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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Discrete velocity computations with stochastic variance reduction of the Boltzmann equation for gas mixtures

We extend a variance reduced discrete velocity method developed at UT Austin [1, 2] to gas mixtures with large mass ratios and flows with trace species. The mixture is stored as a collection of independent velocity distribution functions, each with a unique grid in velocity space. Different collision types (A-A, A-B, B-B, etc.) are treated independently, and the variance reduction scheme is formulated with different equilibrium functions for each separate collision type. The individual treatment of species enables increased focus on species important to the physics of the flow, even if the important species are present in trace amounts. The method is verified through comparisons to Direct Simulation Monte Carlo computations and the computational workload per time step is investigated for the variance reduced method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Constructing auxiliary dynamics for nonequilibrium stationary states by variance minimization

We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study the interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D weakly asymmetric simple exclusion process. We show that with modest resources, we can capture the features of the susceptibility in large systems that mark the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A case study: Comparing testers for means and variances in a balanced incomplete block design

In this article, we present a gauge R & R study that is different from the standard setup in several ways. A balanced incomplete block design (BIBD) was used to collect the data because the measurement is destructive. Besides addressing reproducibility, differences in repeatability (i.e., tester variances) were also of interest. Here we use Bayesian methods to analyze the study data to address whether the three tester means and variances are similar. We also consider what happens if the BIBD structure of the data and possibly different tester variances are ignored in analyzing the study data.

42 ENGINEERING↗
DOE OSTI2012

MAGNETIC VARIANCES AND PITCH-ANGLE SCATTERING TIMES UPSTREAM OF INTERPLANETARY SHOCKS

Recent observations of power-law time profiles of energetic particles accelerated at interplanetary shocks have shown the possibility of anomalous, superdiffusive transport for energetic particles throughout the heliosphere. Those findings call for an accurate investigation of the magnetic field fluctuation properties at the resonance frequencies upstream of the shock's fronts. Normalized magnetic field variances, indeed, play a crucial role in the determination of the pitch-angle scattering times and then of the transport regime. The present analysis investigates the time behavior of the normalized variances of the magnetic field fluctuations, measured by the Ulysses spacecraft upstream of corotating interaction region (CIR) shocks, for those events which exhibit superdiffusion for energetic electrons. We find a quasi-constant value for the normalized magnetic field variances from about 10 hr to 100 hr from the shock front. This rules out the presence of a varying diffusion coefficient and confirms the possibility of superdiffusion for energetic electrons. A statistical analysis of the scattering times obtained from the magnetic fluctuations upstream of the CIR events has also been performed; the resulting power-law distributions of scattering times imply long range correlations and weak pitch-angle scattering, and the power-law slopes are in qualitative agreement with superdiffusive processes described by a Levy random walk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Sample variance in N-body simulations and impact on tomographic shear predictions

We study the effects of sample variance in N-body simulations as a function of the size of the simulation box, namely in connection with predictions on tomographic shear spectra. We make use of a set of eight ΛCDM simulations in boxes of 128, 256, and 512 h{sup −1} Mpc a side, for a total of 24, differing just by the initial seeds. Among the simulations with 128 and 512 h{sup −1} Mpc a side, we suitably select those closest and farthest from average. Numerical and linear spectra P(k,z) are suitably connected at low k to evaluate the effects of sample variance on shear spectra C{sub ij}(ℓ) for 5 or 10 tomographic bands. We find that shear spectra obtained by using 128 h{sup −1} Mpc simulations can vary up to ∼25%, just because of the seed. The sample variance lowers to ∼3.3% when using 512 h{sup −1} Mpc. These percentages could however slightly vary if other sets of the same number of realizations were considered. Accordingly, in order to match the ∼1% precision expected for the data, if still using eight boxes, we require a size of ∼1300–1700 h{sup −1} Mpc for them.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Analyzing the cosmic variance limit of remote dipole measurements of the cosmic microwave background using the large-scale kinetic Sunyaev Zel'dovich effect

