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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Application of multidimensional structural characterization to detect and describe moderate forest disturbance

The study of vegetation community and structural change has been central to ecology for over a century, yet the ways in which disturbances reshape the physical structure of forest canopies remain relatively unknown. Moderate severity disturbances affect different canopy strata and plant species, resulting in variable structural outcomes and ecological consequences. Terrestrial lidar (light detection and ranging) offers an unprecedented view of the interior arrangement and distribution of canopy elements, permitting the derivation of multidimensional measures of canopy structure that describe several canopy structural traits (CSTs) with known links to ecosystem function. We used lidar-derived CSTs within a machine learning framework to detect and describe the structural changes that result from various disturbance agents, including moderate severity fire, ice storm damage, age-related senescence, hemlock woolly adelgid, beech bark disease, and chronic acidification. We found that fire and ice storms primarily affected the amount and position of vegetation within canopies, while acidification, senescence, pathogen, and insect infestation altered canopy arrangement and complexity. Only two of the six disturbance agents significantly reduced leaf area, counter to common assumptions regarding many moderate severity disturbances. While findings are limited in their generalizability due to lack of replication among disturbances, they do suggest that the current limitations of standard disturbance detection methods—such as optical-based remote sensing platforms, which are often above-canopy perspectives—limit our ability to understand the full ecological and structural impacts of disturbance, and to evaluate the consistency of structural patterns within and among disturbance agents. A more broadly inclusive definition of ecological disturbance that incorporates multiple aspects of canopy structural change may potentially improve the modeling, detection, and prediction of functional implications of moderate severity disturbance as well as broaden our understanding of the ecological impacts of disturbance.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Solvation Effects on the Dielectric Constant of 1 M LiPF6 in Ethylene Carbonate: Ethyl Methyl Carbonate 3:7

We report the dielectric constant of 1 M LiPF 6 in EC:EMC 3:7 w/w (ethylene carbonate/ethyl methyl carbonate) in addition to neat EC:EMC 3:7 w/w. Using three Debye relaxations, the static permittivity value, or dielectric constant, is extrapolated to 18.5, which is compared to 18.7 for the neat solvent mixture. The EC solvent is found to strongly coordinate with the Li + cations of the salt, which results in a loss of dielectric contribution to the electrolyte. However, the small amplitude and large uncertainty in relaxation frequency for EMC cloud definitive identification of the Li + solvation shell. Importantly, the loss of the free EC permittivity contribution due to Li + solvation is almost completely balanced by the positive contribution of the associated LiPF 6 salt, demonstrating that a significant quantity of dipolar ion pairs exists in 1 M LiPF 6 in EC:EMC 3:7.

25 ENERGY STORAGE↗
DOE OSTI2023

A phased workflow to define permit‐ready locations for large volume CO 2 injection and storage

Abstract To‐date, only two UIC Class VI permits have been issued by the US Environmental Protection Agency. We illustrate a four‐phase workflow to first identify regional storage resources and then down‐select sites to yield permit‐ready locations that can accept and store large volumes of CO 2 . Specific permit requirements should guide objectives and define deliverables of respective workflow phases. In the first phase we used available regional data and screened structure and injection zones to locate resources that match CO 2 volumes planned to be captured. Available data were also used to assess presence and depth of usable groundwater, the key resource being protected via permitting. We then used advanced, closed‐form, analytical solutions (EASiTool) to estimate CO 2 injectivity into each hydrologically connected injection compartment. In the second phase we acquired and conditioned additional wireline logs and leased available seismic datasets. We interpreted the depositional systems from wireline well‐log character and mapped sandbody geometry to interpolate injection and confining‐zone distribution. Using available data, we mapped faults and locations of freshwater and overpressure (or other capacity‐limiting geologic parameters) in more detail. In the third phase, we used the augmented geologic data to develop a static model for the selected area, extracted the areas of highest interest, and generated and ran dynamic (flow) models. In a fourth phase, we reduced major uncertainties identified in earlier phases. Our case study indicates that to complete preparation of a permit application requires (1) improved lithologic characterization information (thicknesses and horizontal and vertical connectivity) and (2) better definition of poorly defined local faults. © 2023 The Authors. Greenhouse Gases: Science and Technology published by Society of Chemical Industry and John Wiley & Sons Ltd.

