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At least 1,027 records · Page 57

Characterization of extreme precipitation within atmospheric river events over California

Atmospheric rivers (ARs) are large, spatially coherent weather systems with high concentrations of elevated water vapor. These systems often cause severe downpours and flooding over the western coastal United States – and with the availability of more atmospheric moisture in the future under global warming we expect ARs to play an important role as potential causes of extreme precipitation changes. Therefore, we aim to investigate changes in extreme precipitation properties correlated with AR events in a warmer climate, which are large-scale meteorological patterns affecting the weather and climate of California. We have recently developed the TECA (Toolkit for Extreme Climate Analysis) software for automatically identifying and tracking features in climate data sets. Specifically, we can now identify ARs that make landfall on the western coast of North America. Based on this detection procedure, we can investigate the impact of ARs by exploring the spatial extent of AR precipitation using climate model (CMIP5) simulations and characterize spatial patterns of dependence for future projections between AR precipitation extremes under climate change within the statistical framework. Our results show that AR events in the future RCP (Representative Concentration Pathway)8.5 scenario (2076–2100) tend to produce heavier rainfall with higher frequency and longer days than events from the historical run (1981–2005). We also find that the dependence between extreme precipitation events has a shorter spatial range, within localized areas in California, under the high future emissions scenario than under the historical run.

Jeon, S.↗

Signatures of troposphere-stratosphere momentum coupling Implications for global atmospheric angular momentum and earth rotation budgets

During January-August 1978, the global atmospheric angular momentum (M) exhibits distinct patterns of short term momentum interchange across latitudes. In the Northern Hemisphere winter-spring season, 30-50 day modulations of M are present in which momentum enhancements at mid-latitudes (20-30 deg) are closely matched by momentum depressions at high latitudes (50-60 deg). During the same interval there are no corresponding variations in M evident in the Southern Hemisphere. Conversely, during Southern Hemisphere fall-winter, similar anti-correlations in monthly scale momentum excursions are evident between mid and high latitudes. In the Northern Hemisphere, the winter-spring momentum signatures are detected throughout the atmosphere, from the lower troposphere to the stratosphere. During the Southern Hemisphere fall-winter, the modulation patterns are not evident at the higher altitudes. Structural details of the momentum signatures indicate that the coupling is sometimes effective on very short time scales, e.g., 1-2 days, or less. The evidence of distinct anti-correlation between large regions has interesting implications for studies of global atmospheric circulation, and also for studies of the excitation of variations in earth rotation in response to short term modulations of M.

Taylor, H. A.↗

Developmental regulation of N-methyl-D-aspartate- and kainate-type glutamate receptor expression in the rat spinal cord

Spinal motor neurons undergo experience-dependent development during a critical period in early postnatal life. It has been suggested that the repertoire of glutamate receptor subunits differs between young and mature motor neurons and contributes to this activity-dependent development. In the present study we examined the expression patterns of N-methyl-D-aspartate- and kainate-type glutamate receptor subunits during the postnatal maturation of the spinal cord. Young motor neurons express much higher levels of the N-methyl-D-aspartate receptor subunit NR1 than do adult motor neurons. Although there are eight potential splice variants of NR1, only a subgroup is expressed by motor neurons. With respect to NR2 receptor subunits, young motor neurons express NR2A and C, while adult motor neurons express only NR2A. Young motor neurons express kainate receptor subunits GluR5, 6 and KA2 but we are unable to detect these or any other kainate receptor subunits in the adult spinal cord. Other spinal cord regions display a distinct pattern of developmental regulation of N-methyl-D-aspartate and kainate receptor subunit expression in comparison to motor neurons. Our findings indicate a precise spatio-temporal regulation of individual subunit expression in the developing spinal cord. Specific combinations of subunits in developing neurons influence their excitable properties and could participate in the emergence of adult neuronal form and function.

