Conventional Metrics Research Articles

229 Quantitative Imaging Biomarkers for Risk Stratification of Intracranial Aneurysms

INTRODUCTION: Aneurysm wall enhancement (AWE) has emerged as a potential imaging biomarker for risk stratification of Intracranial aneurysms (IAs). Herein, the contrast-enhanced MRI (CE-MRI) exhibits markedly higher intensity on the IA sac as compared to the non-enhanced MRI (NE-MRI). However, currently it is assessed subjectively by clinicians which can introduce subjectivity. METHODS: We retrospectively collected 105 IAs with their NE-MRI, CE-MRI and Time-of-flight angiography images. IAs were classified as high or low risk if they had PHASES >5 or ELAPSS >20. We then identified the significantly different RFs and used them to build a logistic regression model for identifying high-risk IAs. We also compared the performance of this model with traditional AWE metrics like CCRatio (Average intensity on the IA sac normalized by the corpus callosum intensity) and CRStalk (Average intensity on the IA sac normalized by the pituitary stalk intensity). RESULTS: We found 35 high-risk IAs in the cohort and identified 183 RFs that were significantly different between them. After eliminating collinear RFs, we used 52 RFs to build our final model. We observed that the RF based model vastly outperformed the conventional metrics. In the testing set, we observed that the LR model had a higher accuracy as compared to conventional metrics. We observed that non-uniformity in pre-contrast MRI, homogeneity in post-contrast MRI and the difference in gray level non-uniformity had the highest odds ratios in the LR model. CONCLUSIONS: RFs from pre- and post-contrast MRI could identify high-risk IAs better than conventional metrics. This model in combination with 3D visualization could aid in better visualization of VWE and better risk stratification of IAs.

Relationship of Perivascular Space Markers With Incident Dementia in Cerebral Small Vessel Disease.

Recent studies, using diffusion tensor image analysis along the perivascular space (DTI-ALPS), suggest impaired perivascular space (PVS) function in cerebral small vessel disease, but they were cross-sectional, making inferences on causality difficult. We determined associations between impaired PVS, measured using DTI-ALPS and PVS volume, and cognition and incident dementia. In patients with lacunar stroke and confluent white matter hyperintensities, without dementia at baseline, recruited prospectively in a single center, magnetic resonance imaging was performed annually for 3 years, and cognitive assessments, including global, memory, executive function, and processing speed, were performed annually for 5 years. We determined associations between DTI-ALPS and PVS volume with cerebral small vessel disease imaging markers (white matter hyperintensity volume, lacunes, and microbleeds) at baseline and with changes in imaging markers. We determined whether DTI-ALPS and PVS volume at baseline and change over 3 years predicted incident dementia. Analyses were controlled for conventional diffusion tensor image metrics using 2 markers (median mean diffusivity [MD] and peak width of skeletonized MD) and adjusted for age, sex, and vascular risk factors. A total of 120 patients, mean age 70.0 years and 65.0% male, were included. DTI-ALPS declined over 3 years, while no change in PVS volume was found. Neither DTI-ALPS nor PVS volume was associated with cerebral small vessel disease imaging marker progression. Baseline DTI-ALPS was associated with changes in global cognition (β=0.142, P=0.032), executive function (β=0.287, P=0.027), and long-term memory (β=0.228, P=0.027). Higher DTI-ALPS at baseline predicted a lower risk of dementia (hazard ratio, 0.328 [0.183-0.588]; P<0.001), and this remained significant after including median MD as a covariate (hazard ratio, 0.290 [0.139-0.602]; P<0.001). Change in DTI-ALPS predicted dementia conversion (hazard ratio, 0.630 [0.428-0.964]; P=0.048), but when peak width of skeletonized MD and median MD were entered as covariates, the association was not significant. There was no association between baseline PVS volume, or PVS change over 3 years, and conversion to dementia. DTI-ALPS predicts future dementia risk in patients with lacunar strokes and confluent white matter hyperintensities. However, the weakening of the association between change in DTI-ALPS and incident dementia after controlling for peak width of skeletonized MD and median MD suggests part of the signal may represent conventional diffusion tensor image metrics. PVS volume is not a predictor of future dementia risk.

