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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Spurious Correlations between Galaxies and Multiepoch Image Stacks in the DESI Legacy Surveys

A nonnegligible source of systematic bias in cosmological analyses of galaxy surveys is the on-sky modulation that is caused by foregrounds and variable image characteristics, such as observing conditions. Standard mitigation techniques perform a regression between the observed galaxy density field and sky maps of the potential contaminants. Such maps are ad hoc lossy summaries of the heterogeneous sets of coadded exposures that contribute to the survey. We present a methodology for addressing this limitation, and we extract spurious correlations between the observed distributions of galaxies and arbitrary stacks of single-epoch exposures. We study four types of galaxies (luminous red galaxies, emission-line galaxies, quasars, and Lyman-break galaxies) in the three regions of the DESI Legacy Surveys (North, South, and Dark Energy Survey), resulting in 12 samples with varying levels and types of contamination. We find that the new technique outperforms the traditional ones in all cases, and is able to remove higher levels of contamination. This paves the way for new methods that extract more information from multiepoch galaxy survey data and mitigate large-scale biases more effectively.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Aerodynamic Data Fusion Toward the Digital Twin Paradigm

This paper considers the fusion of two aerodynamic data sets originating from differing types of physical or computer experiments. This paper specifically addresses the fusion of 1) noisy and in-complete fields from wind-tunnel measurements and 2) deterministic but biased fields from numerical simulations. These two data sources are fused in order to estimate the true field that best matches measured quantities that serve as the ground truth. For example, two sources of pressure fields about an aircraft are fused based on measured forces and moments from a wind-tunnel experiment. A fundamental challenge in this problem is that the true field is unknown and cannot be estimated with 100% certainty. A Bayesian framework is employed to infer the true fields conditioned on measured quantities of interest; essentially a statistical correction to the data is performed. The fused data may then be used to construct more accurate surrogate models suitable for early stages of aerospace design. An extension of the proper orthogonal decomposition with constraints is also introduced to solve the same problem. In this work, both methods are demonstrated on fusing the pressure distributions for flow past the RAE2822 airfoil and the Common Research Model wing at transonic conditions. Comparison of both methods reveals that the Bayesian method is more robust when data are scarce and capable of also accounting for uncertainties in the data. Furthermore, given adequate data, the proper-orthogonal-decomposition-based and Bayesian approaches lead to surprisingly similar results.

42 ENGINEERING↗
DOE OSTI2025

Identifying preferential flow from soil moisture time series: Review of methodologies

Abstract Identifying and quantifying preferential flow (PF) through soil—the rapid movement of water through spatially distinct pathways in the subsurface—is vital to understanding how the hydrologic cycle responds to climate, land cover, and anthropogenic changes. In recent decades, methods have been developed that use measured soil moisture time series to identify PF. Because they allow for continuous monitoring and are relatively easy to implement, these methods have become an important tool for recognizing when, where, and under what conditions PF occurs. The methods seek to identify a pattern or quantification that indicates the occurrence of PF. Most commonly, the chosen signature is either (1) a nonsequential response to infiltrated water, in which soil moisture responses do not occur in order of shallowest to deepest, or (2) a velocity criterion, in which newly infiltrated water is detected at depth earlier than is possible by nonpreferential flow processes. Alternative signatures have also been developed that have certain advantages but are less commonly utilized. Choosing among these possible signatures requires attention to their pertinent characteristics, including susceptibility to errors, possible bias toward false negatives or false positives, reliance on subjective judgments, and possible requirements for additional types of data. We review 77 studies that have applied such methods to highlight important information for readers who want to identify PF from soil moisture data and to inform those who aim to develop new methods or improve existing ones. Core Ideas Soil moisture data can be used to identify the occurrence of preferential flow (PF) and its initiating conditions. Various data‐analysis methods to identify PF differ in susceptibility to error, bias, and subjectivity. These methods can utilize vast amounts of data from soil moisture monitoring networks to develop understanding of when, where, and under what conditions PF occurs. Newly developed methods may lead to better accuracy and reliability, and reduce the need for subjective judgments. Plain Language Summary Preferential flow through soil occurs when a large amount of water is suddenly available, as during an intense storm. This type of flow moves rapidly through the soil in distinct narrow pathways rather than moving evenly throughout the body of soil, with major consequences for groundwater resources, ecosystems, spreading of contaminants, and other vital concerns. Methods of detecting preferential flow have been developed that utilize measurements of soil water content made by sensors installed at various depths. This measurement technology has been widely implemented, many locations now having datasets years in length, and various methods have been developed for using these to identify preferential flow. The various methods are based on different features in the soil moisture records and vary in their advantages and shortcomings. In this review, we explain and evaluate these methods, highlighting important information for their implementation to identify preferential flow from soil moisture data and for efforts to develop new methods or improve existing ones.

