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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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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Whisper Use of Nuclear Data Covariances [Slides]

Whisper is statistical analysis code using sensitivity/uncertainty-based methods to determine baseline upper subcritical limit (USL) for nuclear criticality safety. Features of Whisper 1.1 include: GLLS method implemented to compute adjusted covariance based on current benchmark suite (1,100+ ICSBEP models), BLO “low-fidelity” covariance data used (44 energy groups), adjusted covariance is pre-computed and saved, and adjusted cross sections are NOT computed. Potential future efforts include: an extension to include angular distributions in benchmark selection and in GLLS adjustment, a move toward more modern covariance data (ENDF/B-VIII.0) and different group structure, and compute and store adjusted cross sections (trivial).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Towards Lightweight Data Integration Using Multi-Workflow Provenance and Data Observability

Modern large-scale scientific discovery requires multidisciplinary collaboration across diverse computing facilities, including High Performance Computing (HPC) machines and the Edge-to-Cloud continuum. Integrated data analysis plays a crucial role in scientific discovery, especially in the current AI era, by enabling Responsible AI development, FAIR, Reproducibility, and User Steering. However, the heterogeneous nature of science poses challenges such as dealing with multiple supporting tools, cross-facility environments, and efficient HPC execution. Building on data observability, adapter system design, and provenance, we propose MIDA: an approach for lightweight runtime Multi-workflow Integrated Data Analysis. MIDA defines data observability strategies and adaptability methods for various parallel systems and machine learning tools. With observability, it intercepts the dataflows in the background without requiring instrumentation while integrating domain, provenance, and telemetry data at runtime into a unified database ready for user steering queries. We conduct experiments showing end-to-end multi-workflow analysis integrating data from Dask and MLFlow in a real distributed deep learning use case for materials science that runs on multiple environments with up to 276 GPUs in parallel. We show near-zero overhead running up to 100,000 tasks on 1,680 CPU cores on the Summit supercomputer.

Santos Souza, Renan↗
DOE OSTI2021

A Targeted Sequencing Assay for Serotyping Escherichia coli Using AgriSeq Technology

The gold standard method for serotyping Escherichia coli has relied on antisera-based typing of the O- and H-antigens, which is labor intensive and often unreliable. In the post-genomic era, sequence-based assays are potentially faster to provide results, could combine O-serogrouping and H-typing in a single test, and could simultaneously screen for the presence of other genetic markers of interest such as virulence factors. Whole genome sequencing is one approach; however, this method has limited multiplexing capabilities, and only a small fraction of the sequence is informative for subtyping or identifying virulence potential. A targeted, sequence-based assay and accompanying software for data analysis would be a great improvement over the currently available methods for serotyping. The purpose of this study was to develop a high-throughput, molecular method for serotyping E. coli by sequencing the genes that are required for production of O- and H-antigens, as well as to develop software for data analysis and serotype identification. To expand the utility of the assay, targets for the virulence factors, Shiga toxins ( stx 1 , and stx 2 ) and intimin ( eae ) were included. To validate the assay, genomic DNA was extracted from O-serogroup and H-type standard strains and from Shiga toxin-producing E. coli , the targeted regions were amplified, and then sequencing libraries were prepared from the amplified products followed by sequencing of the libraries on the Ion S5™ sequencer. The resulting sequence files were analyzed via the SeroType Caller™ software for identification of O-serogroup, H-type, and presence of stx 1 , stx 2 , and eae . We successfully identified 169 O-serogroups and 41 H-types. The assay also routinely detected the presence of stx 1a,c,d (3 of 3 strains), stx 2c−e,g (8 of 8 strains), stx 2f (1 strain), and eae (6 of 6 strains). Taken together, the high-throughput, sequence-based method presented here is a reliable alternative to antisera-based serotyping methods for E. coli .

