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At least 469 records · Page 26

Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks

The computational cost of high-fidelity numerical models makes outer-loop analysis, which requires repeated interrogation of the model such as uncertainty quantification, computationally demanding. Multi-fidelity methods, which construct a surrogate model using data from an ensemble of models of varying cost and accuracy, can substantially reduce the cost of outer-loop analysis. However, these methods can be difficult to apply when the model ensemble does not admit a clear hierarchy a priori and the correlations between models are low. Consequently, in this paper, we present a multi-fidelity method that leverages dimension reduction to enhance the correlation between models, thereby reducing the amount of data needed to train a surrogate from an unordered ensemble of models. Our method utilizes basis adaptation to build low-dimensional polynomial chaos expansions of each model and employs Multi-fidelity Networks to encode the relationships among models. We show that the resulting method exhibit two notable advantages over its counterpart: (1) enhanced accuracy (both reduced bias and variance); and (2) reduced dependency on the graph structure encoding relationships among models. We demonstrate the approach on an analytical test problem and a challenging finite element model for a spent nuclear fuel. Our method produces a surrogate model that is significantly more accurate than either a single-fidelity surrogate or a multi-fidelity surrogate constructed without basis adaptation.

42 ENGINEERING↗

Co-optimized machine-learned manifold models for large eddy simulation of turbulent combustion

Many modeling approaches in large eddy simulation (LES) of turbulent combustion employ a projection of the thermochemical state onto a low-dimensional manifold within state space to reduce the number of transported variables and hence computational cost. Flamelet-generated manifolds (FGM) is an example of a well-established, physics-based approach, but increasingly, principal component analysis (PCA) is being used as a data-driven method for generating manifold models. For both approaches, the nonlinear relationship between the location on the predefined manifold and the outputs of interest, such as reaction rates, can be tabulated or encoded in a neural network. This work proposes a new approach for manifold modeling that extends these existing approaches. A modified neural network structure simultaneously encodes the definition of the manifold variables, the nonlinear mapping, and the subfilter closure for LES. This allows all three of these aspects of the model to be co-optimized, generating a model from any source of combustion thermochemical state data. The manifold parameterizing variables are constrained to be linear combinations of species, as in FGM and PCA-based models, to aid in interpretability and implementation. For LES, subfilter variances of the manifold variables are also included as inputs. Two types of a priori analysis are performed to evaluate the new approach. In the first, the model is trained on data from one-dimensional premixed flames. In this case, the approach recovers the behavior of flamelet-based manifold approaches, and in fact slightly improves performance by identifying an optimized progress variable. The approach is also applied to data from direct numerical simulations of spherical ignition kernels in isotropic turbulence. For any specified manifold dimensionality, the new approach provides substantially lower prediction errors than a PCA-based model developed from the same data set. Additionally, the LES formulation of the new approach can provide accurate predictions for filtered reaction rates across a variety of filter widths.

97 MATHEMATICS AND COMPUTING↗

Self-supervised learning of spatiotemporal thermal signatures in additive manufacturing using reduced order physics models and transformers

Microstructure control via additive manufacturing has enormous potential as manufacturers, materials scientists, and designers alike seek to exploit novel fabrication technologies to improve component performance. Recent works have demonstrated the feasibility of producing materials with controlled microstructures across various length scales. However, the experimental approach towards exploring the process-structure space can be laborious and costly. This is particularly true if also considering scan pattern optimization which is well suited for processes such as powder bed fusion electron beam melting. In this work we propose an approach for encoding additive manufacturing layer-wise thermal response signatures using self-supervised representation learning. Thermal simulations from a reduced order model are utilized to estimate the spatiotemporal response during printing. A machine learning framework, using video-transformers, is utilized to efficiently distill spatiotemporal patterns into a compact latent space representation. This latent state representation encodes the relevant physics which is then utilized to establish a data-driven process-structure model for an additively manufactured Ni-based superalloy. In conclusion, the proposed methodology could potentially be used towards in-situ process monitoring, scan pattern experimental design, and component qualification.

