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Measuring the Properties of Dark Energy with Photometrically Classified Pan-STARRS Supernovae. I. Systematic Uncertainty from Core-collapse Supernova Contamination

The Pan-STARRS (PS1) Medium Deep Survey discovered over 5000 likely supernovae (SNe) but obtained spectral classifications for just 10% of its SN candidates. We measured spectroscopic host galaxy redshifts for 3147 of these likely SNe and estimate that ∼1000 are Type Ia SNe (SNe Ia) with light-curve quality sufficient for a cosmological analysis. We use these data with simulations to determine the impact of core-collapse SN (CC SN) contamination on measurements of the dark energy equation of state parameter, w. Using the method of Bayesian Estimation Applied to Multiple Species (BEAMS), distances to SNe Ia and the contaminating CC SN distribution are simultaneously determined. We test light-curve-based SN classification priors for BEAMS as well as a new classification method that relies upon host galaxy spectra and the association of SN type with host type. By testing several SN classification methods and CC SN parameterizations on large SN simulations, we estimate that CC SN contamination gives a systematic error on w (σ{sub w}{sup CC}) of 0.014, 29% of the statistical uncertainty. Our best method gives σ{sub w}{sup CC}=0.004, just 8% of the statistical uncertainty, but could be affected by incomplete knowledge of the CC SN distribution. This method determines the SALT2 color and shape coefficients, α and β, with ∼3% bias. However, we find that some variants require α and β to be fixed to known values for BEAMS to yield accurate measurements of w. Finally, the inferred abundance of bright CC SNe in our sample is greater than expected based on measured CC SN rates and luminosity functions.

79 ASTRONOMY AND ASTROPHYSICS↗

Highly accelerated life testing (HALT): A review from a statistical perspective

Despite its use in one form or another for at least four decades, HALT and related techniques [e.g., highly accelerated-stress screening (HASS) and stress audits (HASA)] are not well understood within the statistical community and remain controversial. This largely reflects a conflict in motivation between engineers, testing under harsh conditions to discover and eliminate failure modes, and statisticians, taking a more cautious approach to develop quantitative estimates of parameters such as mean time between failures (MTBF). Here, this review article will clarify HALT concepts and methods and explain where it fits within the universe of methods that involve the application of accelerating factors to compress the time required to evaluate or enhance product reliability. A major distinction is between methods such as HALT, a high-stress test-analyze-fix-test iterative process directed at improving reliability by discovering and fixing weak points in a design, and quantitative accelerated life testing (QALT), whose goal is the estimation of product life for a fixed design. We discuss methods such as physics of failure that offer some hope of bridging the gap between the qualitative nature of HALT, and purely quantitative statistical methods. We present a variety of engineering applications of HALT including metal fatigue, piping and pressure vessels, structural damage, radiation damage, and rotating machinery. We also discuss potential synergies between HALT and QALT, such as rapid identification, through HALT, of failure modes requiring quantitative analysis. For further study, extensive references to the applicable literature are provided as well as an appendix that describes related methods.

97 MATHEMATICS AND COMPUTING↗

Measuring representative volume elements from high-resolution grain-scale strain fields

Most crystalline materials present a highly heterogeneous response at the microscale, which can be affected by both internal factors (such as microstructural parameters) and external factors (such as loading). Relating microscale inhomogeneities to the macroscale response of a material requires the use of homogenisation techniques, usually based on the concept of a representative volume element (RVE)—the smallest volume of material that represents the global average response. Here, in this work, we present a new and robust experimental method of measuring the size of a strain-based RVE from high-resolution grain-scale strain fields obtained using digital image correlation (DIC). The proposed method is based on the statistical (stereological) nature of the RVE, which has been widely adopted in numerical studies, and involves dividing a strain field into randomly selected regions of varying sizes and statistically analysing the distributions of average strains within them. To validate the new method, we generate a large number of synthetic strain fields from a fractional Gaussian noise algorithm. The proposed stereological method is shown to be capable of producing reliable RVE measurements from a very large range of possible microscale strain fields while at the same time being robust in that it can produce RVE measurement results even in cases where other existing methods may be unable to do so. The proposed method has a low field-of-view requirement, only needing a field-of-view about 1.2 times as large as the RVE to produce reliable measurements. In addition, the stereological method offers significant flexibility since its statistical nature allows for control over how strict the RVE measurement should be in each case.