Elder, Jacob R.↗
DOE OSTI2021

radkit v1.2

The radkit software suite (python) consists of three primary libraries: stark, trajan, and curie. The trajan library provides the tools to analyze and manipulate data from lidar and inertial measurement unit (IMU) devices as well as trajectories from algorithms such as simultaneous localization and mapping (SLAM). These components allow reading and writing standard data formats, performing rigid affine transformations, discretizing three-dimensional space, and visualizing data products. The curie library comprises a standard set of object-oriented tools for radiation data and analysis in the following modules: (1) listmode and binmode data classes with methods for manipulation, plotting, slicing and file IO; (2) radiological/nuclear source detection/identification analysis results; (3) source encounters of correlated analyses and (4) energy-dependent angular detector response functions. The stark package provides low-level tools that are leveraged by both curie and trajan. The tools are flexible for offline analysis as well as performant for real-time integrations. The radkit libraries have associated Robot Operating System packages for use in real-time and robotic systems.

Joshi, Tenzing↗
DOE OSTI2026

radkit base v1.6

The radkit (base) software suite (python) consists of three primary libraries: stark, trajan, and curie. The trajan library provides the tools to analyze and manipulate data from lidar and inertial measurement unit (IMU) devices, cameras, as well as trajectories from algorithms such as simultaneous localization and mapping (SLAM). These components allow reading and writing standard data formats, performing rigid affine transformations, discretizing three-dimensional space, and visualizing data products. The curie library comprises a standard set of object-oriented tools for radiation data and analysis in the following modules: (1) listmode and binmode data classes with methods for manipulation, plotting, slicing and file IO; (2) radiological/nuclear source detection/identification analysis results; (3) source encounters of correlated analyses and (4) energy-dependent angular detector response functions. The stark package provides low-level tools that are leveraged by both curie and trajan. The tools are flexible for offline analysis as well as performant for real-time integrations.

Salathe, Marco [Lawrence Berkeley National Laborat↗
DOE OSTI2023

Small Angle X-Ray Scattering and Polymers

Polymers are some of the most versatile and useful materials on this planet. Properties of polymers are a result of their processing history, chemical makeup, and physical structure. Therefore, characterization is necessary to develop new polymer formulations and processes. Many established techniques for polymer characterization are destructive, and alternative methods that don’t destroy samples are in high demand. Thermal analysis techniques such as differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) yield important characteristic information for polymer samples while destroying the sample. Non-destructive strategies such as X ray diffraction (XRD) or small angle X-ray scattering (SAXS) can also find polymer characteristics while preserving a sample’s attributes. Sample preservation is desirable when investigating novel formulation and processing methods. SAXS analysis will be done on two different polymers: polyethylene, and a triblock copolymer. Using these two polymers allows for confidence between tests as polyethylene is very common, and well understood. Polyethylene analysis will be done first, and when methods have been refined so that the SAXS data matches accepted thermal analysis values for HDPE, there will be confidence to use the same analysis on block copolymers. Block copolymers remain relatively unexplored, so SAXS data will yield valuable information on their characteristics. Understanding the mechanical properties of these polymers is paramount to their application in upcycling, a process by which waste plastic can be converted into a higher value commodity. For this project, the upcycling process will be done via 3-dimensional (3d) printing.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Understanding Biases in Sample Preparation Techniques for Coupled Scanning Electron Microscopy and MAMA PuO 2 Morphological Analysis

