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DOE OSTI2020

Monte Carlo Global QCD Analyses of the Pion Parton Distribution Functions

As the lightest hadron, the pion presents itself as a dichotomy. While being the pseudo Goldstone boson associated with chiral symmetry breaking, it is simultaneously regarded as the lightest pseudoscalar meson typically composed of constituent quark and antiquark. As the chiral symmetry shares the same global symmetry as QCD, studying the pion and its internal structure is key in understanding one of the four fundamental forces of nature, namely the quantum chromodynamic strong interaction. We study the pion's parton distribution functions (PDFs), which are universal quantities that describe the structure of the pion in terms of its constituent quarks, antiquarks, and gluons. Our goal is to discover what the available data reveal for these universal quantities, namely the PDFs. Through the use of factorization theorems and perturbative QCD, we use Monte Carlo (MC) methods to extract the PDFs from the available Drell-Yan (DY) and leading neutron (LN) data. While the DY process involves two hadrons colliding, the LN electroproduction involves an electron beam incident on a target nucleon. We can constrain well the pion PDFs at large momentum fraction using DY data, and at low momentum fraction using LN data. We also use threshold resummation in the DY process to gather predictable higher order terms associated with the soft gluon radiation because their contributions to the cross section are nontrivial. In this dissertation, we parametrize the pion PDFs and fit those parameters to the available data. We make use of Bayesian inference and use MC techniques to sample the parameter space. Three sets of results are presented. We first extract the pion PDFs by fitting the DY and LN data. Then, we include transverse momentum dependent DY data in conjunction with the DY and LN data to extract the pion PDFs. Finally, we apply various methods of threshold resummation to the DY cross section and extract pion PDFs. The pion PDFs presented here are the first global QCD analyses performed as well as the first MC extracted pion PDFs, which are at the forefront of the pion PDF community.

Barry, Patrick↗

DOE OSTI2024

Shape Optimization of Header Pipes in Power Plants for Enhanced Efficiency and Environmental Sustainability

In a power plant, the header pipe plays a pivotal role in optimizing the performance of diverse systems by serving as a central conduit for the collection and distribution of steam within the plant. This paper investigates the significance of header pipes within power plant setups, highlighting their critical influence on reliability, efficiency, and the performance of the power plant as a whole. The concept of shape optimization emerges as a crucial factor in power plant design and operation, with the potential to maximize performance while minimizing the use of materials. Shape optimization not only enhances efficiency but also contributes to reducing the environmental footprint of power plant installations. In this paper, we initially developed a methodology designed for optimizing header shapes with the primary goal of reducing the usage of costly new alloy materials and lowering the overall maintenance operation expenses. Secondly, we conducted a case study based on an authentic header sourced from an operational power plant.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2021

Distribution and speciation of Sb and toxic metal(loid)s near an antimony refinery and their effects on indigenous microorganisms

Although several studies have investigated the effects of Sb contamination on surrounding environments and indigenous microorganisms, little is known about the effect of co-contamination of Sb and toxic metal(loid)s. In this study, the occurrence of Sb and other toxic metal(loid)s near an operating Sb refinery and near-field landfill site were investigated. Topsoil samples near the refinery had high Sb levels (~3250 mg kg -1 ) but relatively low concentrations of other toxic metal(loid)s. However, several soil samples taken at greater depth from the near-field landfill site contained high concentrations of As and Pb, as well as extremely high Sb contents (~21,400 mg kg -1 ). X-ray absorption fine structure analysis showed that Sb in the soils from both sites was present as Sb(V) in the form of tripuhyite (FeSbO 4 ), a stable mineral. Three-dimensional principal coordinate analysis showed that microbial community compositions in samples with high toxic metal(loid)s concentrations were significantly different from other samples and had lower microbial populations (~10 4 MPN g -1 ). Sequential extraction results revealed that Sb is present primarily in the stable residual fraction (~99 %), suggesting low Sb bioavailability. Finally, however, microbial redundancy analysis suggested that the more easily extractable Pb might be the major factor controlling microbial community compositions at the site.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

