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NASA NTRS1992

Mg II absorption in the spectra of 103 QSOs - Implications for the evolution of gas in high-redshift galaxies

Spectra of 103 low- and intermediate-redshift QSOs with a resolution of 4-6 A were obtained in order to investigate the statistics of the M II 2796, 2803 absorption systems over the redshift range of 0.2-2.2. New emission-line redshifts, based mostly on Mg II 2800 and semiforbidden 1909, were determined for the QSOs. The mean number density of Mg II absorbers per unit redshift range decreased from 0.97 +/-0.10 for a rest equivalent width threshold of 0.3 A to 0.27 +/-0.05 for a threshold of 1.0 A. The results are in agreement with comparable previous work. The observed equivalent width distribution could be fitted with either exponential or power-law analytic distributions, with parameters in line with those found in earlier studies. Statistical tests show that the Mg II absorbers are uniformly distributed in both comoving coordinates and velocity relative to the QSO.

Steidel, Charles C.↗

NASA NTRSDate not supplied

Space-borne Doppler Weather Radar Modeling for Radar Design Evaluation

A model has been developed to predict the reflectivity and Doppler performance of a spaceborne weather radar for atmospheric aerosol and cloud monitoring. The goal is to predict radar sensitivity, resolution, uncertainties and other key performance metrics vs. radar design parameters and hardware nonidealities. Analytical formulas are readily available to predict key performance metrics of a space-borne radar system as a function of design parameters such as antenna size, spacecraft velocity, transmit power, and receive noise figure. Effects of some system nonidealities such as antenna pointing errors, power amplifier nonlinearity and phase noise can be estimated using idealized methods. These analytical formulas use idealized forms of the antenna radiation pattern and weather statistics to predict system performance. However, it is desirable to have a more physical model based on discretized weather volumes in which the particle size distribution, Doppler distribution, and other parameters can be varied to study how the radar hardware design parameters and nonidealities affect the measurement of the weather reflectivity and Doppler characteristics. This would allow the radar designers to have more insight into what is being measured and the hardware parameters and errors that need to be carefully controlled to achieve best radar performance, as well as potential methods to calibrate the system or correct errors. This presentation will demonstrate some proof-of-concept Ka-band simulations where the discretized model agrees with the analytical formulas for a simple case where the elements in the discretized weather volume are defined by a constant reflectivity and simple velocity vectors. In particular, the system sensitivity and Doppler uncertainty are evaluated by analytical formulas as well as the discretized model. Future work will expand on this to include more complex weather scenarios and the addition of system nonidealities.

Sara Tucker↗

DOE OSTI2023

Analytical estimation of the signal to noise ratio efficiency in axion dark matter searches using a Savitzky-Golay filter

The signal to noise ratio efficiency ϵ SNR in axion dark matter searches has been estimated using large-statistic simulation data reflecting the background information and the expected axion signal power obtained from a real experiment. This usually requires a lot of computing time even with the assistance of powerful computing resources. Employing a Savitzky-Golay filter for background subtraction, in this work, we estimated a fully analytical ϵ SNR without relying on large-statistic simulation data, but only with an arbitrary axion mass and the relevant signal shape information. Hence, our work can provide ϵ SNR using minimal computing time and resources prior to the acquisition of experimental data, without the detailed information that has to be obtained from real experiments. Axion haloscope searches have been observing the coincidence that the frequency independent scale factor ξ is approximately consistent with the ϵ SNR . This was confirmed analytically in this work, when the window length of the Savitzky-Golay filter is reasonably wide enough, i.e., at least 5 times the signal window.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Variance Preserving Spectral Subsampling

Generating statistically faithful short-duration gamma-ray spectra from a single long measurement is essential in nuclear safeguards, supporting tasks such as algorithm development and machine-learning applications, especially when list-mode data are unavailable. Existing subsampling methods often distort the statistical characteristics of genuine short-duration measurements, leading to biased or unreliable analytical outcomes and thereby undermining downstream tasks. In this work, we compare five subsampling approaches using a benchmark set of 156 genuine replicate spectra collected with a high-purity germanium detector. We evaluate each method with respect to run-to-run variance, channel-to-channel variance, and preservation of total counts (losslessness). Across a wide range of subsampling ratios, only binomial subsampling without replacement consistently reproduces the statistical properties of genuine short-duration spectra, maintaining proper dispersion even in sparse spectral regions and perfectly preserving total counts. These results provide a mathematically principled and practically validated framework for generating synthetically shortened spectra when true short-duration measurements are unavailable.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2020

