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DOE OSTI2026

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗

DOE OSTI2025

Dark Energy Survey Year 3 Results: Cosmological constraints from second- and third-order shear statistics

Here, we present a cosmological analysis of the third-order aperture mass statistic using Dark Energy Survey Year 3 (DES Y3) data. We perform a complete tomographic measurement of the three-point correlation function of the Y3 weak lensing shape catalog with the four fiducial source redshift bins. Building upon our companion methodology paper, we apply a pipeline that combines the two-point function ξ ± with the mass aperture skewness statistic ⟨ M ap 3 ⟩ , which is an efficient compression of the full shear three-point function. We use a suite of simulated shear maps to obtain a joint covariance matrix. By jointly analyzing ξ ± and ⟨ M ap 3 ⟩ measured from DES Y3 data with a Λ CDM model, we find S 8 = 0.780 ± 0.015 and Ω m = 0.26 6 - 0.040 + 0.039 , yielding 111% of figure-of-merit improvement in the Ω m - S 8 plane relative to ξ ± alone, consistent with expectations from simulated likelihood analyses. With a w CDM model, we find S 8 = 0.74 9 - 0.026 + 0.027 and w 0 = - 1.39 ± 0.31 , which gives an improvement of 22% on the joint S 8 - w 0 constraint. Our results are consistent with w 0 = - 1 . Our new constraints are compared to CMB data from the Planck satellite, and we find that with the inclusion of ⟨ M ap 3 ⟩ the existing tension between the datasets is at the level of 2.3 σ . We show that the third-order statistic enables us to self-calibrate the mean photometric redshift uncertainty parameter of the highest redshift bin with little degradation in the figure of merit. Our results demonstrate the constraining power of higher-order lensing statistics and establish ⟨ M ap 3 ⟩ as a practical observable for joint analyses in current and future surveys.

Gomes, R. C. H. [University of Pennsylvania] (ORCI↗

DOE OSTI2025

Statistical analysis of the performance and long-term stability of unquenched LSC standards ( 3 H, 14 C) used for radiochemical measurements

Multiple sets of toluene-based unquenched standards, procured over the last 3 decades, were analyzed to determine their stability over time. A statistical analysis was performed to provide insight into the variability for tSIE and counting efficiency measurements of 3 H and 14 C isotopes. Our data suggests that standards remain viable even 30 years after the manufacturer’s recommended expiration date. Overall, these standards have shown no statistically significant sign of performance degradation. We have proven through statistical analysis that these standards can provide comparable performance over time well past their manufactured expiration date.

LSC standards↗

DOE OSTI2026

Statistical generic design of glass and optimization: Selective review on oxide glasses

Designing a single glass composition for a multidimensional property space is challenging, and the difficulty increases with the number of design criteria. Traditionally, the task is accomplished using multiple statistical models that describe the relationships between composition (C) and property (P) values, i.e., C-P models. Recently, the structure (S)-property (P) statistical modeling has emerged as a complementary approach. The S-P modeling approach has also been shown to be a preferred method for modeling glass properties, particularly when a small data set is available, such as in single-component studies, or when strong nonlinearities exist between composition and properties. The combined model package, C-S-P, implements the concept of generic glass design, i.e., designing glass for performance by first selecting a specific or optimized set of glass network structural groups using S-P models and then transferring the designed structures (genes) to a particular composition using C-S models. This article reviews a set of supporting cases from the previous C-S-P modeling studies of phosphate, silicate, and borosilicate glasses, which are relevant for many critical commercial applications. The methodology for developing the statistical C-S-P database is presented, enabling the application of P?S?C to achieve a generic glass design and optimization, targeting multiple design criteria for both performance and processing properties simultaneously.