NASA Discipline Cell Biology↗

DETECTION OF PHOSPHORUS, SULPHUR, AND ZINC IN THE CARBON-ENHANCED METAL-POOR STAR BD+44 493

The carbon-enhanced metal-poor star BD+44°493 ([Fe/H] = −3.9) has been proposed as a candidate second-generation star enriched by metals from a single Pop III star. We report the first detections of P and S and the second detection of Zn in any extremely metal-poor carbon-enhanced star, using new spectra of BD+44°493 collected by the Cosmic Origins Spectrograph on the Hubble Space Telescope . We derive [P/Fe] = −0.34 ± 0.21, [S/Fe] = +0.07 ± 0.41, and [Zn/Fe] = −0.10 ± 0.24. We increase by 10-fold the number of Si i lines detected in BD+44°493, yielding [Si/Fe] = +0.15 ± 0.22. The [S/Fe] and [Zn/Fe] ratios exclude the hypothesis that the abundance pattern in BD+44°493 results from depletion of refractory elements onto dust grains. Comparison with zero-metallicity supernova (SN) models suggests that the stellar progenitor that enriched BD+44°493 was massive and ejected much less than 0.07 M {sub ⊙} of {sup 56}Ni, characteristic of a faint SN.

79 ASTRONOMY AND ASTROPHYSICS↗

Recoil imaging for dark matter, neutrinos, and physics beyond the Standard Model

Recoil imaging entails the detection of spatially resolved ionization tracks generated by particle interactions. This is a highly sought-after capability in many classes of detector, with broad applications across particle and astroparticle physics. However, at low energies, where ionization signatures are small in size, recoil imaging only seems to be a practical goal for micro-pattern gas detectors. This white paper outlines the physics case for recoil imaging, and puts forward a decadal plan to advance towards the directional detection of low-energy recoils with sensitivity and resolution close to fundamental performance limits. The science case covered includes: the discovery of dark matter into the neutrino fog, directional detection of sub-MeV solar neutrinos, the precision study of coherent-elastic neutrino-nucleus scattering, the detection of solar axions, the measurement of the Migdal effect, X-ray polarimetry, and several other applied physics goals. We also outline the R&D programs necessary to test concepts that are crucial to advance detector performance towards their fundamental limit: single primary electron sensitivity with full 3D spatial resolution at the $\sim$100 micron-scale. These advancements include: the use of negative ion drift, electron counting with high-definition electronic readout, time projection chambers with optical readout, and the possibility for nuclear recoil tracking in high-density gases such as argon. We also discuss the readout and electronics systems needed to scale-up such detectors to the ton-scale and beyond.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Patterns In Debris Disks: No Planets Required?

Debris disks like those around Fomalhaut and Beta Pictoris show striking dust patterns often attributed to hidden exoplanets. These patterns have been crucial for constraining the masses and orbits of these planets. But adding a bit of gas to our models of debris disks--too little gas to detect--seems to alter this interpretation. Small amounts of gas lead to new dynamical instabilities that may mimic the narrow eccentric rings and other structures planets would create in a gas-free disk. Can we still use dust patterns to find hidden exoplanets?

Kuchner, Marc↗

Latent Viruses: A Space Travel Hazard??

A major issue associated with long-duration space flight is the possibility of infectious disease causing an unacceptable medical risk to crew members. Our proposal is designed to gain information that addresses several issues outlined in the Immunology/Infectious disease critical path. The major hypothesis addressed is that space flight causes alterations in the immune system that may allow latent viruses which are endogenous in the human population to reactivate and shed to higher levels than normal which can affect the health of crew members during a long term space-flight mission. We will initially focus our studies on the human herpesviruses and human polyomaviruses which are important pathogens known to establish latent infections in the human population. Both primary infection and reactivation from latent infection with this group of viruses can cause a variety of illnesses that result in morbidity and occasionally mortality of infected individuals. Effective vaccines exist for only one of the eight known human herpesviruses and the vaccine itself can still reactivate from latent infection. Available antivirals are of limited use and are effective against only a few of the human herpesviruses. Although most individuals display little if any clinical consequences from latent infection, events which alter immune function such as immunosuppressive therapy following solid organ transplantation are known to increase the risk of developing complications as a result of latent virus reactivation. This proposal will measure both the frequency and magnitude of viral shedding and genome loads in the blood from humans participating in activities that serve as ground based models of space flight conditions. Our initial goal is to develop sensitive quantitative competitive PCR- based assays (QC-PCR) to detect the herpesvirus Epstein-Barr virus (EBV), and the polyomaviruses SV40, BKV, and JCV. Using these assays we will establish baseline patterns of viral genome load in the blood and viral shedding from normal volunteers in a longitudinal study over I year in length. As a comparison, we will measure patterns of viral genome loads and shedding from individuals who are severely immunosuppressed, in whom herpesvirus reactivation or primary infection with a herpesvirus is known to cause complications. In addition, we will proceed to testing ground based analogs in collaboration with Dr. Duane Pierson (Lyndon B. Johnson Space Center). This will include measuring samples obtained from individuals living and working in the extreme environment of Antarctica. We expect to detect viral shedding or reactivation from most of the test groups, although the magnitude of shedding or reactivation cannot be predicted. The data accumulated from studies in this proposal should allow us to evaluate whether events that simulate certain aspects of space flight reactivate viral infections severe enough in nature that they may compromise the success of long-term space flight missions. These studies will also provide a foundation to monitor viral reactivation and shedding from crew members participating in actual space flight missions. We will present data showing the establishment of our QC-PCR assay for detection of EBV.

