Correlation Measures Research Articles

Systematic evidence mapping of potential correlates of exposure for per- and poly-fluoroalkyl substances (PFAS) based on measured occurrence in biomatrices and surveys of dietary consumption and product use

Per- and poly-fluoroalkyl substances (PFAS) are widely observed in environmental media and often are found in indoor environments as well as personal-care and consumer products. Humans may be exposed through water, food, indoor dust, air, and the use of PFAS-containing products. Information about relationships between PFAS exposure sources and pathways and the amounts found in human biomatrices can inform source-contribution assessments and provide targets for exposure reduction. This work collected and collated evidence for correlates of PFAS human exposure as measured through sampling of biomatrices and surveys of dietary consumption and use of consumer products and articles. A systematic evidence mapping approach was applied to perform a literature search, conduct title-abstract and full-text screening, and to extract primary data into a comprehensive database for 16 PFAS. Parameters of interest included: sampling dates and locations, cohort descriptors, PFAS measured in a human biomatrix, information about food consumption in 11 categories, use of products/articles in 11 categories, and reported correlation values (and their statistical strength). The literature search and screening process yielded 103 studies with information for correlates of PFAS exposures. Detailed data were extracted and compiled on measures of PFAS correlations between biomatrix concentrations and dietary consumption and other product/article use. A majority of studies (61/103; 59%) were published after 2015 with few (8/103; 8%) prior to 2010. Studies were most abundant for dietary correlates (n = 94) with fewer publications reporting correlate assessments for product use (n = 56), while some examined both. PFOA and PFOS were assessed in almost all studies, followed by PFHxS, PFNA, and PFDA which were included in >50% of the studies. No relevant studies included PFNS or PFPeS. Among the 94 studies of dietary correlates, significant correlations were reported in 83% of the studies for one or more PFAS. The significant dietary correlations most commonly were for seafood, meats/eggs, and cereals/grains/pulses. Among the 56 studies of product/article correlates, significant correlations were reported in 70% of the studies. The significant product/article correlations most commonly were for smoking/tobacco, cosmetics/toiletries, non-stick cookware, and carpet/flooring/furniture and housing. Six of 11 product/article categories included five or fewer studies, including food containers and stain- and water-resistant products. Significant dietary and product/article correlations most commonly were positive. Some studies found a mix of positive and negative correlations depending on the PFAS, specific correlate, and specific response level, particularly for fats/oils, dairy consumption, food containers, and cosmetics/toiletries. Most of the significant findings for cereals/grains/pulses were negative correlations. Substantial evidence was found for correlations between dietary intake and biomatrix levels for several PFAS in multiple food groups. Studies examining product/article use relationships were relatively sparse, except for smoking/tobacco, and would benefit from additional research. The resulting database can inform further assessments of dietary and product use exposure relationships and can inform new research to better understand PFAS source-to-exposure relationships. The search strategy should be extended and implemented to support living evidence review in this rapidly advancing area.

Studying long term relationship between carbon Emissions, Soil, and climate Change: Insights from a global Earth modeling Framework

The persistent increase in greenhouse gas (GHG) emissions, notably carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O), since the mid-20th century has been a key driver of significant climate alterations. This study investigates the complex feedback mechanisms that both influence and are influenced by global climate dynamics, soil processes, and GHG emissions. Our statistical approach incorporates correlation measures, highlighting the limitations of such analyses, namely their inability to confirm causality, sensitivity to outliers, and the exclusive capture of linear relationships. Geographically Weighted Regression (GWR) models reveal spatial variations in the relationship between environmental factors and GHGs, while Path Analysis aids in delineating direct and indirect influences among variables. The research pinpoints significant spatial heterogeneity in the impacts of economic and environmental factors on GHGs, underscoring the necessity of localized strategies for climate change mitigation and sustainable land management. This study also identifies potential threats to agricultural productivity due to soil degradation, which hinder climate adaptation efforts. Our findings advocate for a concerted global response to reduce GHG emissions and address the challenges posed by the interplay of climate change, soil dynamics, and GHG emissions.

Entanglement of purification in random tensor networks

The entanglement of purification EP(A∶B) is a powerful correlation measure, but it is notoriously difficult to compute because it involves an optimization over all possible purifications. In this paper, we prove a new inequality: EP(A∶B)≥12SR(2)(A∶B), where SR(n)(A∶B) is the Renyi reflected entropy. Using this, we compute EP(A∶B) for a large class of random tensor networks at large bond dimension and show that it is equal to the entanglement wedge cross section EW(A∶B), proving a previous conjecture motivated from AdS/CFT. Published by the American Physical Society 2024

A Comparison of Additional Benefit Assessment Methods for Time-to-Event Endpoints Using Hazard Ratio Point Estimates or Confidence Interval Limits by Means of a Simulation Study.

