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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2013

File Specification for GEOS-5 FP-IT (Forward Processing for Instrument Teams)

The GEOS-5 FP-IT Atmospheric Data Assimilation System (GEOS-5 ADAS) uses an analysis developed jointly with NOAA's National Centers for Environmental Prediction (NCEP), which allows the Global Modeling and Assimilation Office (GMAO) to take advantage of the developments at NCEP and the Joint Center for Satellite Data Assimilation (JCSDA). The GEOS-5 AGCM uses the finite-volume dynamics (Lin, 2004) integrated with various physics packages (e.g, Bacmeister et al., 2006), under the Earth System Modeling Framework (ESMF) including the Catchment Land Surface Model (CLSM) (e.g., Koster et al., 2000). The GSI analysis is a three-dimensional variational (3DVar) analysis applied in grid-point space to facilitate the implementation of anisotropic, inhomogeneous covariances (e.g., Wu et al., 2002; Derber et al., 2003). The GSI implementation for GEOS-5 FP-IT incorporates a set of recursive filters that produce approximately Gaussian smoothing kernels and isotropic correlation functions. The GEOS-5 ADAS is documented in Rienecker et al. (2008). More recent updates to the model are presented in Molod et al. (2011). The GEOS-5 system actively assimilates roughly 2 × 10(exp 6) observations for each analysis, including about 7.5 × 10(exp 5) AIRS radiance data. The input stream is roughly twice this volume, but because of the large volume, the data are thinned commensurate with the analysis grid to reduce the computational burden. Data are also rejected from the analysis through quality control procedures designed to detect, for example, the presence of cloud. To minimize the spurious periodic perturbations of the analysis, GEOS-5 FP-IT uses the Incremental Analysis Update (IAU) technique developed by Bloom et al. (1996). More details of this procedure are given in Appendix A. The analysis is performed at a horizontal resolution of 0.625-degree longitude by 0.5-degree latitude and at 72 levels, extending to 0.01 hPa. All products are generated at the native resolution of the horizontal grid. The majority of data products are time-averaged, but four instantaneous products are also available. Hourly data intervals are used for two-dimensional products, while 3-hourly intervals are used for three-dimensional products. These may be on the model's native 72-layer vertical grid or at 42 pressure surfaces extending to 0.1 hPa. This document describes the gridded output files produced by the GMAO near real-time operational GEOS-5 FP-IT processing in support of the EOS instrument teams. Additional details about variables listed in this file specification can be found in a separate document, the GEOS-5 File Specification Variable Definition Glossary.

3D Var↗
NASA NTRS1978

Laser amplification of incoherent radiation

The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The spectral behavior of the radiation in the nonlinear regime is studied and the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is explored in several numerical examples. The connections of this study with the time-domain work on self-pulsing in a ring-laser configuration, are established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ('Raman-type terms'), and saturation phenomena.

Menegozzi, L. N.↗
NASA NTRSDate not supplied

Statistical Classification of Biosignature Information using Multiple Instrument Observations

The accurate identification of biosignatures (indications of life) from data taken from remote or in situ planetary exploration is one of the most important challenges in astrobiology, the interdisciplinary field examining habitability and the potential for extraterrestrial life. This study employs machine learning algorithms to optimize the identification of biosignatures, with an emphasis on those which are agnostic to a specific biochemical basis. We exploit the wealth of terrestrial data available from biogenic and abiogenic systems to enhance efficient feature prioritization. Our dataset, pulled from public databases and laboratory recorded measurements, includes elemental abundance, isotopic fractionation, and VNIR/Raman spectra The data curation process included standardization for detection limits and ranges. Subsequent feature extraction yielded detailed inputs for machine learning, including combinations of elemental content, isotopic ratios, and parameters of spectral peaks and troughs. Feature significance was evaluated across diverse machine learning methodologies, such as k-nearest neighbors, logistic regression, Random Forest, support vector machines, and Gaussian Naïve Bayes, along with a combined voting classifier. We utilized Receiver Operating Characteristic Area Under the Curve (ROC AUC) across 2,000 50% test-train splits as a robust metric of model performance. Results revealed a promising ROC AUC of 0.853 for the combined voting classifier. Removing elemental abundance data notably reduced model accuracy (13% decrease in AUC), highlighting its critical role in biosignature detection. Several other individual data features exhibited significance within their respective data types, offering additional granularity. This research fortifies the relevance of machine learning to astrobiology, potentially enhancing life detection missions by allowing algorithmic prioritization of high-interest samples for further investigation. Future work will refine data standardization, expand the dataset to include more terrestrial systems, and incorporate convolutional neural networks for spectral feature extraction. The potential for public data sharing is also under exploration, reinforcing our commitment to collective scientific advancement.