How About Bug-Triggering Paths? - Understanding and Characterizing Learning-Based Vulnerability Detectors

Machine learning and its promising branch deep learning have proven to be effective in a wide range of application domains. Recently, several efforts have shown success in applying deep learning techniques for automatic vulnerability discovery, as alternatives to traditional static bug detection. In principle, these learning-based approaches are built on top of classification models using supervised learning. Depending on the different granularities to detect vulnerabilities, these approaches rely on learning models which are typically trained with well-labeled source code to predict whether a program method, a program slice, or a particular code line contains a vulnerability or not. The effectiveness of these models is normally evaluated against conventional metrics including precision, recall and F1 score. In this paper, we show that despite yielding promising numbers, the above evaluation strategy can be insufficient and even misleading when evaluating the effectiveness of current learning-based approaches. This is because the underlying learning models only produce the classification results or report individual/isolated program statements, but are unable to pinpoint bug-triggering paths, which is an effective way for bug fixing and the main aim of static bug detection. Our key insight is that a program method or statement can only be stated as vulnerable in the context of a bug-triggering path. In this work, we systematically study the gap between recent learning-based approaches and conventional static bug detectors in terms of fine-grained metrics called BTP metrics using bug-triggering paths. We then characterize and compare the quality of the prediction results of existing learning-based detectors under different granularities. Finally, our comprehensive empirical study reveals several key issues and challenges in developing classification models to pinpoint bug-triggering paths and calls for more advanced learning-based bug detection techniques.

Multi-objective calibration of vertical-axis wind turbine controllers: balancing aero-servo-elastic performance and noise

Abstract. Vertical-axis wind turbines (VAWTs) are considered promising solutions for urban wind energy generation due to their design, low maintenance costs, and reduced noise and visual impact compared to horizontal-axis wind turbines (HAWTs). However, deploying these turbines close to densely populated urban areas often triggers considerable local opposition to wind energy projects. Among the primary concerns raised by communities is the issue of noise emissions. Noise annoyance should be considered in the design and decision-making process to foster the social acceptance of VAWTs in urban environments. At the same time, maximising the operational efficiency of VAWTs in terms of power generation and actuation effort is equally important. This paper balances noise and aero-servo-elastic performance by formulating and solving a multi-objective optimisation problem from a controller calibration perspective. Psychoacoustic annoyance is taken as a novel indicator for the noise objective by providing a more reliable estimate of the human perception of wind turbine noise than conventional sound metrics. The computation of the psychoacoustic annoyance metric is made feasible by integrating it with an accurate and computationally efficient low-fidelity noise prediction model. For optimisation, an advanced partial-load control scheme – often used in industrial turbines – is considered, with the Kω2 controller as a baseline for comparison. Optimal solutions balancing the defined objectives are identified using a multi-criteria decision-making method (MCDM) and are subsequently assessed using a frequency-domain controller analysis framework and mid-fidelity time-domain aero-servo-elastic simulations. The MCDM results indicate the potential application of this controller in small-scale urban VAWTs to attain power gains of up to 39 % on one side and to trade off a reduction in actuation effort of up to 25 % at the cost of only a 2 % power decrease and a 6 % increase in psychoacoustic annoyance on the other side compared to the baseline. These findings confirm the flexible structure of the optimally calibrated wind speed estimator and tip-speed ratio (WSE–TSR) tracking controller, effectively balancing aero-servo-elastic performance with noise emissions and marking the first instance of integrating residential concerns into the decision-making process.

Cross-Subject Brain–Computer Interfaces with Joint Distribution Alignment

Distributions of electroencephalogram (EEG) data vary greatly across different subjects. It is a very important issue how to generalize models across subjects. In this paper, an algorithm is proposed to build high-performance cross-subject motor-imagery brain–computer interfaces (BCIs) for a new subject. First, a novel distance metric is proposed to quantify the joint distribution discrepancy (JDD) between data from different subjects. It gives better evaluations for discrepancies between different distributions than conventional probabilistic metrics. Moreover, it can be extended to design many novel algorithms. Second, a support vector machine combined with JDD (JDMSVM) is proposed for cross-subject classification. For dataset dataIVa, the JDMSVM runs best under 9 out of 15 situations and averagely outperforms counterparts by 10.1%, 9.5%, 3.2% and 1.7%, respectively. For GigaDataset, JDMSVM runs best under 8 of 12 conditions. It averagely outperforms its counterparts by 10.4%, 5.3%, 2.7% and 2.4%, respectively. The experiments demonstrate that the proposed algorithm is effective and competitive for cross-subject BCI.