36 MATERIALS SCIENCE↗

Upper Subcritical Limit Calculations with Correlated Integral Experiments

The American National Standards Institute (ANSI) and American Nuclear Society (ANS) standard for Validation of Neutron Transport Methods for Nuclear Criticality Safety Calculations defines the Upper Subcritical Limit (USL) as “a limit on the calculated k effective value established to ensure that conditions calculated to be subcritical will actually be subcritical.” Often, USL calculations are based on statistical techniques that infer information about a nuclear system of interest (application) from a set of known/well characterized similar systems (experiments). In determining a USL, it is common to statistically determine a calculation bias and bias uncertainty. Bias is “the systematic difference between calculated results and experimental data.” The bias uncertainty is “the uncertainty that accounts for the combined effects of uncertainties in the benchmarks, the calculational models of the benchmarks, and the calculational methods.” Both the bias and the bias uncertainty are often inferred through statistical methods applied to the selected set of experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Validating Nuclear Data Uncertainties Obtained from a Statistical Analysis of Experimental Data with the “Physical Uncertainty Bounds” Method

Concerns within the nuclear data community led to substantial increases of Neutron Data Standards (NDS) uncertainties from its previous to the current version. For example, those associated with the NDS reference cross section 239 Pu(n,f) increased from 0.6–1.6% to 1.3–1.7% from 0.1–20 MeV. These cross sections, among others, were adopted, e.g., by ENDF/B-VII.1 (previous NDS) and ENDF/B-VIII.0 (current NDS). There has been a strong desire to be able to validate these increases based on objective criteria given their impact on our understanding of various application uncertainties. Here, the “Physical Uncertainty Bounds” method (PUBs) by Vaughan et al. is applied to validate evaluated uncertainties obtained by a statistical analysis of experimental data. We investigate with PUBs whether ENDF/B-VII.1 or ENDF/B-VIII.0 239 Pu(n,f) cross-section uncertainties are more realistic given the information content used for the actual evaluation. It is shown that the associated conservative (1.5–1.8%) and minimal realistic (1.1–1.3%) uncertainty bounds obtained by PUBs enclose ENDF/B-VIII.0 uncertainties and indicate that ENDF/B-VII.1 uncertainties are underestimated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Hawai‘i Play Fairway (Final Report)

