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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Accelerating astronomical and cosmological inference with preconditioned Monte Carlo

ABSTRACT We introduce preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates efficient sampling of probability distributions with non-trivial geometry. PMC utilizes a Normalizing Flow (NF) in order to decorrelate the parameters of the distribution and then proceeds by sampling from the preconditioned target distribution using an adaptive Sequential Monte Carlo (SMC) scheme. The results produced by PMC include samples from the posterior distribution and an estimate of the model evidence that can be used for parameter inference and model comparison, respectively. The aforementioned framework has been thoroughly tested in a variety of challenging target distributions achieving state-of-the-art sampling performance. In the cases of primordial feature analysis and gravitational wave inference, PMC is approximately 50 and 25 times faster, respectively, than nested sampling (NS). We found that in higher dimensional applications, the acceleration is even greater. Finally, PMC is directly parallelisable, manifesting linear scaling up to thousands of CPUs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Bayesian Cross-matching of High Proper-motion Stars in Gaia DR2 and Photometric Metallicities for ∼1.7 million K and M Dwarfs

We present a Bayesian method to cross-match 5,827,988 high proper-motion Gaia sources (μ > 40 mas yr{sup −1}) to various photometric surveys: Two Micron All Sky Survey, AllWISE data release from the Wide-field Infrared Explorer (WISE) mission, Galaxy Evolution Explorer, Radial Velocity Experiment, Sloan Digital Sky Survey, and Panoramic Survey Telescope and Rapid Response System (Pan-STARRS). To efficiently associate these objects across catalogs, we develop a technique that compares the multidimensional distribution of all sources in the vicinity of each Gaia star to a reference distribution of random field stars obtained by extracting all sources in a region on the sky displaced 2′. This offset preserves the local field stellar density and magnitude distribution, allowing us to characterize the frequency of chance alignments. The resulting catalog with Bayesian probabilities >95% has a marginally higher match rate than current internal Gaia data release 2 (DR2) matches for most catalogs. However, a significant improvement is found with Pan-STARRS, where ∼99.8% of the sample within the Pan-STARRS footprint is recovered, as compared to a low ∼20.8% in Gaia DR2. Using these results, we train a Gaussian process regressor to calibrate two photometric metallicity relationships. For dwarfs of 3500 < T{sub eff} < 5280 K, we use metallicity values of 4378 stars from the Apache Point Observatory Galactic Evolution Experiment and Hejazi et al. to calibrate the relationship, producing results with a 1σ precision of 0.12 dex and few systematic errors. We then indirectly infer the metallicity of 4018 stars with 2850 < T{sub eff} < 3500 K, which are wide companions of primaries whose metallicities are estimated with our first regressor, to produce a relationship with a 1σ precision of 0.21 dex and significant systematic errors. Additional work is needed to better remove unresolved binaries from this second sample to reduce these systematic errors.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Measuring cosmological distances using cluster edges as a standard ruler

ABSTRACT The line-of-sight velocity dispersion profile of galaxy clusters exhibits a ‘kink’ corresponding to the spatial extent of orbiting galaxies. Because the spatial extent of a cluster is correlated with the amplitude of the velocity dispersion profile, we can utilize this feature as a gravity-calibrated standard ruler. Specifically, the amplitude of the velocity dispersion data allows us to infer the physical cluster size. Consequently, observations of the angular scale of the ‘kink’ in the profile can be translated into a distance measurement to the cluster. Assuming the relation between cluster radius and cluster velocity dispersion can be calibrated from simulations, we forecast that with existing data from the Sloan Digital Sky Survey we will be able to measure the Hubble constant with 3.0 per cent precision. Implementing our method with data from the Dark Energy Spectroscopic Instrument (DESI) will result in a 1.3 per cent measurement of the Hubble constant. Adding cosmological supernova data improves the uncertainty of the DESI measurement to 0.7 per cent. While these error estimates are statistical only, they provide strong motivation for pursuing the necessary simulation program required to characterize and calibrate the systematic uncertainties impacting our proposed measurement. Whether or not our proposed measurement can in fact result in competitive H0 constraints will depend on what the eventual systematics floor for this method is.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Evaluating cosmological biases using photometric redshifts for Type Ia Supernova cosmology with the Dark Energy Survey Supernova Program

