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The strong consistency, asymptotic normality, and asymptotic efficiency of maximum likelihood estimates of the parameters in a finite mixture of multivariate distributions are discussed as well as the asymptotic theory of some hypothesis tests for such mixtures.
We present a method to determine whether an observed sample of data is drawn from a parent distribution that is pure power law. The method starts from a class of statistics which have zero expectation value under the null hypothesis, H(sub 0), that the distribution is a pure power law: F(x) varies as x(exp -alpha). We study one simple member of the class, named the `bending statistic' B, in detail. It is most effective for detection a type of deviation from a power law where the power-law slope varies slowly and monotonically as a function of x. Our estimator of B has a distribution under H(sub 0) that depends only on the size of the sample, not on the parameters of the parent population, and is approximated well by a normal distribution even for modest sample sizes. The bending statistic can therefore be used to test a set of numbers is drawn from any power-law parent population. Since many measurable quantities in astrophysics have distriibutions that are approximately power laws, and since deviations from the ideal power law often provide interesting information about the object of study (e.g., a `bend' or `break' in a luminosity function, a line in an X- or gamma-ray spectrum), we believe that a test of this type will be useful in many different contexts. In the present paper, we apply our test to various subsamples of gamma-ray burst brightness from the first-year Burst and Transient Source Experiment (BATSE) catalog and show that we can only marginally detect the expected steepening of the log (N (greater than C(sub max))) - log (C(sub max)) distribution.
The use of unlabeled samples in improving the performance of classifiers is studied. When the number of training samples is fixed and small, additional feature measurements may reduce the performance of a statistical classifier. It is shown that by using unlabeled samples, estimates of the parameters can be improved and therefore this phenomenon may be mitigated. Various methods for using unlabeled samples are reviewed and experimental results are provided.
Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including environmental factors, factors associated with the fall event, mass and anthropometric values of the astronaut, BMD characteristics, characteristics of the relationship between BMD and bone strength and bone fracture characteristics. The uncertainty in these factors is captured through the use of parameter distributions and the fracture predictions are probability distributions with a mean value and an associated uncertainty. To determine parameter sensitivity, a correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities. Each parameters contribution to the variance is found by squaring the correlation coefficients, dividing by the sum of the squared correlation coefficients, and multiplying by 100. Results: Sensitivity analyses of BFxRM simulations of preflight, 0 days post-flight and 365 days post-flight falls onto the hip revealed a subset of the twelve factors within the model which cause the most variation in the fracture predictions. These factors include the spring constant used in the hip biomechanical model, the midpoint FRI parameter within the equation used to convert FRI to fracture probability and preflight BMD values. Future work: Plans are underway to update the BFxRM by incorporating bone strength information from finite element models (FEM) into the bone strength portion of the BFxRM. Also, FEM bone strength information along with fracture outcome data will be incorporated into the FRI to fracture probability.
Attention is given to a general derivation of the fractional standard deviation (FSD) of any integrated property X such that X(D) = cD to the n. This work extends that of Joss and Waldvogel (1969). The equation is applicable to measuring integrated properties of cloud, rain or hail populations (such as water content, precipitation rate, kinetic energy, or radar reflectivity) which are subject to statistical sampling errors due to the Poisson distributed fluctuations of particles sampled in each particle size interval and the weighted sum of the associated variances in proportion to their contribution to the integral parameter to be measured. Universal curves are presented which are applicable to the exponential size distribution permitting FSD estimation of any parameters from n = 0 to n = 6. The equations and curves also permit corrections for finite upper limits in the size spectrum and a realistic fall speed law.
Because of the importance of surfaces and interfaces in many scientific and technological areas, the use of x-ray photoelectron spectroscopy (XPS) has been growing exponentially. Although XPS is being used to obtain useful information about the surface composition of samples, much more information about materials and their properties can be extracted from XPS data than commonly obtained. This paper describes some of the areas where alternative analysis methods or experimental design can obtain information about the near-surface region of a sample, often information not available in other ways. Experienced XPS analysts are familiar with many of these methods, but they may not be known to new or casual XPS users, and sometimes, they have not been used because of an inappropriately assumed complexity. The information available includes optical, electronic, and electrical properties; nanostructure; expanded chemical information; and enhanced analysis of biological materials and solid/liquid interfaces. Many of these analyses can be conducted on standard laboratory XPS systems, with either no or relatively minor system alterations. Topics discussed include (1) considerations beyond the “traditional” uniform surface layer composition calculation, (2) using the Auger parameter to determine a sample property, (3) use of the D parameter to identify sp 2 and sp 3 carbon information, (4) information from the XPS valence band, (5) using cryocooling to expand range of samples that can be analyzed and minimize damage, and (6) using electrical potential effects on XPS signals to extract chemically resolved electrical measurements including band alignment and electrical property information.