Statistical↗
NASA NTRS1980

Pioneer Venus Sounder Probe Solar Flux Radiometer

The Solar Flux Radiometer aboard the Pioneer Venus Sounder Probe operated successfully during its descent through the atmosphere of Venus. The instrument measured atmospheric radiance over the spectral range from 400 to 1800 nm as a function of altitude. Elevation and azimuthal measurements on the radiation field were made with five optical channels. Twelve filtered Si and Ge photovoltaic detectors were maintained near 30 C with a phase-change material. The detector output currents were processed with logarithmic transimpedance converters and digitized with an 11-bit A/D converter. Atmospheric sampling in both elevation and azimuth was done according to a Gaussian integration scheme. The serial output data averaged 20 bits/sec, including housekeeping (sync, spin period, sample timing and mode). The data were used to determine the deposition of solar energy in the atmosphere of Venus between 67 km and the surface along with upward and downward fluxes and radiances with an altitude resolution of several hundred meters. The results allow for more accurate modeling of the radiation balance of the atmosphere than previously possible.

Tomasko, M. G.↗
DOE OSTI2026

GP Cosmology Surrogate v1.0

GP Cosmology Surrogate is a Python library for building and training a generalized multi-output Gaussian process (GP) framework of @takhtaganov2021cosmic. In this approach, the surrogate is constructed sequentially, guided by a Bayesian optimization acquisition function that targets reduction of emulation error in the regions most consistent with the observational data. This adaptive design concentrates computational resources where they have the greatest impact on inference accuracy. The library supports efficient training for separable GP kernels, which allows the use of Kronecker algebra to handle high-dimensional input spaces and large numbers of correlated outputs. This makes it well suited for applications such as modeling cosmological power spectra, large-scale physical simulations, and multi-output hyperparameter tuning. By combining scalable multi-output GP modeling with data-driven adaptive sampling, GPsurrogate enables parameter inference and optimization with substantially fewer simulations than conventional space-filling designs.

Lukic, Zarija [Lawrence Berkeley National Laborato↗
DOE OSTI2025

Exploring scenarios for enhanced fuel compression and performance on the National Ignition Facility with machine-learning-aided design techniques

Recent fusion experiments on the National Ignition Facility (NIF) have achieved ignition, producing multi-MJ fusion yields for input laser energies of roughly 2 MJ [Abu-Shawareb et al., Phys. Rev. Lett. 132, 065102 (2024)]. Building on the success of the target designs that have achieved ignition, we explore new implosion scenarios predicted to generate significantly more compression of the dense DT ice layer and correspondingly higher yields while preserving many of the key physics characteristics of present-day ignition designs. Our main result is a novel 3-shock implosion scheme that effectively minimizes the shock-induced entropy in the dense, accelerating DT shell and maximizes the resulting fuel compression subject to a fixed leading shock strength consistent with present-day ignition experiments, which is necessary to melt the crystalline high-density carbon ablator. Compared to the first NIF experiment to fulfill Lawson's ignition criterion, shot N210808 [Abu-Shawareb et al., Phys. Rev. Lett. 129, 075001 (2022)], our design exhibits a 40% increase in simulated peak areal density (ρR) and a 5× increase in 1D fusion yield using a 4% lighter ablator and identical DT payloads. We also present a complete integrated 2D hohlraum design and laser pulse specifications capable of generating the desired 3-shock drive and maintaining control of the low-mode capsule implosion symmetry, where the increase in simulated 2D yield relative to N210808 is > 10×. This new implosion regime was discovered with help from a machine-learning-enabled capsule design optimization framework. We outline the workflow this automated tool uses to identify improved design candidates by running several rounds of capsule simulations, constructing a surrogate model mapping input variations to key physics output quantities, and querying the resulting statistical model to propose adjustments to the x-ray drive and capsule to reach a set of physics objectives prescribed by the designer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2012