In this project, the scanning electron microscopy (SEM) sampling method used during the statistical design study (SDS) was investigated to determine if any sampling biases were present in the analyzed data. Using standard particle size distribution powders from the National Institute of Standards and Technology (NIST 1984 standard reference material) with the origin wet dispersion method, it was determined that a bias to smaller particles was present. This was supported by theoretical calculations using Stokes’ law to determine the settling rate of spherical particles of roughly the same size and mass as those found in the SDS. Based on the theoretical calculations, it was determined that the settling rate for each of the 76 powder sets in the SDS could be unique based on specific particle shape and mass distributions, making a universal correction factor/formula not applicable. Therefore, priority shifted to developing an improved wet dispersion method that significantly reduced the particle settling rate for all particle size and shapes. This was achieved by replacing the original solvent (isopropyl alcohol) with a heavy liquid (lithium heteropolytungstates), which dramatically slowed the settling rate and allowed for the capture of a suitable homogeneous aliquot. SEM imaging and Morphological Analysis for Material Attribution (MAMA) software analysis were conducted on the NIST standard, and the SEM/MAMA data were compared to data captured by a dynamic image analysis particle size analyzer. The resulting data confirmed that the new wet dispersion method does indeed deliver an improved representative aliquot to the SEM stub. For instance, in the NIST certificate, the average particle size is ~17.1 µm ± 2.2 µm with a normal distribution. The initial wet dispersion method resulted in a drastically reduced average particle size of 6.1 µm in addition to a non-representative heavy bi-modal distribution whereas the improved LST wet dispersion method resulting in an average particle size that was much closer to the NIST certificate (12.7 µm) with a similar normal distribution. Although the improved method was still short of the NIST certificate average, atomic force microscopy analysis determined that the resulting ~20-25% reduction in size was due to particles sinking into the carbon sticky tape used for SEM imaging. It is believed that that this bias can be calibrated in a much more predicable manner than the original settling rate bias. In addition, the matching normal distribution curves between the NIST certificate and the heavy liquid method indicate a much-improved representative aliquot has been sampled and imaged. A surrogate CeO 2 powder was used to reflect PuO 2 more accurately and to aid in implementing radiological controls and shielding. The resulting data sets from the SEM/MAMA method and the particle size analyzer give almost identical average particle sizes and particle distribution statistics. Future work will re-analyze several select runs from the SDS to determine if morphological signatures can be found with the improved sampling method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Multi-Gas Sensors for Enhanced Reliability of SOFC Operation

GE Research, in partnership with SUNY Polytechnic Institute (SUNY Poly), designed, built, and tested gas sensors for in situ monitoring of H 2 and CO anode tail gases produced with on-site steam reforming in solid oxide fuel cell (SOFC) systems. The knowledge of the H 2 /CO ratio of these anode tail gases should allow accurate determination and control of the efficiency of the reforming process in the SOFC system and should deliver a lower operating cost for SOFC customers. The project objectives were to achieve multi-gas monitoring capability with a single multivariable sensor, and to sustain this performance in the presence of gaseous interferences and a potential poison for the sensor. The duration of the project was 24 months with the project structure that included three technical tasks such as (1) development of design rules of photonic nanostructures for H 2 and CO gas detection, (2) laboratory validation of photonic nanostructures for selective H 2 and CO gas detection, and (3) validation of photonic nanostructures for initial stability and poison-resistance against H 2 S. To build multivariable sensors for selective H 2 and CO gas detection in the presence of interferences, we expanded our earlier knowledge of multi-gas sensors into new fabrication and functionalization methodologies as well as into new methodologies for the spectral data analysis of multi-gas responses. We have advanced our design rules of the three-dimensional (3D) photonic nanostructures that allowed detection of H 2 and CO at high temperatures as individual gases and as their mixtures and rejection of interferences such as CO 2 , H 2 O, CH 4 , and other hydrocarbons for SOFC applications. Our advanced design rules should be attractive for building the new generation of cost-effective industrial sensors. Stability and poison resistance of our 3D photonic nanostructures was tested in the laboratory conditions. While initially we utilized conventional machine learning data analysis tools, we have found that they were unable to correct for the sensor drift. Thus, we have implemented new methods of machine learning for the analysis of our spectral data. These learnings pave the way to move the future studies into advanced testing of effects of interferences, aging and field tests. In future, our work will continue to advance our sensing designs to operate in conditions with known and unknown interferences by implementing nanostructures with enhanced spectral diversity of responses to gaseous species of interest and interferences. Our systematic reduction of technical risks in this completed project and in future studies will ensure transition of this sensing technology to commercialization.

