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At least 1,009 records · Page 56

Uncovering interpretable relationships in high-dimensional scientific data through function preserving projections

Abstract In many fields of science and engineering, we frequently encounter experiments or simulations datasets that describe the behavior of complex systems and uncovering human interpretable patterns between their inputs and outputs via exploratory data analysis is essential for building intuition and facilitating discovery. Often, we resort to 2D embeddings for examining these high-dimensional relationships (e.g. dimensionality reduction). However, most existing embedding methods treat the dimensions as coordinates for samples in a high-dimensional space, which fail to capture the potential functional relationships, and the few methods that do take function into consideration either only focus on linear patterns or produce non-linear embeddings that are hard to interpret. To address these challenges, we proposed function preserving projections (FPP), which construct 2D linear embeddings optimized to reveal interpretable yet potentially non-linear patterns between the domain and the range of a high-dimensional function. The intuition here is that humans are good at understanding potentially non-linear patterns in 2D but unable to interpret non-linear mapping from high-dimensional space to 2D. Therefore, we should restrict the projection to linear but not the pattern we are seeking. Using FPP on real-world datasets, one can obtain fundamentally new insights about high-dimensional relationships in extremely large datasets that could not be processed with existing dimension reduction methods.

97 MATHEMATICS AND COMPUTING↗

Whole genome sequencing of Mycobacterium bovis directly from clinical tissue samples without culture

Advancement in next generation sequencing offers the possibility of routine use of whole genome sequencing (WGS) for Mycobacterium bovis (M. bovis) genomes in clinical reference laboratories. To date, the M. bovis genome could only be sequenced if the mycobacteria were cultured from tissue. This requirement for culture has been due to the overwhelmingly large amount of host DNA present when DNA is prepared directly from a granuloma. To overcome this formidable hurdle, we evaluated the usefulness of an RNA-based targeted enrichment method to sequence M. bovis DNA directly from tissue samples without culture. Initial spiking experiments for method development were established by spiking DNA extracted from tissue samples with serially diluted M. bovis BCG DNA at the following concentration range: 0.1 ng/μl to 0.1 pg/μl (10 –1 to 10 –4 ). Library preparation, hybridization and enrichment was performed using SureSelect custom capture library RNA baits and the SureSelect XT HS2 target enrichment system for Illumina paired-end sequencing. The method validation was then assessed using direct WGS of M. bovis DNA extracted from tissue samples from naturally (n = 6) and experimentally (n = 6) infected animals with variable Ct values. Direct WGS of spiked DNA samples achieved 99.1% mean genome coverage (mean depth of coverage: 108×) and 98.8% mean genome coverage (mean depth of coverage: 26.4×) for tissue samples spiked with BCG DNA at 10 –1 (mean Ct value: 20.3) and 10 –2 (mean Ct value: 23.4), respectively. The M. bovis genome from the experimentally and naturally infected tissue samples was successfully sequenced with a mean genome coverage of 99.56% and depth of genome coverage ranging from 9.2× to 72.1×. The spoligoyping and M. bovis group assignment derived from sequencing DNA directly from the infected tissue samples matched that of the cultured isolates from the same sample. Our results show that direct sequencing of M. bovis DNA from tissue samples has the potential to provide accurate sequencing of M. bovis genomes significantly faster than WGS from cultures in research and diagnostic settings.

59 BASIC BIOLOGICAL SCIENCES↗

Relationship between ductility and the porosity of additively manufactured AlSi10Mg

Additive manufacturing via selective laser melting can result in variable levels of internal porosity both between build plates and within components from the same build. In this work, sample porosity levels were compared to tensile properties for 176 samples spanning eight different build plates. Sample porosity was measured both by Archimedes density, which provided an estimation of overall porosity, and by observation of voids in the fracture surface, which provided an estimation of the porosity at the failure plane. The porosity observed at the fracture surface consistently demonstrated higher porosity than that suggested by Archimedes density. The porosity values obtained from both methods were compared against the mechanical results. Sample porosity appears to have some correlation to the ultimate tensile strength, yield strength, and modulus, but the strongest relationship is observed between porosity and ductility. Three different models were used to relate the fracture surface porosity to the ductility. The first method was a simple linear regression analysis, while the other two models have been used to relate porosity to ductility in cast alloys. It is shown that all three models fit the data well over the observed porosity ranges, suggesting that the models taken from casting theory can extend to additively manufactured metals. Finally, it is proposed that the non-destructive Archimedes method could be used to estimate an approximate sample ductility through the use of correlations realized here. Such a relationship could prove useful for design and for a deeper understanding of the impact of pores on tensile behavior.