Ion Current Density Study of the NASA-300M and NASA-457Mv2 Hall Thrusters

NASA Glenn Research Center is developing a Hall thruster in the 15-50 kW range to support future NASA missions. As a part of the process, the performance and plume characteristics of the NASA-300M, a 20-kW Hall thruster, and the NASA-457Mv2, a 50-kW Hall thruster, were evaluated. The collected data will be used to improve the fidelity of the JPL modeling tool, Hall2De, which will then be used to aid the design of the 15-50 kW Hall thruster. This paper gives a detailed overview of the Faraday probe portion of the plume characterization study. The Faraday probe in this study is a near-field probe swept radially at many axial locations downstream of the thruster exit plane. Threshold-based integration limits with threshold values of 1/e, 1/e2, and 1/e3 times the local peak current density are tried for the purpose of ion current integration and divergence angle calculation. The NASA-300M is operated at 7 conditions and the NASA-457Mv2 at 14 conditions. These conditions span discharge voltages of 200 to 500 V and discharge power of 10 to 50 kW. The ion current density profiles of the near-field plume originating from the discharge channel are discovered to strongly resemble Gaussian distributions. A novel analysis approach involving a form of ray tracing is used to determine an effective point of origin for the near-field plume. In the process of performing this analysis, definitive evidence is discovered that showed the near-field plume is bending towards the thruster centerline.

Huang, Wensheng↗
NASA NTRS1989

Efficient computer algebra algorithms for polynomial matrices in control design

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Baras, J. S.↗
NASA NTRS2022

Gaussian Process Regression Method for Costing SmallSat Bus Capabilities

NASA is responding to the growing interest in, andcapabilities of, small satellites for science applications with an increasingnumber and frequency of Announcements of Opportunityfor small satellite space missions. Estimating the probabilitythat these mission concepts will fit within the small cost capsof these opportunities is largely driven by the probability thatone of the burgeoning number of small satellite providers will beable to meet the payload’s accommodation requirements withinthe budget for the spacecraft. JPL has collected a databasecontaining technical specifications and cost of commerciallyavailable Smallsat buses across various vendors. The primarypurpose of the database is for use in JPL’s Team X architecturestudies to inform cost estimates of a spacecraft bus which fitsthe customer’s technical requirements for their payload andmission. Customer needs are often unique and don’t alignperfectly with an off-the-shelf commercial spacecraft bus, whichmotivates the need to develop a cost model across the continuoustechnical parameter space.Al’s Bus Cost Distribution Estimator (ABCDE) uses Gaussianprocess regression (GPR) to predict commercial Smallsat spacecraftbus cost based on a subset of a customer’s technicalrequirements (payload mass, payload power, delta V, pointingcontrol, and downlink rate). GPR is implemented in ABCDE asa Bayesian method which fits an implied multivariate regressionon the technical parameters and uses kriging to intentionally“overfit” the residuals. Overfitting the residuals allows costestimates to collapse in uncertainty closer to the data pointswhile maintaining larger uncertainty intervals in regions of parameterspace with fewer data records. The data used to fit thismodel is sensitive and represents cost estimates for off-the-shelfcommercial buses. GPR simultaneously protects the sensitivityof the database and uses the sparse nature of the database toaccount for uncertainty in cost in a useful way. For a givenset of customer technical requirements, the tool provides a costestimate distribution, the percentiles of which can be interpretedas a confidence level of finding a commercial bus under a specifiedcost cap. ABCDE dramatically pushes the boundaries ofspacecraft cost estimation models due to its Bayesian methodology(accounting for the maximum uncertainty in the underlyingregression), the mathematically advanced kriging methodology,and the novelty of its application in Team X architecture tradestudies.