Most of Hawai'i's geothermal resources are blind—their manifestations, such as hot springs and steam vents, do not appear on the ground surface because the heated water flows far below. With the exception of $K\bar{i}lauea East Rift Zone$, in most areas of Hawai'i, high lateral permeability in the first kilometer below ground surface prevents surface thermal features from developing. As a methodology for discovering these blind resources, Play Fairway Analysis (PFA) involves finding potential locations of blind hydrothermal systems and describing potential geothermal sources in rift-zone settings. Using the PFA to find Hawai'i's geothermal resources, the University of Hawai'i (UH) conducted the Hawai‘i Play Fairway Project, Hawai'i's first statewide geothermal resource assessment since 1985. Sponsored by the U.S. Department of Energy, the Hawai'i Play Fairway Project provided an updated resource assessment, a roadmap for additional exploration activities, and the identification of areas for further exploration. Benefitting from UH's core competency in earth sciences and experienced geothermal researchers, the project comprised three phases. During the first phase, the team identified, compiled, and ranked existing geologic, groundwater, and geophysical datasets relevant to subsurface heat, fluid and permeability. Using a Bayesian statistical approach, the team developed a statistical methodology to integrate these data into a resource probability map. The team evaluated the confidence in the probability value and considered development viability of areas with geothermal resources. With these analyses, the team identified 10 locations in the Hawaiian Islands for exploration activities. For the second phase, the team collected new groundwater data in 10 locations across the state and new geophysical data on $L\bar{a}na‘i, Maui$, and central Hawai'i Island and modeled topographically induced stress to better characterize subsurface permeability. Analyzing the subsurface stresses, the team evaluated the potential for fracture-induced permeability. The team inverted the MT and gravity data to produce 3D models of resistivity and density, respectively, on $L\bar{a}na‘i$, across $Haleakal\bar{a}'s$ SW rift (Maui), and surrounding Mauna Kea (Hawai‘i Island). The team developed and applied a new method for incorporating depth information about resistivity, density, and potential for fracture-induced permeability into the statistical method for computing resource probability in these three focus areas. The team incorporated the new groundwater results with the new geophysical results and the calculations of potential for fracture-induced permeability to produce updated maps of resource probability and confidence. Through combining data from the first and second phases, the team determined locations for further exploration during the third phase. For MT and gravity surveys, the team recommended $Kaua'i's$ $L\bar{i}hu'e$ $Basin$, the east rift of $Maui's$ $Haleakal\bar{a}$ volcano, and the southwest rift of Hawai'i Island's Mauna Loa volcano. The MT and gravity surveys aimed to enable improved confidence in the resource potential in these locations. For drilling deep groundwater well(s), the team recommended Southeast Mauna Kea and $L\bar{a}na's$ $P\bar{a}l\bar{a}wai$ $Basin$. During the third phase, further exploration involved drilling a groundwater well in $L\bar{a}na's$ $P\bar{a}l\bar{a}wai$ $Basin$ and performing more geophysical surveys. We deepened an existing water well proximal to our target area on $L\bar{a}na'i$ due to funding constraints that precluded us from spudding a new well that would exceed 1km depth. Drilling was preceded by a number of substantial elements including: writing an Environmental Assessment and the subsequent legal process, performance of deviation logging, lowering a camera down the well, coordinating site preparation with $P\bar{u}lama$ $L\bar{a}na'i$, shipping the UH-owned rig interisland, procuring supplies, and leading 3 community meetings on $L\bar{a}na'i$. Drilling occurred 24/7 the entire month of June 2019 over which time $L\bar{a}na'i$ $Well$ 10 was deepened from 427 m to 1057 m, with continuous core collected. We measured a roughly linear temperature gradient averaging 42°C/km and a maximum bottom hole temperature of 66°C. This gradient is more than twice the background for Hawai'i and within a range of gradients measured in this depth range for some exploration wells within KERZ. We consider these results encouraging for $L\bar{a}na'i's$ resource potential and recommend following with a slim hole within $L\bar{a}na'i's$ caldera (our target zone) to ~ 2 km. Further, the positive implications such results have for the island of O‘ahu are substantial - the shield stage of O'ahu's volcanoes ended 1-2 My earlier. However, O'ahu uses more electricity than the rest of the islands combined, and the utility recently called for 500-700MW of firm, dispatchable renewable electricity on O'ahu by 2033. In Phase 3, we also collected limited new encouraging groundwater data, and updated our thoughts on the probabilities of fluid and permeability at resource depths (Pr F = 1; Pr P = mostly unconstrained). Ultimately, we advocate for using our final probability of heat, and confidence in this probability, to drive the next phase of exploration. We contend further development of geothermal in Hawai‘i will enable the state to achieve its 100% renewable policy objective and Hawai'i to transition off of fossil fuels through geothermal discovery and development. The project not only produced a large amount of data and expanded the existing knowledge of Hawai'i's geothermal resources, but also produced publications, theses, presentations, core photos, datasets, media reports, television interviews, community events, and a blog. Students and new professionals benefitted from the project's hands-on research experiences and educational opportunities and earned awards and recognition.

15 GEOTHERMAL ENERGY↗

Enhanced Co-Expression Extrapolation (COXEN) Gene Selection Method for Building Anti-Cancer Drug Response Prediction Models

The co-expression extrapolation (COXEN) method has been successfully used in multiple studies to select genes for predicting the response of tumor cells to a specific drug treatment. Here, we enhance the COXEN method to select genes that are predictive of the efficacies of multiple drugs for building general drug response prediction models that are not specific to a particular drug. The enhanced COXEN method first ranks the genes according to their prediction power for each individual drug and then takes a union of top predictive genes of all the drugs, among which the algorithm further selects genes whose co-expression patterns are well preserved between cancer cases for building prediction models. We apply the proposed method on benchmark in vitro drug screening datasets and compare the performance of prediction models built based on the genes selected by the enhanced COXEN method to that of models built on genes selected by the original COXEN method and randomly picked genes. Models built with the enhanced COXEN method always present a statistically significantly improved prediction performance (adjusted p-value ≤ 0.05). Our results demonstrate the enhanced COXEN method can dramatically increase the power of gene expression data for predicting drug response.

