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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Improving estimates of sub-daily gross primary production from solar-induced chlorophyll fluorescence by accounting for light distribution within canopy

Solar-induced chlorophyll fluorescence (SIF) has long been regarded as a proxy for photosynthesis and has shown superiority in estimating gross primary production (GPP) compared to traditional vegetation indices, especially in evergreen ecosystems. However, current SIF-based GPP estimations regard the canopy as a large leaf and seldom consider the impact of interactions among light, canopy structure, and leaf physiology. In this study, we proposed GPP estimation models with different descriptions of light–structure–physiology interactions (including the layered model, the two-leaf model, and the layered two-leaf model) and compared their performances with the big-leaf model using half-hourly (or hourly) observations at evergreen needleleaf forest sites. First, we found that the big-leaf model underestimated GPP, especially at noon. All models showed higher accuracy than that of the big-leaf model. Second, we investigated the diurnal dynamics of GPP estimations in each canopy layer and found that models with a two-leaf assumption captured the diurnal variations in GPP better than that with the layered assumption. Here we also deduced that the poor performance of the big-leaf model was related to its overestimation of the overall light stress on the redox state of PSII reaction centers (qL). Finally, we noticed that the qL at the canopy scale had lower sensitivity to light change than the single-leaf qL and that the light response of canopy-scale qL was influenced by the leaf area index during seasonal cycles. Overall, this study describes methods to accurately estimate sub-daily GPP from SIF in evergreen needleleaf forests and demonstrates that the interactions among light, canopy structure, and leaf physiology regulate the SIF-GPP relationship at the canopy scale. Further, it indicates the need to consider the description of light distribution within the canopy in next-generation terrestrial biosphere models, even if they incorporate SIF to constrain their parameterization. Thus, upscaling the established leaf-scale mechanistic SIF-GPP relationship or findings to canopy-scale applications still requires much work, especially when there are significant changes in environmental conditions and their within-canopy distributions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Efficient Mass Estimate at the Core of Strong Lensing Galaxy Clusters Using the Einstein Radius

In the era of large surveys, yielding thousands of galaxy clusters, efficient mass proxies at all scales are necessary in order to fully utilize clusters as cosmological probes. At the cores of strong lensing clusters, the Einstein radius can be turned into a mass estimate. This efficient method has been routinely used in literature, in lieu of detailed mass models; however, its scatter, assumed to be similar to 30%, has not yet been quantified. Here, we assess this method by testing it against ray-traced images of cluster-scale halos from the Outer RimN-body cosmological simulation. We measure a scatter of 13.9% and a positive bias of 8.8% in M (<θ E ), with no systematic correlation with total cluster mass, concentration, or lens or source redshifts. We find that increased deviation from spherical symmetry increases the scatter; conversely, where the lens produces arcs that cover a large fraction of its Einstein circle, both the scatter and the bias decrease. While spectroscopic redshifts of the lensed sources are critical for accurate magnifications and time delays, we show that for the purpose of estimating the total enclosed mass, the scatter introduced by source redshift uncertainty is negligible compared to other sources of error. Finally, we derive and apply an empirical correction that eliminates the bias, and reduces the scatter to 10.1% without introducing new correlations with mass, redshifts, or concentration. Our analysis provides the first quantitative assessment of the uncertainties in M (<θ E ), and enables its effective use as a core mass estimator of strong lensing galaxy clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates, with application to analysis of biomarker correlates in vaccine trials

Herein, this article presents generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly robust augmented inverse probability weighted (AIPW) complete-case approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Analysis of spin frustration in an Fe III 7 cluster using a combination of computational, experimental, and magnetostructural correlation methods