Austin, Alex↗
NASA NTRS1989

Laser transit anemometer software development program

Algorithms were developed for the extraction of two components of mean velocity, standard deviation, and the associated correlation coefficient from laser transit anemometry (LTA) data ensembles. The solution method is based on an assumed two-dimensional Gaussian probability density function (PDF) model of the flow field under investigation. The procedure consists of transforming the data ensembles from the data acquisition domain (consisting of time and angle information) to the velocity space domain (consisting of velocity component information). The mean velocity results are obtained from the data ensemble centroid. Through a least squares fitting of the transformed data to an ellipse representing the intersection of a plane with the PDF, the standard deviations and correlation coefficient are obtained. A data set simulation method is presented to test the data reduction process. Results of using the simulation system with a limited test matrix of input values is also given.

Abbiss, John B.↗
NASA NTRS2012

Ion Current Density Study of the NASA-300M and NASA-457Mv2 Hall Thrusters

NASA Glenn Research Center is developing a Hall thruster in the 15-50 kW range to support future NASA missions. As a part of the process, the performance and plume characteristics of the NASA-300M, a 20-kW Hall thruster, and the NASA-457Mv2, a 50-kW Hall thruster, were evaluated. The collected data will be used to improve the fidelity of the JPL modeling tool, Hall2De, which will then be used to aid the design of the 15-50 kW Hall thruster. This paper gives a detailed overview of the Faraday probe portion of the plume characterization study. The Faraday probe in this study is a near-field probe swept radially at many axial locations downstream of the thruster exit plane. Threshold-based integration limits with threshold values of 1/e, 1/e(sup 2), and 1/e(sup 3) times the local peak current density are tried for the purpose of ion current integration and divergence angle calculation. The NASA-300M is operated at 7 conditions and the NASA-457Mv2 at 14 conditions. These conditions span discharge voltages of 200 to 500 V and discharge power of 10 to 50 kW. The ion current density profiles of the near-field plume originating from the discharge channel are discovered to strongly resemble Gaussian distributions. A novel analysis approach involving a form of ray tracing is used to determine an effective point of origin for the near-field plume. In the process of performing this analysis, definitive evidence is discovered that showed the near-field plume is bending towards the thruster centerline.

Huang, Wensheng↗
NASA NTRSDate not supplied

Evaluating Subgrid-Scale Properties of Low Clouds over the Beaufort Sea in Arctic System Reanalysis using ARISE Airborne In Situ Observations

Arctic low clouds influence the evolution of the Arctic system through their effects on radiative fluxes, boundary layer mixing, stability, turbulence, humidity, and precipitation. Unfortunately, atmospheric models and retrospective analysis (reanalysis) products struggle to accurately simulate the occurrence and properties of low clouds in the Arctic. To better understand the magnitude and possible causes of this problem, we analyze the disagreements between the Arctic System Reanalysis version 2 (ASR) and data taken during the September 2014 Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) airborne campaign conducted over the Beaufort Sea. Previous analysis of grid scale-averaged meteorological variables revealed a lack of cloud water produced in ASR, related to warm/dry biases, a failure to produce sufficient cloud water in conditions that are observed to be favorable for large cloud water values, and sampling issues with the ARISE flight paths. However, ARISE collected meteorological observations at one second intervals, offering spatial data resolution comparable to the subgrid scale of ASR. Subgrid scale properties and processes must be parameterized in conventional atmospheric models and reanalyses such as ASR, and often rely on assumed distributions of meteorological variables about the grid box mean state. To enable an examination of the realism of ASR’s subgrid scale properties, we use high resolution data from ARISE determine the “subgrid scale” distributions of cloud water and thermodynamic variables in the real atmosphere. Preliminary results show that the subgrid scale distribution of thermodynamic variables about the grid scale mean resembles the triangular distribution assumed in many bulk microphysical parameterization schemes, but also with tails resembling Gaussian distributions. The main goal is to understand the partitioning of the total available atmospheric water into water vapor and cloud water. Models typically covert some percentage of total water in a grid box to cloud water based on the estimated amount of supersaturation from the assumed vapor distribution. The ARISE measurements can reveal the relationship between subgrid scale supersaturation and the partition between cloud water and water vapor.