For time-to-event endpoints, three additional benefit assessment methods have been developed aiming at an unbiased knowledge about the magnitude of clinical benefit of newly approved treatments. The American Society of Clinical Oncology (ASCO) defines a continuous score using the hazard ratio point estimate (HR-PE). The European Society for Medical Oncology (ESMO) and the German Institute for Quality and Efficiency in Health Care (IQWiG) developed methods with an ordinal outcome using lower and upper limits of the 95% HR confidence interval (HR-CI), respectively. We describe all three frameworks for additional benefit assessment aiming at a fair comparison across different stakeholders. Furthermore, we determine which ASCO score is consistent with which ESMO/IQWiG category. In a comprehensive simulation study with different failure time distributions and treatment effects, we compare all methods using Spearman's correlation and descriptive measures. For determination of ASCO values consistent with categories of ESMO/IQWiG, maximizing weighted Cohen's Kappa approach was used. Our research depicts a high positive relationship between ASCO/IQWiG and a low positive relationship between ASCO/ESMO. An ASCO score smaller than 17, 17 to 20, 20 to 24, and greater than 24 corresponds to ESMO categories. Using ASCO values of 21 and 38 as cutoffs represents IQWiG categories. We investigated the statistical aspects of the methods and hence implemented slightly reduced versions of all methods. IQWiG and ASCO are more conservative than ESMO, which often awards the maximal category independent of the true effect and is at risk of overcompensating with various failure time distributions. ASCO has similar characteristics as IQWiG. Delayed treatment effects and underpowered/overpowered studies influence all methods in some degree. Nevertheless, ESMO is the most liberal one. For the additional benefit assessment, the American Society of Clinical Oncology (ASCO) uses the hazard ratio point estimate (HR-PE) for their continuous score. In contrast, the European Society for Medical Oncology (ESMO) and the German Institute for Quality and Efficiency in Health Care (IQWiG) use the lower and upper 95% HR confidence interval (HR-CI) to specific thresholds, respectively. ESMO generously assigns maximal scores, while IQWiG is more conservative.This research provides the first comparison between IQWiG and ASCO and describes all three frameworks for additional benefit assessment aiming for a fair comparison across different stakeholders. Furthermore, thresholds for ASCO consistent with ESMO and IQWiG categories are determined, enabling a comparison of the methods in practice in a fair manner.IQWiG and ASCO are the more conservative methods, while ESMO awards high percentages of maximal categories, especially with various failure time distributions. ASCO has similar characteristics as IQWiG. Delayed treatment effects and under/-overpowered studies influence all methods. Nevertheless, ESMO is the most liberal one. An ASCO score smaller than 17, 17 to 20, 20 to 24, and greater than 24 correspond to the categories of ESMO. Using ASCO values of 21 and 38 as cutoffs represents categories of IQWiG.

Assessment of consolidative multi-criteria decision making (C-MCDM) algorithms for optimal mapping of polymer materials in additive manufacturing: A case study of orthotic application

ObjectiveThe objectives of this research are twofold. The primary goal is to introduce, investigate, and contrast consolidative multi-criteria decision-making (C-MCDM) approaches. The second objective is the investigation of five alternative additive manufacturing materials. MethodsIt integrates the subjective and objective weights using the Bayes hypothesis in conjunction with a normal method. Chang's Extent Analysis Method under fuzzy logic is used to estimate subjective weights and the CRITIC approach is used for assessing objective weights. Ranking techniques, including the simple ranking process (SRP), multi-objective optimization based on ratio analysis (MOORA), measurement alternatives and ranking according to compromise solution (MARCOS), and technique for order preference by similarity to ideal solution (TOPSIS) are applied. It also encompasses sensitivity analysis based on Kendall's coefficient of concordance and rank reversal phenomenon analysis. Spearman's rank correlation coefficient, a weighted rank measure of correlation, and rank similarity coefficient are among the metrics used to evaluate agreement between different approaches. It entails gathering expert opinions regarding the importance of various criteria as well as conducting extensive experiments. ResultsThe findings of the study indicate that polylactic acid is the best material to use for orthoses. When compared to the other MCDM approaches being discussed, SRP is the most reliable approach. It is also demonstrated that the SRP, MARCOS, and TOPSIS methods are rank reversal-free. Furthermore, SRP exhibits a very poor association with the TOPSIS technique but a strong correlation with the MOORA and MARCOS approaches. ConclusionsTo ensure results reliability, it is necessary to consider both the subjectivity and objectivity of weights as well as apply multiple MCDM methodologies in addition to sensitivity analysis.

