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NASA NTRS2017

Informal Statistics Help Desk

Back by popular demand, the JSC Biostatistics Laboratory and LSAH statisticians are offering an opportunity to discuss your statistical challenges and needs. Take the opportunity to meet the individuals offering expert statistical support to the JSC community. Join us for an informal conversation about any questions you may have encountered with issues of experimental design, analysis, or data visualization. Get answers to common questions about sample size, repeated measures, statistical assumptions, missing data, multiple testing, time-to-event data, and when to trust the results of your analyses.

Young, M.↗
NASA NTRS2017

Updated MISR Dark Water Research Aerosol Retrieval Algorithm - Part 1: Coupled 1.1 km Ocean Surface Chlorophyll a Retrievals with Empirical Calibration Corrections

As aerosol amount and type are key factors in the 'atmospheric correction' required for remote-sensing chlorophyll alpha concentration (Chl) retrievals, the Multi-angle Imaging SpectroRadiometer (MISR) can contribute to ocean color analysis despite a lack of spectral channels optimized for this application. Conversely, an improved ocean surface constraint should also improve MISR aerosol-type products, especially spectral single-scattering albedo (SSA) retrievals. We introduce a coupled, self-consistent retrieval of Chl together with aerosol over dark water. There are time-varying MISR radiometric calibration errors that significantly affect key spectral reflectance ratios used in the retrievals. Therefore, we also develop and apply new calibration corrections to the MISR top-of-atmosphere (TOA) reflectance data, based on comparisons with coincident MODIS (Moderate Resolution Imaging Spectroradiometer) observations and trend analysis of the MISR TOA bidirectional reflectance factors (BRFs) over three pseudo-invariant desert sites. We run the MISR research retrieval algorithm (RA) with the corrected MISR reflectances to generate MISR-retrieved Chl and compare the MISR Chl values to a set of 49 coincident SeaBASS (SeaWiFS Bio-optical Archive and Storage System) in situ observations. Where Chl(sub in situ) less than 1.5 mg m(exp -3), the results from our Chl model are expected to be of highest quality, due to algorithmic assumption validity. Comparing MISR RA Chl to the 49 coincident SeaBASS observations, we report a correlation coefficient (r) of 0.86, a root-mean-square error (RMSE) of 0.25, and a median absolute error (MAE) of 0.10. Statistically, a two-sample Kolmogorov- Smirnov test indicates that it is not possible to distinguish between MISR Chl and available SeaBASS in situ Chl values (p greater than 0.1). We also compare MODIS-Terra and MISR RA Chl statistically, over much broader regions. With about 1.5 million MISR-MODIS collocations having MODIS Chl less than 1.5 mg m(exp -3), MISR and MODIS show very good agreement: r = 0.96, MAE = 0.09, and RMSE = 0.15. The new dark water aerosol/Chl RA can retrieve Chl in low-Chl, case I waters, independent of other imagers such as MODIS, via a largely physical algorithm, compared to the commonly applied statistical ones. At a minimum, MISR's multi-angle data should help reduce uncertainties in the MODIS-Terra ocean color retrieval where coincident measurements are made, while also allowing for a more robust retrieval of particle properties such as spectral single-scattering albedo.

Limbacher, James A.↗
DOE OSTI2023

Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for early DESI data

ABSTRACT We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel’dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, non-trivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable data sets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2002

Incorporating Biological Knowledge into Evaluation of Casual Regulatory Hypothesis

Biological data can be scarce and costly to obtain. The small number of samples available typically limits statistical power and makes reliable inference of causal relations extremely difficult. However, we argue that statistical power can be increased substantially by incorporating prior knowledge and data from diverse sources. We present a Bayesian framework that combines information from different sources and we show empirically that this lets one make correct causal inferences with small sample sizes that otherwise would be impossible.