DOE OSTI2026

District-Scale Analysis of Electricity Load and Strategies to Improve Energy Reliability Using Prototype District Models

Projected increases in electricity demand in the U.S. highlight the urgent need for effective load management to ensure grid reliability. As the building sector accounts for approximately 75% of electricity usage, enhancing energy efficiency and flexibility in this sector is crucial. Adopting district-level approaches offers significant advantages over traditional individual building analyses by enabling shared infrastructure and economies of scale. To navigate the data and computational challenges associated with modeling energy at the district level, prototype district models have been proposed as holistic, system-level solutions that capture complex interactions within typical configurations. This study presents these models as a reference tool for analyzing district-scale energy systems across various climate zones in the U.S. Developed with input from stakeholders, these models integrate varied building characteristics, inter-building connections, and energy system interactions. A case study utilizing the Urban Edge prototype district model, implemented on the URBANopt™ platform, evaluates multiple demand scenarios and the impact of distributed energy resources such as fuel-fired backup generators, photovoltaic systems, and batteries. Findings suggest that while new electric systems can significantly reduce annual energy use, they may also elevate peak electricity loads, with a notable 43% increase in heating-dominant climate zone 5B. The optimal backup power solutions vary based on location, influenced by factors such as utility rates and incentives. For example, PV and batteries perform well in high-cost regions like New York City, while diesel backup generators are more suitable for backup needs in climate zone 3A, such as Atlanta. Thus, this research highlights the importance of prototype district models for future district-scale energy planning.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Deformation of pores in response to uniaxial and hydrostatic stress cycling in Marcellus Shale: Implications for gas recovery

One of the main challenges during gas production from shale reservoirs is low recovery rate. One contributing factor to this outcome is an insufficient understanding of pore systems, especially pore behaviour following changes in reservoir conditions or resulting from gas production practices. Because the pressure in the producing well can be controlled, understanding the effects of pressure variation on the pore size distribution and methane trapping is necessary to help design optimal conditions to improve the gas recovery rate. This work is the first systematic study of sub-millimeter pore deformation in shale caused by uniaxial and hydrostatic stress up to 100 MPa. Overmature samples from the Middle Devonian Marcellus Shale were analyzed using neutron scattering (SANS and USANS) techniques to interpret the response of nanopores to stress cycling of magnitude and duration compatible with the hydraulic fracturing treatments. Experiments reported here are performed at a series of uniaxial pressures up to 100 MPa and at hydrostatic pressures of deuterated methane 0 and 50 MPa. Since at the original depth of the shale samples’ burial of 2184 m the hydrostatic pressure is approximately 27 MPa and the lithostatic pressure is about 55 MPa, the experimental conditions reasonably well simulate the reservoir pressure regime. Our SANS and USANS results show that different pore sizes are affected by uniaxial stress in different ways. Specifically, in the pore size range from 1 nm to 800 nm, a decrease of pore density with pressure is observed, with the most depleted being mesopores of about 100 nm in diameter. The observed decrease is likely related to deformation of kerogen, followed by a loss of pore nano-volume, as well as methane trapped in the micropores. For pores larger than 5 μm, USANS data suggest that the negative trend is reversed at above 74 MPa, and the number density of large macropores may increase with increased stress even above the original value. The increased number of macropores at high pressure may create new interconnected conduits for gas migration, resulting in a better recovery rate. Another important finding of this study is an irreversible rearrangement of pore size distribution taking place after pressure cycling. Furthermore, this irreversible reorganization of pore size distribution should be taken into account during management of well production to maximize recovery rate.