Due to cosmic variance we cannot learn any more about large-scale inhomogeneities from the primary cosmic microwave background (CMB) alone. More information on large scales is essential for resolving large angular scale anomalies in the CMB. Here we consider cross correlating the large-scale kinetic Sunyaev Zel'dovich (kSZ) effect and probes of large-scale structure, a technique known as kSZ tomography. The statistically anisotropic component of the cross correlation encodes the CMB dipole as seen by free electrons throughout the observable Universe, providing information about long wavelength inhomogeneities. We compute the large angular scale power asymmetry, constructing the appropriate transfer functions, and estimate the cosmic variance limited signal to noise for a variety of redshift bin configurations. The signal to noise is significant over a large range of power multipoles and numbers of bins. We present a simple mode counting argument indicating that kSZ tomography can be used to estimate more modes than the primary CMB on comparable scales. A basic forecast indicates that a first detection could be made with next-generation CMB experiments and galaxy surveys. This paper motivates a more systematic investigation of how close to the cosmic variance limit it will be possible to get with future observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Suppressing the sample variance of DESI-like galaxy clustering with fast simulations

Ongoing and upcoming galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) survey, will observe vast regions of sky and a wide range of redshifts. In order to model the observations and address various systematic uncertainties, N-body simulations are routinely adopted, however, the number of large simulations with sufficiently high mass resolution is usually limited by available computing time. Therefore, achieving a simulation volume with the effective statistical errors significantly smaller than those of the observations becomes prohibitively expensive. In this study, we apply the Convergence Acceleration by Regression and Pooling (CARPool) method to mitigate the sample variance of the DESI-like galaxy clustering in the AbacusSummit simulations, with the assistance of the quasi-N-body simulations FastPM. Based on the halo occupation distribution (HOD) models, we construct different FastPM galaxy catalogs, including the luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasars, with their number densities and two-point clustering statistics well matched to those of AbacusSummit. We also employ the same initial conditions between AbacusSummit and FastPM to achieve high cross-correlation, as it is useful in effectively suppressing the variance. Our method of reducing noise in clustering is equivalent to performing a simulation with volume larger by a factor of 5 and 4 for LRGs and ELGs, respectively. We also mitigate the standard deviation of the LRG bispectrum with the triangular configurations k 2 = 2k 1 = 0.2 h Mpc -1 by a factor of 1.6. With smaller sample variance on galaxy clustering, we are able to constrain the baryon acoustic oscillations (BAO) scale parameters to higher precision. The CARPool method will be beneficial to better constrain the theoretical systematics of BAO, redshift space distortions (RSD) and primordial non-Gaussianity (NG).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

THE COLUMN DENSITY VARIANCE-M{sub s} RELATIONSHIP

Although there is a wealth of column density tracers for both the molecular and diffuse interstellar medium, there are few observational studies investigating the relationship between the density variance ({sigma}{sup 2}) and the sonic Mach number (M{sub s}). This is in part due to the fact that the {sigma}{sup 2}-M{sub s} relationship is derived, via MHD simulations, for the three-dimensional (3D) density variance only, which is not a direct observable. We investigate the utility of a 2D column density {sigma}{sub {Sigma}/{Sigma}0}{sup 2}-M{sub s} relationship using solenoidally driven isothermal MHD simulations and find that the best fit follows closely the form of the 3D density {sigma}{sub {rho}/{rho}0}{sup 2}-M{sub s} trend but includes a scaling parameter A such that {sigma}{sub ln({Sigma}/{Sigma}o)} = A x ln(1+b{sup 2} M{sub s}{sup 2}), where A = 0.11 and b = 1/3. This relation is consistent with the observational data reported for the Taurus and IC 5146 molecular clouds with b = 0.5 and A = 0.16, and b = 0.5 and A = 0.12, respectively. These results open up the possibility of using the 2D column density values of {sigma}{sup 2} for investigations of the relation between the sonic Mach number and the probability distribution function (PDF) variance in addition to existing PDF sonic Mach number relations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

ACCOUNTING FOR COSMIC VARIANCE IN STUDIES OF GRAVITATIONALLY LENSED HIGH-REDSHIFT GALAXIES IN THE HUBBLE FRONTIER FIELD CLUSTERS

