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At least 487 records · Page 27

A review of computing-based automated fault detection and diagnosis of heating, ventilation and air conditioning systems

We report faults in Heating, Ventilation, and Air Conditioning (HVAC) systems of buildings result in significant energy waste in building operation. With fast-growing sensing data availability and advancement in computing, computational modeling has demonstrated strong capability to detect and diagnose HVAC system faults, hence, ensuring efficient building operation. This paper comprehensively reviews the state-of-the-art computing-based fault detection and diagnosis (FDD) for HVAC systems. Overall, the reviewed computing-based FDD methods are classified as two major approaches: knowledge-based and data-driven approaches. We then identify multiple important topics, including data availability, training data size, data quality, approach generality, capability, interpretability, and required modeling efforts, along with corresponding metrics to summarize the most updated FDD development. Generally, the knowledge-based approaches are further divided as physics-based modeling, Diagnostic Bayesian Network, and performance indicator-based methods while data-driven approaches include supervised learning, unsupervised learning, and regression and statistics-based methods. State-of-the-art FDD development, remaining challenges, and future research directions are further discussed to push forward FDD in practice. Availability of fault data, capability of existing methods to deal with complex fault situations (such as simultaneous faults), modeling interpretability for data-driven methods, and required engineering efforts for physics-based methods are identified as remaining challenges in FDD development. Improving modeling fidelity and reducing modeling efforts are essential for applying physics-based methods in real buildings. Meanwhile, addressing fault data availability, increasing algorithm adaptability, and handling multiple faults are essential to further enhance the applicability of data-driven FDD approaches.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Power Electronics Materials and Bonded Interfaces - Reliability and Lifetime

High temperature operation of wide bandgap devices continue to be a challenge for the power electronics packages. Thermal performance and reliability are important factors that determine the viability of a bonded interface for operation at high temperatures. In this presentation, we present the technical approach and key results from the research on sintered silver, transient liquid phase alloy, and polymeric materials. A lifetime prediction model that incorporates the thermomechanical behavior of sintered silver at 200C was developed. The copper-aluminum transient alloy completed 350 thermal cycles from -40C to 200C and little increase in the defect level was observed. In addition to material research, we initiated a time-series analysis on the scanning acoustic microscope images of eutectic solder to explore statistical forecasting methods and machine learning techniques. Initial results that report the accuracy of a few different statistical models are presented.

ADVANCED PROPULSION SYSTEMS↗

Reliable noise measure in time-gated NMR data

Time gating is a commonly used approach in the pre-processing of nuclear magnetic resonance data before inversion. Gating suppresses spurious signals that can degrade recovered decay time distributions and therefore often stabilizes inversion. However, care must be taken in applying this technique when assumptions of uncorrelated Gaussianity break down and reduce stacking efficiency. If not properly accounted for, unreliable noise estimates introduce inversion artefacts through over- or underfitting of the data. Block-bootstrap resampling of noise realization proxies obtained through data phasing can be used to generate reliable noise estimates for the windows. Benefits of the approach are demonstrated through inversion of synthetic and borehole data. Finally, analysis confirms that bootstrapped noise metrics are more reliable under variable noise conditions and result in more stable inversion results.

58 GEOSCIENCES↗

Greedy emulators for nuclear two-body scattering

Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. Here, in this paper, we develop, implement, and test two model-driven emulators based on the (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples (“snapshots”) for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires many fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems.

