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The Statistical Consulting Center for Astronomy (SCCA)

The process by which raw astronomical data acquisition is transformed into scientifically meaningful results and interpretation typically involves many statistical steps. Traditional astronomy limits itself to a narrow range of old and familiar statistical methods: means and standard deviations; least-squares methods like chi(sup 2) minimization; and simple nonparametric procedures such as the Kolmogorov-Smirnov tests. These tools are often inadequate for the complex problems and datasets under investigations, and recent years have witnessed an increased usage of maximum-likelihood, survival analysis, multivariate analysis, wavelet and advanced time-series methods. The Statistical Consulting Center for Astronomy (SCCA) assisted astronomers with the use of sophisticated tools, and to match these tools with specific problems. The SCCA operated with two professors of statistics and a professor of astronomy working together. Questions were received by e-mail, and were discussed in detail with the questioner. Summaries of those questions and answers leading to new approaches were posted on the Web (www.state.psu.edu/ mga/SCCA). In addition to serving individual astronomers, the SCCA established a Web site for general use that provides hypertext links to selected on-line public-domain statistical software and services. The StatCodes site (www.astro.psu.edu/statcodes) provides over 200 links in the areas of: Bayesian statistics; censored and truncated data; correlation and regression, density estimation and smoothing, general statistics packages and information; image analysis; interactive Web tools; multivariate analysis; multivariate clustering and classification; nonparametric analysis; software written by astronomers; spatial statistics; statistical distributions; time series analysis; and visualization tools. StatCodes has received a remarkable high and constant hit rate of 250 hits/week (over 10,000/year) since its inception in mid-1997. It is of interest to scientists both within and outside of astronomy. The most popular sections are multivariate techniques, image analysis, and time series analysis. Hundreds of copies of the ASURV, SLOPES and CENS-TAU codes developed by SCCA scientists were also downloaded from the StatCodes site. In addition to formal SCCA duties, SCCA scientists continued a variety of related activities in astrostatistics, including refereeing of statistically oriented papers submitted to the Astrophysical Journal, talks in meetings including Feigelson's talk to science journalists entitled "The reemergence of astrostatistics" at the American Association for the Advancement of Science meeting, and published papers of astrostatistical content.

Akritas, Michael↗

On the spatial distribution of magnetic fields on the solar surface

Recent measurements of solar surface magnetic fields suggest that the spatial distribution of these fields is fractal. In order to understand the physical basis for such geometric complexity, we study here the advection of magnetic flux tubes relatively simple random motions on the surface of a fluid and investigate the spatial statistics of the resulting surface field. While this study does not directly address the question of why solar surface fields have the observed spatial structure, it is designed to build our intuition about how surface flows lead to complex spatial structuring of magnetic fields. As part of our study, we discuss the various methods by which one can describe the spatial distribution of the surface magnetic flux and relate them mathematically; this turns out to be a crucial point of our work since, as we show, a number of previous analyses have misinterpreted the analysis procedures for determining fractal dimensions. Our principal result is the explicit demonstration that simple random flows lead to magnetic flux spatial distributions with a multifractal dimension spectrum. Furthermore, we demonstrate that this magnetic spatial structure is generic, i.e., is characteristic of a very large class of random flows.

Tao, L.↗

Physics-informed semantic inpainting: Application to geostatistical modeling

A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics. Semantic inpainting, a technique for image processing using deep generative models, has been recently applied for this purpose, demonstrating its effectiveness in dealing with complex spatial patterns. However, the original semantic inpainting framework incorporates only information from direct measurements, while in geostatistics indirect measurements are often plentiful. In this work, to overcome this limitation, we propose a physics-informed semantic inpainting framework, employing the Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) and jointly incorporating the direct and indirect measurements by exploiting the underlying physical laws. Our simulation results for a high-dimensional problem with 512 dimensions show that in the new method, the physical conservation laws are satisfied and contribute in enhancing the inpainting performance compared to using only the direct measurements.

