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DOE OSTI2023

Model validation and selection in metabolic flux analysis and flux balance analysis

13C-Metabolic Flux Analysis (13C-MFA) and Flux Balance Analysis (FBA) are widely used to investigate the operation of biochemical networks in both biological and biotechnological research. Both methods use metabolic reaction network models of metabolism operating at steady state so that reaction rates (fluxes) and the levels of metabolic intermediates are constrained to be invariant. They provide estimated (MFA) or predicted (FBA) values of the fluxes through the network in vivo, which cannot be measured directly. These fluxes can shed light on basic biology and have been successfully used to inform metabolic engineering strategies. Several approaches have been taken to test the reliability of estimates and predictions from constraint-based methods and to compare alternative model architectures. Despite advances in other areas of the statistical evaluation of metabolic models, such as the quantification of flux estimate uncertainty, validation and model selection methods have been underappreciated and underexplored. We review the history and state-of-the-art in constraint-based metabolic model validation and model selection. Applications and limitations of the χ 2 -test of goodness-of-fit, the most widely used quantitative validation and selection approach in 13C-MFA, are discussed, and complementary and alternative forms of validation and selection are proposed. A combined model validation and selection framework for 13C-MFA incorporating metabolite pool size information that leverages new developments in the field is presented and advocated for. Finally, we discuss how adopting robust validation and selection procedures can enhance confidence in constraint-based modeling as a whole and ultimately facilitate more widespread use of FBA in biotechnology.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

An introduction to neuromorphic computing and its potential impact for unattended ground sensors

Neuromorphic computers are hardware systems that mimic the brain’s computational process phenomenology. This is in contrast to neural network accelerators, such as the Google TPU or the Intel Neural Compute Stick, which seek to accelerate the fundamental computation and data flows of neural network models used in the field of machine learning. Neuromorphic computers emulate the integrate and fire neuron dynamics of the brain to achieve a spiking communication architecture for computation. While neural networks are brain-inspired, they drastically oversimplify the brain’s computation model. Neuromorphic architectures are closer to the true computation model of the brain (albeit, still simplified). Neuromorphic computing models herald a 1000x power improvement over conventional CPU architectures. Sandia National Labs is a major contributor to the research community on neuromorphic systems by performing design analysis, evaluation, and algorithm development for neuromorphic computers. Space-based remote sensing development has been a focused target of funding for exploratory research into neuromorphic systems for their potential advantage in that program area; SNL has led some of these efforts. Recently, neuromorphic application evaluation has reached the NA-22 program area. This same exploratory research and algorithm development should penetrate the unattended ground sensor space for SNL’s mission partners and program areas. Neuromorphic computing paradigms offer a distinct advantage for the SWaP-constrained embedded systems of our diverse sponsor-driven program areas.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2022

Impacts of Climate Change on Global Food Trade Networks

Countries' reliance on global food trade networks implies that regionally different climate change impacts on crop yields will be transmitted across borders. This redistribution constitutes a significant challenge for climate adaptation planning and may affect how countries engage in cooperative action. This paper investigates the long-term (2070–2099) potential impacts of climate change on global food trade networks of three key crops: wheat, rice and maize. We propose a simple network model to project how climate change impacts on crop yields may be translated into changes in trade. Combining trade and climate impact data, our analysis proceeds in three steps. First, we use network community detection to analyse how the concentration of global production in present-day trade communities may become disrupted with climate change impacts. Second, we study how countries may change their network position following climate change impacts. Third, we study the total climate-induced change in production plus import within trade communities. Results indicate that the stability of food trade network structures compared to today differs between crops, and that countries' maize trade is least stable under climate change impacts. Results also project that threats to global food security may depend on production change in a few major global producers, and whether trade communities can balance production and import loss in some vulnerable countries. Overall, our model contributes a baseline analysis of cross-border climate impacts on food trade networks.

climate change↗

DOE OSTI2024

Determining the Reaction Kinetics and Thermodynamics of a Diels–Alder Network Using Dynamic Gel Criteria