03 NATURAL GAS↗

DOE OSTI2023

Climatic factors and human population changes in Eurasia between the Last Glacial Maximum and the early Holocene

Archaeological records document a significant expansion of populations from the Last Glacial Maximum (LGM, ~23–19 ka) to the early Holocene (EH, ~9 ka) in Eurasia, which is often attributed to the influence of orbital-scale climate changes. Yet, information remains limited concerning the climatic factor(s) which were responsible for conditioning demographic patterns. Here, in this work, we present results from an improved Minimalist Terrestrial Resource Model (MTRM), forced by a transient climate simulation from the LGM to the EH. Simulated potential hunter-gatherer population densities and spatial distributions across Eurasia are supported by observed archaeological sites in Europe and China. In the low latitudes, potential population size change was predominantly controlled by precipitation and its strong influence on plant and animal resources. In the middle-high latitudes, temperature was the dominant driver in influencing potential population size change and animal resource availability. Different regional responses of potential populations to climate change across Eurasia - owing to variations in available food resources between the LGM and EH - provide a better understanding of human dispersal during the Late Pleistocene.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Grain engineering for efficient near-infrared perovskite light-emitting diodes

Metal halide perovskites show promise for next-generation light-emitting diodes, particularly in the near-infrared range, where they outperform organic and quantum-dot counterparts. However, they still fall short of costly III-V semiconductor devices, which achieve external quantum efficiencies above 30% with high brightness. Among several factors, controlling grain growth and nanoscale morphology is crucial for further enhancing device performance. This study presents a grain engineering methodology that combines solvent engineering and heterostructure construction to improve light outcoupling efficiency and defect passivation. Solvent engineering enables precise control over grain size and distribution, increasing light outcoupling to ~40%. Constructing 2D/3D heterostructures with a conjugated cation reduces defect densities and accelerates radiative recombination. The resulting near-infrared perovskite light-emitting diodes achieve a peak external quantum efficiency of 31.4% and demonstrate a maximum brightness of 929 W sr -1 m -2 . These findings indicate that perovskite light-emitting diodes have potential as cost-effective, high-performance near-infrared light sources for practical applications.

42 ENGINEERING↗

DOE OSTI2022

High resolution diagnostic tools for superconducting radio frequency cavities

Superconducting radio-frequency (SRF) cavities are one of the fundamental building blocks of modern particle accelerators. To achieve the highest quality factors (10 10 –10 11 ), SRF cavities are operated at liquid helium temperatures. Magnetic flux trapped on the surface of SRF cavities during cool-down below the critical temperature is one of the leading sources of residual RF losses. Instruments capable of detecting the distribution of trapped flux on the cavity surface are in high demand in order to better understand its relation to the cavity material, surface treatments and environmental conditions. We have designed, developed, and commissioned two high-resolution diagnostic tools to measure the distribution of trapped flux at the surface of SRF cavities. One is a magnetic field scanning system, which uses cryogenic Hall probes and anisotropic magnetoresistance sensors that fit the contour of a 1.3 GHz cavity. This setup has a spatial resolution of ~ 13 μm in the azimuthal direction and ~ 1 cm along the cavity contour. The second setup is a stationary, combined magnetic and temperature mapping system, which uses anisotropic magnetoresistance sensors and carbon resistor temperature sensors, covering the surface of a 3 GHz SRF cavity. This system has a spatial resolution of 5 mm close to the iris and 11 mm at the equator. Initial results show a non-uniform distribution of trapped flux on the cavities’ surfaces, dependent on the magnitude of the applied magnetic field during field-cooling below the critical temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

The minor pilin PilV provides a conserved adhesion site throughout the antigenically variable meningococcal type IV pilus

Type IV pili (T4P) are among the most widespread adhesive factors in prokaryotes. In pathogenic Neisseria, the major pilin, which provides the structural framework for the filamentous T4P, undergoes antigenic variation allowing the bacteria to evade the humoral immune response without impacting host-cell adhesion. Here, we show that a minor pilin, PilV, is distributed throughout the pilus and contributes to Neisseria meningitidis adhesion and that antibodies to PilV block meningococcal adhesion in vivo. Our results provide a mechanism whereby N. meningitidis varies its immunodominant major pilin to escape antibody recognition while maintaining conserved sites throughout the pilus for host receptor binding. They further suggest a strategy to prevent or block deadly N. meningitidis infections by targeting this minor pilin.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Robust Online Sequential RVFLNs for Data Modeling of Dynamic Time-Varying Systems with Application of an Ironmaking Blast Furnace

