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At least 685 records · Page 38

One-shot gas detection with transformer paired neural networks in Mako collected longwave infrared hyperspectral imagery

To date, careful data treatment workflows and statistical detectors are used to perform hyperspectral image (HSI) detection of any gas contained in a spectral library, which is often expanded with physics models to incorporate different spectral characteristics. In general, surrounding evidence or known gas-release parameters are used to provide confidence in or confirm detection capability, respectively. This makes quantifying detection performance difficult as it is nearly impossible to develop an absolute ground truth for gas target pixel presence in collected HSI. Consequently, developing and comparing new detection methods, especially machine learning (ML)-based methods, is susceptible to subjectivity in derived detection map quality. Here, in this work, we demonstrate the first use of transformer-based paired neural networks (PNNs) for one-shot gas target detection for multiple gases while providing quantitative classification and detection metrics for their use on labeled data. Terabytes of training data are generated from a database of long-wave infrared HSI obtained from historical Mako sensor campaigns over Los Angeles. By incorporating labels, singular signature representations, and a model development pipeline, we can tune and select PNNs to detect multiple gas targets that are not seen in training on a quantitative basis. We additionally assess our test set detections using interpretability techniques widely employed with ML-based predictors, but less common with detection methods relying on learned latent spaces.

Hyperspectral imaging↗

Enhanced descriptor identification and mechanism understanding for catalytic activity using a data-driven framework: revealing the importance of interactions between elementary steps

We report accurate identification of descriptors for catalytic activities has long been essential to the in-depth understanding of catalysis and recently to set the basis for catalyst screening. However, commonly used methods suffer from low accuracy in predictability. This study reports an enhanced approach to accurately identify the descriptors from a kinetic dataset using a machine learning (ML) surrogate model. CO hydrogenation to methanol over Cu-based catalysts was taken as a case study. Our model captures not only the contribution from individual elementary steps but also the interaction between relevant steps within a reaction network, which was found to be essential for high accuracy. As a result, six effective descriptors are identified, which are accurate enough to ensure the trained gradient boosted regression (GBR) model for good prediction of the methanol turnover frequency (TOF) over metal (M)-doped Cu(111) model surfaces (M = Au, Cu, Pd, Pt, Ni). More importantly, going beyond the purely mathematical ML model, the catalytic role of each identified descriptor can be revealed by using model-agnostic interpretation tools, which enhances the insight into the promoting effect of alloying. The trained GBR model outperforms the conventional derivative-based methods in terms of both the predictability and the mechanism understanding. It opens alternative possibilities toward accurate descriptor-based rational catalyst optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Technical Assessment of the Application of Digital Twin and Prognostic Tools for Condition Monitoring

This report was prepared for the U.S. Nuclear Regulatory Commission (NRC) to present use cases of the application of advanced technologies toward meeting the current and future regulatory requirements for maintenance and condition monitoring of structures, systems, and components (SSCs). The advanced technologies considered in this work, collectively referred to as digital twin (DT) technologies, are advanced sensors and instrumentation, data analytics, machine learning and artificial intelligence (ML/AI), and physics-based models. The report presents two use cases of reactor coolant pumps (RCPs) and heat pipes in nuclear power plants (NPPs) with technical and regulatory considerations and opportunities in using advanced technologies for conditional monitoring. Key findings from the exploration of these considerations are as follows: - Uncertainties in sensor data and model predictions must be rigorously addressed through validation and verification processes - Regulatory compliance is paramount, necessitating data driven models to be developed in line with existing codes and standards, as well as considering potential future guidelines for advanced reactors - Explainability and transparency in ML/AI models are essential for developing operator trust and regulatory review, including methods that enhance the interpretability of complex data-driven predictions - Condition monitoring programs must be evaluated for their effectiveness in reducing maintenance-preventable function failures (MPFF) and aligning with plant performance criteria - The deployment of advanced technologies for condition monitoring could lead to a transition from periodic to continuous monitoring, thereby optimizing maintenance schedules - Collaborative efforts between industry stakeholders, regulatory bodies, and technology developers are crucial for the successful adoption of advanced technologies for condition monitoring systems in nuclear facilities In summary, the introduction of advanced technologies into condition monitoring programs represents a significant leap forward in the domain of NPP maintenance. By harnessing the capabilities of advanced sensors, data analytics, and ML/AI, NPP operators can transition from a time-based to a condition-based maintenance approach. This shift can potentially enhance the reliability and safety of critical plant components while optimizing maintenance efforts and minimizing unnecessary outages. The NRC is continuing to explore the regulatory aspects of advanced technologies as part of inservice inspection and inservice testing (ISI and IST) programs by pursuing additional research in this technical area.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

