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DOE OSTI2021

Approximating and incorporating model uncertainty in an inversion for seismic source functions: Preliminary results

We present preliminary work on propagating model uncertainty into the estimation of the time domain source time functions of the seismic source. Our method is based on an estimated model covariance function, which we estimate from the data. The model covariance function is then used to construct a suite of surrogate Greens functions which we use in a Monte Carlo type inversion scheme. The result is a probability density function of the six independent source time functions, each of which corresponds to an individual component of the seismic moment tensor. We compare the results of our method with those obtained using a computationally expensive finite difference Monte Carlo method and find that our new method produces results that are deficient in low frequencies. The advantage of our new method, which we term the Karhunen-Loeve Monte Carlo (KLMC) method, is that is several orders of magnitude faster than our current method, which uses a finite difference scheme to produce the suite of forward models.

42 ENGINEERING↗

DOE OSTI2022

Towards mapping biodiversity from above: Can fusing lidar and hyperspectral remote sensing predict taxonomic, functional, and phylogenetic tree diversity in temperate forests?

Abstract Aim Rapid global change is impacting the diversity of tree species and essential ecosystem functions and services of forests. It is therefore critical to understand and predict how the diversity of tree species is spatially distributed within and among forest biomes. Satellite remote sensing platforms have been used for decades to map forest structure and function but are limited in their capacity to monitor change by their relatively coarse spatial resolution and the complexity of scales at which different dimensions of biodiversity are observed in the field. Recently, airborne remote sensing platforms making use of passive high spectral resolution (i.e., hyperspectral) and active lidar data have been operationalized, providing an opportunity to disentangle how biodiversity patterns vary across space and time from field observations to larger scales. Most studies to date have focused on single sites and/or one sensor type; here we ask how multiple sensor types from the National Ecological Observatory Network’s Airborne Observation Platform (NEON AOP) perform across multiple sites in a single biome at the NEON field plot scale (i.e., 40 m × 40 m). Location Eastern USA. Time period 2017–2018. Taxa studied Trees. Methods With a fusion of hyperspectral and lidar data from the NEON AOP, we assess the ability of high resolution remotely sensed metrics to measure biodiversity variation across eastern US temperate forests. We examine how taxonomic, functional, and phylogenetic measures of alpha diversity vary spatially and assess to what degree remotely sensed metrics correlate with in situ biodiversity metrics. Results Models using estimates of forest function, canopy structure, and topographic diversity performed better than models containing each category alone. Our results show that canopy structural diversity, and not just spectral reflectance, is critical to predicting biodiversity. Main conclusions We found that an approach that jointly leverages spectral properties related to leaf and canopy functional traits and forest health, lidar derived estimates of forest structure, fine‐resolution topographic diversity, and careful consideration of biogeographical differences within and among biomes is needed to accurately map biodiversity variation from above.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

The effect of quasar redshift errors on Lyman-α forest correlation functions

ABSTRACT Using synthetic Lyman-α forests from the Dark Energy Spectroscopic Instrument (DESI) survey, we present a study of the impact of errors in the estimation of quasar redshift on the Lyman-α correlation functions. Estimates of quasar redshift have large uncertainties of a few hundred km s−1 due to the broadness of the emission lines and the intrinsic shifts from other emission lines. We inject Gaussian random redshift errors into the mock quasar catalogues, and measure the auto-correlation and the Lyman-α-quasar cross-correlation functions. We find a smearing of the BAO feature in the radial direction, but changes in the peak position are negligible. However, we see a significant unphysical correlation for small separations transverse to the line of sight which increases with the amplitude of the redshift errors. We interpret this contamination as a result of the broadening of emission lines in the measured mean continuum, caused by quasar redshift errors, combined with the unrealistically strong clustering of the simulated quasars on small scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Hydrological niche segregation defines forest structure and drought tolerance strategies in a seasonal Amazon forest