In a world where the increasing complexity of modern industrial processes brings difficulties for accurate mathematical modeling, taking advantage of data has become an efficient solution to complex dynamic process modeling issue. In this paper, we develop a novel robust online sequential version of random vector functional-link networks (RVFLNs) for data-driven modeling of dynamic time-varying system and applied it in a blast furnace (BF) ironmaking process. First, to overcome the time-varying dynamics of process and to enable the RVFLNs to learn online with avoiding data saturation, an improved online sequential version of RVFLNs (OS-RFVLNs) is first presented by online sequential learning with forgetting factor. This improved OS-RVFLNs algorithm is not only suitable for the real-time and large data transfer situation, but also can adjust the sensitivity of the algorithm to different samples with the help of the introduced forgetting factor. Second, since the output weights of the improved OS-RVFLNs as well as other RVFLNs algorithms are obtained by the least squares approach, a robustness problem may occur when the training dataset is contaminated with various outliers. To solve this problem, a Cauchy distribution weighted M-estimator is introduced to improve the robustness of the improved OS- RVFLNs. For this proposed robust OS-RVFLNs (R-OS- RVFLNs), since the weights of different outlier data are properly determined by the Cauchy distribution function, their corresponding contribution on modeling can be properly distinguished. Thus robust and better modeling results can be achieved. Experiments using actual industrial data of BF ironmaking process and comparative studies have demonstrated that the proposed method produces a better estimation accuracy and stronger robustness than other methods.

Blast furnace (BF), Modelling, Dynamic systems↗

DOE OSTI2025

Angle-dependent in Situ Fast Flavor Transformations in Post-neutron-star-merger Disks

Abstract The remnant black hole–accretion disk system resulting from binary neutron star mergers has proven to be a promising site for synthesizing the heaviest elements via rapid neutron capture ( r -process). A critical factor in determining the full r -process pattern in these environments is the neutron richness of the ejecta, which is strongly influenced by neutrino interactions. One key ingredient shaping these interactions is fast neutrino flavor conversions (FFCs), which arise due to angular crossings in neutrino distributions and occur on nanosecond timescales. We present the first three-dimensional in situ angle-dependent modeling of FFCs in postmerger disks, implemented within general relativistic magnetohydrodynamics with Monte Carlo neutrino transport. Our results reveal that, by suppressing electron neutrinos, FFCs more efficiently cool the disk and weaken the early thermally driven wind. Less releptonization due to electron neutrino absorption makes this cooler wind more neutron rich, producing a more robust r -process at higher latitudes of the outflow. This study underscores the necessity of incorporating FFCs in realistic simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Characterization of Losses in Superconducting Radio-Frequency Cavities by Combined Temperature and Magnetic Field Mapping

Superconducting radio-frequency (SRF) cavities are one of the fundamental building blocks of modern particle accelerators. To achieve the highest quality factors (10 10 -10 11 ), SRF cavities are operated at liquid helium temperatures. Magnetic flux trapped on the surface of SRF cavities during cool-down below the critical temperature is one of the leading sources of residual RF losses. Instruments capable of detecting the distribution of trapped flux on the cavity surface are in high demand in order to better understand its relation to the cavity material, surface treatments and environmental conditions. We have designed, developed, and commissioned two novel diagnostic tools to measure the distribution of trapped flux at the surface of SRF cavities. One is a magnetic field scanning system (MFSS) which uses cryogenic Hall probes and anisotropic magnetoresistance sensors that fit the contour of a 1.3 GHz cavity. The second setup is a stationary, combined magnetic and temperature mapping system which uses AMR sensors and carbon resistor temperature sensors, covering the surface of a 3 GHz SRF cavity. The MFSS system revealed a non-uniform distribution of trapped flux on the cavities' surface, dependent on the magnitude of the applied magnetic field during field-cooling below the critical temperature. The MFSS shows that magnetic field scanning as a function of the RF field indicates redistribution of trapped flux at some locations. About ~ 33% of hot-spots observed by temperature mapping during high power RF tests overlapped with the high B-field spots. Almost all high B-field spots observed after field-cool were found to be overlapped on grain boundaries. A clear correlation between the hot- spot formed after quench and local trapped flux was found, providing insight on the RF dissipation of trap vortices. The combined B&T map system showed that the T-map system is capable of detecting hot-spots and quench location on the surface of the 3 GHz SRF cavity. Different distribution of trapped flux was measured after different cool-down and residual B-field, but, no variation in magnetic field distribution was observed during quench, possibly due to magnetic sensors being far from the quench location.

