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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 NTRS1991

Psychophysical evaluation of three-dimensional auditory displays

Work during this reporting period included the completion of our research on the use of principal components analysis (PCA) to model the acoustical head related transfer functions (HRTFs) that are used to synthesize virtual sources for three dimensional auditory displays. In addition, a series of studies was initiated on the perceptual errors made by listeners when localizing free-field and virtual sources. Previous research has revealed that under certain conditions these perceptual errors, often called 'confusions' or 'reversals', are both large and frequent, thus seriously comprising the utility of a 3-D virtual auditory display. The long-range goal of our work in this area is to elucidate the sources of the confusions and to develop signal-processing strategies to reduce or eliminate them.

Wightman, Frederic L.↗
NASA NTRS2002

Evidence of an Intrinsic Intraseasonal Oscillation over Tropical South America During Austral Summer

The intraseasonal variation (ISV) in the 30-60 day band, also known as Madden-Julian oscillation (MJO), has been studied for decades. Madden and Julian showed that the oscillation originated from the western Indian Ocean, propagated eastward, got enhanced over the maritime continent and weakened after passing over the dateline. Composite studies showed evidences of a signal in upper and lower level zonal wind propagating around the globe during an oscillation. Theoretical studies pointed out that the interaction with the warm ocean surface and the coupling with the convective and radiative processes in the atmosphere could manifest the oscillation, which propagates eastward via mutual feedbacks between the wave motions and the cumulus heating. Over tropical South America, no independent 30-60 day oscillation has been reported so far, despite that Amazon is the most distinct tropical convection center over the western hemisphere and the fluxes from its surface of tropical rainforests are close to that from the warm tropical ocean. Liebmann et al. showed a distinct spectral peak of 40-50 day oscillation in outgoing longwave radiation (OLR) over tropical South America and considered that was manifested by the MJO propagation. Nogues-Paegle et al. (2000) focused on a dipole pattern of the OLR anomaly with centers of action over the South Atlantic Convergence Zone (SACZ) and the subtropical plain. They used the regional 10-90 day filtered data and demonstrated this pattern could be represented by the fifth mode of the rotated empirical orthogonal function. Its principal component was further analyzed using the singular spectrum analysis. Their result showed two oscillatory modes with periods of 36-40 days and 22-28 days, of which the former was related to the MJO influence and the latter linked to the remote forcing over southwest of Australia, which produced a wave train propagating southeastward, rounding the southern tip of South America and returning back toward the northeast. The 22-28 day mode has distinct impact on SACZ, responsible for the regional seesaw pattern of alternating dry and wet conditions. In this study we will focus on the 30-60-day spectral band and investigate whether the independent oscillation source over tropical South America is existed. First, we will show the seasonal dependence of the tropical South American ISV in Section 3. Then, the leading principal modes of 30-60 day bandpass filtered 850-hPa velocity potential (VP850) will be computed to distinguish the stationary ISV over tropical South America (SISA) from the propagating MJO in the austral summertime in Section 4. The importance of SISA in representing the regional ISV over South America will be discussed. In Section 5, we will demonstrate the mass oscillation regime of SISA, which is well separated from that of MJO by the Andes, and the convective coupling with rainfall. The dynamical response of SISA and the impact on the South American summer monsoon (SASM) will be presented. Finally, we will give the concluding remarks.