Examining the Sustainability Report, Financial Performance, and Value of Mining Companies in Indonesia

This study employs a quantitative approach to explore the intricate interplay among Sustainability Reports, Financial Performance (measured by Return on Assets - ROA), and Firm Value (quantified by Tobin's Q) in Indonesia's dynamic mining industry. Employing purposive sampling, data from 75 samples encompassing 25 mining businesses listed on the Indonesia Stock Exchange (IDX) is examined over the 2020-2022 period. Utilizing statistical analysis, the study employs the Partial Least Squares (PLS) data processing application for partial regression analysis. The findings highlight a substantial and favorable impact of Sustainability Reports on Firm Value, underscoring the growing acknowledgment within Indonesian mining firms of the pivotal role played by both financial and non-financial disclosures. Intriguingly, the study uncovers that Financial Performance, as gauged by ROA, lacks a discernible influence on Firm Value. This nuanced insight suggests a shifting landscape where stakeholders increasingly prioritize comprehensive reporting beyond conventional financial metrics. The research sheds light on the evolving nature of the Indonesian mining sector, emphasizing companies' recognition of the significance of transparent reporting practices. These revelations align with global sustainable development goals, emphasizing the central role played by mining companies in advancing these objectives. In navigating this complex dynamic, the study underscores the crucial role of Sustainability Reports in shaping perceptions and values of mining firms in Indonesia.

Beyond Conventional Metrics: Alternative Middle-Class Choice among Chinese Homeschooling Families

Sociologists have extensively studied the prevalence of intensive parenting among middle-class families as a response to uncertainties about maintaining their privileged class status. Most studies, however, have focused on traditional school systems, which overlooks the full spectrum of middle-class parenting values and practices, particularly those beyond mainstream schooling. To address this gap, this study explores an alternative middle-class choice for raising and educating children through the lens of Chinese homeschooling. Drawing on in-depth interviews with middle-class parents from 30 Chinese families of school-age children being homeschooled in Taipei and Hong Kong, this study investigates the paradoxes and ambiguities that arose as the parents navigated and negotiated competing values for their children. The findings reveal that the parents mobilised their cultural repertoires to seek a coherent narrative that made sense of and justified their homeschooling goals and practices in the Chinese context.

The need for better metrics for floor-tile topography: Conventional metrics correlate only modestly with shoe-floor friction

Roughness metrics measured with stylus profilometry are commonly used to explain a floor’s friction performance, yet these metrics inconsistently predict shoe-floor friction. While strong correlations have been shown for systematically modified flooring, the goal of this study is to address a gap regarding the predictive ability of these metrics across heterogeneous porcelain flooring products. The predictive ability of four roughness metrics on oily friction performance was assessed using 23 floors and 4 shoe designs. Roughness was moderately correlated with friction (r ranged from 0.374 to 0.760). These results are a reference point for future studies that aim to improve predictions using novel surface characterization approaches that include multiple scales.

Selecting the optimal gridded climate dataset for Nigeria using advanced time series similarity algorithms.

Choosing a suitable gridded climate dataset is a significant challenge in hydro-climatic research, particularly in areas lacking long-term, reliable, and dense records. This study used the most common method (Perkins skill score (PSS)) with two advanced time series similarity algorithms, short time series distance (STS), and cross-correlation distance (CCD), for the first time to evaluate, compare, and rank five gridded climate datasets, namely, Climate Research Unit (CRU), TERRA Climate (TERRA), Climate Prediction Center (CPC), European Reanalysis V.5 (ERA5), and Climatologies at high resolution for Earth's land surface areas (CHELSA), according to their ability to replicate the in situ rainfall and temperature data in Nigeria. The performance of the methods was evaluated by comparing the ranking obtained using compromise programming (CP) based on four statistical criteria in replicating in situ rainfall, maximum temperature, and minimum temperature at 26 locations distributed over Nigeria. Both methods identified CRU as Nigeria's best-gridded climate dataset, followed by CHELSA, TERRA, ERA5, and CPC. The integrated STS values using the group decision-making method for CRU rainfall, maximum and minimum temperatures were 17, 10.1, and 20.8, respectively, while CDD values for those variables were 17.7, 11, and 12.2, respectively. The CP based on conventional statistical metrics supported the results obtained using STS and CCD. CRU's Pbias was between 0.5 and 1; KGE ranged from 0.5 to 0.9; NSE ranged from 0.3 to 0.8; and NRMSE between - 30 and 68.2, which were much better than the other products. The findings establish STS and CCD's ability to evaluate the performance of climate data by avoiding the complex and time-consuming multi-criteria decision algorithms based on multiple statistical metrics.

