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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. Here, we present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discrete variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis—that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. Finally, we illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Data Mining of Polymer Phase Transitions upon Temperature Changes by Small and Wide-Angle X-ray Scattering Combined with Raman Spectroscopy

The complex physical transformations of polymers upon external thermodynamic changes are related to the molecular length of the polymer and its associated multifaceted energetic balance. The understanding of subtle transitions or multistep phase transformation requires real-time phenomenological studies using a multi-technique approach that covers several length-scales and chemical states. A combination of X-ray scattering techniques with Raman spectroscopy and Differential Scanning Calorimetry was conducted to correlate the structural changes from the conformational chain to the polymer crystal and mesoscale organization. Current research applications and the experimental combination of Raman spectroscopy with simultaneous SAXS/WAXS measurements coupled to a DSC is discussed. In particular, we show that in order to obtain the maximum benefit from simultaneously obtained high-quality data sets from different techniques, one should look beyond traditional analysis techniques and instead apply multivariate analysis. Data mining strategies can be applied to develop methods to control polymer processing in an industrial context. Crystallization studies of a PVDF blend with a fluoroelastomer, known to feature complex phase transitions, were used to validate the combined approach and further analyzed by MVA.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Proton Beam Reirradiation for Recurrent Head and Neck Cancer: Multi-institutional Report on Feasibility and Early Outcomes

Purpose: Reirradiation therapy (re-RT) is the only potentially curative treatment option for patients with locally recurrent head and neck cancer (HNC). Given the significant morbidity with head and neck re-RT, interest in proton beam radiation therapy (PBRT) has increased. We report the first multi-institutional clinical experience using curative-intent PBRT for re-RT in recurrent HNC. Methods and Materials: A retrospective analysis of ongoing prospective data registries from 2 hybrid community practice and academic proton centers was conducted. Patients with recurrent HNC who underwent at least 1 prior course of definitive-intent external beam radiation therapy (RT) were included. Acute and late toxicities were assessed with the National Cancer Institute Common Terminology Criteria for Adverse Events version 4.0 and the Radiation Therapy Oncology Group late radiation morbidity scoring system, respectively. The cumulative incidence of locoregional failure was calculated with death as a competing risk. The actuarial 12-month freedom–from–distant metastasis and overall survival rates were calculated with the Kaplan-Meier method. Results: Ninety-two consecutive patients were treated with curative-intent re-RT with PBRT between 2011 and 2014. Median follow-up among surviving patients was 13.3 months and among all patients was 10.4 months. The median time between last RT and PBRT was 34.4 months. There were 76 patients with 1 prior RT course and 16 with 2 or more courses. The median PBRT dose was 60.6 Gy (relative biological effectiveness, [RBE]). Eighty-five percent of patients underwent prior HNC RT for an oropharynx primary, and 39% underwent salvage surgery before re-RT. The cumulative incidence of locoregional failure at 12 months, with death as a competing risk, was 25.1%. The actuarial 12-month freedom–from–distant metastasis and overall survival rates were 84.0% and 65.2%, respectively. Acute toxicities of grade 3 or greater included mucositis (9.9%), dysphagia (9.1%), esophagitis (9.1%), and dermatitis (3.3%). There was 1 death during PBRT due to disease progression. Grade 3 or greater late skin and dysphagia toxicities were noted in 6 patients (8.7%) and 4 patients (7.1%), respectively. Two patients had grade 5 toxicity due to treatment-related bleeding. Conclusions: Proton beam re-RT of the head and neck can provide effective tumor control with acceptable acute and late toxicity profiles likely because of the decreased dose to the surrounding normal, albeit previously irradiated, tissue, although longer follow-up is needed to confirm these findings.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2022

Image feature extraction and galaxy classification: a novel and efficient approach with automated machine learning

ABSTRACT In this work, we explore the possibility of applying machine learning methods designed for 1D problems to the task of galaxy image classification. The algorithms used for image classification typically rely on multiple costly steps, such as the point spread function deconvolution and the training and application of complex Convolutional Neural Networks of thousands or even millions of parameters. In our approach, we extract features from the galaxy images by analysing the elliptical isophotes in their light distribution and collect the information in a sequence. The sequences obtained with this method present definite features allowing a direct distinction between galaxy types. Then, we train and classify the sequences with machine learning algorithms, designed through the platform Modulos AutoML. As a demonstration of this method, we use the second public release of the Dark Energy Survey (DES DR2). We show that we are able to successfully distinguish between early-type and late-type galaxies, for images with signal-to-noise ratio greater than 300. This yields an accuracy of $86{{\ \rm per\ cent}}$ for the early-type galaxies and $93{{\ \rm per\ cent}}$ for the late-type galaxies, which is on par with most contemporary automated image classification approaches. The data dimensionality reduction of our novel method implies a significant lowering in computational cost of classification. In the perspective of future data sets obtained with e.g. Euclid and the Vera Rubin Observatory, this work represents a path towards using a well-tested and widely used platform from industry in efficiently tackling galaxy classification problems at the peta-byte scale.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

