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DOE OSTI2025

Multiscale Physics of Atomic Nuclei from First Principles

Atomic nuclei exhibit multiple energy scales ranging from hundreds of MeV in binding energies to fractions of an MeV for low-lying collective excitations. As the limits of nuclear binding are approached near the neutron and proton drip lines, traditional shell structure starts to melt with an onset of deformation and an emergence of coexisting shapes. It is a long-standing challenge to describe this multiscale physics starting from nuclear forces with roots in quantum chromodynamics. Here, we achieve this within a unified and nonperturbative quantum many-body framework that captures both short- and long-range correlations starting from modern nucleon-nucleon and three-nucleon forces from chiral effective field theory. The short-range (dynamic) correlations which account for the bulk of the binding energy are included within a symmetry-breaking framework, while long-range (static) correlations (and fine details about the collective structure) are included by employing symmetry projection techniques. Our calculations accurately reproduce—within theoretical error bars—available experimental data for low-lying collective states and the electromagnetic quadrupole transitions in 20−30 Ne. In addition, we reveal coexisting spherical and deformed shapes in 30 Ne, which indicates the breakdown of the magic neutron number 𝑁 = 20 as the key nucleus 28 O is approached, and we predict that the drip line nuclei 32,34 Ne are strongly deformed and collective. By developing reduced-order models for symmetry-projected states, we perform a global sensitivity analysis and find that the subleading singlet 𝑆-wave contact and a pion-nucleon coupling strongly impact nuclear deformation in chiral effective field theory. The techniques developed in this work clarify how microscopic nuclear forces generate the multiscale physics of nuclei spanning collective phenomena as well as short-range correlations and allow one to capture emergent and dynamical phenomena in finite fermion systems such as atom clusters, molecules, and atomic nuclei.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2016

SU-G-BRB-06: Commissioning and Evaluation of EPID-Based in Vivo Dosimetry Software Using a Tissue-Maximum Ratio Approach

Purpose: To commission and evaluate an in vivo EPID-based transit dosimetry software (EPIgray, DOSIsoft, Cachan, France) using simple fields and TG119-based IMRT treatment plans. Methods: EPIgray was commissioned on a Truebeam based on finite tissue-maximum ratio (fTMR) measurements with solid water blocks of thicknesses between 0 and 37 cm. Field sizes varied from 2×2 to 20×20 cm{sup 2}. Subsequently, treatment plans of single and opposed beams with field sizes between 4×4 and 15×15 cm{sup 2} as well as IMRT plans were measured to evaluate the dose reconstruction accuracy. Single field dose predictions were made for anterior-posterior and lateral beams. IMRT plans were created based on TG119 recommendations. The reconstructed dose was compared to the planned dose for selected points at isocenter and away from isocenter. Results: For single square fields, the dose in EPIgray was reconstructed within 3% accuracy at isocenter relative to the planned dose. Similarly, the relative deviation of the total dose was accurately reconstructed within 3% for all IMRT plans with points placed inside a high dose region near the isocenter. Predictions became less accurate than 5% when the evaluation point was outside the majority of IMRT beam segments. Additionally, points 5 cm or more away from the isocenter or within an avoidance structure were predicted less reliably. Conclusion: EPIgray formalism accuracy is adequate for an efficient error detection system. It provides immediate intra-fractional feedback on the delivery of treatment plans without affecting the treatment beam. Besides the EPID, no additional hardware is required, which makes it accessible to all clinics. The software evaluates point dose measurements to verify treatment plan delivery and patient positioning within 5% accuracy, depending on the placement of evaluation points. EPIgray is not intended to replace patient-specific quality assurance but should be utilized as an additional layer of safety for continuous patient treatment verification. This research is supported by DOSIsoft.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Exploring Milkyway Halo Substructures with Large-Area Sky Surveys

