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At least 91 records · Page 5

rmap: An R package to plot and compare tabular data on customizable maps across scenarios and time

`rmap` is an R package that allows users to easily plot tabular data (CSV or R data frames) on maps without any Geographic Information Systems (GIS) knowledge. Maps produced by `rmap` are `ggplot` objects and thus capitalize on the flexibility and advancements of the `ggplot2` package and all elements of each map are thus fully customizable. Additionally `rmap` automatically detects and produces comparison maps if the data has multiple scenarios or time periods as well as animations for time series data. Advanced users can load their own shapefiles if desired. `rmap` comes with a range of pre-built color palettes but users can also provide any `R` color palette or create their own as needed. Four different legend types are available to highlight different kinds of data distributions. The input spatial data can be both gridded or polygon data. `rmap` is desgined in particular for comparing spatial data across scenarios and time periods and comes preloaded with standard country, state, and basin maps as well as custom maps compatible with the Global Change Analysis Model (GCAM) spatial boundaries. `rmap` has a growing number of users and its products have been used in multiple multisector dynamics publications as well as a required dependency in other R packages such as `rfasst` and `metis`. `rmap's` automatic processing of tabular data using pre-built map selection, difference map calculations, faceting, and animations offers unique functionality which makes it a powerful and yet simple tool for users looking to explore multi-sector, multi-scenario data across space and time.

58 GEOSCIENCES↗

A Flexible Field Mapping System for Accelerator Magnets

Magnetic field mapping is a fundamental magnetic measurement method that typically uses Hall and NMR sensors. In magnet measurement facilities, such systems are likely used in various configurations suitable for a specific task at hand. To address this diversity, the authors developed a flexible field mapping system capable of being configured and tailored to each particular measurement case. The system needs to address the variability introduced by differences in sensors and their readout systems, probe positioning systems, power supply systems and in required mapping geometry (mapping space and grid, measurement steps and sequences). Although the discussed field mapping systems range from a self-propelled, multi-sensor mapper of a large detector magnet to a single 3D Hall sensor system to scan a small permanent magnet, they were all built with the same core mapping system. The variability present in field mapping systems and the measurement system architecture addressing this variability, as well as examples of several field mapping systems built in this architecture are presented.

43 PARTICLE ACCELERATORS↗

Stellar reddening map from DESI imaging and spectroscopy

We present new Galactic reddening maps of the high Galactic latitude sky using DESI imaging and spectroscopy. We directly measure the reddening of 2.6 million stars by comparing the observed stellar colors in $g-r$ and $r-z$ from DESI imaging with the synthetic colors derived from DESI spectra from the first two years of the survey. The reddening in the two colors is on average consistent with the Fitzpatrick (1999) extinction curve with $R_\mathrm{V}=3.1$ . We find that our reddening maps differ significantly from the commonly used Schlegel et al. (1998) (SFD) reddening map (by up to 80 mmag in $E(B-V)$ ), and we attribute most of this difference to systematic errors in the SFD map. To validate the reddening map, we select a galaxy sample with extinction correction based on our reddening map, and this yields significantly better uniformity than the SFD extinction correction. Finally, we discuss the potential systematic errors in the DESI reddening measurements, including the photometric calibration errors that are the limiting factor on our accuracy. The $E(g-r)$ and $E(r-z)$ maps presented in this work, and for convenience their corresponding $E(B-V)$ maps with SFD calibration, are publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗

Datasets and U-Net Model for "A Deep Learning Based Framework to Identify Undocumented Orphaned Oil and Gas Wells from Historical Maps: a Case Study for California and Oklahoma"