High-performance End-to-End Integrity Verification on Big Data Transfer

The scale of scientific data generated by experimental facilities and simulations in high-performance computing facilities has been proliferating with the emergence of IoT-based big data. In many cases, this data must be transmitted rapidly and reliably to remote facilities for storage, analysis, or sharing, for the Internet of Things (IoT) applications. Simultaneously, IoT data can be verified using a checksum after the data has been written to the disk at the destination to ensure its integrity. However, this end-to-end integrity verification inevitably creates overheads (extra disk I/O and more computation). Thus, the overall data transfer time increases. In this article, we evaluate strategies to maximize the overlap between data transfer and checksum computation for astronomical observation data. Specifically, we examine file-level and block-level (with various block sizes) pipelining to overlap data transfer and checksum computation. We analyze these pipelining approaches in the context of GridFTP, a widely used protocol for scientific data transfers. Theoretical analysis and experiments are conducted to evaluate our methods. The results show that block-level pipelining is effective in maximizing the overlap mentioned above, and can improve the overall data transfer time with end-to-end integrity verification by up to 70% compared to the sequential execution of transfer and checksum, and by up to 60% compared to file-level pipelining.

data integrity↗
DOE OSTI2025

Long‐Term Large‐Scale Atmospheric Forcing Data From Three‐Dimensional Constrained Variational Analysis for the ARM SGP Site

Here, this study presents a long‐term three‐dimensional large‐scale forcing data set (VARANAL3D) derived from the three‐dimensional constrained variational analysis (3DCVA) method at the Atmospheric Radiation Measurement (ARM) program Southern Great Plains (SGP) site from 2004 to 2018. Building on the same input data sets as the conventional continuous forcing data set (VARANAL), VARANAL3D maintains overall consistency in domain‐averaged fields while introducing spatial variability, offering critical insights into the influence of mesoscale synoptic systems on cloud‐related processes. Evaluations are conducted across four cloud and precipitation regimes: Clear‐sky, Shallow‐clouds, Afternoon‐precipitation, and Nocturnal‐precipitation, presenting high consistency of the domain‐mean forcing data sets while emphasizing the role of subdomain forcing variability particularly in precipitating regimes. Single column model (SCM) simulations demonstrate that subdomain VARANAL3D forcing improves cloud and precipitation representation, with the ensemble outperforming domain‐mean forcing in three cloudy and precipitating regimes. Overall, these results highlight VARANAL3D's value for investigating the impacts of spatial variability of large‐scale forcing on atmospheric processes. The VARANAL3D data set provides new opportunities for evaluating model physics, advancing the development of scale‐aware parameterizations and deepening our understanding of cloud and precipitation dynamics.

Environmental sciences↗
DOE OSTI2021

Searching for axionlike particles from core-collapse supernovae with Fermi LAT’s low-energy technique

Light axionlike particles (ALPs) are expected to be abundantly produced in core-collapse supernovae (CCSNe), resulting in a ~ 10 -second long burst of ALPs. These particles subsequently undergo conversion into gamma rays in external magnetic fields to produce a long gamma-ray burst (GRB) with a characteristic spectrum peaking in the 30–100-MeV energy range. At the same time, CCSNe are invoked as progenitors of ordinary long GRBs, rendering it relevant to conduct a comprehensive search for ALP spectral signatures using the observations of long GRBs with the Fermi Large Area Telescope (LAT). We perform a data-driven sensitivity analysis to determine CCSN distances for which a detection of an ALP signal is possible with the LAT’s low-energy technique which, in contrast to the standard LAT analysis, allows for a a larger effective area for energies down to 30 MeV. Assuming an ALP mass m a ≲ 10 - 10 eV and ALP-photon coupling g a γ = 5.3 × 10 - 12 GeV - 1 , values considered and deduced in ALP searches from SN1987A, we find that the distance limit ranges from ~ 0.5 to ~ 10 Mpc , depending on the sky location and the CCSN progenitor mass. Furthermore, we select a candidate sample of 24 GRBs and carry out a model comparison analysis in which we consider different GRB spectral models with and without an ALP signal component. We find that the inclusion of an ALP contribution does not result in any statistically significant improvement of the fits to the data. Finally, we discuss the statistical method used in our analysis and the underlying physical assumptions, the feasibility of setting upper limits on the ALP-photon coupling, and give an outlook on future telescopes in the context of ALP searches.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Practical galaxy morphology tools from deep supervised representation learning