58 GEOSCIENCES↗
DOE OSTI2023

Exploring young adult texts within the Historically Responsive Literacy Framework with preservice teachers

Abstract While culturally responsive texts have become more common in teacher education, too often, preservice teachers (PTs) are not asked to examine how to use these books pedagogically. To address this issue, in a young adult (YA) literature course, the Framework for Culturally and Historically Responsive Literacy (HRL) (Muhammad, 2000) Cultivating genius: An equity framework for culturally and historically responsive literac y, 2020; Scholastic) was used in conjunction with representative and inclusive YA trade books. Data analysis was conducted on PT's course work, including HRL unit plans, to determine whether PTs were able to implement Muhammad's (2020) framework using YA texts. The findings of this study show that PTs' understanding of the HRL tenets was at varying levels. While there were unit plans with learning goals that matched Muhammad's purpose and definition for each tenet and YA connections for every tenet, PTs showed a better understanding of the tenets of identity and intellect than skills and Criticality. Implications of these findings including exposing PTs to learning frameworks “written by people of color and designed for children of color” (Muhammad, 2020, p. 11) to create instruction that meets their future students' needs and does not just skim the surface of culturally responsive pedagogies.

Pule, Heather↗
DOE OSTI2025

Examining the Impact of Local Constraint Violations on Energy Computations in DFT

ABSTRACT This work examines the impact of locally imposed constraints in Density Functional Theory (DFT). Using a metric referred to as the extent of violation index (EVI), we quantify how well exchange‐correlation functionals adhere to local constraints. Applying EVIs to a diverse set of molecules for GGA functionals reveals constraint violations, particularly for semi‐empirical functionals. We leverage EVIs to explore potential connections between these violations and errors in chemical properties. While no correlation is observed for atomization energies, a significant statistical correlation emerges between EVIs and total energies. Similarly, the analysis of reaction energies suggests weak positive correlations for specific constraints. However, definitive conclusions about error cancellation mechanisms cannot be made at this time. These observations revealed by EVIs may be useful for consideration when designing future generations of semilocal functionals.

Khanna, Vaibhav [Department of Chemistry Universit↗
DOE OSTI2022

D 3 -creatine dilution for skeletal muscle mass measurement: historical development and current status

The French chemist Michel Eugène Chevreul discovered creatine in meat two centuries ago. Extensive biochemical and physiological studies of this organic molecule followed with confirmation that creatine is found within the cytoplasm and mitochondria of human skeletal muscles. Two groups of investigators exploited these relationships five decades ago by first estimating the creatine pool size in vivo with 14 C and 15 N labelled isotopes. Skeletal muscle mass (kg) was then calculated by dividing the creatine pool size (g) by muscle creatine concentration (g/kg) measured on a single muscle biopsy or estimated from the literature. This approach for quantifying skeletal muscle mass is generating renewed interest with the recent introduction of a practical stable isotope (creatine-(methyl-d 3 )) dilution method for estimating the creatine pool size across the full human lifespan. The need for a muscle biopsy has been eliminated by assuming a constant value for whole-body skeletal muscle creatine concentration of 4.3 g/kg wet weight. The current single compartment model of estimating creatine pool size and skeletal muscle mass rests on four main assumptions: tracer absorption is complete; tracer is all retained; tracer is distributed solely in skeletal muscle; and skeletal muscle creatine concentration is known and constant. Three of these assumptions are false to varying degrees. Not all tracer is retained with urinary isotope losses ranging from 0% to 9%; an empirical equation requiring further validation is used to correct for spillage. Not all tracer is distributed in skeletal muscle with non-muscle creatine sources ranging from 2% to 10% with a definitive value lacking. Lastly, skeletal muscle creatine concentration is not constant and varies between muscles (e.g. 3.89–4.62 g/kg), with diets (e.g. vegetarian and omnivore), across age groups (e.g. middle-age, ~4.5 g/kg; old-age, 4.0 g/kg), activity levels (e.g. athletes, ~5 g/kg) and in disease states (e.g. muscular dystrophies, <3 g/kg). Some of the variability in skeletal muscle creatine concentrations can be attributed to heterogeneity in the proportions of wet skeletal muscle as myofibres, connective tissues, and fat. These observations raise serious concerns regarding the accuracy of the deuterated-creatine dilution method for estimating total body skeletal muscle mass as now defined by cadaver analyses of whole wet tissues and in vivo approaches such as magnetic resonance imaging. A new framework is needed in thinking about how this potentially valuable method for measuring the creatine pool size in vivo can be used in the future to study skeletal muscle biology in health and disease.