Zhou, Jiayu↗
DOE OSTI2016

PROPERTIES OF CARBON–OXYGEN WHITE DWARFS FROM MONTE CARLO STELLAR MODELS

We investigate properties of carbon–oxygen white dwarfs with respect to the composite uncertainties in the reaction rates using the stellar evolution toolkit, Modules for Experiments in Stellar Astrophysics (MESA) and the probability density functions in the reaction rate library STARLIB. These are the first Monte Carlo stellar evolution studies that use complete stellar models. Focusing on 3 M{sub ⊙} models evolved from the pre main-sequence to the first thermal pulse, we survey the remnant core mass, composition, and structure properties as a function of 26 STARLIB reaction rates covering hydrogen and helium burning using a Principal Component Analysis and Spearman Rank-Order Correlation. Relative to the arithmetic mean value, we find the width of the 95% confidence interval to be ΔM{sub 1TP} ≈ 0.019 M{sub ⊙} for the core mass at the first thermal pulse, Δt{sub 1TP} ≈ 12.50 Myr for the age, Δlog(T{sub c}/K) ≈ 0.013 for the central temperature, Δlog(ρ{sub c}/g cm{sup −3}) ≈ 0.060 for the central density, ΔY{sub e,c} ≈ 2.6 × 10{sup −5} for the central electron fraction, ΔX{sub c}({sup 22}Ne) ≈ 5.8 × 10{sup −4}, ΔX{sub c}({sup 12}C) ≈ 0.392, and ΔX{sub c}({sup 16}O) ≈ 0.392. Uncertainties in the experimental {sup 12}C(α,γ){sup 16}O, triple-α, and {sup 14}N(p,γ){sup 15}O reaction rates dominate these variations. We also consider a grid of 1–6 M{sub ⊙} models evolved from the pre main-sequence to the final white dwarf to probe the sensitivity of the initial–final mass relation to experimental uncertainties in the hydrogen and helium reaction rates.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Using the optimal combined index weight ratio to improve the probability of anomaly detection in big area additive manufacturing

Big Area Additive Manufacturing (BAAM) of composites requires significant time, energy, and material, so it is critical to reduce production inefficiencies to make functional parts without multiple iterations. Statistical process control coupled with Principal Component Analysis (PCA) is a powerful technique that provides a quick, computationally inexpensive, and intuitive way for operators to detect defects that form in a manufacturing process without massive datasets. Recently, a combined index that is a weighted sum of the Hotelling's T 2 and squared residual error statistics has been proposed that can be monitored in one chart, improving interpretation accuracy and simplicity. However, the literature does not offer a formal method to optimise the weights. Here, we introduce two new approaches to the traditional weight selection approach using simulated and BAAM image data. Approach 1 uses a theoretically motivated optimum inspired by probabilistic principal component analysis. Approach 2 systematically varies the ratio of the weights to find the optimum. We show that approach 1 delivers optimal anomaly detection performance in select cases while approach 2 fares better in practice. Surprisingly, we also show that choosing a more complex PCA model has a minimal negative impact on anomaly detection performance compared to a more simplistic model.

3-dimensional printing↗
DOE OSTI2024

Beyond PCA: Additional Dimension Reduction Techniques to Consider in the Development of Climate Fingerprints

Abstract Dimension reduction techniques are an essential part of the climate analyst’s toolkit. Due to the enormous scale of climate data, dimension reduction methods are used to identify major patterns of variability within climate dynamics, to create compelling and informative visualizations, and to quantify major named modes such as El Niño–Southern Oscillation. Principal components analysis (PCA), also known as the method of empirical orthogonal functions (EOFs), is the most commonly used form of dimension reduction, characterized by a remarkable confluence of attractive mathematical, statistical, and computational properties. Despite its ubiquity, PCA suffers from several difficulties relevant to climate science: high computational burden with large datasets, decreased statistical accuracy in high dimensions, and difficulties comparing across multiple datasets. In this paper, we introduce several variants of PCA that are likely to be of use in climate sciences and address these problems. Specifically, we introduce non-negative , sparse , and tensor PCA and demonstrate how each approach provides superior pattern recognition in climate data. We also discuss approaches to comparing PCA-family results within and across datasets in a domain-relevant manner. We demonstrate these approaches through an analysis of several runs of the E3SM climate model from 1991 to 1995, focusing on the simulated response to the Mt. Pinatubo eruption; our findings are consistent with a recently identified stratospheric warming fingerprint associated with this type of stratospheric aerosol injection.