Nimmo, John R↗
DOE OSTI2020

Scaling carbon fluxes from eddy covariance sites to globe: synthesis and evaluation of the FLUXCOM approach

FLUXNET comprises globally distributed eddy-covariance-based estimates of carbon fluxes between the biosphere and the atmosphere. Since eddy covariance flux towers have a relatively small footprint and are distributed unevenly across the world, upscaling the observations is necessary to obtain global-scale estimates of biosphere–atmosphere exchange. Based on cross-consistency checks with atmospheric inversions, sun-induced fluorescence (SIF) and dynamic global vegetation models (DGVMs), here we provide a systematic assessment of the latest upscaling efforts for gross primary production (GPP) and net ecosystem exchange (NEE) of the FLUXCOM initiative, where different machine learning methods, forcing data sets and sets of predictor variables were employed. Spatial patterns of mean GPP are consistent across FLUXCOM and DGVM ensembles (R 2 >0.94 at 1° spatial resolution) while the majority of DGVMs show, for 70 % of the land surface, values outside the FLUXCOM range. Global mean GPP magnitudes for 2008–2010 from FLUXCOM members vary within 106 and 130 PgC yr -1 with the largest uncertainty in the tropics. Seasonal variations in independent SIF estimates agree better with FLUXCOM GPP (mean global pixel-wise R 2 ~0.75) than with GPP from DGVMs (mean global pixel-wise R 2 ~0.6). Seasonal variations in FLUXCOM NEE show good consistency with atmospheric inversion-based net land carbon fluxes, particularly for temperate and boreal regions (R 2 >0.92). Interannual variability of global NEE in FLUXCOM is underestimated compared to inversions and DGVMs. The FLUXCOM version which also uses meteorological inputs shows a strong co-variation in interannual patterns with inversions (R 2 =0.87 for 2001–2010). Mean regional NEE from FLUXCOM shows larger uptake than inversion and DGVM-based estimates, particularly in the tropics with discrepancies of up to several hundred grammes of carbon per square metre per year. These discrepancies can only partly be reconciled by carbon loss pathways that are implicit in inversions but not captured by the flux tower measurements such as carbon emissions from fires and water bodies. We hypothesize that a combination of systematic biases in the underlying eddy covariance data, in particular in tall tropical forests, and a lack of site history effects on NEE in FLUXCOM are likely responsible for the too strong tropical carbon sink estimated by FLUXCOM. Furthermore, as FLUXCOM does not account for CO 2 fertilization effects, carbon flux trends are not realistic. Overall, current FLUXCOM estimates of mean annual and seasonal cycles of GPP as well as seasonal NEE variations provide useful constraints of global carbon cycling, while interannual variability patterns from FLUXCOM are valuable but require cautious interpretation. Exploring the diversity of Earth observation data and of machine learning concepts along with improved quality and quantity of flux tower measurements will facilitate further improvements of the FLUXCOM approach overall.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Moving-horizon false data injection attack design against cyber–physical systems

Systematic attack design is essential to understanding the vulnerabilities of cyber–physical systems (CPSs), to better design for resiliency. In particular, false data injection attacks (FDIAs) are well-known and have been shown to be capable of bypassing bad data detection (BDD) while causing targeted biases in resulting state estimates. However, their effectiveness against moving horizon estimators (MHE) is not well understood. In fact, this paper shows that conventional FDIAs are generally ineffective against MHE. One of the main reasons is that the moving window renders the static FDIA recursively infeasible. Here, this paper proposes a new attack methodology, moving-horizon FDIA (MH-FDIA), by considering both the performance of historical attacks and the current system’s status. Theoretical guarantees for successful attack generation and recursive feasibility are given. Numerical simulations on the IEEE-14 bus system further validate the theoretical claims and show that the proposed MH-FDIA outperforms state-of-the-art counterparts in both stealthiness and effectiveness. In addition, an experiment on a path-tracking control system of an autonomous vehicle shows the feasibility of the MH-FDIA in real-world nonlinear systems.