body composition↗
DOE OSTI2021

Subacute safety assessment of recombinant Lactococcus lactis on the gut microbiota of male Sprague–Dawley rats

Abstract BACKGROUND Lactococcus lactis strain pGSMT/MG1363 is a genetically modified microorganism (GMM) that constitutively expresses human metallothionein‐I fusion protein to combine with intracellular lead. Unlike traditional probiotics, pGSMT/MG1363 lacks a history of safe use in food. Administration of microorganism could influence the gut microbial community and consequently confer health benefits or cause disadvantages to the host. To date, little has been done to assess the influence of recombinant strain pGSMT/MG1363 on the stability of gut microbiota. RESULTS Liver, testis and kidney sections of male Sprague–Dawley rats orally administered pGSMT/MG1363 for 6 weeks showed normal structure and no pathological damage. There were no adverse effects on the analyzed serum biochemical parameters between the pGSMT/MG1363 group and the MG1363 group. Principal coordinate analysis showed that, compared with the MG1363 group, the 6‐week‐old fecal gut microbiota of rats fed with pGSMT/MG1363 was not significantly different (Adonis, P = 0.802). pGSMT/MG1363 treatment for 6 weeks did not significantly change the relative abundance of gut microbiota at the phylum and genus levels in comparison with MG1363 treatment. CONCLUSION Compared to the non‐GM strain MG1363 group, administration of the recombinant strain pGSMT/MG1363 for 6 weeks showed no adverse effects on the analyzed physiological parameters and gut microbial compositions of male Sprague–Dawley rats. The results suggested that, in terms of gut microbiota stability, pGSMT/MG1363 could be considered as safe as MG1363, at least for short‐term intake. Further toxicological evaluations still need to be considered before drawing a definite conclusion concerning the safe use of pGSMT/MG1363. © 2021 Society of Chemical Industry.

Chen, Guowei↗
DOE OSTI2022

Ionic Liquid Facilitated Solvent‐Phase Polymerization of Ultrasmooth Coatings of Polycatecholamines

Mussel-inspired polycatecholamine coatings and films have proven to be versatile materials for surface modification. However, the progress of chemically modified coatings with tailored properties has been slow due to the lack of definitive evidence of their polymeric structure. Polycatecholamines form aggregates during polymerization, and their formation mechanism has been a subject of debate owing to their insolubility in traditional molecular solvents. Exploiting the capability of ionic liquids (ILs) to exhibit strong electrostatic interactions, herein, the first solution-phase polymerization approach is reported to achieve polymerization of four catecholamines – dopamine (DA), norepinephrine (NE), L-3,4-dihydroxyphenylalanine (L-DOPA), and adrenaline (AD). Kinetic control over the polymerization process in the solution phase enabled it to follow the process with 1 H NMR spectroscopy, revealing the formation of structural features of resulting complex heterogeneous and soluble polymers. The polymers are both covalent and associative in nature. Solution phase polymerization prevented the formation of large aggregates in the solution, thus facilitating the formation of coatings that are ultra-smooth and have root mean square roughness of the order of sub-nm to nm scale.