The relationship between rooting depth and above-ground hydraulic traits can potentially define drought resistance strategies that are important in determining species distribution and coexistence in seasonal tropical forests, and understanding this is important for predicting the effects of future climate change in these ecosystems. We assessed the rooting depth of 12 dominant tree species (representing c. 42% of the forest basal area) in a seasonal Amazon forest using the stable isotope ratios (δ 18 O and δ 2 H) of water collected from tree xylem and soils from a range of depths. We took advantage of a major ENSO-related drought in 2015/2016 that caused substantial evaporative isotope enrichment in the soil and revealed water use strategies of each species under extreme conditions. We measured the minimum dry season leaf water potential both in a normal year (2014; Ψ non-ENSO ) and in an extreme drought year (2015; Ψ ENSO ). Furthermore, we measured xylem hydraulic traits that indicate water potential thresholds trees tolerate without risking hydraulic failure (P 50 and P 88 ). We demonstrate that coexisting trees are largely segregated along a single hydrological niche axis defined by root depth differences, access to light and tolerance of low water potential. These differences in rooting depth were strongly related to tree size; diameter at breast height (DBH) explained 72% of the variation in the δ 18 Oxylem. Additionally, δ 18 O xylem explained 49% of the variation in P50 and 70% of P88, with shallow-rooted species more tolerant of low water potentials, while δ 18 O of xylem water explained 47% and 77% of the variation of minimum Ψ non-ENSO and Ψ ENSO . We propose a new formulation to estimate an effective functional rooting depth, i.e. the likely soil depth from which roots can sustain water uptake for physiological functions, using DBH as predictor of root depth at this site. Based on these estimates, we conclude that rooting depth varies systematically across the most abundant families, genera and species at the Tapajós forest, and that understorey species in particular are limited to shallow rooting depths. Our results support the theory of hydrological niche segregation and its underlying trade-off related to drought resistance, which also affect the dominance structure of trees in this seasonal eastern Amazon forest. Synthesis. Our results support the theory of hydrological niche segregation and demonstrate its underlying trade-off related to drought resistance (access to deep water vs. tolerance of very low water potentials). We found that the single hydrological axis defining water use traits was strongly related to tree size, and infer that periodic extreme droughts influence community composition and the dominance structure of trees in this seasonal eastern Amazon forest.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2013

THE RICH GLOBULAR CLUSTER SYSTEM OF ABELL 1689 AND THE RADIAL DEPENDENCE OF THE GLOBULAR CLUSTER FORMATION EFFICIENCY

We study the rich globular cluster (GC) system in the center of the massive cluster of galaxies Abell 1689 (z = 0.18), one of the most powerful gravitational lenses known. With 28 Hubble Space Telescope/Advanced Camera for Surveys orbits in the F814W bandpass, we reach a magnitude I{sub 814} = 29 with ∼>90% completeness and sample the brightest ∼5% of the GC system. Assuming the well-known Gaussian form of the GC luminosity function (GCLF), we estimate a total population of N{sup total}{sub GC}= 162,850{sup +75,450}{sub -51,310} GCs within a projected radius of 400 kpc. As many as half of the GCs may comprise an intracluster component. Even with the sizable uncertainties, which mainly result from the uncertain GCLF parameters, this system is by far the largest GC population studied to date. The specific frequency S{sub N} is high, but not uncommon for central galaxies in massive clusters, rising from S{sub N} ≈ 5 near the center to ∼12 at large radii. Passive galaxy fading would increase S{sub N} by ∼20% at z = 0. We construct the radial mass profiles of the GCs, stars, intracluster gas, and lensing-derived total mass, and we compare the mass fractions as a function of radius. The estimated mass in GCs, M{sub GC}{sup total} = 3.9 × 10{sup 10} M{sub ☉}, is comparable to ∼80% of the total stellar mass of the Milky Way. The shape of the GC mass profile appears intermediate between those of the stellar light and total cluster mass. Despite the extreme nature of this system, the ratios of the GC mass to the baryonic and total masses, and thus the GC formation efficiency, are typical of those in other rich clusters when comparing at the same physical radii. The GC formation efficiency is not constant, but varies with radius, in a manner that appears similar for different clusters; we speculate on the reasons for this similarity in profile.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Discovery of a very large structure at z = 3.78