NMF-Based Anomaly Detection in CMS 2D Tracking Occupancy Histograms

The CMS experiment relies on Data Quality Monitoring (DQM) to ensure that recorded collision data are suitable for physics analysis. During LHC Run 3, each run contains many lumisections and tracking monitoring elements, making offline inspection challenging, especially for localized detector effects that may appear only for short periods of time. This poster presents an unsupervised machine-learning approach to identify anomalous lumisections in CMS tracking occupancy histograms using Non-Negative Matrix Factorization (NMF). The workflow uses offline CMS DQMIO tracking histograms retrieved with the CMS DIALS API and organized as two-dimensional occupancy maps for each lumisection. After selecting stable lumisections, the occupancy maps are normalized and arranged into a non-negative data matrix. The NMF model learns a compact set of basis patterns describing normal tracking occupancy. Each lumisection is then reconstructed from these learned components, and the reconstruction error is used as an anomaly score. Large residuals indicate occupancy patterns that deviate from normal detector behavior and are flagged for further inspection. This NMF-based approach provides a fast and interpretable way to flag lumisections whose tracking occupancy patterns differ from normal detector behavior. Preliminary studies show sensitivity to known tracking anomalies, and ongoing work is focused on validating the method across additional Run 3 Pixel and Strip detector issues.

Rodríguez Ramos, Iliomar [Puerto Rico U., Mayaguez↗

Adoption of image-driven machine learning for microstructure characterization and materials design: A Perspective

Microstructure characterization enables the development of structure-processing-property relationships critical to several research areas within the broad field of materials science, from alloy design to the assessment of corrosion resistance, and failure analysis. Conventional approaches to material characterization have relied on either qualitative inference by the human ex-pert or software applications that can extract high-level features from images, such as boundary segmentation, average grain diameter, etc. Such approaches rely heavily on subject matter expert user intervention and knowledge of what phases or more generally, what microstructural features, are of interest. The recent surge in the adoption of machine learning techniques to address problems in materials engineering has brought with it an increased interest and application of Image Driven Machine Learning (IDML) approaches. In this work, we review the applications of IDML to the field of materials characterization. A canonical hierarchy of stages is defined, which when put sequentially together completes an IDML study: problem definition, dataset building, model selection and training, model evaluation, and integration with existing instrumentation or simulation workflow. The studies reviewed in this work are analyzed from the perspective of each of these stages. Such a review permits agranular assessment of the field, for example the impact of IDML on materials characterization at the nanoscale, the size of a typical dataset required to train a semantic segmentation model on electron microscopy images, ubiquitousness of transfer learning in the domain, etc. Finally, we discuss the importance of interpretability and explainability in the field of IDML for materials characterization, and provide an overview of two emerging techniques in the field: semantic segmentation and generative adversarial networks.

Baskaran, Arun↗

Predicting the dissolution kinetics of silicate glasses by topology-informed machine learning

Machine learning (ML) regression methods are promising tools to develop models predicting the properties of materials by learning from existing databases. However, although ML models are usually good at interpolating data, they often do not offer reliable extrapolations and can violate the laws of physics. Here, to address the limitations of traditional ML, we introduce a “topology-informed ML” paradigm—wherein some features of the network topology (rather than traditional descriptors) are used as fingerprint for ML models—and apply this method to predict the forward (stage I) dissolution rate of a series of silicate glasses. We demonstrate that relying on a topological description of the atomic network (i) increases the accuracy of the predictions, (ii) enhances the simplicity and interpretability of the predictive models, (iii) reduces the need for large training sets, and (iv) improves the ability of the models to extrapolate predictions far from their training sets. As such, topology-informed ML can overcome the limitations facing traditional ML (e.g., accuracy vs. simplicity tradeoff) and offers a promising route to predict the properties of materials in a robust fashion.

