior-posterior (AP) vs superior-inferior (SI)], sampling frequency (40 vs 80 vs 120 Hz), and interference from OR equipment (present vs absent). The mean and standard deviation of the localization offset in each direction and the corresponding error vectors were calculated. For dynamic analysis, the paths of five straight catheters were tracked to study the effects of directions, sampling frequency, and interference of EM field. Statistical analysis was conducted to compare the results in different configurations. Results: When interference was present in the static analysis, the error vectors were significantly higher at the top table position (3.3 {+-} 1.3 vs 1.8 {+-} 0.9 mm at bottom and 1.7 {+-} 1.0 mm at middle, p < 0.001), at catheter end position (3.1 {+-} 1.1 vs 1.4 {+-} 0.7 mm at the tip position, p < 0.001), and at 40 Hz sampling frequency (2.6 {+-} 1.1 vs 2.4 {+-} 1.5 mm at 80 Hz and 1.8 {+-} 1.1 at 160 Hz, p < 0.001). So did the mean offset errors in the LR direction (-1.7 {+-} 1.4 vs 0.4 {+-} 0.5 mm in AP and 0.8 {+-} 0.8 mm in SI directions, p < 0.001). The error vectors were significantly higher with surrounding interference (2.2 {+-} 1.3 mm) vs without interference (1.0 {+-} 0.7 mm, p < 0.001). An accuracy of 1.6 {+-} 0.2 mm can be reached when using optimum configuration (160 Hz at middle table position). When interference was present in the dynamic tracking, the mean tracking errors in LR direction (1.4 {+-} 0.5 mm) was significantly higher than that in AP direction (0.3 {+-} 0.2 mm, p < 0.001). So did the mean vector errors at 40 Hz (2.1 {+-} 0.2 mm vs 1.3 {+-} 0.2 mm at 80 Hz and 0.9 {+-} 0.2 mm at 160 Hz, p < 0.05). However, when interference was absent, they were comparable in the both directions and at all sampling frequencies. An accuracy of 0.9 {+-} 0.2 mm was obtained for the dynamic tracking when using optimum configuration. Conclusions: The performance of an EM tracking system depends highly on the system configuration and surrounding environment. The accuracy of EM tracking for catheter reconstruction in a prostate HDR brachytherapy procedure can be improved by reducing interference from surrounding equipment, decreasing distance from transmitter to tracking area, and choosing appropriated sampling frequency. A calibration scheme is needed to further reduce the tracking error when the interference is high.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2024

NovaDemux v39.07

This program is a sequence demultiplexer intended primarily for, but not limited to, Illumina sequencing machines. Typically, multiple experiments ("libraries") are pooled together and sequenced at once, with genetic molecules of these libraries tagged with a synthetic DNA "barcode". After sequencing, the data is demultiplexed into one file per library based on the barcode. However, errors in barcode reading cause misassignment and decrease yield. NovaDemux uses advanced statistical methods to maximize yield while minimizing misassignment compared to existing software.

Bushnell, Brian [Lawrence Berkeley National Labora↗