We report the discovery of a large-scale structure containing multiple protoclusters at z = 3.78 in the Boötes field. The spectroscopic discovery of five galaxies at z = 3.783 ± 0.002 lying within 1 Mpc of one another led us to undertake a deep narrow- and broadband imaging survey of the surrounding field. Within a comoving volume of 72 × 72 × 25 Mpc{sup 3}, we have identified 65 Lyα emitter (LAE) candidates at z = 3.795 ± 0.015, and four additional galaxies at z {sub spec} = 3.730, 3.753, 3.780, 3.835. The galaxy distribution within the field is highly non-uniform, exhibiting three large (≈3-5 ×) overdensities separated by 8-14 Mpc (physical) and possibly connected by filamentary structures traced by LAEs. The observed number of LAEs in the entire field is nearly twice the average expected in field environments based on estimates of the Lyα luminosity function at these redshifts. We estimate that by z = 0 the largest overdensity will grow into a cluster of mass ≈10{sup 15} M {sub ☉}; the two smaller overdensities will grow into clusters of mass (2-6) × 10{sup 14} M {sub ☉}. The highest concentration of galaxies is located at the southern end of the image, suggesting that the current imaging may not map the true extent of the large-scale structure. Finding three large protocluster candidates within a single 0.3 deg{sup 2} field is highly unusual; expectations from theory suggest that such alignments should occur less than 2% of the time. Searching for and characterizing such structures and accurately measuring their volume space density can therefore place constraints on the theory of structure formation. Such regions can also serve as laboratories for the study of galaxy formation in dense environments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Cone beam breast CT with a high pitch (75 μm), thick (500 μm) scintillator CMOS flat panel detector: Visibility of simulated microcalcifications

Purpose: To measure and investigate the improvement of microcalcification (MC) visibility in cone beam breast CT with a high pitch (75 μm), thick (500 μm) scintillator CMOS/CsI flat panel detector (Dexela 2923, Perkin Elmer).Methods: Aluminum wires and calcium carbonate grains of various sizes were embedded in a paraffin cylinder to simulate imaging of calcifications in a breast. Phantoms were imaged with a benchtop experimental cone beam CT system at various exposure levels. In addition to the Dexela detector, a high pitch (50 μm), thin (150 μm) scintillator CMOS/CsI flat panel detector (C7921CA-09, Hamamatsu Corporation, Hamamatsu City, Japan) and a widely used low pitch (194 μm), thick (600 μm) scintillator aSi/CsI flat panel detector (PaxScan 4030CB, Varian Medical Systems) were also used in scanning for comparison. The images were independently reviewed by six readers (imaging physicists). The MC visibility was quantified as the fraction of visible MCs and measured as a function of the estimated mean glandular dose (MGD) level for various MC sizes and detectors. The modulation transfer functions (MTFs) and detective quantum efficiencies (DQEs) were also measured and compared for the three detectors used.Results: The authors have demonstrated that the use of a high pitch (75 μm) CMOS detector coupled with a thick (500 μm) CsI scintillator helped make the smaller 150–160, 160–180, and 180–200 μm MC groups more visible at MGDs up to 10.8, 9, and 10.8 mGy, respectively. It also made the larger 200–212 and 212–224 μm MC groups more visible at MGDs up to 7.2 mGy. No performance improvement was observed for 224–250 μm or larger size groups. With the higher spatial resolution of the Dexela detector based system, the apparent dimensions and shapes of MCs were more accurately rendered. The results show that with the aforementioned detector, a 73% visibility could be achieved in imaging 160–180 μm MCs as compared to 28% visibility achieved by the low pitch (194 μm) aSi/CsI flat panel detector. The measurements confirm that the Hamamatsu detector has the highest MTF, followed by the Dexel detector, and then the Varian detector. However, the Dexela detector, with its thick (500 μm) CsI scintillator and low noise level, has the highest DQE at all frequencies, followed by the Varian detector, and then the Hamamatsu detector. The findings on the MC visibility correlated well with the differences in MTFs, noise power spectra, and DQEs measured for these three detectors.Conclusions: The authors have demonstrated that the use of the CMOS type Dexela detector with its high pitch (75 μm) and thick (500 μm) CsI scintillator could help improve the MC visibility. However, the improvement depended on the exposure level and the MC size. For imaging larger MCs or scanning at high exposure levels, there was little advantage in using the Dexela detector as compared to the aSi type Varian detector. These findings correlate well with the higher measured DQEs of the Dexela detector, especially at higher frequencies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2013