Cosmological analyses with Type Ia Supernovae (SNe Ia) have traditionally been reliant on spectroscopy for both classifying the type of supernova and obtaining reliable redshifts to measure the distance–redshift relation. While obtaining a host-galaxy spectroscopic redshift for most SNe is feasible for small-area transient surveys, it will be too resource intensive for upcoming large-area surveys such as the Vera Rubin Observatory Legacy Survey of Space and Time, which will observe on the order of millions of SNe. Here, we use data from the Dark Energy Survey (DES) to address this problem with photometric redshifts (photo-z) inferred directly from the SN light curve in combination with Gaussian and full p(z) priors from host-galaxy photo-z estimates. Using the DES 5-yr photometrically classified SN sample, we consider several photo-z algorithms as host-galaxy photo-z priors, including the Self-Organizing Map redshifts (SOMPZ), Bayesian Photometric Redshifts (BPZ), and Directional-Neighbourhood Fitting (DNF) redshift estimates employed in the DES 3 × 2 point analyses. With detailed catalogue-level simulations of the DES 5-yr sample, we find that the simulated w can be recovered within ±0.02 when using SN+SOMPZ or DNF prior photo-z, smaller than the average statistical uncertainty for these samples of 0.03. With data, we obtain biases in w consistent with simulations within ~1σ for three of the five photo-z variants. We further evaluate how photo-z systematics interplay with photometric classification and find classification introduces a subdominant systematic component. This work lays the foundation for next-generation fully photometric SNe Ia cosmological analyses.

(cosmology:) dark energy↗
DOE OSTI2026

An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

We present a simple analytic approximation for the covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction two-point correlation functions. This cross-covariance is essential for joint analyses that combine full-shape clustering information with baryon acoustic oscillation (BAO) measurements, as commonly performed in modern spectroscopic surveys. Our model builds on the disconnected contribution to the covariance and accounts for the damping of correlations due to the BAO reconstruction process. We validate our analytic prescription against numerical simulations from the Dark Energy Spectroscopic Instrument (DESI), testing both idealized cubic geometries and realistic survey configurations including complex footprints and fiber assignment effects. Despite neglecting survey window functions in the analytic calculation, we find excellent agreement with simulation-based covariances and demonstrate that cosmological parameter constraints are virtually unchanged when using our approximation. Our results show that the pre-post cross-covariance is sufficiently small that even approximate treatments are adequate for cosmological inference, opening a pathway toward fully analytic covariance matrices for next-generation galaxy surveys.

baryon acoustic oscillations↗
DOE OSTI2023

Variational deep learning of equilibrium transition path ensembles

Here, we present a time-dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off of the variational path sampling methodology by approximating the time-dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems, and in the isomerization of a solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics and gain unique insights into transitions through the analysis of their commitment probability.

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

Exploring physics of ferroelectric domain walls via Bayesian analysis of atomically resolved STEM data

The physics of ferroelectric domain walls is explored using the Bayesian inference analysis of atomically resolved STEM data. We demonstrate that domain wall profile shapes are ultimately sensitive to the nature of the order parameter in the material, including the functional form of Ginzburg-Landau-Devonshire expansion, and numerical value of the corresponding parameters. The preexisting materials knowledge naturally folds in the Bayesian framework in the form of prior distributions, with the different order parameters forming competing (or hierarchical) models. Here, we explore the physics of the ferroelectric domain walls in BiFeO 3 using this method, and derive the posterior estimates of relevant parameters. More generally, this inference approach both allows learning materials physics from experimental data with associated uncertainty quantification, and establishing guidelines for instrumental development answering questions on what resolution and information limits are necessary for reliable observation of specific physical mechanisms of interest.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Evaluation of data driven low-rank matrix factorization for accelerated solutions of the Vlasov equation

Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization method using artificial neural networks, specifically with convolutional layer architecture, that trains on existing simulation data. At inference time, the model outputs a low-rank decomposition of the distribution field of the charged particles, and we demonstrate that this step is faster than the standard linear algebra technique. Numerical experiments show that the method achieves comparable reconstruction accuracy for interpolation tasks, generalizing to unseen test data in a manner beyond just memorizing training data; patterns in factorization also inherently followed the same numerical trend as those within algebraic methods (e.g., truncated singular-value decomposition). However, when training on the first 70% of a time-series data and testing on the remaining 30%, the method fails to meaningfully extrapolate. Despite this limiting result, the technique may have benefits for simulations in a statistical steady-state or otherwise showing temporal stability. These results suggest that while the model offers a computationally efficient alternative for datasets with temporal stability, its current formulation is best suited for interpolation rather than for predicting future states in time-evolving systems. This study thus lays the groundwork for further refinement of neural network-based approaches to low-rank matrix factorization in high-dimensional plasma simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Feature-agnostic metabolomics for determining effective subcytotoxic doses of common pesticides in human cells

Although classical molecular biology assays can provide a measure of cellular response to chemical challenges, they rely on a single biological phenomenon to infer a broader measure of cellular metabolic response. These methods do not always afford the necessary sensitivity to answer questions of subcytotoxic effects, nor do they work for all cell types. Likewise, boutique assays such as cardiomyocyte beat rate may indirectly measure cellular metabolic response, but they too, are limited to measuring a specific biological phenomenon and are often limited to a single cell type. For these reasons, toxicological researchers need new approaches to determine metabolic changes across various doses in differing cell types, especially within the low-dose regime. Here, the data collected herein demonstrate that LC-MS/MS-based untargeted metabolomics with a feature-agnostic view of the data, combined with a suite of statistical methods including an adapted environmental threshold analysis, provides a versatile, robust, and holistic approach to directly monitoring the overall cellular metabolomic response to pesticides. When employing this method in investigating two different cell types, human cardiomyocytes and neurons, this approach revealed separate subcytotoxic metabolomic responses at doses of 0.1 and 1 µM of chlorpyrifos and carbaryl. These findings suggest that this agnostic approach to untargeted metabolomics can provide a new tool for determining effective dose by metabolomics of chemical challenges, such as pesticides, in a direct measurement of metabolomic response that is not cell type-specific or observable using traditional assays.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Toward In Situ Synchrotron Mapping of Crystal Selection Processes during Crystal Growth

In this work, we present an automated and rapid method for non-destructive mapping of crystal grains in a rod-shaped sample. The approach was designed for application to in situ float-zone crystal growth experiments at an x-ray synchrotron source, but could be useful in other applications. The methods have been tested on a TiO 2 boule grown in an optical float zone furnace. The approach applies a statistical filter to polycrystalline diffraction patterns on 2D detectors to rapidly determine the degree of powder-quality 1of the signal. When larger crystals emerge in the growth, their position, size and shape can be tracked using an automated blob-tracking algorithm that follows individual Bragg peaks as a function of position in a grid-scan, even when multiple crystals are contributing spots to diffraction images. This method is found to be robust as the same crystal shape can be independently reconstructed using different sets of Bragg reflections. Image segmentation methods are then used to map out the polycrystalline grains. We also note that other information about crystal quality, such as mosaicity or strain state, may be inferred and mapped from the intensity variation of the Bragg peaks at different locations within the sample.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Identification of drug repurposing candidates for amyotrophic lateral sclerosis using electronic health records: a retrospective cohort study