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

Feature‐shared adaptive‐boost deep learning for invasiveness classification of pulmonary subsolid nodules in CT images

Purpose In clinical practice, invasiveness is an important reference indicator for differentiating the malignant degree of subsolid pulmonary nodules. These nodules can be classified as atypical adenomatous hyperplasia (AAH), adenocarcinoma in situ (AIS), minimally invasive adenocarcinoma (MIA), or invasive adenocarcinoma (IAC). The automatic determination of a nodule's invasiveness based on chest CT scans can guide treatment planning. However, it is challenging, owing to the insufficiency of training data and their interclass similarity and intraclass variation. To address these challenges, we propose a two‐stage deep learning strategy for this task: prior‐feature learning followed by adaptive‐boost deep learning. Methods The adaptive‐boost deep learning is proposed to train a strong classifier for invasiveness classification of subsolid nodules in chest CT images, using multiple 3D convolutional neural network (CNN)‐based weak classifiers. Because ensembles of multiple deep 3D CNN models have a huge number of parameters and require large computing resources along with more training and testing time, the prior‐feature learning is proposed to reduce the computations by sharing the CNN layers between all weak classifiers. Using this strategy, all weak classifiers can be integrated into a single network. Results Tenfold cross validation of binary classification was conducted on a total of 1357 nodules, including 765 noninvasive (AAH and AIS) and 592 invasive nodules (MIA and IAC). Ablation experimental results indicated that the proposed binary classifier achieved an accuracy of with an AUC of 81.3 . These results are superior compared to those achieved by three experienced chest imaging specialists who achieved an accuracy of , , and , respectively. About 200 additional nodules were also collected. These nodules covered 50 cases for each category (AAH, AIS, MIA, and IAC, respectively). Both binary and multiple classifications were performed on these data and the results demonstrated that the proposed method definitely achieves better performance than the performance achieved by nonensemble deep learning methods. Conclusions It can be concluded that the proposed adaptive‐boost deep learning can significantly improve the performance of invasiveness classification of pulmonary subsolid nodules in CT images, while the prior‐feature learning can significantly reduce the total size of deep models. The promising results on clinical data show that the trained models can be used as an effective lung cancer screening tool in hospitals. Moreover, the proposed strategy can be easily extended to other similar classification tasks in 3D medical images.

Wang, Jun↗
DOE OSTI2020

Matrix-free preconditioning for high-order H (curl) discretizations

The greater arithmetic intensity of high-order finite element discretizations makes them attractive for implementation on next-generation hardware, but assembly of high-order finite element operators as matrices is prohibitively expensive. As a result, the development of general algebraic solvers for such operators has been an open research challenge. Fast matrix-free application of high-order operators has received significant attention in the literature in the context of Poisson-type problems, but preconditioners and solvers for inverting more general operators are not very well-developed. In this paper, we consider the problem of preconditioning a definite Maxwell operator at high polynomial order without assembling a matrix. We show that given efficient preconditioners for high-order H 1 finite element problems on the same mesh, efficient H(curl) preconditioners can be constructed in an auxiliary space framework. We demonstrate the resulting preconditioners in a practical setting with tensor-product basis functions on an unstructured mesh of quadrilaterals. Overall, our approach uses a sparsified H 1 solver constructed on a low-order mesh of the nodal points of the underlying high-order space, and we show that the resulting H(curl) preconditioner is effective at very high polynomial orders for two-dimensional model problems with complicated geometry, varying piecewise constant coefficients, and curved elements. The resulting preconditioner scales with nearly optimal O(p d+1 ) floating point operation count and optimal O(p d ) memory transfer requirements, outperforming existing Maxwell preconditioners in the high-order regime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Informing forest carbon inventories under the Paris Agreement using ground-based forest monitoring data

