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DOE OSTI2015

TRUE MASSES OF RADIAL-VELOCITY EXOPLANETS

We study the task of estimating the true masses of known radial-velocity (RV) exoplanets by means of direct astrometry on coronagraphic images to measure the apparent separation between exoplanet and host star. Initially, we assume perfect knowledge of the RV orbital parameters and that all errors are due to photon statistics. We construct design reference missions for four missions currently under study at NASA: EXO-S and WFIRST-S, with external star shades for starlight suppression, EXO-C and WFIRST-C, with internal coronagraphs. These DRMs reveal extreme scheduling constraints due to the combination of solar and anti-solar pointing restrictions, photometric and obscurational completeness, image blurring due to orbital motion, and the “nodal effect,” which is the independence of apparent separation and inclination when the planet crosses the plane of the sky through the host star. Next, we address the issue of nonzero uncertainties in RV orbital parameters by investigating their impact on the observations of 21 single-planet systems. Except for two—GJ 676 A b and 16 Cyg B b, which are observable only by the star-shade missions—we find that current uncertainties in orbital parameters generally prevent accurate, unbiased estimation of true planetary mass. For the coronagraphs, WFIRST-C and EXO-C, the most likely number of good estimators of true mass is currently zero. For the star shades, EXO-S and WFIRST-S, the most likely numbers of good estimators are three and four, respectively, including GJ 676 A b and 16 Cyg B b. We expect that uncertain orbital elements currently undermine all potential programs of direct imaging and spectroscopy of RV exoplanets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Cluster Mass Calibration at High Redshift: HST Weak Lensing Analysis of 13 Distant Galaxy Clusters from the South Pole Telescope Sunyaev-Zel’dovich Survey

We present an HST/Advanced Camera for Surveys (ACS) weak gravitational lensing analysis of 13 massive high-redshift (z(median) = 0.88) galaxy clusters discovered in the South Pole Telescope (SPT) Sunyaev-Zel'dovich Survey. This study is part of a larger campaign that aims to robustly calibrate mass-observable scaling relations over a wide range in redshift to enable improved cosmological constraints from the SPT cluster sample. We introduce new strategies to ensure that systematics in the lensing analysis do not degrade constraints on cluster scaling relations significantly. First, we efficiently remove cluster members from the source sample by selecting very blue galaxies in V - I colour. Our estimate of the source redshift distribution is based on Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) data, where we carefully mimic the source selection criteria of the cluster fields. We apply a statistical correction for systematic photometric redshift errors as derived from Hubble Ultra Deep Field data and verified through spatial cross-correlations. We account for the impact of lensing magnification on the source redshift distribution, finding that this is particularly relevant for shallower surveys. Finally, we account for biases in the mass modelling caused by miscentring and uncertainties in the concentration-mass relation using simulations. In combination with temperature estimates from Chandra we constrain the normalization of the mass-temperature scaling relation ln (E(z) M-500c/10(14)M(circle dot)) = A + 1.5ln (kT/7.2 keV) to A = 1.81(-0.14)(+0.24)(stat.)+/- 0.09(sys.), consistent with self-similar redshift evolution when compared to lower redshift samples. Additionally, the lensing data constrain the average concentration of the clusters to c(200c) = 5.6(-1.8)(+3.7).

cosmology: observations↗

DOE OSTI2023

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Seeing through noise in power laws

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Coordinated Ramping Product and Regulation Reserve Procurements in CAISO and MISO using Multi-Scale Probabilistic Solar Power Forecasts (Pro2R)

