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At least 19 records

Data for Attributing Differences of Solar-Induced Chlorophyll Fluorescence (SIF)-Gross Primary Production (GPP) Relationships between Two C4 Crops, Corn and Miscanthus

Information to characterize the solar-induced chlorophyll fluorescence (SIF)-gross primary production (GPP) relationship in C4 cropping systems remains limited. The annual C4 crop corn and perennial C4 crop miscanthus differ in phenology, canopy structure and leaf physiology. Investigating the SIF-GPP relationships in these species could deepen our understanding of SIF-GPP relationships within C4 crops. Using in situ canopy SIF and GPP measurements for both species along with leaf-level measurements, we found considerable differences in the SIF-GPP relationships between corn and miscanthus, with a stronger SIF-GPP relationship and higher slope of SIF-GPP observed in corn compared to miscanthus. These differences were mainly caused by leaf physiology. For miscanthus, high non-photochemical quenching (NPQ) under high light, temperature and water vapor deficit (VPD) conditions caused a large decline of fluorescence yield (ΦF), which further led to a SIF midday depression and weakened the SIF-GPP relationship. The larger slope in corn than miscanthus was mainly due to its higher GPP in mid-summer, largely attributed to the higher leaf photosynthesis and less NPQ. Our results demonstrated variation of the SIF-GPP relationship within C4 crops and highlighted the importance of leaf physiology in determining canopy SIF behaviors and SIF-GPP relationships.

Feedstock Production↗

Spectro-Microscopic Analysis of Soot Particle Composition and Source Attribution

Ambient soot particles significantly impact Earth’s radiative balance, human health, and atmospheric visibility. Their microstructural properties depend on formation and aging mechanisms, which vary by emission source and atmospheric processes. Hence, accurately identifying sources of soot enhances our understanding of their physicochemical properties and atmospheric implications. This study used a multi-modal approach to characterize and attribute sources of submicron soot particles collected in Israel during new particle formation events, biomass burning episodes, and background atmospheric conditions. Synchrotron-based X-ray microscopy was used to map soot (elemental carbon), organic carbon, and inorganic species. Implemented atomic force microscopy showed highly diverse phase states, with soot consistently exhibiting a solid-like phase. Automated µ-Raman analysis was subsequently performed on ~690 particles, identifying three soot classes based on spectral features corresponding to the "Defect" (D) and "Graphite" (G) bands of soot. We applied two-peak and five-peak fitting approaches to deconvolute the “Defect” peaks (D1, D2, D3, and D4) and G band from average Raman, revealing varying degrees of graphitic order. The degree of graphitic order was determined from metrics such as the D3 peak area, often observed when soot was internally mixed with organic material. Raman spectral features, along with temporal variations in particle classes contributions, suggest that Particle Type 1 corresponds to traffic related soot and Particle Type 2 to less graphitic soot from biomass burning, while Particle Type 3 is associated with more heterogeneous particulate representative of soot-OC mixtures emitted during new particle formation and biomass burning episodes.

Rivera-Adorno, Felipe (ORCID:0000000273557999)↗

Biomass Attributes and Attribute Modifications Affecting Systems and Methods to Separate and Fractionate

Chemical and physical heterogeneity in biomass feedstocks such as agricultural or forestry residues is due to substantial differences in plant tissue types. These differences can contribute significant challenges to handling, preprocessing, and conversion in biorefining processes. An understanding of this chemical and physical heterogeneity can be used to inform fractionation technologies that could facilitate more streamlined processing and potentially be employed to yield multiple co-product streams for a single feedstock. In this chapter, the motivation and scope of biomass fractionation is first outlined. Physical and chemical properties of biomass feedstocks, along with their distribution and diversity within plants, are next discussed with respect to how these differences can be exploited in a fractionation process. A summary of some of the key physical principles that allow for fractionation is next covered along with how these physical principles are exploited in equipment designs. Examples from the literature are briefly discussed that highlight how these approaches can be employed to achieve processing objectives. Several case studies on physical fractionation of corn stover and forestry residues are presented that illustrate how integrated fractionation processes could be employed. Lastly, prospects and potential economic drivers for adoption of biomass fractionation technologies are discussed.