The synthesis, structure, and magnetic properties are reported for [Fe 7 O 3 (O 2 C t Bu) 9 (mda) 3 (H 2 O) 3 ] ( 1 ), where mdaH 2 is N -methyldiethanolamine. 1 was prepared from the reaction of [Fe 3 O(O 2 C t Bu) 6 (H 2 O) 3 ](NO 3 ) with mdaH 2 in a 1:~3 ratio in MeCN. The core of 1 consists of a central octahedral Fe III ion held within a non-planar Fe 6 loop by three μ 3 -O 2- and three μ 2 -RO - arms from the three mda 2- chelates. Variable-temperature dc and ac magnetic susceptibility studies revealed dominant antiferromagnetic coupling, leading to a ground state spin of S = 5 / 2 . The ground state was confirmed by a fit of magnetization data collected in the 0.1–7.0 T and 1.8–10.0 K ranges. The four Fe 2 pairwise exchange parameters ( J 1 - J 4 ) were estimated by independent methods: theoretical calculations using either broken symmetry energy differences (-46.3, -16.2, -3.9, and - 28.1 cm -1 , respectively) or Green’s function approximation methods (-41.4, -14.8, -13.2, and - 24.7 cm -1 ), and a magnetostructural correlation (MSC) previously developed for high nuclearity Fe III /O complexes (-39.5, -13.8, -6.7, and - 23.5 cm -1 ). Additionally, the J 1 - J 4 obtained from the MSC and theoretical methods were used with the program PHI to both simulate χ M T vs T as well as to serve as reasonable input values to fit the experimental data (-41.0, -11.4, -5.0, and - 27.3 cm -1 ). Analysis of the J ij led to identification of the spin frustration effects operative and the resultant spin vector alignments at each Fe III ion, thus allowing for the rationalization of the experimental ground state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Local radiative feedbacks over the Arctic based on observed short-term climate variations

We compare various radiative feedbacks in response to short-term climate variations estimated from reanalysis, satellite, and global climate model datasets using the combined Kernel-Gregory approach over the Arctic (60-90°N). Except for the shortwave cloud feedback, all feedbacks are positive over the Arctic. Lapse rate feedback is comparable with surface albedo feedback. Relative to the tropics (30°S-30°N), the temperature feedback (lapse rate feedback plus Planck feedback deviation from its global mean) is the largest contributor to Arctic amplification among all feedbacks, followed by surface albedo feedback. The choice of meteorological fields has a small impact on the cloud feedback estimate, but different top-of-the-atmosphere clear-sky fluxes datasets can result in a wide spread of estimated cloud feedbacks. The net cloud feedback over the Arctic is positive due to a larger positive in longwave than the negative shortwave feedback, but has the largest uncertainty. Relative to the tropics, the longwave cloud feedback largely contributes to the Arctic amplification.

Zhang, Rudong↗
DOE OSTI2026

HostSub_GP: Precise Galaxy Background Subtraction in Transient Long-slit Spectroscopy with Gaussian Processes

We present a novel host galaxy subtraction technique in long-slit spectroscopy for extragalactic transients. Unlike classic methods which generally estimate the background using simple interpolation of local galaxy flux in the 2D spectrum, our approach leverages multi-band archival images of the host galaxies to model the background emission from the galaxy in the 2D spectrum. Such imaging encodes the wavelength-dependent galaxy profile along the slit, and is readily accessible through wide-field imaging surveys. We construct a smooth prior for the 2D galaxy profile with a Gaussian process (GP) based on these reference images, and use another GP to model the correlated deviations from the prior in the observed spectrum. This enables accurate inference of the galaxy flux blended with the transient. On synthetic long-slit data of a spiral galaxy extracted from a Multi Unit Spectroscopic Explorer hyper-spectral cube, the GP method remains robust as long as the host galaxy is spatially resolved and consistently outperforms classic methods. We apply the method to archival Keck spectra of two real transients, SN 2019eix and AT 2019qiz, to further demonstrate how the method uniquely recovers weak spectral features amid strong galaxy contamination, enabling refined constraints on the properties of both transients. We have released the software implementation, HostSub_GP, a scalable toolkit that leverages JAX, with an MIT license.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Neural Posterior Estimation for Scalable and Accurate Inverse Parameter Inference in Li-Ion Batteries

