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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Cosmological angular trispectra and non-Gaussian covariance

Angular cosmological correlators are infamously difficult to compute due to the highly oscillatory nature of the projection integrals. Motivated by recent development on analytic approaches to cosmological perturbation theory, in this paper we present an efficient method for computing cosmological four-point correlations in angular space, generalizing previous works on lower-point functions. This builds on the FFTLog algorithm that approximates the matter power spectrum as a sum over power-law functions, which makes certain momentum integrals analytically solvable. The computational complexity is drastically reduced for correlators in a "separable" form—we define a suitable notion of separability for cosmological trispectra, and derive formulas for angular correlators of different separability classes. As an application of our formalism, we compute the angular galaxy trispectrum at tree level, with and without primordial non-Gaussianity. This includes effects of redshift space distortion and bias parameters up to cubic order. We also compute the non-Gaussian covariance of the angular matter power spectrum due to the connected four-point function, beyond the Limber approximation. Finally, we demonstrate that, in contrast to the standard lore, the Limber approximation can fail for the non-Gaussian covariance computation even for large multipoles.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2022

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic partial differential equations. This loss of variance has been attributed to reduced-rank representations of the covariance matrix, as in ensemble methods for example, or else to the use of dissipative numerical methods. Through a combination of analytical work and numerical experiments, we demonstrate that significant variance loss, as well as gain, typically occurs during covariance propagation, even at full rank. The cause of this unusual behavior is a discontinuous change in the continuum covariance dynamics as correlation lengths become small, for instance in the vicinity of sharp gradients in the velocity field. This discontinuity in the covariance dynamics arises from hyperbolicity: the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments demonstrate that standard numerical methods for evolving the state are not adequate for propagating the covariance, because16they do not capture the discontinuity in the continuum covariance dynamics as correlations lengths tend to zero. Our analytical and numerical results show that this leads to significant, spurious variance loss in certain regions, and gain in others. The results suggest that developing local covariance propagation methods designed specifically to capture covariance evolution near the diagonal may prove a useful alternative to current methods of covariance propagation.

covariance propagation↗
DOE OSTI2022

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates, with application to analysis of biomarker correlates in vaccine trials

Herein, this article presents generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly robust augmented inverse probability weighted (AIPW) complete-case approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Proof-of-concept chemometric approach for environmental forensic sourcing of crude oil samples using SPME-GC-MS

Environmental exposure to crude oil through seepage and spillage poses risks to the immediate environment and the broader ecosystem as areas along the oil distribution path are affected by the influx of crude petroleum as well as the environmental, economic, and civil unrest that accompanies it. There is a large financial burden associated with the lost resources, including the cost of rehabilitation, and the affected sources of revenue for communities affected by oil spills. As such, it is crucial to determine the responsible parties. This work outlines an environmental forensics approach to determining the source of an un-weathered crude oil sample. The researchers employed solid phase microextraction coupled with gas chromatography mass spectrometry (SPME-GC-MS) to capture and analyze the gaseous components emitted by crude oil samples sourced from five locations. Samples were analyzed using Spearman's rank correlation and 3D covariance analysis. Both chemometric approaches yielded optimal performance results with no misclassifications, true positive rate (TPR) = 100 % and false positive rate (FPR) = 0 %. The similarity metrics calculated by each test noted clear delineations between the values of same-source and differently sourced samples. The Spearman's rank correlation test and 3D covariance calculations both demonstrated the ability to correctly identify sample source origin in this dataset. Finally, the authors outline an approach to the future application of these tests and suggest their joint use in future crude oil sourcing endeavors.

3D covariance mapping↗
NASA NTRS2002

Sensitivity of Lower Stratospheric Assimilated Ozone on Error Covariance Modeling and Data Selection

Assimilated ozone is produced at the NASA/Goddard Data Assimilation Office by blending ozone retrieved from the Solar Backscatter UltraViolet/2 (SBUV/2) instrument and the Earth Probe Total Ozone Mapping Spectrometer (EP TOMS) measurements into an off-line transport model. The current system tends to overestimate the amount of lower stratospheric ozone. This is a region where ozone plays a key role in the forcing of climate. A biased ozone field in this region will adversely impact calculations of the stratosphere-troposphere exchange and, when used as a first guess in retrievals, the values determined from satellite observations. Since these are all important applications of assimilated ozone products, effort is being directed towards reducing this bias. The SBUV ozone data have a coarse vertical resolution with increased uncertainty below the ozone maximum, and TOMS provides only total ozone columns. Thus, the assimilated ozone in the lower stratosphere, and its vertical distribution in particular, are only weakly constrained by the incoming SBUV and TOMS data. Consequently, the assimilated ozone distribution should be sensitive to changes in inputs to the statistical analysis scheme. Accordingly, the sensitivity of the assimilated lower stratospheric ozone fields to changes in the TOMS error-covariance modeling and the SBUV data selection has been investigated. The use of a spatially correlated TOMS error covariance model led to improvements in the product. However, withholding the SBUV/2 data for the layer between 63 and 126 hPa typically degraded the product, a result which vindicates the use of this layer ozone product, despite its known errors. These efforts to improve the lower stratospheric distribution will be extended to include a more advanced forecast error covariance model, and by assimilating ozone products from new instruments on Envisat and EOS Aura.

