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At least 1,567 records · Page 87

Image Analysis for Rapid Assessment and Quality-Based Sorting of Corn Stover

Imaging in the visible spectrum is a low-cost tool that can be readily deployed for in-field or over-belt monitoring of biomass quality for bio-refining operations. Rapid image analysis coupled with innovative preprocessing may reduce the impacts of feedstock variability through identification of contaminants or other material attributes to guide selective sorting and quality management. Image analysis was employed to evaluate the quality of corn stover in red-green-blue (RGB) chromatic space. This study used controlled, bench-scale imaging as a proof-of-concept for rapid quality assessment of corn stover based on variations in material attributes, including chemical and physical attributes, that relate to biological degradation and soil contamination. Additionally, logistic regression-based classification algorithms were used to develop a method for biomass screening as a function of biological degradation or soil contamination. This study demonstrated the use of image analysis to extract features from RGB color space to investigate variations in critical material attributes from chemical composition of corn stover. Fourier transform infrared (FT-IR) suggested a correlation between red band intensity and biological degradation, while detailed surface texture analysis was found to distinguish among variations in ash. These insights offer promise for development of a rapid screening tool that could be deployed by farmers for in-field assessment of biomass quality or biorefinery operators for in-line sorting and process optimization.

09 BIOMASS FUELS↗

EVIDENCE FOR REDUCED SPECIFIC STAR FORMATION RATES IN THE CENTERS OF MASSIVE GALAXIES AT z = 4

We perform the first spatially resolved stellar population study of galaxies in the early universe ( z = 3.5–6.5), utilizing the Hubble Space Telescope Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey imaging data set over the GOODS-S field. We select a sample of 418 bright and extended galaxies at z = 3.5–6.5 from a parent sample of ∼8000 photometric-redshift-selected galaxies from Finkelstein et al. We first examine galaxies at 3.5 ≲ z ≲ 4.0 using additional deep K -band survey data from the HAWK-I UDS and GOODS Survey which covers the 4000 Å break at these redshifts. We measure the stellar mass, star formation rate, and dust extinction for galaxy inner and outer regions via spatially resolved spectral energy distribution fitting based on a Markov Chain Monte Carlo algorithm. By comparing specific star formation rates (sSFRs) between inner and outer parts of the galaxies we find that the majority of galaxies with high central mass densities show evidence for a preferentially lower sSFR in their centers than in their outer regions, indicative of reduced sSFRs in their central regions. We also study galaxies at z ∼ 5 and 6 (here limited to high spatial resolution in the rest-frame ultraviolet only), finding that they show sSFRs which are generally independent of radial distance from the center of the galaxies. This indicates that stars are formed uniformly at all radii in massive galaxies at z ∼ 5–6, contrary to massive galaxies at z ≲ 4.

79 ASTRONOMY AND ASTROPHYSICS↗

Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we examine the factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and $\mathbb{Z}$ 2 ). We examine the relationships between the different ranks, and discuss when factorization is unique. In particular, we characterize when a Boolean factorization X = W$\land$H has a unique W, a unique H (for a fixed W), and when both W and H are unique, given a rank constraint. We introduce a method for robust Boolean model selection, called BMFk, and show on numerical examples that BMFk not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.

97 MATHEMATICS AND COMPUTING↗

Exposure Risks Among Children Undergoing Radiation Therapy: Considerations in the Era of Image Guided Radiation Therapy