Over the last two decades, our understanding of the Milky Way has been improved thanks to large data sets arising from large-area digital sky surveys. The stellar halo is now known to be inhabited by a variety of spatial and kinematic stellar substructures, including stellar streams and stellar clouds, all of which are predicted by hierarchical Lambda Cold Dark Matter models of galaxy formation. In this dissertation, we first present the analysis of spectroscopic observations of individual stars from the two candidate structures discovered using an M-giant catalog from the Two Micron All-Sky Survey. The follow-up observations show that one of the candidates is a genuine structure which might be associated with the Galactic Anticenter Stellar Structure, while the other one is a false detection due to the systematic photometric errors in the survey or dust extinction in low Galactic latitudes. We then presented the discovery of an excess of main sequence turn-off stars in the direction of the constellations of Eridanus and Phoenix from the first-year data of the Dark Energy Survey (DES) – a five-year, 5,000 deg2 optical imaging survey in the Southern Hemisphere. The Eridanus-Phoenix (EriPhe) overdensity is centered around l ~ 285° and b ~ -60° and the Poisson significance of the detection is at least 9σ. The EriPhe overdensity has a cloud-like morphology and the extent is at least ~ 4 kpc by ~ 3 kpc in projection, with a heliocentric distance of about d ~ 16 kpc. The EriPhe overdensity is morphologically similar to the previously-discovered Virgo overdensity and Hercules-Aquila cloud. These three overdensities lie along a polar plane separated by ~ 120° and may share a common origin. In addition to the scientific discoveries, we also present the work to improve the photometric calibration in DES using auxiliary calibration systems, since the photometric errors can cause false detection in first the halo substructure. We present a detailed description of the two auxiliary calibration systems built at Texas A&M University. We then discuss how the auxiliary systems in DES can be used to improve the photometric calibration of the systematic chromatic errors – source color-dependent systematic errors that are caused by variations in the wavelength dependence of the atmospheric transmission and the instrumental throughput.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Updating PV and Battery Bill Savings Calculations for Net Billing: New Best Practices for Input Data and Uncertainty

Jurisdictions are increasingly adopting compensation structures for distributed PV and PV-battery systems that price exported energy lower than energy consumed onsite (net billing rates). Standard methods for calculating the bill savings from PV and PV-battery systems were developed for net metering structures, and applying these same methods to net billing structures (such as using Typical Meteorological Year weather with actual year load) introduces bias errors that underestimate PV-battery system bill savings by between 1.5\% and 9\%, depending on the utility rate. We assess the magnitude of these errors and compare them to other sources of uncertainty when estimating the bill savings from PV and PV-battery systems under more complex utility rates.

14 SOLAR ENERGY↗

DOE OSTI2017

Why wind-farm developers should care about measuring atmospheric turbulence? [Chaos in the Air: Unraveling the Complex Relationship Between Wind Power and Atmospheric turbulence]

The role of atmospheric turbulence in influencing wind-turbine power production remains an unsolved mystery despite a growing number of researchers who have attempted to make sense of this issue. Turbulence, a term for short-term deviations around the average wind speed, can cause fluctuations in turbine power production and structural loads. While research strongly suggests that ignoring atmospheric turbulence can result in significant errors in power-curve measurements and annual energy production, it appears that there may be no universal relationship between turbulence and power production. Typically when we think of a wind farm operating in a turbulent atmosphere, we picture a waked turbine, battered by vortex eddies (circular wind flow) shed from turbine blades upwind. However, turbulence is present nearly everywhere, and is constantly produced and diminished over a wide range of temporal and spatial scales. This article aims to unravel some of the complex factors that remain unsolved regarding turbulence and wind power

17 WIND ENERGY↗

DOE OSTI2020

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Poisson-response Tensor-on-Tensor Regression and Applications

We introduce Poisson-response tensor-on-tensor regression (PToTR), a novel regression framework designed to handle tensor responses composed element-wise of random Poisson-distributed counts. Tensors, or multi-dimensional arrays, composed of counts are common data in fields such as inter national relations, social networks, epidemiology, and medical imaging, where events occur across multiple dimensions like time, location, and dyads. PToTR accommodates such tensor responses alongside tensor covariates, providing a versatile tool for multi dimensional data analysis. We propose algorithms for maximum likelihood estimation under a canonical polyadic (CP) structure on the regression coefficient tensor that satisfy the positivity of Poisson parameters and then provide an initial theoretical error analysis for PToTR estimators. We also demonstrate the utility of PToTR through three concrete applications: longitudinal data analysis of the Integrated Crisis Early Warning System database, positron emission tomography (PET) image reconstruction, and change-point detection of communication patterns in longitudinal dyadic data. These applications highlight the versatility of PToTR in addressing complex, structured count data across various domains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Can Large Language Models Understand Intermediate Representations?