60 APPLIED LIFE SCIENCES↗

MODELING THE Ly α FOREST IN COLLISIONLESS SIMULATIONS

Cosmological hydrodynamic simulations can accurately predict the properties of the intergalactic medium (IGM), but only under the condition of retaining the high spatial resolution necessary to resolve density fluctuations in the IGM. This resolution constraint prohibits simulating large volumes, such as those probed by BOSS and future surveys, like DESI and 4MOST. To overcome this limitation, we present “Iteratively Matched Statistics” (IMS), a novel method to accurately model the Ly α forest with collisionless N -body simulations, where the relevant density fluctuations are unresolved. We use a small-box, high-resolution hydrodynamic simulation to obtain the probability distribution function (PDF) and the power spectrum of the real-space Ly α forest flux. These two statistics are iteratively mapped onto a pseudo-flux field of an N -body simulation, which we construct from the matter density. We demonstrate that our method can reproduce the PDF, line of sight and 3D power spectra of the Ly α forest with good accuracy (7%, 4%, and 7% respectively). We quantify the performance of the commonly used Gaussian smoothing technique and show that it has significantly lower accuracy (20%–80%), especially for N -body simulations with achievable mean inter-particle separations in large-volume simulations. In addition, we show that IMS produces reasonable and smooth spectra, making it a powerful tool for modeling the IGM in large cosmological volumes and for producing realistic “mock” skies for Ly α forest surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Method of Determining the Reliability of Real-Time In-reactor Monitoring of VVER

A methodological approach and the basic tenets for evaluating the reliability of in-reactor monitoring of VVER are presented. The method is based on the statistical analysis of indications in real time and includes methods for evaluating the admissible maximum error of the measurement channels used for monitoring as well as the average value and admissible deviation of indications in groups of parallel monitoring channels, as well as a method of evaluating reliability by comparing the values of a parameter with the regime values. In comparing the indications of a monitoring channel with the indications of other parallel channels, the median value is proposed as the baseline value. The developed method is implemented in the Diagnostika SVRK special software, which has been successfully tested during the commissioning of the No. 1 unit at the Novovoronezh NPP-2.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

SU-E-T-769: T-Test Based Prior Error Estimate and Stopping Criterion for Monte Carlo Dose Calculation in Proton Therapy

Purpose: The Monte Carlo (MC) method is a gold standard for dose calculation in radiotherapy. However, it is not a priori clear how many particles need to be simulated to achieve a given dose accuracy. Prior error estimate and stopping criterion are not well established for MC. This work aims to fill this gap. Methods: Due to the statistical nature of MC, our approach is based on one-sample t-test. We design the prior error estimate method based on the t-test, and then use this t-test based error estimate for developing a simulation stopping criterion. The three major components are as follows.First, the source particles are randomized in energy, space and angle, so that the dose deposition from a particle to the voxel is independent and identically distributed (i.i.d.).Second, a sample under consideration in the t-test is the mean value of dose deposition to the voxel by sufficiently large number of source particles. Then according to central limit theorem, the sample as the mean value of i.i.d. variables is normally distributed with the expectation equal to the true deposited dose.Third, the t-test is performed with the null hypothesis that the difference between sample expectation (the same as true deposited dose) and on-the-fly calculated mean sample dose from MC is larger than a given error threshold, in addition to which users have the freedom to specify confidence probability and region of interest in the t-test based stopping criterion. Results: The method is validated for proton dose calculation. The difference between the MC Result based on the t-test prior error estimate and the statistical Result by repeating numerous MC simulations is within 1%. Conclusion: The t-test based prior error estimate and stopping criterion are developed for MC and validated for proton dose calculation. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)

60 APPLIED LIFE SCIENCES↗

A two-stage method for microcalcification cluster segmentation in mammography by deformable models