This dataset has results and the model associated with the publication Ciulla et al., (2024). It contains a U-Net semantic segmentation model (unet_model.h5) and associated code implemented in tensorflow 2.0 for the model training and identification of oil and gas well symbols in USGS historical topographic maps (HTMC). Given a quadrangle map (7.5 minutes), downloadable at this url: https://ngmdb.usgs.gov/topoview/, and a list of coordinates of the documented wells present in the area, the model returns the coordinates of oil and gas symbols in the HTMC maps. For reproducibility of our workflow, we provide a sample map in California and the documented well locations for the entire State of California (CalGEM_AllWells_20231128.csv) downloaded from https://www.conservation.ca.gov/calgem/maps/Pages/GISMapping2.aspx. Additionally, the locations of 1,301 potential undocumented orphaned wells identified using our deep learning framework or the counties of Los Angeles and Kern in California, and Osage and Oklahoma in Oklahoma are provided in the file found_potential_UOWs.zip. The results of the visual inspection of satellite imagery in Osage County is in the file visible_potential_UOWs.zip. The dataset also includes a custom tool to validate the detected symbols in the HTMC maps (vetting_tool.py). More details about the methodology can be found in the associated paper: Ciulla, F., Santos, A., Jordan, P., Kneafsey, T., Biraud, S.C., and Varadharajan, C. (2024) A Deep Learning Based Framework to Identify Undocumented Orphaned Oil and Gas Wells from Historical Maps: a Case Study for California and Oklahoma. Accepted for publication in Environmental Science and Technology. The geographical coordinates provided correspond to the locations of potential undocumented orphaned oil and gas wells (UOWs) extracted from historical maps. The actual presence of wells need to be confirmed with on-the-ground investigations. For your safety, do not attempt to visit or investigate these sites without appropriate safety training, proper equipment, and authorization from local authorities. Approaching these well sites without proper personal protective equipment (PPE) may pose significant health and safety risks. Oil and gas wells can emit hazardous gasses including methane, which is flammable, odorless and colorless, as well as hydrogen sulfide, which can be fatal even at low concentrations. Additionally, there may be unstable ground near the wellhead that may collapse around the wellbore. This dataset was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California.

Artificial Intelligence↗

Multi-Sensor Optimal Motion Planning for Radiological Contamination Surveys by Using Prediction-Difference Maps

Distributed and networked mobile sensor platforms using unmanned aerial and/or ground vehicles to survey areas of interest offer a safer and more efficient method for radiological contamination mapping; however, most applications rely on uniformly sweeping of the area in a raster-type motion without utilizing the information available in a dynamic sense. We have developed a fully autonomous optimal motion planning procedure for networks with two or more mobile sensors. The procedure utilizes well-established concepts of Gaussian processes in combination with control laws based on centroidal Voronoi tessellations to achieve optimal next-iteration sensor movements. A new method of informing optimal motion planning is proposed, whereby the absolute difference between the prior and current full-map prediction, referred to as the prediction-difference map, is used as the spatial density function within each Voronoi cell, providing immediate and iterative feedback for dynamic use of available information. The Gaussian process regression model used to estimate the contamination in unvisited locations also provides prediction uncertainties, and can be used as a quantitative metric to assess the confidence in the calculated contamination map; these estimates and prediction uncertainties are unavailable for standard uniform survey routines as they can only produce maps in the vicinity of observed locations. We present through simulation the achievable performance gains from using this new method by directly comparing to a uniform survey method. Results show that using the prediction-difference maps to inform motion planning procedures offers a faster rate of producing an accurate and convergent map relative to a uniform survey route.

47 OTHER INSTRUMENTATION↗

How to correct relative voxel scale factors for calculations of vector-difference Fourier maps in cryo-EM

The atomic coordinates derived from cryo-electron microscopy (cryo-EM) maps can be inaccurate when the voxel scaling factors are not properly calibrated. Here, we describe a method for correcting relative voxel scaling factors between pairs of cryo-EM maps for the same or similar structures that are expanded or contracted relative to each other. We find that the correction of scaling factors reduces the amplitude differences of Fourier-inverted structure factors from voxel-rescaled maps by up to 20–30%, as shown by two cryo-EM maps of the SARS-CoV-2 spike protein measured at pH 4.0 and pH 8.0. This allows for the calculation of the difference map after properly scaling, revealing differences between the two structures for individual amino acid residues. Unexpectedly, the analysis uncovers two previously overlooked differences of amino acid residues in structures and their local structural changes. Furthermore, we demonstrate the method as applied to two cryo-EM maps of monomeric apo-photosystem II from the cyanobacteria Synechocystis sp. PCC 6803 and Thermosynechococcus elongatus. The resulting difference maps reveal many changes in the peripheral transmembrane PsbX subunit between the two species.