Data reconstruction for tunnel structural health monitoring: An updated KNN model with gray relational analysis

Structural health monitoring (SHM) system is an important way to evaluate the tunnel structural performance. In practice, the missing data is inevitably induced in the SHM dataset, which may cause deviation or even misleading results of the data analysis, and hence, need to be accurately reconstructed. This study proposes a new KNN data reconstruction method based on a gray correlation measure (GRA-KNN). Compared to the traditional KNN, the GRA-KNN can measure the structural similarity of data better, and the pre-filling can make full use of the information of known data to estimate missing data. By comparing with the other five machine learning methods (i.e., Ridge Regression, Support Vector Regression, Multilayer Perceptron, RandomForest, and XGBoost), the imputation performance of this method is examined using two real-time SHM datasets from Nanjing Yangtze River tunnel and Hong Kong-Zhuhai-Macao Bridge Undersea Tunnel. Results show that the GRA-KNN method possesses a better performance and stronger robustness under a wide range of missing ratios from 10% to 90%, showing great potential in SHM data reconstruction. In particular, when the missing ratio is larger than 60%, the imputation error of the proposed method is the smallest compared to that of the other machine learning methods.

Correlation-based tests for the formal comparison of polygenic scores in multiple populations.

Polygenic scores (PGS) are measures of genetic risk, derived from the results of genome wide association studies (GWAS). Previous work has proposed the coefficient of determination (R2) as an appropriate measure by which to compare PGS performance in a validation dataset. Here we propose correlation-based methods for evaluating PGS performance by adapting previous work which produced a statistical framework and robust test statistics for the comparison of multiple correlation measures in multiple populations. This flexible framework can be extended to a wider variety of hypothesis tests than currently available methods. We assess our proposed method in simulation and demonstrate its utility with two examples, assessing previously developed PGS for low-density lipoprotein cholesterol and height in multiple populations in the All of Us cohort. Finally, we provide an R package 'coranova' with both parametric and nonparametric implementations of the described methods.

Multi-association evidential feature selection and its application to identifying schizophrenia

Granular Computing (GrC)-based feature selection can remove redundant features from a massive amount of data and improve the efficiency of information processing. However, the existing method of neighborhood-based information granule only considers the distance between samples, ignoring other significant relationships existing between them. To fill this gap, this paper proposes a novel feature selection approach based on two-step multi-association neighborhood evidence entropy. This approach is constructed in three phases. Firstly, adaptive k value corresponding to each sample in sparse representation method is determined. Sparse correlation and distance measure are fused to form a multi-association information granule. Then, the samples in the multi-association information granule are estimated and weak-related information is removed to constitute a two-step multi-association information granule. Secondly, sparse correlation information is processed using Dempster-Shafer evidence theory, and a new credibility-based function is developed. In addition, the credibility is used to construct a novel neighborhood evidence entropy, which can effectively reflect the uncertainty of data. Thirdly, the proposed neighborhood evidence entropy is applied to assess the importance of features. As a result, several vital features are selected. The experimental results on twelve datasets demonstrate that the effectiveness of the proposed method is superior to other algorithms in construction of information granules and classification accuracy, respectively. Finally, the proposed method is applied to the selection of brain regions in schizophrenia. It can effectively analyze the lesions of schizophrenia and improve the prediction of the disorder. The code is available at https://github.com/fxx-Aurora/TMAE-FS/tree/main.

Weakly supervised classification through manifold learning and rank-based contextual measures

Over the last decade, significant advances have been achieved by machine learning approaches, notably in supervised learning scenarios. Supported by the advent of deep learning and comprehensive training sets, the accuracy achieved on classification tasks has improved significantly. Simultaneously, we have experienced massive growth in multimedia data and applications, which have become ubiquitous in several domains. However, with the increase in multimedia data collections, significant bottlenecks associated with the lack of labeled data emerged. To surpass this critical issue, developing methods capable of exploiting the unlabeled data and operating under weak supervision has become imperative. This work proposes a rank-based model capable of using contextual information encoded in the unlabeled data to perform weakly supervised classification. We evaluated the proposed weakly supervised approach on multimedia classification tasks with and without manifold learning algorithms, considering several combinations of rank correlation measures and classifiers. An experimental evaluation was conducted on 6 public image datasets considering different features, including convolutional neural networks and visual transformers. Positive gains were achieved compared to supervised and semi-supervised baselines for the same amount of labeled data. For instance, the proposed approach with manifold learning enhanced the accuracy of the Optimum-Path Forest (OPF) classifier from 71.77% to 83.24% when applied to the Flowers dataset and ResNet features. Among the conclusions, this work reveals that rank-based correlation measures and manifold learning can be used for a more effective labeled set expansion.