03 NATURAL GAS↗
DOE OSTI2024

Commercial, industrial, and institutional discount rate estimation for efficiency standards analysis: Sector-level data 1998–2023

Underlying each of the U.S. Department of Energy’s (DOE’s) federal appliance and equipment energy conservation standards are a set of complex analyses of the projected costs and benefits of regulation. Any new or amended standard must be designed to achieve significant additional energy conservation, provided that it is technologically feasible and economically justified (42 U.S.C. 6295(o)(2)(A)). DOE determines economic justification based on whether the benefits exceed the burdens, considering a variety of factors, including the economic impact of the standard on consumers of the product and the savings in lifetime operating cost compared to any increase in price or maintenance expenses (42 U.S.C. 6295(o)(2)(B)). As part of this determination, DOE conducts a life-cycle cost (LCC) analysis, which models the combined impact of appliance first cost and operating cost changes on a representative commercial building sample to identify the fraction of customers achieving LCC savings or incurring net cost at the considered efficiency levels. Thus, the commercial discount rate value(s) used to calculate the present value of energy cost savings within the LCC model implicitly plays a role in estimating the economic impact of potential standard levels. This report provides an in-depth discussion of the commercial discount rate estimation process relying on the Capital Asset Pricing Model (CAPM) to estimate a business’ cost of equity, and by adding a risk adjustment factor to the risk-free rate associated with long-term U.S. Treasury bonds to estimate their cost of debt. It is an update to previous reports on estimating commercial discount rates from firm-level and sector-level financial data (e.g., Fujita, 2021, 2016). Major topics covered in this report include the following: • Discount rate estimation methods and rationale • Data sources used and data limitations • Discount rate distributions for use in standards analysis • Discount rate estimation methods and distributions specific to the small business subgroup analysis.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Extending quantum-mechanical benchmark accuracy to biological ligand-pocket interactions

Predicting the binding affinity of ligands to protein pockets is key in the drug design pipeline. The flexibility of ligand-pocket motifs arises from a range of attractive and repulsive electronic interactions during binding. Accurately accounting for all interactions requires robust quantum-mechanical (QM) benchmarks, which are scarce for ligand-pocket systems. Additionally, disagreement between “gold standard” Coupled Cluster (CC) and Quantum Monte Carlo (QMC) methods casts doubt on many benchmarks for larger non-covalent systems. We introduce the “QUantum Interacting Dimer” (QUID) benchmark framework containing 170 non-covalent (non-)equilibrium systems modeling chemically and structurally diverse ligand-pocket motifs. Symmetry-adapted perturbation theory shows that QUID broadly covers non-covalent binding motifs and energetic contributions. Robust binding energies are obtained using complementary CC and QMC methods, achieving agreement of 0.5 kcal/mol. The benchmark data analysis reveals that several dispersion-inclusive density functional approximations provide accurate energy predictions, though their atomic van der Waals forces differ in magnitude and orientation. Contrarily, semiempirical methods and empirical force fields require improvements in capturing non-covalent interactions (NCIs) for out-of-equilibrium geometries. The wide span of NCIs, highly accurate interaction energies, and analysis of molecular properties take QUID beyond the “gold standard” for QM benchmarks of ligand-protein systems.

Puleva, Mirela [University of Luxembourg, Luxembou↗
DOE OSTI2023

Combining cosmic shear data with correlated photo-z uncertainties: constraints from DESY1 and HSC-DR1