Chrisman, Lonnie↗
NASA NTRS1990

Sampling errors for satellite-derived tropical rainfall - Monte Carlo study using a space-time stochastic model

Estimates of monthly average rainfall based on satellite observations from a low earth orbit will differ from the true monthly average because the satellite observes a given area only intermittently. This sampling error inherent in satellite monitoring of rainfall would occur even if the satellite instruments could measure rainfall perfectly. The size of this error is estimated for a satellite system being studied at NASA, the Tropical Rainfall Measuring Mission (TRMM). First, the statistical description of rainfall on scales from 1 to 1000 km is examined in detail, based on rainfall data from the Global Atmospheric Research Project Atlantic Tropical Experiment (GATE). A TRMM-like satellite is flown over a two-dimensional time-evolving simulation of rainfall using a stochastic model with statistics tuned to agree with GATE statistics. The distribution of sampling errors found from many months of simulated observations is found to be nearly normal, even though the distribution of area-averaged rainfall is far from normal. For a range of orbits likely to be employed in TRMM, sampling error is found to be less than 10 percent of the mean for rainfall averaged over a 500 x 500 sq km area.

Bell, Thomas L.↗
DOE OSTI2016

Application of Variance Reduction Techniques in RMC Burnup and Thermal-Hydraulic Coupled Calculation

In reactor analog simulation, the Monte Carlo method has relatively high fidelity since it can reduce calculation errors resulting from using approximation methods by describing complex geometry and neutron energy spectra. The Monte Carlo method is, in essence, a stochastic simulation of the neutron transport process, and statistical uncertainty of all the computed results must be provided. In large-scale reactor computation, this method can accurately estimate integral quantities such as the effective multiplication factor (K{sub eff}), and it can limit the uncertainty within an acceptable range via reasonably selecting simulation particles. Nevertheless, it faces great challenges in estimating local quantities like neutron flux and fission power, with uncertainty of estimators beyond acceptance. To decrease the uncertainty of local quantities by increasing simulation particles may cost much time and reduce efficiency. The main reasons are as follows. Firstly, the scale of reactors is so large that common pressurized water reactors have tens of thousands of lattice cells; secondly, uneven distribution of neutron flux and fission power causes uneven distribution of uncertainty. Smith K. puts forward the 95/95 principle to estimate whether uncertainty calculated with Monte Carlo Code satisfies the requirement. According to the principle, with a confidence level of 95%, statistical errors of power density in more than 95% of the regions should be less than 1%. To meet the requirement of the principle, the uniform fission site (UFS) method is raised currently. UFS aims at redistributing fission sources to uniformize the fission source sampling, which can make statistical variance distribution more uniform. This method, which is easy to use, will not obviously increase computation time. Many studies show that UFS has a good variance reduction effect in Monte Carlo criticality calculation, but less attention is paid to its performance in burnup calculation and thermal-hydraulic coupled calculation. Uncertainty arising from the Monte Carlo method has a large impact on burnup calculation and thermal-hydraulic coupled calculation. Variance propagates between burnup steps and between iterative steps of coupled calculation, which causes asymmetry of results of the physical symmetrical regions and instability of coupled iterative convergence errors. To further verify the effect of UFS, this study uses it in the RMC (the Reactor Monte Carlo code) burnup calculation module and the neutronics/thermohydraulics coupled calculation module, and conducts two-dimensional pressurized water reactor burnup calculation and BEAVRS benchmark thermalhydraulic coupled calculation. In this way, it verifies the improvement effect of UFS on variance propagation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

CHARACTERIZING THE SHARDS OF DISRUPTED MILKY WAY SATELLITES WITH LAMOST

We derive the fraction of substructure in the Galactic halo using a sample of over 10,000 spectroscopically confirmed halo giant stars from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) spectroscopic survey. By observing 100 synthetic models along each line of sight with the LAMOST selection function in that sky area, we statistically characterize the expected halo populations. We define as Stellar Halo Accretion Related Debris Structures (SHARDS) any stars in >3σ excesses above the model predictions. We find that at least 10% of the Milky Way (MW) halo stars from LAMOST are part of SHARDS. By running our algorithm on smooth halos observed with the LAMOST selection function, we show that the LAMOST data contain excess substructure over all Galactocentric radii R{sub GC}<40 kpc, beyond what is expected due to statistical fluctuations and incomplete sampling of a smooth halo. The level of substructure is consistent with the fraction of stars in SHARDS in model halos created entirely from accreted satellites. This work illustrates the potential of vast spectroscopic surveys with high filling factors over large sky areas to recreate the merging history of the MW.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Investigation of the thermal decomposition of Pu(IV) oxalate: a transmission electron microscopy study