97 MATHEMATICS AND COMPUTING↗

An orphan gene BOOSTER enhances photosynthetic efficiency and plant productivity

Organelle-to-nucleus DNA transfer is an ongoing process playing an important role in the evolution of eukaryotic life. Here, genome-wide association studies (GWAS) of non-photochemical quenching parameters in 743 Populus trichocarpa accessions identified a nuclear-encoded genomic region associated with variation in photosynthesis under fluctuating light. The identified gene, BOOSTER (BSTR), comprises three exons, two with apparent endophytic origin and the third containing a large fragment of plastid-encoded Rubisco large subunit. Higher expression of BSTR facilitated anterograde signaling between nucleus and plastid, which corresponded to enhanced expression of Rubisco, increased photosynthesis, and up to 35% greater plant height and 88% biomass in poplar accessions under field conditions. Overexpression of BSTR in Populus tremula × P. alba achieved up to a 200% in plant height. Similarly, Arabidopsis plants heterologously expressing BSTR gained up to 200% in biomass and up to 50% increase in seed.

60 APPLIED LIFE SCIENCES↗

Multiscale simulation of spatially correlated microstructure via a latent space representation

When deformation gradients act on the scale of the microstructure of a part due to geometry and loading, spatial correlations and finite-size effects in simulation cells cannot be neglected. We propose a multiscale method that accounts for these effects using a variational autoencoder to encode the structure–property map of the stochastic volume elements making up the statistical description of the part. In this paradigm the autoencoder can be used to directly encode the microstructure or, alternatively, its latent space can be sampled to provide likely realizations. Furthermore, we demonstrate the method on three examples using the common additively manufactured material AlSi10Mg in: (a) a comparison with direct numerical simulation of the part microstructure, (b) a push forward of microstructural uncertainty to performance quantities of interest, and (c) a simulation of functional gradation of a part with stochastic microstructure.

Elastoplasticity↗

A conserved chaperone protein is required for the formation of a noncanonical type VI secretion system spike tip complex

Type VI secretion systems (T6SSs) are dynamic protein nanomachines found in Gram-negative bacteria that deliver toxic effector proteins into target cells in a contact-dependent manner. Prior to secretion, many T6SS effector proteins require chaperones and/or accessory proteins for proper loading onto the structural components of the T6SS apparatus. However, despite their established importance, the precise molecular function of several T6SS accessory protein families remains unclear. In this study, we set out to characterize the DUF2169 family of T6SS accessory proteins. Using gene co-occurrence analyses, we find that DUF2169-encoding genes strictly co-occur with genes encoding T6SS spike complexes formed by valine-glycine repeat protein G (VgrG) and DUF4150 domains. Although structurally similar to Pro-Ala-Ala-Arg (PAAR) domains, “PAAR-like” DUF4150 domains lack PAAR motifs and instead contain a conserved PIPY motif, leading us to designate them PIPY domains. Next, we present both genetic and biochemical evidence that PIPY domains require a cognate DUF2169 protein to form a functional T6SS spike complex with VgrG. This contrasts with canonical PAAR proteins, which bind VgrG on their own to form functional spike complexes. By solving the first crystal structure of a DUF2169 protein, we show that this T6SS accessory protein adopts a novel protein fold. Furthermore, biophysical and structural modeling data suggest that DUF2169 contains a dynamic loop that physically interacts with a hydrophobic patch on the surface of its cognate PIPY domain. Based on these findings, we propose a model whereby DUF2169 proteins function as molecular chaperones that maintain VgrG–PIPY spike complexes in a secretion-competent state prior to their export by the T6SS apparatus.