36 MATERIALS SCIENCE↗

MO-PIS-Exhibit Hall-01: Tools for TG-142 Linac Imaging QA I

Partners in Solutions is an exciting new program in which AAPM partners with our vendors to present practical “hands-on” information about the equipment and software systems that we use in our clinics. The therapy topic this year is solutions for TG-142 recommendations for linear accelerator imaging QA. Note that the sessions are being held in a special purpose room built on the Exhibit Hall Floor, to encourage further interaction with the vendors. Automated Imaging QA for TG-142 with RIT Presentation Time: 2:45 – 3:15 PM This presentation will discuss software tools for automated imaging QA and phantom analysis for TG-142. All modalities used in radiation oncology will be discussed, including CBCT, planar kV imaging, planar MV imaging, and imaging and treatment coordinate coincidence. Vendor supplied phantoms as well as a variety of third-party phantoms will be shown, along with appropriate analyses, proper phantom setup procedures and scanning settings, and a discussion of image quality metrics. Tools for process automation will be discussed which include: RIT Cognition (machine learning for phantom image identification), RIT Cerberus (automated file system monitoring and searching), and RunQueueC (batch processing of multiple images). In addition to phantom analysis, tools for statistical tracking, trending, and reporting will be discussed. This discussion will include an introduction to statistical process control, a valuable tool in analyzing data and determining appropriate tolerances. An Introduction to TG-142 Imaging QA Using Standard Imaging Products Presentation Time: 3:15 – 3:45 PM Medical Physicists want to understand the logic behind TG-142 Imaging QA. What is often missing is a firm understanding of the connections between the EPID and OBI phantom imaging, the software “algorithms” that calculate the QA metrics, the establishment of baselines, and the analysis and interpretation of the results. The goal of our brief presentation will be to establish and solidify these connections. Our talk will be motivated by the Standard Imaging, Inc. phantom and software solutions. We will present and explain each of the image quality metrics in TG-142 in terms of the theory, mathematics, and algorithms used to implement them in the Standard Imaging PIPSpro software. In the process, we will identify the regions of phantom images that are analyzed by each algorithm. We then will discuss the process of the creation of baselines and typical ranges of acceptable values for each imaging quality metric.

07 ISOTOPE AND RADIATION SOURCES↗

Identifying Critical Infrastructure in Imagery Data Using Explainable Convolutional Neural Networks

To date, no method utilizing satellite imagery exists for detailing the locations and functions of critical infrastructure across the United States, making response to natural disasters and other events challenging due to complex infrastructural interdependencies. This paper presents a repeatable, transferable, and explainable method for critical infrastructure analysis and implementation of a robust model for critical infrastructure detection in satellite imagery. This model consists of a DenseNet-161 convolutional neural network, pretrained with the ImageNet database. The model was provided additional training with a custom dataset, containing nine infrastructure classes. The resultant analysis achieved an overall accuracy of 90%, with the highest accuracy for airports (97%), hydroelectric dams (96%), solar farms (94%), substations (91%), potable water tanks (93%), and hospitals (93%). Critical infrastructure types with relatively low accuracy are likely influenced by data commonality between similar infrastructure components for petroleum terminals (86%), water treatment plants (78%), and natural gas generation (78%). Local interpretable model-agnostic explanations (LIME) was integrated into the overall modeling pipeline to establish trust for users in critical infrastructure applications. The results demonstrate the effectiveness of a convolutional neural network approach for critical infrastructure identification, with higher than 90% accuracy in identifying six of the critical infrastructure facility types.

97 MATHEMATICS AND COMPUTING↗

Physics-guided logistic classification for tool life modeling and process parameter optimization in machining

This paper describes a physics-guided logistic classification method for tool life modeling and process parameter optimization in machining. Tool life is modeled using a classification method since the exact tool life cannot be measured in a typical production environment where tool wear can only be directly measured when the tool is replaced. Here, in this study, laboratory tool wear experiments are used to simulate tool wear data normally collected during part production. Two states are defined: tool not worn (class 0) and tool worn (class 1). The non-linear reduction in tool life with cutting speed is modeled by applying a logarithmic transformation to the inputs for the logistic classification model. A method for interpretability of the logistic model coefficients is provided by comparison with the empirical Taylor tool life model. The method is validated using tool wear experiments for milling. Results show that the physics-guided logistic classification method can predict tool life using limited datasets. A method for pre-process optimization of machining parameters using a probabilistic machining cost model is presented. The proposed method offers a robust and practical approach to tool life modeling and process parameter optimization in a production environment.