An accurate calibration of the source redshift distribution p(z) is a key aspect in the analysis of cosmic shear data. This, one way or another, requires the use of spectroscopic or high-quality photometric samples. However, the difficulty to obtain colour-complete spectroscopic samples matching the depth of weak lensing catalogs means that the analyses of different cosmic shear datasets often use the same samples for redshift calibration. This introduces a source of statistical and systematic uncertainty that is highly correlated across different weak lensing datasets, and which must be accurately characterised and propagated in order to obtain robust cosmological constraints from their combination. In this paper we introduce a method to quantify and propagate the uncertainties on the source redshift distribution in two different surveys sharing the same calibrating sample. The method is based on an approximate analytical marginalisation of the p(z) statistical uncertainties and the correlated marginalisation of residual systematics. We apply this method to the combined analysis of cosmic shear data from the DESY1 data release and the HSC-DR1 data, using the COSMOS 30-band catalog as a common redshift calibration sample. We find that, although there is significant correlation in the uncertainties on the redshift distributions of both samples, this does not change the final constraints on cosmological parameters significantly. The same is true also for the impact of residual systematic uncertainties from the errors in the COSMOS 30-band photometric redshifts. Additionally, we show that these effects will still be negligible in Stage-IV datasets. Finally, the combination of DESY1 and HSC-DR1 allows us to constrain the "clumpiness" parameter to S 8 = ${0.768}_{-0.017}^{+0.021}$. This corresponds to a ~√(2) improvement in uncertainties with respect to either DES or HSC alone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Tracking the topology of neural manifolds across populations

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Monte Carlo toolkit for designing and validating step-range-filter spectrometer designs

Here, we present a Monte Carlo toolkit for validating step range filter (SRF) spectrometer designs. Geant4 is used to transport charged particles through the SRF filters to generate synthetic SRF data that include realistic CR-39 effects. Synthetic SRF spectra generated by this method inherently account for instrument response and allow for the quantification of SRF performance before shots. The usefulness of this toolkit is demonstrated through its application to a number of problems. A new broadband SRF for the ∼10 MeV wide 3He3He proton spectrum is validated, and an analysis method for analyzing 3He3He-p SRF data that accounts for instrument response is put forth. In addition, an SRF design for the compact recoil-proton spectrometer (CRS) on the Z-machine is validated. Finally, a new calibration technique for the DD-p SRF is proposed and validated.

Johnson, T. M. (ORCID:0000000193032949)↗
DOE OSTI2024

Leveraging graph clustering techniques for cyber‐physical system analysis to enhance disturbance characterisation

Abstract Cyber‐physical systems have behaviour that crosses domain boundaries during events such as planned operational changes and malicious disturbances. Traditionally, the cyber and physical systems are monitored separately and use very different toolsets and analysis paradigms. The security and privacy of these cyber‐physical systems requires improved understanding of the combined cyber‐physical system behaviour and methods for holistic analysis. Therefore, the authors propose leveraging clustering techniques on cyber‐physical data from smart grid systems to analyse differences and similarities in behaviour during cyber‐, physical‐, and cyber‐physical disturbances. Since clustering methods are commonly used in data science to examine statistical similarities in order to sort large datasets, these algorithms can assist in identifying useful relationships in cyber‐physical systems. Through this analysis, deeper insights can be shared with decision‐makers on what cyber and physical components are strongly or weakly linked, what cyber‐physical pathways are most traversed, and the criticality of certain cyber‐physical nodes or edges. This paper presents several types of clustering methods for cyber‐physical graphs of smart grid systems and their application in assessing different types of disturbances for informing cyber‐physical situational awareness. The collection of these clustering techniques provide a foundational basis for cyber‐physical graph interdependency analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Physics-informed graph neural networks for predicting cetane number with systematic data quality analysis

Designing alternative fuels for advanced compression ignition engines necessitates a predictive model for cetane number (CN). In this study, the physics-informed graph neural networks are introduced for a reliable CN prediction by considering molecular features pertinent to the physical properties of molecules that affect CN. The reliability of measured data is another key factor to consider for improving the predictive model. Various experimental instruments for measuring CN exist, including standard and non-standard methods. In this regard, a systematic data quality analysis was carried out for the total 630 CNs collected from literature and new measurements in this study using Advanced Fuel Ignition Delay Analyzer (AFIDA). The results from this data curation process were reflected in the model by imposing lower sample weights on the data coming from less reliable measurement techniques. This approach effectively maximized the prediction accuracy while incorporating data from all available sources. Using the sample weights decreased the mean absolute error (MAE) up to 0.8 CN units. The accuracy was also improved by introducing the CN-related physical properties (the number of hydrogen bond donors and acceptors); the test set MAE is 5.74 and 7.01 for the model with and without such properties, respectively. Investigating molecular structural effects on CN was also carried out to gain chemical insights into factors used to design new fuel candidates. The dimensionality reduction analysis of feature vectors showed a clear clustering in terms of functional groups and CN and the structural effect derived from the model was consistent with the physicochemical insights. Finally, this physics-informed model and data curation would be helpful for accurate CN prediction and inform rational fuel design.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Data Mining and Machine Learning for Power System Monitoring, Understanding, and Impact Evaluation