Defects are a leading issue for the rejection of parts manufactured through the Directed Energy Deposition (DED) Additive Manufacturing (AM) process. In an attempt to illuminate and advance in situ quality monitoring and control of workpieces, we present an innovative data-driven method that synchronously collects sensing data and AM process parameters with a low sampling rate during the DED process. The proposed data-driven technique determines the important influences that individual printing parameters and sensing features have on prediction at the inter-layer qualification to perform feature selection. Three Machine Learning (ML) algorithms including Random Forest (RF), Support Vector Machine (SVM), and Convolutional Neural Network (CNN) are used. During post-production, a threshold is applied to detect low-density occurrences such as porosity sizes and quantities from CT scans that render individual layers acceptable or unacceptable. This information is fed to the ML models for training. Training/testing are completed offline on samples deemed “high-quality” and “low-quality”, utilizing only features recorded from the build process. CNN results show that the classification of acceptable/unacceptable layers can reach between 90% accuracy while training/testing on a “high-quality” sample and dip to 65% accuracy when trained/tested on “low-quality”/“high-quality” (respectively), indicating over-fitting but showing CNN as a promising inter-layer classifier.
This study investigates the variations of structural parameters and chemistry of a partially metamict and seven detrital zircon samples from different localities using single-crystal X-ray diffraction, synchrotron high-resolution powder X-ray diffraction, and electron-probe micro-analysis techniques. The unit-cell parameters for the eight zircon samples vary linearly with increasing unit-cell volume, V. A zircon sample from the Canadian Arctic Islands has the smallest unit-cell parameters, bond distances, ideal stoichiometric composition, unaffected by α-radiation damage, and is chemically pure. A zircon sample from Jemaa, Nigeria has the largest unit-cell parameters because of the effect of α-radiation doses received over a long time (2384 Ma). All the samples show good correlations between Zr and Si apfu (atom per formula unit) versus unit-cell volume, V. The α-radiation doses in the samples are lower than ~3.5 × 1015 α-decay events/mg. Substitutions of other cations at the Zr and Si sites control the variations of the structural parameters. Relatively large unit-cell parameters and bond distances occur because the Zr site accommodates other cations that have larger ionic radii than the Zr atom. Geological age increases the radiation doses in zircon and it is related to V.
Context. When selecting a light curve classifier for use as part of a photometric supernova Ia (SN Ia) cosmological analysis, it is common to make decisions based on metrics of classification performance, such as the contamination within the photometrically classified SN Ia sample, rather than a measure of cosmological constraining power. If the former is an appropriate proxy for the latter, this practice would eliminate the computational expense of a full cosmology forecast in the analysis pipeline design process. Aims. This study tests the assumption that light curve classification metrics are an appropriate proxy for cosmology metrics. Methods. We emulated photometric SN Ia cosmology light curve samples with controlled contamination rates of individual contaminant classes and evaluated each of them under a set of classification metrics. We then derived cosmological parameter constraints from all samples under two common analysis approaches and quantified the impact of contamination by each contaminant class on the resulting cosmological parameter estimates. Results. We observe that cosmology metrics are sensitive to both the contamination rate and the class of the contaminating population, whereas the classification metrics are shown to be insensitive to the latter. Conclusions. Based on these findings, we discourage any exclusive reliance on light curve classification-based metrics for analysis design decisions, which (counterintuitively) include but are not limited to the classifier choice. Instead, we recommend optimising science analysis pipeline design choices using a metric of the information gained about the physical parameters of interest.
This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 1,830 airfoil shapes computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this dataset, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We sampled airfoil designs over both parameter spaces to explore the full range of possible shape variations. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, for or three different Reynolds' numbers (3M, 6M, and 9M), and for 25 angles of attack from -4 deg. to 20 deg. with 1 degree increments. Across all these various parameters, this dataset includes the results from over 250,000 CFD simulations. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy, in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_2k_data.ipynb.