The degradation of the internal structure of plutonium (IV) oxalate during calcination was investigated with Transmission Electron Microscopy (TEM), electron diffraction, Electron Energy-Loss Spectroscopy (EELS), and 4D Scanning TEM (STEM). TEM lift-outs were prepared from samples that had been calcined at 300°C, 450°C, 650°C and 950°C. The resulting phase at all calcination temperatures was identified as PuO 2 with electron diffraction. The grain size range was obtained with high-resolution TEM. In addition, 4D STEM images were analyzed to provide grain size distributions. In the 300°C calcined sample, the grains were <10 nm in diameter, at 650°C, the grains ranged from 10 to 20 nm, and by 950°C, the grains were 95–175 nm across. Using the Kolmogorov-Smirnov (K-S) two sample test, it was shown that morphological measurements obtained from 4D-STEM provided statistically significant distributions to distinguish samples at the different calcination conditions. Using STEM-EELS, carbon was shown to be present in the low temperature calcined samples associated with oxalate but had formed carbon (possibly graphite) deposits in the 950°C calcined sample. This work highlights the new methods of STEM-EELS and 4D-STEM for studying the internal structure of special nuclear materials (SNM).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2014

The 60 Month All-Sky Burst Alert Telescope Survey of Active Galactic Nucleus and the Anisotropy of Nearby AGNs

Surveys above 10 keV represent one of the best resources to provide an unbiased census of the population of active galactic nuclei (AGNs). We present the results of 60 months of observation of the hard X-ray sky with Swift/Burst Alert Telescope (BAT). In this time frame, BAT-detected (in the 15-55 keV band) 720 sources in an all-sky survey of which 428 are associated with AGNs, most of which are nearby. Our sample has negligible incompleteness and statistics a factor of approx. 2 larger over similarly complete sets of AGNs. Our sample contains (at least) 15 bona fide Compton-thick AGNs and 3 likely candidates. Compton-thick AGNs represent approx. 5% of AGN samples detected above 15 keV. We use the BAT data set to refine the determination of the log N-log S of AGNs which is extremely important, now that NuSTAR prepares for launch, toward assessing the AGN contribution to the cosmic X-ray background. We show that the log N-log S of AGNs selected above 10 keV is now established to approx. 10% precision. We derive the luminosity function of Compton-thick AGNs and measure a space density of 7.9(+4.1/−2.9)× 10(exp −5)/cubic Mpc for objects with a de-absorbed luminosity larger than 2 × 10(exp 42) erg / s. As the BAT AGNs are all mostly local, they allow us to investigate the spatial distribution of AGNs in the nearby universe regardless of absorption. We find concentrations of AGNs that coincide spatially with the largest congregations of matter in the local (much < 85 Mpc) universe. There is some evidence that the fraction of Seyfert 2 objects is larger than average in the direction of these dense regions..

SURVEY↗
DOE OSTI2022

Towards the Accurate Thermodynamic Characterization of Enzyme Reaction Mechanisms

We employed QM/MM molecular dynamics (MD) simulations to characterize the rate-limiting step of the glycosylation reaction of pancreatic α-amylase with combined DFT/molecular dynamics methods (PBE/def2-SVP : AMBER). Upon careful choice of four starting active site conformations based on thorough reactivity criteria, Gibbs energy profiles were calculated with umbrella sampling simulations within a statistical convergence of 1 -2 kcal · mol -1 . Nevertheless, Gibbs activation barriers and reaction energies still varied from 11.0 to 16.8 kcal · mol -1 and -6.3 to +3.8 kcal · mol -1 depending on the starting conformations, showing that despite significant state-of-the-art QM/MM MD sampling (0.5 ns/profile) the result still depends on the starting structure. In conclusion, the results supported the one step dissociative mechanism of Asp197 glycosylation preceded by an acid-base reaction by the Glu233, which are qualitatively similar to those from multi-PES QM/MM studies, and thus support the use of the latter to determine enzyme reaction mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

How bad or good are the external forward shock afterglow models of gamma-ray bursts?