Ling, P. D.↗

PET Imaging of Tau Deposition in the Aging Human Brain

Tau pathology is a hallmark of Alzheimer’s disease (AD) but also occurs in normal cognitive aging. In this study, using the tau PET agent 18 F-AV-1451, we examined retention patterns in cognitively normal older people in relation to young controls and AD patients. Age and β-amyloid (measured using PiB PET) were differentially associated with tau tracer retention in healthy aging. Older age was related to increased tracer retention in regions of the medial temporal lobe, which predicted worse episodic memory performance. PET detection of tau in other isocortical regions required the presence of cortical β-amyloid and was associated with decline in global cognition. Furthermore, patterns of tracer retention corresponded well with Braak staging of neurofibrillary tau pathology. In conclusion, the present study defined patterns of tau tracer retention in normal aging in relation to age, cognition, and β-amyloid deposition.

60 APPLIED LIFE SCIENCES↗

Elucidating structural order and disorder phenomena in mullite-type Al{sub 4}B{sub 2}O{sub 9} by automated electron diffraction tomography

The crystal structure and disorder phenomena of Al{sub 4}B{sub 2}O{sub 9}, an aluminum borate from the mullite-type family, were studied using automated diffraction tomography (ADT), a recently established method for collection and analysis of electron diffraction data. Al{sub 4}B{sub 2}O{sub 9}, prepared by sol-gel approach, crystallizes in the monoclinic space group C2/m. The ab initio structure determination based on three-dimensional electron diffraction data from single ordered crystals reveals that edge-connected AlO{sub 6} octahedra expanding along the b axis constitute the backbone. The ordered structure (A) was confirmed by TEM and HAADF-STEM images. Furthermore, disordered crystals with diffuse scattering along the b axis are observed. Analysis of the modulation pattern implies a mean superstructure (AAB) with a threefold b axis, where B corresponds to an A layer shifted by ½a and ½c. Diffraction patterns simulated for the AAB sequence including additional stacking disorder are in good agreement with experimental electron diffraction patterns. - Graphical abstract: Crystal structure and disorder phenomena of B-rich Al{sub 4}B{sub 2}O{sub 9} studied by automated electron diffraction tomography (ADT) and described by diffraction simulation using DISCUS. - Highlights: • Ab-initio structure solution by electron diffraction from single nanocrystals. • Detected modulation corresponding mainly to three-fold superstructure. • Diffuse diffraction streaks caused by stacking faults in disordered crystals. • Observed streaks explained by simulated electron diffraction patterns.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantitative Evaluations of Surface Cleanliness in IF Steel Slabs at Unsteady Casting