09 BIOMASS FUELS↗

Biomass Attributes and Attribute Modifications Affecting Systems and Methods to Separate and Fractionate. In: Handbook of Biorefinery Research and Technology

Chemical and physical heterogeneity in biomass feedstocks such as agricultural or forestry residues is due to substantial differences in plant tissue types. These differences can contribute significant challenges to handling, preprocessing, and conversion in biorefining processes. An understanding of this chemical and physical heterogeneity can be used to inform fractionation technologies that could facilitate more streamlined processing and potentially be employed to yield multiple co-product streams for a single feedstock. In this chapter, the motivation and scope of biomass fractionation is first outlined. Physical and chemical properties of biomass feedstocks, along with their distribution and diversity within plants is next discussed with respect to how these differences can be exploited in a fractionation process. A summary of some of the key physical principles that allow for fractionation is next covered along with how these physical principles are exploited in equipment designs. Examples from the literature are briefly discussed that highlight how these approaches can be employed to achieve processing objectives. Several case studies on physical fractionation of corn stover and forestry residues are presented that illustrate how integrated fractionation processes could be employed. Finally, prospects and potential economic drivers for adoption of biomass fractionation technologies are discussed.

Biomass chemical properties↗

Granger causal inference for climate change attribution

Abstract Climate change detection and attribution (D&A) is concerned with determining the extent to which anthropogenic activities have influenced specific aspects of the global climate system. D&A fits within the broader field of causal inference, the collection of statistical methods that identify cause and effect relationships. There are a wide variety of methods for making attribution statements, each of which require different types of input data and focus on different types of weather and climate events and each of which are conditional to varying extents. Some methods are based on Pearl causality (direct experimental interference) while others leverage Granger (predictive) causality, and the causal framing provides important context for how the resulting attribution conclusion should be interpreted. However, while Granger-causal attribution analyses have become more common, there is no clear statement of their strengths and weaknesses relative to Pearl-causal attribution and no clear consensus on where and when Granger-causal perspectives are appropriate. In this prospective paper, we provide a formal definition for Granger-based approaches to trend and event attribution and a clear comparison with more traditional methods for assessing the human influence on extreme weather and climate events. Broadly speaking, Granger-causal attribution statements can be constructed quickly from observations and do not require computationally-intesive dynamical experiments. These analyses also enable rapid attribution, which is useful in the aftermath of a severe weather event, and provide multiple lines of evidence for anthropogenic climate change when paired with Pearl-causal attribution. Confidence in attribution statements is increased when different methodologies arrive at similar conclusions. Moving forward, we encourage the D&A community to embrace hybrid approaches to climate change attribution that leverage the strengths of both Granger and Pearl causality.

Risser, Mark D. (ORCID:0000000319561783)↗

Key environmental and production factors for understanding variation in switchgrass chemical attributes

Abstract Switchgrass ( Panicum virgatum L.) is a promising feedstock for bioenergy and bioproducts; however, its inherent variability in chemical attributes creates challenges for uniform conversion efficiencies and product quality. It is necessary to understand the range of variation and factors (i.e., field management, environmental) influencing chemical attributes for process improvement and risk assessment. The objectives of this study were to (1) examine the impact of nitrogen fertilizer application rate, year, and location on switchgrass chemical attributes, (2) examine the relationships among chemical attributes, weather and soil data, and (3) develop models to predict chemical attributes using environmental factors. Switchgrass samples from a field study spanning four locations including upland cultivars, one location including a lowland cultivar, and between three and six harvest years were assessed for glucan, xylan, lignin, volatiles, carbon, nitrogen, and ash concentrations. Using variance estimation, location/cultivar, nitrogen application rate, and year explained 65%–96% of the variation for switchgrass chemical attributes. Location/cultivar × year interaction was a significant factor for all chemical attributes indicating environmental‐based influences. Nitrogen rate was less influential. Production variables and environmental conditions occurring during the switchgrass field trials were used to successfully predict chemical attributes using linear regression models. Upland switchgrass results highlight the complexity in plant responses to growing conditions because all production and environmental variables had strong relationships with one or more chemical attributes. Lowland switchgrass was limited to observations of year‐to‐year environmental variability and nitrogen application rate. All explanatory variable categories were important for lowland switchgrass models but stand age and precipitation relationships were particularly strong. The relationships found in this study can be used to understand spatial and temporal variation in switchgrass chemical attributes. The ability to predict chemical attributes critical for conversion processes in a geospatial/temporal manner would provide state‐of‐the‐art knowledge for risk assessment in the bioenergy and bioproducts industry.