36 MATERIALS SCIENCE↗

A new route to obtain fluorescence X-ray absorption spectra of compounds and to remove the self-absorption induced nonlinearity in the spectra

A new route to obtain fluorescence X-ray absorption spectra of compounds and to remove the self-absorption induced nonlinearity in the spectra is described. The fluorescent intensity If is linearly proportional to the absorption coefficient μ. For studies of surface structures around an element (κ) the fluorescence detection is often the mode of choice. However, the measurement may suffer from a self-absorption (SA) effect which nonlinearly distorts the spectra. The effect is severe when κ is concentrated or the measurements are carried out in certain geometries. Here, the correlations among emission events in compounds are examined following resonance X-ray core-electron excitation within κ. Under conditions leading to SA, If emitted from κ apparently has a conjugated relationship with the fluorescent intensities simultaneously emitted from other elements (ξ). Normalizing the former (κ) by the latter (ξ) will largely remove SA effects and reduce this nonlinear problem to a tractable linear problem. This does result in a moderate reduction of the spectral amplitude due to the so-called secondary emission from ξ excited by the emission from κ. Nonetheless, the resulting spectra will allow one to accurately determine bond distances and disorder and, in some respects, can be superior to spectra obtained via the absorption channel. For μξ < μκ and grazing incidence geometry, the amplitude reduction can be small and simple normalization is sufficient to restore the spectral integrity with remarkable accuracy. This has been instrumental in unravelling the surface and subsurface structures around cations in amorphous Ga–In–O and Zn–Sn–O films which are otherwise inaccessible due to severe SA effects. This method has also been applied to several samples with μξ ≃ μκ to examine its applicability. For these samples, the amplitude reduction is 12 ± 4% versus their standards for the data measured with the classical 45°/45° geometry. This experimental method is easy to implement. Since If from κ and ξ are measured by the same detector system, it is also superior to other methods in removing systematic errors such as detector system nonlinearity, electronic noise, and some beam instabilities, and in removing spectral imperfections due to, for example, SA effects, diffraction effects and sample inhomogeneity. The distortions resulting from the latter can be severe in the spectra measured in transmission mode.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Scalable Techniques for Stochastic Power Flow Problems (Final Report)

The proposed research focuses on developing scalable algorithms for two-stage security-constrained OPF problems with AC power flow constraints, a class of problems complicated by (i) scale arising from a scenario representation; and (ii) the presence of nonlinearity, nonconvexity, and possibly second-stage discreteness or complementarity. Unfortunately, most existing solvers cannot contend with both challenges simultaneously; accordingly, the proposed research focuses on developing solution techniques that can both scale with the number of scenarios and contend with nonconvexity and second-stage complementarity. We consider three avenues for addressing such problems: (i) Variable sample-size SQP (VS-SQP) methods that combine sparse Quasi-Newton updates with a scalable variance-reduced stochastic gradient scheme for stochastic QP subproblems, allowing for contending with second-stage complementarity via regularization; (ii) Variable sample-size stochastic Interior-point (VS-sIP) schemes that propose a sampling-based regularized (to allow for contending with complementarity) interior-point schemes in which a Schur-complement technique is employed for decomposing the Newton direction computation step; (iii) Variable sample-size tractable ADMM (VS-tADMM) schemes combine variable sample-sizes with carefully designed techniques for resolving each of the nonconvex updates (by leveraging the QCQP structures). We intend to compare the three schemes using performance profiles in terms of solution quality, scalability, etc. and then select one scheme which will then be developed and further refined in Python for purposes of the GO competition.