Intermediate Representations (IRs) are essential in compiler design and program analysis, yet their comprehension by Large Language Models (LLMs) remains underexplored. This paper presents a pioneering empirical study to investigate the capabilities of LLMs, including GPT-4, GPT-3, Gemma 2, LLaMA 3.1, and Code Llama, in understanding IRs. We analyze their performance across four tasks: Control Flow Graph (CFG) reconstruction, decompilation, code summarization, and execution reasoning. Our results indicate that while LLMs demonstrate competence in parsing IR syntax and recognizing high-level structures, they struggle with control flow reasoning, execution semantics, and loop handling. Specifically, they often misinterpret branching instructions, omit critical IR operations, and rely on heuristic-based reasoning, leading to errors in CFG reconstruction, IR decompilation, and execution reasoning. The study underscores the necessity for IR-specific enhancements in LLMs, recommending fine-tuning on structured IR datasets and integration of explicit control flow models to augment their comprehension and handling of IR-related tasks.

Jiang, Hailong↗

DOE OSTI2023

Artificial Neural Network Models for Octane Number and Octane Sensitivity: A Quantitative Structure Property Relationship Approach to Fuel Design

Octane sensitivity (OS), defined as the research octane number (RON) minus the motor octane number (MON) of a fuel, has gained interest among researchers due to its effect on knocking conditions in internal combustion engines. Compounds with a high OS enable higher efficiencies, especially within advanced compression ignition engines. RON/MON must be experimentally tested to determine OS, requiring time, funding, and specialized equipment. Thus, predictive models trained with existing experimental data and molecular descriptors (via quantitative structure-property relationships (QSPRs)) would allow for the preemptive screening of compounds prior to performing these experiments. Here, the present work proposes two methods for predicting the OS of a given compound: using artificial neural networks (ANNs) trained with QSPR descriptors to predict RON and MON individually to compute OS (derived octane sensitivity (dOS)), and using ANNs trained with QSPR descriptors to directly predict OS. Twenty-five ANNs were trained for both RON and MON and their test sets achieved an overall 6.4% and 5.2% error, respectively. Twenty-five additional ANNs were trained for both dOS and OS; dOS calculations were found to have 15.3% error while predicting OS directly resulted in 9.9% error. A chemical analysis of the top QSPR descriptors for RON/MON and OS is conducted, highlighting desirable structural features for high-performing molecules and offering insight into the inner mathematical workings of ANNs; such chemical interpretations study the interconnections between structural features, descriptors, and fuel performance showing that connectivity, structural diversity, and atomic hybridization consistently drive fuel performance.

09 BIOMASS FUELS↗

DOE OSTI2018

Adaptive wavelet compression of large additive manufacturing experimental and simulation datasets

New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. Furthermore, these results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations.

42 ENGINEERING↗

DOE OSTI2017

Structural refinement of Pbnm-type perovskite films from analysis of half-order diffraction peaks

Engineering structural modifications of epitaxial perovskite thin films is an effective route to induce new functionalities or enhance existing properties due to the close relation of the electronic ground state to the local bonding environment. As such, there is a necessity to systematically refine and precisely quantify these structural displacements, particularly those of the oxygen octahedra, which is a challenge due to the weak scattering factor of oxygen and the small diffraction volume of thin films. In this paper, we present an optimized algorithm to refine the octahedral rotation angles using specific unit-cell-doubling half-order diffraction peaks for the a - a - c + Pbnm structure. The oxygen and A-site positions can be obtained by minimizing the squared-error between calculated and experimentally determined peak intensities using the (1/2 1/2 3/2) and (1/2 1/2 5/2) reflections to determine the rotation angle α about in-plane axes and the (1/2 5/2 1), (1/2 3/2 1), and (1/2 3/2 2) reflections to determine the rotation angle γ about the out-of-plane axis, whereas the convoluting A-site displacements associated with the octahedral rotation pattern can be determined using (1 1 1/2) and (1/2 1/2 1/2) reflections to independently determine A-site positions. The validity of the approach is confirmed by applying the refinement procedure to determine the A-site and oxygen displacements in a NdGaO 3 single crystal. Finally, the ability to refine both the oxygen and A-site displacements relative to the undistorted perovskite structure enables a deeper understanding of how structural modifications alter functionality properties in epitaxial films exhibiting this commonly occurring crystal structure.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Quantification and prediction of error in MIMO tests