Amyotrophic lateral sclerosis (ALS) is a progressive neurodegenerative disease with a life expectancy of only 3–5 years and few approved treatments. To identify drug repurposing candidates for the treatment of ALS, we analysed the electronic health records (EHRs) of a large cohort of military veterans with ALS. We analysed the EHRs of individuals in the US Veterans Health Administration (VHA) database who were diagnosed with ALS between Jan 1, 2009 and Dec 31, 2019 to assess medication effects. Individuals without recorded prescriptions after the date of diagnosis were excluded. Two sets of criteria were applied to ascertain exposure. Exposure criteria A were met if the dispense date or the end date of the medication was within 12 months of ALS diagnosis and the end date was at least 6 months after the dispense date. Exposure criteria B were met if there were at least two dispenses within 6 months before diagnosis and 12 months after diagnosis. Propensity score-matched control groups were generated on the basis of confounders included in the EHR, with methodology of potential outcomes used to infer treatment effects. The primary outcome was death. A standard Cox proportional hazards analysis was done to assess association with survival. Survival was defined as the time from diagnosis date recorded in the EHR to death reported in the Department for Veterans Affairs Vital Status File. Follow-up survival time was censored on Dec 31, 2020, for those alive on this date. Downstream protein targets of drugs with clinically significant effects were analysed using the protein–protein interaction networks-based algorithm PathFX. The EHRs of 11 003 individuals with ALS in the VHA database were appropriate for analysis. 162 medications with treatment groups of 30 or more individuals were identified. Among these 162 medications, 27 were associated with statistically significant changes (≥0·1) in the hazard ratio (HR) for death. 18 of the medications were associated with a reduced HR for death (prolonged survival), and nine were associated with an increased HR for death (reduced survival). Drugs associated with reduced HR included HMG-CoA reductase inhibitors (simvastatin, pravastatin, lovastatin, and atorvastatin), PDE5 inhibitors (vardenafil and sildenafil), and α-adrenergic antagonists (tamsulosin and terazosin). The medications associated with an increased HR were drugs used either in the management of clinical features of ALS associated with poor outcomes or in end-of-life care. PathFx analysis identified a complex of proteins interacting with several of the identified drugs. To our knowledge, this analysis is the largest EHR-based study for identifying drug repurposing candidates for ALS. We identified several drugs that warrant further assessment as therapeutic options in ALS, as well as a protein network complex that might serve as a therapeutic target for ALS.

Reimer, Richard J. [Stanford Univ., CA (United Sta↗
DOE OSTI2020

A measurement of the Hubble constant from Type II supernovae

ABSTRACT Progressive increases in the precision of the Hubble-constant measurement via Cepheid-calibrated Type Ia supernovae (SNe Ia) have shown a discrepancy of ∼4.4σ with the current value inferred from Planck satellite measurements of the cosmic microwave background radiation and the standard $\Lambda $cold dark matter (ΛCDM) cosmological model. This disagreement does not appear to be due to known systematic errors and may therefore be hinting at new fundamental physics. Although all of the current techniques have their own merits, further improvement in constraining the Hubble constant requires the development of as many independent methods as possible. In this work, we use SNe II as standardisable candles to obtain an independent measurement of the Hubble constant. Using seven SNe II with host-galaxy distances measured from Cepheid variables or the tip of the red giant branch, we derive H$_0= 75.8^{+5.2}_{-4.9}$ km s−1 Mpc−1 (statistical errors only). Our value favours that obtained from the conventional distance ladder (Cepheids + SNe Ia) and exhibits a difference of 8.4 km s−1 Mpc−1 from the Planck + ΛCDM value. Adding an estimate of the systematic errors (2.8 km s−1 Mpc−1) changes the ∼1.7σ discrepancy with Planck +ΛCDM to ∼1.4σ. Including the systematic errors and performing a bootstrap simulation, we confirm that the local H0 value exceeds the value from the early Universe with a confidence level of 95 per cent. As in this work, we only exchange SNe II for SNe Ia to measure extragalactic distances, we demonstrate that there is no evidence that SNe Ia are the source of the H0 tension.

de Jaeger, T.↗
DOE OSTI2026

Modeling the Cosmological Lyman-𝛼 Forest at the Field Level

The distribution of absorption lines in the spectra of distant quasars, called the Lyman-𝛼 (Ly-𝛼) forest, is a unique probe of cosmology and the intergalactic medium at high redshifts and small scales. The statistical power of ongoing redshift surveys demands precise theoretical tools to model the Ly-𝛼 forest. We address this challenge by developing an analytic, perturbative forward model to predict the Ly-𝛼 forest at the field level for a given set of cosmological initial conditions. Our model shows a remarkable performance when compared with the Sherwood hydrodynamic simulations: it reproduces the Ly-𝛼 forest flux power spectrum, its cross-correlation with dark matter halos, and the one-point probability distribution function of both fields at the percent level down to scales of a few Mpc. Our work provides crucial tools that bridge analytic modeling on large scales with simulations on small scales, enabling field-level inference from Ly-𝛼 forest data and simulation-based priors for cosmological analyses. Furthermore, this is especially timely for realizing the full scientific potential of the Ly-𝛼 forest measurements by the dark energy spectroscopic instrument.