Bayesian methods↗

Active learning emulators for nuclear two-body scattering in momentum space

In this work we extend the active learning emulators for two-body scattering in coordinate space with error estimation, recently developed by Maldonado et al. [Phys. Rev. C 112, 024002], to coupled-channel scattering in momentum space. Our full-order model (FOM) solver is based on the Lippmann-Schwinger integral equation for the scattering t-matrix as opposed to the radial Schrödinger equation. We use (Petrov-)Galerkin projections and high-fidelity calculations at a few snapshots across the parameter space of the interaction to construct efficient reduced-order models (ROMs), trained by a greedy algorithm for locally optimal snapshot selection. Both the FOM solver and the corresponding ROMs are implemented efficiently in Python using Google's JAX library. We present results for emulating scattering phase shifts in coupled and uncoupled channels and cross sections, and assess the accuracy of the developed ROMs and their computational speedup factors. We also develop emulator error estimation for both the t-matrix and the total cross section. The software framework for reproducing and extending our results is publicly available. Together with our recent advances in developing active-learning emulators for three-body scattering, these emulator frameworks set the stage for full Bayesian calibrations of chiral nuclear interactions and optical models against scattering data with quantified emulator errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SU-D-BRB-05: Quantum Learning for Knowledge-Based Response-Adaptive Radiotherapy

Purpose: There is tremendous excitement in radiotherapy about applying data-driven methods to develop personalized clinical decisions for real-time response-based adaptation. However, classical statistical learning methods lack in terms of efficiency and ability to predict outcomes under conditions of uncertainty and incomplete information. Therefore, we are investigating physics-inspired machine learning approaches by utilizing quantum principles for developing a robust framework to dynamically adapt treatments to individual patient’s characteristics and optimize outcomes. Methods: We studied 88 liver SBRT patients with 35 on non-adaptive and 53 on adaptive protocols. Adaptation was based on liver function using a split-course of 3+2 fractions with a month break. The radiotherapy environment was modeled as a Markov decision process (MDP) of baseline and one month into treatment states. The patient environment was modeled by a 5-variable state represented by patient’s clinical and dosimetric covariates. For comparison of classical and quantum learning methods, decision-making to adapt at one month was considered. The MDP objective was defined by the complication-free tumor control (P{sup +}=TCPx(1-NTCP)). A simple regression model represented state-action mapping. Single bit in classical MDP and a qubit of 2-superimposed states in quantum MDP represented the decision actions. Classical decision selection was done using reinforcement Q-learning and quantum searching was performed using Grover’s algorithm, which applies uniform superposition over possible states and yields quadratic speed-up. Results: Classical/quantum MDPs suggested adaptation (probability amplitude ≥0.5) 79% of the time for splitcourses and 100% for continuous-courses. However, the classical MDP had an average adaptation probability of 0.5±0.22 while the quantum algorithm reached 0.76±0.28. In cases where adaptation failed, classical MDP yielded 0.31±0.26 average amplitude while the quantum approach averaged a more optimistic 0.57±0.4, but with high phase fluctuations. Conclusion: Our results demonstrate that quantum machine learning approaches provide a feasible and promising framework for real-time and sequential clinical decision-making in adaptive radiotherapy.

60 APPLIED LIFE SCIENCES↗

Collective mode Brownian dynamics: A method for fast relaxation of statistical ensembles

Sampling equilibrium configurations of correlated systems of particles with long relaxation times (e.g., polymeric solutions) using conventional molecular dynamics and Monte Carlo methods can be challenging. This is especially true for systems with complicated, extended bond network topologies and other interactions that make the use and design of specialized relaxation protocols infeasible. We introduce a method based on Brownian dynamics simulations that can reduce the computational time it takes to reach equilibrium and draw decorrelated samples. Importantly, the method is completely agnostic to the particle configuration and the specifics of interparticle forces. In particular, we develop a mobility matrix that excites non-local, collective motion of N particles and can be computed efficiently in $\mathcal{O}(N)$ time. Particle motion in this scheme is computed by integrating the overdamped Langevin equation with an Euler–Maruyama scheme, in which Brownian displacements are drawn efficiently using a low-rank representation of the mobility matrix in position and wave space. We demonstrate the efficacy of the method with various examples from the realm of soft condensed matter and release a massively parallel implementation of the code as a plugin for the open-source package HOOMD-blue [J. A. Anderson et al., J. Comput. Phys. 227, 5342 (2008) and J. Glaser et al., Comput. Phys. Commun. 192, 97 (2015)] which runs on graphics processing units

