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Statistical Methods for Improved Evaluation of Environmental Sample Data quarterly FY18Q2

We will develop an enhanced statistical framework to evaluate environmental swipe samples collected at nuclear facilities with the goal of identifying anomalies associated with potential undeclared activities. Our approach will be based on Bayesian methodology and time series analysis. This overall framework should result in a more cost effective and operationally effective approach to environmental swipe sample analysis and interpretation.

97 MATHEMATICS AND COMPUTING↗

The Populations of Carina. I. Decoding the Color–Magnitude Diagram

We investigate the color–magnitude diagram (CMD) of the Carina dwarf spheroidal galaxy using data of Stetson et al. and synthetic CMDs based on isochrones of Dotter et al., in terms of the parameters [Fe/H], age, and [ α /Fe], for the cases when (i) [ α /Fe] is held constant and (ii) [ α /Fe] is varied. The data are well described by four basic epochs of star formation, having [Fe/H] = −1.85, −1.5, −1.2, and ∼−1.15 and ages ∼13, 7, ∼3.5, and ∼1.5 Gyr, respectively (for [ α /Fe] = 0.1, constant [ α /Fe], and [ α /Fe] = 0.2, 0.1, −0.2, −0.2, variable [ α /Fe]), with small spreads in [Fe/H] and age of order 0.1 dex and 1–3 Gyr. Within an elliptical radius 13.′1, the mass fractions of the populations, at their times of formation, were (in decreasing age order) 0.34, 0.39, 0.23, and 0.04. This formalism reproduces five observed CMD features (two distinct subgiant branches of old and intermediate-age populations, two younger, main-sequence components, and the small color dispersion on the red giant branch (RGB). The parameters of the youngest population are less certain than those of the others, and given it is less centrally concentrated, it may not be directly related to them. High-resolution spectroscopically analyzed RGB samples appear statistically incomplete compared with those selected using radial velocity, which contain bluer stars comprising ∼5%–10% of the samples. We conjecture these objects may, at least in part, be members of the youngest population. We use the CMD simulations to obtain insight into the population structure of Carina's upper RGB.

79 ASTRONOMY AND ASTROPHYSICS↗

Statistical properties of IRAS galaxies

Statistical approaches to the study of galaxies seen by IRAS are reviewed, stressing the contrast between IR complete and optically complete samples. A statistical overview is given of the Cataloged Galaxies and Quasars Observed in the IRAS Survey. The bi-variate distribution of ESO/U galaxies as a function of 60 microns flux and optical size is used to predict the size of an IR complete sample from the optically complete sample. To within the uncertainties, both samples are found to belong to the same population, leaving little room for a fundamentally new class of extragalactic objects, besides IR bright galaxies like Arp220.

Helou, G.↗

The Discovery of λ Bootis Stars: The Southern Survey I

The λ Boo stars are a class of chemically peculiar Population I A-type stars characterized by under-abundances of the refractory elements, but near-solar abundances of carbon, nitrogen, oxygen, and sulfur. There is some evidence that λ Boo stars have higher frequencies of “bright” debris disks than normal A-type stars. The discovery of four exoplanets orbiting HR 8799, a λ Boo star with a resolved debris disk, suggests that the λ Boo phenomenon may be related to the presence of a dynamic debris disk, perhaps perturbed by migrating planets. However, only 64 λ Boo stars are known, and those stars were discovered with different techniques, making it problematic to use that sample for statistical purposes, including determining the frequency of debris disks. The purpose of this paper is to derive a new sample of λ Boo stars using a technique that does not lead to biases with respect to the presence of infrared excesses. Through spectroscopic observations in the southern hemisphere, we have discovered 33 λ Boo stars and have confirmed 12 others. As a step toward determining the proportion of λ Boo stars with infrared excesses, we have used WISE data to examine the infrared properties of this sample out to 22 μ m. On this basis, we cannot conclude that λ Boo stars have a greater tendency than normal A-type stars to show infrared excesses. However, observing this sample at longer wavelengths may change that conclusion, as many λ Boo debris disks are cool and do not radiate strongly at 22 μ m.