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter estimation via Bayesian calibration, diagnostics can account for the uncertainty due to model fitness, data noise, and the observability of any given parameter. However, Bayesian calibration in Li-ion batteries using electrochemical data is computationally intensive even when using a fast surrogate in place of physics-based models, requiring many thousands of model evaluations. A fully amortized alternative is neural posterior estimation (NPE). NPE shifts the computational burden from the parameter estimation step to data generation and model training, reducing the parameter estimation time from minutes to milliseconds, enabling real-time applications. The present work shows that NPE can infer parameters equally or more accurately than Bayesian calibration, even if it leads to higher voltage reconstruction errors. We also demonstrate that the higher computational costs for data generation are tractable even in high-dimensional cases (ranging from 6 to 27 estimated parameters). The NPE method also offers several interpretability advantages over Bayesian calibration, such as local parameter sensitivity to specific regions of the voltage curve. The NPE method is demonstrated using an experimental fast charge dataset, with parameter estimates validated against measurements of loss of lithium inventory and loss of active material. The implementation is made available in a companion repository (https://github.com/NatLabRockies/BatFIT).

25 ENERGY STORAGE↗
DOE OSTI2020

High-temperature 2D ferromagnetism in conjugated microporous porphyrin-type polymers

The need for magnetic 2D materials that are stable to the enviroment and have high Curie temperatures is very important for various electronic and spintronic applications. We have found that two-dimensional porphyrin-type aza-conjugated microporous polymer crystals are such a material (Fe-aza-CMPs). Fe-aza-CMPs are stable to CO, CO 2 , and O 2 atmospheres and show unusual adsorption, electronic, and magnetic properties. Indeed, they are semiconductors with small energy band gaps ranging from 0.27 eV to 0.626 eV. CO, CO 2 , and O 2 molecules can be attached in three different ways where single, double, or triple molecules are bound to iron atoms in Fe-aza-CMPs. For different attachment configurations we find that for CO and CO 2 a uniform distribution of the molecules is most energetically favorable while for O 2 molecules aggregation is most energetically preferable. The magnetic moments decrease from 4 to 2 to 0 for singly, doubly, triply occupied configurations for all gasses respectively. The most interesting magnetic properties are found for O 2 molecules attached to the Fe-aza-CMP. For a single attachment configuration we find that an antiferromagnetic state is favorable. When two O 2 molecules are attached, the calculations show the highest exchange integral with a value of J = 1071 μeV. This value has been verified by two independent methods where in the first method J is calculated by the energy difference between ferromagnetic and anitferromagnetic configurations. The second method is based on the frozen magnon approach where the magnon dispersion curve has been fitted by the Ising model. Finally, for the second method J has been estimated at J = 1100 μeV in excellent agreement with the first method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

In situ high-temperature X-ray diffraction study of Sc-doped titanium oxide nanocrystallites

Titanium dioxide is an inexpensive wide-gap highly ionic semiconductor with striking photocatalytic capabilities in several heterogeneous photoredox reactions. A small crystal size is desirable to maximize the surface area, since photocatalytic reactions occur at the surface of a photocatalyst. Presented in this work are the synthesis and microstructural characterization of 4 at.% Sc-doped TiO 2 (4SDT) prepared by water-based co-precipitation. The crystal structure of 4SDT was examined via in situ high-temperature powder X-ray diffraction experiments from 25 to 1200°C. Rietveld analysis revealed single-phase anatase up to 875°C, while at 900°C the anatase-to-rutile phase transformation occurred and at higher temperatures additional reflections of Sc-rich phases (Sc 2 TiO 5 from 975°C and Ti 3 Sc 4 O 12 or Sc 2 O 3 at 1200°C) were observed. Debye function analysis (DFA) was applied to model the total scattering pattern directly in reciprocal space, allowing the reconstruction of Ti vacancies. Both Rietveld and DFA methods were applied to estimate the nanocrystallite size and shape with consistent growth in crystallite size with temperature: an ellipsoid shape with equatorial ~4.7 nm / axial (001) ~6.9 nm at 25°C to equatorial ~27.9 nm / axial (001) ~39.6 nm at 900°C refined by Rietveld analysis, versus a cylinder shape with D a , b = 4.3 nm and size dispersion σ ab = 1.5 nm, L c = 4.9 nm and σ c = 2.3 nm at 25°C to D a , b = 21.4 nm, σ ab = 8.3 nm, L c = 23.9 and σ c = 10.9 nm at 900°C estimated by DFA. The microstructural changes obtained by Rietveld and DFA methods were supported by high-resolution transmission electron microscopy image analysis, as well as by the less direct nitrogen sorption techniques that provide information on the size of non-agglomerated and dense particles. The Ti site-occupancy factor showed a linear increase from 0.6–0.8 at 25°C to unity at 900°C for anatase, and from ~0.7 at 900°C to unity at 1200°C for rutile, via Rietveld analysis and DFA.