Weylandt, Michael↗
NASA NTRS1990

Regional climate change predictions from the Goddard Institute for Space Studies high resolution GCM

Model simulations of global climate change are seen as an essential component of any program aimed at understanding human impact on the global environment. A major weakness of current general circulation models (GCMs), however, is their inability to predict reliably the regional consequences of a global scale change, and it is these regional scale predictions that are necessary for studies of human/environmental response. This research is directed toward the development of a methodology for the validation of the synoptic scale climatology of GCMs. This is developed with regard to the Goddard Institute for Space Studies (GISS) GCM Model 2, with the specific objective of using the synoptic circulation form a doubles CO2 simulation to estimate regional climate change over North America, south of Hudson Bay. This progress report is specifically concerned with validating the synoptic climatology of the GISS GCM, and developing the transfer function to derive grid-point temperatures from the synoptic circulation. Principal Components Analysis is used to characterize the primary modes of the spatial and temporal variability in the observed and simulated climate, and the model validation is based on correlations between component loadings, and power spectral analysis of the component scores. The results show that the high resolution GISS model does an excellent job of simulating the synoptic circulation over the U.S., and that grid-point temperatures can be predicted with reasonable accuracy from the circulation patterns.

Crane, Robert G.↗
NASA NTRS1991

Intraseasonal oscillations in the global atmosphere. II - Southern Hemisphere

A systematic examination of oscillatory modes in the global atmosphere is completed by studying 12 years of 500 mb geopotential heights in the Southern Hemisphere. The data were band-pass filtered to focus on intraseasonal (IS) phenomena, and spatial empirical orthogonal functions (EOFs) were obtained. The leading principal components were subjected to singular spectrum analysis in order to identify nonlinear IS oscillations with high statistical confidence. In the Southern Hemisphere, the dominant mode has a period of 23 days, with spatial patterns carried by the second and third winter EOF of the IS band. It has a zonal wavenumber-four structure. The 40-day mode is second, and is dominated by wavenumbers three and four, while a 16-day mode is too weak to separate its spatial behavior from the previous two. The IS dynamics in the Southern Hemisphere is more complex and dominated by shorter wavenumbers than the Northern Hemisphere. No statistically significant correlations between the Southern Hemisphere and the tropics or the Northern Hemisphere are apparent in the IS band.

Ghil, Michael↗
DOE OSTI2019

Variational quantum state diagonalization

Abstract Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost evaluation), and a classical computer uses this information to adjust the parameters of the gate sequence. Here we present such an algorithm for quantum state diagonalization. State diagonalization has applications in condensed matter physics (e.g., entanglement spectroscopy) as well as in machine learning (e.g., principal component analysis). For a quantum state ρ and gate sequence U , our cost function quantifies how far $$U\rho U^\dagger$$ U ρ U † is from being diagonal. We introduce short-depth quantum circuits to quantify our cost. Minimizing this cost returns a gate sequence that approximately diagonalizes ρ . One can then read out approximations of the largest eigenvalues, and the associated eigenvectors, of ρ . As a proof-of-principle, we implement our algorithm on Rigetti’s quantum computer to diagonalize one-qubit states and on a simulator to find the entanglement spectrum of the Heisenberg model ground state.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Non-Gaussianity in the weak lensing correlation function likelihood – implications for cosmological parameter biases

ABSTRACT We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in 1D marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ωm and σ8 due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data (100 deg2). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ∼5.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

