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At least 109 records · Page 6

Backpropagation-based learning with local derivative approximation and memory replay in biologically plausible neural systems

When learning, the brain modifies individual synaptic connections to reach a desired behavior. Animal and human brains have been shown to be incredibly capable of learning complex and varied functions across a wide variety of tasks. In recent years, artificial neural networks, inspired by human and animal brains, have shown great capabilities in learning a wide variety of difficult tasks. However, artificial neural networks primarily teach themselves through the use of backpropagation, a learning method which has no clear analogue within the brain. Additionally, Artificial Neural Networks primarily use continuous activation functions, which differ significantly from the spiking neuronal behavior present in the brain. In this paper, we discuss and demonstrate a biologically plausible learning method that approximates backpropagation through two techniques on Spiking Neural Networks. First, we show that the local temporal derivatives that are necessary for backpropagation can be approximately recovered through reconstruction using spike timings. Second, we show that through learning during a sleep phase, inspired by neuroscience research into memory replay, the localized parallel feedback path can learn to approximate the derivative through the forward path weight matrix, thus solving the weight transport problem. Lastly, we demonstrate that the combination of these two methods can approach or exceed the accuracy of backpropagation-based methods for a variety of neuromorphic vision tasks while maintaining biological plausibility.

42 ENGINEERING↗

Role of redox-active biochar with distinctive electrochemical properties to promote methane production in anaerobic digestion of waste activated sludge

Biochar has been reported as an effective additive to improve methane production during anaerobic digestion (AD). However, the mechanism for such a stimulatory impact remains unclear. Here we investigated the capability of three pyrolytic biochars with distinctive electrochemical properties (BC300, BC500, BC700) to promote methanogenic performance of anaerobic digesters treating waste activated sludge (WAS). The cumulative methane production and the maximum methane production rate were increased by 46.9% and 181.6%, respectively, with BC300 amendment. By characterizing the electrochemical properties of biochar, our research team found out that methane production in AD of sludge was positively correlated to biochar’s electron-donating capacity (EDC) rather than its bulk electrical conductivity. These results indicate that the electron transfer mediated by the redox-active functional groups may prevail over the direct electron migration as the predominant mechanism to facilitate interspecies electron transfer in syntrophic communities for enhanced methanogenesis. Microbial community analysis suggests that biochar enriched Methanosarcina and Methanobacterium. Overall, this study shows that functional groups-mediated electron transfer contributes greatly to the improved methane production in WAS digester with biochar amendment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Triangle Method for Dense ReLU Layers [SWR-25-72]

This software is an implementation of the methods for initializing and training neural networks to be more efficient per parameter, described more fully below and in the related publication: In theory, depth should make a ReLU network EXPONENTIALLY more efficient by enabling it to produce an exponential number of piecewise linear sections in its output. This reasoning is largely based on the work of mathematicians that have hand-constructed networks that make good use of depth. In practice however, even very deep ReLU networks that have been randomly initialized will behave identically to their shallow counterparts - missing an entire exponential dimension of efficiency. The triangle method is a first attempt at realizing the exponential potential of deep networks. Instead of randomly setting weights, we force pairs of neurons in each layer learn to build triangles (i.e. functions from [0,1] -> [0,1] that look like triangles). This is a very efficient pattern for generating lots of linear pieces because composing two triangular functions doubles the number of pieces with each composition. The triangle method is more than just a different initialization, it is a new paradigm of training. Instead of making direct updates to the matrix weights, we do an extra step of backpropagation to collect the derivatives of the loss function with respect to the shapes of the triangles, training them to tilt left or right. This process essentially holds the networks hand throughout the loss landscape and forces it to always use depth effectively by producing triangular shapes internally. This can produce several orders of magnitude of improvement on convex one-dimensional regression problems. Much more theoretical work is needed to realize its full potential beyond this context, but the implementation in this repository will still work in arbitrary numbers of dimensions. The file Triangle_Method.py is a generalized form of the method that will build each neuron its own custom 1-d convex activation function (with exponential efficiency). Example usage on one dimensional problems can be found in Example_Usage.ipynb and an example of using this in a real neural network can be found in Example_VGG16_CIFAR10.ipynb.

