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DOE OSTI2023

Large-Scale Inference of Multivariate Regression for Heavy-Tailed and Asymmetric Data

Large-scale multivariate regression is a fundamental statistical tool with a wide range of applications. Here, this study considers the problem of simultaneously testing a large number of general linear hypotheses, encompassing covariate-effect analysis, analysis of variance, and model comparisons. The challenge that accompanies a large number of tests is the ubiquitous presence of heavy-tailed and/or highly skewed measurement noise, which is the main reason for the failure of conventional least squares-based methods. For large-scale multivariate regression, we develop a set of robust inference methods to explore data features such as heavy tailedness and skewness, which are not visible to least squares methods. The new testing procedure is based on the data-adaptive Huber regression and a new covariance estimator of regression estimates. Under mild conditions, we show that our methods produce consistent estimates of the false discovery proportion. Extensive numerical experiments and an empirical study on quantitative linguistics demonstrate the advantage of the proposed method over many state-of-the-art methods when the data are generated from heavy-tailed and/or skewed distributions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Approximate Bacon-Shor code and holography

We explicitly construct a class of holographic quantum error correction codes with non-trivial centers in the code subalgebra. Specifically, we use the Bacon-Shor codes and perfect tensors to construct a gauge code (or a stabilizer code with gauge-fixing), which we call the holographic hybrid code. This code admits a local log-depth encoding/decoding circuit, and can be represented as a holographic tensor network which satisfies an analog of the Ryu-Takayanagi formula and reproduces features of the sub-region duality. We then construct approximate versions of the holographic hybrid codes by “skewing” the code subspace, where the size of skewing is analogous to the size of the gravitational constant in holography. These approximate hybrid codes are not necessarily stabilizer codes, but they can be expressed as the superposition of holographic tensor networks that are stabilizer codes. For such constructions, different logical states, representing different bulk matter content, can “back-react” on the emergent geometry, resembling a key feature of gravity. The locality of the bulk degrees of freedom becomes subspace-dependent and approximate. Such subspace-dependence is manifest from the point of view of the “entanglement wedge” and bulk operator reconstruction from the boundary. Exact complementary error correction breaks down for certain bipartition of the boundary degrees of freedom; however, a limited, state-dependent form is preserved for particular subspaces. We also construct an example where the connected two-point correlation functions can have a power-law decay. Coupled with known constraints from holography, a weakly back-reacting bulk also forces these skewed tensor network models to the “large N limit” where they are built by concatenating a large N number of copies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Higher order cumulants of net baryon-number distributions at non-zero μ

Using recent results on higher order cumulants of conserved charge fluctuations from lattice QCD, we construct mean, variance, skewness, kurtosis, hyper-skewness and hyper-kurtosis of net-baryon number distributions for small baryon chemical potentials μ B . For the strangeness neutral case ( μ S = 0) at fixed ratio of electric charge to baryon number density ( n Q n B = 0.4 ), which is appropriate for a comparison with heavy ion collisions, we present results for κ B σ 2 B , S B σ 3 B / M B , κ H B σ 4 B and S H B σ 5 B / M B on the crossover line for the chiral transition, T pc ( μ B ). Furthermore, continuum extrapolations for this pseudo-critical transition line have recently been reported by HotQCD up to baryon chemical potentials μ B ≃ 300 MeV [A. Bazavov, et al., Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795 (2019) 15–21. arXiv:1812.08235 .]. These cumulant ratios are of direct relevance for comparisons with corresponding ratios measured by STAR in the BES-I and II runs at beam energies s NN ≥ 20 GeV . In particular, we point out that recent high statistics results on skewness and kurtosis of net-baryon number distributions obtained by STAR at s NN = 54.4 GeV put strong constraints on freeze-out parameters and are consistent with predictions from thermal QCD.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Stellar angular momentum distribution linked to galaxy morphology

ABSTRACT We study the spatially resolved stellar specific angular momentum j* in a high-quality sample of 24 Calar Alto Legacy Integral Field Area galaxies covering a broad range of visual morphology, accounting for stellar velocity and velocity dispersion. The shape of the spaxelwise probability density function of normalized s = j*/j*mean, PDF(s), deviates significantly from the near-universal initial distribution expected of baryons in a dark matter halo and can be explained by the expected baryonic effects in galaxy formation that remove and redistribute angular momentum. Further we find that the observed shape of the PDF(s) correlates significantly with photometric morphology, where late-type galaxies have a PDF(s) that is similar to a normal distribution, whereas early types have a strongly skewed PDF(s) resulting from an excess of low-angular momentum material. Galaxies that are known to host pseudo-bulges (bulge Sérsic index nb < 2.2) tend to have less skewed bulge PDF(s), with skewness (b1rb) ≲ 0.8. The PDF(s) encodes both kinematic and photometric information and appears to be a robust tracer of morphology. Its use is motivated by the desire to move away from traditional component-based classifications which are subject to observer bias, to classification on a galaxy’s fundamental (stellar mass and angular momentum) properties. In future, PDF(s) may also be useful as a kinematic decomposition tool.