79 ASTRONOMY AND ASTROPHYSICS↗

Huge ensembles – Part 2: Properties of a huge ensemble of hindcasts generated with spherical Fourier neural operators

Abstract. In Part 1, we created an ensemble based on spherical Fourier neural operators. As initial condition perturbations, we used bred vectors, and as model perturbations, we used multiple checkpoints trained independently from scratch. Based on diagnostics that assess the ensemble's physical fidelity, our ensemble has comparable performance to operational weather forecasting systems. However, it requires orders-of-magnitude fewer computational resources. Here in Part 2, we generate a huge ensemble (HENS), with 7424 members initialized each day of summer 2023. We enumerate the technical requirements for running huge ensembles at this scale. HENS precisely samples the tails of the forecast distribution and presents a detailed sampling of internal variability. HENS has two primary applications: (1) as a large dataset with which to study the statistics and drivers of extreme weather and (2) as a weather forecasting system. For extreme climate statistics, HENS samples events 4σ away from the ensemble mean. At each grid cell, HENS increases the skill of the most accurate ensemble member and enhances coverage of possible future trajectories. As a weather forecasting model, HENS issues extreme weather forecasts with better uncertainty quantification. It also reduces the probability of outlier events, in which the verification value lies outside the ensemble forecast distribution.

Mahesh, Ankur↗

Experimental analysis of computer system dependability

This paper reviews an area which has evolved over the past 15 years: experimental analysis of computer system dependability. Methodologies and advances are discussed for three basic approaches used in the area: simulated fault injection, physical fault injection, and measurement-based analysis. The three approaches are suited, respectively, to dependability evaluation in the three phases of a system's life: design phase, prototype phase, and operational phase. Before the discussion of these phases, several statistical techniques used in the area are introduced. For each phase, a classification of research methods or study topics is outlined, followed by discussion of these methods or topics as well as representative studies. The statistical techniques introduced include the estimation of parameters and confidence intervals, probability distribution characterization, and several multivariate analysis methods. Importance sampling, a statistical technique used to accelerate Monte Carlo simulation, is also introduced. The discussion of simulated fault injection covers electrical-level, logic-level, and function-level fault injection methods as well as representative simulation environments such as FOCUS and DEPEND. The discussion of physical fault injection covers hardware, software, and radiation fault injection methods as well as several software and hybrid tools including FIAT, FERARI, HYBRID, and FINE. The discussion of measurement-based analysis covers measurement and data processing techniques, basic error characterization, dependency analysis, Markov reward modeling, software-dependability, and fault diagnosis. The discussion involves several important issues studies in the area, including fault models, fast simulation techniques, workload/failure dependency, correlated failures, and software fault tolerance.

Iyer, Ravishankar, K.↗

The orbital nature of 81 ellipsoidal red giant binaries in the large magellanic cloud

In this paper, we collect a sample of 81 ellipsoidal red giant binaries in the Large Magellanic Cloud (LMC), and we study their orbital natures individually and statistically. The sample contains 59 systems with circular orbits and 22 systems with eccentric orbits. We derive orbital solutions using the 2010 version of the Wilson–Devinney code. The sample is selection-bias corrected, and the orbital parameter distributions are compared to model predictions for the LMC and to observations in the solar vicinity. The masses of the red giant primaries are found to range from about 0.6 to 9 M{sub ⊙} with a peak at around 1.5 M{sub ⊙}, in agreement with studies of the star formation history of the LMC, which find a burst of star formation beginning around 4 Gyr ago. The observed distribution of mass ratios q=m{sub 2}/m{sub 1} is more consistent with the flat q distribution derived for the solar vicinity by Raghavan et al. than it is with the solar vicinity q distribution derived by Duquennoy and Mayor. There is no evidence for an excess number of systems with equal mass components. We find that about 20% of the ellipsoidal binaries have eccentric orbits, twice the fraction estimated by Soszynski et al. Our eccentricity evolution test shows that the existence of eccentric ellipsoidal red giant binaries on the upper parts of the red giant branch (RGB) can only be explained if tidal circularization rates are ∼1/100 the rates given by the usual theory of tidal dissipation in convective stars.