Stajner, Ivanka↗
DOE OSTI2023

Improvements of Nuclear Data Evaluations for Lead Isotopes in Support of Next Generation Lead-Cooled Fast Systems

The neutron evaluation of the isotopes that comprise natural lead were undertaken as a part of DOE-NEUP Project #19-16739. The goal of the project was to update the neutron cross sections to account for new differential measurements and incorporate the most up-to-date physics. Shortcomings in the lead cross sections was made known by several independent reports. The work performed here repeated the simulation of all the “benchmark” validation systems and concluded that the major issue is the scattering cross sections in the major lead isotopes above 100 keV. Re-evaluation of 206,207,208 Pb included both the resolved resonance region and fast region evaluations of the cross sections. Combined these regions cover energies from thermal to 20 MeV. The most drastic improvement is the resolved resonance region evaluation of 208 Pb which is now extended from 1.0 to 1.5 MeV. Parameterization of these resonances in the R-matrix provides a superior reconstruction of not only the experimental cross section but also the scattering distributions via the Blatt-Biedenharn formalism. Fast region evaluations of the three major isotopes were done to include new inelastic experimental data from the neutron Time-of-Flight facility at CERN. The culmination of all the changes to the cross section is a drastic improvement in the scattering kernel as shown in Rensselaer Polytechnic Institute (RPI) Quasi-Differential scattering measurements and improved prediction of keff for fast integral experiments. Alongside the new cross sections, new nuclear data covariance (uncertainties) have been computed and are included in the evaluation. Little is changed in the magnitude of the uncertainties but the correlations within the covariance display non-trivial changes. The new evaluations of 206,207,208 Pb have been submitted to the National Nuclear Data Center to be included in the ENDF/B-VIII.1 library. While the cross sections have been updated extensively, knowledge and modeling of the cross sections between 1.0 and 3.0 MeV for the isotopes remain a challenge. Most notably is the double differential elastic cross section for 208 Pb and 206 Pb. New quasi-differential measurements for pure samples of these two nuclei would go a long way in reducing compensating errors in the evaluations. Qualitatively, the project has produced a prosperous collaboration between the nuclear data group at RPI with staff scientists at Brookhaven National Laboratory, Naval Nuclear Laboratory, Oak Ridge National Laboratory, Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratories. Quantitatively this is reflected in seven conference presentations, at least one journal submission, and one doctoral thesis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1995

Causal correlation of foliar biochemical concentrations with AVIRIS spectra using forced entry linear regression

A major goal of airborne imaging spectrometry is to estimate the biochemical composition of vegetation canopies from reflectance spectra. Remotely-sensed estimates of foliar biochemical concentrations of forests would provide valuable indicators of ecosystem function at regional and eventually global scales. Empirical research has shown a relationship exists between the amount of radiation reflected from absorption features and the concentration of given biochemicals in leaves and canopies (Matson et al., 1994, Johnson et al., 1994). A technique commonly used to determine which wavelengths have the strongest correlation with the biochemical of interest is unguided (stepwise) multiple regression. Wavelengths are entered into a multivariate regression equation, in their order of importance, each contributing to the reduction of the variance in the measured biochemical concentration. A significant problem with the use of stepwise regression for determining the correlation between biochemical concentration and spectra is that of 'overfitting' as there are significantly more wavebands than biochemical measurements. This could result in the selection of wavebands which may be more accurately attributable to noise or canopy effects. In addition, there is a real problem of collinearity in that the individual biochemical concentrations may covary. A strong correlation between the reflectance at a given wavelength and the concentration of a biochemical of interest, therefore, may be due to the effect of another biochemical which is closely related. Furthermore, it is not always possible to account for potentially suitable waveband omissions in the stepwise selection procedure. This concern about the suitability of stepwise regression has been identified and acknowledged in a number of recent studies (Wessman et al., 1988, Curran, 1989, Curran et al., 1992, Peterson and Hubbard, 1992, Martine and Aber, 1994, Kupiec, 1994). These studies have pointed to the lack of a physical link between wavelengths chosen by stepwise regression and the biochemical of interest, and this in turn has cast doubts on the use of imaging spectrometry for the estimation of foliar biochemical concentrations at sites distant from the training sites. To investigate this problem, an analysis was conducted on the variation in canopy biochemical concentrations and reflectance spectra using forced entry linear regression.