Machine learning↗

Exploring Transport Behavior in Hybrid Perovskites Solar Cells via Machine Learning Analysis of Environmental-Dependent Impedance Spectroscopy

Hybrid organic–inorganic perovskites are one of the promising candidates for the next-generation semiconductors due to their superlative optoelectronic properties. However, one of the limiting factors for potential applications is their chemical and structural instability in different environments. Herein, the stability of (FAPbI3)0.85(MAPbBr3)0.15 perovskite solar cell is explored in different atmospheres using impedance spectroscopy. An equivalent circuit model and distribution of relaxation times (DRTs) are used to effectively analyze impedance spectra. DRT is further analyzed via machine learning workflow based on the non-negative matrix factorization of reconstructed relaxation time spectra. This exploration provides the interplay of charge transport dynamics and recombination processes under environment stimuli and illumination. The results reveal that in the dark, oxygen atmosphere induces an increased hole concentration with less ionic character while ionic motion is dominant under ambient air. Under 1 Sun illumination, the environment-dependent impedance responses show a more striking effect compared with dark conditions. In this case, the increased transport resistance observed under oxygen atmosphere in equivalent circuit analysis arises due to interruption of photogenerated hole carriers. The results not only shed light on elucidating transport mechanisms of perovskite solar cells in different environments but also offer an effective interpretation of impedance responses.

36 MATERIALS SCIENCE↗

AP-Net: An atomic-pairwise neural network for smooth and transferable interaction potentials

Intermolecular interactions are critical to many chemical phenomena, but their accurate computation using ab initio methods is often limited by computational cost. The recent emergence of machine learning (ML) potentials may be a promising alternative. Useful ML models should not only estimate accurate interaction energies but also predict smooth and asymptotically correct potential energy surfaces. However, existing ML models are not guaranteed to obey these constraints. Indeed, systemic deficiencies are apparent in the predictions of our previous hydrogen-bond model as well as the popular ANI-1X model, which we attribute to the use of an atomic energy partition. As a solution, we propose an alternative atomic-pairwise framework specifically for intermolecular ML potentials, and we introduce AP-Net—a neural network model for interaction energies. The AP-Net model is developed using this physically motivated atomic-pairwise paradigm and also exploits the interpretability of symmetry adapted perturbation theory (SAPT). We show that in contrast to other models, AP-Net produces smooth, physically meaningful intermolecular potentials exhibiting correct asymptotic behavior. Initially trained on only a limited number of mostly hydrogen-bonded dimers, AP-Net makes accurate predictions across the chemically diverse S66x8 dataset, demonstrating significant transferability. On a test set including experimental hydrogen-bonded dimers, AP-Net predicts total interaction energies with a mean absolute error of 0.37 kcal mol−1, reducing errors by a factor of 2–5 across SAPT components from previous neural network potentials. The pairwise interaction energies of the model are physically interpretable, and an investigation of predicted electrostatic energies suggests that the model “learns” the physics of hydrogen-bonded interactions.

Glick, Zachary L. (ORCID:0000000309002849)↗

Factors Governing Oxygen Vacancy Formation in Oxide Perovskites

The control of oxygen vacancy (V O ) formation is critical to advancing multiple metal-oxide-perovskite-based technologies. In this work, we report the construction of a compact linear model for the neutral V O formation energy in ABO 3 perovskites that reproduces, with reasonable fidelity, Hubbard-U-corrected density functional theory calculations based on the state-of-the-art, strongly constrained and appropriately normed exchange-correlation functional. We obtain a mean absolute error of 0.45 eV for perovskites stable at 298 K, an accuracy that holds across a large, electronically diverse set of ABO 3 perovskites. Our model considers perovskites containing alkaline-earth metals (Ca, Sr, and Ba) and lanthanides (La and Ce) on the A-site and 3d transition metals (Ti, V, Cr, Mn, Fe, Co, and Ni) on the B-site in six different crystal systems (cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, and monoclinic) common to perovskites. Physically intuitive metrics easily extracted from existing experimental thermochemical data or via inexpensive quantum mechanical calculations, including crystal bond dissociation energies and (solid phase) reduction potentials, are key components of the model. Beyond validation of the model against known experimental trends in materials used in solid oxide fuel cells, the model yields new candidate perovskites not contained in our training data set, such as (Bi,Y)(Fe,Co)O 3 , which we predict may have favorable thermochemical water-splitting properties. The confluence of sufficient accuracy, efficiency, and interpretability afforded by our model not only facilitates high-throughput computational screening for any application that requires the precise control of V O concentrations but also provides a clear picture of the dominant physics governing V O formation in metal-oxide perovskites.