Formulation and solution approach for calibrating activity-based travel demand model-system via microsimulation

This study addresses the problem of calibrating utility-maximizing nested logit activity-based travel demand model-systems. After estimation, it is common practice to use aggregate measurements to calibrate the estimated model-system’s parameters prior to their application in transportation planning, policy making, and operations. However, calibration of activity-based model-systems has received much less attention. Existing calibration approaches are myopic heuristics in the sense that they do not consider the fundamental inter-dependencies among choice-models and do not have a systematic way to adjust model parameters. Also, other purely simulation-based approaches do not perform well in large-scale applications. In this study, we focus on utility-maximizing nested logit activity-based model-systems and calibrating aggregate statistics such as activity shares, mode shares, time-dependent & mode-specific OD flows, and time-dependent & mode-specific sensor counts. We formulate the calibration problem as a simulation-based optimization problem and propose a stochastic gradient-based solution procedure to solve it. The solution procedure relies on microsimulation to calculate expectations of the aggregate statistics of interest to the calibration problem. Additionally, we derive approximate analytical expressions for the gradient of the objective function —that are evaluated through microsimulation on mini-batches of the population. The proposed solution procedure is sensitive to the fundamental structure of the activity-based model-system and is non-myopic in considering the dependencies across its model components. The formulated optimization problem is non-convex, highly nonlinear, and potentially has multiple-minima. Lastly, we show —through a real-world application— that the proposed solution procedure outperforms other state-of-the-art purely simulation-based optimization approaches in terms of computational efficiency, stability, and convergence. We also compare various gradient-based solution algorithms to determine the best algorithm to update the parameters. This work has the potential to facilitate wider and easier application of activity-based model-systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A forward modeling approach to analyzing galaxy clustering with S IM BIG

We present cosmological constraints from a simulation-based inference (SBI) analysis of galaxy clustering from the SimBIG forward modeling framework. SimBIG leverages the predictive power of high-fidelity simulations and provides an inference framework that can extract cosmological information on small nonlinear scales. In this work, we apply SimBIG to the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS galaxy sample and analyze the power spectrum, P ℓ (k), to k max = 0.5 h/Mpc. We construct 20,000 simulated galaxy samples using our forward model, which is based on 2,000 high-resolution Quijote N -body simulations and includes detailed survey realism for a more complete treatment of observational systematics. We then conduct SBI by training normalizing flows using the simulated samples and infer the posterior distribution of ΛCDM cosmological parameters: Ω m , Ω b , h, n s , σ 8 . We derive significant constraints on Ω m and σ 8 , which are consistent with previous works. Our constraint on σ 8 is 27% more precise than standard P ℓ analyses because we exploit additional cosmological information on nonlinear scales beyond the limit of current analytic models, k > 0.25 h/Mpc. This improvement is equivalent to the statistical gain expected from a standard P ℓ analysis of galaxy sample ~ 60% larger than CMASS. While we focus on P ℓ in this work for validation and comparison to the literature, SimBIG provides a framework for analyzing galaxy clustering using any summary statistic. We expect further improvements on cosmological constraints from subsequent SimBIG analyses of summary statistics beyond P ℓ .

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Historic climate, cosmogenic 10Be, denudation-rate, and geospatial datasets from the Pikes Peak region, Colorado, USA

This data package contains geographic information system (GIS) layers and tabular datasets associated with the study of elevation-dependent denudation rates on Pikes Peak in the Front Range of the Rocky Mountains, Colorado, USA. The package includes GIS layers used to produce the study-area map, including sample locations, sample watershed boundaries, the Pikes Peak batholith, Pleistocene glacier extent, weather station locations, and elevation and hillshade rasters, together with comma-separated value (CSV) tables and matching CSV data dictionaries. These mapped layers provide the geographic framework for interpreting denudation patterns across the Pikes Peak region and for relating sample locations to watershed geometry, bedrock setting, glacial history, and nearby climate stations. The first group of tables reports climate and geospatial context for the study area. These files include station-based temperature and precipitation data used to characterize elevational gradients in mean annual climate and monthly climate seasonality, sample locations, denudation-rate and topographic metrics, fixed frost-cracking model parameters, frost-cracking intensity and precipitation-frequency metrics, and stream-power inversion results. Together, these data provide the basis for evaluating how denudation varies with elevation, climate, and landscape form across sampled catchments on Pikes Peak. The second group of tables reports cosmogenic nuclide and erosion-model results used in the denudation analysis. Included files contain accelerator mass spectrometry (AMS) measurements for in situ-produced cosmogenic beryllium-10 (10Be), including sample identifiers, measured 10Be:9Be ratios, analytical uncertainties, carrier mass, quartz mass, blank corrections, blank-group statistics, and calculated 10Be concentrations and uncertainties. Additional tables summarize stream-power-law inversion results for sampled catchments, including optimized model parameters, predicted erosion rates, residual metrics, channel-pixel counts, and convergence status, as well as regression equations and summary statistics used to evaluate relationships among elevation, climate, frost cracking, precipitation forcing, and denudation rate. The package contains GIS files, comma-separated value files (.csv), Microsoft Excel files (.xlsx), CSV data dictionaries, a file-level metadata table, and a readme text file.