Strong gravitational lensing provides a powerful means for studying faint galaxies in the distant universe. By magnifying the apparent brightness of background sources, massive clusters enable the detection of galaxies fainter than the usual sensitivity limit for blank fields. However, this gain in effective sensitivity comes at the cost of a reduced survey volume and, in this Letter, we demonstrate that there is an associated increase in the cosmic variance uncertainty. As an example, we show that the cosmic variance uncertainty of the high-redshift population viewed through the Hubble Space Telescope Frontier Field cluster Abell 2744 increases from ∼35% at redshift z ∼ 7 to ≳ 65% at z ∼ 10. Previous studies of high-redshift galaxies identified in the Frontier Fields have underestimated the cosmic variance uncertainty that will affect the ultimate constraints on both the faint-end slope of the high-redshift luminosity function and the cosmic star formation rate density, key goals of the Frontier Field program.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Propagating sample variance uncertainties in redshift calibration: simulations, theory, and application to the COSMOS2015 data

ABSTRACT Cosmological analyses of galaxy surveys rely on knowledge of the redshift distribution of their galaxy sample. This is usually derived from a spectroscopic and/or many-band photometric calibrator survey of a small patch of sky. The uncertainties in the redshift distribution of the calibrator sample include a contribution from shot noise, or Poisson sampling errors, but, given the small volume they probe, they are dominated by sample variance introduced by large-scale structures. Redshift uncertainties have been shown to constitute one of the leading contributions to systematic uncertainties in cosmological inferences from weak lensing and galaxy clustering, and hence they must be propagated through the analyses. In this work, we study the effects of sample variance on small-area redshift surveys, from theory to simulations to the COSMOS2015 data set. We present a three-step Dirichlet method of resampling a given survey-based redshift calibration distribution to enable the propagation of both shot noise and sample variance uncertainties. The method can accommodate different levels of prior confidence on different redshift sources. This method can be applied to any calibration sample with known redshifts and phenotypes (i.e. cells in a self-organizing map, or some other way of discretizing photometric space), and provides a simple way of propagating prior redshift uncertainties into cosmological analyses. As a worked example, we apply the full scheme to the COSMOS2015 data set, for which we also present a new, principled SOM algorithm designed to handle noisy photometric data. We make available a catalogue of the resulting resamplings of the COSMOS2015 galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A multishock model for the density variance of anisotropic, highly magnetized, supersonic turbulence

ABSTRACT Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $\sigma ^2_{\rho /\rho _0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parametrizes the star formation (SF) rate of a cloud. However, models for $\sigma ^2_{\rho /\rho _0}$ all share a common feature – the variance is assumed to be isotropic. This assumption does not hold when a trans-/sub-Alfvénic mean magnetic field, ${B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $\sigma _{\rho /\rho _0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $\sigma _{\rho /\rho _0}^2$ in the high Mach number $(\mathcal {M})$ limit as small-scale density fluctuations become suppressed by the strong ${B}_0$. The model reduces to the isotropic $\sigma _{\rho /\rho _0}^2\!-\!\mathcal {M}$ relation in the hydrodynamical limit. To validate our model, we calculate $\sigma _{\rho /\rho _0}^2$ from 12 high-resolution, three-dimensional, supersonic, sub-Alfvénic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented overdensities observed in some MCs and the implications for SF theory in the presence of a sub-Alfvénic ${B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.

Beattie, James R.↗
DOE OSTI2023

Cosmic variance and the inhomogeneous UV luminosity function of galaxies during reionization

When the first galaxies formed and starlight escaped into the intergalactic medium to reionize it, galaxy formation and reionization were both highly inhomogeneous in time and space, and fully coupled by mutual feedback. To show how this imprinted the UV luminosity function (UVLF) of reionization-era galaxies, we use our large-scale, radiation-hydrodynamics simulation CoDa II to derive the time- and space-varying halo mass function and UVLF, from z ≃ 6–15. That UVLF correlates strongly with local reionization redshift: earlier-reionizing regions have UVLFs that are higher, more extended to brighter magnitudes, and flatter at the faint end than later-reionizing regions observed at the same z. In general, as a region reionizes, the faint-end slope of its local UVLF flattens, and, by z = 6 (when reionization ended), the global UVLF, too, exhibits a flattened faint-end slope, ‘rolling-over’ at M UV ≳ -17. CoDa II’s UVLF is broadly consistent with cluster-lensed galaxy observations of the Hubble Frontier Fields at z = 6–8, including the faint end, except for the faintest data point at z = 6, based on one galaxy at M UV = -12.5. According to CoDa II, the probability of observing the latter is $\sim 5~{{\ \rm per\ cent}}$. However, the effective volume searched at this magnitude is very small, and is thus subject to significant cosmic variance. Here, we find that previous methods adopted to calculate the uncertainty due to cosmic variance underestimated it on such small scales by a factor of 2–4, primarily by underestimating the variance in halo abundance when the sample volume is small.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Cosmic variance of the galaxy cluster weak lensing signal