Human interactions with forests have shaped Earth's climate for millennia and will continue to do so as we target net-zero emission goals. Accurately characterizing these climate impacts requires making reliable forest carbon data available for forest monitoring and planning. Here, we develop a semi-automated process for submitting forest carbon measurements from the largest relevant scientific database to the International Panel on Climate Change's Emission Factor Database, which currently has sparse forest carbon data. Building this bridge from scientific research to international policy is an important step towards managing forests in a net-zero motivated future. Humans have been influencing Earth's climate via transformative impacts on forests for millennia, and forests are now recognized as critical to climate change mitigation under the Paris Agreement. The efficacy of climate change mitigation planning and reporting depends on quality data on forest carbon (C) stocks and changes. The Emission Factor Database (EFDB) of the International Panel on Climate Change (IPCC) is intended to be a definitive source for such data, but needs comprehensive and well-documented data to be so. To facilitate submission of forest C estimates from scientific studies to EFDB, we develop and document a process for semi-automated data submission from the Global Forest C database (ForC v4.0), which is the largest compilation of ground-based forest C estimates. We then assess the data currently available through ForC and provide recommendations for improving forest data collection, analysis, and reporting. As of September 2024, ForC contained ~19,286 records potentially relevant to EFDB, 1068 of which had been submitted and posted to EFDB. These represented 19% of the total EFDB records for forest land. Records were unevenly distributed across variables and geographic regions. ForC records (37%) reviewed could not be submitted because the original publication lacked required information. In the future, ground-based forest C estimates should target gaps in the record, and studies should ensure that they report all information necessary for inclusion in EFDB. Given that climate change is rapidly impacting the world's forests, timely reporting of recent estimates will be critical to accurate forest C inventories.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

The Table of Standard Atomic Weights—an exercise in consensus

The present Table of Standard Atomic Weights (TSAW) of the elements is perhaps one of the most familiar datasets in science. Unlike most parameters in physical science whose values and uncertainties are evaluated using the “Guidelines for Uncertainty in Measurement” (GUM), the majority of standard atomic-weight values and their uncertainties are consensus values, not GUM-evaluated values. The Commission on Isotopic Abundances and Atomic Weights of the International Union of Pure and Applied Chemistry (IUPAC) regularly evaluates the literature for new isotopic-abundance measurements that can lead to revised standard atomic-weight values, A r (E) for element E. The Commission strives to provide utmost clarity in products it disseminates, namely the TSAW and the Table of Isotopic Compositions of the Elements (TICE). In 2016, it was recognized by the Commission that a guideline recommending expression of uncertainty listed in parentheses following the standard atomic-weight value, e.g. A r (Se) = 78.971(8), is not in accord with the GUM, which suggests that this parenthetic notation be reserved to express standard uncertainty, not the expanded uncertainty used in the TSAW and TICE. In 2017, to eliminate this noncompliance with the GUM, a new format was adopted in which the uncertainty value is specified by the plus-minus symbol, e.g. A r (Se) = 78.971 ± 0.008. To clarify the definition of uncertainty, a new footnote has been added to the TSAW. This footnote emphasizes that an atomic-weight uncertainty is a consensus (decisional) uncertainty. Not only has the Commission shielded users of the TSAW and TICE from unreliable measurements that appear in the literature as a result of unduly small uncertainties, but the aim of IUPAC has been fulfilled by which any scientist, taking any natural sample from commerce or research, can expect their sample atomic weight to lie within A r (E) ± its uncertainty almost all of the time.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Driving mode analysis—How uncertain functional inputs propagate to an output

Abstract Driving mode analysis elucidates how correlated features of uncertain functional inputs jointly propagate to produce uncertainty in the output of a computation. Uncertain input functions are decomposed into three terms: the mean functions, a zero‐mean driving mode, and zero‐mean residual. The random driving mode varies along a single direction, having fixed functional shape and random scale. It is uncorrelated with the residual, and under linear error propagation, it produces an output variance equal to that of the full input uncertainty. Finally, the driving mode best represents how input uncertainties propagate to the output because it minimizes expected squared Mahalanobis distance amongst competitors. These characteristics recommend interpretation of the driving mode as the single‐degree‐of‐freedom component of input uncertainty that drives output uncertainty. We derive the functional driving mode, show its superiority to other seemingly sensible definitions, and demonstrate the utility of driving mode analysis in an application. The application is the simulation of neutron transport in criticality experiments. The uncertain input functions are nuclear data that describe how Pu reacts to bombardment by neutrons. Visualization of the driving mode helps scientists understand what aspects of correlated functional uncertainty have effects that either reinforce or cancel one another in propagating to the output of the simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

What is (quantitative) system dynamics modeling? Defining characteristics and the opportunities they create