10Be cosmogenic nuclides↗

DOE OSTI2021

Evaluating Offshore Infrastructure Integrity

Drilling in the offshore environment involves a complex network of infrastructure including pipelines, platforms, rigs, subsea installations, ports, and terminals. Government and industry partners have developed this network over many decades and it remains a critical part of the United States (U.S.) energy portfolio. Many of the major components of this system have been designed with a 20- to 30-year lifespan, yet consistent and growing energy demands support the need to extend the design life of existing infrastructure or repurpose it for secondary needs (i.e. enhanced oil recovery, carbon storage, and new wells). As a result, a growing portion of the offshore infrastructure in the U.S. is approaching or has exceeded its original design life. A critical step in ensuring the continued safe and effective operation of offshore infrastructure is developing a comprehensive understanding of the state of offshore infrastructure and the factors that effect it. The purpose of this project is to assess the current state of existing infrastructure and identify the factors involved in infrastructure degradation through the development and application of big data analytics, machine learning, and advanced spatio-temporal analysis. The project leverages existing data at NETL and combines it with new information on offshore oil and gas structures and the ambient offshore environment in an effort to identify patterns associated with infrastructure integrity. Building on the identified trends and patterns, this project incorporates exploratory analytics and spatial analysis tools in conjunction with machine learning and statistical models to characterize the condition of existing platforms in the offshore environment and predict their risk of failure.

02 PETROLEUM↗

DOE OSTI2022

Algebraic Bethe Circuits

The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method on the spin-$\frac{1}{2}$ XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run small-scale error mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models on 4 sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

Non-Gaussian approach for parametric random vibration of non-linear structures

The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

Ibrahim, R. A.↗

NASA NTRS1986

Pattern recognition characterizations of micromechanical and morphological materials states via analytical quantitative ultrasonics

One potential approach to the quantitative acquisition of discriminatory information that can isolate a single structural state is pattern recognition. The pattern recognition characterizations of micromechanical and morphological materials states via analytical quantiative ultrasonics are outlined. The concepts, terminology, and techniques of statistical pattern recognition are reviewed. Feature extraction and classification and states of the structure can be determined via a program of ultrasonic data generation.

Williams, J. H., Jr.↗

NASA NTRS1994

System engineering toolbox for design-oriented engineers

This system engineering toolbox is designed to provide tools and methodologies to the design-oriented systems engineer. A tool is defined as a set of procedures to accomplish a specific function. A methodology is defined as a collection of tools, rules, and postulates to accomplish a purpose. For each concept addressed in the toolbox, the following information is provided: (1) description, (2) application, (3) procedures, (4) examples, if practical, (5) advantages, (6) limitations, and (7) bibliography and/or references. The scope of the document includes concept development tools, system safety and reliability tools, design-related analytical tools, graphical data interpretation tools, a brief description of common statistical tools and methodologies, so-called total quality management tools, and trend analysis tools. Both relationship to project phase and primary functional usage of the tools are also delineated. The toolbox also includes a case study for illustrative purposes. Fifty-five tools are delineated in the text.

Goldberg, B. E.↗

DOE OSTI2022

Variable wildfire impacts on the seasonal water temperatures of western US streams: A retrospective study