The external forward shock models have been the standard paradigm to interpret the broadband afterglow data of gamma-ray bursts (GRBs). One prediction of the models is that some afterglow temporal breaks at different energy bands should be achromatic; that is, the break times should be the same in different frequencies. Multiwavelength observations in the Swift era have revealed chromatic afterglow behaviors at least in some GRBs, casting doubts on the external forward shock origin of GRB afterglows. In this paper, using a large sample of GRBs with both X-ray and optical afterglow data, we perform a systematic study to address the question: how bad or good are the external forward shock models? Our sample includes 85 GRBs up to 2014 March with well-monitored X-ray and optical light curves. Based on how well the data abide by the external forward shock models, we categorize them into five grades and three samples. The first two grades (Grade I and II) include 45 of 85 GRBs. They show evidence of, or are consistent with having, an achromatic break. The temporal and spectral behaviors in each afterglow segment are consistent with the predictions (the “closure relations”) of the forward shock models. These GRBs are included in the Gold sample. The next two grades (Grade III and IV) include 37 of 85 GRBs. They are also consistent with having an achromatic break, even though one or more afterglow segments do not comply with the closure relations. These GRBs are included in the Silver sample. Finally, Grade V (3/85) shows direct evidence of chromatic behaviors, suggesting that the external shock models are inconsistent with the data. These are included in the Bad sample. We further perform statistical analyses of various observational properties (temporal index α, spectral index β, break time t{sub b}) and model parameters (energy injection index q, electron spectral index p, jet opening angle θ{sub j}, radiative efficiency η{sub γ}, and so on) of the GRBs in the Gold sample, and derive constraints on the magnetization parameter ϵ{sub B} in the forward shock. Overall, we conclude that the simplest external forward shock models can account for the multiwavelength afterglow data of at least half of the GRBs. When more advanced modeling (e.g., long-lasting reverse shock, structured jets, arbitrary circumburst medium density profile) is invoked, up to >90% of the afterglows may be interpreted within the framework of the external shock models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Probabilistic Multi-Hazard Performance Assessment of Concrete Structures in Nuclear Installations

Concrete structures in nuclear installations are subject to time-dependent degradation mechanisms that can deteriorate their physical and mechanical properties, potentially exacerbating the risk of structural failure under external forces such as a seismic event. Previous research has extensively investigated the seismic response of nuclear concrete structures and the associated risk, as well as their effect on structural components safety margins. However, substantial work is still necessary to incorporate concrete aging effects into such evaluations. In fact, most models in the literature assume pristine concrete conditions and do not account for the impact of aging on the structural components’ fragility curves. This work identifies relevant time-dependent degradation mechanisms and provides simplified models to predict the the evolution of key material properties based on data from the literature. Namely, this work focuses on the aging effects of corrosion, alkali–silica reaction (ASR), and irradiation on reinforced concrete within US Department of Energy (DOE) nuclear facilities and nuclear power plants (NPP) structures. Furthermore, degradation models based on literature data are presented that define the relationship between probabilistic material properties and the concrete’s age. In this work, sampled material properties served as input for a simplified finite element model (FEM) of a critical nuclear structural system, with the output of the FEM being the seismic response for a given ground motion. The results of the FEM were then used within a probabilistic performance assessment with a statistically significant number of samples. The research presented herein addresses the detrimental effects of hazards caused by natural phenomena on deteriorated concrete elements of nuclear installations. This work directly benefits the safety analysis performed on US DOE/ National Nuclear Security Administration (NNSA) nuclear facilities located in areas prone to seismic activity. The results presented herein could aid in the improvement of DOE-STD-1020, the DOE Standard that addresses seismic risk analysis and capacity evaluation in DOE facilities. DOE-STD-1020 refers to the requirements in American Society of Civil Engineers (ASCE) 4-98, now superseded by ASCE 4-16, that shall be met in performing dynamic response analyses and generating in-structure response spectra, provided that such requirements are consistent with the requirements of ASCE/Structural Engineering Institute (SEI) 43-05. Moreover, the results presented herein could also aid in the updating of section C3.1.1. of ASCE 4-16 to account for the effects of aging on the stiffness of reinforced elements and American Concrete Institute (ACI) 349.3R-18, “Report on Evaluation and Repair of Existing Nuclear Safety-Related Concrete Structures.” Ultimately, this work can assist the risk assessment of potential lifetime extension of the existing US commercial nuclear fleet (light water reactors) and the safety analysis of the emerging advanced nuclear reactors. The proposed proof-of-concept methodology employs open-source DOE computational tools and is transferable to commercial software commonly used by engineering firms.