Jason Brant Dodson↗
DOE OSTI2024

On learning what to learn: Heterogeneous observations of dynamics and establishing possibly causal relations among them

Abstract Before we attempt to (approximately) learn a function between two sets of observables of a physical process, we must first decide what the inputs and outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven ways of first deciding “the right quantities” to relate through such a function, and then proceeding to learn it. This is accomplished by first processing simultaneous heterogeneous data streams (ensembles of time series) from observations of a physical system: records of multiple observation processes of the system. We determine (i) what subsets of observables are common between the observation processes (and therefore observable from each other, relatable through a function); and (ii) what information is unrelated to these common observables, therefore particular to each observation process, and not contributing to the desired function. Any data-driven technique can subsequently be used to learn the input–output relation—from k-nearest neighbors and Geometric Harmonics to Gaussian Processes and Neural Networks. Two particular “twists” of the approach are discussed. The first has to do with the identifiability of particular quantities of interest from the measurements. We now construct mappings from a single set of observations from one process to entire level sets of measurements of the second process, consistent with this single set. The second attempts to relate our framework to a form of causality: if one of the observation processes measures “now,” while the second observation process measures “in the future,” the function to be learned among what is common across observation processes constitutes a dynamical model for the system evolution.

Sroczynski, David W.↗
NASA NTRS2015

Anomaly Detection in Power Quality at Data Centers

The goal during my internship at the National Center for Critical Information Processing and Storage (NCCIPS) is to implement an anomaly detection method through the StruxureWare SCADA Power Monitoring system. The benefit of the anomaly detection mechanism is to provide the capability to detect and anticipate equipment degradation by monitoring power quality prior to equipment failure. First, a study is conducted that examines the existing techniques of power quality management. Based on these findings, and the capabilities of the existing SCADA resources, recommendations are presented for implementing effective anomaly detection. Since voltage, current, and total harmonic distortion demonstrate Gaussian distributions, effective set-points are computed using this model, while maintaining a low false positive count.

Grichine, Art↗
DOE OSTI2025

Unified nonparametric equation-of-state inference from the neutron-star crust to perturbative-QCD densities

Perturbative quantum chromodynamics (pQCD), while valid only at densities exceeding those found in the cores of neutron stars, could provide constraints on the dense-matter equation of state (EOS). Here, in this work, we examine the impact of pQCD information on the inference of the EOS using a nonparametric framework based on Gaussian processes (GPs). We examine the application of pQCD constraints through a ``pQCD likelihood,'' and verify the findings of previous works; namely, a softening of the EOS at the central densities of the most massive neutron stars and a reduction in the maximum neutron-star mass. Although the pQCD likelihood can be easily integrated into existing EOS inference frameworks, this approach requires an arbitrary selection of the density at which the constraints are applied. The EOS behavior is also treated differently on either side of the chosen density. To mitigate these issues, we extend the EOS model to higher densities, thereby constructing a ``unified'' description of the EOS from the neutron-star crust to densities relevant for pQCD. In this approach the pQCD constraints effectively become part of the prior. Since the EOS is unconstrained by any calculation or data between the densities applicable to neutron stars and pQCD, we argue for maximum modeling flexibility in that regime. We compare the unified EOS with the traditional pQCD likelihood, and although we confirm the EOS softening, we do not see a reduction in the maximum neutron-star mass or any impact on macroscopic observables. Though residual model dependence cannot be ruled out, we find that pQCD suggests the speed of sound in the densest neutron-star cores has already started decreasing toward the asymptotic limit; we find that the speed of sound squared at the center of the most massive neutron star has an upper bound of $\sim 0.5$ at the 90% level.