36 MATERIALS SCIENCE↗
DOE OSTI2018

County-level Estimates for Carbon Distribution in U.S. Croplands, 1990-2005

Net Primary Productivity (NPP) for croplands can be estimated using a statistical method that includes factors for dry weight, harvest indices, and root:shoot ratios multiplied by yield data from the National Agricultural Statistics Service (NASS). This method has been documented and published by Prince et al. (2001), Hicke and Lobell (2004), and Hicke et al. (2004). We expanded this method by including factors for more crops and by using an estimated carbon content of 0.45 for agricultural crops to estimate (a) total net carbon uptake, (b) carbon in aboveground biomass, (c) carbon in belowground biomass, (d) carbon harvested and transported off site, and (e) the amount of carbon remaining on the surface following harvest. These five variables are included with their respective Federal Information Processing Standards (FIPS) codes for all counties in the contiguous U.S. from 1990-2005. A mean harvest efficiency of 0.95 was assumed across all crops. Total cropland NPP for the U.S. ranges from 378-527 Tg C yr-1 within years 1990-2005, and total carbon harvested and removed ranges from 161-228 Tg C yr-1 within years 1990-2005.For access to the data files, click this link to the CDIAC data transition website: http://cdiac.ess-dive.lbl.gov/carbonmanagement/cropcarbon/

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Improving the flux calibration in reverberation mapping by spectral fitting: application to the Seyfert galaxy MCG-6-30-15

We propose a method for the flux calibration of reverberation mapping spectra, based on accurate measurement of [O iii] λ5007 emission by spectral fitting. Our method can achieve better accuracy than the traditional method of Groningen and Wanders, allowing reverberation mapping measurements for objects with variability amplitudes as low as ∼5%. As a demonstration, we reanalyze the data of the Seyfert 1 galaxy MCG–6-30-15, taken from the 2008 campaign of the Lick active galactic nucleus monitoring project, which previously failed to obtain a time lag for this weakly variable object, owing to a relatively large flux calibration uncertainty. We detect a statistically significant rest-frame time lag of 6.38{sub −2.69}{sup +3.07} days between the Hβ and V-band light curves. Combining this lag with FWHM(Hβ) = 1933 ± 81 km s{sup −1} and a virial coefficient of f = 0.7, we derive a virial black hole mass of 3.26{sub −1.40}{sup +1.59}×10{sup 6} M {sub ⊙}, which agrees well with previous estimates by other methods.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

A Minimum Variance Algorithm for Overdetermined TOA Equations with an Altitude Constraint.