79 ASTRONOMY AND ASTROPHYSICS↗

Local measurement of bulk thermal diffusivity using photothermal radiometry

Here, an experimental methodology using photothermal radiometry is developed for the accurate measurement of bulk thermal diffusivity of nuclear fuels and materials irradiated to high doses. Under these conditions, nuclear fuels, such as uranium oxide, and moderator materials, such as graphite, become friable, which requires characterization techniques that can accommodate irregularly shaped fragments. Photothermal radiometry, a good candidate for this application, involves locally heating a sample by using a laser and measuring the temperature field by monitoring blackbody radiation. The interaction volume for this study, less than a millimeter, is carefully chosen to sample a statistically significant number of large-scale structural features, such as pores and gas filled bubbles, and is small enough that the sample fragments can be treated as a thermal half-space. The thermal diffusivity standards considered in this study cover a range of thermal diffusivities representative of both fresh and spent nuclear fuels. We also consider a sample having a porous microstructure representative of large-scale structures found in materials irradiated to high doses. Our measurement methodology circumvents complex thermal wave models that address optical diffraction, nonlinear transfer function associated with blackbody radiation, and finite sample size effects. Consequently, the large measurement uncertainty associated with modeling these effects can be avoided. While the emphasis here is on nuclear fuels and materials, this measurement approach is well suited to measure thermal transport in a variety of technologically important materials associated with advanced synthesis techniques. Examples range from small, exotic single crystals grown using hydrothermal growth techniques to additively manufactured components having complex geometries.

36 MATERIALS SCIENCE↗

ASSESSING THE SIGNIFICANCE OF APPARENT CORRELATIONS BETWEEN RADIO AND GAMMA-RAY BLAZAR FLUXES

Whether or not a correlation exists between the radio and gamma-ray flux densities of blazars is a long-standing question, and one that is difficult to answer confidently because of various observational biases, which may either dilute or apparently enhance any intrinsic correlation between radio and gamma-ray luminosities. We introduce a novel method of data randomization to evaluate quantitatively the effect of these biases and to assess the intrinsic significance of an apparent correlation between radio and gamma-ray flux densities of blazars. The novelty of the method lies in a combination of data randomization in luminosity space (to ensure that the randomized data are intrinsically, and not just apparently, uncorrelated) and significance assessment in flux space (to explicitly avoid Malmquist bias and automatically account for the limited dynamical range in both frequencies). The method is applicable even to small samples that are not selected with strict statistical criteria. For larger samples we describe a variation of the method in which the sample is split in redshift bins, and the randomization is applied in each bin individually; this variation is designed to yield the equivalent to luminosity-function sampling of the underlying population in the limit of very large, statistically complete samples. We show that for a smaller number of redshift bins, the method yields a worse significance, and in this way it is conservative: although it may fail to confirm an existing intrinsic correlation in a small sample that cannot be split into many redshift bins, it will not assign a stronger, artificially enhanced significance. We demonstrate how our test performs as a function of number of sources, strength of correlation, and number of redshift bins used, and we show that while our test is robust against common-distance biases and associated false positives for uncorrelated data, it retains the power of other methods in rejecting the null hypothesis of no correlation for correlated data.

79 ASTRONOMY AND ASTROPHYSICS↗

Convergence of oscillator spectral estimators for counted-frequency measurements.

A common intermediary connecting frequency-noise calibration or testing of an oscillator to useful applications is the spectral density of the frequency-deviating process. In attempting to turn test data into predicts of performance characteristics, one is naturally led to estimation of statistical values by sample-mean and sample-variance techniques. However, sample means and sample variances themselves are statistical quantities that do not necessarily converge (in the mean-square sense) to actual ensemble-average means and variances, except perhaps for excessively large sample sizes. This is especially true for the flicker noise component of oscillators. This article shows, for the various types of noises found in oscillators, how sample averages converge (or do not converge) to their statistical counterparts. The convergence rate is shown to be the same for all oscillators of a given spectral type.