Sweet, Sarah M.↗

DOE OSTI2021

Intrinsic correlations among characteristics of neutron-rich matter imposed by the unbound nature of pure neutron matter

The unbound nature of pure neutron matter (PNM) requires intrinsic correlations between the symmetric nuclear matter (SNM) EOS parameters (incompressibility K 0 , skewness J 0 and kurtosis I 0 ) and those (slope L, curvature K sym and skewness J sym ) characterizing the symmetry energy independent of any nuclear many-body theory. We investigate these intrinsic correlations and their applications in better constraining the poorly known high-density behavior of nuclear symmetry energy. Several novel correlations connecting the characteristics of SNM EOS with those of nuclear symmetry energy are found. In particular, at the lowest-order of approximations, the bulk parts of the slope L, curvature K sym and skewness J sym of the symmetry energy are found to be L ≈ K 0 /3, K sym ≈ LJ 0 /2K 0 and J sym ≈ I 0 L/3K 0 , respectively. High-order corrections to these simple relations can be written in terms of the small ratios of high-order EOS parameters. The resulting intrinsic correlations among some of the EOS parameters reproduce very nicely their relations predicted by various microscopic nuclear many-body theories and phenomenological models constrained by available data of terrestrial experiments and astrophysical observations in the literature. Here, the unbound nature of PNM is fundamental and the required intrinsic correlations among the EOS parameters characterizing both the SNM EOS and symmetry energy are universal. These intrinsic correlations provide a novel and model-independent tool not only for consistency checks but also for investigating the poorly known high-density properties of neutron-rich matter by using those with smaller uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Parametrization of Generalized Parton Distributions from 𝑡-Channel String Exchange in AdS Spaces

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) that is valid for all skewness. Our approach leverages conformal moments, representing them as the sum of spin-𝑗 nucleon 𝐴-form factor and skewness-dependent spin-𝑗 nucleon 𝐷-form factor, derived from 𝑡-channel string exchange in AdS spaces consistent with Lorentz invariance and unitarity. This model-independent framework, satisfying the polynomiality condition due to Lorentz invariance, uses Mellin moments from empirical data to estimate these form factors. With just five Regge slope parameters, our method accurately produces various nucleon quark GPD types and symmetric nucleon gluon GPDs through pertinent Mellin-Barnes integrals. Our isovector nucleon quark GPD is in agreement with existing lattice data, promising to improve the empirical extraction and global analysis of nucleon GPDs in exclusive processes, by avoiding the deconvolution problem at any skewness, for the first time.

QCD phenomenology↗

DOE OSTI2021

Erosion of focus rings in capacitively coupled plasma etching reactors

In plasma etching reactors, the structure surrounding the wafer, often called a focus ring (FR), plays an important role in maintaining uniform fluxes of reactants across the wafer. The FR is typically made of dielectric materials. During the plasma etching process, the sheath that forms over the wafer to accelerate ions anisotropically into the surface extends over the FR. Electrical charging of the FR modifies the sheath relative to that over the wafer. On the one hand, one wants the sheath to be uniform across the wafer-FR boundary to enable uniform fluxes to the edge of the wafer. On the other hand, maintaining a high voltage sheath over the FR will erode the FR, which is undesirable as the FR is a consumable component that must be periodically replaced in high volume manufacturing. In this work, we computationally investigated the consequences of dielectric constant ε of the FR materials on erosion of the FR. The series capacitance of the FR and its underlying structure is typically smaller than that of the wafer and its underlying structure. As a result, the FR charges quickly relative to the wafer, which then reduces the voltage across the sheath on top of the FR. The ion energy and angular distributions (IEADs) striking the FR are, therefore, generally lower in energy with a broader angular distribution. With ε = 2, the ion energies striking the middle to the outer edge of the FR are 30–180 eV, whereas for ε = 100, the ion energies are 120–380 eV. At the transition between the wafer and the FR, there is a skew in the IEAD as large as 15° that results from the difference in sheath thickness above the wafer and the FR. This skew and the erosion rate across the FR are functions of the dielectric constant of the FR material. With low ε, the FR charges quickly, less plasma is produced above the FR, and there is less voltage across the sheath that results in less FR erosion. Increasing ε of the FR produces a higher sheath voltage as well as higher ion fluxes over the FR, which increases erosion, while the skew at the edge of the wafer is less severe. Further, the material of the subsurface portion of the FR, which dominates its capacitance, is an important consideration in the design of the substrate assembly.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Residential Solar-Adopter Income and Demographic Trends: November 2022 Update [Slides]