How can probabilistic solar forecasts lower costs and improve reliability for independent system operator (ISO) markets? We tackle this question in three steps. First, we enhance an existing solar forecasting system to provide well-calibrated hours-ahead probabilistic forecasts. We then relate the degree of uncertainty in those forecasts to error distributions for net load ramps for the California ISO (CAISO) using statistical and machine learning methods. Projected net load errors conditioned on solar uncertainty are translated into flexible ramp requirements that therefore reflect real-time meteorological and solar conditions, improving on typical ISO procedures. Finally, a multi-period look-ahead production cost model quantifies how conditional ramp requirements can a) decrease operating costs by lowering requirements compared to often conservative unconditional methods, and b) reduce generation scarcity events and consequently improve reliability by increasing flexibility requirements at times when unconditional forecast-based requirements understate actual ramp uncertainty. In addition to the products just described (quantification of solar uncertainty, its translation into requirements for ramp capability product, and quantification of the benefits of more accurate ramp requirements), this project also developed a visualization system that alerts system operators of ramp and uncertainty conditions within the network based on solar forecasts. The system is called Resource Forecast and Ramp Visualization for Situational Awareness (RaVIS). These four products represent significant advances in the state-of-the-art of probabilistic solar forecasting, development of weather-informed reserve requirements, production costing methods for estimating the benefits of more accurate reserve requirements, and visualization of system status, respectively. Yet the products are also practical and can be immediately implemented, potentially enabling system operators to save millions of dollars in ramp product procurement costs per year.

14 SOLAR ENERGY↗

DOE OSTI2016

WE-DE-201-02: A Statistical Analysis Tool for Plan Quality Verification in HDR Brachytherapy Forward Planning for Cervix Cancer

Purpose: High Dose Rate (HDR) brachytherapy forward planning is principally an iterative process; hence, plan quality is affected by planners’ experiences and limited planning time. Thus, this may lead to sporadic errors and inconsistencies in planning. A statistical tool based on previous approved clinical treatment plans would help to maintain the consistency of planning quality and improve the efficiency of second checking. Methods: An independent dose calculation tool was developed from commercial software. Thirty-three previously approved cervical HDR plans with the same prescription dose (550cGy), applicator type, and treatment protocol were examined, and ICRU defined reference point doses (bladder, vaginal mucosa, rectum, and points A/B) along with dwell times were collected. Dose calculation tool then calculated appropriate range with a 95% confidence interval for each parameter obtained, which would be used as the benchmark for evaluation of those parameters in future HDR treatment plans. Model quality was verified using five randomly selected approved plans from the same dataset. Results: Dose variations appears to be larger at the reference point of bladder and mucosa as compared with rectum. Most reference point doses from verification plans fell between the predicted range, except the doses of two points of rectum and two points of reference position A (owing to rectal anatomical variations & clinical adjustment in prescription points, respectively). Similar results were obtained for tandem and ring dwell times despite relatively larger uncertainties. Conclusion: This statistical tool provides an insight into clinically acceptable range of cervical HDR plans, which could be useful in plan checking and identifying potential planning errors, thus improving the consistency of plan quality.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Magnetic Resonance Imaging Assessment of Spinal Cord and Cauda Equina Motion in Supine Patients With Spinal Metastases Planned for Spine Stereotactic Body Radiation Therapy

Purpose: To assess motion of the spinal cord and cauda equina, which are critical neural tissues (CNT), which is important when evaluating the planning organ-at-risk margin required for stereotactic body radiation therapy. Methods and Materials: We analyzed CNT motion in 65 patients with spinal metastases (11 cervical, 39 thoracic, and 24 lumbar spinal segments) in the supine position using dynamic axial and sagittal magnetic resonance imaging (dMRI, 3T Verio, Siemens) over a 137-second interval. Motion was segregated according to physiologic cardiorespiratory oscillatory motion (characterized by the average root mean square deviation) and random bulk shifts associated with gross patient motion (characterized by the range). Displacement was evaluated in the anteroposterior (AP), lateral (LR), and superior-inferior (SI) directions by use of a correlation coefficient template matching algorithm, with quantification of random motion measure error over 3 separate trials. Statistical significance was defined according to P<.05. Results: In the AP, LR, and SI directions, significant oscillatory motion was observed in 39.2%, 35.1%, and 10.8% of spinal segments, respectively, and significant bulk motions in all cases. The median oscillatory CNT motions in the AP, LR, and SI directions were 0.16 mm, 0.17 mm, and 0.44 mm, respectively, and the maximal statistically significant oscillatory motions were 0.39 mm, 0.41 mm, and 0.77 mm, respectively. The median bulk displacements in the AP, LR, and SI directions were 0.51 mm, 0.59 mm, and 0.66 mm, and the maximal statistically significant displacements were 2.21 mm, 2.87 mm, and 3.90 mm, respectively. In the AP, LR, and SI directions, bulk displacements were greater than 1.5 mm in 5.4%, 9.0%, and 14.9% of spinal segments, respectively. No significant differences in axial motion were observed according to cord level or cauda equina. Conclusions: Oscillatory CNT motion was observed to be relatively minor. Our results support the importance of controlling bulk patient motion and the practice of applying a planning organ-at-risk margin.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2013