DUF2169↗

KEBLM: Knowledge-Enhanced Biomedical Language Models

Pretrained language models (PLMs) have demonstrated strong performance on many natural language processing (NLP) tasks. Despite their great success, these PLMs are typically pretrained only on unstructured free texts without leveraging existing structured knowledge bases that are readily available for many domains, especially scientific domains. As a result, these PLMs may not achieve satisfactory performance on knowledge-intensive tasks such as biomedical NLP. Comprehending a complex biomedical document without domain-specific knowledge is challenging, even for humans. Inspired by this observation, we propose a general framework for incorporating various types of domain knowledge from multiple sources into biomedical PLMs. We encode domain knowledge using lightweight adapter modules, bottleneck feed-forward networks that are inserted into different locations of a backbone PLM. For each knowledge source of interest, we pretrain an adapter module to capture the knowledge in a self-supervised way. We design a wide range of self-supervised objectives to accommodate diverse types of knowledge, ranging from entity relations to description sentences. Once a set of pretrained adapters is available, we employ fusion layers to combine the knowledge encoded within these adapters for downstream tasks. Each fusion layer is a parameterized mixer of the available trained adapters that can identify and activate the most useful adapters for a given input. Our method diverges from prior work by including a knowledge consolidation phase, during which we teach the fusion layers to effectively combine knowledge from both the original PLM and newly-acquired external knowledge using a large collection of unannotated texts. After the consolidation phase, the complete knowledge-enhanced model can be fine-tuned for any downstream task of interest to achieve optimal performance. Extensive experiments on many biomedical NLP datasets show that our proposed framework consistently improves the performance of the underlying PLMs on various downstream tasks such as natural language inference, question answering, and entity linking. These results demonstrate the benefits of using multiple sources of external knowledge to enhance PLMs and the effectiveness of the framework for incorporating knowledge into PLMs. Finally, while primarily focused on the biomedical domain in this work, our framework is highly adaptable and can be easily applied to other domains, such as the bioenergy sector.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOME: Directional medical embedding vectors from Electronic Health Records

Motivation: The increasing availability of Electronic Health Record (EHR) systems has created enormous potential for translational research. Recent developments in representation learning techniques have led to effective large-scale representations of EHR concepts along with knowledge graphs that empower downstream EHR studies. However, most existing methods require training with patient-level data, limiting their abilities to expand the training with multi-institutional EHR data. On the other hand, scalable approaches that only require summary-level data do not incorporate temporal dependencies between concepts. Methods: We introduce a DirectiOnal Medical Embedding (DOME) algorithm to encode temporally directional relationships between medical concepts, using summary-level EHR data. Specifically, DOME first aggregates patient-level EHR data into an asymmetric co-occurrence matrix. Then it computes two Positive Pointwise Mutual Information (PPMI) matrices to correspondingly encode the pairwise prior and posterior dependencies between medical concepts. Following that, a joint matrix factorization is performed on the two PPMI matrices, which results in three vectors for each concept: a semantic embedding and two directional context embeddings. They collectively provide a comprehensive depiction of the temporal relationship between EHR concepts. Results: We highlight the advantages and translational potential of DOME through three sets of validation studies. First, DOME consistently improves existing direction-agnostic embedding vectors for disease risk prediction in several diseases, for example achieving a relative gain of 5.5% in the area under the receiver operating characteristic (AUROC) for lung cancer. Second, DOME excels in directional drug-disease relationship inference by successfully differentiating between drug side effects and indications, correspondingly achieving relative AUROC gain over the state-of-the-art methods by 10.8% and 6.6%. Finally, DOME effectively constructs directional knowledge graphs, which distinguish disease risk factors from comorbidities, thereby revealing disease progression trajectories. The source codes are provided at https://github.com/celehs/Directional-EHRembedding.