Recent improvements in toxicity profiles of pediatric oncology patients are attributable, in part, to advances in the field of radiation oncology such as intensity modulated radiation (IMRT) and proton therapy (IMPT). While IMRT and IMPT deliver highly conformal dose to targeted volumes, they commonly demand the addition of 2- or 3-dimensional imaging for precise positioning—a technique known as image guided radiation therapy (IGRT). In this manuscript we address strategies to further minimize exposure risk in children by reducing effective IGRT dose. Portal X rays and cone beam computed tomography (CBCT) are commonly used to verify patient position during IGRT and, because their relative radiation exposure is far less than the radiation absorbed from therapeutic treatment beams, their sometimes significant contribution to cumulative risk can be easily overlooked. Optimizing the conformality of IMRT/IMPT while simultaneously ignoring IGRT dose may result in organs at risk being exposed to a greater proportion of radiation from IGRT than from therapeutic beams. Over a treatment course, cumulative central-axis CBCT effective dose can approach or supersede the amount of radiation absorbed from a single treatment fraction, a theoretical increase of 3% to 5% in mutagenic risk. In select scenarios, this may result in the underprediction of acute and late toxicity risk (such as azoospermia, ovarian dysfunction, or increased lifetime mutagenic risk) in radiation-sensitive organs and patients. Although dependent on variables such as patient age, gender, weight, body habitus, anatomic location, and dose-toxicity thresholds, modifying IGRT use and acquisition parameters such as frequency, imaging modality, beam energy, current, voltage, rotational degree, collimation, field size, reconstruction algorithm, and documentation can reduce exposure, avoid unnecessary toxicity, and achieve doses as low as reasonably achievable, promoting a culture and practice of “gentle IGRT.”.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

An Approach to Bayesian Optimization for Design Feasibility Check on Discontinuous Black-Box Functions

The paper presents a novel approach to applying Bayesian Optimization (BO) in predicting an unknown constraint boundary, also representing the discontinuity of an unknown function, for a feasibility check on the design space, thereby representing a classification tool to discern between a feasible and infeasible region. Bayesian optimization is a low-cost black-box global optimization tool in the Sequential Design Methods where one learns and updates knowledge from prior evaluated designs, and proceeds to the selection of new designs for future evaluation. However, BO is best suited to problems with the assumption of a continuous objective function and does not guarantee true convergence when having a discontinuous design space. This is because of the insufficient knowledge of the BO about the nature of the discontinuity of the unknown true function. In this paper, we have proposed to predict the location of the discontinuity using a BO algorithm on an artificially projected continuous design space from the original discontinuous design space. The proposed approach has been implemented in a thin tube design with the risk of creep-fatigue failure under constant loading of temperature and pressure. The stated risk depends on the location of the designs in terms of safe and unsafe regions, where the discontinuities lie at the transition between those regions; therefore, the discontinuity has also been treated as an unknown creep-fatigue failure constraint. The proposed BO algorithm has been trained to maximize sampling toward the unknown transition region, to act as a high accuracy classifier between safe and unsafe designs with minimal training cost. The converged solution has been validated for different design parameters with classification error rate and function evaluations at an average of <1% and ~150, respectively. Finally, the performance of our proposed approach in terms of training cost and classification accuracy of thin tube design is shown to be better than the existing machine learning (ML) algorithms such as Support Vector Machine (SVM), Random Forest (RF), and Boosting.

Engineering↗

Structure- and Physics-Preserving Reductions of Power Grid Models

The large size of multiscale, distribution and transmission, power grids hinders fast systemwide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable for fast simulations and follow-up applications. While the classical Kron reduction has been successful in reduced order modeling of power grids with traditional, hierarchical design, the selection of reference nodes for the reduced model in a multiscale, distribution and transmission, network becomes ambiguous. In this work we extend the use of the iterative Kron reduction by utilizing the electric grid's graph topology for the selection of reference nodes, consistent with the design features of multiscale networks. Additionally, we propose further reductions by aggregation of coherent subnetworks of triangular meshes, based on the graph topology and network characteristics, in order to preserve currents and build another power-flow equivalent network. Our reductions are achieved through the use of iterative aggregation of subgraphs that include general tree structures, lines, and triangles. Important features of our reduction algorithms include that (i) the reductions are either equivalent to the Kron reduction or otherwise produce a power-flow equivalent network; (ii) due to the mentioned power-flow equivalence, the reduced network can model the dynamic of the swing equations for a lossless, inductive, steady state network; (iii) the algorithms efficiently utilize hash tables to store the sequential reduction steps. The third feature allows for easy reintroduction of detailed models into the reduced, conceptual network and makes the final reduced order model backward compatible with a sequence of intermediate, partially reduced networks with varying resolution---the ordered sequence of iterative reductions corresponds to a sequence of reduced order models. The performance of our graph reduction algorithms and features of the reduced grids are discussed on a real-word transmission and distribution grid. We produce visualizations of the reduced models through open source libraries and release our reduction algorithms with example code and toy data.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Fast Machine Learning for Quantum Control of Microwave Qudits on Edge Hardware