A clear definition of system dynamics modeling can provide shared understanding and clarify the impact of the field. We introduce a set of characteristics that define quantitative system dynamics, selected to capture core philosophy, describe theoretical and practical principles, and apply to historical work but be flexible enough to remain relevant as the field progresses. The defining characteristics are: (1) models are based on causal feedback structure, (2) accumulations and delays are foundational, (3) models are equation-based, (4) concept of time is continuous, and (5) analysis focuses on feedback dynamics. We discuss the implications of these principles and use them to identify research opportunities in which the system dynamics field can advance. These research opportunities include causality, disaggregation, data science and AI, and contributing to scientific advancement. Progress in these areas has the potential to improve both the science and practice of system dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Contribution of the Sub-Surface to Electrocatalytic Activity in Atomically Precise La 0.7 Sr 0.3 MnO 3 Heterostructures

Electrocatalytic reactions are known to take place at the catalyst/electrolyte interface. Whereas recent studies of size-dependent activity in nanoparticles and thickness-dependent activity of thin films imply that the sub-surface layers of a catalyst can contribute to the catalytic activity as well, most of these studies consider actual modification of the surfaces. Here, in this study, the role of catalytically active sub-surface layers was investigated by employing atomic-scale thickness control of the La 0.7 Sr 0.3 MnO 3 (LSMO) films and heterostructures, without altering the catalyst/electrolyte interface. The activity toward the oxygen evolution reaction (OER) shows a non-monotonic thickness dependence in the LSMO films and a continuous screening effect in LSMO/SrRuO 3 heterostructures. The observation leads to the definition of an “electrochemically-relevant depth” on the order of 10 unit cells. This study on the electrocatalytic activity of epitaxial heterostructures provides new insight in designing efficient electrocatalytic nanomaterials and core-shell architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

An overview of the evolving jurisdictional scope of the U.S. Clean Water Act for hydrologists

Abstract The Clean Water Act (CWA) is the primary federal mechanism by which the physical, chemical, and biological integrity of streams, lakes, and wetlands are protected in the United States. The CWA has evolved considerably since its initial passage in 1948, including explicit expansions and contractions of jurisdictional scope through a series of legislative actions, court decisions, and agency rules. Here, we provide a practical summary of the CWA's evolution, detailing the major updates or revisions and their circumstances. Additionally, we identify the jurisdictional scope of the law for rivers and streams, lakes, and wetlands based on the language used and implementation by the agencies during the same time period. While the rulemaking process commonly uses language that will be abstract to many hydrologists, understanding the on‐the‐ground implications, quantifying regulatory (un)certainties, and assessing the magnitude of changes through time is important to understanding the implications of environmental regulation development, litigation, and enforcement. Thus, we translate the enforcement norms and definitions into quantitative estimates for Clean Water Act scope in the Wabash River Basin (Illinois, Indiana, and Ohio, USA) as a demonstration of the spatial consequences of changing regulatory language. This article is categorized under: Engineering Water > Planning Water Human Water > Water Governance Water and Life > Conservation, Management, and Awareness

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Just-in-Time Compilation and Link-Time Optimization for OpenMP Target Offloading

Following the mass adoption of external accelerators for high performance computing, the overall performance of many applications has become increasingly dependent on relatively small accelerated kernels. As static analysis is fundamentally limited by dynamic values and external definitions, standard ahead-of-time compilation is not always sufficient to achieve the best performance. Furthermore, many users looking to port an existing application to run on an external accelerator will not want to fundamentally restructure their programs. These and other problems can be addressed through both link-time optimization (LTO) and just-in-time (JIT) compilation, but until now had sparse and inconsistent support from the compiler. In this work, we present a new compilation method that enables device-side LTO as well as a transparent JIT compilation tool-chain for OpenMP target offloading. Our contributions include an entirely new device linking and embedding scheme to enable LTO as well as a novel JIT engine to efficiently optimize OpenMP offloading regions at run-time. We also introduce a persistent caching system to improve end-to-end runtime using the JIT engine and minimize kernel launching overheads. We measure the performance of our LTO and JIT implementation via several real-world scientific applications. With our optimizations we observe significant improvements through LTO on large applications as well as significant end-to-end execution time improvement using JIT.

Tian, Shilei↗