42 ENGINEERING↗
DOE OSTI2020

A physics-informed operator regression framework for extracting data-driven continuum models

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering continuum models from high fidelity molecular simulation data. Our approach applies a neural network parameterization of governing physics in modal space, allowing a characterization of differential operators while providing structure which may be used to impose biases related to symmetry, isotropy, and conservation form. Here, we demonstrate the effectiveness of our framework for a variety of physics, including local and nonlocal diffusion processes and single and multiphase flows. For the flow physics we demonstrate this approach leads to a learned operator that generalizes to system characteristics not included in the training sets, such as variable particle sizes, densities, and concentration.

42 ENGINEERING↗
DOE OSTI2020

Exploration of Electrochemical Reactions at Organic–Inorganic Halide Perovskite Interfaces via Machine Learning in In Situ Time-of-Flight Secondary Ion Mass Spectrometry

The instability of hybrid organic–inorganic perovskite (HOIP) devices is one of the significant challenges preventing commercialization. Exploring these phenomena is severely limited by the complexity of the intrinsic electrochemistry of HOIPs, the presence of multiple volatile and mobile ionic species, and the possible role of environmentally induced reactions at surfaces and triple-phase junctions. Here, in situ studies of the electrochemistry of methylammonium lead bromide perovskite with the Au electrode interface are reported via light- and voltage-dependent time-of-flight secondary ion mass spectrometry (ToF-SIMS) imaging of lateral perovskite heterostructures. While ToF-SIMS allows for the visualization of the chemical composition along the surface and its evolution with light and electrical bias, the interpretation of the multidimensional data obtained is often limited due to strong correlations between chemical signatures and the need to track multiple peaks at once. Here, a machine learning workflow combining the Hough transform and non-negative matrix factorization and no-negative tensor decomposition is developed to avoid this limitation and extract salient features of associated chemical changes and to separate the light- and voltage-dependent dynamics. Finally, combining these in situ characterizations and the machine learning workflow provides comprehensive information on the chemical nature of moving species, ion accumulation, and interfacial electrochemical reactions in HOIP devices.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Metals and methylotrophy: Via global gene expression studies

A number of minerals, such as copper, cobalt, and rare earth elements (REE), are essential modulators of microbial one-carbon metabolism. This chapter provides an overview of the gene expression study design and analysis protocols for uncovering REE-induced changes in methylotrophic bacteria. By interrogating relationships and differences in total gene expression induced by mineral micronutrients, a deeper understanding of gene regulation at a systems scale can be gained. With careful design and execution of RNA-sequencing experiments, thorough processing and assessment of read quality can be utilized to assess and adjust for possible biases. Here, by ensuring only quality data are utilized in downstream processes, differential gene expression, overrepresented analyses, and gene-set enrichment analyses provide reliable and reproducible representation of pathways and functions which are being affected by changes in environmental conditions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Characterizing Defects Inside Hexagonal Boron Nitride Using Random Telegraph Signals in van der Waals 2D Transistors

Single-crystal hexagonal boron nitride (hBN) is used extensively in many two-dimensional electronic and quantum devices, where defects significantly impact performance. Therefore, characterizing and engineering hBN defects are crucial for advancing these technologies. Here, we examine the capture and emission dynamics of defects in hBN by utilizing low-frequency noise (LFN) spectroscopy in hBN-encapsulated and graphene-contacted MoS 2 field-effect transistors (FETs). The low disorder of this heterostructure allows the detection of random telegraph signals (RTS) in large device dimensions of 100 μm 2 at cryogenic temperatures. Analysis of gate bias- and temperature-dependent LFN data indicate that RTS originates from a single trap species within hBN. By performing multi-space density functional theory (MS-DFT) calculations on a gated defective hBN/MoS 2 heterostructure model, we assign substitutional carbon atoms in boron sites as the atomistic origin of RTS. This study demonstrates the utility of LFN spectroscopy combined with MS-DFT analysis on a low-disorder all-vdW FET as a powerful means for characterizing the atomistic defects in single-crystal hBN.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