08 HYDROGEN↗

Learning Weight Uncertainty with Stochastic Gradient MCMC for Shape Classification

Learning the representation of shape cues in 2D & 3D objects for recognition is a fundamental task in computer vision. Deep neural networks (DNNs) have shown promising performance on this task. Due to the large variability of shapes, accurate recognition relies on good estimates of model uncertainty, ignored in traditional training of DNNs, typically learned via stochastic optimization. This paper leverages recent advances in stochastic gradient Markov Chain Monte Carlo (SG-MCMC) to learn weight uncertainty in DNNs. It yields principled Bayesian interpretations for the commonly used Dropout/DropConnect techniques and incorporates them into the SG-MCMC framework. Extensive experiments on 2D & 3D shape datasets and various DNN models demonstrate the superiority of the proposed approach over stochastic optimization. Our approach yields higher recognition accuracy when used in conjunction with Dropout and Batch-Normalization.

convolutional neural network↗

FAIR AI models in high energy physics

Abstract The findable, accessible, interoperable, and reusable (FAIR) data principles provide a framework for examining, evaluating, and improving how data is shared to facilitate scientific discovery. Generalizing these principles to research software and other digital products is an active area of research. Machine learning models—algorithms that have been trained on data without being explicitly programmed—and more generally, artificial intelligence (AI) models, are an important target for this because of the ever-increasing pace with which AI is transforming scientific domains, such as experimental high energy physics (HEP). In this paper, we propose a practical definition of FAIR principles for AI models in HEP and describe a template for the application of these principles. We demonstrate the template’s use with an example AI model applied to HEP, in which a graph neural network is used to identify Higgs bosons decaying to two bottom quarks. We report on the robustness of this FAIR AI model, its portability across hardware architectures and software frameworks, and its interpretability.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Biochemical Process Modeling and Simulation (BPMS)

The Biochemical Process Modeling and Simulation project aims to reduce the cost and time of research by applying theory, modeling, and simulation to the most relevant bottlenecks in the biochemical process. We use molecular modeling, quantum mechanics, metabolic modeling, fluid dynamics, and reaction-diffusion methods in close collaboration with pretreatment, hydrolysis, upgrading, and TEA. The project's outcomes are increased yields and efficiency of the biochemical process, added value to products, and reduced price of fuels by specifically targeting catalytic efficiency, reactor design, enzyme efficiency, and microbial design. We work closely with experimental projects to identify problems and iterate with experiments to find and refine solutions. By working with experimentalists, we decide on problems that can be solved with simulation that could otherwise not be solved or would take too long with experiment alone to reach BETO's targets. Over the years, we have produced solutions that have resulted in determining the most likely fatty-acid derivative for passive transport out of bacteria that upgrade biomass, and we have also designed enzyme mutations for enhanced lignin upgrading. Metabolic models have been developed to tune the activity of 2,3 butanediol production for the 2030 target. A computational method to deliver understanding of how complex omics data can be interpreted in the metabolic pathways of organisms used in the Agile Biofoundry. We have found methods to overcome specific barriers and continue to develop those methods. Our reactor studies have guided the design of both the microbes and reactors for aerobic and micro-aerobic production at all scales and have been instrumental in improving the accuracy of techno-economic analysis models. This project is essential in the process of selecting the final processes for 2030 SAF production targets. More specifically, recently, we have: 1) Predicted the strength of the basic structural interactions in commodity plastics to provide guidance for plastics upcycling strategies. 2) Developed computational tool to improve the characterization of lignin-derived compounds 3) Developed new methodologies to enable Machine Learning-based Directed Evolution for protein engineering. 4) Developed Machine Learning methods to predict protein promiscuity and mutations to further improve microbial and enzymatic driven processes and demonstrated the utility of ML approaches to engineering proteins from sparse experimental datasets. 5) Developed new methods to enable high-fidelity simulation of aerobic fermentation at industrial scale and resolving mismatch of time scales through subcycling/operator splitting 7) Identified the difficulty in preventing local high-oxygen conditions in industrial bubble columns, which leads to less-desirable acetoin production, suggesting future research directions in alternative reactor configurations (e.g loop reactors, shallow-channel reactors).