Network structure↗

DOE OSTI2024

Rapid measurement of soluble xylo-oligomers using near-infrared spectroscopy (NIRS) and multivariate statistics: calibration model development and practical approaches to model optimization

Rapid monitoring of biomass conversion processes using techniques such as near-infrared (NIR) spectroscopy can be substantially quicker and less labor-, resource-, and energy-intensive than conventional measurement techniques such as gas or liquid chromatography (GC or LC) due to the lack of solvents and preparation methods, as well as removing the need to transfer samples to an external lab for analytical evaluation. The purpose of this study was to determine the feasibility of rapid monitoring of a biomass conversion process using NIR spectroscopy combined with multivariate statistical modeling, and to examine the impact of (1) subsetting the samples in the original dataset by process location and (2) reducing the spectral range used in the calibration model on model performance. We develop multivariate calibration models for the concentrations of soluble xylo-oligosaccharides (XOS), monomeric xylose, and total solids at multiple points in a biomass conversion process which produces and then purifies XOS compounds from sugar cane bagasse. A single model using samples from multiple locations in the process stream showed acceptable performance as measured by standard statistical measures. However, compared to the single model, we show that separate models built by segregating the calibration samples according to process location show improved performance. We also show that combining an understanding of the sample spectra with simple multivariate analysis tools can result in a calibration model with a substantially smaller spectral range that provides essentially equal performance to the full-range model. We demonstrate that real-time monitoring of soluble xylo-oligosaccharides (XOS), monomeric xylose, and total solids concentration at multiple points in a process stream using NIR spectroscopy coupled with multivariate statistics is feasible. Segregation of sample populations by process location improves model performance. Models using a reduced spectral range containing the most relevant spectral signatures show very similar performance to the full-range model, reinforcing the importance of performing robust exploratory data analysis before beginning multivariate modeling.

09 BIOMASS FUELS↗

DOE OSTI2024

Statistically-driven Experimental Design to Improve Reference-free Quantification of Small Molecules by Liquid Chromatography-Mass Spectrometry

Non-targeted analysis of small molecules and metabolites in unknown, complex samples using liquid chromatography-tandem mass spectrometry remains challenging. One of the main bottlenecks is the extensive unannotated regions of metabolomics mass spectrometry data, resulting in knowledge gaps. Small molecule annotation in mass spectrometry data has conventionally relied on reference standards and libraries for compound identification and confirmation, which can constrain compound identification to those molecules already known, thus limiting the ability to discover new knowledge and new markers. Retention time prediction can facilitate and expedite unknown compound identification in non-targeted analysis of complex metabolomics samples. Additionally, accurate retention time predictions can also inform sample mixture design for LC-MS/MS analyses. However, current machine learning-based methods for retention time prediction are typically developed for specific chromatographic platforms and are not generalizable across scales. And while technologies and methods to improve reference-free metabolite identification for more comprehensive annotation of unknowns has received much attention, development of the same for quantitation without reference standards has been much more limited, despite its importance in toxicological, environmental, food safety, forensics, and clinical applications. We believe that a reference-free quantitation strategy that exploits mass spectrometry data already collected for reference-free identification can provide much more insight on unknowns, and move the metabolomics field for more complete unknowns characterization. As such, we pursue two efforts to improve upon current state-of-the-art methods in non-targeted analysis: (1) machine learning-based retention time prediction and (2) statistical design of experiments framework for reference-free quantitation. In this work, we develop and demonstrate (1) a generalizable retention time prediction capability across chromatographic conditions and scales, and (2) a statistical design-based framework for response factor contribution elucidation and reference-free quantitation. Evaluation of our retention time prediction model, PrediToR, showed approximately 24% improvement over current models, and we observed approximately 10X improvement in concentration estimation accuracy from our statistical design-based response factor model over a primarily ionization efficiency-based model. We expect that future efforts to improve upon these new capabilities will further advance non-targeted analysis of small molecules towards truly reference-free metabolomics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Statistics of base polytopes in F-theory

We propose a new statistical ensemble of toric bases for elliptic Calabi-Yaus used in F-theory models, by focusing on only the convex hull of the base, i.e., the base polytope. This physically motivated coarse-graining greatly simplifies the combinatorial complexity of the part of the 4d F-theory landscape with toric bases. We develop a Monte Carlo approach that randomly samples the base polytopes within fixed boxes, with proper statistical weights. We first apply the algorithm to the set of 2d base polytopes, generating an enlarged set of toric 2d bases that include certain types of codimension-two (4,6) points, and we validate our approach against exact numbers. We then explore the set of 3d base polytopes which fit in a set of “maximal” 3d boxes, and estimate the total number of inequivalent 3d base polytopes to be 10 85 –10 90 . We provide statistical data such as the distribution of non-Higgsable gauge groups on these bases. Amusingly, a similar method can also be applied to generate reflexive polytopes in various dimensions. In both the reflexive and base polytope cases, the number of relevant polytopes obeys a Gaussian distribution as a function of the number of vertices, which can be understood in terms of other results on random polytopes in the math literature.