Astronomers have typically set out to solve supervised machine learning problems by creating their own representations from scratch. We show that deep learning models trained to answer every Galaxy Zoo DECaLS question learn meaningful semantic representations of galaxies that are useful for new tasks on which the models were never trained. We exploit these representations to outperform several recent approaches at practical tasks crucial for investigating large galaxy samples. The first task is identifying galaxies of similar morphology to a query galaxy. Given a single galaxy assigned a free text tag by humans (e.g. ‘#diffuse’), we can find galaxies matching that tag for most tags. The second task is identifying the most interesting anomalies to a particular researcher. Our approach is 100 per cent accurate at identifying the most interesting 100 anomalies (as judged by Galaxy Zoo 2 volunteers). The third task is adapting a model to solve a new task using only a small number of newly labelled galaxies. Models fine-tuned from our representation are better able to identify ring galaxies than models fine-tuned from terrestrial images (ImageNet) or trained from scratch. We solve each task with very few new labels; either one (for the similarity search) or several hundred (for anomaly detection or fine-tuning). This challenges the longstanding view that deep supervised methods require new large labelled data sets for practical use in astronomy. To help the community benefit from our pretrained models, we release our fine-tuning code zoobot. Zoobot is accessible to researchers with no prior experience in deep learning.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Efficient method for estimating the time evolution of the proto-neutron star mass and radius from a supernova neutrino signal

In this paper, we present a novel method to estimate the time evolution of the proto-neutron star (PNS) structure from the neutrino signal in a core-collapse supernova (CCSN). Employing recent results from multidimensional CCSN simulations, we delve into a relation between the total emitted neutrino energy (TONE) and PNS mass/radius, and we find that they are strongly correlated with each other. We fit the relation by simple polynomial functions connecting the TONE to the mass and radius of the PNS as a function of time. By combining another fitting function representing the correlation between the TONE and the cumulative number of events at each neutrino observatory, the PNS mass and radius can be retrieved from purely observed neutrino data. We demonstrate retrievals of PNS mass and radius from mock data of the neutrino signal, and we assess the capability of our proposed method. While underlining the limitations of the method, we also discuss the importance of the joint analysis with the gravitational wave signal. This would reduce uncertainties of parameter estimations in our method, and may narrow down the possible neutrino oscillation model. The proposed method is a very easy and inexpensive computation, which will be useful in real data analysis of the CCSN neutrino signal.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2018

A kernel machine method for detecting higher order interactions in multimodal datasets: Application to schizophrenia

Technological advances are enabling us to collect multimodal datasets at an increasing depth and resolution while with decreasing labors. Understanding complex interactions among multimodal datasets, however, is challenging. Here in this study, we tested the interaction effect of multimodal datasets using a novel method called the kernel machine for detecting higher order interactions among biologically relevant multimodal data. Using a semiparametric method on a reproducing kernel Hilbert space, we formulated the proposed method as a standard mixed-effects linear model and derived a score-based variance component statistic to test higher order interactions between multimodal datasets. The method was evaluated using extensive numerical simulation and real data from the Mind Clinical Imaging Consortium with both schizophrenia patients and healthy controls. Our method identified 13-triplets that included 6 gene-derived SNPs, 10 ROIs, and 6 gene-specific DNA methylations that are correlated with the changes in hippocampal volume, suggesting that these triplets may be important for explaining schizophrenia-related neurodegeneration. The performance of the proposed method is compared with the following methods: test based on only first and first few principal components followed by multiple regression, and full principal component analysis regression, and the sequence kernel association test. With strong evidence (p-value ≤0.000001), the triplet (MAGI2, CRBLCrus1.L, FBXO28) is a significant biomarker for schizophrenia patients. This novel method can be applicable to the study of other disease processes, where multimodal data analysis is a common task.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Acceptable Knowledge Technologist Procedure

Process acceptable knowledge (AK) is a waste stream characterization method that can be used to meet all or part of the waste analysis requirements appropriate for the waste. The method may include documented knowledge of process (KOP), additional characterization data, and/or facility records of analysis. LANL will use process AK to ensure chemical compatibility; assign matrix parameter categories and Environmental Protection Agency (EPA) hazardous waste numbers (HWNs) commonly referred to as EPA codes to waste streams; and determine the waste material parameters and radionuclides present in waste streams.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