We undertook a detailed rheological investigation to evaluate the kinetic parameters of the forward and reverse Diels–Alder (DA) reactions of a model network cross-linked using a furan prepolymer and a common aromatic bismaleimide. At high temperature where the Winter–Chambon’s criterion of frequency-independence was more applicable, a multiwave technique permitted van’t Hoff analysis and calculation of the reaction thermodynamic parameters, specifically the enthalpy and entropy of the reaction: ΔH° = –38.3 ± 5.2 kJ mol –1 and ΔS° = –94.3 ± 13.4 J mol –1 . At mild temperatures where the G'–G" crossover point is experimentally convenient to measure gelation, isothermal tests were used to obtain reasonable fDA kinetic parameters from Eyring analysis such as the apparent activation enthalpy and entropy of ΔH$^{‡}_{fDA}$ = 76.8 ± 6.9 kJ mol –1 and ΔS$^{‡}_{fDA}$= –82.8 ± 22.2 J mol –1 K –1 . Comparable rheokinetic methods include cross-linking density measurements and stress relaxation tests to calculate effective kinetics, whereas the critical gel conversion was consistently applied here. As a result, rate data are fitted with the Arrhenius equation for comparison purposes and the Eyring equation to demonstrate its broader utility.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Graph-Based Approaches for Predicting Solvation Energy in Multiple Solvents: Open Datasets and Machine Learning Models

The solvation properties of molecules, often estimated using quantum chemical simulations, are important in the synthesis of energy storage materials, drugs, and industrial chemicals. Here, we develop machine learning models of solvation energies to replace expensive quantum chemistry calculations with inexpensive-to-compute message-passing neural network models that require only the molecular graph as inputs. Our models are trained on a new database of solvation energies for 130,258 molecules taken from the QM9 dataset computed in five solvents (acetone, ethanol, acetonitrile, dimethyl sulfoxide, and water) via an implicit solvent model. Our best model achieves a mean absolute error of 0.5 kcal/mol for molecules with nine or fewer non-hydrogen atoms and 1 kcal/mol for molecules with between 10 and 14 non-hydrogen atoms. We make the entire dataset of 651,290 computed entries openly available and provide simple web and programmatic interfaces to enable others to run our solvation energy model on new molecules. This model calculates the solvation energies for molecules using only the SMILES string and also provides an estimate of whether each molecule is within the domain of applicability of our model. We envision that the dataset and models will provide the functionality needed for the rapid screening of large chemical spaces to discover improved molecules for many applications.

25 ENERGY STORAGE↗

DOE OSTI2020

Phase behavior of continuous-space systems: A supervised machine learning approach

The phase behavior of complex fluids is a challenging problem for molecular simulations. Supervised machine learning (ML) methods have shown potential for identifying the phase boundaries of lattice models. In this work, we extend these ML methods to continuous-space systems. We propose a convolutional neural network model that utilizes grid-interpolated coordinates of molecules as input data of ML and optimizes the search for phase transitions with different filter sizes. We test the method for the phase diagram of two off-lattice models, namely, the Widom–Rowlinson model and a symmetric freely jointed polymer blend, for which results are available from standard molecular simulations techniques. The ML results show good agreement with results of previous simulation studies with the added advantage that there is no critical slowing down. We find that understanding intermediate structures near a phase transition and including them in the training set is important to obtain the phase boundary near the critical point. The method is quite general and easy to implement and could find wide application to study the phase behavior of complex fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1995