54 ENVIRONMENTAL SCIENCES↗

Plasma Distribution in Mercury's Magnetosphere Derived from MESSENGER Magnetometer and Fast Imaging Plasma Spectrometer Observations

We assess the statistical spatial distribution of plasma in Mercury's magnetosphere from observations of magnetic pressure deficits and plasma characteristics by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft. The statistical distributions of proton flux and pressure were derived from 10months of Fast Imaging Plasma Spectrometer (FIPS) observations obtained during the orbital phase of the MESSENGER mission. The Magnetometer-derived pressure distributions compare favorably with those deduced from the FIPS observations at locations where depressions in the magnetic field associated with the presence of enhanced plasma pressures are discernible in the Magnetometer data. The magnitudes of the magnetic pressure deficit and the plasma pressure agree on average, although the two measures of plasma pressure may deviate for individual events by as much as a factor of approximately 3. The FIPS distributions provide better statistics in regions where the plasma is more tenuous and reveal an enhanced plasma population near the magnetopause flanks resulting from direct entry of magnetosheath plasma into the low-latitude boundary layer of the magnetosphere. The plasma observations also exhibit a pronounced north-south asymmetry on the nightside, with markedly lower fluxes at low altitudes in the northern hemisphere than at higher altitudes in the south on the same field line. This asymmetry is consistent with particle loss to the southern hemisphere surface during bounce motion in Mercury's offset dipole magnetic field.

magnetic↗

Downscaling MODIS Land Surface Temperature for Urban Public Health Applications

This study is part of a project funded by the NASA Applied Sciences Public Health Program, which focuses on Earth science applications of remote sensing data for enhancing public health decision-making. Heat related death is currently the number one weather-related killer in the United States. Mortality from these events is expected to increase as a function of climate change. This activity sought to augment current Heat Watch/Warning Systems (HWWS) with NASA remotely sensed data, and models used in conjunction with socioeconomic and heatrelated mortality data. The current HWWS do not take into account intra-urban spatial variation in risk assessment. The purpose of this effort is to evaluate a potential method to improve spatial delineation of risk from extreme heat events in urban environments by integrating sociodemographic risk factors with estimates of land surface temperature (LST) derived from thermal remote sensing data. In order to further improve the consideration of intra-urban variations in risk from extreme heat, we also developed and evaluated a number of spatial statistical techniques for downscaling the 1-km daily MODerate-resolution Imaging Spectroradiometer (MODIS) LST data to 60 m using Landsat-derived LST data, which have finer spatial but coarser temporal resolution than MODIS. In this paper, we will present these techniques, which have been demonstrated and validated for Phoenix, AZ using data from the summers of 2000-2006.

Al-Hamdan, Mohammad↗

Downscaling MODIS Land Surface Temperature for Urban Public Health Applications

This study is part of a project funded by the NASA Applied Sciences Public Health Program, which focuses on Earth science applications of remote sensing data for enhancing public health decision-making. Heat related death is currently the number one weather-related killer in the United States. Mortality from these events is expected to increase as a function of climate change. This activity sought to augment current Heat Watch/Warning Systems (HWWS) with NASA remotely sensed data, and models used in conjunction with socioeconomic and heatrelated mortality data. The current HWWS do not take into account intra-urban spatial variation in risk assessment. The purpose of this effort is to evaluate a potential method to improve spatial delineation of risk from extreme heat events in urban environments by integrating sociodemographic risk factors with estimates of land surface temperature (LST) derived from thermal remote sensing data. In order to further improve the consideration of intra-urban variations in risk from extreme heat, we also developed and evaluated a number of spatial statistical techniques for downscaling the 1-km daily MODerate-resolution Imaging Spectroradiometer (MODIS) LST data to 60 m using Landsat-derived LST data, which have finer spatial but coarser temporal resolution than MODIS. In this paper, we will present these techniques, which have been demonstrated and validated for Phoenix, AZ using data from the summers of 2000-2006.

Al-Hamdan, Mohammad↗

Single molecule insights into interfacial molecular recognition for model electrochemical DNA biosensors

Electrochemical sensors that use surface-immobilized DNA to bind analytes and transduce the binding into electrochemical signals, have the potential for rapid, specific, and sensitive detection of bioanalytes via a compact and portable platform. However, accessing the structure of these surfaces/interfaces at the relevant spatial scale (< 10 nm), which determines the interfacial interactions and ultimately sensing performance, remains an unsolved challenge. Here, we review studies that have used high resolution atomic force microscope imaging and spatial statistical analysis tools to understand crowding interactions between thiolated DNA probes immobilized on gold electrodes and how such interactions impact target binding. We also review related studies that attempt to control the nanoscale spatial arrangement of the immobilized recognition elements to optimize sensing performance. Furthermore, these efforts have led to new advances in understanding of the structure-function relationships of DNA-based electrochemical biosensors to move the field toward rational engineering of these biosensing interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