We present a direct (non-iterative) method for solving for the location of a radio frequency (RF) emitter, or an RF navigation receiver, using four or more time of arrival (TOA) measurements and an assumed altitude above an ellipsoidal earth. Both the emitter tracking problem and the navigation application are governed by the same equations, but with slightly different interpreta- tions of several variables. We treat the assumed altitude as a soft constraint, with a specified noise level, just as the TOA measurements are handled, with their respective noise levels. With 4 or more TOA measurements and the assumed altitude, the problem is overdetermined and is solved in the weighted least squares sense for the 4 unknowns, the 3-dimensional position and time. We call the new technique the TAQMV (TOA Altitude Quartic Minimum Variance) algorithm, and it achieves the minimum possible error variance for given levels of TOA and altitude estimate noise. The method algebraically produces four solutions, the least-squares solution, and potentially three other low residual solutions, if they exist. In the lightly overdermined cases where multiple local minima in the residual error surface are more likely to occur, this algebraic approach can produce all of the minima even when an iterative approach fails to converge. Algorithm performance in terms of solution error variance and divergence rate for bas eline (iterative) and proposed approach are given in tables.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Quantitative soil zymography: Mechanisms, processes of substrate and enzyme diffusion in porous media

Soil membrane zymography enables 2D mapping of enzyme activities on the surface of soil samples. The method is according to diffusion of components of enzymatically-mediated reactions to/from membrane, and, hence, reflects the distribution of enzyme activities at the intact soil surface. Zymography has been already successfully implemented in numerous soil ecology applications. Here we identify two methodological aspects for further improvement and expansion of the method at micro and macro scales: first, accounting for the area of contact between the soil surface and the zymography membranes and, second, accounting for diffusion effects during the zymography procedure. We tested three methods, namely, laser-scanning, staining with a fluorescent product (e.g. MUF: 4-methylumbelliferone), and X-ray computed micro-tomography, for assessing the area of the soil surface in contact with the membranes. We quantified diffusion of MUF, enzymes and substrate between the substrate-saturated membrane and soil as well as diffusion processes during membrane zymography via HP2 software. Diffusion of the substrate from the membrane and of the MUF-product to the membrane was detected, while there were no clear evidence of enzyme diffusion to/in the membrane. According to the model simulations, the enzyme activities detected via 2D zymography probably represent only a small portion, about 20%, of the actual reactions within the soil volume that is in both direct contact and in hydrological contact with zymography membranes. This is a result of omnidirectional diffusion of reaction products. The membrane contact with the soil surface estimated by three methods ranged from 3.4 to 36.5% further signifying that only a fraction of enzymes activity is detectable in a course of 2D soil zymography.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding

The optical spectra of neutral oxygen vacancies (F 0 centers) in the bulk MgO lattice are investigated using density matrix embedding theory. The impurity Hamiltonian is solved with the complete active space self-consistent field and second-order n-electron valence state perturbation theory (NEVPT2-DMET) multireference methods. Here, to estimate defect-localized vertical excitation energies at the nonembedding and thermodynamic limits, a double extrapolation scheme is employed. The extrapolated NEVPT2-DMET vertical excitation energy value of 5.24 eV agrees well with the experimental absorption maxima at 5.03 eV, whereas the excitation energy value of 2.89 eV at the relaxed triplet defect-localized state geometry overestimates the experimental emission at 2.4 eV by only nearly 0.5 eV, indicating the involvement of the triplet–singlet decay pathway.

embedding↗
DOE OSTI2024

An extension of Thwaites’ method for turbulent boundary layers

Thwaites developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations. The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