59 BASIC BIOLOGICAL SCIENCES↗

Integrating very-high-resolution UAS data and airborne imaging spectroscopy to map the fractional composition of Arctic plant functional types in Western Alaska

Widespread changes in vegetation cover and composition are driving strong impacts on Arctic ecosystem functioning and global climate feedbacks. An accurate characterization of tundra vegetation composition is required to understand how the Arctic will respond to future climate change. However, quantifying tundra vegetation composition over large areas is challenging as commonly-used satellite observations are too coarse, spatially and spectrally, to differentiate low-lying tundra vegetation types. Recent airborne and spaceborne imaging spectroscopy platforms provide better data to characterize vegetation composition. Yet, our ability to characterize vegetation composition with imaging spectroscopy remains largely unexplored in the Arctic, particularly due to a lack of ground observations needed to train and test classification models. To address this problem, we collected very-high-resolution (VHR, ~5 cm) unoccupied aerial system (UAS) imagery at three low-Arctic tundra sites located on the Seward Peninsula, western Alaska. In this paper, we examine the feasibility of integrating imagery from the UAS and the hyperspectral Airborne Visible/Infrared Imaging Spectrometer, Next Generation (AVIRIS-NG) airborne instrument to map the fractional composition of 12 key Arctic plant functional types (PFTs). To this end, we first mapped the 12 PFTs from our VHR UAS imagery using random forest classification. We then used these UAS-derived PFT maps as ground truth to develop partial least squares regression (PLSR) models to predict the fractional cover (FCover) of each PFT from AVIRIS-NG imagery. Further, we evaluated the performance of our PLSR models using reserved UAS samples, as well as by mapping PFT FCover and dominant PFT for large tundra landscapes. Our results show that 1) Arctic PFTs can be effectively mapped using VHR UAS imagery, with overall accuracy between 86% and 92%, 2) when the UAS mapped PFTs were used to inform PLSR scaling models, the FCover of the 12 PFTs could be effectively estimated from AVIRIS-NG imagery with a mean absolute error (MAE) <0.13, and 3) our PLSR models outperformed traditional, fully constrained least-squares (FCLS) linear mixture analysis and produced high-quality, spatially contiguous PFT FCover and PFT maps that captured vegetation spatial patterns with similar accuracy to those developed from UAS imagery. The developed PLSR models have the potential to be broadly applied for quantifying vegetation composition with AVIRIS-NG images to help monitor tundra vegetation dynamics and improve process-based modeling of tundra ecosystems.

54 ENVIRONMENTAL SCIENCES↗

Integrating very-high-resolution imagery, Sentinel-2 time-series data, and machine learning to map shrub fractional abundance across arid and semi-arid ecosystems in China

Shrub fractional abundance (SFA), the proportion of shrub cover per unit area, serves as a critical indicator of environmental aridity and ecosystem health in arid and semi-arid regions, particularly across the Mongolian steppe. However, large-scale SFA mapping in Mongolian steppe ecosystems remains challenging due to the small crown size of shrubs, their sparse distribution, and spectral overlap with coexisting low vegetation (e.g., grasses and herbs), which hinders accurate detection using coarser-resolution satellite data or traditional field surveys. To address these challenges, we developed a two-step approach that integrates very-high-resolution (VHR) imagery, time-series Sentinel-2 data, and deep learning techniques. First, we generated high-accuracy benchmark maps of individual shrub crowns from 0.5 m VHR imagery by combining manual segmentation with a hybrid deep learning framework (Dino V2 and convolutional neural networks). Second, we used these shrub crown maps as training data to build an XGBoost model for predicting SFA from 20 m Sentinel-2 time-series data, leveraging phenological information to improve estimation. We validated our approach across 70 sites (1km 2 each) in the Inner Mongolia Autonomous Region, which is representative of Mongolian steppe ecosystems. From VHR imagery, we mapped 1.31 million shrub crowns with an accuracy of R 2 = 0.92. Scaling up with Sentinel-2 data yielded regional SFA maps with an R 2 = 0.60. Further SHAP (SHapley Additive exPlanations) analysis on the developed XGBoost model revealed that phenological metrics (particularly observations in early-May, mid-July, and late-September), which distinguish shrub phenology from that of other land cover types (e.g., grasses and bare soil), were the most influential predictors of SFA. Finally, our regional SFA maps uncovered unimodal relationships between shrub distribution and climate variables, peaking at mean annual minimum temperatures near 0 °C and annual precipitation around 200 mm. Collectively, these findings demonstrate how the integration of multi-source remote sensing and machine learning can overcome historical limitations in SFA mapping, enabling accurate, spatially continuous assessments across vast Inner-Mongolian steppe ecosystems. Our framework has the potential to be applied to other steppe ecosystems and dryland ecosystems across the Mongolian steppe and beyond, offering a foundation for improved monitoring and ecological impact assessments in the face of global climate changes.