equations of state of nuclear matter↗
NASA NTRS1984

State estimation Kalman filter using optical processings Noise statistics known

Reference is made to a study by Casasent et al. (1983), which gave a description of a frequency-multiplexed acoustooptic processor and showed how it was capable of performing all the individual operations required in Kalman filtering. The data flow and organization of all required operations however, were not detailed in that study. Consideration is given here to a simpler Kalman filter state estimation problem. Equally spaced time-sampled intervals (k times T sub s, with k the iterative time index) are assumed. It is further assumed that the system noise vector w and the measurement noise vector v are uncorrelated and Gaussian distributed and that the noise statistics (Q and R) and the system model (Phi, Gamma, H) are known. The error covariance matrix P and the extrapolated error covariance matrix M can thus be precomputed and the Kalman gain matrix K sub k can be precomputed and stored for each input time sample.

Jackson, J.↗
NASA NTRS2022

Modeling the East-West Asymmetry of Energetic Particle Fluence in Large Solar Energetic Particle Events Using the iPATH Model

It has been noted that in large solar energetic particle (SEP) events, the peak intensities show an East-West asymmetry with respect to the source flare locations. Using the 2D improved Particle Acceleration and Transport in the Heliosphere (iPATH) model, we investigate the origin of this longitudinal trend. We consider multiple cases with different solar wind speeds and eruption speeds of the coronal mass ejections (CMEs) and fit the longitudinal distributions of time-averaged fluence by symmetric/asymmetric Gaussian functions with three time intervals of 8, 24 and 48 hr after the flare onset time respectively. The simulation results are compared with a statistical study of three-spacecraft events. We suggest that the East-West asymmetry of SEP fluence and peak intensity can be primarily caused the combined effect of an extended shock acceleration process and the evolution of magnetic field connection to the shock front. Our simulations show that the solar wind speed and the CME speed are important factors determining the East-West fluence asymmetry.

Zheyi Ding↗
DOE OSTI2026

Automated scanning probe microscopy of combinatorial ferroelectric libraries: Gaussian-process-guided exploration and noise-aware experiment planning

Combinatorial materials libraries provide an efficient route for mapping composition–property relationships, but their broader impact depends on rapid, quantitative, and functionally relevant characterization. Scanning Probe Microscopy (SPM), including piezoresponse force microscopy (PFM), offers significant potential for quantitative, functionally relevant combi-library readouts. Here, we implement a fully automated SPM workflow for ferroelectric combinatorial libraries and benchmark Gaussian-process-based Bayesian optimization strategies for autonomous experiment planning. The workflow integrates automated probe motion, contact optimization, imaging, and dual amplitude resonance tracking-PFM spectroscopy, and uses scalarized spectroscopic observables to guide subsequent measurements. Stage motion, probe engagement, in-contact tuning, imaging, spectroscopy, and the choice of the next measurement location all proceed without human input. We demonstrate the approach on Sm-doped BiFeO 3 and Zn x Mg 1−x O libraries. By comparing vanilla Bayesian optimization with a measured-noise variant, we show that explicit treatment of local reproducibility can improve modeling of composition-dependent response when the measured variance is physically meaningful, but can also reduce robustness when variability is dominated by outliers or topographic artifacts. Furthermore, these results establish automated SPM as a bridge between combinatorial synthesis and quantitative functional characterization.

Liu, Yu [University of Tennessee, Knoxville, TN (U↗