42 ENGINEERING↗

UN Synthesis, Fabrication, and Characterization and UC Oxidation Study in support of Advanced LEU Fuel Concepts

Uranium nitride and carbide-based fuels are proposed for use in advanced LEU fuel systems. This report details recent development work to study synthesis, sintering and fabrication methods for single phase UN in monolithic geometries. These samples were intended to support a variety of irradiation testing conditions by tailoring enrichment, geometry, and compositional requirements. Two methods were under evaluation for synthesizing uranium nitride powder – carbothermic reduction-nitridation (CTR-N) of UO 2 powder feedstock and hydride-dehydride/nitridation (HDN) of uranium metal feedstock. Pellets were fabricated from powder feedstocks via conventional pressing and sintering methods. As-fabricated feedstocks and pellets were evaluated via X-ray diffraction (XRD) for phase purity and sintered materials were characterized for density. Both the CTR N and the HDN methods were successfully demonstrated as an effective process for fabricating phase pure UN. Additionally, results from machining efforts for UN are detailed. This report also contains information on a study trying to elucidate the oxidation mechanisms of sintered uranium carbide samples fabricated from feedstock synthesized via an arc-melting method.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Probabilistic Methods for Cyclical and Coupled Systems with Changing Failure Rates

Advancements in nuclear system designs with automated control features provide many benefits, but can lead to complex coupled systems and dynamic failure scenarios. This is especially true for microreactor designs where components are not expected to be replaced during the reactor’s lifetime. Hence, the life of the system, in addition to the safety, needs to be evaluated. Modeling these sequences of time-dependent events requires addressing cyclical processes and changing failure rates in ways that represent the actual system dynamics in contrast to a single sampling for a component’s time to failure. This research presents two distinct analytical methods for several failure distributions that evaluate a final time to failure used for different scenarios where the time to failure must be sampled multiple times. The first method is used when evaluating a component whose failure rate increases due to an outside event after the initial sampling but before the initially sampled time to failure. The second method is used when evaluating multiple identical components or a component that has been replaced with a new identical version before the second sampling. The two methods were implemented in a few representative case studies developed in the dynamic probabilistic risk assessment tool Event Modeling Risk Assessment using Linked Diagrams. Overall, this paper provides guidelines on how these approaches give a more realistic and accurate dynamic probabilistic risk assessment of complex systems.

97 MATHEMATICS AND COMPUTING↗

Trocylation of 3-quinuclidinol, a key marker for the chemical warfare agent 3-quinuclidinyl benzilate, for its enhanced detection at low levels in complex soil matrices by electron ionization gas chromatography–mass spectrometry

Detection of 3-quinuclidinol (3Q), a marker for the chemical warfare agent 3-quinuclidinyl benzilate, is very difficult by gas chromatography–mass spectrometry (GC/MS), providing low, broad signals even when analyzed in isolated form. Therefore, a method that can convert 3Q into a substrate with enhanced detectability by GC/MS would be an important tool for its analysis. 2,2,2-Trichloroethoxycarbonyl chloride (TrocCl) was used in the derivatization of 3Q in three different soils of varying composition and total organic content (Virginia type A soil, Nebraska EPA standard soil and Ottawa sand) when present at a 10 μg g -1 concentration in each. A direct derivatization protocol and one involving the pre-extraction of the analyte were evaluated for their individual efficiencies and subsequent analysis using electron ionization GC/MS. The practical derivatization of 3Q, when present at low levels (10 μg g -1 ) in three different soil matrices, was found to be rapid (1 h) and to take place smoothly at ambient temperature (and as low as 4°C). The method detection limit was determined to be 30 ng mL -1 for the Virginia type A soil, 49 ng mL -1 for the Nebraska EPA standard soil and 72 ng mL -1 for the Ottawa sand sample. An expedient and practical derivatization method for 3Q, a chemical warfare degradation product difficult to detect by GC/MS, has been realized using trichloroethyl chloroformate. The reaction provides 3Q-Troc, a derivative with better detectability than 3Q by electron ionization GC/MS such as peak sharpness and a unique mass spectrum for its unambiguous identification.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Determining P, S, Br, and I content in uranium by triple quadrupole inductively coupled plasma mass spectrometry