Toward Cancer Chemoprevention: Mathematical Modeling of Chemically Induced Carcinogenesis and Chemoprevention

Cancer, which is currently rated as the second-leading cause of mortality across the globe, is one of the most hazardous disease groups that has plagued humanity for centuries. The experiments presented here span over two decades and were conducted on a specific species of mice, aiming to neutralize a highly carcinogenic agent by altering its chemical structure when combined with certain compounds. A plethora of growth models, each of which makes use of distinctive qualities, are utilized in the investigation and explanation of the phenomena of chemically induced oncogenesis and prevention. The analysis ultimately results in the formalization of the process of locating the growth model that provides the best descriptive power based on predefined criteria. This is accomplished through a methodological workflow that adopts a computational pipeline based on the Levenberg–Marquardt algorithm with pioneering and conventional metrics as well as a ruleset. The developed process simplifies the investigated phenomena as the parameter space of growth models is reduced. The predictability is proven strong in the near future (i.e., a 0.61% difference between the predicted and actual values). The parameters differentiate between active compounds (i.e., classification results reach up to 96% in sensitivity and other performance metrics). The distribution of parameter contribution complements the findings that the logistic growth model is the most appropriate (i.e., 44.47%). In addition, the dosage of chemicals is increased by a factor of two for the next round of trials, which exposes parallel behavior between the two dosages. As a consequence, the study reveals important information on chemoprevention and the cycles of cancer proliferation. If developed further, it might lead to the development of nutritional supplements that completely inhibit the expansion of cancerous tumors. The methodology provided can be used to describe other phenomena that progress over time and it has the power to estimate future results.

Autoencoder based image quality metric for modelling semantic noise in semantic communications

AbstractSemantic communication has attracted significant attention as a key technology for emerging 6G communications. This paper proposes an autoencoder based image quality metric to quantify the semantic noise. An autoencoder is initially trained with the reference image to generate the encoder‐decoder model and calculate its Latent Vector Space (LVS) and then a semantically generated/received image is inserted into the same autoencoder to create the corresponding LVS. Finally, both LVS are used to define the Euclidean space to calculate the mean square error between two LVS. Results indicate that the proposed model has a high correlation coefficient of 88% with subjective quality assessment and commonly used conventional metrics completely failed in semantic noise modelling.

Heart Rate Variability as a Tool for Seizure Prediction: A Scoping Review

The most critical burden for People with Epilepsy (PwE) is represented by seizures, the unpredictability of which severely impacts quality of life. The design of real-time warning systems that can detect or even predict ictal events would enhance seizure management, leading to high benefits for PwE and their caregivers. In the past, various research works highlighted that seizure onset is anticipated by significant changes in autonomic cardiac control, which can be assessed through heart rate variability (HRV). This manuscript conducted a scoping review of the literature analyzing HRV-based methods for detecting or predicting ictal events. An initial search on the PubMed database returned 402 papers, 72 of which met the inclusion criteria and were included in the review. These results suggest that seizure detection is more accurate in neonatal and pediatric patients due to more significant autonomic modifications during the ictal transitions. In addition, conventional metrics are often incapable of capturing cardiac autonomic variations and should be replaced with more advanced methodologies, considering non-linear HRV features and machine learning tools for processing them. Finally, studies investigating wearable systems for heart monitoring denoted how HRV constitutes an efficient biomarker for seizure detection in patients presenting significant alterations in autonomic cardiac control during ictal events.