60 APPLIED LIFE SCIENCES↗

Data-driven Whitney forms for structure-preserving control volume analysis

Control volume analysis models physics via the exchange of generalized fluxes between subdomains. Here, we introduce a scientific machine learning framework adopting a partition of unity architecture to identify physically-relevant control volumes, with generalized fluxes between subdomains encoded via Whitney forms. The approach provides a differentiable parameterization of geometry which may be trained in an end-to-end fashion to extract reduced models from full field data while exactly preserving physics. The architecture admits a data-driven finite element exterior calculus allowing discovery of mixed finite element spaces with closed form quadrature rules. An equivalence between Whitney forms and graph networks reveals that the geometric problem of control volume learning is equivalent to an unsupervised graph discovery problem. The framework is developed for manifolds in arbitrary dimension, with examples provided for H(div) problems in $\mathbb{R}$ establishing convergence and structure preservation properties. Finally, we consider a lithium-ion battery problem where we discover a reduced finite element space encoding transport pathways from high-fidelity microstructure resolved simulations. The approach reduces the 5.89M finite element simulation to 136 elements while reproducing pressure to under 0.1% error and preserving conservation.

97 MATHEMATICS AND COMPUTING↗

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Here, currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

36 MATERIALS SCIENCE↗

Latent space dynamics identification for interface tracking with application to shock-induced pore collapse

Capturing sharp, evolving interfaces remains a central challenge in reduced-order modeling, especially when data is limited and the system exhibits localized nonlinearities or discontinuities. Here, we propose LaSDI-IT (Latent Space Dynamics Identification for Interface Tracking), a data-driven framework that combines low-dimensional latent dynamics learning with explicit interface-aware encoding to enable accurate and efficient modeling of physical systems involving moving material boundaries. At the core of LaSDI-IT is a revised autoencoder architecture that jointly reconstructs the physical field and an indicator function representing material regions or phases, allowing the model to track complex interface evolution without requiring detailed physical models or mesh adaptation. The latent dynamics are learned through linear regression in the encoded space and generalized across parameter regimes using Gaussian process interpolation with greedy sampling. We demonstrate LaSDI-IT on the problem of shock-induced pore collapse in high explosives, a process characterized by sharp temperature gradients and dynamically deforming pore geometries. The method achieves relative prediction errors below 9% across the parameter space, accurately recovers key quantities of interest such as pore area and hot spot formation, and matches the performance of dense training with only half the data. This latent dynamics prediction was 10 6 times faster than the conventional high-fidelity simulation, proving its utility for multi-query applications. These results highlight LaSDI-IT as a general, data-efficient framework for modeling discontinuity-rich systems in computational physics, with potential applications in multiphase flows, fracture mechanics, and phase change problems.

Gaussian process↗

Stochasticity and robustness in spiking neural networks

Despite drawing inspiration from biological systems which are inherently noisy and variable, artificial neural networks have been shown to require precise weights to carry out the task which they are trained to accomplish. This creates a challenge when adapting these artificial networks to specialized execution platforms which may encode weights in a manner which restricts their accuracy and/or precision.Reflecting back on the non-idealities which are observed in biological systems, we investigated the effect these properties have on the robustness of spiking neural networks under perturbations to weights. First, we examined techniques extant in conventional neural networks which resemble noisy processes, and postulated they may produce similar beneficial effects in spiking neural networks. Second, we evolved a set of spiking neural networks utilizing biological non-idealities to solve a pole-balancing task, and estimated their robustness. We showed it is higher in networks using noisy neurons, and demonstrated that one of these networks can perform well under the variance expected when a hafnium-oxide based resistive memory is used to encode synaptic weights. Lastly, we trained a series of networks using a surrogate gradient method on the MNIST classification task. We confirmed that these networks demonstrate similar trends in robustness to the evolved networks. We discuss these results and argue that they display empirical evidence supporting the role of noise as a regularizer which can increase network robustness.

97 MATHEMATICS AND COMPUTING↗

Convolution-based frequency domain multiplexing of SiPM readouts using the $\mathrm{DRS4}$ digitizer