The ASTM G72/G72M-15 Standard Test Method for Autogenous Ignition Temperature of Liquids and Solids in a High-Pressure Oxygen-Enriched Environment is currently used to evaluate materials for the ignition susceptibility driven by exposure to external heat in an enriched oxygen environment. Testing performed on highly volatile liquids such as cleaning solvents has proven problematic due to inconsistent test results (non-ignitions). Non-ignition results can be misinterpreted as favorable oxygen compatibility, although they are more likely associated with inadequate fuel-to-oxidizer ratios. Forced evaporation during purging and inadequate sample size were identified as two potential causes for inadequate available sample material during testing. In an effort to maintain adequate fuel-to-oxidizer ratios within the reaction vessel during test, several parameters were considered, including sample size, pretest sample chilling, pretest purging, and test pressure. Tests on a variety of solvents exhibiting a range of volatilities are presented in this paper. A proposed improvement to the standard test protocol as a result of this evaluation is also presented. Execution of the final proposed improved test protocol outlines an incremental step method of determining optimal conditions using increased sample sizes while considering test system safety limits. The proposed improved test method increases confidence in results obtained by utilizing the ASTM G72 autogenous ignition temperature test method and can aid in the oxygen compatibility assessment of highly volatile liquids and other conditions that may lead to false non-ignition results.
The ASTM G72/G72M-15 Standard Test Method for Autogenous Ignition Temperature of Liquids and Solids in a High-Pressure Oxygen-Enriched Environment is currently used to evaluate materials for the ignition susceptibility driven by exposure to external heat in an enriched oxygen environment. Testing performed on highly volatile liquids such as cleaning solvents has proven problematic due to inconsistent test results (non-ignitions). Non-ignition results can be misinterpreted as favorable oxygen compatibility, although they are more likely associated with inadequate fuel-to-oxidizer ratios. Forced evaporation during purging and inadequate sample size were identified as two potential causes for inadequate available sample material during testing. In an effort to maintain adequate fuel-to-oxidizer ratios within the reaction vessel during test, several parameters were considered, including sample size, pretest sample chilling, pretest purging, and test pressure. Tests on a variety of solvents exhibiting a range of volatilities are presented in this paper. A proposed improvement to the standard test protocol as a result of this evaluation is also presented. Execution of the final proposed improved test protocol outlines an incremental step method of determining optimal conditions using increased sample sizes while considering test system safety limits. The proposed improved test method increases confidence in results obtained by utilizing the ASTM G72 autogenous ignition temperature test method and can aid in the oxygen compatibility assessment of highly volatile liquids and other conditions that may lead to false non-ignition results.
Efficient sampling of interdependent and multiplex infrastructure networks is critical for effectively applying failure and recovery algorithms in real-world settings, as well as to generate property-preserving reduced-order graph-based ensembles that address topological uncertainties. In this paper, we first explore the performance, i.e. the success in preserving graph properties, of graph sampling algorithms for interdependent and multiplex networks with synthetic and real-world graphs. We simulate sampling algorithms under different parameter settings. These settings include probabilistic graph generators, coupling patterns, and various performance metrics. Our results show that while Random Node and Random Walk sampling algorithms perform best for interdependent networks, Random Edge and Forest Fire sampling algorithms perform best for multiplex networks. Second, we propose and implement a novel similarity-based sampling algorithm for multiplex networks that samples only log(N) number of layers of an N-layer multiplex network while yielding computational savings with performance guarantees. Experimental results show that similarity sampling outperforms complete sampling of all layers while decreasing performance costs from a linear scale to a logarithmic one. Our results also indicate that similarity-based sampling outperforms complete sampling and random selection in nearly all scenarios when tested with real-world data.