Milkert, Max [National Renewable Energy Laboratory↗

Structural delineation and phase-dependent activation of the costimulatory CD27:CD70 complex

CD27 is a tumor necrosis factor (TNF) receptor, which stimulates lymphocytes and promotes their differentiation upon activation by TNF ligand CD70. Activation of the CD27 receptor provides a costimulatory signal to promote T cell, B cell, and NK cell activity to facilitate antitumor and anti-infection immunity. Aberrant increased and focused expression of CD70 on many tumor cells renders CD70 an attractive therapeutic target for direct tumor killing. However, despite their use as drug targets to treat cancers, the molecular basis and atomic details of CD27 and CD70 interaction remain elusive. Here we report the crystal structure of human CD27 in complex with human CD70. Analysis of our structure shows that CD70 adopts a classical TNF ligand homotrimeric assembly to engage CD27 receptors in a 3:3 stoichiometry. By combining structural and rational mutagenesis data with reported disease-correlated mutations, we identified the key amino acid residues of CD27 and CD70 that control this interaction. We also report increased potency for plate-bound CD70 constructs compared with solution-phase ligand in a functional activity to stimulate T-cells in vitro. These findings offer new mechanistic insight into this critical costimulatory interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Binding and activation of major histocompatibility complex class II-deficient macrophages by staphylococcal exotoxins

Macrophages from C2D transgenic mice deficient in the expression of major histocompatibility complex (MHC) class II proteins were used to identify binding sites for superantigens distinct from the MHC class II molecule. Iodinated staphylococcal enterotoxins A and B (SEA and SEB) and exfoliative toxins A and B (ETA and ETB) bound to C2D macrophages in a concentration-dependent and competitive manner. All four toxins increased F-actin concentration within 30 s of their addition to C2D macrophages, indicating that signal transduction occurred in response to toxin in the absence of class II MHC. Furthermore, ETA, ETB, SEA, and, to a lesser extent, SEB induced C2D macrophages to produce interleukin 6. Several molecular species on C2D macrophages with molecular masses of 140, 97, 61, 52, 43, and 37 kDa bound SEA in immunoprecipitation experiments. These data indicate the presence of novel, functionally active toxin binding sites on murine macrophages distinct from MHC class II molecules.

Non-NASA Center↗

Nitrogen and dry-matter partitioning in soybean plants during onset of and recovery from nitrogen stress

The study tested the hypothesis that resupplying nitrogen after a period of nitrogen stress leads to restoration of the balance between root and shoot growth and normal functional activity. Nonnodulated soybean plants were grown hydroponically for 14 days with 1.0 mM NO3- in a complete nutrient solution. One set of plants was continued on the complete nutrient solution for 25 days; a second set was given 0.0 mM NO3- for 25 days; and the third set was given 0.0 mM NO3- for 10 days followed by transfer to the complete solution with 1.0 mM NO3- for 15 days. In continuously nitrogen-stressed plants, emergence and expansion of main-stem and branch leaves were severely inhibited as low nitrogen content limited further growth. This was followed by a shift in partitioning of dry matter from the leaves to the roots, resulting in an initial stimulation of root growth and a decreased shoot:root ratio. Reduced nitrogen also was redistributed from the leaves into the stem and roots. When nitrogen stress was relieved, leaf initiation and expansion were renewed. With the restoration of the balance between root and shoot function, the shoot:root ratio and distribution of reduced nitrogen within the plant organs returned to levels similar to those of nonstressed plants.

NASA Discipline Number 61-10↗

Shape Anisotropy-Dependent Leaking in Magnetic Neurons for Bio-Mimetic Neuromorphic Computing

Spiking neural networks seek to emulate biological computation through interconnected artificial neuron and synapse devices. Spintronic neurons can leverage magnetization physics to mimic biological neuron functions, such as integration tied to magnetic domain wall (DW) propagation in a patterned nanotrack and firing tied to the resistance change of a magnetic tunnel junction (MTJ), captured in the domain wall-magnetic tunnel junction (DW-MTJ) device. Leaking, relaxation of a neuron when it is not under stimulation, is also predicted to be implemented based on DW drift as a DW relaxes to a low energy position, but it has not been well explored or demonstrated in device prototypes. Here, in this work, we study DW-MTJ artificial neurons capable of leaky integrate-and-fire (LIF) behavior and demonstrate geometry-dependent leaking dynamics that results in repeatable, tunable LIF operation. Studying the behavior of five different device designs, we show tuning the geometry, stimulating fields and currents, and location of electrical contacts results in a wide range of neuron behavior. Additionally, implementation of an asymmetric notch allows for nonlinear pinning which increased expressivity without sacrificing leaking. The measured behavior is implemented in a simulated spiking neural network that outperforms a 1D model of continuous DW motion and approaches the performance of an ideal LIF activation function. The results show that the analog LIF capability of DW-MTJ neurons combines many desirable neuron functions into a single device, which can result in varied forms of multifunctional neuromorphic computing.