The report describes income, demographic, and other socio-economic trends among U.S. residential rooftop solar adopters. The report is based on address-level data for roughly 2.8 million residential rooftop solar systems installed through 2021, representing 86% of all U.S. systems. With its unique size, geographic scope, and level of detail, this report is intended to serve as a foundational reference document for policy-makers, industry stakeholders, and researchers. Key findings include the following: -Median solar adopter income was about $\$110$k/year in 2021, compared to a U.S. median of about $\$63$k/year for all households and $\$79$k/year for all owner-occupied households -The degree of income skew varies significantly across all states, but all states exhibit some positive income skew, with median solar-adopter incomes ranging from 131-168% of the respective county-median income for all households -Notwithstanding the fact that solar adopter incomes skew high, a substantial share of adopters could be considered low-to-moderate income (LMI), with 22% of all 2021 adopters earning less than 80% of area median income, and an additional 21% between 80% and 120% of area median income. -Solar-adopter incomes are declining over time, with median incomes dropping from $\$129$k in 2010 to $\$110$k in 2021, as adoption becomes more proportionately distributed across the population and has started to broaden into low- and middle-income states since 2016. -Solar-adopter incomes are consistently higher for systems paired with battery storage, for host-owned systems, and for systems installed on single-family homes; higher income adopters also consistently install larger systems. -Solar adopters tend to live in Census Tracts not identified as “disadvantaged communities” (using the U.S. Department of Energy’s interim definitions developed March 2022), making up 11% of adopters compared to 18% of U.S. households. -Compared to the broader population, solar adopters tend to: identify as Non-Hispanic White, be primarily English-speaking, have higher education levels, be middle-aged, work in business and finance-related occupations, and live in higher-value homes In conjunction with the report, Berkeley Lab has published an updated accompanying set of online data visualizations that allow users to further explore the underlying data. Berkeley Lab is also offering related analytical support to states, local agencies, and other organizations on issues related to solar adoption among low-to-moderate income households; requests for analytical support may be submitted through this online form.

13 HYDRO ENERGY↗

NASA NTRS1975

Effects of asymmetry on the dynamic stability of aircraft

The oblique wing concept for transonic aircraft was proposed to reduce drag. The dynamic stability of the aircraft was investigated by analytically determining the stability derivatives at angles of skew ranging from 0 and 45 deg and using these stability derivatives in a linear analysis of the coupled aircraft behavior. The stability derivatives were obtained using a lifting line aerodynamic theory and found to give reasonable agreement with derivatives developed in a previous study for the same aircraft. In the dynamic analysis, no instability or large changes occurred in the root locations for skew angles varying from 0 to 45 deg with the exception of roll convergence. The damping in roll, however, decreased by an order of magnitude. Rolling was a prominent feature of all the oscillatory mode shapes at high skew angles.

Fantino, R. E.↗

NASA NTRS1980

Data acquisition techniques for exploiting the uniqueness of the time-of-flight mass spectrometer: Application to sampling pulsed gas systems

Mass spectra are produced in most mass spectrometers by sweeping some parameter within the instrument as the sampled gases flow into the ion source. It is evident that any fluctuation in the gas during the sweep (mass scan) of the instrument causes the output spectrum to be skewed in its mass peak intensities. The time of flight mass spectrometer (TOFMS) with its fast, repetitive mode of operation produces spectra without skewing or varying instrument parameters and because all ion species are ejected from the ion source simultaneously, the spectra are inherently not skewed despite rapidly changing gas pressure or composition in the source. Methods of exploiting this feature by utilizing fast digital data acquisition systems, such as transient recorders and signal averagers which are commercially available are described. Applications of this technique are presented including TOFMS sampling of vapors produced by both pulsed and continuous laser heating of materials.

Lincoln, K. A.↗

NASA NTRS1983

Mean velocities and Reynolds stresses upstream of a simulated wing-fuselage juncture

Values of three mean velocity components and six turbulence stresses measured in a turbulent shear layer upstream of a simulated wing-fuselage juncture and immediately downstream of the start of the juncture are presented nd discussed. Two single-sensor hot-wire probes were used in the measurements. The separated region just upstream of the wing contains an area of reversed flow near the fuselage surface where the turbulence level is high. Outside of this area the flow skews as it passes around the body, and in this skewed region the magnitude and distribution of the turbulent normal and shear stresses within the shear layer are modified slightly by the skewing and deceleration of the flow. A short distance downstream of the wing leading edge the secondary flow vortext is tightly rolled up and redistributes both mean flow and turbulence in the juncture. The data acquisition technique employed here allows a hot wire to be used in a reversed flow region to indicate flow direction.