09 BIOMASS FUELS↗

Industry Initiated Core Safety Attributes for Human Spaceflight for the 7th IAASS Conference

Now that the NASA Commercial Crew Program (CCP) is beginning its full certification contract for crew transportation to the International Space Station (ISS), is it time for industry to embrace a minimum set of core safety attributes? Those attributes can then be evolved into an industry-led set of basic safety standards and requirements. After 50 years of human space travel sponsored by governments, there are two basic conditions that now exist within the international space industry. The first, there is enough of a space-faring history to encourage the space industry to design, develop and operate human spaceflight systems without government contracts for anything other than services. Second, industry is capable of defining and enforcing a set of industry-based safety attributes and standards for human spaceflight to low-Earth orbit (LEO). This paper will explore both of these basic conditions with a focus on the safety attributes and standards. In the United States, the Federal Aviation Administration (FAA) is now starting to dialogue with industry about the basic safety principles and attributes needed for potential future regulatory oversight. This process is not yet formalized and will take a number of years once approval is given to move forward. Therefore, throughout the next few years, it is an excellent time and opportunity for industry to collaborate together and develop the core set of attributes and standards. As industry engages and embraces a common set of safety attributes, then government agencies, like the FAA and NASA can use that industry-based product to strengthen their efforts on a safe commercial spaceflight foundation for the future. As the commercial space industry takes the lead role in establishing core safety attributes, and then enforcing those attributes, the entire planet can move away from governmental control of design and development and let industry expand safe and successful space operations in LEO. At that point the governmental agencies can focus on oversight of the industries' defined standards and enforcement for common welfare of the space-faring populous and overall public safety.

crew transportation↗

Climate change and federal aid disbursements after Hurricane Harvey: an extreme event attribution analysis

The role climate change plays in increasing the burden placed on governments and insurers to pay for recovery has not been extensively explored and is the focus of this study. This study examines the impacts of climate change attributed flooding on federal disaster aid disbursement in Harris County, Texas following Hurricane Harvey in 2017. Our approach uses flood models to estimate the amount of flood damages attributable and not attributable to climate change under two climate change attribution scenarios from peer reviewed studies: 20% and 38% increases in rainfall associated with the hurricane due to climate change. These estimates are combined with census tract-level disbursement data for FEMA’s National Flood Insurance Program (NFIP) and the Individual Assistance (IA) part of the Individuals and Households Program. We employ spatial lag regression models with direct and spatial spillover effects to analyze the relationship between a tract’s flood damages—both attributed and not attributed to climate change—and federal disaster aid. We find that both types of flood damage shape federal aid disbursements, but that climate change attributed damages tend to have larger effect sizes (elasticities) especially for IA. Specifically, for a 1% increase in additional climate change attributed damages per household in a census tract (under the 20% scenario), expected NFIP levels in that census tract are 0.26% higher and IA levels are 0.3% higher. Implications center on federal funding in an era of climate change.

FEMA↗

Attributable human-induced changes in the magnitude of flooding in the Houston, Texas region during Hurricane Harvey

Abstract The human influence on precipitation during tropical cyclones due to the global warming is now well documented in the literature. Several studies have found increases in Hurricane Harvey’s total precipitation over the Greater Houston area ranging from the Clausius-Clapeyron limit of 7% to as much as 38% locally. Here we use a hydraulic model to translate these attribution statements about precipitation to statements about the resultant flooding and associated damages. We find that while the attributable increase in the total volume of flood waters is the same as the attributable increase in precipitation, the attributable increase in the total area of the flood is less. However, we also find that in the most heavily flooded parts of Houston, the local attributable increases in flood area and volume are substantially larger than the increase in total precipitation. The results of this storyline attribution analysis of the Houston flood area are used to make an intuitive best estimate of the cost of Hurricane Harvey attributable to anthropogenic global warming as thirteen billion US dollars.