Dawson, Terence P.↗
NASA NTRS1985

Electromagnetic wave scattering in a two-layer anisotropic random medium

For electromagnetic wave propagation and scattering in an anisotropic random medium, the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field were derived. With the random permittivity expressed in a general anisotropic form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation, and the ladder approximation to solve the Bethe-Salpeter equation. The mean dyadic Green's function for a two-layer anisotropic random medium with arbitrary three-dimensional correlation functions has been investigated with the zeroth-order solutions to the Dyson equation under the nonlinear approximation. The effective propagation constants are calculated for the four characteristic waves associated with the coherent vector fields, propagating in an anisotropic random-medium layer, which are the ordinary and extraordinary waves with upward- and downward-propagating vectors.

Lee, J. K.↗
NASA NTRS1985

Remote sensing of earth terrain

Progress on the investigation of the anisotropy of the terrain media, such as vegetation canopy and sea ice, and the study of the fluctuation-dissipation theorem in conjunction with the application of strong fluctuation theory for passive remote sensing of snowpacks is reported. The Feynman diagrammatic technique is used to derive the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field for electromagnetic wave propagation and scattering in an anisotropic random medium. With the random permittivity expressed in a general form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation and the ladder approximation to the Bethe-Salpeter equation. The mean dyadic Green's function for a two layer anisotropic random medium with arbitrary three dimensional correlation function was investigated with the zeroth-order solutions to the Dyson equation under the four characteristic waves associated with the coherent vector fields propagating in an anisotropic random medium layer, which are the ordinary and extraordinary waves with upward and downward propagating vectors.

Kong, J. A.↗
NASA NTRS1996

Macroscopic Violation of Three Cauchy-Schwarz Inequalities Using Correlated Light Beams From an Infra-Red Emitting Semiconductor Diode Array

We briefly review quantum mechanical and semi-classical descriptions of experiments which demonstrate the macroscopic violation of the three Cauchy-Schwarz inequalities: g(sup 2)(sub 11)(0) greater than or equal to 1; g(sup 2)(sub 11)(0) greater than or equal to g(sup 2)(sub 11)(t), (t approaches infinity); (the absolute value of g(sup 2)(sub 11)(0))(exp 2) less than or equal to g(sup 2)(sub 11)(0) g(sup 2)(sub 11)(0). Our measurements demonstrate the violation, at macroscopic intensities, of each of these inequalities. We show that their violation, although weak, can be demonstrated through photodetector current covariance measurements on correlated sub-Poissonian Poissonian, and super Poissonian light beams. Such beams are readily generated by a tandem array of infrared-emitting semiconductor junction diodes. Our measurements utilize an electrically coupled array of one or more infrared-emitting diodes, optically coupled to a detector array. The emitting array is operated in such a way as to generate highly correlated beams of variable photon Fano Factor. Because the measurements are made on time scales long compared with the first order coherence time and with detector areas large compared with the corresponding coherence areas, first order interference effects are negligible. The first and second inequalities are violated, as expected, when a sub-Poissonian light beam is split and the intensity fluctuations of the two split beams are measured by two photodetectors and subsequently cross-correlated. The third inequality is violated by bunched (as well as anti-bunched) beams of equal intensity provided the measured cross correlation coefficient exceeds (F - 1)/F, where F is the measured Fano Factor of each beam. We also investigate the violation for the case of unequal beams.