Towards a generic model evaluation metric for non-normally distributed measurements in water quality and ecosystem models

Model evaluation is a crucial process in model development and quantified model evaluation metrics play a pivotal role in model calibration and validation. However, in current water quality and ecosystem models, conventional model evaluation metrics are derived from hydrological models and often overlook the non-normal distribution of water quality and ecological state variables. In this study, we proposed a series of metrics that consider non-normal distributions by modifying components of the Kling-Gupta efficiency. Subsequently, we tested the existing metrics and newly proposed metrics using four different synthetic datasets and the actual simulation case of total phosphorus, chlorophyll a, and dissolved oxygen concentrations. The results demonstrate that the newly proposed metric, Fu-Zhang efficiency, which replaces the ratio of standard deviations with the ratio of interquartile ranges to measure dispersion similarity, is more suitable for evaluating simulation results with lots of outliers in the measurements. Our study reveals the hidden perils in conventional integrated model evaluation metrics of water quality and ecosystem models and calls for the development of comprehensive and feasible quantitative evaluation frameworks to drive the next paradigm shift.

Color Capability of RGB Laser Displays

AbstractThe high color saturation of laser light sources suggests that RGB laser displays should have superior color reproduction, although standardized gamut rings and ISO test images reveal this is not always true, and conventional chromaticity gamut area metrics must be abandoned.

Pedagogy of Relation and Educational Communities

The paper challenges the efficacy of traditional educational reforms focused on accountability, choice, and technology, proposing that the essence of education lies in the relational dynamics between teachers and students. The author explores the concept of the relational self, arguing that education involves the development of diverse relational selves through various life stages. The author critiques dominant educational theories for neglecting the fundamental caregiver-child relationship, emphasizing the need for educational relationships that balance support and challenge. The text advocates for a new dimension of educational accountability that measures relational well-being, calling for a paradigm shift to recognize the importance of relational dynamics in educational outcomes and student experiences. The work presents a case for redefining educational success beyond conventional metrics, underscoring the transformative power of relational pedagogy.

Uzaklık Metriklerinin Performansı Üzerine Ampirik Bir Çalışma

Metrics are used to measure the distance, similarity, or dissimilarity between two points in a metric space. Metric learning algorithms perform the finding task of data points that are closest or furthest to a query point in m-dimensional metric space. Some metrics take into account the assumption that the whole dimensions are of equal importance, and vice versa. However, this assumption does not incorporate a number of real-world problems that classification algorithms tackle. In this research, the existing information gain, the information gain ratio, and some well-known conventional metrics have been compared by each other. The 1-Nearest Neighbor algorithm taking these metrics as its meta-parameter has been applied to forty-nine benchmark datasets. Only the accuracy rate criterion has been employed in order to quantify the performance of the metrics. The experimental results show that each metric is successful on datasets corresponding to its own domain. In other words, each metric is favorable on datasets overlapping its own assumption. In addition, there also exists incompleteness in classification tasks for metrics just like there is for learning algorithms.

Reflection-enabled HDOP-weighted underwater acoustic passive localization with a small aperture array

This paper addresses the localization problem of a noncooperative source in the multipath-rich environment. Unlike conventional schemes that only use the line-of-sight (LOS) and the once-surface-reflected (S1B0) path, the proposed scheme utilizes the complete spatial diversity of all multipaths by quantifying their positioning confidence. In the proposed scheme, all the measurement metrics (angle, relative delay and amplitude) extracted from multipath arrival structure, are combined to achieve localization with a small aperture array.Specifically, we first propose an algorithm for extracting multipath arrival structure based on spatial time-frequency analysis of underwater multipath signals. In this algorithm, each path is iteratively extracted, and the extraction error is close to the Cramér–Rao lower bound (CRLB). Then, the obtained CRLB is used to derive horizontal dilution of precision (HDOP) to quantify the positioning confidence of each path. Finally, the source location is estimated from an optimal HDOP-weighted multipath localization algorithm that assigns different weights to the LOS path and non-line-of-sight (NLOS) paths.Statistical-channel-model-based simulations and lake trial corroborate that the proposed scheme reduces the localization error by at least 128% compared with angle-only, relative-delay-only, and conventional hybrid metrics localization schemes.Index Terms--Underwater acoustic passive localization; Multipath arrival structure; Horizontal dilution of precision; Hybrid metrics.