Dynamic testing of systems is most realistic of real-world conditions when multiple input and multiple output (MIMO) techniques are used. To replicate measured environmental conditions, a series of desired outputs (responses) on the system must be realized by inverting the frequency response functions (FRF) matrix for input estimation. System identification is dependent on the number of inputs and outputs, which affect the type of solutions. In input estimation, the auto spectra of the determined inputs are affected by both the auto spectra and cross spectra of the desired outputs. This research evaluates errors and investigates two sources in an experimental setting. The first significant error source is test-to-test variability in FRFs from system identification tests, quantified by magnitude variability from long-duration tests. The second significant error source is the realization of time histories from frequency domain inputs. The spectral content of the realized random process deviates from the desired content and is also quantified. The structure is a linear three-story frame fixed at the base; two inputs are provided uniaxially with the use of suspended electrodynamic shakers. The proposed model for error sources was found to be effective in predicting errors in a SISO (single-input single-output) and a square (2-input 2-output) MIMO test.

Yousef, Odey↗

DOE OSTI2019

Rationalizing accurate structure prediction in the meta-GGA SCAN functional

The ability of first-principles computational methods to reproduce ground-state crystal structure selection is key to their application in the discovery of new materials, and yet presents a formidable challenge due to the low-energy scale of the problem and lack of systematic error cancellation. The recently developed Strongly Constrained and Appropriately Normed (SCAN) functional is notable for accurately calculating physical properties such as formation energies and in particular, correctly predicting ground-state structures. Here in this paper, we attempt to rationalize the improved structure prediction accuracy in SCAN by investigating the relationship between preferred coordination environments, the description of attractive van der Waals (vdW) interactions, and the overall ground-state prediction in bulk main-group solids. We observe a systematic undercoordination error in the traditional Perdew, Burke, and Ernzerhof (PBE) functional which is not present in SCAN results and find that semiempirical dispersion corrections in the form of PBE + D 3 fail to correct this error in a consistent or physical manner. We conclude that the medium-range vdW interaction is correctly parametrized in SCAN and yields meaningful relative energies between coordination environments.

36 MATERIALS SCIENCE↗

DOE OSTI2025

PDF Entity Annotation Tool (PEAT)

While different text mining approaches – including the use of Artificial Intelligence (AI) and other machine based methods - continue to expand at a rapid pace, the tools used by researchers to create the labeled datasets required for training, modeling, and evaluation remain rudimentary. Labeled datasets contain the target attributes the machine is going to learn; for example, training an algorithm to delineate between images of a car or truck would generally require a set of images with a quantitative description of the underlying features of each vehicle type. Development of labeled textual data that can be used to build natural language machine learning models for scientific literature is not currently integrated into existing manual workflows used by domain experts. Published literature is rich with important information, such as different types of embedded text, plots, and tables that can all be used as inputs to train ML/natural language processing (NLP) models, when extracted and prepared in machine readable formats. Currently, both normalized data extraction of use to domain experts and extraction to support development of ML/NLP models are labor intensive and cumbersome manual processes. Automatic extraction of data and information from formats such as PDFs that are optimized for layout and human readability, not machine readability. The PDF (Portable Document Format) Entity Annotation Tool (PEAT) was developed with the goal of allowing users to annotate publications within their current print format, while also allowing those annotations to be captured in a machine-readable format. One of the main issues with traditional annotation tools is that they require transforming the PDF into plain text to facilitate the annotation process. While doing so lessens the technical challenges of annotating data, the user loses all structure and provenance that was inherent in the underlying PDF. Also, textual data extraction from PDFs can be an error prone process. Challenges include identifying sequential blocks of text and a multitude of document formats (multiple columns, font encodings, etc.). As a result of these challenges, using existing tools for development of NLP/ML models directly from PDFs is difficult because the generated outputs are not interoperable. We created a system that allows annotations to be completed on the original PDF document structure, with no plain text extraction. The result is an application that allows for easier and more accurate annotations. In addition, by including a feature that grants the user the ability to easily create a schema, we have developed a system that can be used to annotate text for different domain-centric schemas of relevance to subject matter experts. Different knowledge domains require distinct schemas and annotation tags to support machine learning.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dynamic compressed sensing for real-time tomographic reconstruction