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A cross-sectional study of the temporal evolution of electricity consumption of six commercial buildings

Current approaches to building efficiency diagnoses include conventional energy audit techniques that can be expensive and time consuming. In contrast, virtual energy audits of readily available 15-minute-interval building electricity consumption are being explored to provide quick, inexpensive, and useful insights into building operation characteristics. A cross sectional analysis of six buildings in two different climate zones provides methods for data cleaning, population-based building comparisons, and relationships (correlations) of weather and electricity consumption. Data cleaning methods have been developed to categorize and appropriately filter or correct anomalous data including outliers, missing data, and erroneous values (resulting in < 0.5% anomalies). The utility of a cross-sectional analysis of a sample set of building's electricity consumption is found through comparisons of baseload, daily consumption variance, and energy use intensity. Correlations of weather and electricity consumption 15-minute interval datasets show important relationships for the heating and cooling seasons using computed correlations of a Time-Specific-Averaged- Ordered Variable (exterior temperature) and corresponding averaged variables (electricity consumption)(TSAOV method). The TSAOV method is unique as it introduces time of day as a third variable while also minimizing randomness in both correlated variables through averaging. This study found that many of the pair-wise linear correlation analyses lacked strong relationships, prompting the development of the new TSAOV method to uncover the causal relationship between electricity and weather. We conclude that a combination of varied HVAC system operations, building thermal mass, plug load use, and building set point temperatures are likely responsible for the poor correlations in the prior studies, while the correlation of time-specific-averaged-ordered temperature and corresponding averaged variables method developed herein adequately accounts for these issues and enables discovery of strong linear pair-wise correlation R values. TSAOV correlations lay the foundation for a new approach to building studies, that mitigates plug load interferences and identifies more accurate insights into weather-energy relationship for all building types. Over all six buildings analyzed the TSAOV method reported very significant average correlations per building of 0.94 to 0.82 in magnitude. Our rigorous statistics-based methods applied to 15- minute-interval electricity data further enables virtual energy audits of buildings to quickly and inexpensively inform energy savings measures.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Best Practices of Uncertainty Estimation for the National Solar Radiation Database (NSRDB 1998-2015): Preprint

It is essential to apply a traceable and standard approach to determine the uncertainty of solar resource data. Solar resource data are used for all phases of solar energy conversion projects, from the conceptual phase to routine solar power plant operation, and to determine performance guarantees of solar energy conversion systems. These guarantees are based on the available solar resource derived from a measurement station or modeled data set such as the National Solar Radiation Database (NSRDB). Therefore, quantifying the uncertainty of these data sets provides confidence to financiers, developers, and site operators of solar energy conversion systems and ultimately reduces deployment costs. In this study, we implemented the Guide to the Expression of Uncertainty in Measurement (GUM) 1 to quantify the overall uncertainty of the NSRDB data. First, we start with quantifying measurement uncertainty, then we determine each uncertainty statistic of the NSRDB data, and we combine them using the root-sum-of-the-squares method. The statistics were derived by comparing the NSRDB data to the seven measurement stations from the National Oceanic and Atmospheric Administration's Surface Radiation Budget Network, National Renewable Energy Laboratory's Solar Radiation Research Laboratory, and the Atmospheric Radiation Measurement program's Southern Great Plains Central Facility, in Billings, Oklahoma. The evaluation was conducted for hourly values, daily totals, monthly mean daily totals, and annual mean monthly mean daily totals. Varying time averages assist to capture the temporal uncertainty of the specific modeled solar resource data required for each phase of a solar energy project; some phases require higher temporal resolution than others. Overall, by including the uncertainty of measurements of solar radiation made at ground stations, bias, and root mean square error, the NSRDB data demonstrated expanded uncertainty of 17 percent - 29 percent on hourly and an approximate 5 percent - 8 percent annual bases.