54 ENVIRONMENTAL SCIENCES↗

Cervical Precancers and Cancers Attributed to HPV Types by Race and Ethnicity: Implications for Vaccination, Screening, and Management

Abstract Background Racial and ethnic variations in attribution of cervical precancer and cancer to human papillomavirus (HPV) types may result in different HPV vaccine protection, screening test coverage, and clinical management. Methods Pooling data from 7 US studies, we calculated the proportional attribution of precancers and cancers to HPV types using HPV DNA typing from diagnosis. All statistical tests were 2-sided. Results For all racial and ethnic groups, most cases of cervical intraepithelial neoplasia grade 3 (CIN3) (84.2%-90.8% of 5526) and squamous cell carcinoma (SCC) (90.4%-93.8% of 1138) were attributed to types targeted by the 9-valent vaccine. A higher proportion of CIN3s were attributed to nonvaccine HPV types among non-Hispanic Black women (15.8%) compared with non-Hispanic Asian or Pacific Islander (9.7%; P = .002), non-Hispanic White (9.2%; P < .001), and Hispanic (11.3%; P = .004) women. The proportion of SCCs attributed to 9-valent types was similar by race and ethnicity (P = .80). A higher proportion of CIN3s were attributed to nonvaccine HPV35 among non-Hispanic Black (9.0%) compared with non-Hispanic Asian or Pacific Islander (2.2%), non-Hispanic White (2.5%), and Hispanic (3.0%; all P < .001) women. Compared with CIN3, the proportion of SCCs attributed to HPV35 among non-Hispanic Black women (3.2%) was lower and closer to other groups (0.3%-2.1%; P = .70). Conclusion The 9-valent HPV vaccine will prevent nearly all cervical precancers and invasive cancers among major racial and ethnic groups in the United States. Adding HPV35 to vaccines could prevent a small percentage of CIN3s and SCCs, with greater potential impact for CIN3s among Black women. HPV screening tests target high-risk HPV types, including HPV35. Future genotyping triage strategies could consider the importance of HPV35- and other HPV16-related types.

Mix, Jacqueline (ORCID:0000000164187706)↗

Attributing Tropical Cyclogenesis to Equatorial Waves in the Western North Pacific

The direct influences of equatorial waves on the genesis of tropical cyclones are evaluated. Tropical cyclogenesis is attributed to an equatorial wave when the filtered rainfall anomaly exceeds a threshold value at the genesis location. For an attribution threshold of 3 mm/day, 51% of warm season western North Pacific tropical cyclones are attributed to tropical depression (TD)-type disturbances, 29% to equatorial Rossby waves, 26% to mixed Rossby-Gravity waves, 23% to Kelvin waves, 13% to the Madden-Julian oscillation (MJO), and 19% are not attributed to any equatorial wave. The fraction of tropical cyclones attributed to TD-type disturbances is consistent with previous findings. Past studies have also demonstrated that the MJO significantly modulates tropical cyclogenesis, but fewer storms are attributed to the MJO than any other wave type. This disparity arises from the difference between attribution and modulation. The MJO produces broad regions of favorable conditions for cyclogenesis, but the MJO alone might not determine when and where a storm will develop within these regions. Tropical cyclones contribute less than 17% of the power in any portion of the equatorial wave spectrum because tropical cyclones are relatively uncommon equatorward of 15deg latitude. In regions where they are active, however, tropical cyclones can contribute more than 20% of the warm season rainfall and up to 50% of the total variance. Tropical cyclone-related anomalies can significantly contaminate wave-filtered precipitation at the location of genesis. To mitigate this effect, the tropical cyclone-related rainfall anomalies were removed before filtering in this study.

Schreck, Carl J., III↗

Generative attribute optimization

A generative attribute optimization (“GAO”) system facilitates understanding of effects of changes of attribute values of an object on a characteristic of the object and automatically identifying attribute values to achieve a desired result for the characteristic. The GAO system trains a generator (encoder and decoder) using an attribute generative adversarial network. The GAO model includes the trained generator and a separately trained predictor model. The GAO model inputs an input image and modified attribute values and employs the encoder and the decoder to generate a modified image that is the input image modified based on the modified attribute values. The GAO model then employs the predictor model to that inputs the modified image and generate a prediction of a characteristic of the modified image. The GAO system may employ an optimizer to modify the attribute values until an objective based on the desired result is achieved.