42 ENGINEERING↗

High thermal conductivity in wafer-scale cubic silicon carbide crystals

High thermal conductivity electronic materials are critical components for high-performance electronic and photonic devices as both active functional materials and thermal management materials. We report an isotropic high thermal conductivity exceeding 500 W m –1 K –1 at room temperature in high-quality wafer-scale cubic silicon carbide (3C-SiC) crystals, which is the second highest among large crystals (only surpassed by diamond). Furthermore, the corresponding 3C-SiC thin films are found to have record-high in-plane and cross-plane thermal conductivity, even higher than diamond thin films with equivalent thicknesses. Our results resolve a long-standing puzzle that the literature values of thermal conductivity for 3C-SiC are lower than the structurally more complex 6H-SiC. We show that the observed high thermal conductivity in this work arises from the high purity and high crystal quality of 3C-SiC crystals which avoids the exceptionally strong defect-phonon scatterings. Moreover, 3C-SiC is a SiC polytype which can be epitaxially grown on Si. We show that the measured 3C-SiC-Si thermal boundary conductance is among the highest for semiconductor interfaces. These findings provide insights for fundamental phonon transport mechanisms, and suggest that 3C-SiC is an excellent wide-bandgap semiconductor for applications of next-generation power electronics as both active components and substrates.

42 ENGINEERING↗

Interactions between molecular-scale processes and hyporheic exchange for understanding Fe-S-C cycling in riparian wetlands (Final Report)

Wetlands represent some of the most productive ecosystems on the planet and critically influence global environmental health. Specifically, wetlands promote water quality by transforming nutrients and organic compounds and sequestering metals and contaminants. Riparian wetland hyporheic zones, where toxic surface water and anoxic groundwater mix, exhibit dynamic conditions that drive steep redox gradients and promote hotspots of diverse and fluctuating microbial activity. Changes in climate, water quality, and water quantity can disturb hydrologic flow and biogeochemical processing in these environments. Understanding how sulfate loading, impacted by hydrologic flux and anthropogenic inputs, influences iron and carbon cycling in wetlands will be crucial for predicting water quality issues driven by iron mineral precipitation and sorption, such as the release of heavy metals and other toxic elements. We used a fully integrated multi-scale and multi-method approach to develop a mechanistic understanding of how hydrologic flow influences coupled iron and sulfur cycles in riparian wetlands. This entailed hydrological, geochemical, and microbial observations at two locations: an anthropogenic sulfate-impacted riparian wetland in northern Minnesota, and a low-sulfate Fe-rich riparian wetland in Tims Branch at the Savannah River Site (SRS). These sites were characterized by hydrologically dynamic conditions where the stream and wetland systems oscillated between gaining (upward flow) and losing (downward flow) conditions that recharged the system occasionally with oxidants that fueled a variety of biogeochemical reactions. Aqueous geochemical measurements of surface water, groundwater, and porewater samples were made alongside solid-phase geochemical analyses of sediment gravity cores. Bulk X-ray absorption spectroscopy at the Advanced Photon Source (APS; Argonne) interrogated the speciation and distribution of Fe and S mineral phases of the sediments. Interestingly, it was discovered that, despite strongly reducing conditions, Fe(III) compounds and a variety of intermediate valence S compounds were stable in the subsurface. Indeed, compounds like thiosulfate, S(0), and intermediate valence organosulfur compounds were more prevalent than FeS and pyrite. The composition of the sediments did change with changes in hydrologic flow, showing their reactivity in changing redox conditions. The abundance of these intermediate S compounds was likely formed as a result of anaerobic oxidation by aqueous and solid-phase Fe(III) compounds, fueling a cryptic S cycle that is driving the breakdown of organic matter in the hyporheic zone. Microbiome surveys showed a core community that seemed stable across the landscape, but changed with increasing depth into the sediment. The community composition did not seem to change dramatically with changes in season or hydrologic flow, except for some organisms that have the potential to contribute to S cycling. More work is needed to confirm their functional activity. These fine process-scale analyses were placed within a dynamic field context using physical flow parameters from surface water and groundwater level measurements. These data helped shed light on sulfur-driven biogeochemical processes in hydrologically dynamic riparian wetlands, addressing a gap in our understanding about the impacts of pollution and other anthropogenic changes on ecologically sensitive environments.