Here we present 4:1 multiplexing of organic scintillators, each coupled to a silicon photomultiplier (SiPM), to reduce the need for a large number of digitizer input channels to readout highly pixelated radiation detection systems. Frequency domain multiplexing (FDM) encodes a detector pulse by assigning it a unique frequency via convolution before combining the encoded signal into a single channel. The combined signal is then read through a digitizer input channel. We have designed an FDM system to multiplex four SiPMs using DRS4 digitizer evaluation board from Paul Scherrer Institute (PSI). We demonstrate 4:1 multiplexing of the SiPM fast output signals and pulse recovery from the digitized multiplexed signal using deconvolution. The noise in the recovered pulse introduces a bias and uncertainty in the estimate of energy and timing that changes with pulse height. The relative uncertainty in the estimated energy from the recovered pulse decreases with pulse height with a maximum uncertainty of 3.1% for the low energy pulses (corresponding to 100 keV); the uncertainty in the estimated time pick-off also decreases with pulse height with a maximum uncertainty of 110 ps for the low energy pulses.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

AI-assisted object condensation clustering for calorimeter shower reconstruction at CLAS12

Several nuclear physics studies using the CLAS12 detector rely on the accurate reconstruction of neutrons and photons from its forward angle calorimeter system. These studies often place restrictive cuts when measuring neutral particles due to an overabundance of false clusters created by the existing calorimeter reconstruction software. In this work, we present a new AI approach to clustering CLAS12 calorimeter hits based on the object condensation framework. The model learns a latent representation of the full detector topology using GravNet layers, serving as the positional encoding for an event’s calorimeter hits which are processed by a Transformer encoder. This unique structure allows the model to contextualize local and long range information, improving its performance. Evaluated on one million simulated $e^-$ $+$ $p$ collision events, our method significantly improves cluster trustworthiness: the fraction of reliable neutron clusters, increasing from 8.88% to 30.73%, and photon clusters, increasing from 51.07% to 64.73%. In conclusion, our study also marks the first application of AI clustering techniques for hodoscopic detectors, showing potential for usage in many other experiments.

Calorimeters↗

Two-phase accurate multiplexed structured image capture (2pAc-MUSIC)

Multiplexed Structural Image Capture (MUSIC) technique uses modulation of light from a scene prior to imaging to encode the temporal evolution of target into spatial frequency shifts, with each shift corresponding to a unique time and resulting in individual distinct snapshots. Computational-processing of the multiplexed single-shot image can recover the nanosecond-resolution scene evolution. One of the limitations is the loss of spatial resolution of the recovered image due to limitations of the low-pass spatial frequency filtering depth. Here we demonstrated that two images with complementary spatial phases can be used to enhance the spatial resolutions. For this application, 2 Phase Accurate (2pAc)-MUSIC is implemented that a scene is encoded with two complementary phases. The increased spatial information captured reduces the lower frequency noise in the Fourier domain found in single-phase MUSIC. A recovery algorithm combines the 180-degree spatial frequency shifted images into a single scene and applies a spatial filter in the Fourier domain that has a larger depth than previously possible to achieve a scene with increased spatial resolution. The 2pAc-MUSIC can effectively enhance the spatial resolution by removing the overlapping zero-order spatial frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Expression and characterization of spore coat Cot$\mathrm{H}$ kinases from the cellulosomes of anaerobic fungi ( Neocallimastigomycetes )

Anaerobic fungi (Neocallimastigomycetes) found in the guts of herbivores are biomass deconstruction specialists with a remarkable ability to extract sugars from recalcitrant plant material. Anaerobic fungi, as well as many species of anaerobic bacteria, deploy multi-enzyme complexes called cellulosomes, which modularly tether together hydrolytic enzymes, to accelerate biomass hydrolysis. While the majority of genomically encoded cellulosomal genes in Neocallimastigomycetes are biomass degrading enzymes, the second largest family of cellulosomal genes encode spore coat CotH domains, whose contribution to fungal cellulosome and/or cellular function is unknown. Structural bioinformatics of CotH proteins from the anaerobic fungus Piromyces finnis shows anaerobic fungal CotH domains conserve key ATP and Mg 2+ binding motifs from bacterial Bacillus CotH proteins known to act as protein kinases. Experimental characterization further demonstrates ATP hydrolysis activity in the presence and absence of substrate from two cellulosomal P. finnis CotH proteins when recombinantly produced in E. coli. These results present foundational evidence for CotH activity in anaerobic fungi and provide a path towards elucidating the functional contribution of this protein family to fungal cellulosome assembly and activity.