42 ENGINEERING↗
DOE OSTI2016

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Double-probe measurements from BOSS galaxy clustering and Planck data – towards an analysis without informative priors

Here, we develop a new methodology called double-probe analysis with the aim of minimizing informative priors in the estimation of cosmological parameters. We extract the dark-energy-model-independent cosmological constraints from the joint data sets of Baryon Oscillation Spectroscopic Survey (BOSS) galaxy sample and Planck cosmic microwave background (CMB) measurement. We measure the mean values and covariance matrix of {R, l a , Ω b h 2 , n s , log(A s ), Ω k , H(z), D A (z), f(z)σ 8 (z)}, which give an efficient summary of Planck data and 2-point statistics from BOSS galaxy sample, where R = √Ω m H 2 0 , and l a = πr(z * )/r s (z * ), z * is the redshift at the last scattering surface, and r(z * ) and r s (z * ) denote our comoving distance to z * and sound horizon at z * respectively. The advantage of this method is that we do not need to put informative priors on the cosmological parameters that galaxy clustering is not able to constrain well, i.e. Ω b h 2 and n s . Using our double-probe results, we obtain Ω m = 0.304 ± 0.009, H 0 = 68.2 ± 0.7, and σ 8 = 0.806 ± 0.014 assuming ΛCDM; and Ω k = 0.002 ± 0.003 and w = –1.00 ± 0.07 assuming owCDM. The results show no tension with the flat ΛCDM cosmological paradigm. By comparing with the full-likelihood analyses with fixed dark energy models, we demonstrate that the double-probe method provides robust cosmological parameter constraints which can be conveniently used to study dark energy models. We extend our study to measure the sum of neutrino mass and obtain Σm ν < 0.10/0.22 (68%/95%) assuming ΛCDM and Σm ν < 0.26/0.52 (68%/95%) assuming wCDM. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Radio properties of optically selected quasars

Approximately one-quarter (256 objects) of the Large Bright Quasar Survey (LBQS) has been observed with the VLA at 8.4 GHz, resulting in 44 detections (17%) with a median 3 sigma noise limit of 0.29 mJy. Quasars with radio luminosity detectable at this limit are underrepresented at faint absolute blue magnitudes (M(sub B) greater than or equal to -24), an effect which cannot be explained by a potential LBQS selection bias against quasars which have large radio luminosities and small optical luminosities. The radio-loud (8 GHz luminosity greater than 10(exp 25) W/Hz) fraction is observed to change as a function of redshift and M(sub B), for M(sub B) less than -24, although the causal variable is ambiguous. The description most consistent with the available data is that radio-loud fraction is approximately constant over the range -27.5 less than or equal to M(sub B) less than or equal to -24 and increases at brighter absolute magnitudes. The radio-loud fraction as a function of redshift reaches a local maximum at z approximately equal to 1, and, aside from the effects of icreased radio-loud fraction at bright M(sub B), remains roughly constant to redshifts approaching 5. The log R(sub 8.4) distribution (radio-to-optical luminosity ratio) of the current LBQS sample may be bimodal, but the results of statistical tests are ambiguous, requiring a larger sample size to become definite.