MEAN SPECTRAL ENERGY DISTRIBUTIONS AND BOLOMETRIC CORRECTIONS FOR LUMINOUS QUASARS

We explore the mid-infrared (mid-IR) through ultraviolet (UV) spectral energy distributions (SEDs) of 119,652 luminous broad-lined quasars with 0.064 < z < 5.46 using mid-IR data from Spitzer and WISE, near-infrared data from the Two Micron All Sky Survey and UKIDSS, optical data from the Sloan Digital Sky Survey, and UV data from the Galaxy Evolution Explorer. The mean SED requires a bolometric correction (relative to 2500 A) of BC{sub 2500A} =2.75 {+-} 0.40 using the integrated light from 1 {mu}m-2 keV, and we further explore the range of bolometric corrections exhibited by individual objects. In addition, we investigate the dependence of the mean SED on various parameters, particularly the UV luminosity for quasars with 0.5 {approx}< z {approx}< 3 and the properties of the UV emission lines for quasars with z {approx}> 1.6; the latter is a possible indicator of the strength of the accretion disk wind, which is expected to be SED-dependent. Luminosity-dependent mean SEDs show that, relative to the high-luminosity SED, low-luminosity SEDs exhibit a harder (bluer) far-UV spectral slope ({alpha}{sub UV}), a redder optical continuum, and less hot dust. Mean SEDs constructed instead as a function of UV emission line properties reveal changes that are consistent with known Principal Component Analysis trends. A potentially important contribution to the bolometric correction is the unseen extreme UV (EUV) continuum. Our work suggests that lower-luminosity quasars and/or quasars with disk-dominated broad emission lines may require an extra continuum component in the EUV that is not present (or much weaker) in high-luminosity quasars with strong accretion disk winds. As such, we consider four possible models and explore the resulting bolometric corrections. Understanding these various SED-dependent effects will be important for accurate determination of quasar accretion rates.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Early-Universe constraints on dark matter-baryon scattering and their implications for a global 21 cm signal

Here we present and compare several cosmological constraints on the cross section for elastic scattering between dark matter (DM) and baryons, for cross sections with a range of power-law dependences on the DM-baryon relative velocity v , especially focusing on the case of σ ∝ v - 4 . We study constraints spanning a wide range of epochs in cosmological history, from prerecombination distortions to the blackbody spectrum and anisotropies of the cosmic microwave background (CMB), to modifications to the intergalactic medium temperature and the resulting 21 cm signal, and discuss the allowed signals in the latter channels given the constraints from the former. Furthermore, we improve previous constraints on DM-baryon scattering from the CMB anisotropies, demonstrate via principal component analysis that the effect on the CMB can be written as a simple function of DM mass for v - 4 scattering, and map out the redshifts dominating this signal. We show that given high-redshift constraints on DM-baryon scattering, a v - 4 scaling of the cross section for light DM would be sufficient to explain the deep 21 cm absorption trough recently claimed by the Experiment to Detect the Reionization Step, if 100% of the DM scatters with baryons; we estimate the minimal necessary velocity scaling and find that it is close to v - 4 . For millicharged DM models proposed to explain the observation, where only a small fraction of the DM interacts, we estimate that a PIXIE-like future experiment measuring CMB spectral distortion could test the relevant parameter space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Multispectral medical image fusion in Contourlet domain for computer based diagnosis of Alzheimer’s disease

Computer based diagnosis of Alzheimer’s disease can be performed by dint of the analysis of the functional and structural changes in the brain. Multispectral image fusion deliberates upon fusion of the complementary information while discarding the surplus information to achieve a solitary image which encloses both spatial and spectral details. This paper presents a Non-Sub-sampled Contourlet Transform (NSCT) based multispectral image fusion model for computer-aided diagnosis of Alzheimer’s disease. The proposed fusion methodology involves color transformation of the input multispectral image. The multispectral image in YIQ color space is decomposed using NSCT followed by dimensionality reduction using modified Principal Component Analysis algorithm on the low frequency coefficients. Further, the high frequency coefficients are enhanced using non-linear enhancement function. Two different fusion rules are then applied to the low-pass and high-pass sub-bands: Phase congruency is applied to low frequency coefficients and a combination of directive contrast and normalized Shannon entropy is applied to high frequency coefficients. The superiority of the fusion response is depicted by the comparisons made with the other state-of-the-art fusion approaches (in terms of various fusion metrics).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Assisted migration in a warmer and drier climate: less climate buffering capacity, less facilitation and more fires at temperate latitudes?