54 ENVIRONMENTAL SCIENCES↗

Chemical Recycling Processes of Waste Polyethylene Terephthalate Using Solid Catalysts

Polyethylene terephthalate (PET) is a non-degradable single-use plastic and a major component of plastic waste in landfills. Chemical recycling is one of the most widely adopted methods to transform post-consumer PET into PET's building block chemicals. Non-catalytic depolymerization of PET is very slow and requires high temperatures and/or pressures. Recent advancements in the field of material science and catalysis have delivered several innovative strategies to promote PET depolymerization under mild reaction conditions. Particularly, heterogeneous catalysts assisted depolymerization of post-consumer PET to monomers and other value-added chemicals is the most industrially compatible method. Here, this review includes current progresses on the heterogeneously catalyzed chemical recycling of PET. It describes four key pathways for PET depolymerization including, glycolysis, pyrolysis, alcoholysis, and reductive depolymerization. The catalyst function, active sites and structure-activity correlations are briefly outlined in each section. An outlook for future development is also presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Human IgE monoclonal antibodies define two unusual epitopes trapping dog allergen Can f 1 in different conformations

Abstract Molecular analysis of interactions between IgE antibody and allergen allows the structural basis of IgE recognition to be defined. Human IgE (hIgE) epitopes of respiratory lipocalin allergens, including Can f 1, remain elusive due to a lack of IgE‐allergen complexes. This study aims to map the structure of allergenic epitopes on Can f 1. The fragment antigen‐binding (Fab) regions of Can f 1 specific human IgE monoclonal antibodies (hIgE mAb) were used to determine the structures of IgE epitopes. Epitope mutants were designed to target Can f 1 epitopes. Immunoassays and a human FcεRIαtransgenic mouse model of passive anaphylaxis in vivo were used to assess the functional activity of epitope mutants. Crystal structures of natural or recombinant Can f 1 complexed with two hIgE mAb 1J11 and 12F3 Fabs, respectively, were determined. The hIgE mAb bound to two partially overlapping epitopes and recognized two different Can f 1 conformations. The hIgE mAb 12F3 showed an unusual mode of binding by protruding its heavy chain CDR3 inside the Can f 1 calyx. Epitope mutants generated based on the structural analyses displayed a 64%–89% reduction in IgE antibody binding and failed to induce passive anaphylaxis in a human FcεRIαtransgenic mouse model. In summary, the structures of Can f 1‐hIgE Fab complexes revealed two unique and partially overlapping epitopes on Can f 1. The modification of the identified IgE epitopes provides a pathway for the design of hypoallergens to treat dog allergies.

Biochemistry & Molecular Biology↗

The Psyche Gamma-Ray and Neutron Spectrometer

A Gamma-Ray and Neutron Spectrometer (GRNS) instrument has been developed as part of the science payload for NASA’s Discovery Program Psyche mission to the M-class asteroid (16) Psyche. The GRNS instrument is designed to measure the elemental composition of Psyche with the goal to understand the origin of this mysterious, potentially metal-rich planetary body. The GRNS will measure the near-surface abundances for the elements Ni, Fe, Si, K, S, Al, and Ca, as well as the spatial distribution of Psyche’s metal-to-silicate fraction (or metal fraction). These measurements address three of the five Psyche mission science objectives: determine if Psyche is a core; determine whether small metal bodies incorporate light elements into the metal phase; and determine whether Psyche was formed under reducing conditions. The Gamma-Ray Spectrometer (GRS) uses a cryocooled, high-purity Ge (HPGe) sensor to detect cosmic-ray generated gamma rays in the 60 to 9000-keV energy range. The HPGe sensor is surrounded by a borated plastic anticoincidence shield that provides three functions: active background rejection from charged particle interactions in the HPGe sensor; fast neutron measurements; and direct measurements of the incident galactic cosmic ray flux. The Neutron Spectrometer (NS) uses three 3 He gas proportional sensors, each with different material wraps to measure thermal (<0.4 eV), low-energy epithermal (0.4 eV to 1 keV), and high-energy epithermal (up to 100 keV) neutrons. This paper provides an overview of the Psyche GRNS, including: its science and measurement objectives; the design of the instrument hardware, software, and operation; pre-launch performance measurements and its initial performance in space; and an overview of its data products and expected operation for different Psyche mission phases.

Engineering - Instrumentation related to nuclear s↗

From PINNs to PIKANs: recent advances in physics-informed machine learning

Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Lastly, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.

Kolmogorov-Arnold networks↗

Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems

Here, we present a novel physics-informed neural networks (PINNs) framework for modeling interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks for any two subdomains separated by a sharp interface such that the neural networks differ only through their activation functions while the other parameters remain identical. The performance of I-PINNs, conventional PINNs, and other existing domain-decomposition PINNs methods such as extended PINNs (XPINNs) and multi-domain PINN (M-PINN) is compared through several one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems. The results demonstrate that I-PINNs provides a root-mean-square-error accuracy, at least two orders of magnitude better than conventional PINNs and XPINNs at approximately one-tenth of the computational cost of conventional PINNs and half the cost of XPINNs. Additionally, while I-PINNs and M-PINN provide comparable accuracies, M-PINN is found to be approximately 50% more expensive.