Cosmological parameters↗
DOE OSTI2026

Peering down the barrel with DESI DR2: 10 000+ inflows at $z$ < 0.6 reveal how galaxies accrete cold gas

Direct observational constraints on how galaxies acquire their gas remain remarkably limited, hindering our understanding of the baryon cycle. We present a search for down-the-barrel NaI D absorption towards 15.6 million galaxies at $z < 0.6$ in DESI Data Release 2. We use Bayesian evidence ratios to assess whether the absorption requires additional components tracing interstellar gas distinct from the systemic component of the galaxy. We construct a catalogue of 50 088 (27 420) galaxies with moderate (strong) evidence for down-the-barrel absorption. The inferred absorption components are broadly distributed in velocity, with approximately 50% at $v_{\rm flow} < -50$ km/s, 30% within 50 km/s of the systemic velocity and the remaining 20% at $v_{\rm flow} > 50$ km/s. We find strong evidence for a large population of low-velocity, infalling absorbers with velocities $\sim$20 km/s in edge-on galaxies, consistent with radial inflows predicted in simulations. The stronger correlation in early-type galaxies between inflow velocity and stellar velocity dispersion, compared to that with stellar mass, suggests that a portion of these inflows may be associated with accreting satellites. These results reveal the multiple pathways in which galaxies accrete gas at redshift $z < 0.6$ for the first time in a statistically significant sample.

Weng, S. [Marseille, Lab. Astrophys.]↗
DOE OSTI2020

TDCOSMO - IV. Hierarchical time-delay cosmography – joint inference of the Hubble constant and galaxy density profiles

The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H0 = 73.3−1.8+1.7 km s−1 Mpc−1, describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in H0. We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H0. Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H0 = 74.5−6.1+5.6 km s−1 Mpc−1. Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H0 = 67.4−3.2+4.1 km s−1 Mpc−1. This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H0. While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data.Key words: gravitational lensing: strong / galaxies: general / galaxies: kinematics and dynamics / distance scale / cosmological parameters / cosmology: observations⋆ The full analysis is available at https://github.com/TDCOSMO/hierarchy_analysis_2020_public.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

T -matrix analysis of static Wilson line correlators from lattice QCD at finite temperature

Here, we utilize a previously constructed thermodynamic T -matrix approach to the quark-gluon plasma (QGP) to derive constaints on its input by using results on Wilson line correlators (WLCs) of a static quark-antiquark pair from 2 + 1-flavor lattice-QCD (lQCD) computations with realistic pion mass. The self-consistent T -matrix results, which include previous constraints from the lQCD equation of state in the light-parton sector, can describe the lQCD data for WLCs fairly well once refinements of its driving kernel are applied. In particular, the input potential requires less screening than what has been inferred from previous T-matrix analyses. Pertinent predictions for the spectral and transport properties of the QGP are discussed, including the spatial diffusion coefficient for heavy quarks; the latter turns out to have a rather weak temperature dependence, in approximate agreement with recent unquenched lQCD results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Small angle scattering of diblock copolymers profiled by machine learning

We outline a machine learning strategy for quantitively determining the conformation of AB-type diblock copolymers with excluded volume effects using small angle scattering. Complemented by computer simulations, a correlation matrix connecting conformations of different copolymers according to their scattering features is established on the mathematical framework of a Gaussian process, a multivariate extension of the familiar univariate Gaussian distribution. We show that the relevant conformational characteristics of copolymers can be probabilistically inferred from their coherent scattering cross sections without any restriction imposed by model assumptions. This work not only facilitates the quantitative structural analysis of copolymer solutions but also provides the reliable benchmarking for the related theoretical development of scattering functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