A FREQUENCY RESPONSE APPROACH TO MODEL VALIDATION FOR THE COMPACT INTEGRAL EFFECTS TEST FACILITY IN TRANSFORM

One of the key challenges to licensing new reactor designs is validating the integral transient response models of a novel system. This work used a frequency response approach for model validation of the Compact Integral Effects Test (CIET) facility at the University of California, Berkeley. This facility was built as a scaled integral effects test for verifying transient modeling tools for fluoride-salt-cooled hightemperature reactors using Dowtherm A as a simulant fluid for molten salt. The dynamic system model of CIET was created using the Modelica-based TRANSFORM tool developed by Oak Ridge National Laboratory (ORNL). Analysis of the model’s performance as compared with experimental results indicates good agreement under both steady-state and transient conditions. This paper describes the Modelica model creation process using TRANSFORM and the modeling assumptions and methods for matching dynamic behavior with frequency response data. Results, analysis, and a discussion of future work are also presented.

De wet, Dane↗
DOE OSTI2016

Particle-image Velocimetry Sensitivity through Automatic Differentiation

A commonly encountered difficulty in modern experimental fluid dynamics experiments is the need for full-flow visualization and measurement; traditional techniques such as hot-wire probes and laser Doppler velocimetry cannot provide such information without difficult scanning procedures. Particle-image velocimetry (PIV) is a measurement technique which can overcome this spatial limitation to provide real-time three-dimensional fluid velocity vectors for an entire plane within the flow, as opposed to a single point that is provided by other measurement techniques. To accomplish this, a PIV system seeds the fluid flow with tracer particles; these must have nearly the same density as that of the fluid and a high drag coefficient to ensure that they follow the fluid flow without deviation. A laser is sent through optics to expand its beam into a sheet which illuminates the plane of interest in the fluid. The particles reflect more light than the fluid, and their image is recorded using a high speed camera. Due to limitations in bandwidth, video cannot be taken fast enough to be useful, and instead pairs of images are captured with a known separation in time. The illuminated particles will move between the two images taken by the camera, and their relative motion can be used to compute the fluid velocity at that point. When a single camera is used, only two-dimensional velocity vectors can be computed, but with the addition of another camera this can be improved to full three-dimensional vectors. The flow's time evolution can be measured by taking series of image pairs and processing each pair to get the velocity field at the time between each image pair. Only the two-dimensional version will be considered in this work. To compute the velocity vectors of the flow, the images are broken up into interrogation regions, usually in a uniform grid. In the most basic PIV algorithm, corresponding regions in the image pairs are cross-correlated to compute the most likely displacement from one image to the next. This is used since the cross correlation will achieve a maximum value when the two interrogation regions line up the best. The location of the peak in the correlation map and scaling information for the optical setup is used to compute the particle displacement from one image to the next. This process is similar to holding two semi-transparent images and moving one until they match as well as possible. Sub-pixel displacements between images can be obtained by fitting a Gaussian function to the correlation peak. Knowing the displacement vector for each set of interrogation regions in the image pair, it is a simple matter to divide by the time gap between the two images to compute the fluid velocity at the point in time and space. Since there are many interrogation regions in each image pair, the velocity field for a sheet is sampled according to the arrangement of the interrogation regions. The sensitivity of the final computed vector to the input images is difficult to compute, and has led most considerations of uncertainty in the PIV field to apply Monte Carlo methods and correlations to quantify the systematic and random errors which result from application of various PIV algorithms. In this work, automatic differentiation (AD) has been used to trace the dependence of velocity vectors computed using the correlation-peak PIV algorithm back to the input values given to an artificial image generator. These initial results form the foundation for continued work in the application of AD to algorithms in PIV. They demonstrate that AD methods can be successfully applied to PIV algorithms without undue complexity. The derivatives of each individual vector with regard to the coefficients of the velocity field used to create the artificial images can be computed and the statistics of them considered collectively, or correlated between each other to quantify the effectiveness of a PIV algorithm. With the initial implementation complete, adding extra algorithms is relatively simple and considerable data can be generated for analysis. It is hoped that application of these methods can lead to improved PIV algorithms which demonstrate better sensitivity to small variations in particle displacement. While these methods can be used as an analysis tool for refinement of new algorithms, computation of actual resultant vector sensitivities to input images' individual pixels is the next logical step of this work. Such information will be analyzed with experimental data to produce a better understanding of how output vectors' uncertainty relates to the actual image pairs, and lead to automatic bad vector removal. (authors)