14 SOLAR ENERGY↗

An implementation of neural simulation-based inference for parameter estimation in ATLAS

Neural simulation-based inference (NSBI) is a powerful class of machine-learning-based methods for statistical inference that naturally handles high-dimensional parameter estimation without the need to bin data into low-dimensional summary histograms. Such methods are promising for a range of measurements, including at the Large Hadron Collider, where no single observable may be optimal to scan over the entire theoretical phase space under consideration, or where binning data into histograms could result in a loss of sensitivity. This work develops a NSBI framework for statistical inference, using neural networks to estimate probability density ratios, which enables the application to a full-scale analysis. It incorporates a large number of systematic uncertainties, quantifies the uncertainty due to the finite number of events in training samples, develops a method to construct confidence intervals, and demonstrates a series of intermediate diagnostic checks that can be performed to validate the robustness of the method. As an example, the power and feasibility of the method are assessed on simulated data for a simplified version of an off-shell Higgs boson couplings measurement in the four-lepton final states. This approach represents an extension to the standard statistical methodology used by the experiments at the Large Hadron Collider, and can benefit many physics analyses.

frequentist statistics↗

What drives the variance of galaxy spectra?

We present a study aimed at understanding the physical phenomena underlying the formation and evolution of galaxies following a data-driven analysis of spectroscopic data based on the variance in a carefully selected sample. We apply principal component analysis (PCA) independently to three subsets of continuum-subtracted optical spectra, segregated into their nebular emission activity as quiescent, star-forming, and active galactic nuclei (AGNs). We emphasize that the variance of the input data in this work only relates to the absorption lines in the photospheres of the stellar populations. The sample is taken from the Sloan Digital Sky Survey (SDSS) in the stellar velocity dispersion range 100–150 km s −1 , to minimize the ‘blurring’ effect of the stellar motion. We restrict the analysis to the first three principal components (PCs) and find that PCA segregates the three types with the highest variance mapping SSP-equivalent age, along with an inextricable degeneracy with metallicity, even when all three PCs are included. Spectral fitting shows that stellar age dominates PC1, whereas PC2 and PC3 have a mixed dependence of age and metallicity. The trends support – independently of any model fitting – the hypothesis of an evolutionary sequence from star formation to AGN to quiescence. As a further test of the consistency of the analysis, we apply the same methodology in different spectral windows, finding similar trends, but the variance is maximal in the blue wavelength range, roughly around the 4000 Å break.

79 ASTRONOMY AND ASTROPHYSICS↗

The Impact of Below Detection Limit Samples in (NPP) Decommissioning Residual Risk Assessment - 17033

There are some technical problems with finalizing regulations and standards that address nuclear power plant (NPP) decommissioning site soil analyses for license termination. It is difficult to know how to best include detection limit observations from site soil analysis, because typical soil collection data is reported above, at, and below the detection limit. In addition, multiple detection limits are required to adequately estimate the soil radionuclide concentrations. In the literature, researchers analyzing environmental data refer to below the detection limit observations as 'left-censored data'. Left-censored data are less than the detection limit of the instrument(s) that made the measurements. Conventional approaches to managing left-censored data either ignore or simply replace the detection limits with zero, a fraction of the detection limit, or the detection limit itself. However, these approaches are statistically biased and limited in their usefulness. The Kaplan-Meier method, robust regression on order statistics method, and maximum likelihood estimation method are proposed to estimate the left-censored data more precisely. The proposed methods are applied to data from a Monazite powder manufacturing plant and the Colorado School of Mines Research Institute. Summary statistics such as the sample mean, sample standard deviation, sample percentiles are calculated from each data set and are used in risk and volume estimation calculations. Previous environmental analyses, such as the exposure assessment, recognize the uncertainty issue that is addressed in this research using the Latin hypercube sampling approach. Next, probabilistic distributions of the input parameters are developed for the uncertainty analyses. Finally, a framework methodology depicting the decision-making process in the proposed method is presented. The framework defines the critical steps, the amount of radioactivity, types of distributions, censoring percentage, sample size, and number of detection limits; it also allows the user to select the appropriate approach based on their site-specific data and analyses. The goal of this research is to develop a more precise risk assessment, estimate of the volume of soil removal, examine potential cost savings. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Out-of-Distribution Detection and Radiological Data Monitoring Using Statistical Process Control