Differential and algebraic geometry↗

DOE OSTI2025

Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime

Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.

36 MATERIALS SCIENCE↗

DOE OSTI2024

On the statistical theory of self-gravitating collisionless dark matter flow: High order kinematic and dynamic relations

Dark matter, if it exists, accounts for five times as much as ordinary baryonic matter. To better understand the self-gravitating collisionless dark matter flow on different scales, a statistical theory involving kinematic and dynamic relations must be developed for different types of flow, e.g., incompressible, constant divergence, and irrotational flow. This is mathematically challenging because of the intrinsic complexity of dark matter flow and the lack of a self-closed description of flow velocity. Here, this paper extends our previous work on second-order statistics Xu to kinematic relations of any order for any type of flow. Dynamic relations were also developed to relate statistical measures of different orders. The results were validated by N-body simulations. On large scales, we found that (i) third-order velocity correlations can be related to density correlation or pairwise velocity; (ii) the pth-order velocity correlations follow ∝ a (p+2)/2 for odd p and ∝ a p/2 for even p, where a is the scale factor; (iii) the overdensity δ is proportional to density correlation on the same scale, $\langle$δ$\rangle$∝$\langle$δδ'$\rangle$; (iv) velocity dispersion on a given scale r is proportional to the overdensity on the same scale. On small scales, (i) a self-closed velocity evolution is developed by decomposing the velocity into motion in haloes and motion of haloes; (ii) the evolution of vorticity and enstrophy are derived from the evolution of velocity; (iii) dynamic relations are derived to relate second- and third-order correlations; (iv) while the first moment of pairwise velocity follows $\langle$Δu L $\rangle$=-Har (H is the Hubble parameter), the third moment follows $\langle$(Δu L ) 3 $\rangle$ ∝ ε u ar that can be directly compared with simulations and observations, where ε u ≈ 10 -7 m 2 /s 3 is the constant rate for energy cascade; (v) the pth order velocity correlations follow ∝ a (3p-5)/4 for odd p and ∝ a 3p/4 for even p. Finally, the combined kinematic and dynamic relations lead to exponential and one-fourth power-law velocity correlations on large and small scales, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Impact of classical statistics on thermal conductivity predictions of BAs and diamond using machine learning molecular dynamics

Machine learning interatomic potentials (MLIPs) have greatly enhanced molecular dynamics (MD) simulations, achieving near-first-principles accuracy in thermal conductivity studies. In this work, we reveal that this accuracy, observed in BAs and diamond at sub-Debye temperatures, stems from an accidental error cancelation: classical statistics overestimates specific heat while underestimating phonon lifetimes, balancing out in thermal conductivity predictions. However, this balance is disrupted when isotopes are introduced, leading MLIP-based MD to significantly underpredict thermal conductivity compared to experiments and quantum statistics-based Boltzmann transport equation. This discrepancy arises not from classical statistics affecting phonon–isotope scattering rates but from its impact on the interplay between phonon–isotope and phonon–phonon scattering in the normal scattering-dominated BAs and diamond. In conclusion, this work underscores the limitations of MLIP-based MD for thermal conductivity studies at sub-Debye temperatures.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Map-level baryonification: unified treatment of weak lensing two-point and higher-order statistics

Precision cosmology benefits from extracting maximal information from cosmic structures, motivating the use of higher-order statistics (HOS) at small spatial scales. However, predicting how baryonic processes modify matter statistics at these scales has been challenging. The baryonic correction model (BCM) addresses this by modifying dark-matter-only simulations to mimic baryonic effects, providing a flexible, simulation-based framework for predicting both two-point and HOS. We show that a 3-parameter version of the BCM can jointly fit weak lensing maps' two-point statistics, wavelet phase harmonics coefficients, scattering coefficients, and the third and fourth moments to within 2% accuracy across all scales ℓ < 2000 and tomographic bins for a DES-Y3-like redshift distribution ( z ≲ 2), using the FLAMINGO simulations. These results demonstrate the viability of BCM-assisted, simulation-based weak lensing inference of two-point and HOS, paving the way for robust cosmological constraints that fully exploit non-Gaussian information on small spatial scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Dark energy survey year 3 results: likelihood-free, simulation-based w CDM inference with neural compression of weak-lensing map statistics