42 ENGINEERING↗
DOE OSTI2017

Weak-lensing magnification as a probe for the dark Universe

This Thesis is devoted to the analysis of weak-lensing magnification on the Dark Energy Survey. Two analysis with different goals each are made on different data-sets: the Science Verification (DES-SV) and the Year 1 (DES-Y1). The DES-SV analysis aims the development of techniques to detect the weak-lensing number count magnification signal and the mitigation of systematic errors. The DES-Y1 analysis employs the methods used with the DES-SV data to measure the convergence profile of the emptiest regions of the Universe –voids and troughs–to use them as a new cosmological probe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Low Activity Tritium Detection in CCDs Using Deep Learning Techniques

Here, this study explores the use of charge-coupled devices (CCDs) for detecting low-energy beta particles from tritium decay - a critical signal for nuclear safety, nuclear nonproliferation, and environmental monitoring. We employ a dual approach utilizing both measured CCD data and detailed Geant4 simulations. Our analysis compares classical techniques with advanced deep learning methods, including convolutional neural networks (CNNs), autoencoders trained exclusively on tritium data, and preliminary studies on boosted decision trees (BDTs). The CNN, trained on mixed signal/background datasets, demonstrates superior classification performance, while the autoencoder shows the potential of unsupervised, background-agnostic strategies when background characteristics are poorly defined. These results highlight the excellent sensitivity achievable thanks to the background rejection made possible by information-rich CCD data, paving the way for improved portable tritium monitoring.

Autoencoder↗
DOE OSTI2019

X-ray analysis methods for sources from self-modulated laser wakefield acceleration driven by picosecond lasers

A versatile set of methods for analyzing x-ray energy spectra and photon flux has been developed for laser plasma accelerator experiments driven by picosecond lasers. Forward fit provides extrapolated broad energy spectrum measurements, while Ross pair and differential average transmission analysis provide directly measured data points using a particular diagnostic. Combining these methods allows the measurement of x-ray energy spectra with improved confidence. We apply here the methods to three diagnostics (filter wheel, stacked image plate spectrometer, and step wedge), each sensitive to a different region of x-ray energies (<40 keV, 35–100 keV, and 60–1000 keV, respectively), to characterize the analysis methods using laser-driven bremsstrahlung x-rays. We then apply the methods to measure three x-ray mechanisms, betatron, inverse Compton scattering, and bremsstrahlung, driven by a laser plasma accelerator. The analysis results in the measurement of x-ray energy spectra ranging from 10 keV to 1 MeV with peak flux greater than 10 10 photons/keV/Sr. The combined analysis methods provide a robust tool to accurately measure broadband x-ray sources (keV to MeV) driven by laser plasma acceleration with picosecond, kilojoule-class lasers.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Analyzing Wildland Fire Smoke Emissions Data Using Compositional Data Techniques

By conservation of mass, the mass of wildland fuel that is pyrolyzed and combusted must equal the mass of smoke emissions, residual char and ash. For a given set of conditions, these amounts are fixed. This places a constraint on smoke emissions data which violates statistical assumptions for many of the methods currently used to analyze these data such as linear regression, analysis of variance, and t-tests. These data are inherently multivariate and non-negative parts of a whole. This paper introduces the field of compositional data analysis to the emissions community and provides examples of appropriate statistical treatment of emissions data. It is shown that modified combustion efficiency should not be used as a predictor variable for other smoke emissions because it is not an independent variable. An alternative method based on compositional linear trends to estimate trace gas composition using CO and CO2 is presented. The data used in this paper resulted from projects the DOD/DOE/EPA Strategic 586 Environmental Research and Development Program projects RC-1648 and 1649. The senior 587 author appreciates the guidance and R scripts provided by Prof. Girty at San Diego State 588 University to estimate linear trends by perturbation. J. P.-A. was supported by the Spanish 589 Ministry of Science, Innovation and Universities under the project CODAMET (RTI2018-590 095518-B-C21, 2019-2021). The data used in this study have been previously published and are 591 available in the original publications. DRW conceived the initial manuscript (70 percent) and 592 performed the bulk of the data analysis. JPA provided statistical guidance and compositional data 593 expertise and contributed 20 percent of the manuscript. TJJ and HJ were extensively involved in 594 the study that provided the data. TJJ provide smoke emissions expertise and HJ provided 595 combustion expertise. The authors declare that they have no conflict of interest. The use of trade 596 or firm names in this publication is for reader information and does not imply endorsement by 597 the U.S. Department of Agriculture of any product or service.

simplex, compositional data analysis, balance, log↗