Arid and semi-arid landscapes↗

Improvement of cryo-EM maps by density modification

A density-modification procedure for improving maps from single-particle electron cryogenic microscopy (cryo-EM) is presented here. The theoretical basis of the method is identical to that of maximum-likelihood density modification, previously used to improve maps from macromolecular X-ray crystallography. Key differences from applications in crystallography are that the errors in Fourier coefficients are largely in the phases in crystallography but in both phases and amplitudes in cryo-EM, and that half-maps with independent errors are available in cryo-EM. These differences lead to a distinct approach for combination of information from starting maps with information obtained in the density-modification process. The density-modification procedure was applied to a set of 104 datasets and improved map-model correlation and increased the visibility of details in many of the maps. The procedure requires two unmasked half-maps and a sequence file or other source of information on the volume of the macromolecule that has been imaged.

47 OTHER INSTRUMENTATION↗

Impact Mapping for Geospatial Reasoning and Decision Making

Objective The reported study evaluated a novel approach to aiding geospatial reasoning and decision making. Background Impact mapping aims to alleviate the cognitive demands of geospatial tasks in part by externalizing data in the form of an integrated decision surface. This is achieved by aggregating data across multiple sources of information and visualizing their combined utility rather than objective measurements or individual utility. Previous research has shown that geospatial decisions improve when aided in this manner, but it remains unknown if dynamic decision making, often plagued by fatigue and anchoring bias, would benefit similarly. Method The experiment implemented a systematic manipulation of the presence of a composite impact map and the number of attributes present in a two-stage disaster relief, resource allocation task to investigate when and how impact mapping is beneficial or deleterious to decision makers. Results The presence of the composite impact map increased the utility of selected sites, increased re-planning decisions, reduced information display views, and reduced workload. Generally, the effect of the composite impact map was greater when participants were asked to evaluate more attributes. Conclusion Composite impact maps appear to improve repeated geospatial reasoning and minimize anchoring bias because they alleviate the cognitive demands otherwise necessary to interpret and maintain information from multiple attributes. Application Data visualization techniques, such as impact mapping, can improve repeated geospatial decision making in environments that include high cognitive demand.

Illingworth, David A.↗

McMillan map and nonlinear Twiss parameters

In this article we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings originally introduced by Edwin McMillan; the second one is also known as canonical McMillan map. Both of them are simplest symmetric McMillan maps with only one intrinsic parameter, the trace of the Jacobian at the fixed point. While these dynamical systems have numerous of applications and are used in many areas of math and physics, some of their dynamical properties have not been described yet. We fulfill the gap and provide complete description of all stable trajectories including parametrization of invariant curves, Pioncaré rotation numbers and canonical action-angle variables. In the second part we relate these maps with general chaotic map in McMillan-Turaev form. We show that McMillan sextupole and octupole mappings are first order approximations of dynamics around the fixed point, in a similar way as linear map and quadratic invariant (Courant-Snyder invariant in accelerator physics) is the zeroth order approximation (known as linearization). Finally we suggest the new formalism of nonlinear Twiss parameters which incorporate dependence of rotation number as a function of amplitude, in contrast to e.g. betatron phase advance used in accelerator physics which is independent of amplitude. Specifically in application to accelerator physics this new formalism is capable of predicting dynamical aperture around 1-st, 2-nd, 3-rd and 4-th order resonances for flat beams, which is critical for beam injection/extraction.