Parajuli, Ishwari↗

DOE OSTI2025

Front-of-Meter Model Results

These files contains aggregations of key variables from the NREL Distributed Wind Futures Study using full parcel level data. These variables describe total technical and economic potential for distributed wind turbine deployment. Aggregations are available at the (1) county, (2) zipcode (zip code tabulation area or zcta), and (3) US Census block group level. Each scenario is coded with the scenario name (e.g., baseline) and year (e.g., 2022). Those files postfixed with 'econpot' contain results for only those parcels that are economically viable while the files postfixed with 'techpot' include results for all parcels that are technically feasible. Hence these correspond to technoeconomic and technical potential respectively. The data are available as CSV or Geopackage. Columns in the files are as follows: * geoid: geographic identifier (FIPS code or similar) * min_techpot_sum_kw: technical potential for all parcels in kW using turbines downsized to demand when appropriate * max_techpot_sum_kw: technical potential for all parcels in kW without downsizing turbines * aep_sum_kwh: annual energy production estimate in kWh * cf_mean_ratio: mean capacity factor * lcoe_mean_cents_per_kwh: mean levelized cost of energy for parcels in geography in cents per kWh * lcoe_std_cents_per_kwh: standard deviation of the above * parcel_area_sum_acres: total area of viable parcels in acres * n_turbines: number of cited turbines (one per viable parcel currently) Note: These are preliminary results from the full-parcel 2024 update of the Distributed Wind Energy Futures study. Please take care when making use of the data, and feel free to contact the team with any questions. Full documentation in support of these data is in progress and will follow.

17 WIND ENERGY↗

DOE OSTI2020

Renormalization and matching for the Collins-Soper kernel from lattice QCD

The Collins-Soper kernel, which governs the energy evolution of transverse- momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI'/MOM) scheme, as well as the conversion factor from the RI'/MOM-renormalized quasi-TMDPDF to the \( \overline{\mathrm{MS}} \) scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Shrubs Strongly Influence Snow Properties in Two Subarctic Watersheds

Understanding changes in snow distribution in permafrost ecosystems is fundamental to predicting their response to future climate change. The expansion of tall shrubs into tundra ecosystems can trap snow and insulate permafrost ecosystems during the winter, but the overall insulation effect is dependent upon many ecosystem properties. To study shrub–snow–ground interactions, small temperature sensors were deployed at two research sites on the Seward Peninsula of Alaska, USA, during the 2019–2020 winter. Snow temperatures were used to extrapolate multiple metrics, including freezing n-factors, the snow insulation effect, snow cover duration, and the length of the snowmelt period. Statistical and spatial analysis showed that shrub patches were a dominant control on all snow metrics. Within shrub patches, average ground temperatures were 2.1°C warmer, snow persisted 50 days longer, snow insulation was double, and a longer, later spring snowmelt period occurred compared to nonshrubby areas. Site-level differences contributed relatively little to variation in snow metrics, indicating that shrub presence is an overarching driver of snow–ground interactions at the locations examined. Shrub expansion, which is anticipated under climate change, will strongly impact future permafrost distribution and Arctic energy, water, and carbon cycles through snow–shrub–ground feedbacks.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Large-momentum effective theory’s asymptotic extrapolation vs the inverse problem