Abstract Machine learning (ML) models often fail with data that deviates from their training distribution. This is a significant concern for ML-enabled devices as data drift may lead to unexpected performance. This work introduces a new framework for out of distribution (OOD) detection and data drift monitoring that combines ML and geometric methods with statistical process control (SPC). We investigated different design choices, including methods for extracting feature representations and drift quantification for OOD detection in individual images and as an approach for input data monitoring. We evaluated the framework for both identifying OOD images and demonstrating the ability to detect shifts in data streams over time. We demonstrated a proof-of-concept via the following tasks: 1) differentiating axial vs. non-axial CT images, 2) differentiating CXR vs. other radiographic imaging modalities, and 3) differentiating adult CXR vs. pediatric CXR. For the identification of individual OOD images, our framework achieved high sensitivity in detecting OOD inputs: 0.980 in CT, 0.984 in CXR, and 0.854 in pediatric CXR. Our framework is also adept at monitoring data streams and identifying the time a drift occurred. In our simulations tracking drift over time, it effectively detected a shift from CXR to non-CXR instantly, a transition from axial to non-axial CT within few days, and a drift from adult to pediatric CXRs within a day—all while maintaining a low false positive rate. Through additional experiments, we demonstrate the framework is modality-agnostic and independent from the underlying model structure, making it highly customizable for specific applications and broadly applicable across different imaging modalities and deployed ML models.

Zamzmi, Ghada↗

Nonequilibrium information entropy approach to ternary fission of actinides

Ternary fission of actinides probes the state of the nucleus at scission. Light clusters are produced in space and time very close to the scission point. Within the nonequilibrium statistical operator method, a generalized Gibbs distribution is constructed from the information given by the observed yields of isotopes. Using this relevant statistical operator, yields are calculated taking excited states and continuum correlations into account, in accordance with the virial expansion of the equation of state. Furthermore, clusters with mass number A≤10 are well described using the nonequilibrium generalizations of temperature and chemical potentials. Improving the virial expansion, in-medium effects may become of importance in determining the contribution of weakly bound states and continuum correlations to the intrinsic partition function. Yields of larger clusters, which fail to reach this quasiequilibrium form of the relevant distribution, are described by nucleation kinetics, and a saddle-to-scission relaxation time of about 7000 fm/c is inferred. Light-charged particle emission, described by reaction kinetics and virial expansions, may therefore be regarded as a very important tool to probe the nonequilibrium time evolution of actinide nuclei during fission.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Photometric redshift uncertainties in weak gravitational lensing shear analysis: models and marginalization

ABSTRACT Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the uncertainties on the sample redshift distribution n(z). Due to the challenge of running Markov chain Monte Carlo (MCMC) in the high-dimensional parameter spaces in which the n(z) uncertainties may be parametrized, it is common practice to simplify the n(z) parametrization or combine MCMC chains that each have a fixed n(z) resampled from the n(z) uncertainties. In this work, we propose a statistically principled Bayesian resampling approach for marginalizing over the n(z) uncertainty using multiple MCMC chains. We self-consistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC three-year shape catalogue, and find that these methods recover statistically consistent error bars for the cosmological parameter constraints for predicted HSC three-year analysis, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for data sets with the constraining power of the full HSC survey data set (and, by implication, those upcoming surveys with even tighter constraints), the choice of method for marginalizing over n(z) uncertainty among the several methods from the literature may modify the 1σ uncertainties on Ωm–S8 constraints by ∼4 per cent, and a careful model selection is needed to ensure credible parameter intervals.

Zhang, Tianqing (ORCID:000000025596198X)↗

Optimizing observables with machine learning for better unfolding

Most measurements in particle and nuclear physics use matrix-based unfolding algorithms to correct for detector effects. In nearly all cases, the observable is defined analogously at the particle and detector level. We point out that while the particle-level observable needs to be physically motivated to link with theory, the detector-level need not be and can be optimized. We show that using deep learning to define detector-level observables has the capability to improve the measurement when combined with standard unfolding methods.