This chapter presents results from the Big Data analysis framework to improve power system situational awareness and system reliability. For this purpose, a dataset with real-world phasor measurement unit data and historical transmission system outage data has been created and used to carry out the analysis. Several statistical analysis and machine learning methods have been developed and implemented for event and anomaly detection and modeling. Detection and analysis results for actual examples of power system events are presented. Finally, data-driven characterization and risk assessment methods for weather-related extremes in power systems are developed and demonstrated on the Bonneville Power Administration system. These applications demonstrate the capability of Machine Learning (ML) methods to monitor system abnormalities, to predict system events, and to characterize the impact of extreme events on power grid

data mining, power grid, machine learning, anomaly↗
DOE OSTI2020

A novel CMB component separation method: hierarchical generalized morphological component analysis

ABSTRACT We present a novel technique for cosmic microwave background (CMB) foreground subtraction based on the framework of blind source separation. Inspired by previous work incorporating local variation to generalized morphological component analysis (GMCA), we introduce hierarchical GMCA (HGMCA), a Bayesian hierarchical graphical model for source separation. We test our method on Nside = 256 simulated sky maps that include dust, synchrotron, free–free, and anomalous microwave emission, and show that HGMCA reduces foreground contamination by $25{{\ \rm per\ cent}}$ over GMCA in both the regions included and excluded by the Planck UT78 mask, decreases the error in the measurement of the CMB temperature power spectrum to the 0.02–0.03 per cent level at ℓ > 200 (and $\lt 0.26{{\ \rm per\ cent}}$ for all ℓ), and reduces correlation to all the foregrounds. We find equivalent or improved performance when compared to state-of-the-art internal linear combination type algorithms on these simulations, suggesting that HGMCA may be a competitive alternative to foreground separation techniques previously applied to observed CMB data. Additionally, we show that our performance does not suffer when we perturb model parameters or alter the CMB realization, which suggests that our algorithm generalizes well beyond our simplified simulations. Our results open a new avenue for constructing CMB maps through Bayesian hierarchical analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A General Framework for Progressive Data Compression and Retrieval

In scientific simulations, observations, and experiments, the transfer of data to and from disk and across networks has become a major bottleneck for data analysis and visualization. Compression techniques have been employed to tackle this challenge, but traditional lossy methods often demand conservative error tolerances to meet the numerical accuracy requirements of both anticipated and unknown data analysis tasks. Progressive data compression and retrieval has emerged as a promising solution, where each analysis task dictates its own accuracy needs. However, few analysis algorithms inherently support progressive data processing, and adapting compression techniques, file formats, client/server frameworks, and APIs to support progressivity can be challenging. Here, this paper presents a framework that enables progressive-precision data queries for any data compressor or numerical representation. Our strategy hinges on a multi-component representation that successively reduces the error between the original and compressed field, allowing each field in the progressive sequence to be expressed as a partial sum of components. We have implemented this approach with four established scientific data compressors and assessed its effectiveness using real-world data sets from the SDRBench collection. The results show that our framework competes in accuracy with the standalone compressors it is based upon. Additionally, (de)compression time is proportional to the number of components requested by the user. Finally, our framework allows for fully lossless compression using lossy compressors when a sufficient number of components are employed.

97 MATHEMATICS AND COMPUTING↗