Two-component modeling of the solar IR CO lines

One-dimensional hydrostatic models of quiet and active solar regions can be constructed that generally account for the observed intensities of lines and continue throughout the spectrum, except for the infrared CO lines. There is an apparent conflict between: (1) observations of the strongest infrared CO lines formed in LTE at low-chromospheric heights but at temperatures much cooler than the average chromospheric values; and (2) observations of Ca II, UV (ultraviolet), and microwave intensities that originate from the same chromospheric heights but at the much higher temperatures characteristic of the average chromosphere. A model M(sub CO) has been constructed which gives a good fit to the full range of mean CO line profiles (averaged over the central area of the solar disk and over time) but this model conflicts with other observations of average quiet regions. A model L(sub CO) which is approximately 100 K cooler than M(sub CO) combined with a very bright network model F in the proportions 0.6 L(sub CO) + 0.4 F is found to be generally consistent with the CO, Ca II, UV, and microwave observations. Ayres, Testerman, and Brault found that models COOLC and FLUXT in the proportions 0.925 and 0.075 account for the CO and Ca II lines, but these combined models give an average UV intensity at 140 nm about 20 times larger than observed. The 0.6 L(sub CO) + 0.4 F result may give a better description of the cool and hot components that produce the space- and time-averaged spectra. Recent observations carried out by Uitenbroek, Noyes, and Rabine with high spatial and temporal resolution indicate that the faintest intensities in the strong CO lines measured at given locations usually become much brighter within 1 to 3 minutes. The cool regions thus seem to be mostly the low-temperature portions of oscillatory waves rather than cool structures that are stationary.

Avrett, Eugene H.↗

DOE OSTI2023

Modeling the 4D discharge of lithium-ion batteries with a multiscale time-dependent deep learning framework

The lithium-ion battery (LIB) field is moving towards the direction of investigating spatially resolved physical phenomena in the 3D porous microstructure of electrodes. These pore-scale simulations give new insights into the local dynamics of lithiation/de-lithiation and charge transport, Nevertheless, the computational time of these simulations limits the integration of these models in optimization workflows of cycling conditions or electrode manufacturing processes. Machine learning models present a way of assessing in real-time the performance of materials. While several successful techniques for replicating simulations with machine learning have been proposed, this case study presents a more demanding problem, due to the necessity of understanding the behavior of heterogeneous 3D local data, as it evolves in time: this poses both a scientific and a technical challenge. To this end, we propose an autoregressive multiscale convolutional neural network model to predict relevant quantities at the pore-scale in the solid phase: the lithium concentration (in the active material) and potential (in the active material and carbon binder). Here, these are ultimately used to reconstruct the battery discharge curve. 3D images of the electrode microstructures are the input to the network, trained with a dataset of finite element method simulations to predict the discharge behavior of the cathode side in lithium ion batteries. We propose this machine learning model as a proof-of-concept of the applicability of multiscale networks for time-dependent physics problems. The trained model exhibits very high accuracy (with errors lower than 2 %) in forecasting the discharge behavior of new unseen cathodes.

25 ENERGY STORAGE↗

NASA NTRS2016

Architecture for Cognitive Networking within NASAs Future Space Communications Infrastructure

Future space mission concepts and designs pose many networking challenges for command, telemetry, and science data applications with diverse end-to-end data delivery needs. For future end-to-end architecture designs, a key challenge is meeting expected application quality of service requirements for multiple simultaneous mission data flows with options to use diverse onboard local data buses, commercial ground networks, and multiple satellite relay constellations in LEO, MEO, GEO, or even deep space relay links. Effectively utilizing a complex network topology requires orchestration and direction that spans the many discrete, individually addressable computer systems, which cause them to act in concert to achieve the overall network goals. The system must be intelligent enough to not only function under nominal conditions, but also adapt to unexpected situations, and reorganize or adapt to perform roles not originally intended for the system or explicitly programmed. This paper describes architecture features of cognitive networking within the future NASA space communications infrastructure, and interacting with the legacy systems and infrastructure in the meantime. The paper begins by discussing the need for increased automation, including inter-system collaboration. This discussion motivates the features of an architecture including cognitive networking for future missions and relays, interoperating with both existing endpoint-based networking models and emerging information-centric models. From this basis, we discuss progress on a proof-of-concept implementation of this architecture as a cognitive networking on-orbit application on the SCaN Testbed attached to the International Space Station.

space networks↗

DOE OSTI2023

Lithium-Ion Battery Diagnostics Using Electrochemical Impedance via Machine-Learning