BIOMASS FUELS↗

Veridical data science

Building and expanding on principles of statistics, machine learning, and scientific inquiry, we propose the predictability, computability, and stability (PCS) framework for veridical data science. Our framework, composed of both a workflow and documentation, aims to provide responsible, reliable, reproducible, and transparent results across the data science life cycle. The PCS workflow uses predictability as a reality check and considers the importance of computation in data collection/storage and algorithm design. It augments predictability and computability with an overarching stability principle. Stability expands on statistical uncertainty considerations to assess how human judgment calls impact data results through data and model/algorithm perturbations. As part of the PCS workflow, we develop PCS inference procedures, namely PCS perturbation intervals and PCS hypothesis testing, to investigate the stability of data results relative to problem formulation, data cleaning, modeling decisions, and interpretations. We illustrate PCS inference through neuroscience and genomics projects of our own and others. Moreover, we demonstrate its favorable performance over existing methods in terms of receiver operating characteristic (ROC) curves in high-dimensional, sparse linear model simulations, including a wide range of misspecified models. Finally, we propose PCS documentation based on R Markdown or Jupyter Notebook, with publicly available, reproducible codes and narratives to back up human choices made throughout an analysis. The PCS workflow and documentation are demonstrated in a genomics case study available on Zenodo.

97 MATHEMATICS AND COMPUTING↗

Deeply uncertain: comparing methods of uncertainty quantification in deep learning algorithms

We present a comparison of methods for uncertainty quantification (UQ) in deep learning algorithms in the context of a simple physical system. Three of the most common uncertainty quantification methods - Bayesian Neural Networks (BNN), Concrete Dropout (CD), and Deep Ensembles (DE) - are compared to the standard analytic error propagation. We discuss this comparison in terms endemic to both machine learning ("epistemic" and "aleatoric") and the physical sciences ("statistical" and "systematic"). The comparisons are presented in terms of simulated experimental measurements of a single pendulum - a prototypical physical system for studying measurement and analysis techniques. Our results highlight some pitfalls that may occur when using these UQ methods. For example, when the variation of noise in the training set is small, all methods predicted the same relative uncertainty independently of the inputs. This issue is particularly hard to avoid in BNN. On the other hand, when the test set contains samples far from the training distribution, we found that no methods sufficiently increased the uncertainties associated to their predictions. This problem was particularly clear for CD. In light of these results, we make some recommendations for usage and interpretation of UQ methods.

59 BASIC BIOLOGICAL SCIENCES↗

Interpretable design of Ir-free trimetallic electrocatalysts for ammonia oxidation with graph neural networks

The electrochemical ammonia oxidation to dinitrogen as a means for energy and environmental applications is a key technology toward the realization of a sustainable nitrogen cycle. The state-of-the-art metal catalysts including Pt and its bimetallics with Ir show promising activity, albeit suffering from high overpotentials for appreciable current densities and the soaring price of precious metals. Herein, the immense design space of ternary Pt alloy nanostructures is explored by graph neural networks trained on ab initio data for concurrently predicting site reactivity, surface stability, and catalyst synthesizability descriptors. Among a few Ir-free candidates that emerge from the active learning workflow, Pt 3 Ru-M (M: Fe, Co, or Ni) alloys were successfully synthesized and experimentally verified to be more active toward ammonia oxidation than Pt, Pt 3 Ir, and Pt 3 Ru. More importantly, feature attribution analyses using the machine-learned representation of site motifs provide fundamental insights into chemical bonding at metal surfaces and shed light on design strategies for high-performance catalytic systems beyond the d-band center metric of binding sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