42 ENGINEERING↗

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

42 ENGINEERING↗

Learning interpretable surface elasticity properties from bulk properties via neural network equation learners

Surface elasticity is central to understanding the mechanics and stability of surfaces and interfaces. It is characterized by quantities such as surface tension, residual surface stress, and surface stiffness. However their analytical expressions are typically difficult to derive from atomistic data, and depend strongly on modeling choices. This work presents a neural network-based equation learner which combines customized activation functions and connection-based pruning to discover parsimonious, closed-form equations for surface elasticity from atomistic simulations. Applying the method to seven face-centered cubic (FCC) metals, our equation learner uncovers interpretable equations that describe both low-Miller index and high-Miller index surface properties, capturing long-tail property distributions accurately. The discovered expressions are decoupled into two components: a universal, geometry-driven orientation function, and material-specific baseline coefficients. We find that lower-order properties such as surface tension are fundamentally geometry dependent, while higher-order properties such as surface stress and elasticity show more complex geometry and material dependence. We also relate material dependent coefficients to bulk properties, forming a clear map from bulk material properties to surface elasticity. Overall, this approach demonstrates that interpretable neurosymbolic machine learning can bridge the gap between atomistic simulations and physical laws, enabling the discovery of generalizable structure–property relationships for materials science phenomena such as surface elasticity.

Equation learning↗

Latent code-based fusion: A Volterra neural network approach

We propose a deep structure encoder using Volterra Neural Networks (VNNs) to seek a latent representation of multi-modal data whose features are jointly captured by a union of subspaces. The so-called self-representation embedding of the latent codes leads to a simplified fusion which is driven by a similarly constructed decoding. The Volterra Filter architecture achieved reduction in parameter complexity is primarily due to controlled non-linearities being introduced by the higher-order convolutions in lieu of generalized activation functions. Experimental results on two different datasets have shown a significant improvement in the clustering performance for VNNs auto-encoder over conventional Convolutional Neural Networks (CNNs) auto-encoder. In addition, we also show that the proposed approach demonstrates a much-improved sample complexity over CNN-based auto-encoder with a robust classification performance.

97 MATHEMATICS AND COMPUTING↗

In Situ Attenuated Total Reflectance Infrared Spectroelectrochemistry (ATR-IR-SEC) for the Characterization of Molecular Redox Processes on Surface-Proximal Doped Silicon ATR Crystal Working Electrodes

In situ mid-infrared spectroscopy is a powerful technique for understanding the mechanism of CO 2 reduction (CO 2 R) catalysts because it enables the direct detection of catalytic intermediates and products. Moreover, spectroelectrochemistry (SEC), the coupling of spectroscopy with electrochemistry, allows spectroscopic changes to be correlated with applied potentials to reveal potential-dependent intermediates that are often relevant to photoelectrochemical reactions. Hybrid photoelectrodes, comprised of a narrow bandgap semiconductor, like silicon (Si), with a covalently-linked molecular catalyst, are a promising platform for sunlight-driven catalysis, but characterization of the catalytic mechanism(s) is challenging under photoelectrochemical conditions, particularly when the catalyst is present in monolayer or less concentrations. Here, we have developed a new strategy to use multiple-reflection attenuated total reflectance IR spectroscopy (ATR-IR) coupled with electrochemistry to characterize catalysts directly integrated with a semiconductor surface under applied potential. We show that by surface-proximal n-type or p-type doping of the top ~100-200 nm of the crystal surface, Si ATR crystals can be used simultaneously as the internal reflection element and semiconductor working electrode for ATR-IR-SEC measurements. The surface-proximal doping strategy yields a quasi-equipotential surface with excellent infrared transparency that would have been compromised by free carrier absorption if the crystal was uniformly doped. This approach permits the catalytically-active functionalized surface to be directly probed without modification and overcomes signal-to-noise limitations of other strategies that use separately deposited working electrodes on Si ATR crystals. Proof-of-concept ATR-IR-SEC spectra were collected during the reduction and oxidation of monolayers of Re- and Ru-based transition metal carbonyl complexes, respectively, verifying the viability of the technique to probe redox processes associated with CO 2 R catalysts on Si electrode surfaces with high sensitivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