Diagnosing battery states such as health, state-of-charge, or temperature is crucial for ensuring the safety and reliability of electrochemical energy storage systems. While some states, such as temperature, may be measured using cheap sensors, accurate diagnosis of battery health metrics usually requires time-consuming performance measurements, making them infeasible for use in real-world operation. These health metrics can be measured during lab-testing and then estimated on-line using predictive life models or via state observer algorithms such as Kalman filters, but these predictive methods should be supplemented by actual measurement of battery health whenever possible to ensure reliability. Rapid measurement of battery health may be done by various types of fast diagnostic techniques such as electrochemical impedance spectroscopy (EIS), which can be performed in only a few minutes and require only a fraction of the energy and power needed for a full charge and discharge measurement. But there is a substantial challenge for estimating battery health using EIS data, as EIS is sensitive to cell temperature, state-of-charge, current, and resting time in addition to health. Thus, utilizing EIS data to predict battery capacity requires correcting for all these additional variables, a task that is extremely difficult to handle analytically. This talk utilizes machine-learning methods to estimate the effectiveness of battery capacity prediction from EIS data, leveraging a data set of hundreds of EIS measurements recorded at varying temperature and state-of-charge throughout a 500-day aging study of 32 commercial, large-format NMC-Graphite lithium-ion batteries. Using EIS as input to machine-learning models is complicated by the nonlinear response of impedance to battery health, temperature, and state-of-charge, as well as the collinearity between the impedance response at neighboring frequencies, which can easily lead to overfit models. To train robust models, features from EIS data need to be extracted from the data or some subset of critical frequencies selected. Many approaches for extracting and selecting features from EIS data from electrochemical analysis and machine-learning fields were identified for analysis: using the entire raw spectra; selection of one, two, or many frequencies from the entire spectra; selecting interesting points from the EIS measurement using domain knowledge; fitting EIS with an equivalent-circuit model; calculating statistics on the raw impedance values; and reducing the dimensionality of the data using unsupervised linear (principal component analysis) and non-linear (uniform manifold approximation and projection) methods. These approaches were rigorously compared using a machine-learning pipeline approach, training linear, Gaussian process, and random forest regression models and quantifying performance using cross-validation as well as a held-out test set. An artificial neural network model trained on the raw spectra was also tested. Promising pipelines were fine-tuned via Bayesian hyperparameter optimization using cross-validation loss and training with class-specific weights to counter data set imbalance. The most reliable method for utilizing impedance in this work was the selection of two optimal frequencies through an exhaustive search, resulting in about 2% mean absolute error on test data for both Gaussian process and random forest model architectures. Interrogation of a variety of models reveals critical frequencies of 100 Hz and 103 Hz for this data set, though the optimal set of frequencies is not necessarily intuitive, i.e., the best performing models are not simply those that use impedance at frequencies that have the highest correlation to the relative discharge capacity. The best performing model is an ensemble model, which is able to predict battery capacity with 1.9% mean absolute error for unseen cells using impedance recorded at a variety of temperatures and states-of-charge.

battery↗

NASA NTRS2021

Applying Machine Learning to Predict Alaskan Ionospheric Irregularities

In this work several machine-learning (ML) techniques for predicting ionospheric irregularities in the northern auroral zone were tested. The techniques include Ridge Regression, Long Short-Term Memory Neural Network (LSTM), Classification Neural Network (CNN), Autoencoder Classification Neural Network (ACNN), and LSTM Autoencoder Classification Neural Network (LACNN). These techniques were tested with the rate of total electron content (TEC) index (ROTI) data collected during 2008 and 2009 from a geodetic station in Fairbanks, Alaska (64.98°N, 147.50°W), which is in the auroral zone. Using ROTI data with the ML techniques, experiments were conducted to reach two goals: (1) examine what space weather measurements present good correlation with ROTI so that they may be helpful in ML-based prediction of ionospheric irregularities in the polar region; (2) predict ROTI hours and days ahead by training the neural network models with historical ROTI data alone. The Ridge Regression experiments indicate that a combination of measurements of local geomagnetic horizontal components, geomagnetic SYM-H index, 3-hour Kp and ap indices, and F10.7 solar flux index appears to be more correlated to the single-site ROTI measurements than other parameters. The neural network (NN) experiments show that although the LACNN model allows for predictions of non-irregularity and irregularity conditions defined by ROTI levels up to 3 hours in advance, with an overall accuracy ≥ 92%, a number of irregularity events can still be missed. Hence, further development is needed to reduce the number of missed events. In this paper, the models, data processing, model performance, prediction results, and potential applications are presented.