The trace impurities of a uranium ore concentrate (UOC) can be examined to determine mine source, methods of production, and quality. This study presents a method to determine the concentration of halides and main group elements, specifically P, S, Br and I, utilizing triple quadrupole inductively coupled plasma–mass spectrometry. These analytes were measured in a uranium matrix to simulate a UOC sample. The concentrations determined with this method showed agreement with known values. Solutions with and without uranium were compared. A UOC certified reference material, CUP-2, was analyzed to further demonstrate the effectiveness of the method.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Uranium particle age dating, aggregation, and model age best estimators

We present important aspects of uranium particle age dating by Large-Geometry Secondary Ion Mass Spectrometry (LG-SIMS) that can introduce bias and increase model age uncertainties, especially for small, young, and/or low-enriched particles. This metrology is important for applications related to International Nuclear Safeguards. We explore influential factors related to model age estimation, including the effects of evolving surface chemistry on inter-element measurements of particles (e.g., Th and U), detector background, and aggregation methods using simulated and actual particle samples. We introduce a new model age estimator, called “mid68”, that supplements 95% confidence intervals, providing a “best estimate” and uncertainty about the most likely age. The mid68 estimator can be calculated using the Feldman and Cousins method or Bayesian methods and provides a value with a symmetric uncertainty that can be used for calculations and approximate aggregation of processed model age values when the raw data and correction factors are not available. For particles yielding low 230 Th counts amidst nonzero detector background, their underlying model age probability distributions are asymmetric, so the mid68 estimator provides additional robust information regarding the underlying model age likelihood. This study provides a comprehensive and timely examination of critical aspects of uranium particle age dating as more laboratories establish particle chronometry capabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Discovery top-down proteomics in symbiotic soybean root nodules

Proteomic methods have been widely used to study proteins in complex biological samples to understand biological molecular mechanisms. Most well-established methods (known as bottom-up proteomics, BUP) employ an enzymatic digestion step to cleave intact proteins into smaller peptides for liquid chromatography (LC) mass spectrometry (MS) detection. In contrast, top-down proteomics (TDP) directly characterizes intact proteins including all possible post-translational modifications (PTMs), thus offering unique insights into proteoform biology where combinations of individual PTMs may play important roles. We performed TDP on soybean root nodules infected by the symbiotic Bradyrhizobium japonicum in both the wildtype bacterium and a nifH- mutant, which lacks the ability to fix nitrogen in the soybean root nodule. TDP captured 1648 proteoforms derived from 313 bacterial genes and 178 soybean genes. Leghemoglobin, the most abundant protein in the sample, existed in many truncated proteoforms. Interestingly, these truncated proteoforms were considerably more abundant in the wildtype relative to the nifH- mutant, implicating protease activity as an important factor in nitrogen fixation. Proteoforms with various PTMs and combinations thereof were identified using an unrestricted open modification search. This included less common PTMs such as myristoylation, palmitoylation, cyanylation, and sulfation. In parallel, we collected high resolution MS imaging (MSI) data of intact proteins and biopolymers (<20 kDa due to current technical limitations) from sections of the soybean root nodules using matrix-assisted laser desorption/ionization (MALDI) coupled to high resolution Orbitrap. Several detected proteoforms exhibited unique spatial distributions inside the infection zone and cortex, suggesting functional compartmentalization in these regions. A subset of peaks from the MALDI-MSI were assigned to proteoforms detected in TDP LCMS data based on matching accurate masses. Many of the proteins detected in both LCMS and MALDI-MSI are currently uncharacterized in UniProt: the PTM and spatial information presented here will be valuable in understanding their biological functions. Taken together, our study demonstrates how untargeted TDP approach can provide unique insights into plant proteoform biology. On-going technology developments are expected to further improve TDP coverage for more comprehensive high-throughput analysis of proteoforms.