Purpose: Segmentation of microcalcification (MC) clusters in x-ray mammography is a difficult task for radiologists. Accurate segmentation is prerequisite for quantitative image analysis of MC clusters and subsequent feature extraction and classification in computer-aided diagnosis schemes. Methods: In this study, a two-stage semiautomated segmentation method of MC clusters is investigated. The first stage is targeted to accurate and time efficient segmentation of the majority of the particles of a MC cluster, by means of a level set method. The second stage is targeted to shape refinement of selected individual MCs, by means of an active contour model. Both methods are applied in the framework of a rich scale-space representation, provided by the wavelet transform at integer scales. Segmentation reliability of the proposed method in terms of inter and intraobserver agreements was evaluated in a case sample of 80 MC clusters originating from the digital database for screening mammography, corresponding to 4 morphology types (punctate: 22, fine linear branching: 16, pleomorphic: 18, and amorphous: 24) of MC clusters, assessing radiologists’ segmentations quantitatively by two distance metrics (Hausdorff distance—HDIST{sub cluster}, average of minimum distance—AMINDIST{sub cluster}) and the area overlap measure (AOM{sub cluster}). The effect of the proposed segmentation method on MC cluster characterization accuracy was evaluated in a case sample of 162 pleomorphic MC clusters (72 malignant and 90 benign). Ten MC cluster features, targeted to capture morphologic properties of individual MCs in a cluster (area, major length, perimeter, compactness, and spread), were extracted and a correlation-based feature selection method yielded a feature subset to feed in a support vector machine classifier. Classification performance of the MC cluster features was estimated by means of the area under receiver operating characteristic curve (Az ± Standard Error) utilizing tenfold cross-validation methodology. A previously developed B-spline active rays segmentation method was also considered for comparison purposes. Results: Interobserver and intraobserver segmentation agreements (median and [25%, 75%] quartile range) were substantial with respect to the distance metrics HDIST{sub cluster} (2.3 [1.8, 2.9] and 2.5 [2.1, 3.2] pixels) and AMINDIST{sub cluster} (0.8 [0.6, 1.0] and 1.0 [0.8, 1.2] pixels), while moderate with respect to AOM{sub cluster} (0.64 [0.55, 0.71] and 0.59 [0.52, 0.66]). The proposed segmentation method outperformed (0.80 ± 0.04) statistically significantly (Mann-Whitney U-test, p < 0.05) the B-spline active rays segmentation method (0.69 ± 0.04), suggesting the significance of the proposed semiautomated method. Conclusions: Results indicate a reliable semiautomated segmentation method for MC clusters offered by deformable models, which could be utilized in MC cluster quantitative image analysis.

60 APPLIED LIFE SCIENCES↗

Fluctuating Hydrodynamic Methods for Fluid-Structure Interactions in Confined Channel Geometries

Computational methods are developed for the study of fluid-structure interactions subject to thermal fluctuations when conned within channels having slit-like geometry. The methods take into account the hydrodynamic coupling and diusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochastic numerical methods subject to no-slip boundary conditions using a staggered nite volume discretization. We show that by imposing an exact fluctuation-dissipation condition to discretize the stochastic driving elds combined with using an exact projection method to enforce incompressibility is sucient to ensure results consistent with statistical mechanics. We demonstrate our methods by investigating how the proximity of ellipsoidal colloids to the channel wall eects their active hydrodynamic responses and passive diusivity. We also study the collective dynamics of a large number of particles by considering the intermediate scattering functions for the relaxation of density fluctuations. We expect our introduced stochastic computational methods to be applicable broadly to applications in which confinement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations. uctuations.

Wang, Yaohong↗

A novel approach to assess the treatment response using Gaussian random field in PET