The Illumination of Thunderclouds by Lightning: 2. The Effect of GLM Instrument Threshold on Detection and Clustering

Abstract Lightning is measured from space using optical instruments that detect transient changes in the illumination of the cloud top. How much of the flash (if any) is recorded by the instrument depends on the instrument detection threshold. NOAA's Geostationary Lightning Mapper (GLM) employs a dynamic threshold that varies across the imaging array and changes over time. This causes flashes in certain regions and at night to be recorded in greater detail than other flashes, and threshold inconsistencies will impose biases on all levels of GLM data products. In this study, we quantify the impact of the varying GLM threshold on event/group/flash detection, flash clustering, and gridded product generation by imposing artificial thresholds on the event data taken from a thunderstorm with a low instrument threshold (∼0.7 fJ). We find that even modest increases in threshold severely impact event (60% loss by 2 fJ, 90% loss by 10 fJ) and group (25% loss by 2 fJ, 81% loss by 10 fJ) detection by suppressing faint illumination of the cloud top from weak sources and scattering. Flash detection is impacted less by threshold increases (4% loss by 2 fJ), but reductions are still significant at higher thresholds (35% loss by 10 fJ, or 44% if single‐group flashes are removed). Undetected pulses cause individual flashes to be split and severely impact the construction of gridded products. All of these factors complicate the interpretation of GLM data, particularly when trended over time under a changing threshold.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

E3SM‐Arctic: Regionally Refined Coupled Model for Advanced Understanding of Arctic Systems Interactions

Earth system models are essential tools for climate projections, but coarse resolutions limit regional accuracy, especially in the Arctic. Regionally refined meshes (RRMs) enhance resolution in key areas while maintaining computational efficiency. This paper provides an overview of the United States (U.S.) Department of Energy's (DOE's) Energy Exascale Earth System Model version 2.1 with an Arctic RRM, hereafter referred to as E3SMv2.1-Arctic, for the atmosphere (25 km), land (25 km), and ocean/ice (10 km) components. We evaluate the atmospheric component and its interactions with land, ocean, and cryosphere by comparing the RRM (E3SM2.1-Arctic) historical simulations (1950–2014) with the uniform low-resolution (LR) counterpart, reanalysis products, and observational data sets. The RRM generally reduces biases in the LR model, improving simulations of Arctic large-scale mean fields, such as precipitation, atmospheric circulation, clouds, atmospheric river frequency, and sea ice thickness. However, it introduces a seasonally dependent surface air temperature bias, reducing the LR cold bias in summer but enhancing the LR warm bias in winter, which contributes to the underestimated winter sea ice area and volume. Radiative feedback analysis shows similar climate feedback strengths in both model configurations, with the RRM exhibiting a more positive surface albedo feedback and contributing to a stronger surface warming than LR. These findings underscore the importance of high-resolution modeling for advancing our understanding of Arctic climate changes and their broader global impacts, although some persistent biases appear to be independent of model resolution at 10–100 km scales.

Energy Exascale Earth System Model (E3SM)↗
DOE OSTI2025

Autonomous platform for solution processing of electronic polymers

The manipulation of electronic polymers’ solid-state properties through processing is crucial in electronics and energy research. Yet, efficiently processing electronic polymer solutions into thin films with specific properties remains a formidable challenge. We introduce Polybot, an artificial intelligence (AI) driven automated material laboratory designed to autonomously explore processing pathways for achieving high-conductivity, low-defect electronic polymers films. Leveraging importance-guided Bayesian optimization, Polybot efficiently navigates a complex 7-dimensional processing space. In particular, the automated workflow and algorithms effectively explore the search space, mitigate biases, employ statistical methods to ensure data repeatability, and concurrently optimize multiple objectives with precision. The experimental campaign yields scale-up fabrication recipes, producing transparent conductive thin films with averaged conductivity exceeding 4500 S/cm. Feature importance analysis and morphological characterizations reveal key design factors. This work signifies a significant step towards transforming the manufacturing of electronic polymers, highlighting the potential of AI-driven automation in material science.