Assisted tree migration has been proposed as a conceptual solution to mitigate lags in biotic responses to anthropogenic climate change. The rationale behind this concept is that tree species currently growing under warmer and drier climates will be more resistant and resilient to the new climatic conditions than tree species naturally growing in currently wetter and colder climates. However, we hypothesize that, by being more stress‐tolerant to warmer and drier conditions, translocated species should exhibit different functional attributes, which could induce important ecological and societal costs and overcome the desired benefits of maintaining wood production and other ecosystem services. We used principal component analysis (PCA) to analyze variation in seven traits of 106 tree and tall shrub species from contrasting latitudinal distributions in western North America and Europe to predict the potential functional changes of forest ecosystems due to the translocation of tree species from low to high latitudes. We show that species from both continents differed primarily by their position on the leaf economy spectrum (LES) and their size traits. Even though, in Europe, differences in LES were significantly correlated to species southern latitudinal positions, in both continents differences in size traits were significantly correlated to latitude. These results suggest that assisted migration by translocating more conservative species of shorter stature in currently cooler climates should decrease the buffering capacity of forest canopies, decrease facilitation for understory species, and increase wildfire risks, whose effects have the potential to accelerate climate warming through negative atmospheric feedback processes. As an alternative solution to assisted migration that may accelerate rather than mitigate climate change, we recommend that foresters gradually diversify the vertical structure and layering of the existing forest canopy to maintain a sustainable water cycle and energy balance between the soil, the tree and the atmosphere without increasing the wildfire risk.

Environmental Sciences & Ecology↗
NASA NTRS2002

Multi-wavelength Luminosity Functions of Galaxies

Multivariate or multi-wavelength luminosity functions will reveal the interplay between star formation, chemical evolution, and absorption and re-emission of dust within evolving galaxy populations. By using principal component analysis to reduce the dimensionality of the problem, we optimally extract the relevant photometric information from large galaxy catalogs. As a demonstration of the technique, we derive the multi-wavelength luminosity function for the galaxies in the released SDSS catalog, and compare the results with those obtained by traditional methods. This technique will be applicable to catalogs of galaxies from datasets obtained by 2MASS, and the SIRTF and GALEX missions.

Gardner, J. P.↗
DOE OSTI2025

Global teleconnections influencing large-scale drought in the United States using SVDI

Understanding recent large-scale drought patterns and the mechanisms producing extreme drought events is vital for future drought forecasts and understanding future drought risks. Increasingly, vapor pressure deficit (VPD) has been used as an important measure of evaporative demand and proxy for drought detection. In this study, VPD is used to calculate the new Standardized VPD Drought Index (SVDI) with NASA North American Land Data Assimilation System (NLDAS) data. Previous studies have shown that SVDI accurately identifies the timing and magnitude short-term droughts in the United States (U.S). In the present study, SVDI is now used to identify large-scale drought patterns between 1980 and 2021 and drought variability driven by selected global teleconnections originating in the Pacific and Atlantic Oceans. Spatial drought characteristics were extracted from SVDI using empirical orthogonal function (EOF) analysis. Then a k-means clustering algorithm was applied to both EOF principal components and primary teleconnections, including the El Nino-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) to identify drought events driven by the Pacific Ocean. Results show that the SVDI is useful in evaluating large-scale drought variability in the U.S. related to global teleconnections, and that mechanisms influencing summer drought patterns in the Western and Southwestern U.S. are driven by a tropical-extratropical interactions originating in the equatorial Pacific Ocean related to ENSO dynamics with interdecadal variability modulated by PDO. The large-scale droughts in the Central and Southern U.S., like those in 2011 and 2012, on the other hand, are driven by the North Pacific Ocean warm pool during a strong negative PDO, which subsequently influenced variability in the Bermuda-Azores High in the Atlantic Ocean. In summer 2011, the Bermuda-Azores High weakened, reducing the onshore winds and moisture transport along the eastern Gulf of Mexico and contributing to ongoing drought in the region. The Northern Pacific and Atlantic Ocean sea surface temperatures (SSTs) have increased between 1980 and 2021. In conclusion, as SSTs continue to rise in the Northern Pacific Ocean, one consequence of the coupled North Pacific warm pool and atmospheric dynamics, is to increase summer drought variability over a large region in the southern and midwestern U.S. under global warming.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2002