97 MATHEMATICS AND COMPUTING↗

On the attribution of the impacts of extreme weather events to anthropogenic climate change

Investigations into the role of anthropogenic climate change in extreme weather events are now starting to extend into analysis of anthropogenic impacts on non-climate (e.g. socio-economic) systems. However, care needs to be taken when making this extension, because methodological choices regarding extreme weather attribution can become crucial when considering the events’ impacts. The fraction of attributable risk (FAR) method, useful in extreme weather attribution research, has a very specific interpretation concerning a class of events, and there is potential to misinterpret results from weather event analyses as being applicable to specific events and their impact outcomes. Using two case studies of meteorological extremes and their impacts, we argue that FAR is not generally appropriate when estimating the magnitude of the anthropogenic signal behind a specific impact. Attribution assessments on impacts should always be carried out in addition to assessment of the associated meteorological event, since it cannot be assumed that the anthropogenic signal behind the weather is equivalent to the signal behind the impact because of lags and nonlinearities in the processes through which the impact system reacts to weather. Whilst there are situations where employing FAR to understand the climate change signal behind a class of impacts is useful (e.g. ‘system breaking’ events), more useful results will generally be produced if attribution questions on specific impacts are reframed to focus on changes in the impact return value and magnitude across large samples of factual and counterfactual climate model and impact simulations. We advocate for constant interdisciplinary collaboration as essential for effective and robust impact attribution assessments.

54 ENVIRONMENTAL SCIENCES↗

A Machine Learning Method for the Forensics Attribution of Separated Plutonium

Plutonium (Pu) source attribution would be a powerful tool to support nuclear nonproliferation efforts. This capability to find the source of a Pu sample would act as a deterrent to smuggling efforts, and also help regulatory agencies verify declared nuclear activities. Work at Texas A&M University yielded a nuclear forensics methodology, which is capable of determining separated Pu’s reactor of origin, fuel burnup, and the time since irradiation (TSI)—three parameters of interest. The methodology used a set of ten intra-element isotopic ratios found in separated Pu, which was compared to a library of isotopic ratio values produced using neutronics simulations for reactors of interest. By calculating the probability that unknown Pu sample’s isotopic ratio set matched a set in the library, the methodology could predict the three parameters of interest of the sample. One shortcoming of this methodology was an inability to correctly attribute spoofed Pu, where Pu sourced from two different reactors or two different fuel burnup levels are mixed. A new methodology to rectify this vulnerability using machine learning (ML) technique is developed, instead of the maximum likelihood calculation previously used and the results are satisfactory. The ML approach leverages the existing simulated data for training the algorithm, but use them efficiently by only using intra-element isotope ratios that contribute to the attribution one of the three parameters at a time. Previously, all isotope ratios were used to attribute all three parameters together. The new methodology attributes the Pu parameters in three steps, one for each parameter, rather than resolving all of the three parameters simultaneously like the previous maximum likelihood approach. First, a support vector machine classifier with a set of seven isotopic ratios finds the reactor of origin and a set of regression models trained using gaussian process predicts the burnup with a different set of seven isotopes. Finally, TSI is calculated analytically using decay equations. Thus far, the new methodology is capable of attributing pure Pu samples and has been validated using experimental data. The next step will to be augment the classifier training data set with spoofed Pu data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The challenges of detecting and attributing ocean acidification impacts on marine ecosystems

Abstract A substantial body of research now exists demonstrating sensitivities of marine organisms to ocean acidification (OA) in laboratory settings. However, corresponding in situ observations of marine species or ecosystem changes that can be unequivocally attributed to anthropogenic OA are limited. Challenges remain in detecting and attributing OA effects in nature, in part because multiple environmental changes are co-occurring with OA, all of which have the potential to influence marine ecosystem responses. Furthermore, the change in ocean pH since the industrial revolution is small relative to the natural variability within many systems, making it difficult to detect, and in some cases, has yet to cross physiological thresholds. The small number of studies that clearly document OA impacts in nature cannot be interpreted as a lack of larger-scale attributable impacts at the present time or in the future but highlights the need for innovative research approaches and analyses. We summarize the general findings in four relatively well-studied marine groups (seagrasses, pteropods, oysters, and coral reefs) and integrate overarching themes to highlight the challenges involved in detecting and attributing the effects of OA in natural environments. We then discuss four potential strategies to better evaluate and attribute OA impacts on species and ecosystems. First, we highlight the need for work quantifying the anthropogenic input of CO2 in coastal and open-ocean waters to understand how this increase in CO2 interacts with other physical and chemical factors to drive organismal conditions. Second, understanding OA-induced changes in population-level demography, potentially increased sensitivities in certain life stages, and how these effects scale to ecosystem-level processes (e.g. community metabolism) will improve our ability to attribute impacts to OA among co-varying parameters. Third, there is a great need to understand the potential modulation of OA impacts through the interplay of ecology and evolution (eco–evo dynamics). Lastly, further research efforts designed to detect, quantify, and project the effects of OA on marine organisms and ecosystems utilizing a comparative approach with long-term data sets will also provide critical information for informing the management of marine ecosystems.