Intrinsic variations of the projected density profiles of clusters of galaxies at fixed mass are a source of uncertainty for cluster weak lensing. We present a semi-analytical model to account for this effect, based on a combination of variations in halo concentration, ellipticity and orientation, and the presence of correlated haloes. We calibrate the parameters of our model at the 10 per cent level to match the empirical cosmic variance of cluster profiles at M 200m ≈ 10 14 …10 15 h –1 M ⊙ , z = 0.25…0.5 in a cosmological simulation. We show that weak lensing measurements of clusters significantly underestimate mass uncertainties if intrinsic profile variations are ignored, and that our model can be used to provide correct mass likelihoods. Effects on the achievable accuracy of weak lensing cluster mass measurements are particularly strong for the most massive clusters and deep observations (with ≈20 per cent uncertainty from cosmic variance alone at M 200m ≈ 10 15 h –1 M ⊙ and z = 0.25), but significant also under typical ground-based conditions. We show that neglecting intrinsic profile variations leads to biases in the mass-observable relation constrained with weak lensing, both for intrinsic scatter and overall scale (the latter at the 15 per cent level). Furthermore, these biases are in excess of the statistical errors of upcoming surveys and can be avoided if the cosmic variance of cluster profiles is accounted for.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Variance reduction in lattice QCD observables via normalizing flows

Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters. This work implements the approach for observables involving gluonic operator insertions in the SU(3) Yang-Mills theory and two-flavor QCD in four space-time dimensions. Variance reduction by factors of 10–60 is achieved in glueball correlation functions and in gluonic matrix elements related to hadron structure, with demonstrated computational advantages. The observed variance reduction is found to be approximately independent of the lattice volume, so volume transfer can be utilized to minimize training costs.

Abbott, Ryan [Columbia U.; MIT, Cambridge, CTP; IA↗
DOE OSTI2018

Mean-Variance Optimization-Based Energy Storage Scheduling Considering Day-Ahead and Real-Time LMP Uncertainties

In this letter, a new mean-variance optimization-based energy storage scheduling method is proposed with the consideration of both day-ahead (DA) and real-time (RT) energy markets price uncertainties. It considers the locational marginal price (LMP) forecast uncertainties in the DA and RT markets. The energy storage arbitrage risk associated with the LMP forecast uncertainty is explicitly modeled through the variance component in the objective function. The quadratic term of this variance is transformed into a second-order cone constraint using the charging and discharging power complementarity of the energy storage system. Finally, the proposed model is formulated as a mixed-integer conic programming problem. Numerical case studies demonstrate the effectiveness of the proposed model for energy storage scheduling considering price uncertainty.

25 ENERGY STORAGE↗
DOE OSTI2016

Variance components in confocal scanning laser tomography measurements of neuro‐retinal rim area and the effect of repeated measurements on the power to detect loss over time

Abstract Purpose To estimate the variation in measurements of neuro‐retinal rim area (NRA) determined by confocal scanning laser tomography and consequences for clinical follow‐up. Methods Altogether, 24 healthy subjects were randomized on –320 μ m, Moorfields and Standard NRA plane strategies. Additionally, NRA was measured in 32 glaucoma subjects. Variance components for subjects, visits and measurements were estimated with analysis of variance. Sample sizes required to detect a 6.0 × 10 −2 mm 2 NRA change were estimated assuming a significance level of 0.05 and a power of 0.8. Consequences for independent group, and paired comparison design, respectively, were analysed. Further, precision in estimates within subjects over time was investigated. Results The variation of NRA among subjects was considerably larger than the variation among visits and measurements. For glaucoma subjects, the variation among visits and measurements were of the same order but larger than in healthy subjects. It was found that independent group comparisons require inconveniently large sample sizes. Within‐subject paired comparisons over time require sample sizes of below 15 subjects. The estimated variations for glaucoma subjects imply that 54 months of follow‐up is required for detection of change from baseline. Conclusions The variance for subjects is substantial in relation to those for visits and measurements. Cross‐sectional independent group comparisons of levels of NRA are unsuitable, due to considerable subject variation. Levels of NRA differences within subjects between visits can be estimated with acceptable precision. Neuro‐retinal rim area (NRA) measurement can be used for long‐term follow‐up of glaucoma progression.