Macro-inclusions in the surface layer of slabs are mainly responsible for the sliver defects in IF steel sheets. In the present work, macro-inclusions in six kinds of unsteady cast IF steel slabs involving four unsteady states (casting start, ladle change, nozzle change and casting end) in one casting sequence were quantitatively characterized using an automatic inclusion analyzer with a total detection area of 238,048 mm{sup 2}. The cleanliness of corresponding normal slabs was also evaluated as the benchmark study, and the number density (ND) of inclusions > 50 µm was used to describe the surface slab cleanliness. Generally, alumina-based and mold powder inclusions were detected, and the former type was further subdivided into alumina clusters, alumina associated with bubbles, refractory-related alumina, Al-Ti complex oxides and CaO-Al{sub 2}O{sub 3}-MgO. Several large-sized alumina-based inclusions were detected in the normal slabs with an average ND of 0.31 N/cm{sup 2}, although they had very low total oxygen (TO) contents (10~13 ppm). No mold powder inclusions were found in normal slabs. For all the unsteady slabs, alumina-based and mold powder inclusions were both observed, and the percentage of the former kind was ≥ 90 pct. The average density of macro-inclusions for the first slab was 1.621 N/cm{sup 2}, whose cleanliness was much worse than any of the other unsteady slabs. The first slab should be downgraded. For the second slab, the ND of macro-inclusions was 0.385 N/cm{sup 2}, which was still larger than the normal slabs because of the lasting effect of the re-oxidation. For the penultimate, cap-off and SEN changed slabs, the density of macro-inclusions fluctuated from 0.25~0.35 N/cm{sup 2}, which was close to the average level of normal slabs. However, mold flux-originated inclusions were frequently observed in these slabs because of flow pattern variations due to the casting speed change. In terms of the slab during the ladle change process, mold powder inclusions were frequently detected even though the casting speed remained constant. A mold powder entrapment mechanism was proposed, which showed the entrapment occurred owing to the flow pattern change induced by forming/dropping of SEN clogs due to re-oxidation by FeO in the ladle slag and tundish steel temperature variations during the ladle change practice. The severity of powder entrapment and re-oxidation was also given for different kinds of unsteady slabs, which provides a direct guide to treating these slabs in the steel plant.

36 MATERIALS SCIENCE↗

Enhanced Line Integral Convolution with Flow Feature Detection

The Line Integral Convolution (LIC) method, which blurs white noise textures along a vector field, is an effective way to visualize overall flow patterns in a 2D domain. The method produces a flow texture image based on the input velocity field defined in the domain. Because of the nature of the algorithm, the texture image tends to be blurry. This sometimes makes it difficult to identify boundaries where flow separation and reattachments occur. We present techniques to enhance LIC texture images and use colored texture images to highlight flow separation and reattachment boundaries. Our techniques have been applied to several flow fields defined in 3D curvilinear multi-block grids and scientists have found the results to be very useful.

Lane, David↗

Test pattern generation for ILA sequential circuits

An efficient method of generating test patterns for sequential machines implemented using one-dimensional, unilateral, iterative logic arrays (ILA's) of BTS pass transistor networks is presented. Based on a transistor level fault model, the method affords a unique opportunity for real-time fault detection with improved fault coverage. The resulting test sets are shown to be equivalent to those obtained using conventional gate level models, thus eliminating the need for additional test patterns. The proposed method advances the simplicity and ease of the test pattern generation for a special class of sequential circuitry.

Feng, YU↗

Severe Convective Storms in Limited Instability Organized by Pattern and Distribution

Abstract Severe convection occurring in high-shear, low-CAPE (HSLC) environments is a common cool-season threat in the southeastern United States. Previous studies of HSLC convection document the increased operational challenges that these environments present compared to their high-CAPE counterparts, corresponding to higher false-alarm ratios and lower probability of detection for severe watches and warnings. These environments can exhibit rapid destabilization in the hours prior to convection, sometimes associated with the release of potential instability. Here, we use self-organizing maps (SOMs) to objectively identify environmental patterns accompanying HSLC cool-season severe events and associate them with variations in severe weather frequency and distribution. Large-scale patterns exhibit modest variation within the HSLC subclass, featuring strong surface cyclones accompanied by vigorous upper-tropospheric troughs and northward-extending regions of instability, consistent with prior studies. In most patterns, severe weather occurs immediately ahead of a cold front. Other convective ingredients, such as lower-tropospheric vertical wind shear, near-surface equivalent potential temperature (θ e ) advection, and the release of potential instability, varied more significantly across patterns. No single variable used to train SOMs consistently demonstrated differences in the distribution of severe weather occurrence across patterns. Comparison of SOMs based on upper and lower quartiles of severe occurrence demonstrated that the release of potential instability was most consistently associated with higher-impact events in comparison to other convective ingredients. Overall, we find that previously developed HSLC composite parameters reasonably identify high-impact HSLC events. Significance Statement Even when atmospheric instability is not optimal for severe convective storms, in some situations they can still occur, presenting increased challenges to forecasters. These marginal environments may occur at night or during the cool season, when people are less attuned to severe weather threats. Here, we use a sorting algorithm to classify different weather patterns accompanying such storms, and we distinguish which specific patterns and weather system features are most strongly associated with severe storms. Our goals are to increase situational awareness for forecasters and to improve understanding of the processes leading to severe convection in marginal environments.