Enhancing the Vietoris–Rips simplicial complex for topological data analysis: applications in cancer gene expression datasets

AbstractThe aim of this study is to enhance the extraction of informative features from complex data through the application of topological data analysis (TDA) using novel topological overlapping measures. Topological data analysis has emerged as a promising methodology for extracting meaningful insights from complex datasets. Existing approaches in TDA often involve extrapolating data points using distance correlation measures, which subsequently constrain downstream predictive tasks. Our objective is to improve the construction of the Vietoris–Rips simplicial complex by introducing topological overlapping measures. These measures take into account the interplay of direct connection strengths and shared neighbours, leading to the identification of persistent topological features. We propose the utilisation of topological overlapping measures to optimise the construction of the Vietoris–Rips simplicial complex, offering a more refined representation of complex data structures. The application of topological overlapping measures results in the identification of plentiful persistent topological features. This enhancement contributes to an improvement of up to 20% in cancer phenotype prediction across different cancer types. Our study demonstrates the effectiveness of utilising topological overlapping measures in optimising the construction of the Vietoris–Rips simplicial complex. The identified persistent topological features significantly enhance the predictive accuracy of cancer phenotypes. This novel approach has the potential to advance the field of topological data analysis and improve our understanding of complex data structures, particularly in the context of cancer research and predictive modelling. Further exploration and application of these measures may yield valuable insights in various domains dealing with intricate datasets.

Polygamy of quantum correlation measures for tripartite systems

Polygamy of quantum correlation measures for tripartite systems

Pearson Correlation and Ordered Weighted Average Operator in The World Stock Exchange Market

Due to the large number of transactions carried out in the stock market, it becomes of great importance for the financial development of a country. Analyzing the correlation between indices in the world helps us to know the way towards the variables that impact. This paper proposes the use of ordered weighted average (OWA) operators in combination with Pearson Coefficient to create a measure of correlation that can analyze a wide range of possible scenarios that go minimum to maximum. The new frameworks can add additional information to the process of correlation. The work presents an application in ten of the largest stock exchanges in the world. The results suggest a broad positive correlation between them that is reinforced in times of instability.

Similarity in evoked responses does not imply similarity in macroscopic network states.

It is commonplace in neuroscience to assume that if two tasks activate the same brain areas in the same way, then they are recruiting the same underlying networks. Yet computational theory has shown that the same pattern of activity can emerge from many different underlying network representations. Here we evaluated whether similarity in activation necessarily implies similarity in network architecture by comparing region-wise activation patterns and functional correlation profiles from a large sample of healthy subjects (N = 242). Participants performed two executive control tasks known to recruit nearly identical brain areas, the color-word Stroop task and the Multi-Source Interference Task (MSIT). Using a measure of instantaneous functional correlations, based on edge time series, we estimated the task-related networks that differed between incongruent and congruent conditions. We found that the two tasks were much more different in their network profiles than in their evoked activity patterns at different analytical levels, as well as for a wide range of methodological pipelines. Our results reject the notion that having the same activation patterns means two tasks engage the same underlying representations, suggesting that task representations should be independently evaluated at both node and edge (connectivity) levels.

A fair bed allocation during COVID-19 pandemic using TOPSIS technique based on correlation coefficient for interval-valued pythagorean fuzzy hypersoft set

The relationship between two variables is an essential factor in statistics, and the accuracy of the results depends on the data collected. However, the data collected for statistical analysis can be unclear and difficult to interpret. One way to predict how one variable will change about another is by using the correlation coefficient (CC), but this method is not commonly used in interval-valued Pythagorean fuzzy hypersoft set (IVPFHSS). The IVPFHSS is a more advanced and generalized form of the Pythagorean fuzzy hypersoft set (PFHSS), which allows for more precise and accurate analysis. In this research, we introduce the correlation coefficient (CC) and weighted correlation coefficient (WCC) for IVPFHSS and their essential properties. To demonstrate the applicability of these measures, we use the COVID-19 pandemic as an example and establish a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) model. The technique is used to study the problem of optimizing the allocation of hospital beds during the pandemic. This study provides insights into the importance of utilizing correlation measures for decision-making in uncertain and complex situations like the COVID-19 pandemic. It is a robust multi-attribute decision-making (MADM) methodology with significant importance. Subsequently, it is planned to increase a dynamic bed allocation algorithm based on biogeography to accomplish the superlative decision-making system. Moreover, numerical investigations deliberate the best decision structures and deliver sensitivity analyses. The efficiency of our encouraged algorithm is more consistent than prevalent models, and it can effectively control and determine the optimal configurations for the study.