U.S. Offshore Pipeline and Reported Incident Datasets

The U.S. Offshore Pipeline and Reported Incident Datasets provide a compilation of data from a variety of credible resources, spatially-temporally integrated into multivariate resources. This spatial resource includes more than 80,000 points along existing and abandoned pipelines in the Gulf with matched incidents based on similar lease blocks and temporal timelines (e.g., the incident date occurs within reported pipeline lifespan), structural characteristics, geologic and seafloor data, and meteorological, oceanographic, and biochemical statistics spatially and temporally matched to each point. This is provided as both a feature class in a file geodatabase, as well as a CSV file for ease of use. The pipeline incidents table is a CSV file containing more than 900 reported incidents from 1986 to 2021, including incident date, area (Outer Continental Shelf (OCS) lease block and area code), reported causes, reported incident information, and results (i.e., cost, repairs, inspections), along with quantitative severity metrics. Field dictionaries are included for both the pipeline locations and incidents datasets, which detail field definitions. The pipeline locations field dictionary includes original resource reference information.

Advanced Infrastructure Integrity Model↗

Ice tracking techniques, implementation, performance, and applications

Present techniques of ice tracking make use both of cross-correlation and of edge tracking, the former being more successful in heavy pack ice, the latter being critical for the broken ice of the pack margins. Algorithms must assume some constraints on the spatial variations of displacements to eliminate fliers, but must avoid introducing any errors into the spatial statistics of the measured displacement field. We draw our illustrations from the implementation of an automated tracking system for kinematic analyses of ERS-1 and JERS-1 SAR imagery at the University of Alaska - the Alaska SAR Facility's Geophysical Processor System. Analyses of the ice kinematic data that might have some general interest to analysts of cloud-derived wind fields are the spatial structure of the fields, and the evaluation and variability of average deformation and its invariants: divergence, vorticity and shear. Many problems in sea ice dynamics and mechanics can be addressed with the kinematic data from SAR.

Rothrock, D. A.↗

Estimating Ground-Level PM(sub 2.5) Concentrations in the Southeastern United States Using MAIAC AOD Retrievals and a Two-Stage Model

Previous studies showed that fine particulate matter (PM(sub 2.5), particles smaller than 2.5 micrometers in aerodynamic diameter) is associated with various health outcomes. Ground in situ measurements of PM(sub 2.5) concentrations are considered to be the gold standard, but are time-consuming and costly. Satellite-retrieved aerosol optical depth (AOD) products have the potential to supplement the ground monitoring networks to provide spatiotemporally-resolved PM(sub 2.5) exposure estimates. However, the coarse resolutions (e.g., 10 km) of the satellite AOD products used in previous studies make it very difficult to estimate urban-scale PM(sub 2.5) characteristics that are crucial to population-based PM(sub 2.5) health effects research. In this paper, a new aerosol product with 1 km spatial resolution derived by the Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm was examined using a two-stage spatial statistical model with meteorological fields (e.g., wind speed) and land use parameters (e.g., forest cover, road length, elevation, and point emissions) as ancillary variables to estimate daily mean PM(sub 2.5) concentrations. The study area is the southeastern U.S., and data for 2003 were collected from various sources. A cross validation approach was implemented for model validation. We obtained R(sup 2) of 0.83, mean prediction error (MPE) of 1.89 micrograms/cu m, and square root of the mean squared prediction errors (RMSPE) of 2.73 micrograms/cu m in model fitting, and R(sup 2) of 0.67, MPE of 2.54 micrograms/cu m, and RMSPE of 3.88 micrograms/cu m in cross validation. Both model fitting and cross validation indicate a good fit between the dependent variable and predictor variables. The results showed that 1 km spatial resolution MAIAC AOD can be used to estimate PM(sub 2.5) concentrations.

aerosol optical depth↗

Fitting Matérn smoothness parameters using automatic differentiation

The Mat$\acute{e}$rn covariance function is ubiquitous in the application of Gaussian processes to spatial statistics and beyond. Perhaps the most important reason for this is that the smoothness parameter $\nu$ gives complete control over the mean-square differentiability of the process, which has significant implications for the behavior of estimated quantities such as interpolants and forecasts. Unfortunately, derivatives of the Mat$\acute{e}$rn covariance function with respect to $\nu$ require derivatives of the modified second-kind Bessel function $K$ $\nu$ with respect to $\nu$. While closed form expressions of these derivatives do exist, they are prohibitively difficult and expensive to compute. For this reason, many software packages require fixing $\nu$ as opposed to estimating it, and all existing software packages that attempt to offer the functionality of estimating $\nu$ use finite difference estimates for $\partial$ $\nu$ $K$ $\nu$ . In this work, we introduce a new implementation of $K$$\nu$ that has been designed to provide derivatives via automatic differentiation (AD), and whose resulting derivatives are significantly faster and more accurate than those computed using finite differences. Here, we provide comprehensive testing for both speed and accuracy and show that our AD solution can be used to build accurate Hessian matrices for second-order maximum likelihood estimation in settings where Hessians built with finite difference approximations completely fail.