Probabilistic assessment of cloud fraction using Bayesian blending of independent datasets: Feasibility study of a new method

We describe and evaluate a novel method to blend two observed cloud fraction (CF) datasets through Bayesian posterior estimation. The research reported here is a feasibility study designed to explore the method. In this proof‐of‐concept study, we illustrate the approach using specific observational datasets from the U. S. Department of Energy Atmospheric Radiation Measurement Program's Southern Great Plains site in the central United States, but the method is quite general and is readily applicable to other datasets. The total sky image (TSI) camera observations are used to determine the prior distribution. A regression model and the active remote sensing of clouds (ARSCL) radar/lidar observations are used to determine the likelihood function. The posterior estimate is a probability density function (pdf) of the CF whose mean is taken to be the optimal blend of the two observations. The data at hourly, daily, 5‐day, monthly, and annual time scales are considered. Some physical and probabilistic properties of the CFs are explored from radar/lidar, camera, and satellite observations and from simulations using the Community Atmosphere Model (CAM5). Our results imply that (a) the Beta distribution is a reasonable model for CF for both short‐ and long‐time means, the 5‐day data are skewed right, and the annual data are almost normally distributed, and (b) the Bayesian method developed successfully yields a pdf of CF, rather than a deterministic CF value, and it is feasible to blend the TSI and ARSCL data with a capability for bias correction.

58 GEOSCIENCES↗

DOE OSTI2019

Public charging infrastructure for plug-in electric vehicles: What is it worth?

A lack of charging infrastructure is an important barrier to the growth of the plug-in electric vehicle (PEV) market. Public charging infrastructure has tangible and intangible value, such as reducing range anxiety or building confidence in the future of the PEV market. Quantifying the value of public charging infrastructure can inform analysis of investment decisions and can help predict the impact of charging infrastructure on future PEV sales. Estimates of willingness to pay (WTP) based on stated preference surveys are limited by consumers' lack of familiarity with PEVs. As an alternative, we focus on quantifying the tangible value of public PEV chargers in terms of their ability to displace gasoline use for PHEVs and to enable additional electric (e-) vehicle miles for BEVs, thereby mitigating the limitations of shorter range and longer recharging time. Simulation studies provide data that can be used to quantify e-miles enabled by public chargers and the value of additional e-miles can be inferred from econometric estimates of WTP for increased vehicle range. Functions are synthesized that estimate the WTP for public charging infrastructure by plug-in hybrid and battery electric vehicles, conditional on vehicle range, annual vehicle travel, pre-existing charging infrastructure, energy prices, vehicle efficiency, and household income. A case study based on California's public charging network in 2017 indicates that, to the purchaser of a new BEV with a 100-mile range and home recharging, existing public fast chargers are worth about $1500 for intraregional travel, and fast chargers along intercity routes are valued at over $6500.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2013

THE STRUCTURE OF THE MERGING RCS 231953+00 SUPERCLUSTER AT z {approx} 0.9

The RCS 2319+00 supercluster is a massive supercluster at z = 0.9 comprising three optically selected, spectroscopically confirmed clusters separated by <3 Mpc on the plane of the sky. This supercluster is one of a few known examples of the progenitors of present-day massive clusters (10{sup 15} M{sub Sun} by z {approx} 0.5). We present an extensive spectroscopic campaign carried out on the supercluster field resulting, in conjunction with previously published data, in 1961 high-confidence galaxy redshifts. We find 302 structure members spanning three distinct redshift walls separated from one another by {approx}65 Mpc ({Delta} z = 0.03). The component clusters have spectroscopic redshifts of 0.901, 0.905, and 0.905. The velocity dispersions are consistent with those predicted from X-ray data, giving estimated cluster masses of {approx}10{sup 14.5}-10{sup 14.9} M{sub Sun }. The Dressler-Shectman test finds evidence of substructure in the supercluster field and a friends-of-friends analysis identified five groups in the supercluster, including a filamentary structure stretching between two cluster cores previously identified in the infrared by Coppin et al. The galaxy colors further show this filamentary structure to be a unique region of activity within the supercluster, comprised mainly of blue galaxies compared to the {approx}43%-77% red-sequence galaxies present in the other groups and cluster cores. Richness estimates from stacked luminosity function fits result in average group mass estimates consistent with {approx}10{sup 13} M{sub Sun} halos. Currently, 22% of our confirmed members reside in {approx}> 10{sup 13} M{sub Sun} groups/clusters destined to merge onto the most massive cluster, in agreement with the massive halo galaxy fractions important in cluster galaxy pre-processing in N-body simulation merger tree studies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Uncertainty Quantification for Point Spread Functions in X-Ray Radiography