Meteorology & Atmospheric Sciences↗

Operating displays - new concept: high performance displays - 118

New control rooms in Nuclear Power Plants using digital Distributed Control System (DCS) operated with software displays, are providing thousands of signals to the operating crew. When an event happens, the Flood of information provided to operators could obscure the initiator event increasing the operator response time, work load and complicating the selection of the actions to be performed. There are some initiatives that are trying to minimize the 'avalanche effect' as the alarm engineering filtering and prioritization or diagnostic displays. Likewise, new control rooms are lost the availability to know the plant status just with a quick glance to the panel indicators. Regarding Small Modular Reactors, where in some cases four operators should monitor and control twelve reactors, these problems are even more significant. The challenge is to find a solution, based on current digital systems, that supply information to operators in order to prevent events and take early actions to minimize or avoid any unexpected incident. In order to minimize human errors, Tecnatom has developed a specific set of displays, called 'High Performance Displays' (HPD) based on objectives, work environment limitation, and non-anticipated events. These displays are being design following the HFE standards: applying the NUREG-0711 elements to identify the information that they have to content and the NUREG-0700 to design the interface. The function of these displays is monitoring the plant situation in a way that the operators are able to recognize any potential event at a simple glance but controlling thousands of signals through pattern recognition, symmetries, regular polygons and colors. The objective of the HPD is to provide an integrated function minimizing the tunnel effect and reduce the workload during the diagnosis phase. Moreover, HPD enhance operators to take the right actions to anticipate the response to any event, even avoiding it, if possible This paper analyzes how HPD's have been design as well as presents the results of a preliminary validation of their capabilities. The preliminary validation is a reduce validation in a full scope simulator running two representative scenarios of abnormal and emergency operation. The analysis is focused on the first stage of the event, i.e. the detection phase, HPD's have been installed in a generic full scope simulator of a nuclear power plant, digital controlled. Both scenarios have been performed by two different operator crews. The first operator shift has worked with the conventional human machine interface, that is, displays similar to the ones currently installed in existing nuclear power plant with digital control. The second crew, reproduce the same scenarios but with HPD available. The studio collects preliminary data in order to compare results, draw lesson learned from the experience to improve HPD design, and find solutions in terms of reducing human errors, human workload, and increase the availability of the plant. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Acoustic space occupancy: Combining ecoacoustics and lidar to model biodiversity variation and detection bias across heterogeneous landscapes

There is global interest in quantifying changing biodiversity in human-modified landscapes. Ecoacoustics may offer a promising pathway for supporting multi-taxa monitoring, but its scalability has been hampered by the sonic complexity of biodiverse ecosystems and the imperfect detectability of animal-generated sounds. The acoustic signature of a habitat, or soundscape, contains information about multiple taxa and may circumvent species identification, but robust statistical technology for characterizing community-level attributes is lacking. Here, we present the Acoustic Space Occupancy Model, a flexible hierarchical framework designed to account for detection artifacts from acoustic surveys in order to model biologically relevant variation in acoustic space use among community assemblages. We illustrate its utility in a biologically and structurally diverse Amazon frontier forest landscape, a valuable test case for modeling biodiversity variation and acoustic attenuation from vegetation density. We use complementary airborne lidar data to capture aspects of 3D forest structure hypothesized to influence community composition and acoustic signal detection. Our novel analytic framework permitted us to model both the assembly and detectability of soundscapes using lidar-derived estimates of forest structure. Our empirical predictions were consistent with physical models of frequency-dependent attenuation, and we estimated that the probability of observing animal activity in the frequency channel most vulnerable to acoustic attenuation varied by over 60%, depending on vegetation density. There were also large differences in the biotic use of acoustic space predicted for intact and degraded forest habitats, with notable differences in the soundscape channels predominantly occupied by insects. This study advances the utility of ecoacoustics by providing a robust modeling framework for addressing detection bias from remote audio surveys while preserving the rich dimensionality of soundscape data, which may be critical for inferring biological patterns pertinent to multiple taxonomic groups in the tropics. Our methodology paves the way for greater integration of remotely sensed observations with high-throughput biodiversity data to help bring routine, multi-taxa monitoring to scale in dynamic and diverse landscapes.