97 MATHEMATICS AND COMPUTING↗

Analysis of structure-property gradients in orthogonally machined chips and workpiece subsurface

Production of machined surfaces with optimized mechanical properties requires fundamental process-structure-property knowledge. In this paper, we focus on structure-property gradients in orthogonally cut OFHC Copper chips and the workpiece subsurface. We utilize orientation imaging microscopy and statistical spatial correlation metrics to quantify the microstructure. Constitutive elastic-plastic properties of the workpiece subsurface and chips are measured using spherical nanoindentation. Analysis of the data reveals significant structure and property gradients in both regions. Differences and similarities in structure and property gradients near the workpiece surface and tool-chip interface, and in the chip middle are discussed and explained.

42 ENGINEERING↗

Graph neural networks for efficient learning of mechanical properties of polycrystals

Herein we present graph neural networks (GNNs) as an efficient and accurate machine learning approach to predict mechanical properties of polycrystalline materials. Here, a GNN was developed based on graph representation of polycrystals incorporating only fundamental features of grains including their crystallographic orientation, size, and grain neighbor connectivity information. We tested our method on modeling stiffness and yield strength of α -Ti microstructures, varying in their crystallographic texture. We find the GNN predicts both properties with high accuracy with mean relative errors of ~1% for unseen microstructures from a given set of textures and < 2% for microstructures of unseen texture, even when presented with limited training data. This accuracy is comparable to methods that require high-resolution three-dimensional (3D) microstructure data, such as 3D convolutional neural networks (3D-CNNs) and models that depend on the computation of spatial statistics. The present results show that graph-based deep learning is a promising framework for property prediction, especially considering the high cost associated with obtaining high-resolution 3D microstructure data and the general scarcity of experimental materials datasets.

36 MATERIALS SCIENCE↗

Morphostatistical characterization of the spatial galaxy distribution through Gibbs point processes

ABSTRACT This paper proposes a morphostatistical characterization of the galaxy distribution through spatial statistical modelling based on inhomogeneous Gibbs point processes. The galaxy distribution is supposed to exhibit two components. The first one is related to the major geometrical features exhibited by the observed galaxy field, here, its corresponding filamentary pattern. The second one is related to the interactions exhibited by the galaxies. Gibbs point processes are statistical models able to integrate these two aspects in a probability density, controlled by some parameters. Several such models are fitted to real observational data via the ABC shadow algorithm. This algorithm provides simultaneous parameter estimation and posterior-based inference, hence allowing the derivation of the statistical significance of the obtained results.

79 ASTRONOMY AND ASTROPHYSICS↗

Scaled Vecchia Approximation for Fast Computer-Model Emulation

Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia’s ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction, and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.

97 MATHEMATICS AND COMPUTING↗

Data Summarization and Inference at Scale

This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.

97 MATHEMATICS AND COMPUTING↗

Data from: Understanding the biogeochemical and spatial drivers of methane and carbon dioxide fluxes in a large temperate reservoir

This dataset contains spatially resolved measurements of CO₂ and CH₄ fluxes and associated environmental variables collected across 200 sites in Douglas Reservoir (Tennessee, USA) between July 29-August 2, 2024. Measurements include diffusive fluxes of CO₂ and CH₄, CH₄ ebullition, and biogeochemical and spatial variables such as dissolved oxygen, temperature, conductivity, chlorophyll-a, pH, water depth, and distance from the dam. Sampling was conducted using a spatially balanced design to capture longitudinal and depth-related gradients throughout the reservoir. The dataset is structured to support analyses of spatial variability, flux pathway comparisons, and modeling approaches (e.g., spatial statistics and machine learning) aimed at understanding controls on reservoir CO₂ and CH₄ fluxes and improving upscaling to whole-reservoir and regional estimates.

Neeper, Jamie [ORNL] (ORCID:0009000842342101)↗