X-ray radiographers have tools for estimating the point spread function (PSF) which determines the extent of the blur in images. Knowledge of uncertainties in their estimations can be extremely valuable, and existing methods do not provide this information. We have developed a new technique using a Bayesian framework that will provide useful uncertainties to the estimated PSF.

point spread function↗

DOE OSTI2024

A Cellular Automaton Simulation for Predicting Phase Evolution in Solid-State Reactions

New computational tools for solid-state synthesis recipe design are needed in order to accelerate the experimental realization of novel functional materials proposed by high-throughput materials discovery workflows. This work contributes a cellular automaton simulation framework for predicting the time-dependent evolution of intermediate and product phases during solid-state reactions as a function of precursor choice and amount, reaction atmosphere, and heating profile. The simulation captures the effects of reactant particle spatial distribution, particle melting, and reaction atmosphere. Reaction rates based on rudimentary kinetics are estimated using density functional theory data from the Materials Project and machine learning estimators for the melting point and the vibrational entropy component of the Gibbs free energy. The resulting simulation framework allows for the prediction of the likely outcome of a reaction recipe before any experiments are performed. We analyze five experimental solid-state recipes for BaTiO 3 , CaZrN 2 , and YMnO 3 found in the literature to illustrate the performance of the model in capturing reaction selectivity and reaction pathways as a function of temperature and precursor choice. This simulation framework offers an easier way to optimize existing recipes, aid in the identification of intermediates, and design effective recipes for yet unrealized inorganic solids in silico .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a nonparametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications.

42 ENGINEERING↗

DOE OSTI2019

GMLS-Nets: Scientific Machine Learning Methods for Unstructured Data

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Statistical estimates of the binary properties of rotational variables

ABSTRACT We present a model to estimate the average primary masses, companion mass ranges, the inclination limit for recognizing a rotational variable, and the primary mass spreads for populations of binary stars. The model fits a population’s binary mass function distribution and allows for a probability that some mass functions are incorrectly estimated. Using tests with synthetic data, we assess the model’s sensitivity to each parameter, finding that we are most sensitive to the average primary mass and the minimum companion mass, with less sensitivity to the inclination limit and little to no sensitivity to the primary mass spread. We apply the model to five populations of binary spotted rotational variables identified in ASAS-SN, computing their binary mass functions using RV data from APOGEE. Their average primary mass estimates are consistent with our expectations based on their CMD locations ($\sim 0.75 \, {\rm M}_{\odot }$ for lower main sequence primaries and $\sim 0.9$–$1.2 \, {\rm M}_{\odot }$ for RS CVn and sub-subgiants). Their companion mass range estimates allow companion masses down to $M_2/M_1\simeq 0.1$, although the main sequence population may have a higher minimum mass fraction ($\sim 0.4$). We see weak evidence of an inclination limit $\gtrsim 50^{\circ }$ for the main sequence and sub-subgiant groups and no evidence of an inclination limit in the other groups. No groups show strong evidence for a preferred primary mass spread. We conclude by demonstrating that the approach will provide significantly better estimates of the primary mass and the minimum mass ratio and reasonable sensitivity to the inclination limit with 10 times as many systems.

Phillips, Anya (ORCID:000900051914974X)↗

DOE OSTI2021

Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, ( x ) u - d , helicity moment, ( x ) Δ u - Δ d , and the transversity moment, ( x ) δu - δd , of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass M π . The final results are obtained using a simultaneous fit in the lattice spacing a , pion mass M π and the finite volume parameter M π L keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the $ \overline{\mathrm{MS}} $ scheme at 2 GeV, are ( x ) u - d = 0 . 155(17)(20), ( x ) Δ u - Δ d = 0 . 183(14)(20) and ( x ) δu - δd = 0 . 220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