Quantum optimal control is a promising approach to improve the accuracy of quantum gates, but it relies on complex algorithms to determine the best control settings. CPU or GPU-based approaches often have delays that are too long to be applied in practice. It is paramount to have systems with extremely low delays to quickly and with high fidelity adjust quantum hardware settings, where fidelity is defined as overlap with a target quantum state. Here, we utilize machine learning (ML) models to determine control-pulse parameters for preparing Selective Number-dependent Arbitrary Phase (SNAP) gates in microwave cavity qudits, which are multi-level quantum systems that serve as elementary computation units for quantum computing. The methodology involves data generation using classical optimization techniques, ML model development, design space exploration, and quantization for hardware implementation. Our results demonstrate the efficacy of the proposed approach, with optimized models achieving low gate trace infidelity near $10^{-3}$ and efficient utilization of programmable logic resources.

Sanders, Flor [Columbia U.]↗

SU-E-J-67: Evaluation of Adaptive MLC Morphing for Online Correction of Prostate Cancer Radiotherapy

Purpose: Online adaptive MLC morphing is desirable over translational couch shifts to accommodate target position as well as anatomic changes. A reliable method of adaptive MLC segment to target during prostate cancer IMRT treatment is proposed and evaluated by comparison with daily online-image guidance (IGRT) correction and online-IMRT planning. Methods: The MLC adaptive algorithm involves following steps; move the MLC segments according to target translational shifts, and then morph the segment shape to maintain the spatial relationship between the planning-target contour and MLC segment. Efficacy of this method was evaluated retrospectively using daily-CBCT images on seven prostate patients treated with seven-beam IMRT treatment to deliver 64Gy in 20 fractions. Daily modification was simulated with three approaches; daily-IGRT correction based on implanted radio-markers, adaptive MLC morphing, and online-IMRT planning, with no-residual variation. The selected dosimetric endpoints and nEUD (normalized equivalent uniform dose to online-IMRT planning) of each organ of interest were determined for evaluation and comparison. Results: For target(prostate), bladder and rectal-wall, the mean±sd of nEUD were 97.6%+3.2%, 103.9%±4.9% and 97.4%±1.1% for daily-IGRT correction; and 100.2%+0.2%, 108.9%±5.1% and 99.8%±1.2% for adaptive MLC morphing, respectively. For daily-IGRT correction, adaptive MLC morphing and online-IMRT planning, target D99 was <95% of the prescription dose in 30%, 0% and 0% of 140 fractions, respectively. For the rectal-wall, D5 exceeded 105% of the planned-D5 in 2.8%, 11.4% and 0% of 140 fractions, respectively. For the bladder, Dmax exceeded 105% of the planned-D5 in 2.8%, 5.6% and 0% of 140 fractions, respectively. D30 of bladder and rectal-wall were well within the planned-D30 for all three approaches. Conclusion: The proposed method of adaptive MLC morphing can be beneficial for the prostate patient population with large deformation and rotation. It is superior to the daily-IGRT correction, and comparable to the online-IMRT planning for dose to the target and rectal-wall.