Multi-Wavelength Luminosity Functions of Galaxies

Multivariate or multi-wavelength luminosity functions will reveal the interplay between star formation, chemical evolution, and ab- sorption and re-emission of dust within evolving galaxy populations. By using principal component analysis to reduce the dimensionality of the problem, I optimally extract the relevant photometric information from large galaxy catalogs. As a demonstration of the technique, I derive the multi-wavelength luminosity function for the galaxies in the released SDSS catalog, and compare the results with those obtained by traditional methods. This technique will be applicable to catalogs of galaxies from datasets obtained by 2MASS, and the SIRTF and GALEX missions.

Gardner, Jonathan P.↗
DOE OSTI2019

Early Cardiac Mitochondrial Molecular and Functional Responses to Acute Anthracycline Treatment in Wistar Rats

Abstract Doxorubicin (DOX) is an anticancer drug widely used to treat human and nonhuman tumors but the late and persistent cardio-toxicity reduces the therapeutic utility of the drug. The full mechanism(s) of DOX-induced acute, subchronic and delayed toxicity, which has a preponderant mitochondrial component, remains unclear; therefore, it is clinically relevant to identify early markers to identify patients who are predisposed to DOX-related cardiovascular toxicity. To address this, Wistar rats (16 weeks old) were treated with a single DOX dose (20 mg/kg, i.p.); then, mRNA, protein levels and functional analysis of mitochondrial endpoints were assessed 24 h later in the heart, liver, and kidney. Using an exploratory data analysis, we observed cardiac-specific alterations after DOX treatment for mitochondrial complexes III, IV, and preferentially for complex I. Conversely, the same analysis revealed complex II alterations are associated with DOX response in the liver and kidney. Interestingly, H2O2 production by the mitochondrial respiratory chain as well as loss of calcium-loading capacity, markers of subchronic toxicity, were not reliable indicators of acute DOX cardiotoxicity in this animal model. By using sequential principal component analysis and feature correlation analysis, we demonstrated for the first time alterations in sets of transcripts and proteins, but not functional measurements, that might serve as potential early acute markers of cardiac-specific mitochondrial toxicity, contributing to explain the trajectory of DOX cardiac toxicity and to develop novel interventions to minimize DOX cardiac liabilities.

Pereira, Gonçalo C.↗
DOE OSTI2019

Applications of principal component analysis for energy reconstruction in position-sensitive semiconductor detectors

We report semiconductor detectors with pixelated anodes offer a desirable combination of position sensitivity and energy resolution that are suitable for numerous applications in gamma-ray detection and imaging. Pixelization of electrodes also entails a non-uniform amplitude response as a function of gamma-ray interaction position. Energy calibrations as a function of interaction position improve energy resolution, but systematic errors in the energy reconstruction process persist and limit energy resolution at fixed electronic noise. Digitization of signals induced on collecting and adjacent electrodes offers rich information about gamma-ray interactions and their charge drift and collection as a function of time. Despite the abundance of signals for each interaction, human intuition and rule-based approaches fail to utilize the entire set of observed signals to mitigate the sources of systematic error. In order to maximize the utility of digitized signals and improve energy resolution, principal component analysis is applied towards digitized signals observed in semiconductor detectors with pixelated anodes. Principal components identified in the process form the basis for position-specific energy corrections. By leveraging this additional information encoded within digitized signals, energy resolution improves by factors between 10 and 15% with respect to full-width at half and tenth maximum values. The feature that accounts for the maximum amount of explained variance between interactions in any given pixel correlates strongly with the depth of interaction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