Pi, Xiaoqing↗

DOE OSTI2025

Solving sparse finite element problems on neuromorphic hardware

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

Applied mathematics↗

DOE OSTI2021

Predictability of Seawater DMS During the North Atlantic Aerosol and Marine Ecosystem Study (NAAMES)

This work presents an overview of a unique set of surface ocean dimethylsulfide (DMS) measurements from four shipboard field campaigns conducted during the North Atlantic Aerosol and Marine Ecosystem Study (NAAMES) project. Variations in surface seawater DMS are discussed in relation to biological and physical observations. Results are considered at a range of timescales (seasons to days) and spatial scales (regional to sub-mesoscale). Elevated DMS concentrations are generally associated with greater biological productivity, although chlorophyll a (Chl) only explains a small fraction of the DMS variability (15%). Physical factors that determine the location of oceanic temperature fronts and depth of vertical mixing have an important influence on seawater DMS concentrations during all seasons. The interplay of biomass and physics influences DMS concentrations at regional/seasonal scales and at smaller spatial and shorter temporal scales. Seawater DMS measurements are compared with the global seawater DMS climatology and predictions made using a recently published algorithm and by a neural network model. The climatology is successful at capturing the seasonal progression in average seawater DMS, but does not reproduce the shorter spatial/temporal scale variability. The input terms common to the algorithm and neural network approaches are biological (Chl) and physical (mixed layer depth, photosynthetically active radiation, seawater temperature). Both models predict the seasonal North Atlantic average seawater DMS trends better than the climatology. However, DMS concentrations tend to be under-predicted and the episodic occurrence of higher DMS concentrations is poorly predicted. The choice of climatological seawater DMS product makes a substantial impact on the estimated DMS flux into the North Atlantic atmosphere. These results suggest that additional input terms are needed to improve the predictive capability of current state-of-the-art approaches to estimating seawater DMS.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Gaussian Process Classification for Galaxy Blend Identification in LSST

Abstract A significant fraction of observed galaxies in the Rubin Observatory Legacy Survey of Space and Time (LSST) will overlap at least one other galaxy along the same line of sight, in a so-called “blend.” The current standard method of assessing blend likelihood in LSST images relies on counting up the number of intensity peaks in the smoothed image of a blend candidate, but the reliability of this procedure has not yet been comprehensively studied. Here we construct a realistic distribution of blended and unblended galaxies through high-fidelity simulations of LSST-like images, and from this we examine the blend classification accuracy of the standard peak-finding method. Furthermore, we develop a novel Gaussian process blend classifier model, and show that this classifier is competitive with both the peak finding method as well as with a convolutional neural network model. Finally, whereas the peak-finding method does not naturally assign probabilities to its classification estimates, the Gaussian process model does, and we show that the Gaussian process classification probabilities are generally reliable.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1973

Ion thruster thermal characteristics and performance.

Experimental and analytical results for a typical 20-cm-diam, hollow-cathode ion thrustor are reported. The foundation of the investigation was the application of thermal model correction techniques. Pertinent thermal properties and plasma heating characteristics of the thrustor were determined through correlation and integration of temperature measurement data with a single-state Wiener-Kalman filter. The thrustor self-heating levels on various parts were realistically estimated. Analytically predicted temperatures were forced to agree with the measured values for the purpose of constructing a corrected thermal model, which could then be used to evaluate more realistic thrustor circumstances and environments. The expected accuracy of the resultant analytical network model was demonstrated to be plus or minus 10 K. Thrustor thermal performance data for a typical five-thrustor array are presented as functions of environmental solar intensities. The thermal analyses are also extended to a 30-cm thrustor system.