Recent increases in the burn area and severity of wildfires in the western US have raised concerns about the impact on stream water temperature–a key determinant of cold-water fish habitats. However, the effect on seasonal water temperatures of concern, including winter and summer, are not fully understood. In this study, we assessed the impact of wildfire burns at Boulder Creek (Oregon), Elk Creek (Oregon), and Gibbon River (Wyoming) watersheds on the downstream winter and summer water temperatures for the first three post-fire years. To obtain results independent of the choice of the analytical method, we evaluated the consequence of each burn using three different statistical approaches that utilize local water temperature data. Our results from the three approaches indicated that the response of water temperatures to wildfire burns varied across seasons and sites. Wildfire burns were associated with a median increase of up to 0.56°C (Standard Error; S.E. < 0.23°C) in the summer mean water temperatures (MWT) and 62 degree-day Celsius (DDC; S.E. < 20.7 DDC) in the summer accumulated degree days (ADD) for the three subsequent years across studied stream sites. Interestingly, these burns also corresponded to a median decrease of up to 0.49°C (S.E. < 0.45°C) in the winter MWT and 39 DDC (S.E. < 40.5 DDC) in the winter ADD for the same period across sites. Wildfire effects on the downstream water temperatures diminished with increasing site distance from the burn perimeter. Our analyses demonstrated that analytical methods that utilize local watershed data could be applied to evaluate fire effects on downstream water temperatures.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1987

A computer program for model verification of dynamic systems

Dynamic model verification is the process whereby an analytical model of a dynamic system is compared with experimental data, and then qualified for future use in predicting system response in a different dynamic environment. There are various ways to conduct model verification. The approach adopted in MOVER II employs Bayesian statistical parameter estimation. Unlike curve fitting whose objective is to minimize the difference between some analytical function and a given quantity of test data (or curve), Bayesian estimation attempts also to minimize the difference between the parameter values of that function (the model) and their initial estimates, in a least squares sense. The objectives of dynamic model verification, therefore, are to produce a model which: (1) is in agreement with test data, (2) will assist in the interpretation of test data, (3) can be used to help verify a design, (4) will reliably predict performance, and (5) in the case of space structures, facilitate dynamic control.

Chrostowski, J. D.↗

DOE OSTI2022

Covariance matrices for variance-suppressed simulations

ABSTRACT Cosmological N-body simulations provide numerical predictions of the structure of the Universe against which to compare data from ongoing and future surveys, but the growing volume of the Universe mapped by surveys requires correspondingly lower statistical uncertainties in simulations, usually achieved by increasing simulation sizes at the expense of computational power. It was recently proposed to reduce simulation variance without incurring additional computational costs by adopting fixed-amplitude initial conditions. This method has been demonstrated not to introduce bias in various statistics, including the two-point statistics of galaxy samples typically used for extracting cosmological parameters from galaxy redshift survey data, but requires us to revisit current methods for estimating covariance matrices of clustering statistics for simulations. In this work, we find that it is not trivial to construct covariance matrices analytically for fixed-amplitude simulations, but we demonstrate that ezmock (Effective Zel’dovich approximation mock catalogue), the most efficient method for constructing mock catalogues with accurate two- and three-point statistics, provides reasonable covariance matrix estimates for such simulations. We further examine how the variance suppression obtained by amplitude-fixing depends on three-point clustering, small-scale clustering, and galaxy bias, and propose intuitive explanations for the effects we observe based on the ezmock bias model.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1999

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Williams Colin P.↗

DOE OSTI2022

On reading Youden: Learning about the practice of statistics and applied statistical research from a master applied statistician

From reading William John “Jack” Youden’s books and articles, Youden (1900-1971), an analytical chemist, becomes an applied statistician by the time he joins the National Bureau of Standards (NBS) in 1948. Here, this article traces his transition from chemist to applied statistician and what his body of work mostly at NBS (1948-1965) demonstrates about his practice of statistics and the role that applied statistical research plays in it. There is much we can learn from a master applied statistician.

42 ENGINEERING↗

DOE OSTI2022

Pyomo.DOE: An open-source package for model-based design of experiments in Python

Predictive mathematical models are a cornerstone of science and engineering. Yet selecting, calibrating, and validating said science-based models often remains an art in practice. Model-based design of experiments (MBDoE) provides a systematic framework to maximize information gain from experiments while minimizing time and resource costs. But MBDoE remains limited to niche application areas, in part because practitioners must integrate expertise in statistics, computational optimization, and modeling. To help reduce this barrier, we introduce Pyomo.DOE, an open-source package for MBDoE. Pyomo.DOE uses a nonlinear sensitivity analysis code k_aug to quickly approximate the Fisher information matrix and leverages a new stochastic programming abstraction. We demonstrate Pyomo.DOE with the first application of MBDoE to fixed-bed breakthrough experiments, which highlights the power of Pyomo.DOE to quantify the value of experimental modifications a priori for large-scale partial differential-algebraic equation (PDAE) models. Here we also provide a mathematical primer on MBDoE targeted at general chemical engineers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