Tausworthe, R. C.↗

Training and Validation of Spectral Gap Filling Algorithm for Cpf-Ceres Intercalibration

The Climate Absolute Radiance and Refractivity Observatory (CLARREO) Pathfinder (CPF) mission is set to launch an SI-traceable reflective solar (RS) spectrometer aboard the International Space Station to measure Earth-reflected solar radiation with a radiometric uncertainty of 0.3% (k=1). The CPF intercalibration team has devised a cutting-edge methodology to accurately transfer the benchmark CPF calibration reference to the shortwave (SW) channel (200-5000 nm) of the Clouds and the Earth’s Radiant Energy System (CERES) instrument. The spectral range of CPF measurements spans from 350-2300 nm, while the CERES SW channel measures the Earth-reflected broadband solar radiances between 200 nm to 5 μm. To conduct precise CPF-CERES intercalibration analysis, the CPF-like spectral radiances outside the CPF spectral range need to be estimated to match the CERES SW spectral range. In response, the team has developed a fast algorithm that leverages spectrally redundant information within the CPF-measured portion through principal component analysis (PCA) and utilizes pre-established spectral correlation relationships among wavelengths to extend the CPF spectrum below 350 nm and above 2300 nm. Our results show that the algorithm achieves excellent accuracy in generating the missing energy in the UV and IR portions. The RMS error in the UV region is less than 4.5x10-3 W/m2/sr/nm, while in the IR region, it is smaller than 8x10-5 W/m2/sr/nm. Our methodology was validated using measured EMIT radiance data, which covers the spectral range from 0.381 μm to 2.493 μm. We employed EMIT radiances within the wavelength range of 0.43 – 2.25 μm to generate radiances for both the shorter wavelength range (0.381 – 0.43 μm) and longer wavelength range (2.25 – 2.493 μm). The generated radiances agree very well with the measured EMIT radiances. The standard deviation in the integrated broadband radiances was about 0.1%, and the bias is less than 0.004% for over 1.5 million EMIT measured samples. These statistics show that the spectral gap filling algorithm is robust and effective in substantially reducing the spectral difference-induced uncertainty in the CPF-CERES intercalibration samples.

Qiguang Yang↗

Cluster cosmology without cluster finding

ABSTRACT We propose that observations of supermassive galaxies contain cosmological statistical constraining power similar to conventional cluster cosmology, and we provide promising indications that the associated systematic errors are comparably easier to control. We consider a fiducial spectroscopic and stellar mass complete sample of galaxies drawn from the Dark Energy Spectroscopic Instrument (DESI) and forecast how constraints on Ωm–σ8 from this sample will compare with those from number counts of clusters based on richness λ. At fixed number density, we find that massive galaxies offer similar constraints to galaxy clusters. However, a mass-complete galaxy sample from DESI has the potential to probe lower halo masses than standard optical cluster samples (which are typically limited to λ ≳ 20 and Mhalo ≳ 1013.5 M⊙ h−1); additionally, it is straightforward to cleanly measure projected galaxy clustering wp for such a DESI sample, which we show can substantially improve the constraining power on Ωm. We also compare the constraining power of M*-limited samples to those from larger but mass-incomplete samples [e.g. the DESI Bright Galaxy Survey (BGS) sample]; relative to a lower number density M*-limited samples, we find that a BGS-like sample improves statistical constraints by 60 per cent for Ωm and 40 per cent for σ8, but this uses small-scale information that will be harder to model for BGS. Our initial assessment of the systematics associated with supermassive galaxy cosmology yields promising results. The proposed samples have a ∼10 per cent satellite fraction, but we show that cosmological constraints may be robust to the impact of satellites. These findings motivate future work to realize the potential of supermassive galaxies to probe lower halo masses than richness-based clusters and to potentially avoid persistent systematics associated with optical cluster finding.

(cosmology): large-scale structure of Universe↗

A flux-limited sample of Galactic carbon stars

Published observational data (including IRAS observations) for a flux-limited sample of 215 Galactic carbon stars (CSs) selected from the 2-micron sky survey of Neugebauer and Leighton (1969) are compiled in extensive tables and graphs and analyzed statistically. The sample is found to penetrate a volume of radius 1.5 kpc, and the local CS space density and surface density are calculated as log rho0 (per cu kpc) = 2.0 + or - 0.4 and log N (per sq kpc) = 1.6 + or - 0.2, respectively. The total Galactic mass-return rate from these CSs is estimated as 0.013 solar mass/yr, implying a time scale of 0.1-1 Myr for the CS evolutionary phase and a mass of 1.2-1.6 solar mass for the (probably F-type) main-seqence progenitors of CSs.