Wen, L.↗

NASA NTRSDate not supplied

NEUROSPF: A Tool For the Symbolic Analysis of Neural Networks

This paper presents NEUROSPF, a tool for the symbolic analysis of neural networks. Given a trained neural network model, the tool extracts the architecture and model parameters and translates them into a Java representation that is amenable for analysis using the Symbolic PathFinder symbolic execution tool. Notably, NEUROSPF encodes specialized peer classes for parsing the model’s parameters, thereby enabling efficient analysis. With NEUROSPF the user has the flexibility to specify either the inputs or the network internal parameters as symbolic, promoting the application of program analysis and testing approaches from software engineering to the field of machine learning. For instance, NEUROSPF can be used for coverage-based testing and test generation, finding adversarial examples and also constraint-based repair of neural networks, thus improving the reliability of neural networks and of the applications that use them.

neural networks↗

NASA NTRSDate not supplied

Pilot Workload Rating Predictions Using Image Data and Recurrent Neural Networks

In this work, we augmented existing methods for estimating pilot workload ratings with deep neural networks trained using data from simulated flight tests in the Vertical Motion Simulator (VMS). We used an existing method, Spare Capacity Operations Estimator (SCOPE), along with a recurrent neural network and conducted comparison studies between the two methods individually, and when used together. We found that using both methods together can improve the result over using either approach alone. In our first test case, we achieved an improved linear correlation coefficient of 0.409 over that of SCOPE alone at 0.352 on the training dataset. Through cross validation, we also found that the results may be dependent on the split of training vs. validation data, and that further investigation should be conducted to understand what additional inputs to the neural network model should be made.

Image Data↗

DOE OSTI2021

Importance of Engineered and Learned Molecular Representations in Predicting Organic Reactivity, Selectivity, and Chemical Properties

Machine-readable chemical structure representations are foundational in all attempts to harness machine learning for the prediction of reactivities, selectivities, and chemical properties directly from molecular structure. The featurization of discrete chemical structures into a continuous vector space is a critical phase undertaken before model selection, and the development of new ways to quantitatively encode molecules is an active area of research. Here, we highlight the application and suitability of different representations, from expert-guided “engineered” descriptors to automatically “learned” features, in different prediction tasks relevant to organic and organometallic chemistry, where differing amounts of training data are available. These tasks include statistical models of stereo- and enantioselectivity, thermochemistry, and kinetics developed using experimental and quantum chemical data. The use of expert-guided molecular descriptors provides an opportunity to incorporate chemical knowledge, domain expertise, and physical constraints into statistical modeling. In applications to stereoselective organic and organometallic catalysis, where data sets may be relatively small and 3D-geometries and conformations play an important role, mechanistically informed features can be used successfully to obtain predictive statistical models that are also chemically interpretable. We provide an overview of several recent applications of this approach to obtain quantitative models for reactivity and selectivity, where topological descriptors, quantum mechanical calculations of electronic and steric properties, along with conformational ensembles, all feature as essential ingredients of the molecular representations used. Alternatively, more flexible, general-purpose molecular representations such as attributed molecular graphs can be used with machine learning approaches to learn the complex relationship between a structure and prediction target. This approach has the potential to out-perform more traditional representation methods such as “hand-crafted” molecular descriptors, particularly as data set sizes grow. One area where this is particularly relevant is in the use of large sets of quantum mechanical data to train quantitative structure–property relationships. A general approach toward curating useful data sets and training highly accurate graph neural network models is discussed in the context of organic bond dissociation enthalpies, where this strategy outperforms regression using precomputed descriptors. Finally, we describe how graph neural network predictions can be incorporated into mechanistically informed statistical models of chemical reactivity and selectivity. Once trained, this approach avoids the expensive computational overhead associated with quantum mechanical calculations, while maintaining chemical interpretability. We illustrate examples for which fast predictions of bond dissociation enthalpy and of the identities of radicals formed through cleavage of a molecule’s weakest bond are used in simple physical models of site-selectivity and reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