Purpose: The assessment of early therapeutic response to anticancer therapy is vital for treatment planning and patient management in clinic. With the development of personal treatment plan, the early treatment response, especially before any anatomically apparent changes after treatment, becomes urgent need in clinic. Positron emission tomography (PET) imaging serves an important role in clinical oncology for tumor detection, staging, and therapy response assessment. Many studies on therapy response involve interpretation of differences between two PET images, usually in terms of standardized uptake values (SUVs). However, the quantitative accuracy of this measurement is limited. This work proposes a statistically robust approach for therapy response assessment based on Gaussian random field (GRF) to provide a statistically more meaningful scale to evaluate therapy effects. Methods: The authors propose a new criterion for therapeutic assessment by incorporating image noise into traditional SUV method. An analytical method based on the approximate expressions of the Fisher information matrix was applied to model the variance of individual pixels in reconstructed images. A zero mean unit variance GRF under the null hypothesis (no response to therapy) was obtained by normalizing each pixel of the post-therapy image with the mean and standard deviation of the pretherapy image. The performance of the proposed method was evaluated by Monte Carlo simulation, where XCAT phantoms (128{sup 2} pixels) with lesions of various diameters (2–6 mm), multiple tumor-to-background contrasts (3–10), and different changes in intensity (6.25%–30%) were used. The receiver operating characteristic curves and the corresponding areas under the curve were computed for both the proposed method and the traditional methods whose figure of merit is the percentage change of SUVs. The formula for the false positive rate (FPR) estimation was developed for the proposed therapy response assessment utilizing local average method based on random field. The accuracy of the estimation was validated in terms of Euler distance and correlation coefficient. Results: It is shown that the performance of therapy response assessment is significantly improved by the introduction of variance with a higher area under the curve (97.3%) than SUVmean (91.4%) and SUVmax (82.0%). In addition, the FPR estimation serves as a good prediction for the specificity of the proposed method, consistent with simulation outcome with ∼1 correlation coefficient. Conclusions: In this work, the authors developed a method to evaluate therapy response from PET images, which were modeled as Gaussian random field. The digital phantom simulations demonstrated that the proposed method achieved a large reduction in statistical variability through incorporating knowledge of the variance of the original Gaussian random field. The proposed method has the potential to enable prediction of early treatment response and shows promise for application to clinical practice. In future work, the authors will report on the robustness of the estimation theory for application to clinical practice of therapy response evaluation, which pertains to binary discrimination tasks at a fixed location in the image such as detection of small and weak lesion.

61 RADIATION PROTECTION AND DOSIMETRY↗

Evidence for Unresolved γ -Ray Point Sources in the Inner Galaxy

We propose a new method to characterize unresolved point sources (PSs) generalizing traditional template fits to account for non-Poissonian photon statistics. We apply this method to Fermi Large Area Telescope γ-ray data to characterize PS populations at high latitudes and in the Inner Galaxy. We discover that PSs (resolved and unresolved) account for ~50% of the total extragalactic γ-ray background in the energy range ~1.9 to 11.9 GeV.Within 10° of the Galactic Center with |b| ≥ 2°, we find that ~5%–10% of the flux can be accounted for by a population of unresolved PSs distributed consistently with the observed ~GeV γ-ray excess in this region. The excess is fully absorbed by such a population, in preference to dark-matter annihilation. The inferred source population is dominated by near-threshold sources, which may be detectable in future searches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

VALIDATION, VERIFICATION, AND CALIBRATION THROUGH A CAUSAL LENS

This paper presents an alternative method based on causal inference to perform validation, verification, and calibration of simulation models. While classical validation and verification approaches focus on the identification of the associations between data elements using statistical and machine learning methods, the novel methods in this paper focus instead on the identification of causal relationships between data elements. Statistical and machine learning-based approaches are strictly data-driven, meaning that they provide quantitative comparison measures between datasets without explicitly considering the hypotheses behind them. This can lead to the erroneous conclusion that, if two data sets are close enough, then the models that generated them are similar. In addition, when experimental and simulated data differ to an extent that fails to meet the acceptance criteria, calibration techniques are used to tweak simulation model parameters to reduce the gap between the two types of data. This produces the false expectation that a simulation model will match reality. The methods presented in this paper move away from these strictly data-driven methods for validation and calibration toward more robust, model-driven methods based on causal inference. Causal inference aims to identify the possible mechanisms that might have generated data. Thus, this analysis targets the prediction of the effects when one (or more) of the identified mechanisms are altered. There are many approaches to identify, quantify and illustrate causal relationships. For the scope of this paper, directed graphs are employed as causal models. If the directed graph lacks cycles it is known as a directed acyclic graph (DAG). A node in such a graph represents an observed data element while a directed edge connecting two nodes represents a causal relationship between two variables. The developed causal methods are designed to extract causal models from simulation models and from experimental data. Causal models capture the causal relationships between data elements (e.g., simulated and experimental data). In this context, validation and verification are performed by comparing causal models. The proposed approach does not only inform system analysts on how a simulation model matches real-world data, but also identifies elements of the simulation model that should be revised when discrepancies between simulation and experimental data are observed. Through these causal methods, analysts have a means to identify the portion of the model equation(s) that are behind an edge connecting two variables. Hence, once the structural differences between causal models have been determined, model calibration can occur by changing only those model parameters that impact the identified causal relationships.