We present constraints on cosmological parameters based on a sample of Sunyaev-Zel'dovich-selected galaxy clusters detected in a millimeter-wave survey by the Atacama Cosmology Telescope. The cluster sample used in this analysis consists of 9 optically-confirmed high-mass clusters comprising the high-significance end of the total cluster sample identified in 455 square degrees of sky surveyed during 2008 at 148 GHz. We focus on the most massive systems to reduce the degeneracy between unknown cluster astrophysics and cosmology derived from SZ surveys. We describe the scaling relation between cluster mass and SZ signal with a 4-parameter fit. Marginalizing over the values of the parameters in this fit with conservative priors gives (sigma)8 = 0.851 +/- 0.115 and w = -1.14 +/- 0.35 for a spatially-flat wCDM cosmological model with WMAP 7-year priors on cosmological parameters. This gives a modest improvement in statistical uncertainty over WMAP 7-year constraints alone. Fixing the scaling relation between cluster mass and SZ signal to a fiducial relation obtained from numerical simulations and calibrated by X-ray observations, we find (sigma)8 + 0.821 +/- 0.044 and w = -1.05 +/- 0.20. These results are consistent with constraints from WMAP 7 plus baryon acoustic oscillations plus type Ia supernova which give (sigma)8 = 0.802 +/- 0.038 and w = -0.98 +/- 0.053. A stacking analysis of the clusters in this sample compared to clusters simulated assuming the fiducial model also shows good agreement. These results suggest that, given the sample of clusters used here, both the astrophysics of massive clusters and the cosmological parameters derived from them are broadly consistent with current models.
Estimation of two-phase fluid flow properties is important to understand and predict water and gas movement through the vadose zone for agricultural, hydrogeological, and engineering applications, such as for vapor-phase contaminant transport and/or containment of noble gases in the subsurface. In this second progress report of FY22, we present two ongoing activities related to imbibition testing on volcanic rock samples. We present the development of a new analytical solution predicting the temperature response observed during imbibition into dry samples, as discussed in our previous first progress report for FY22. We also illustrate the use of a multi-modal capillary pressure distribution to simulate both early- and late-time imbibition data collected on tuff core that can exhibit multiple pore types. These FY22 imbibition tests were conducted for an extended period (i.e., far beyond the time required for the wetting front to reach the top of the sample), which is necessary for parameter estimation and characterization of two different pore types within the samples.
An extension of the continuous aperture Woodward-Lawson sampling theorem has been developed for a finite linear array of equidistant identical elements with arbitrary excitations. It is shown that by sampling the array factor at a finite number of specified points in the far field, the exact array factor over all space can be efficiently reconstructed in closed form. The specified sample points lie in real space and hence are measurable provided that the interelement spacing is greater than approximately one half of a wavelength. This paper provides insight as to why the length parameter used in the sampling formulas for discrete arrays is larger than the physical span of the lattice points in contrast with the continuous aperture case where the length parameter is precisely the physical aperture length.
This study presents a test method and its theoretical framework to determine the acoustic nonlinearity parameters (α, β, δ) of material using thermal modulation of ultrasonic waves. Temperature change-induced thermal strain excites the nonlinear response of the material and modulates the ultrasonic wave propagating in it. Experimental results showed a strong correlation between the relative wave velocity change and the temperature change. With a quadratic polynomial model, the acoustic nonlinearity parameters were obtained from the polynomial coefficients by curve fitting the experimental data. Their effects on thermal-induced velocity change were discussed. The parameters α, β, and δ govern the hysteretic gap, average slope, and curvature of the correlation curve, respectively. The proposed theory was validated on aluminum, steel, intact and damaged concrete samples. The obtained nonlinear parameters show reasonable agreement with values reported in the literature. Compared to other nonlinear acoustic methods using vibration or acoustic excitation, the thermal modulation method generates more uniform, slow changing, and larger strain field in the test sample. Employing the thermal effect as the driving force for nonlinearity instead of an undesired influencing factor, this method can measure the absolute values of α, β, and δ with good accuracy using a simple ultrasonic test setup.
Be-D co-deposit samples are produced over an extended range of plasma-material interaction parameters reflective of the conditions expected in ITER deposition dominant locations. Deposition temperature, D impact energy, atomic Be deposition rate, and D2 neutral pressure were varied in the ranges 373–623 K, ~2–100 eV, 1–10 × 10 19 m 2 s –1 , and 0.27–13.3 Pa respectively. Thermal desorption spectrometry was carried out on samples, subsequently, to measure the D release profile and retention. In this work, it was found that the D retention in samples agrees well with the existing GDT D/Be scaling over the extended parameter space, and that increased D impact energy and D2 pressure can lead to the observation of a sharp low-temperature release peak at ~440 K in desorption data. Desorption data without the presence of the sharp release mechanism are modeled with TMAP-7 utilizing three traps of de-trapping energies, 0.8, 0.9 and 1.0 eV.