Hooper, Eric J.↗
DOE OSTI2016

SU-F-T-327: Total Body Irradiation In-Vivo Dose Measurements Using Optically Stimulated Luminescence (OSL) NanoDots and Farmer Type Ion Chamber

Purpose: This study was performed to analyze the agreement between optically stimulated luminescence (OSL) nanoDots measured doses and 0.6 cc Farmer type ionization chamber measured doses during total body irradiation (TBI). Methods: In-vivo dose measurements using OSL nanoDots and Farmer chamber were done in a total of twelve patients who received TBI at our center by bilateral parallel-opposed beams technique. In this technique, the patient is kept inside the TBI box which is filled with rice bags and irradiated using two bilateral parallel opposed beams of 40×40 cm{sup 2} size with 45° collimator rotation at an SSD of 333.5 cm in an Elekta Synergy linear accelerator. All patients received a dose of 2 Gy in single fraction as conditioning regimen. The beams were equally weighted at the midplane of the box. The nanoDots were placed over forehead, right and left neck, right and left lung, umbilicus, right and left abdomen, medial part of thigh, knee and toe. A 0.6 cc Farmer chamber was placed in between the thighs of the patient. Measured doses are reported along with the statistical comparisons using paired sample t-test. Results: For the above sites the mean doses were 212.2±21.1, 218.2±7.6, 218.7±9.3, 215.6±9.5, 217.5±11.5, 214.5±7.7, 218.3±6.8, 221.5±15, 229.1±11.0, 220.5±7.7 and 223.3±5.1 cGy respectively. For all OSL measurements the mean dose was 218.6±11.8 cGy. Farmer chamber measurements yielded a mean dose of 208.8±15.6 cGy. Statistical analysis revealed that there was no significant difference between OSL measured doses in forehead, right and left neck, right and left lung, umbilicus, right and left abdomen and toe and Farmer chamber measured doses (0.72≤p≤0.06). However the mean OSL doses at thigh and knee were statistically different (p<0.05) from the Farmer chamber measurements. Conclusion: OSL measurements were found to be in agreement with Farmer type ionization chamber measurements in in-vivo dosimetry of TBI.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Ranking and Selection of Populations on the Base of Sample Means

A number of directions is indicated in which for statistical problems of decision making related to ordering the parameters of distributions, it is expedient to lean on comparison of sample means. It is assumed that the corresponding parametric family has no nontrivial sufficient statistics. The key role is played by establishing conditions under which the reliability of inferences increases monotonically with increasing the sampling size. Examples of applications are given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗
DOE OSTI2021

Nearly hyperuniform, nonhyperuniform, and antihyperuniform density fluctuations in two-dimensional transition metal dichalcogenides with defects

Hyperuniform many-body systems in d-dimensional Euclidean space R d are characterized by completely suppressed (normalized) infinite-wavelength density fluctuations, and appear to be endowed with novel exotic physical properties. Recently, hyperuniform systems of disordered varieties have been observed in the context of various atomic-scale two-dimensional (2D) materials. Here, we analyze the effects of localized defects on the density fluctuations across length scales and on the hyperuniformity property of experimental samples of two-dimensional transition metal dichalcogenides. In particular, we extract atomic coordinates from time series annular dark field-scanning transmission electron microscopy (ADF-STEM) imaging data of 2D tungsten chalcogenides with the 2H structure (Te-doped 2H-WSe 2 ) showing continuous development and evolution of electron-beam induced defects, and construct the corresponding chemical-bonding informed coordination networks between the atoms. We then compute a variety of pair statistics and bond-orientational statistics to characterize the samples. At low defect concentrations, the corresponding materials are nearly hyperuniform, characterized by significantly suppressed scattering at the zero wave-number limit (omitting forward/ballistic scattering). As more defects are introduced, the (approximate) hyperuniformity of the materials is gradually destroyed, and the system becomes non-hyperuniform even when the material still contains a significant amount of crystalline regions. At high defect concentrations, the structures become antihyperuniform with diverging (normalized) large-scale density fluctuations, mimicking those typically observed at the thermal critical points associated with phase transitions. Overall, the defected materials possess varying degrees of orientation order, and there is apparently no intermediate hexatic phase emerging. To understand the observed nearly hyperuniform density fluctuations in the slightly defected materials, we construct a minimalist structural model and demonstrate that the experimental samples can be essentially viewed as perturbed honeycomb crystals with small correlated displacements and double chalcogen vacancies. Moreover, the small correlated displacements alone can significantly degrade hyperuniformity of the perfect honeycomb structure. Therefore, even a small amount of vacancies, when coupled with correlated displacements, can completely destroy hyperuniformity of the system.

77 NANOSCIENCE AND NANOTECHNOLOGY↗