97 MATHEMATICS AND COMPUTING↗

Understanding Biases in Sample Preparation Techniques for Coupled Scanning Electron Microscopy and MAMA PuO 2 Morphological Analysis

In this project, the scanning electron microscopy (SEM) sampling method used during the statistical design study (SDS) was investigated to determine if any sampling biases were present in the analyzed data. Using standard particle size distribution powders from the National Institute of Standards and Technology (NIST 1984 standard reference material) with the origin wet dispersion method, it was determined that a bias to smaller particles was present. This was supported by theoretical calculations using Stokes’ law to determine the settling rate of spherical particles of roughly the same size and mass as those found in the SDS. Based on the theoretical calculations, it was determined that the settling rate for each of the 76 powder sets in the SDS could be unique based on specific particle shape and mass distributions, making a universal correction factor/formula not applicable. Therefore, priority shifted to developing an improved wet dispersion method that significantly reduced the particle settling rate for all particle size and shapes. This was achieved by replacing the original solvent (isopropyl alcohol) with a heavy liquid (lithium heteropolytungstates), which dramatically slowed the settling rate and allowed for the capture of a suitable homogeneous aliquot. SEM imaging and Morphological Analysis for Material Attribution (MAMA) software analysis were conducted on the NIST standard, and the SEM/MAMA data were compared to data captured by a dynamic image analysis particle size analyzer. The resulting data confirmed that the new wet dispersion method does indeed deliver an improved representative aliquot to the SEM stub. For instance, in the NIST certificate, the average particle size is ~17.1 µm ± 2.2 µm with a normal distribution. The initial wet dispersion method resulted in a drastically reduced average particle size of 6.1 µm in addition to a non-representative heavy bi-modal distribution whereas the improved LST wet dispersion method resulting in an average particle size that was much closer to the NIST certificate (12.7 µm) with a similar normal distribution. Although the improved method was still short of the NIST certificate average, atomic force microscopy analysis determined that the resulting ~20-25% reduction in size was due to particles sinking into the carbon sticky tape used for SEM imaging. It is believed that that this bias can be calibrated in a much more predicable manner than the original settling rate bias. In addition, the matching normal distribution curves between the NIST certificate and the heavy liquid method indicate a much-improved representative aliquot has been sampled and imaged. A surrogate CeO 2 powder was used to reflect PuO 2 more accurately and to aid in implementing radiological controls and shielding. The resulting data sets from the SEM/MAMA method and the particle size analyzer give almost identical average particle sizes and particle distribution statistics. Future work will re-analyze several select runs from the SDS to determine if morphological signatures can be found with the improved sampling method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Overview of Electric Vehicle Load Modeling Strategies for Grid Integration Studies

The adoption of electric vehicles (EVs) has emerged as a solution to reduce greenhouse gas emissions in the transportation sector, which has motivated the implementation of public policies to promote their use in several countries. However, the high adoption of EVs poses challenges for the electricity sector, as it would imply an increase in energy demand and possible impacts on the power quality (PQ) of the power grid. Therefore, it is important to conduct EV integration studies in the power grid to determine the amount that can be incorporated without causing problems and identify the areas of the power sector that will require reinforcements. Accurate EV load patterns are required for this type of study that, through mathematical modeling, reflect both the dynamic behavior and the factors that influence the decision to recharge EVs. This article aims to present an overview of EVs, examine the different factors considered in the literature for modeling EV load patterns, and review modeling methods. EV load modeling methods are classified into deterministic, statistical, and machine learning. The article shows that each modeling method has its advantages, disadvantages, and data requirements, ranging from simple load modeling to more accurate models requiring large datasets.

Computer Science↗