47 OTHER INSTRUMENTATION↗

Joint inference of multiplicative and additive systematics in galaxy density fluctuations and clustering measurements

Galaxy clustering measurements are a key probe of the matter density field in the Universe. With the era of precision cosmology upon us, surveys rely on precise measurements of the clustering signal for meaningful cosmological analysis. However, the presence of systematic contaminants can bias the observed galaxy number density, and thereby bias the galaxy two-point statistics. As the statistical uncertainties get smaller, correcting for these systematic contaminants becomes increasingly important for unbiased cosmological analysis. We present and validate a new method for understanding and mitigating both additive and multiplicative systematics in galaxy clustering measurements (two-point function) by joint inference of contaminants in the galaxy overdensity field (one-point function) using a maximum-likelihood estimator (MLE). We test this methodology with Kilo-Degree Survey-like mock galaxy catalogues and synthetic systematic template maps. We estimate the cosmological impact of such mitigation by quantifying uncertainties and possible biases in the inferred relationship between the observed and the true galaxy clustering signal. Our method robustly corrects the clustering signal to the sub-percent level and reduces numerous additive and multiplicative systematics from 1.5σ to less than 0.1σ for the scenarios we tested. In addition, we provide an empirical approach to identifying the functional form (additive, multiplicative, or other) by which specific systematics contaminate the galaxy number density. Even though this approach is tested and geared towards systematics contaminating the galaxy number density, the methods can be extended to systematics mitigation for other two-point correlation measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Understanding the bias introduced in quantum dot blinking using change point analysis

Quantum dots are semiconductor crystals that are less than 100 nanometers in size; that is, between 1 billionth and 100 billionths of a meter. They can be composed of one semiconductor material or a core of one semiconductor surrounded by a shell of another. The quantum dots studied in this work consisted of a cadmium selenide core surrounded by a cadmium sulfide shell. When a quantum dot is illuminated with light, some of it can be absorbed and excites the quantum dot to a higher energy state. To relax back down to its resting state, light can be emitted in the form of fluorescence. The nature of the fluorescence that is emitted from a single quantum dot differs from that which is emitted from a bulk sample (usually a solid film or a solution of quantum dots). While in bulk samples the fluorescence over time fluctuates randomly about some average, maintaining a continuous average intensity, single quantum dot fluorescence switches between two or more intensities. This phenomenon is referred to as quantum dot blinking, and its origin is of significant relevance to solar cell, light emitting diode and biological tracking applications. Quantum dot blinking can be studied by exciting an isolated quantum dot with light and recording the ensuing fluorescence using sensitive detectors. This is done over many minutes, resulting in a fluorescence intensity (in counts per second) versus time trajectory. These trajectories must be further analyzed in order to understand the nature of the blinking behavior. Conventionally, a bin and threshold analysis is used, whereby the arrival times of fluorescent photons are binned to reduce the signal noise, and a threshold is used to separate the trajectory into periods of high and low fluorescence. In this study, the effects of bin size and threshold on the blinking kinetics were investigated, and the assumption that there is only one bright and one dark state was tested. To do so, a statistically rigorous method called change point analysis was needed which does not require binning and which can determine the number of intensity levels present. Blinking in 17 quantum dots was studied using both analysis methods. The primary parameter that was compared between the two methods is called a truncation time. Increasing the bin size was found to generally lead to a larger truncation time while increasing the threshold always decreased the truncation time. Using the change point analysis method, 12 out of 17 quantum dots were found to exhibit more than two intensity levels. Lastly, the assumption that only two intensity levels exist was found to significantly affect the blinking statistics: when individual levels were combined into one bright level, the truncation time would increase. The change point analysis method was found to be more suitable for studying multilevel blinking in quantum dots than the conventional bin and threshold method, since the effects of binning and thresholding can be alleviated and the two-level assumption relaxed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