Subcell resolution in simplex stochastic collocation for spatial discontinuities

Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSC–SR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers’ equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSC–SR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Tribological behavior prediction of friction materials for ultrasonic motors using Monte Carlo‐based artificial neural network

ABSTRACT In this article, the relationship of complexity, diversity, and uncertainty between components and tribological properties of friction materials based on a Monte Carlo‐based artificial neural network (MC‐ANN) model was predicted precisely. Meanwhile, the grey relational analysis was applied to figure out weight of factors, optimize formulation design, and calculate nonlinear dependency of ingredients. The accuracy of model was studied by comparing experimental and simulated values on the basis of statistical methods (root‐mean‐squared error). It was found that the model exhibited an excellent performance in predicting and fitting effect. Moreover, comprehensive analysis of weight indicated that nano‐SiO 2 and mica exerted a significant role in improving the friction stability and wear resistance. According to different contents of each ingredient, the corresponding friction coefficient and specific wear rate could be obtained by virtue of a well‐trained MC‐ANN model without experiments, which saved a lot of time and money. It can be expected that the results of this work will extend the current research and pave a route for further in‐depth studies of friction materials. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136 , 47157.

Li, Song↗

DOE OSTI2017

RElative QUantitation Inferred by Evaluating Mixtures (REQUIEM)

Motivated by the lack of easily implementable and generally applicable strategies to increase and assess data accuracy, we devised a novel label-free approach, termed REQUIEM, to address challenges in relative quantitation. For comparing the relative amounts of analytes in two samples, a mixture is prepared from aliquots of the samples, and the samples and the mixture are analyzed in parallel according to the intended workflow. Processing of the resulting data using the REQUIEM algorithm yields unbiased analyte fold-changes and associated statistics, allowing several types of errors to be diagnosed or eliminated. Extensive simulations and analysis of carefully prepared standard samples demonstrated the rigorous foundations of REQUIEM. We applied REQUIEM to several real-world analytical techniques and workflows, notably to tandem mass spectrometry analysis by using isomeric oligosaccharides as test analytes. Finally, we conclude that REQUIEM can reveal inaccuracies in the data that are difficult to identify by using traditional approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States

The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Here, our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

TDCOSMO. I. An exploration of systematic uncertainties in the inference of $H_0$ from time-delay cosmography

Time-delay cosmography of lensed quasars has achieved 2.4% precision on the measurement of the Hubble constant, H0. As part of an ongoing effort to uncover and control systematic uncertainties, we investigate three potential sources: 1- stellar kinematics, 2- line-of-sight effects, and 3- the deflector mass model. To meet this goal in a quantitative way, we reproduced the H0LiCOW/SHARP/STRIDES (hereafter TDCOSMO) procedures on a set of real and simulated data, and we find the following. First, stellar kinematics cannot be a dominant source of error or bias since we find that a systematic change of 10% of measured velocity dispersion leads to only a 0.7% shift on H0 from the seven lenses analyzed by TDCOSMO. Second, we find no bias to arise from incorrect estimation of the line-of-sight effects. Third, we show that elliptical composite (stars + dark matter halo), power-law, and cored power-law mass profiles have the flexibility to yield a broad range in H0 values. However, the TDCOSMO procedures that model the data with both composite and power-law mass profiles are informative. If the models agree, as we observe in real systems owing to the “bulge-halo” conspiracy, H0 is recovered precisely and accurately by both models. If the two models disagree, as in the case of some pathological models illustrated here, the TDCOSMO procedure either discriminates between them through the goodness of fit, or it accounts for the discrepancy in the final error bars provided by the analysis. This conclusion is consistent with a reanalysis of six of the TDCOSMO (real) lenses: the composite model yields H0 = 74.0−1.8+1.7 km s−1 Mpc−1, while the power-law model yields 74.2−1.6+1.6 km s−1 Mpc−1. In conclusion, we find no evidence of bias or errors larger than the current statistical uncertainties reported by TDCOSMO.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