Fisheries↗

The Detection and Attribution Model Intercomparison Project (DAMIP v2.0) contribution to CMIP7

The first version of the Detection and Attribution Model Intercomparison Project (DAMIP v1.0) coordinated key simulations exploring the role of individual forcings in past, current and future climate as part of the Coupled Model Intercomparison Project, Phase 6 (CMIP6). The simulations have been used extensively in the literature for detection and attribution of long-term changes, constraining projections of climate change, attributing extreme events and understanding drivers of past and future simulated climate changes. Attribution studies using DAMIP v1.0 simulations underpinned prominent assessments of human-induced warming in the Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report. Here, we describe the set of DAMIP v2.0 simulations, proposed for the next phase of CMIP, CMIP7. Detection and attribution studies rely on pre-industrial control simulations and historical simulations, which will be part of the Diagnostic, Evaluation and Characterization of Klima (DECK) set of simulations for CMIP7. In addition, we identify the three highest-priority single-forcing experiments for CMIP7 to be run as “Assessment Fast Track” simulations in support of the Seventh Assessment Report of the IPCC: simulations with natural forcings only, anthropogenic well-mixed greenhouse gases only and anthropogenic aerosols only. Beyond this, the DAMIP v2.0 experimental design includes full-column ozone-only simulations and land-use-only simulations, such that the set of individual forcing experiments, when these are considered together, represents the full set of historical forcings. While concentration-driven simulations are prioritised for attribution, emissions-driven versions of the DAMIP experiments are also proposed to support understanding of the influence of carbon-cycle feedbacks on the simulated responses to individual forcings.

Gillett, Nathan P. [Environment and Climate Change↗

Quality Attributes for Mission Flight Software: A Reference for Architects

In the international standards for architecture descriptions in systems and software engineering (ISO/IEC/IEEE 42010), "concern" is a primary concept that often manifests itself in relation to the quality attributes or "ilities" that a system is expected to exhibit - qualities such as reliability, security and modifiability. One of the main uses of an architecture description is to serve as a basis for analyzing how well the architecture achieves its quality attributes, and that requires architects to be as precise as possible about what they mean in claiming, for example, that an architecture supports "modifiability." This paper describes a table, generated by NASA's Software Architecture Review Board, which lists fourteen key quality attributes, identifies different important aspects of each quality attribute and considers each aspect in terms of requirements, rationale, evidence, and tactics to achieve the aspect. This quality attribute table is intended to serve as a guide to software architects, software developers, and software architecture reviewers in the domain of mission-critical real-time embedded systems, such as space mission flight software.

Software architecture↗

Interactive Visual Study of Multiple Attributes Learning Model of X-Ray Scattering Images

Existing interactive visualization tools for deep learning are mostly applied to the training, debugging, and refinement of neural network models working on natural images. However, visual analytics tools are lacking for the specific application of x-ray image classification with multiple structural attributes. In this paper, we present an interactive system for domain scientists to visually study the multiple attributes learning models applied to x-ray scattering images. It allows domain scientists to interactively explore this important type of scientific images in embedded spaces that are defined on the model prediction output, the actual labels, and the discovered feature space of neural networks. Users are allowed to flexibly select instance images, their clusters, and compare them regarding the specified visual representation of attributes. The exploration is guided by the manifestation of model performance related to mutual relationships among attributes, which often affect the learning accuracy and effectiveness. The system thus supports domain scientists to improve the training dataset and model, find questionable attributes labels, and identify outlier images or spurious data clusters. Case studies and scientists feedback demonstrate its functionalities and usefulness.

97 MATHEMATICS AND COMPUTING↗