59 BASIC BIOLOGICAL SCIENCES↗

Deep-learning-based workflow for boundary and small target segmentation in digital rock images using UNet++ and IK-EBM

We report three-dimensional (3D) X-ray micro-computed tomography (μCT) has been widely used in petroleum engineering because it can provide detailed pore structural information for a reservoir rock, which can be imported into a pore-scale numerical model to simulate the transport and distribution of multiple fluids in the pore space. The partial volume blurring (PVB) problem is a major challenge in segmenting raw μCT images of rock samples, which impacts boundaries and small targets near the resolution limit. We developed a deep-learning (DL)-based workflow for accurate and fast partial volume segmentation. The DL model's performance depends primarily on the training data quality and model architecture. This study employed the entropy-based-masking indicator kriging (IK-EBM) to segment 3D Berea sandstone images as training datasets. The comparison between IK-EBM and manual segmentation using a 3D synthetic sphere pack, which had a known ground truth, showed that IK-EBM had higher accuracy on partial volume segmentation. We then trained and tested the UNet++ model, a state-of-the-art supervised encoder-decoder model, for binary (i.e., void and solid) and four-class segmentation. We compared the UNet++ with the commonly used U-Net and wide U-Net models and showed that the UNet++ had the best performance in terms of pixel-wise and physics-based evaluation metrics. Specifically, boundary-scaled accuracy demonstrated that the UNet++ architecture outperformed the regular U-Net architecture in the segmentation of pixels near boundaries and small targets, which were subjected to the PVB effect. Feature map visualization illustrated that the UNet++ bridged the semantic gaps between the feature maps extracted at different depths of the network, thereby enabling faster convergence and more accurate extraction of fine-scale features. The developed workflow significantly enhances the performance of supervised encoder-decoder models in partial volume segmentation, which has extensive applications in fundamental studies of subsurface energy, water, and environmental systems.

02 PETROLEUM↗

Synthesis and characterization of isotopically barcoded nickel, molybdenum, and tungsten taggants for intentional nuclear forensics

Intentional nuclear forensics is a concept wherein the deliberate addition of benign and persistent material signatures to nuclear material can be used to reduce the time between the discovery of material outside of regulatory control and determination of its original provenance. One concept within intentional nuclear forensics involves the use of perturbed stable isotopes to generate unique isotope ratio “barcodes” to encode information (e.g., production batch, location, etc.) and track material throughout the nuclear fuel cycle. Synthesis of taggant species of nickel (Ni), molybdenum (Mo), and tungsten (W) was undertaken via a double-spike mechanism, wherein two highly enriched isotopes of interest per elemental taggant were mixed to form an enriched “double-spike” which was subsequently isotopically diluted with bulk material having a natural isotopic composition. Two taggant species perturbing isotopic ratios, alpha (α) and beta (β), for each of Ni, Mo, and W were synthesized. Independent measurements of double spikes and alpha and beta taggant species agreed within uncertainty and are clearly resolvable from natural compositions. High-precision analyses were independently performed by MC-ICP-MS at two U.S. National Laboratories, with consensus values and uncertainties calculated for all samples. Observed isotopic perturbations in the final taggant species measured on the order of hundreds to thousands of permille (‰) with respect to natural for isotope ratios of interest (e.g., 60 Ni/ 58 Ni, 100 Mo/ 98 Mo, 186 W/ 183 W). Discrepancies between modeled and measured isotopic compositions were observed and are largely attributed to imprecise vendor assay values for starting materials. Using measured starting material compositions as inputs for the mixing model improved the level of agreement between predicted and measured α and β taggant isotope ratios. Overall, characterization of all taggant species demonstrates that this “barcode” concept could have viability for use in nuclear forensics. Finally, it is expected that for any two-isotope mixing array dozens of isotopic barcodes could be encoded into a material system and subsequently resolved utilizing modern mass spectrometric methods.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