A realistic assessment of the CTA sensitivity to dark matter annihilation

We estimate the sensitivity of the upcoming CTA gamma-ray observatory to DM annihilation at the Galactic centre, improving on previous analyses in a number of significant ways. First, we perform a detailed analyses of all backgrounds, including diffuse astrophysical emission for the first time in a study of this type. Second, we present a statistical framework for including systematic errors and estimate the consequent degradation in sensitivity. These errors may come from e.g. event reconstruction, Monte Carlo determination of the effective area or uncertainty in atmospheric conditions. Third, we show that performing the analysis on a set of suitably optimised regions of interest makes it possible to partially compensate for the degradation in sensitivity caused by systematics and diffuse emission. To probe dark matter with the canonical thermal annihilation cross-section, CTA systematics like non-uniform variations in acceptance over a single field of view must be kept below the 0.3% level, unless the dark matter density rises more steeply in the centre of the Galaxy than predicted by a typical Navarro-Frenk-White or Einasto profile. For a contracted r{sup −1.3} profile, and systematics at the 1% level, CTA can probe annihilation to b b-bar at the canonical thermal level for dark matter masses between 100 GeV and 10 TeV.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

CMB signatures of metal-free star formation and Planck 2015 polarization data

Standard analyses of the reionization history of the Universe from Planck cosmic microwave background (CMB) polarization measurements consider only the overall optical depth to electron scattering (τ), and further assume a step-like reionization history. However, the polarization data contain information beyond the overall optical depth, and the assumption of a step-like function may miss high redshift contributions to the optical depth and leads to biased τ constraints. Accounting for its full reionization information content, we reconsider the interpretation of Planck 2015 Low-Frequency Instrument (LFI) polarization data using simple, yet physically motivated reionization models. We show that these measurements still, in fact, allow a non-negligible contribution from metal-free (Pop-III) stars forming in mini-haloes of mass M ~ 10 5 –10 6 M ⊙ at z ≳ 15, provided this mode of star formation is fairly inefficient. We find that an early, self-regulated phase of Pop-III star formation with a gradual, plateau feature in the ionization history provides a good match to the Planck LFI measurements. In this case, as much as 20 percent of the volume of the Universe is ionized by z ~ 20. Although preferred when the full information content of the data is incorporated, this model would spuriously be disfavoured in the standard analysis. This preference is driven mostly by excess power from E-mode polarization at multipoles of 10 ≲ ℓ ≲ 20, which may reflect remaining systematic errors in the data, a statistical fluctuation or signatures of the first stars. Measurements from the Planck High-Frequency Instrument should be able to confirm or refute this hint and future cosmic-variance-limited E-mode polarization surveys can provide substantially more information on these signatures.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