17 WIND ENERGY↗
DOE OSTI2016

SU-F-T-128: Dose-Volume Constraints for Particle Therapy Treatment Planning

Purpose: Determine equivalent Organ at Risk (OAR) tolerance dose (TD) constraints for MV x-rays and particle therapy. Methods: Equivalent TD estimates for MV x-rays are determined from an isoeffect, regression-analysis of published and in-house constraints for various fractionation schedules (n fractions). The analysis yields an estimate of (α/β) for an OAR. To determine equivalent particle therapy constraints, the MV x-ray TD(n) values are divided by the RBE for DSB induction (RBE{sub DSB}) or cell survival (RBE{sub S}). Estimates of (RBE{sub DSB}) are computed using the Monte Carlo Damage Simulation, and estimates of RBES are computed using the Repair-Misrepair-Fixation (RMF) model. A research build of the RayStation™ treatment planning system implementing the above model is used to estimate (RBE{sub DSB}) for OARs of interest in 16 proton therapy patient plans (head and neck, thorax, prostate and brain). Results: The analysis gives an (α/β) estimate of about 20 Gy for the trachea and heart and 2–4 Gy for the esophagus, spine, and brachial plexus. Extrapolation of MV x-ray constraints (n = 1) to fast neutrons using RBE{sub DSB} = 2.7 are in excellent agreement with clinical experience (n = 10 to 20). When conventional (n > 30) x-ray treatments are used as the reference radiation, fast neutron RBE increased to a maximum of 6. For comparison to a constant RBE of 1.1, the RayStation™ analysis gave estimates of proton RBE{sub DSB} from 1.03 to 1.33 for OARs of interest. Conclusion: The presented system of models is a convenient formalism to synthesize from multiple sources of information a set of self-consistent plan constraints for MV x-ray and hadron therapy treatments. Estimates of RBE{sub DSB} from the RayStation™ analysis differ substantially from 1.1 and vary among patients and treatment sites. A treatment planning system that incorporates patient and anatomy-specific corrections in proton RBE would create opportunities to increase the therapeutic ratio. The research build of the RayStation used in the study was made available to the University of Washington free of charge. RaySearch Laboratories did not provide any monetary support for the reported studies.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Explainable multi-fidelity Bayesian neural network for distribution system state estimation

Distribution System State Estimation (DSSE) is frequently constrained by limited real-time measurements, the uncertainties introduced by distributed energy resources, and the presence of bad data. To address them, this paper proposes an enhanced Multi-Fidelity Bayesian Neural Network (MFBNN) DSSE approach. A low-fidelity layer based on a Deep Neural Network (DNN) is first pre-trained on pseudo-measurement data to learn fundamental state features. Subsequently, a high-fidelity Bayesian Neural Network (BNN) layer leverages limited but high-quality real-time measurements to refine these features, thereby achieving accurate DSSE. Additionally, the deep SHapley Additive exPlanation (SHAP) is developed to quantify the influence of measurement data on DSSE through dual perspectives of global feature importance and local nodal contributions, establishing a hierarchical explainability framework for machine learning-based DSSE. Comparative studies conducted on the IEEE 13-bus system and a real-world 2135-node system from Dominion Energy demonstrate that the proposed method excels in estimation accuracy, even under situations of high noise levels, bad data, and missing data. Further comparisons with Weighted Least Squares (WLS) and other machine learning-based DSSE approaches verify that the proposed framework offers higher accuracy, improved interpretability, and enhanced robustness.

Bad data↗
DOE OSTI2026

Determination of nuclear PDFs using Markov chain Monte Carlo methods

Global QCD analyses of nuclear parton distribution functions (nPDFs) have traditionally relied on the Hessian method for uncertainty estimation. However, the inherent Gaussian approximation and reliance on local curvature often prove insufficient for nPDF fits, which are frequently characterized by limited data constraints and non-Gaussian likelihoods. In this paper, we present the first nPDF determination based on Markov Chain Monte Carlo (MCMC) techniques, implemented within the nCTEQ framework using an adaptive Metropolis-Hastings algorithm. The MCMC approach enables a direct mapping of the posterior distribution and reveals a highly nontrivial parameter-space structure, including multiple modes and pronounced non-Gaussian behavior, particularly for the valence PDFs. We perform the first single-nucleus global analysis of lead PDFs using exclusively lead data and compare it to a multi-nuclei fit employing a standard analytic A dependence. The inclusion of lighter nuclei reduces quark uncertainties and modifies the shape of the lead PDFs, while leaving the gluon distribution largely unaffected. A complementary Hessian analysis exposes systematic limitations of the Gaussian approximation. Our results demonstrate that MCMC methods provide a more reliable framework for uncertainty quantification in nPDF determinations.

Derakhshanian, N. [Institute of Nuclear Physics Po↗