Claussen, M. J.↗

Elastomeric Seal Performance after Terrestrial Ultraviolet Radiation Exposure

Ultraviolet radiation was evaluated to determine its negative effects on the performance of elastomeric gas pressure seals. The leak rates of the silicone elastomer S0383-70 O-ring test articles were used to quantify the degradation of the seals after exposure to vacuum-ultraviolet and/or middle-to-near-ultraviolet wavelength radiation. Three groups of seals were exposed in terrestrial facilities to 115-165 nm wavelength radiation, 230-500 nm wavelength radiation, or both spectrums, for an orbital spaceflight equivalent of 125 hours. The leak rates of the silicone elastomer S0383-70 seals were quantified and compared to samples that received no radiation. Each lot contained six samples and statistical t-tests were used to determine the separate and combined influences of exposure to the two wavelength ranges. A comparison of the mean leak rates of samples exposed to 115-165 nm wavelength radiation to the control specimens showed no difference, suggesting that spectrum was not damaging. The 230-500 nm wavelength appeared to be damaging, as the mean leak rates of the specimens exposed to that range of wavelengths, and those exposed to the combined 115-165 nm and 230-500 nm spectrums, were significantly different from the leak rates of the control specimens. Most importantly, the test articles exposed to both wavelength spectrums exhibited mean leak rates two orders of magnitude larger than any other exposed specimens, which suggested that both wavelength spectrums are important when simulating the orbital environment.

leakage↗

The Feynman-Y Statistic in Relation to Shift-Register Neutron Coincidence Counting: Precision and Dead Time

The Feynman-Y statistic is a type of autocorrelation analysis. It is defined as the excess variance-to-mean ratio, Y = VMR - 1, of the number count distribution formed by sampling a pulse train using a series of non-overlapping gates. It is a measure of the degree of correlation present on the pulse train with Y = 0 for Poisson data. In the context of neutron coincidence counting we show that the same information can be obtained from the accidentals histogram acquired using the multiplicity shift-register method, which is currently the common autocorrelation technique applied in nuclear safeguards. In the case of multiplicity shift register analysis however, overlapping gates, either triggered by the incoming pulse stream or by a periodic clock, are used. The overlap introduces additional covariance but does not alter the expectation values. In this paper we discuss, for a particular data set, the relative merit of the Feynman and shift-register methods in terms of both precision and dead time correction. Traditionally the Feynman approach is applied with a relatively long gate width compared to the dieaway time. The main reason for this is so that the gate utilization factor can be taken as unity rather than being treated as a system parameter to be determined at characterization/calibration. But because the random trigger interval gate utilization factor is slow to saturate this procedure requires a gate width many times the effective 1/e dieaway time. In the traditional approach this limits the number of gates that can be fitted into a given assay duration. We empirically show that much shorter gates, similar in width to those used in traditional shift register analysis can be used. Because the way in which the correlated information present on the pulse train is extracted is different for the moments based method of Feynman and the various shift register based approaches, the dead time losses are manifested differently for these two approaches. The resulting estimates for the dead time corrected first and second order reduced factorial moments should be independent of the method however and this allows the respective dead time formalism to be checked. We discuss how to make dead time corrections in both the shift register and the Feynman approaches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Assessing Risk Due to Small Sample Size in Probability of Detection Analysis Using Tolerance Intervals