60 APPLIED LIFE SCIENCES↗

BIPSPI+: Mining Type-Specific Datasets of Protein Complexes to Improve Protein Binding Site Prediction

Computational approaches for predicting protein-protein interfaces are extremely useful for understanding and modelling the quaternary structure of protein assemblies. In particular, partner-specific binding site prediction methods allow delineating the specific residues that compose the interface of protein complexes. In recent years, new machine learning and other algorithmic approaches have been proposed to solve this problem. However, little effort has been made in finding better training datasets to improve the performance of these methods. With the aim of vindicating the importance of the training set compilation procedure, in this work we present BIPSPI+, a new version of our original server trained on carefully curated datasets that outperforms our original predictor. We show how prediction performance can be improved by selecting specific datasets that better describe particular types of protein interactions and interfaces (e.g. homo/hetero). In addition, our upgraded web server offers a new set of functionalities such as the sequence-structure prediction mode, hetero- or homo-complex specialization and the guided docking tool that allows to compute 3D quaternary structure poses using the predicted interfaces. BIPSPI+ is freely available at https://bipspi.cnb.csic.es.

59 BASIC BIOLOGICAL SCIENCES↗

Counterpart identification and classification for eRASS1 and characterisation of the active galactic nuclei content

Context. Accurately accounting for the Active Galactic Nucleus (AGN) phase in galaxy evolution requires a large, clean AGN sample. This is now possible with SRG/eROSITA, which completed its first all-sky X-ray survey (eRASS1) on June 12, 2020. The public Data Release 1 (DR1, Jan 31, 2024) includes 930,203 sources from the western Galactic hemisphere. Aims. The data enable the selection of a large AGN sample and the discovery of rare sources. However, scientific return depends on accurate characterisation of the X-ray emitters, requiring high-quality multi-wavelength data. This paper presents the identification and classification of optical and infrared counterparts to eRASS1 sources. Methods. Counterparts to eRASS1 X-ray point sources were identified using Gaia DR3, CatWISE2020, and Legacy Survey DR10 (LS10) with the Bayesian NWAY algorithm and trained priors. Sources were classified as Galactic or extragalactic via a machine-learning model combining optical/IR and X-ray properties, trained on a reference sample. For extragalactic LS10 sources, photometric redshifts were computed using CIRCLEZ. Results. Within the LS10 footprint, all 656,614 eROSITA/DR1 sources have at least one possible optical counterpart; ∼570 000 are extragalactic and likely AGN. Half are new detections compared to AllWISE, Gaia, and Quaia AGN catalogues. Gaia and CatWISE2020 counterparts are less reliable, due to the survey’s shallowness and the limited amount of features available to assess the probability of being an X-ray emitter. In the Galactic plane, where the overdensity of stellar sources also increases the chance of associations, using conservative reliability cuts, we identified approximately 18 000 Gaia and 55 000 CatWISE2020 extragalactic sources. Conclusions. We have released three high-quality counterpart catalogues – plus the training and validation sets – as a benchmark for the field. These datasets have many applications, but in particular, they empower researchers to build AGN samples tailored for completeness and purity, accelerating the hunt for the Universe’s most energetic engines.

X-rays: general↗

Syncopated dynamical decoupling to suppress crosstalk in quantum circuits

Theoretically understanding and experimentally characterizing and modifying the underlying Hamiltonian of a quantum system is of utmost importance in achieving high-fidelity quantum gates for quantum computing. Here, in this work, we explore the use of dynamical decoupling (DD) in characterizing and suppressing undesired two-qubit couplings as well as the underlying single-qubit decoherence, both significant hurdles to achieving precise quantum control and realizing quantum computing on many hardware prototypes. Through discrete search of DD sequences, we identify sequences that protect against decoherence and selectively target unwanted two-qubit interactions of general form. On a transmon-qubit-based superconducting quantum device, we identify separate white and 1/𝑓 noise components underlying the single-qubit decoherence and a static ZZ coupling between pairs of qubits. A family of syncopated DD sequences is found and their efficiency is demonstrated in two-qubit benchmarking experiments. The syncopated decoupling technique significantly boosts performance in a realistic algorithmic quantum circuit.