Sandberg Melin, Camilla↗
DOE OSTI2014

WE-D-BRE-07: Variance-Based Sensitivity Analysis to Quantify the Impact of Biological Uncertainties in Particle Therapy

Purpose: In particle therapy, treatment planning and evaluation are frequently based on biological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2). In the context of the linear-quadratic model, these quantities depend on biological parameters (α, β) for ions as well as for the reference radiation and on the dose per fraction. The needed biological parameters as well as their dependency on ion species and ion energy typically are subject to large (relative) uncertainties of up to 20–40% or even more. Therefore it is necessary to estimate the resulting uncertainties in e.g. RBE or EQD2 caused by the uncertainties of the relevant input parameters. Methods: We use a variance-based sensitivity analysis (SA) approach, in which uncertainties in input parameters are modeled by random number distributions. The evaluated function is executed 10{sup 4} to 10{sup 6} times, each run with a different set of input parameters, randomly varied according to their assigned distribution. The sensitivity S is a variance-based ranking (from S = 0, no impact, to S = 1, only influential part) of the impact of input uncertainties. The SA approach is implemented for carbon ion treatment plans on 3D patient data, providing information about variations (and their origin) in RBE and EQD2. Results: The quantification enables 3D sensitivity maps, showing dependencies of RBE and EQD2 on different input uncertainties. The high number of runs allows displaying the interplay between different input uncertainties. The SA identifies input parameter combinations which result in extreme deviations of the result and the input parameter for which an uncertainty reduction is the most rewarding. Conclusion: The presented variance-based SA provides advantageous properties in terms of visualization and quantification of (biological) uncertainties and their impact. The method is very flexible, model independent, and enables a broad assessment of uncertainties. Supported by DFG grant WI 3745/1-1 and DFG cluster of excellence: Munich-Centre for Advanced Photonics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-T-56: A Novel Approach to Computing Expected Value and Variance of Point Dose From Non-Gated Radiotherapy Delivery

Purpose: Randomness in patient internal organ motion phase at the beginning of non-gated radiotherapy delivery may introduce uncertainty to dose received by the patient. Concerns of this dose deviation from the planned one has motivated many researchers to study this phenomenon although unified theoretical framework for computing it is still missing. This study was conducted to develop such framework for analyzing the effect. Methods: Two reasonable assumptions were made: a) patient internal organ motion is stationary and periodic; b) no special arrangement is made to start a non -gated radiotherapy delivery at any specific phase of patient internal organ motion. A statistical ensemble was formed consisting of patient’s non-gated radiotherapy deliveries at all equally possible initial organ motion phases. To characterize the patient received dose, statistical ensemble average method is employed to derive formulae for two variables: expected value and variance of dose received by a patient internal point from a non-gated radiotherapy delivery. Fourier Series was utilized to facilitate our analysis. Results: According to our formulae, the two variables can be computed from non-gated radiotherapy generated dose rate time sequences at the point’s corresponding locations on fixed phase 3D CT images sampled evenly in time over one patient internal organ motion period. The expected value of point dose is simply the average of the doses to the point’s corresponding locations on the fixed phase CT images. The variance can be determined by time integration in terms of Fourier Series coefficients of the dose rate time sequences on the same fixed phase 3D CT images. Conclusion: Given a non-gated radiotherapy delivery plan and patient’s 4D CT study, our novel approach can predict the expected value and variance of patient radiation dose. We expect it to play a significant role in determining both quality and robustness of patient non-gated radiotherapy plan.

60 APPLIED LIFE SCIENCES↗