We present simulation-based cosmological wcold dark matter (wCDM) inference using dark energy survey year 3 weak-lensing maps, via neural data compression of weak-lensing map summary statistics: power spectra, peak counts, and direct map-level compression/inference with convolutional neural networks (CNN). Using simulation-based inference, also known as likelihood-free or implicit inference, we use forward-modelled mock data to estimate posterior probability distributions of unknown parameters. This approach allows all statistical assumptions and uncertainties to be propagated through the forward-modelled mock data; these include sky masks, non-Gaussian shape noise, shape measurement bias, source galaxy clustering, photometric redshift uncertainty, intrinsic galaxy alignments, non-Gaussian density fields, neutrinos, and non-linear summary statistics. We include a series of tests to validate our inference results. This paper also describes the Gower Street simulation suite: 791 full-sky pkdgrav3 dark matter simulations, with cosmological model parameters sampled with a mixed active-learning strategy, from which we construct over 3000 mock dark energy survey lensing data sets. For wCDM inference, for which we allow –1 < w < –$\frac{1}{3}$⁠, our most constraining result uses power spectra combined with map-level (CNN) inference. Using gravitational lensing data only, this map-level combination gives Ω m = 0.283$^{+0.020}_{–0.027}$⁠, S 8 = 0.804$^{+0.025}_{–0.017⁠}$, and w < –0.80 (with a 68 per cent credible interval); compared to the power spectrum inference, this is more than a factor of two improvement in dark energy parameter (Ω⁠ DE , w⁠) precision.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Cosmology with second- and third-order shear statistics for the Dark Energy Survey: Methods and simulated analysis

We present a new pipeline designed for the robust inference of cosmological parameters using both second- and third-order shear statistics. We build a theoretical model for rapid evaluation of three-point correlations using our fastnc code and integrate it into the cosmosis framework. We measure the two-point functions 𝜉 ± and the full configuration-dependent three-point shear correlation functions across all auto- and cross-redshift bins. We compress the three-point functions into the mass aperture statistic ⟨ℳ$^{3}_{ap}$⟩ for a set of 796 simulated shear maps designed to model the Dark Energy Survey Year 3 data. We estimate from it the full covariance matrix and model the effects of intrinsic alignments, shear calibration biases and photometric redshift uncertainties. We apply scale cuts to minimize the contamination from the baryonic signal as modeled through hydrodynamical simulations. We find a significant improvement of 83% on the figure of merit in the Ω m − 𝑆 8 plane when we add the ⟨ℳ$^{3}_{ap}$⟩ data to 𝜉 ± . Here, we present our findings for all relevant cosmological and systematic uncertainty parameters and discuss the complementarity of third-order and second-order statistics.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Improving statistical precision in Monte Carlo samples with negative weights via reweighting and uncertainty quantification

High statistical precision is critical for Monte Carlo (MC) samples in high energy physics and is degraded by negatively weighted events. This paper investigates a procedure to learn the relationship between the negative and positive weight distributions of any sample, allowing the reduction of statistical uncertainty by reweighting kinematically equivalent events with the same sign. A robust uncertainty quantification method is required for the practical application of such method. Two methods for the estimation of the reweighting uncertainty are developed: one at the event and another one at the final observable level. The latter method is strongly favored. The gains in statistical precision are then quantified. The method is demonstrated on Sherpa vector boson plus jets samples when using all generated events and when restricted to the signal region of a mock analysis. It is demonstrated to significantly reduce stochastic behavior in sparse MC samples while decreasing the overall uncertainty with a sufficiently well-known reweighting function.