97 MATHEMATICS AND COMPUTING↗

Quantified Gamow shell model interaction for p s d -shell nuclei

Background: The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interaction approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant many-body states on equal footing. Purpose: To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the psdf-shell-model space. The resulting interaction is expected to describe nuclei with 5 ≤ A ≲ 12 at the p-sd-shell interface. Method: The one-body potential of the 4 He core is modeled by a Woods-Saxon + spin-orbit + Coulomb potential, and the finite-range nucleon-nucleon interaction between the valence nucleons consists of central, spin-orbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ 2 optimization is performed using the Gauss-Newton algorithm augmented by the singular value decomposition technique. The resulting covariance matrix enables quantification of statistical errors within the linear regression approach. Results: The optimized one-body potential reproduces nucleon- 4 He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the helium, lithium, and beryllium isotopes up to A = 9 . A very good agreement with experimental results was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. In conclusion: The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the psd region of the nuclear chart.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

3D reconstruction identifies loci linked to variation in angle of individual sorghum leaves

Selection for yield at high planting density has reshaped the leaf canopy of maize, improving photosynthetic productivity in high density settings. Further optimization of canopy architecture may be possible. However, measuring leaf angles, the widely studied component trait of leaf canopy architecture, by hand is a labor and time intensive process. Here, we use multiple, calibrated, 2D images to reconstruct the 3D geometry of individual sorghum plants using a voxel carving based algorithm. Automatic skeletonization and segmentation of these 3D geometries enable quantification of the angle of each leaf for each plant. The resulting measurements are both heritable and correlated with manually collected leaf angles. This automated and scaleable reconstruction approach was employed to measure leaf-by-leaf angles for a population of 366 sorghum plants at multiple time points, resulting in 971 successful reconstructions and 3,376 leaf angle measurements from individual leaves. A genome wide association study conducted using aggregated leaf angle data identified a known large effect leaf angle gene, several previously identified leaf angle QTL from a sorghum NAM population, and novel signals. Genome wide association studies conducted separately for three individual sorghum leaves identified a number of the same signals, a previously unreported signal shared across multiple leaves, and signals near the sorghum orthologs of two maize genes known to influence leaf angle. Automated measurement of individual leaves and mapping variants associated with leaf angle reduce the barriers to engineering ideal canopy architectures in sorghum and other grain crops.

3D reconstruction↗

An adaptive synchronous extraction (ASE) method for estimating intensity and footprint of surface urban heat islands: A case study of 254 North American cities

The urban heat island (UHI) effect has attracted great attention due to its potential impacts on rapidly growing urban areas. Using remotely sensed estimates of land surface temperature (LST), a large number of studies have focused on the surface UHI (SUHI) effect, which can be characterized by its two fundamental properties: intensity and footprint. The SUHI intensity reflects the LST difference between the urban area and the background reference area (BRA), and the SUHI footprint indicates the spatial extent influenced by the heat island. Currently, numerous methods have been developed to estimate the SUHI intensity and footprint, but are still greatly challenged by three main issues. Namely, the discrepancy in BRA selection criterion brings great uncertainty to the estimated SUHI intensity, the estimation of SUHI footprint is largely constrained by the predefined models, and the quantification of SUHI effect is potentially influenced by several confounding factors. Here, we proposed an adaptive synchronous extraction (ASE) method, which is capable of adaptively selecting the most optimal BRA while removing the influence of confounding factors, and achieving synchronous estimation of SUHI intensity and footprint. We applied the ASE method to 254 North American cities and conducted an in-depth comparative analysis to discuss its applicability and benefits. The main results include: (1) The ASE method avoids the limitations of existing methods in BRA selection and model presetting, and shows resilience to parameter variations. This makes the ASE method highly applicable to quantify the SUHI intensity and footprint in cities with various thermal characteristics. (2) The ASE method can better highlight the spatial, seasonal and day-night contrasts in the estimated SUHI intensity. This superiority is particularly evident when comparing it to methods based on the equal-area buffer or the simplified urban-extent algorithm. (3) Confounding factors pose non-negligible impacts on the quantification of the SUHI effect. Typically, ignoring the influence of topographic relief or missing LST data can lead to an overall overestimation of the SUHI intensity, while not removing surrounding urban areas will cause some underestimation of the SUHI intensity. In conclusion, overall, the proposed ASE method provides a new generalizable tool for quantifying the SUHI effect, which has great potentials for future studies and urban climate assessments.