Small sample size (e.g.6-30) poses risk in results of probability of detection (POD) analysis using tolerance intervals. This method is also called as the limited sample or LS POD. The analysis is performed either during NDE procedure qualification or for assessment of reliability of an NDE procedure. The risk is primarily due to sampling error. Smaller samples are not likely to be random to the population or representative of the population. The small samples are likely to be biased. Biased samples have smaller standard deviation compared to the population. POD analysis with small biased sample can lead to overestimation of POD. Many sampling schemes are available in statistics to mitigate sampling risk. Primary objective of POD analysis is to determine a decision threshold from signal response measurements of a sample such that it is less than or equal to population decision threshold for 90% POD. Sampling error implies that this NDE reliability condition is violated. One of sampling types is called a representative sample. Representative samples reduce variance in POD estimates but also reduce magnitude of the error. Sampling sensitivity analysis for some sampling types is performed here using repetitive random sampling or Monte Carlo method. Six sampling types are considered for comparison. Some of the sampling types are similar to drawing a representative sample. LS POD model assumes random sampling. Therefore, random sampling is used as a basis for comparison with each sampling type. The sampling types used in the analysis are, A. Nominal and worst-case sampling, B. Worst-case sampling, C. Nominal case sampling, D. Random sampling, E. Random target, and sub-target sampling. F. Nominal target and sub-target sampling. Results of Monte Carlo simulation indicate that type F sampling can mitigate sampling risk and is also more practical to implement. Type A sampling may also mitigate the sampling risk, but it may be less practical to implement.

Ajay M Koshti↗

Scale Mixtures of Frechet Distributions as Asymptotic Approximations of Extreme Precipitation

This paper is a further development of the results of [20] where, based on the negative binomial model for the duration of wet periods measured in days [16], an asymptotic approximation was proposed for the distribution of the maximum daily precipitation volume within a wet period. This approximation has the form of a scale mixture of the Fr´echet distribution with the gamma mixing distribution and coincides with the distribution of a positive power of a random variable having the Snedecor–Fisher distribution. Here we extend this result to the mth extremes, m ∈ ℕ, and sample quantiles. The proof of this result is based on the representation of the negative binomial distribution as a mixed geometric (and hence, mixed Poisson) distribution [17] and limit theorems for extreme order statistics in samples with random sizes having mixed Poisson distributions [10]. Some analytic properties of the obtained limit distribution are described. In particular, it is demonstrated that under certain conditions the limit distribution of the maximum precipitation is mixed exponential and hence, is infinitely divisible. It is shown that under the same conditions this limit distribution can be represented as a scale mixture of stable or Weibull or Pareto or folded normal laws. The corresponding product representations for the limit random variable can be used for its computer simulation. The results of fitting this distribution to real data are presented illustrating high adequacy of the proposed model. It is also shown that the limit distribution of sample quantiles is the well-known Student distribution. Several methods are proposed for the estimation of the parameters of the asymptotic distributions. The obtained mixture representations for the limit laws and the corresponding asymptotic approximations provide better insight into the nature of mixed probability (“Bayesian”) models.

97 MATHEMATICS AND COMPUTING↗

The Sloan Digital Sky Survey Reverberation Mapping Project: Composite Lags at z ≤ 1

We present composite broad-line region (BLR) reverberation mapping lag measurements for H α , H β , He ii λ 4686, and Mg ii for a sample of 144, z ≲ 1 quasars from the Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) project. Using only the 32-epoch spectroscopic light curves in the first six-month season of SDSS-RM observations, we compile correlation function measurements for individual objects and then coadd them to allow the measurement of the average lags for our sample at mean redshifts of 0.4 (for H α ) and ∼0.65 (for the other lines). At similar quasar luminosities and redshifts, the sample-averaged lag decreases in the order of Mg ii, H α , H β , and He ii. This decrease in lags is accompanied by an increase in the mean line width of the four lines, and is roughly consistent with the virialized motion for BLR gas in photoionization equilibrium. These are among the first RM measurements of stratified BLR structure at z > 0.3. Dividing our sample by luminosity, H α shows clear evidence of increasing lags with luminosity, consistent with the expectation from the measured BLR size–luminosity relation based on H β . The other three lines do not show a clear luminosity trend in their average lags due to the limited dynamic range of luminosity probed and the poor average correlation signals in the divided samples, a situation that will be improved with the incorporation of additional photometric and spectroscopic data from SDSS-RM. We discuss the utility and caveats of composite lag measurements for large statistical quasar samples with reverberation mapping data.

79 ASTRONOMY AND ASTROPHYSICS↗