Wang, Chengshi [Argonne National Laboratory (ANL),↗
DOE OSTI2022

Data-driven causal model discovery and personalized prediction in Alzheimer's disease

Abstract With the explosive growth of biomarker data in Alzheimer’s disease (AD) clinical trials, numerous mathematical models have been developed to characterize disease-relevant biomarker trajectories over time. While some of these models are purely empiric, others are causal, built upon various hypotheses of AD pathophysiology, a complex and incompletely understood area of research. One of the most challenging problems in computational causal modeling is using a purely data-driven approach to derive the model’s parameters and the mathematical model itself, without any prior hypothesis bias. In this paper, we develop an innovative data-driven modeling approach to build and parameterize a causal model to characterize the trajectories of AD biomarkers. This approach integrates causal model learning, population parameterization, parameter sensitivity analysis, and personalized prediction. By applying this integrated approach to a large multicenter database of AD biomarkers, the Alzheimer’s Disease Neuroimaging Initiative, several causal models for different AD stages are revealed. In addition, personalized models for each subject are calibrated and provide accurate predictions of future cognitive status.

Zheng, Haoyang (ORCID:0000000168358242)↗
DOE OSTI2024

O Corona, where art thou? eROSITA’s view of UV-optical-IR variability-selected massive black holes in low-mass galaxies

Finding massive black holes (MBHs,M BH ≈ 10 4 –10 7 M ⊙ ) in the nuclei of low-mass galaxies $\left( {{M_*}\mathop {\mathop < \limits_ }\limits_ {{10}^{10}}{M_ \odot }} \right)$ is crucial to constrain seeding and growth of black holes over cosmic time, but it is particularly challenging due to their low accretion luminosities. Variability selection via long-term photometric ultraviolet, optical, or infrared (UVOIR) light curves has proved effective and identifies lower-Eddington ratios compared to broad and narrow optical spectral lines searches. In the inefficient accretion regime, X-ray and radio searches are effective, but they have been limited to small samples. Therefore, differences between selection techniques have remained uncertain. Here, we present the first large systematic investigation of the X-ray properties of a sample of known MBH candidates in dwarf galaxies. We extracted X-ray photometry and spectra of a sample of ~200 UVOIR variability-selected MBHs and significantly detected 17 of them in the deepest available SRG/eROSITA image, of which four are newly discovered X-ray sources and two are new secure MBHs. This implies that tens to hundreds of LSST MBHs will have SRG/eROSITA counterparts, depending on the seeding model adopted. Surprisingly, the stacked X-ray images of the many non-detected MBHs are incompatible with standard disk-corona relations, typical of active galactic nuclei, inferred from both the optical and radio fluxes. They are instead compatible with the X-ray emission predicted for normal galaxies. After careful consideration of potential biases, we identified that this X-ray weakness needs a physical origin. A possibility is that a canonical X-ray corona might be lacking in the majority of this population of UVOIR-variability selected low-mass galaxies or that unusual accretion modes and spectral energy distributions are in place for MBHs in dwarf galaxies. This result reveals the potential for severe biases in occupation fractions derived from data from only one waveband combined with SEDs and scaling relations of more massive black holes and galaxies.

Astronomy & Astrophysics↗
DOE OSTI2023

DESI luminous red galaxy samples for cross-correlations

We present two galaxy samples, selected from DESI Legacy Imaging Surveys (LS) DR9, with approximately 20,000 square degrees of coverage and spectroscopic redshift distributions designed for cross-correlations such as with CMB lensing, galaxy lensing, and the Sunyaev-Zel'dovich effect. The first sample is identical to the DESI Luminous Red Galaxy (LRG) sample, and the second sample is an extended LRG sample with 2–3 times the DESI LRG density. We present the improved photometric redshifts, tomographic binning and their spectroscopic redshift distributions and imaging systematics weights, and magnification bias coefficients. The catalogs and related data products will be made publicly available. The cosmological constraints using this sample and Planck lensing maps are presented in a companion paper. Here, we also make public the new set of general-purpose photometric redshifts trained using DESI spectroscopic redshifts, which are used in this work, for all galaxies in LS DR9.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Congenital Malformations and Perinatal Deaths Among the Children of Atomic Bomb Survivors: A Reappraisal