A measurement of CMB cluster lensing with SPT and DES year 1 data

Clusters of galaxies gravitationally lens the cosmic microwave background (CMB) radiation, resulting in a distinct imprint in the CMB on arcminute scales. Measurement of this effect offers a promising way to constrain the masses of galaxy clusters, particularly those at high redshift. We use CMB maps from the South Pole Telescope Sunyaev-Zel'dovich (SZ) survey to measure the CMB lensing signal around galaxy clusters identified in optical imaging from first year observations of the Dark Energy Survey. The cluster catalog used in this analysis contains 3697 members with mean redshift of $\bar{z} = 0.45$. We detect lensing of the CMB by the galaxy clusters at $8.1\sigma$ significance. Using the measured lensing signal, we constrain the amplitude of the relation between cluster mass and optical richness to roughly $17\%$ precision, finding good agreement with recent constraints obtained with galaxy lensing. The error budget is dominated by statistical noise but includes significant contributions from systematic biases due to the thermal SZ effect and cluster miscentering.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: structure growth rate measurement from the anisotropic quasar power spectrum in the redshift range 0.8 < z < 2.2

We analyse the clustering of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample (DR14Q).We measure the redshift space distortions using the power-spectrum monopole, quadrupole, and hexadecapole inferred from 148 659 quasars between redshifts 0.8 and 2.2, covering a total sky footprint of 2112.9 deg 2 . We constrain the logarithmic growth of structure times the amplitude of dark matter density fluctuations, fσ 8 , and the Alcock–Paczynski dilation scales that allow constraints to be placed on the angular diameter distance D A (z) and the Hubble H(z) parameter. At the effective redshift of z eff = 1.52, fσ 8 (z eff ) = 0.420 ± 0.076, H(z eff ) = [162 ± 12] (r$fid\atop{s}$ /r s ) kms -1 Mpc -1 , and DA(z eff ) = [1.85 ± 0.11] × 10 3 (r s/ r$fid\atop{s}$) Mpc, where r s is the comoving sound horizon at the baryon drag epoch and the superscript ‘fid’ stands for its fiducial value. The errors take into account the full error budget, including systematics and statistical contributions. These results are in full agreement with the current Λ-Cold Dark Matter cosmological model inferred from Planck measurements. Finally, we compare our measurements with other eBOSS companion papers and find excellent agreement, demonstrating the consistency and complementarity of the different methods used for analysing the data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables

We explore the constraints on the three-nucleon force (3NF) of chiral effective field theory (χ EFT) that are provided by bound-state observables in the A = 3 and A = 4 sectors. Our statistically rigorous analysis incorporates experimental error, computational method uncertainty, and the uncertainty due to truncation of the χ EFT expansion at next-to-next-to-leading order. A consistent solution for the 3 H binding energy, the 4 He binding energy and radius, and the 3 H β-decay rate can only be obtained if χ EFT truncation errors are included in the analysis. Here, the β-decay rate is the only one of these that yields a nondegenerate constraint on the 3NF low-energy constants, which makes it crucial for the parameter estimation. We use eigenvector continuation for fast and accurate emulation of no-core shell model calculations of the few-nucleon observables. This facilitates sampling of the posterior probability distribution, allowing us to also determine the distributions of the parameters that quantify the truncation error. We find a χ EFT expansion parameter of Q = 0.33 ± 0.06 for these observables.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

$B\to Kl^+l^-$ decay form factors from three-flavor lattice QCD

We compute the form factors for the B → Kl + l - semileptonic decay process in lattice QCD using gauge-field ensembles with 2+1 flavors of sea quark, generated by the MILC Collaboration. The ensembles span lattice spacings from 0.12 to 0.045 fm and have multiple sea-quark masses to help control the chiral extrapolation. The asqtad improved staggered action is used for the light valence and sea quarks, and the clover action with the Fermilab interpretation is used for the heavy b quark. We present results for the form factors f+(q 2 ), f 0 (q 2 ), and f T (q 2 ), where q 2 is the momentum transfer, together with a comprehensive examination of systematic errors. Lattice QCD determines the form factors for a limited range of q 2 , and we use the model-independent z expansion to cover the whole kinematically allowed range. We present our final form-factor results as coefficients of the z expansion and the correlations between them, where the errors on the coefficients include statistical and all systematic uncertainties. Lastly, we use this complete description of the form factors to test QCD predictions of the form factors at high and low q 2 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