Monte Carlo methods↗

DOE OSTI2024

Divide and conquer: using RhizoVision Explorer to aggregate data from multiple root scans using image concatenation and statistical methods

Roots are important in agricultural and natural systems for determining plant productivity and soil carbon inputs. Sometimes, the amount of roots in a sample is too much to fit into a single scanned image, so the sample is divided among several scans, and there is no standard method to aggregate the data. Here, we describe and validate two methods for standardizing measurements across multiple scans: image concatenation and statistical aggregation. We developed a Python script that identifies which images belong to the same sample and returns a single, larger concatenated image. These concatenated images and the original images were processed with RhizoVision Explorer, a free and open-source software. An R script was developed, which identifies rows of data belonging to the same sample and applies correct statistical methods to return a single data row for each sample. These two methods were compared using example images from switchgrass, poplar, and various tree and ericaceous shrub species from a northern peatland and the Arctic. Most root measurements were nearly identical between the two methods except median diameter, which cannot be accurately computed by statistical aggregation. We believe the availability of these methods will be useful to the root biology community.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Multidimensional scaling informed by F -statistic: Visualizing grouped microbiome data with inference

Multidimensional scaling (MDS) is a widely used dimensionality reduction technique in microbial ecology data analysis that captures the multivariate structure of the data while preserving pairwise distances between samples. While improvements in MDS have enhanced the ability to reveal group-specific data patterns, these MDS-based methods require prior assumptions for inference, limiting their application in general microbiome analysis. Here, in this study, we introduce a new MDS-based ordination method, “F-informed MDS,” which configures the data distribution based on the F-statistic, the ratio of dispersion between groups sharing common and different characteristics. Using semisynthetic datasets, we demonstrate that the proposed method is robust to hyperparameter selection while maintaining statistical significance throughout the ordination process. Various quality metrics for evaluating dimensionality reduction confirm that F-informed MDS is comparable to state-of-the-art methods in preserving both local and global data structures. Its application to a diatom-associated bacterial community suggests the role of this new method in interpreting the community’s response to the host. Our approach offers a well-founded refinement of MDS that aligns with statistical test results, which can be beneficial for broader multidimensional data analyses in microbiology and ecology. This new visualization tool can be incorporated into standard microbiome data analyses.

Biological and medical sciences↗

DOE OSTI2025

Hot Droughts and Forest Tree Dynamics in the Amazon - Statistical Models, Scripts, Data, and Outputs

This package contains data, outputs, equations, and R scripts for analyses for manuscript entitled "Hot droughts in the Amazon: A window to a future hypertropical climate" by J. Chambers et al., in particular it contains statistical models and analyses for the INPA BIONTE tree mortality study. The Models folder contains details for all statistical models in PDF files. The Scripts folder contains the R scripts for Bayesian Hierarchical Models (two text files) and SEMs (one text file) are separate and reasonably annotated. All data associated with these scripts are in the data folder. The Data folder contains two of the three CSV files used for the analyses and are called by the R scripts. Two of them are part of published datasets (`BIONTE_mortality-rates.csv` from Lima et al. 2024, DOI:10.15486/ngt/1898910 and `SPEI.csv` from Pastorello et al. 2023 DOI:10.15486/ngt/1958257) and also provided in this package for convenience (please see the corresponding datasets for usage and citation terms). The third dataset (`BIONTE_gapfilled_wd.csv`) contains sensitive information and can be obtained by contacting the manuscript lead author. The Outputs folder contains the two output files that provide extra information about the analyses. The file `figuresFeb2025d.pdf` contains all the figures from the manuscript - captions are in the manuscript. The file `ChambersMS.pdf` contains primary results from Bayesian statistical models, regression analyses, and validation steps applied to the tree mortality data from the INPA experiments. The document includes visual summaries, model diagnostics, and leave-one-out (LOO) validation results. A breakdown of file contents can be found in the README file that is part of this package.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Plan Position Indicator Hydrometeor Field Statistics (PPIHYD) Evaluation Data Product Version 1.0

The PPIHYD evaluation data product provides distinct hydrometeor field statistics calculated from U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility scanning radar plan position indicator (PPI) scans. These statistics include the equivalent reflectivity factor and Doppler spectral width percentiles, min/max values, and first four moments (mean, standard deviation, skewness, and kurtosis) of distinct hydrometeor features (clustered hydrometeor fields). Statistics also include morphological properties, water content and precipitation rate parameterization-based estimates, and thermodynamic properties interpolated using the Interpolated Sonde value-added product (INTERPSONDE VAP). The data set is organized in tabular form and is accompanied by mask arrays with corresponding indices. This straightforward file structure simplifies scanning radar data processing and renders this data set useful for process understanding and model evaluation studies. This report describes the data set and its processing algorithm and provides some examples.

54 ENVIRONMENTAL SCIENCES↗