From 1948 to 1954, the Atomic Bomb Casualty Commission conducted a study of pregnancy outcomes among births to atomic bomb survivors (Hiroshima and Nagasaki, Japan) who had received radiation doses ranging from 0 Gy to near-lethal levels. Past reports (1956, 1981, and 1990) on the cohort did not identify significant associations of radiation exposure with untoward pregnancy outcomes, such as major congenital malformations, stillbirths, or neonatal deaths, individually or in aggregate. We reexamined the risk of major congenital malformations and perinatal deaths in the children of atomic bomb survivors (n = 71,603) using fully reconstructed data to minimize the potential for bias, using refined estimates of the gonadal dose from Dosimetry System 2002 and refined analytical methods for characterizing dose-response relationships. The analyses showed that parental exposure to radiation was associated with increased risk of major congenital malformations and perinatal death, but the estimates were imprecise for direct radiation effects, and most were not statistically significant. Nonetheless, the uniformly positive estimates for untoward pregnancy outcomes among children of both maternal and paternal survivors are useful for risk assessment purposes, although extending them to populations other than the atomic bomb survivors comes with uncertainty as to generalizability.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Constraints on S 8 from a full-scale and full-shape analysis of redshift-space clustering and galaxy–galaxy lensing in BOSS

ABSTRACT We present a novel simulation-based cosmological analysis of galaxy–galaxy lensing and galaxy redshift-space clustering. Compared to analysis methods based on perturbation theory, our simulation-based approach allows us to probe a much wider range of scales, $0.4 \, h^{-1} \, \mathrm{Mpc}$ to $63 \, h^{-1} \, \mathrm{Mpc}$, including highly non-linear scales, and marginalizes over astrophysical effects such as assembly bias. We apply this framework to data from the Baryon Oscillation Spectroscopic Survey LOWZ sample cross-correlated with state-of-the-art gravitational lensing catalogues from the Kilo Degree Survey and the Dark Energy Survey. We show that gravitational lensing and redshift-space clustering when analysed over a large range of scales place tight constraints on the growth-of-structure parameter $S_8 = \sigma _8 \sqrt{\Omega _{\rm m} / 0.3}$. Overall, we infer S8 = 0.792 ± 0.022 when analysing the combination of galaxy–galaxy lensing and projected galaxy clustering and S8 = 0.771 ± 0.027 for galaxy redshift-space clustering. These findings highlight the potential constraining power of full-scale studies over studies analysing only large scales and also showcase the benefits of analysing multiple large-scale structure surveys jointly. Our inferred values for S8 fall below the value inferred from the CMB, S8 = 0.834 ± 0.016. While this difference is not statistically significant by itself, our results mirror other findings in the literature whereby low-redshift large-scale structure probes infer lower values for S8 than the CMB, the so-called S8-tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Design and characterization of a phonon-mediated cryogenic particle detector with an eV-scale threshold and 100 keV-scale dynamic range

We present the design and characterization of a cryogenic phonon-sensitive Si detector exploiting the Neganov-Tromov-Luke effect to detect single-charge excitations. This device achieved 2.65(2) eV phonon energy resolution when operated without a voltage bias across the crystal and a corresponding charge resolution of 0.03 electron-hole pairs at 100 V bias. With a continuous-readout data acquisition system and an oine optimum-filter trigger, we obtain a 9.2 eV threshold with a trigger rate of the order of 20 Hz. The detector's energy scale is calibrated up to 120 keV using an energy estimator based on the pulse area. The high performance of this device allows its application to different fields where excellent energy resolution, low threshold, and large dynamic range are required, including dark matter searches, precision measurements of coherent neutrino-nucleus scattering, and ionization yield measurements.

Ren, R↗