59 BASIC BIOLOGICAL SCIENCES↗

A Digital Imaging Method for Evaluating the Kinetics of Vapochromic Response

This work describes the use of a cell phone camera and the L*a*b method (color space specified by the International Commission on Illumination) to characterize the color change in different vapochromic systems. In this study we have developed a semi-automatic color change analysis software that digitally analyzes images (e.g., video frames) collected while a vapochromic material is absorbing vapor. The advantages of using this method, as compared to reflectance spectroscopy or transmission spectroscopy through a thin film, include low cost, convenience, portability, ease of sample preparation, the absence of need for specialized equipment, and the ease of simultaneously collecting data on different samples under identical conditions. In addition, this method arguably provides direct insight into what a human would observe when monitoring these color changes by eye. Limitations of the method also are discussed in this paper.

cell phone camera, colorimetric sensing, vapor det↗

In situ observation of irradiation-induced enhancement to the desorption pressure of zirconium hydride in a nuclear reactor

We quantify the effect of a nuclear-reactor environment on the hydrogen isotope equilibrium vapor pressure over pure zirconium and zirconium hydride. A vacuum-sealed capsule containing a zirconium foil with 6 atom% deuterium was irradiated at a neutron flux of ~10 14 cm -2 s -1 at the University of Missouri Research Reactor (MURR). The internal stainless-steel (SS) sample holder acted as the heat source via gamma absorption. To measure low desorption pressures in a high-flux environment, we developed a method to transduce pressure from the measured sample temperature during irradiation, calibrating with known deuterium pressures in unirradiated capsules at various heating powers using an internal filament-heated system designed to mimic irradiation-induced heating. Our temperature-pressure transduction method operates similarly to a Pirani or thermocouple pressure gauge. The in-reactor measurements revealed a roughly 4-fold enhancement in desorption pressure after only 6 h of irradiation (~2 × 10 18 cm -2 neutron fluence) compared to thermal desorption in control experiments, indicating a nonthermal contribution from neutron irradiation. The slower temperature/pressure stabilization rate in the reactor suggests that desorption pressure enhancement increases with neutron fluence. Further, this enhancement signifies increased solubility of hydrogen isotopes in zirconium during irradiation. We propose that high-energy neutron collisions with hydrogen isotopes in hydrides lead to their decomposition at lower temperatures, supersaturating the surrounding αZr lattice and resulting in higher desorption pressure, which continues to rise as more hydrides dissolve with increasing neutron fluence.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗

Fluidic impedance platform for in-situ detection and quantification of PFAS in groundwater

Materials for binding per- and polyfluoroalkyl substances (PFAS) are disclosed. A fluidic device comprising the materials for detection and quantification of PFAS in a sample is disclosed. The fluidic device may be configured for multiplexed analyses. Also disclosed are methods for sorbing and remediating PFAS in a sample. The sample may be groundwater containing, or suspected of containing, one or more PFAS.

Chatterjee, Sayandev↗

Selecting XFEL single-particle snapshots by geometric machine learning

A promising new route for structural biology is single-particle imaging with an X-ray Free-Electron Laser (XFEL). This method has the advantage that the samples do not require crystallization and can be examined at room temperature. However, high-resolution structures can only be obtained from a sufficiently large number of diffraction patterns of individual molecules, so-called single particles. Here, we present a method that allows for efficient identification of single particles in very large XFEL datasets, operates at low signal levels, and is tolerant to background. This method uses supervised Geometric Machine Learning (GML) to extract low-dimensional feature vectors from a training dataset, fuse test datasets into the feature space of training datasets, and separate the data into binary distributions of “single particles” and “non-single particles.” As a proof of principle, we tested simulated and experimental datasets of the Coliphage PR772 virus. We created a training dataset and classified three types of test datasets: First, a noise-free simulated test dataset, which gave near perfect separation. Second, simulated test datasets that were modified to reflect different levels of photon counts and background noise. These modified datasets were used to quantify the predictive limits of our approach. Third, an experimental dataset collected at the Stanford Linear Accelerator Center. The single-particle identification for this experimental dataset was compared with previously published results and it was found that GML covers a wide photon-count range, outperforming other single-particle identification methods. Moreover, a major advantage of GML is its ability to retrieve single particles in the presence of structural variability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Deployment of salt sample extraction system at an engineering-scale electrorefiner