Electron tomography has achieved higher resolution and quality at reduced doses with recent advances in compressed sensing. Compressed sensing (CS) exploits the inherent sparse signal structure to efficiently reconstruct three-dimensional (3D) volumes at the nanoscale from undersampled measurements. However, the process bottlenecks 3D reconstruction with computation times that run from hours to days. Here we demonstrate a framework for dynamic compressed sensing that produces a 3D specimen structure that updates in real-time as new specimen projections are collected. Researchers can begin interpreting 3D specimens as data is collected to facilitate high-throughput and interactive analysis. Using scanning transmission electron microscopy (STEM), we show that dynamic compressed sensing accelerates the convergence speed by ~3-fold while also reducing its error by 27% for a Au/SrTiO 3 nanoparticle specimen. Before a tomography experiment is completed, the 3D tomogram has interpretable structure within ~33% of completion and fine details are visible as early as ~66%. Upon completion of an experiment, a high-fidelity 3D visualization is produced without further delay. Additionally, we report reconstruction parameters that tune data fidelity can be manipulated throughout the computation without re-running the entire process.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Computational investigation of the impact of metal–organic framework topology on hydrogen storage capacity

Metal–organic frameworks (MOFs) are promising, tunable materials for hydrogen storage. For application under cryogenic operating conditions, past work has run into a ceiling on performance due to a trade-off in the volumetric deliverable capacity (VDC) versus the gravimetric deliverable capacity (GDC). In this study, we computationally constructed and screened 105 230 MOF structures based on 529 nets to explore the effect of underlying topology on the hydrogen storage performance of the resulting materials. A machine learning model was developed based on simulated hydrogen uptake to facilitate screening of the entire dataset, and it successfully identified the top 10% of materials with a root-mean-square error of approximately 1 g L −1 as validated by subsequent grand canonical Monte Carlo simulations. We identified a promising structure based on the tsx topology that exhibits both VDC and GDC higher than the current benchmark material, MOF-5. Our data-driven analysis indicates that nets with higher net density yield MOFs with enhanced volumetric and gravimetric surface areas, thereby improving maximum VDC while shifting the capacity trade-off toward higher GDC.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Sparse Bayesian mass mapping with uncertainties: hypothesis testing of structure

ABSTRACT A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous ‘dark core’ – an overdense region with no optical counterpart – which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at $99{{\ \rm per\ cent}}$ confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

Price, M. A.↗

DOE OSTI2017

Parameter Estimation for Thurstone Choice Models

We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates the well-known choice models such as the Luce choice model for comparison sets of two or more items and the Bradley-Terry model for pair comparisons. We provide a tight characterization of the mean squared error of the maximum likelihood parameter estimator. We also provide similar characterizations for parameter estimators defined by a rank-breaking method, which amounts to deducing one or more pair comparisons from a comparison of two or more items, assuming independence of these pair comparisons, and maximizing a likelihood function derived under these assumptions. We also consider a related binary classification problem where each individual parameter takes value from a set of two possible values and the goal is to correctly classify all items within a prescribed classification error. The results of this paper shed light on how the parameter estimation accuracy depends on given Thurstone choice model and the structure of comparison sets. In particular, we found that for unbiased input comparison sets of a given cardinality, when in expectation each comparison set of given cardinality occurs the same number of times, for a broad class of Thurstone choice models, the mean squared error decreases with the cardinality of comparison sets, but only marginally according to a diminishing returns relation. On the other hand, we found that there exist Thurstone choice models for which the mean squared error of the maximum likelihood parameter estimator can decrease much faster with the cardinality of comparison sets. We report empirical evaluation of some claims and key parameters revealed by theory using both synthetic and real-world input data from some popular sport competitions and online labor platforms.

97 MATHEMATICS AND COMPUTING↗