Edwards, P. J.↗
DOE OSTI2022

The impact and mitigation of broad-absorption-line quasars in Lyman α forest correlations

ABSTRACT Correlations in and with the flux transmission of the Lyman α (Ly α) forest in the spectra of high-redshift quasars are powerful cosmological tools, yet these measurements can be compromised if the intrinsic quasar continuum is significantly uncertain. One particularly problematic case is broad-absorption-line (BAL) quasars, which exhibit blueshifted absorption associated with many spectral features that are consistent with outflows of up to ∼0.1c. As these absorption features can both fall in the forest region and be difficult to distinguish from Ly α absorption, cosmological analyses eliminate the ∼12–16 per cent of quasars that exhibit BALs. In this paper, we explore an alternate approach that includes BALs in the Ly α autocorrelation function, with the exception of the expected locations of the BAL absorption troughs. This procedure returns over 95 per cent of the path-length that is lost by the exclusion of BALs, as well as increasing the density of sightlines. We show that including BAL quasars reduces the fractional uncertainty in the covariance matrix and correlation function by 12 per cent and does not significantly change the shape of the correlation function relative to analyses that exclude BAL quasars. We also evaluate different definitions of BALs, masking strategies, and potential differences in the quasar continuum in the forest region for BALs with different amounts of absorption.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Pursuing Dark Energy with Large Galaxy Redshift Surveys: Baryon Acoustic Oscillations and Beyond (Final Technical Report)

We have developed and applied methods of large-scale structure from galaxy redshift surveys to the study of dark energy. This program supported my group's development of the baryon acoustic method and our participation in the Dark Energy Spectroscopic Instrument (DESI) survey. In addition to my leadership role in the DESI collaboration, my group at Harvard focused on several topics addressing key needs of the DESI science program. 1) We continued our design, validation, and documentation of DESI target selection of the luminous red galaxy and emission-line galaxy samples. 2) We applied simulations from our novel and extremely fast N-body code to make DESI catalogs. With these, we will search for possible systematic shifts in the acoustic scale due to clustering bias with an unprecedented volume of simulations. 3) We extended our method for the fast construction of covariance matrices for correlation functions. 4) We developed new large-scale structure methods, including density-field reconstruction and three-point function analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1974

A dual frequency radar for ocean roughness sampling

A microwave technique for determining the roughness (rms wave height) of a randomly varying air-water interface has been developed theoretically, verified with laboratory wavetank studies and is currently being implemented for ocean surface measurements in a series of applications flight experiments. These aircraft observations will be near the Chesapeake Light Tower and will include a range of altitudes and sea conditions. The measurement concept involves cross-correlating the envelope fluctuations on two received carriers that are monochromatic when transmitted in a normal direction to the interface and are observed in a backscatter direction after reflection by the large number of randomly distributed specular points on the surface. The measured correlation coefficient (normalized covariance) as a function of carrier frequency separation will depend on the surface roughness, specifically the probability density function of the specular point height. Details of the flight system are discussed, and preliminary flight results are presented.

Weissman, D. E.↗
NASA NTRS1975

A study of sound generation in subsonic rotors, volume 2

Computer programs were developed for use in the analysis of sound generation by subsonic rotors. Program AIRFOIL computes the spectrum of radiated sound from a single airfoil immersed in a laminar flow field. Program ROTOR extends this to a rotating frame, and provides a model for sound generation in subsonic rotors. The program also computes tone sound generation due to steady state forces on the blades. Program TONE uses a moving source analysis to generate a time series for an array of forces moving in a circular path. The resultant time series are than Fourier transformed to render the results in spectral form. Program SDATA is a standard time series analysis package. It reads in two discrete time series and forms auto and cross covariances and normalizes these to form correlations. The program then transforms the covariances to yield auto and cross power spectra by means of a Fourier transformation.

Chalupnik, J. D.↗
NASA NTRSDate not supplied

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

We demonstrate for state dynamics governed by the continuity equation and related hyperbolic partial differential equations that significant, spurious variance loss occurs during covariance propagation by traditional methods used in data assimilation, even at full rank. This inaccurate variance evolution is caused not by numerical dissipation, but rather by a discontinuous change in the continuum covariance dynamics as correlation lengths tend to zero.

Shay Gilpin↗
DOE OSTI2026

An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

We present a simple analytic approximation for the covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction two-point correlation functions. This cross-covariance is essential for joint analyses that combine full-shape clustering information with baryon acoustic oscillation (BAO) measurements, as commonly performed in modern spectroscopic surveys. Our model builds on the disconnected contribution to the covariance and accounts for the damping of correlations due to the BAO reconstruction process. We validate our analytic prescription against numerical simulations from the Dark Energy Spectroscopic Instrument (DESI), testing both idealized cubic geometries and realistic survey configurations including complex footprints and fiber assignment effects. Despite neglecting survey window functions in the analytic calculation, we find excellent agreement with simulation-based covariances and demonstrate that cosmological parameter constraints are virtually unchanged when using our approximation. Our results show that the pre-post cross-covariance is sufficiently small that even approximate treatments are adequate for cosmological inference, opening a pathway toward fully analytic covariance matrices for next-generation galaxy surveys.

baryon acoustic oscillations↗