The goal of the salt sampling program at Argonne is to develop and deploy automated molten salt sampling approaches for interfacing relevant unit operations with salt analysis to improve the timeliness of sampling-based accountancy measurements. Two technologies under development in support of this goal are a vacuum sampling loop module and a high-throughput pneumatic sample generator module. Compared to traditional point sampling approaches (i.e., dip probes), the vacuum sampling loop facilitates the collection of a larger cross-section of the bulk salt in order to collect more representative samples. The vacuum sampling approach also eliminates the risk of dross contamination of samples and avoids the use of moving parts in the salt. The pneumatic sample generator module is used to facilitate high-throughput sample analysis to improve the measurement precision of any given analytical technique by averaging out random sampling and measurement errors. In FY21, two methods for integrating these two modules were tested including direct fluidic coupling and coupling using a solid salt transfer mechanism. Solid salt transfer was ultimately selected over fluidic coupling, primarily to enable the transport of samples over longer distances to support automated at-line integration with high-precision techniques (such as microcalorimetry) that cannot withstand the conditions near an electrorefining process. To facilitate rapid solid salt coupling, new mechanisms were developed for rapidly charging and discharging salt sample tubes at the vacuum sampling loop and pneumatic sample generator modules, respectively. While the charging mechanism will be deployed in FY22, the discharge mechanism was tested in FY21 and is described here. The solid salt tube transfer method was deployed at one of Argonne’s engineering-scale electrorefiners to implement at-line high-throughput pneumatic micro-sample generation capabilities. The approach was used to generate precise uranium- and lanthanide-bearing electrorefiner micro-samples with the specific dimensions requested by researchers at Los Alamos National Laboratory for use in testing their novel microcalorimeter x-ray techniques. The solid salt transfer mechanism proved not only to be an effective means of integrating the precision sample generator with vacuum sampling, but also improved the performance of the sampler generator. To discharge salt from the sample tubes at the sampler generator, tube segments were inserted directly into the sample generator’s Helmholtz chamber and pressure pulse actuations were used to generate precision molten salt samples directly from the tube segments. The direct insertion of sample tubes into the sample generator enabled rapid loading of the salt and prevented salt from contacting most of the interior surfaces of the sample generator, which eliminated cross-contamination between runs. The vacuum sampling-loop tube charging mechanism will support high-throughput tube sampling operations by employing a dynamic vacuum filling process to fill short charge tubes that are configured to be rapidly connected and disconnected from the loop. The dynamic vacuum sampling operation will be automated, and sample tube handling can be executed with simple overhead actuation. Because the modular sampling approach described here eliminates the need for new high-radiation sample handling capabilities, salt-wetted seals, salt-wetted moving parts, and heated transfer lines outside the electrorefiner, it will address most of the remaining technical challenges for the at-line deployment of high-precision analytical techniques which will enable significant reductions in the time delay for sampling-based high-precision accountancy measurements.

42 ENGINEERING↗

High-dimensional maximum-entropy phase space tomography

Reconstructing 4D or 6D phase space distributions from 1D or 2D measurements is a challenging inverse problem encountered in particle accelerators. Entropy maximization is an established method to incorporate prior information in the reconstruction, but it is typically infeasible in high-dimensional spaces. In this paper, I review two recent approaches to high-dimensional entropy maximization. The first approach utilizes differentiable simulations and a class of generative models known as normalizing flows, whereas the second approach employs the method of Lagrange multipliers and Markov Chain Monte Carlo (MCMC) sampling. My aim is to provide a short explanation of each method using a common notation. I conclude by mentioning several unsolved problems in phase space tomography.

Hoover, Austin [ORNL] (ORCID:0000000153136962)↗