43 PARTICLE ACCELERATORS↗

Mapping entry invalidation

A memory access system may include a first memory address translator, a second memory address translator and a mapping entry invalidator. The first memory address translator translates a first virtual address in a first protocol of a memory access request to a second virtual address in a second protocol and tracks memory access request completions. The second memory address translator is to translate the second virtual address to a physical address of a memory. The mapping entry invalidator requests invalidation of a first mapping entry of the first mapping address translator requests invalidation of a second mapping entry of the second memory address translator corresponding to the first mapping entry following invalidation of the first mapping entry and based upon the tracked memory access request completions.

Walker, Shawn K.↗

A new flow pattern map for flow boiling of R410A in horizontal micro-fin tubes considering the effect of the helix angle

This paper presents an improved flow pattern map for flow boiling in horizontal micro-fin tubes considering the effect of helix angle. The proposed map is modified from the one developed for horizontal smooth tubes by Wojtan et al. (2005) and takes the early transition to annular flow due to micro-fin geometry into account. Visualization of R410A flow boiling is carried out through the transparent smooth and micro-fin tubes with 0°, 10° and 18° helix angle and plotted on the proposed map for comparison. The result shows that the flow pattern map for micro-fin tube with 0° helix angle is generally similar to that for the smooth tube. For the tube with 10° and 18° helix angle, the annular flow occurs at lower vapor quality and lower mass flux. The proposed map shows good agreements when compared with the visualization and reflects the downward shift (to lower mass flux and vapor quality conditions) of the SW-WA transition with the increase of the helix angle. In order to further validate the proposed model, the flow pattern transitions calculated from the equations are also compared with the experimental data of the micro-fin tube in literature. The results show that the modified map increase the prediction accuracy of the flow patterns in the micro-fin tube.

42 ENGINEERING↗

Adaptive sampling for accelerating neutron diffraction-based strain mapping *

Abstract Neutron diffraction is a useful technique for mapping residual strains in dense metal objects. The technique works by placing an object in the path of a neutron beam, measuring the diffracted signals and inferring the local lattice strain values from the measurement. In order to map the strains across the entire object, the object is stepped one position at a time in the path of the neutron beam, typically in raster order, and at each position a strain value is estimated. Typical dwell times at neutron diffraction instruments result in an overall measurement that can take several hours to map an object that is several tens of centimeters in each dimension at a resolution of a few millimeters, during which the end users do not have an estimate of the global strain features and are at risk of incomplete information in case of instruments outages. In this paper, we propose an object adaptive sampling strategy to measure the significant points first. We start with a small initial uniform set of measurement points across the object to be mapped, compute the strain in those positions and use a machine learning technique to predict the next position to measure in the object. Specifically, we use a Bayesian optimization based on a Gaussian process regression method to infer the underlying strain field from a sparse set of measurements and predict the next most informative positions to measure based on estimates of the mean and variance in the strain fields estimated from the previously measured points. We demonstrate our real-time measure-infer-predict workflow on additively manufactured steel parts—demonstrating that we can get an accurate strain estimate even with 30%–40% of the typical number of measurements—leading the path to faster strain mapping with useful real-time feedback. We emphasize that the proposed method is general and can be used for fast mapping of other material properties such as phase fractions from time-consuming point-wise neutron measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Genome_shuffling_enables_quantitative_trait_locus_mapping_in_Bacillus_subtilis

Genetic mapping is a powerful tool for eukaryotic genetics that has only been applied to bacteria in limited circumstances. Quantitative trait locus (QTL) mapping generally relies on sexual recombination to break linkages between genes, yet bacteria rarely undergo sufficient homologous recombination to generate suitable mapping populations. In this work, we used iterative biparental genome shuffling by protoplast fusion inBacillus subtilisto generate a population of bacteria with substantial random recombination throughout their genomes. Individual shuffled progeny were arrayed in well plates, resequenced, and characterized for a range of complex phenotypes including spore germination and swarming motility. Genetic mapping of the resulting phenotypes identified high-confidence QTLs of moderate size (∼10 kb), and these associations were validated through targeted genetic swaps. ThisB. subtilisQTL population can easily be used to map additional phenotypes, and the general approach for QTL mapping is applicable in a wide range of bacteria.