Airborne lidar↗

Long-term pattern and magnitude of soil carbon feedback to the climate system in a warming world

In a 26-year soil warming experiment in a mid-latitude hardwood forest, we documented changes in soil carbon cycling to investigate the potential consequences for the climate system. We found that soil warming results in a four-phase pattern of soil organic matter decay and carbon dioxide fluxes to the atmosphere, with phases of substantial soil carbon loss alternating with phases of no detectable loss. Several factors combine to affect the timing, magnitude, and thermal acclimation of soil carbon loss. These include depletion of microbially accessible carbon pools, reductions in microbial biomass, a shift in microbial carbon use efficiency, and changes in microbial community composition. Our results support projections of a long-term, self-reinforcing carbon feedback from mid-latitude forests to the climate system as the world warms.

Science & Technology - Other Topics↗

The analysis of polar clouds from AVHRR satellite data using pattern recognition techniques

The cloud cover in a set of summertime and wintertime AVHRR data from the Arctic and Antarctic regions was analyzed using a pattern recognition algorithm. The data were collected by the NOAA-7 satellite on 6 to 13 Jan. and 1 to 7 Jul. 1984 between 60 deg and 90 deg north and south latitude in 5 spectral channels, at the Global Area Coverage (GAC) resolution of approximately 4 km. This data embodied a Polar Cloud Pilot Data Set which was analyzed by a number of research groups as part of a polar cloud algorithm intercomparison study. This study was intended to determine whether the additional information contained in the AVHRR channels (beyond the standard visible and infrared bands on geostationary satellites) could be effectively utilized in cloud algorithms to resolve some of the cloud detection problems caused by low visible and thermal contrasts in the polar regions. The analysis described makes use of a pattern recognition algorithm which estimates the surface and cloud classification, cloud fraction, and surface and cloudy visible (channel 1) albedo and infrared (channel 4) brightness temperatures on a 2.5 x 2.5 deg latitude-longitude grid. In each grid box several spectral and textural features were computed from the calibrated pixel values in the multispectral imagery, then used to classify the region into one of eighteen surface and/or cloud types using the maximum likelihood decision rule. A slightly different version of the algorithm was used for each season and hemisphere because of differences in categories and because of the lack of visible imagery during winter. The classification of the scene is used to specify the optimal AVHRR channel for separating clear and cloudy pixels using a hybrid histogram-spatial coherence method. This method estimates values for cloud fraction, clear and cloudy albedos and brightness temperatures in each grid box. The choice of a class-dependent AVHRR channel allows for better separation of clear and cloudy pixels than does a global choice of a visible and/or infrared threshold. The classification also prevents erroneous estimates of large fractional cloudiness in areas of cloudfree snow and sea ice. The hybrid histogram-spatial coherence technique and the advantages of first classifying a scene in the polar regions are detailed. The complete Polar Cloud Pilot Data Set was analyzed and the results are presented and discussed.

Smith, William L.↗

Application health monitoring for extreme-scale resiliency using cooperative fault management

Resiliency is and will be a critical factor in determining scientific productivity on current and exascale supercomputers, and beyond. Applications oblivious to and incapable of handling transient soft and hard errors could waste supercomputing resources or, worse, yield misleading scientific insights. In this work, we introduce a novel application-driven silent error detection and recovery strategy based on application health monitoring. Our methodology uses application output that follows known patterns, as indicators of an application's health and knowledge that violation of these patterns could be indication of faults. Information from system monitors that report hardware and software health status is used to corroborate faults. Collectively, this information is used by a fault coordinator agent to take preventive and corrective measures by applying computational steering to an application between checkpoints. This cooperative fault management system uses the Fault Tolerance Backplane as a communication channel. The benefits of this framework are demonstrated with two real application case studies, molecular dynamics, and quantum chemistry simulations, on scalable clusters with simulated memory and I/O corruptions. Lastly, the developed approach is general and can be easily applied to other applications.

97 MATHEMATICS AND COMPUTING↗