An explainable AI framework for robust and transparent data-driven wind turbine power curve models

In recent years, increasingly complex machine learning methods have become state-of-the-art in modelling wind turbine power curves based on operational data. While these methods often exhibit superior performance on test sets, they face criticism due to a perceived lack of transparency and concerns about their robustness in dynamic, non-stationary environments encountered by wind turbines. In this work, we address these issues and present a framework that leverages explainable artificial intelligence methods to gain systematic insights into data-driven power curve models. At its core, we propose a metric to quantify how well a learned model strategy aligns with the underlying physical principles of the problem. This novel tool enables model validation beyond the conventional error metrics in an automated manner. We demonstrate, for instance, its capacity as an indicator for model generalization even when limited data is available. Moreover, it facilitates understanding how decisions made during the machine learning development process, such as data selection, pre-processing, or training parameters, affect learned strategies. As a result, we obtain physically more reasonable models, a prerequisite not only for robustness but also for meaningful insights into turbine operation by domain experts. The latter, we illustrate in the context of wind turbine performance monitoring. In summary, the framework aims to guide researchers and practitioners alike toward a more informed selection and utilization of data-driven wind turbine power curve models.

Resurveying inner-alpine dry grasslands after 70 years calls for integrative conservation efforts

European inner-alpine dry grasslands face substantial threats within the increasingly human-altered landscape, endangering their persistence. To understand changes in dry grassland communities, we revisited historical vegetation plots of Josias Braun-Blanquet after 70 years in Val Venosta, Italy, hosting rare steppe-like grassland vegetation. By disentangling the key environmental factors encompassing climate, land use and human management, and ecological site preferences, we aimed at explaining changes in dry grassland communities with implications for future conservation.By extending our analysis beyond conventional dissimilarity metrics and adopting a landscape-ecological perspective accounting for species-environment interactions, we assessed how environmental changes affect dissimilarity patterns among historical sites, recent non-protected sites, and recent protected sites with generalized additive modelling. Moreover, we examined ecologically significant species changes to evaluate their contribution to community variation within and between sites, discerning their consequences at the landscape scale.Our results revealed significant changes in dry grassland sites, both on non-protected and protected sites. The encroachment of shrubs was associated with a significant increase in generalist species, including various woody species on sites where grazing had ceased. Furthermore, we observed a higher abundance of nutrient-demanding species on sites next to intensive agriculture. These trends were consistent regardless of the protection status, implying that current conservation measures may be insufficient to guarantee their future persistence. To ensure the long-term conservation of typical inner-alpine dry grasslands, interdisciplinary conservation efforts are essential to address adverse environmental impacts across the entire landscape.

New unifying metric for NMR/MRI probe evaluation based on optimized solenoid coil geometry

A three-dimensional numerical simulation of the magnetic field distribution and Bloch equations for arbitrary radio frequency (RF) coils is developed and compared against nuclear magnetic resonance (NMR) experimental results to evaluate the NMR signal intensity. Because NMR is inherently insensitive and its signal intensity is dependent on RF coil geometry, the investigation of RF coil geometry to maximize signal intensity for a given sample volume is important for improving the signal-to-noise ratio (SNR) and shortening the accumulation time. The developed simulation can optimize the RF coil geometry, specifically a single-layer solenoid coil with a constant winding pitch, and the result of the solenoid coil simulation serves as a new unifying metric for evaluating NMR/MRI probes. It is found that the most efficient sample aspect ratio (ratio of sample length to sample diameter) and pitch to wire diameter ratio for the highest signal intensity are around 2.2 and 1.65, respectively. Some discrepancies from the solenoid coil geometry ratios for higher signal intensity in previous studies can be explained by the difference in the gap between the inner diameter of the solenoid coil and the sample diameter. These results are confirmed through NMR signal intensity expressed in voltages with three approaches: 3D simulation, experiment, and estimation based on probe parameters. The simulated signal intensity shows a maximum error of approximately 5 % and an average error of 1 % when compared to the experimental results. This result suggests that the developed methods hold the potential for application in quantitative NMR (qNMR) without relying on standard reference materials. Finally, this study introduces a standardized geometry for the optimized solenoid coil for higher signal intensity and uses it to establish an evaluation metric called the signal-to-optimized-solenoid-signal ratio (3SR). The 3SR addresses the volume-dependence problem in conventional metrics like SNR and SNR per sample volume. It provides a standardized approach for the unified evaluation of all RF coils and probe designs, regardless of sample volume and measurement frequency. Therefore, 3SR can be utilized as a useful metric in the search for optimal coil geometry, while metrics such as SNR or SNR per sample volume are currently used for such purpose. This metric is expected to be useful for NMR/magnetic resonance imaging (MRI) users and developers.