Bacillus subtilis↗

Introducing a New Spitzer Master BLISS Map to Remove the Instrument Systematic Phase-curve-parameter Degeneracy, as Demonstrated by a Reanalysis of the 4.5 μm WASP-43b Phase Curve

While Spitzer Infrared Array Camera (IRAC) systematics are generally well understood, each data set can provide its own challenges that continue to teach us about the underlying functional form of these systematics. Multiple groups have analyzed the phase curves of WASP-43b with varying detrending techniques, each obtaining different results. In this work, we take another look at WASP-43b while exploring the degenerate relation between Bilinearly Interpolated Subpixel Sensitivity (BLISS) mapping, point response function (PRF)–FWHM detrending, and phase curve parameters. We find that there is a strong correlation between the detrending parameters in the two models, and best-fit phase curve amplitudes vary strongly when the data are temporally binned. To remove this degeneracy, we present a new Gaussian centroided intrapixel sensitivity map (hereafter fixed sensitivity map), generated using 3,712,830 exposures spanning 5 yr, for a variety of aperture sizes at 4.5 μm. We find evidence for time variability in the sensitivity at 3.6 μm and do not generate a visit-independent map for this channel. With the fixed 4.5 μm intrapixel sensitivity map, the best fits for WASP-43b no longer vary strongly with bin size and PRF–FWHM detrending is no longer required to remove correlated noise. For data sets that do not fall completely within the sweet spot, temporal binning should not be used in the analysis of Spitzer phase curves. We confirm nightside emission for WASP-43b with a disk-integrated nightside temperature of 806 ± 48 K at 4.5 μm. The 4.5 μm maps are available at github.com/kevin218/POET.

79 ASTRONOMY AND ASTROPHYSICS↗

A New Residual Strain Mapping Program Using Energy Dispersive X-Ray Diffraction at the Advanced Photon Source

Here, the ability to non-destructively map the residual strain field inside an engineering component is important for predicting its fatigue life or developing processing methods to prevent failure or enhance performance. In this paper, we describe a new residual strain mapping program at the Advanced Photon Source, Argonne National Laboratory. The new program is based on energy dispersive x-ray diffraction (EDXRD). It is capable of non-destructively penetrating a several- cm thick polycrystalline sample fabricated from engineering alloys using high-energy x-rays and measuring the residual strain field with mm or better spatial resolution and approximately ±1 x 10 -4 strain resolution. A multi-element detector array is employed to measure multiple strain components simultaneously. The residual strain mapping setup is augmented with a high-energy tomography capability, allowing precise alignment of the material volume of interest for residual strain mapping and providing a complementary view of the structure to understand the measured strain field. These measurement capabilities are demonstrated using several strain mapping examples ranging from polycrystalline structural alloys to biological materials. We also provide some guidance for the future users of the program for a successful residual strain mapping experiment. We are expanding the capabilities of the new setup with various in situ capabilities including thermo-mechanical loading.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Mapping use cases and dataset needs for benchmarking buildings data

A perennial challenge in buildings research is the lack of high-quality datasets that can be relied upon for a wide array of tasks, including model calibration and improving energy efficiency and load flexibility. Instrumenting a building for data collection is resource intensive, so it is important to be methodical in the approach and ensure that resulting data are flexible and useful for a broad range of analyses. This study aims to fill the gaps in characterizing potential use cases for buildings datasets and mapping them to dataset needs using a well-defined data infrastructure. Here, we have developed a systematic mapping strategy between buildings dataset needs and use cases to help streamline the processes of efficiently targeting datasets, designing building sensing systems, and determining buildings research use cases. We selected 14 prospective use cases and 11 refined buildings data categories for developing the preliminary dataset-needs-to-use-cases mapping matrix (‘DN-UC mapping matrix’) with generic ‘Tags’—a detailed sub-level of data categories extracted by justifying the needs of an aspect of the datasets to use cases. We present two example applications of the developed mapping matrix to demonstrate use of the mapping matrix and its effectiveness.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