Mcmahon, H.↗

NASA NTRS1985

Unsteady analysis of rotor blade tip flow

The development of the VSAERO-TS and VSAERO-H computer programs for calculating the unsteady aerodynamic characteristics of arbitrarily shaped wings oscillating in pitch is presented. The effect of several wake parameters on chordwise pressure distribution in VSAERO-TS is given and the convergence characteristics of both programs are discussed. In the program, the influence coefficient for each panel is formulated for a planar surface and so a skewed panel is represented by a projected flat quadrilateral lying in the mean plane. Since panels in the extreme roll-up region of the tip vortex are highly skewed the program was modified to treat each highly skewed panel as a pair of triangles. The programs are validated by comparing the chordwise pressure distribution of several blade tip planforms with experimental data. The comparison, for the most part, is good. The triangular panel representation improved the chordwise pressure distribution near the tip region for higher mean angle of attack.

Maskey, B.↗

NASA NTRS1986

Aeroelastic control of oblique-wing aircraft

The U.S. Navy and NASA are currently involved in the design and development of an unsymmetric-skew-wing aircraft capable of 65 deg wing sweep and flight at Mach 1.6. A generic skew-wing aircraft model was developed for 45 deg wing skew at a flight condition of Mach 0.70 and 3048 m altitude. At this flight condition the aircraft has a wing flutter mode. An active implementable control law was developed using the linear quadratic Gaussian design technique. A method of modal residualization was used to reduce the order of the controller used for flutter suppression.

Burken, J. J.↗

NASA NTRS1986

Aeroelastic control of oblique-wing aircraft

Burken, J. J.↗

NASA NTRS1987

Design of supersonic Coanda jet nozzles

The thrust vectoring of supersonic Coanda jets was improved by designing a nozzle to skew the initial jet velocity profile. A new nozzle design procedure, based on the method of characteristics, was developed to design a nozzle which produces a specified exit velocity profile. The thrust vectoring of a simple convergent nozzle, a convergent-divergent nozzle, and a nozzle which produces a skewed velocity profile matched to the curvature of the Coanda surface were expermentially compared over a range of pressure ratios from 1.5 to 3.5. Elimination of the expansion shocks with the C-D nozzle is shown to greatly improve the thrust vectoring; elimination of turning shocks with the skewed profile nozzle further improves the vectoring.

Bevilaqua, Paul M.↗

NASA NTRS1992

Experimental validation of clock synchronization algorithms

The objective of this work is to validate mathematically derived clock synchronization theories and their associated algorithms through experiment. Two theories are considered, the Interactive Convergence Clock Synchronization Algorithm and the Midpoint Algorithm. Special clock circuitry was designed and built so that several operating conditions and failure modes (including malicious failures) could be tested. Both theories are shown to predict conservative upper bounds (i.e., measured values of clock skew were always less than the theory prediction). Insight gained during experimentation led to alternative derivations of the theories. These new theories accurately predict the behavior of the clock system. It is found that a 100 percent penalty is paid to tolerate worst-case failures. It is also shown that under optimal conditions (with minimum error and no failures) the clock skew can be as much as three clock ticks. Clock skew grows to six clock ticks when failures are present. Finally, it is concluded that one cannot rely solely on test procedures or theoretical analysis to predict worst-case conditions.

Palumbo, Daniel L.↗

NASA NTRS1991

Thermal buckling and postbuckling of symmetrically laminated composite plates

The thermal buckling and postbuckling response of symmetrically laminated composite plates are discussed. Using variational methods in conjunction with a Rayleigh-Ritz formulation, thermal buckling and postbuckling are investigated for two laminates, a (+/- 45/0/90) and a (+/- 45/02), under two different simple support conditions, fixed and sliding. These laminates are subjected to the condition of a uniform temperature change. The effects of the principal material axis not being aligned with the edges of the plate, referred to here as material axis skewing, are also investigated. Although differences between buckling temperatures for the two support conditions were small, support conditions can have a large influence on thermal postbuckling response. In general, plates with fixed simple supports deflect more than plates with sliding simple supports. In addition, support conditions can influence modal interaction. Skewing of the material axis decreases the buckling temperatures of both laminates and, like fixed support conditions, causes increased postbuckling deflections. Skewing also influences modal interaction.

Meyers, C. A.↗

NASA NTRS1992

On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models

An independent, comprehensive, critical review of the 'renormalization group' (RNG) theory of turbulence developed by Yakhot and Orszag (1986) is provided. Their basic theory for the Navier-Stokes equations is confirmed, and approximations in the scale removal procedure are discussed. The YO derivations of the velocity-derivative skewness and the transport equation for the energy dissipation rate are examined. An algebraic error in the derivation of the skewness is corrected. The corrected RNG skewness value of -0.59 is in agreement with experiments at moderate Reynolds numbers. Several problems are identified in the derivation of the energy dissipation rate equations which suggest that the derivation should be reformulated.

Smith, L. M.↗