54 ENVIRONMENTAL SCIENCES↗

A Robust Approach to Sequential Information Theoretic Planning

In many sequential planning applications a natural approach to generating high quality plans is to maximize an information reward such as mutual information (MI). Unfortunately, MI lacks a closed form in all but trivial models, and so must be estimated. In applications where the cost of plan execution is expensive, one desires planning estimates which admit theoretical guarantees. Through the use of robust M-estimators we obtain bounds on absolute deviation of estimated MI. Moreover, we propose a sequential algorithm which integrates inference and planning by maximally reusing particles in each stage. We validate the utility of using robust estimators in the sequential approach on a Gaussian Markov Random Field wherein information measures have a closed form. Lastly, we demonstrate the benefits of our integrated approach in the context of sequential experiment design for inferring causal regulatory networks from gene expression levels. Here, our method shows improvements over a recent method which selects intervention experiments based on the same MI objective.

Zheng, Sue↗

SU-F-T-06: Development of a Formalism for Practical Dose Measurements in Brachytherapy in the German Standard DIN 6803

Purpose: In the steep dose gradients in the vicinity of a radiation source and due to the properties of the changing photon spectra, dose measurements in Brachytherapy usually have large uncertainties. Working group DIN 6803-3 is presently discussing recommendations for practical brachytherapy dosimetry incorporating recent theoretical developments in the description of brachytherapy radiation fields as well as new detectors and phantom materials. The goal is to prepare methods and instruments to verify dose calculation algorithms and for clinical dose verification with reduced uncertainties. Methods: After analysis of the distance dependent spectral changes of the radiation field surrounding brachytherapy sources, the energy dependent response of typical brachytherapy detectors was examined with Monte Carlo simulations. A dosimetric formalism was developed allowing the correction of their energy dependence as function of source distance for a Co-60 calibrated detector. Water equivalent phantom materials were examined with Monte Carlo calculations for their influence on brachytherapy photon spectra and for their water equivalence in terms of generating equivalent distributions of photon spectra and absorbed dose to water. Results: The energy dependence of a detector in the vicinity of a brachytherapy source can be described by defining an energy correction factor kQ for brachytherapy in the same manner as in existing dosimetry protocols which incorporates volume averaging and radiation field distortion by the detector. Solid phantom materials were identified which allow precise positioning of a detector together with small correctable deviations from absorbed dose to water. Recommendations for the selection of detectors and phantom materials are being developed for different measurements in brachytherapy. Conclusion: The introduction of kQ for brachytherapy sources may allow more systematic and comparable dose measurements. In principle, the corrections can be verified or even determined by measurement in a water phantom and comparison with dose distributions calculated using the TG43 dosimetry formalism. Project is supported by DIN Deutsches Institut fuer Normung.

60 APPLIED LIFE SCIENCES↗

Nonequilibrium design strategies for functional colloidal assemblies

Here, we use a nonequilibrium variational principle to optimize the steady-state, shear-induced interconversion of self-assembled nanoclusters of DNA-coated colloids. Employing this principle within a stochastic optimization algorithm allows us to identify design strategies for functional materials. We find that far-from-equilibrium shear flow can significantly enhance the flux between specific colloidal states by decoupling trade-offs between stability and reactivity required by systems in equilibrium. For isolated nanoclusters, we find nonequilibrium strategies for amplifying transition rates by coupling a given reaction coordinate to the background shear flow. We also find that shear flow can be made to selectively break detailed balance and maximize probability currents by coupling orientational degrees of freedom to conformational transitions. For a microphase consisting of many nanoclusters, we study the flux of colloids hopping between clusters. We find that a shear flow can amplify the flux without a proportional compromise on the microphase structure. This approach provides a general means of uncovering design principles for nanoscale, autonomous, functional materials driven far from equilibrium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