Large-momentum effective theory is a physics-guided systematic expansion to calculate light-cone parton distributions, including collinear (PDFs) and transverse-momentum-dependent ones, at any fixed momentum fraction 𝑥 within a range of [𝑥 min , 𝑥 max ]. It theoretically solves the ill-posed inverse problem that afflicts other theoretical approaches to collinear PDFs, such as short-distance factorizations. Recently, Dutrieux et al. raised practical concerns about whether current or even future lattice data will have sufficient precision in the subasymptotic correlation region to support an error-controlled extrapolation—and if not, whether it becomes an inverse problem where the relevant uncertainties cannot be properly quantified. While we agree that not all current lattice data have the desired precision to qualify for an asymptotic extrapolation, some calculations do, and more are expected in the future. We comment on the analysis and results in Dutrieux et al. and argue that a physics-based systematic extrapolation still provides the most reliable error estimates, even when the data quality is not ideal. In contrast, reframing the long-distance asymptotic extrapolation as a data-driven-only inverse problem with ad hoc mathematical conditioning could lead to unnecessarily conservative errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

238 PuO 2 In Vitro Lung Dissolution Rate and Particle Size Determination for Material Involved in the June 8, 2020 Incident at the Los Alamos National Laboratory PF-4 Facility

As part of the LANL response to the June 8, 2020 238 PuO 2 inhalation exposure incident in PF-4, the Nuclear and Radiochemistry Group (C-NR) was asked to assist in determining the lung dissolution rate and particle size distribution of the airborne material. These material characteristics, along with urine and fecal bioassay data, are used by the Radiation Protection Services (RP-SVS) internal dosimetrists to refine dose estimates for exposed workers. Similar to previous studies, an in vitro lung dissolution rate study was performed to assess how fast 238 Pu is cleared from the lungs. Given that PuO 2 is a relatively insoluble material, it dissolves very slowly and requires in vitro studies of 100 or more days to estimate dissolution rates. This report details the results of a 100 day in vitro dissolution rate study and the particle size characteristics of 238 PuO 2 collected on an air filters during the incident. Results show that the 238 PuO 2 involved in this incident has behavior comparable to PuO 2 from previous in vitro studies, with approximately 1% of material dissolving quickly, and 99% of the material dissolving very slowly, with a half-time of approximately 120 years. This is somewhat slower than what was determined in a previous study of LANL 238 PuO 2 , which had an experimental dissolution half-time of 3 years, but significantly faster than 3000 years measured for 239 PuO 2 . Particle size distribution measurements indicate that particle sizes range from 0.10 µm – 6 µm, with most < 2 µm, which is reasonable based on our understanding of the process history of the 238 PuO 2 . Particle size, specific surface area, calcining temperature, specific activity, and age all are known factors that can impact the dissolution rate of refractory materials, however, there are too few studies to quantify the exact influence of these parameters on a measured dissolution rate. The results of this study add to that knowledge base, and provide new insights into the dissolution rates for this LANL process-specific 238 PuO 2 material.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

DOE OSTI2023

Spatio-Temporal Surrogates for Interaction of a Jet with High Explosives: Part II - Clustering Extremely High-Dimensional Grid-Based Data

Building an accurate surrogate model for the spatio-temporal outputs of a computer simulation is a challenging task. A simple approach to improve the accuracy of the surrogate is to cluster the outputs based on similarity and build a separate surrogate model for each cluster. This clustering is relatively straightforward when the output at each time step is of moderate size. However, when the spatial domain is represented by a large number of grid points, numbering in the millions, the clustering of the data becomes more challenging. In this report, we consider output data from simulations of a jet interacting with high explosives. These data are available on spatial domains of different sizes, at grid points that vary in their spatial coordinates, and in a format that distributes the output across multiple files at each time step of the simulation. We first describe how we bring these data into a consistent format prior to clustering. Borrowing the idea of random projections from data mining, we reduce the dimension of our data by a factor of thousand, making it possible to use the iterative k-means method for clustering. We show how we can use the randomness of both the random projections, and the choice of initial centroids in k-means clustering, to determine the number of clusters in our data set. Our approach makes clustering of extremely high dimensional data tractable, generating meaningful cluster assignments for our problem, despite the approximation introduced in the random projections.

97 MATHEMATICS AND COMPUTING↗