A spherical fuzzy correlation coefficient based on statistical viewpoint with its applications in classification and bidirectional approximate reasoning

Spherical fuzzy sets are more powerful in modelling the uncertain situations than picture fuzzy sets, fermatean fuzzy sets, Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. In this paper, we first define the variance and covariance of spherical fuzzy sets. Then, using variance and covariance, we define the unique spherical fuzzy set correlation metric in line with the statistical coefficient of correlation. Two spherical fuzzy sets are correlated in both direction and strength using the provided measure of correlation. We discussed its many characteristics. We compared the measure of correlation with the current ones through linguistic variables. We established its validity by showing its application in bidirectional approximate reasoning. We also resolve a pattern identification issue in the spherical fuzzy environment using the provided correlation function, and we compare the results with several current measurements.

Identification of miR-125a and miR-106b signature as a potential diagnostic biomarker in breast cancer tissues

MicroRNAs (miRNAs) have essential roles in the etiology of breast cancer and are regarded as possible markers in this malignancy. In order to find new markers for breast cancer, the current study has measured expression level of four miRNAs, namely miR-125a, miR-106b, miR-96 and miR-92a-3p in the paired breast samples. Expression levels of miR-125a and miR-106b were higher in tumoral tissues compared with control tissues (Expression ratios (95% CI) = 4.01 (1.96–8.19) and 3.9 (1.95–7.81); P values = 0.0005 and 0.0003, respectively). miR-106b and miR-125a differentiated between malignant and non-malignant tissues with AUC values of 0.7 and 0.67, respectively. We detected association between expression of miR-106b and clinical stage (P = 0.03), in a way that its expression was the lowest in the advanced stages. Finally, significant relationships were found between miR-96 and miR-125a in both tumoral and non-tumoral specimens (ρ = 0.76 and 0.69, respectively). This nonparametric measure of rank correlation also showed relationship between miR-106b and miR-96 in both sets of samples (ρ = 0.63 and 0.61, respectively). Cumulatively, the assessed miRNAs, particularly miR-125a and miR-106b are putative targets for further expression and functional assays in breast cancer.

Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state

Out-of-equilibrium states of many-body systems tend to evade a description by standard statistical mechanics, and their uniqueness is epitomized by the possibility of certain long-range correlations that cannot occur in equilibrium. In quantum many-body systems, coherent correlations of this sort may lead to the emergence of remarkable entanglement structures. In this work, we analytically study the asymptotic scaling of quantum correlation measures—the mutual information (MI) and the fermionic negativity—within the zero-temperature steady state of voltage-biased free fermions on a one-dimensional lattice containing a non-interacting impurity. Previously, we have shown that two subsystems on opposite sides of the impurity exhibit volume-law entanglement, which is independent of the absolute distances of the subsystems from the impurity. Here, we go beyond that result and derive the exact form of the subleading logarithmic corrections to the extensive terms of correlation measures, in excellent agreement with numerical calculations. In particular, the logarithmic term of the MI asymptotics can be encapsulated in a concise formula, depending only on simple four-point ratios of subsystem length scales and on the impurity scattering probabilities at the Fermi energies. This echoes the case of equilibrium states, where such logarithmic terms may convey universal information about the physical system. To compute these exact results, we devise a hybrid method that relies on Toeplitz determinant asymptotics for correlation matrices in both real space and momentum space, successfully circumventing the inhomogeneity of the system. This method could potentially find wider use for analytical calculations of entanglement measures in similar scenarios.

Measures of conditional dependence for nonlinearity, asymmetry and beyond

Detecting the correlation between two random variables is widely used in many empirical problems in economics. Among them, Pearson’s correlation can be used to quantify the degree of dependence between variables. However, it cannot handle asymmetric correlations. To deal with this situation, we proposed a pair of widely applicable measures of conditional dependence (MCDs), which can not only account for the asymmetry but also the linear or nonlinear conditional dependencies in the presence of multiple variables. We give instances: when the paired measures are the same, resulting in symmetric correlation measures that are equivalent to the square of the Pearson coefficient; when no condition variables are given, MCDs are used to assess the relationship between two variables. Consequently, Pearson’s correlation is a particular instance of MCDs. Theoretical attributes of MCDs show that they have wide applicability. In statistical inference, we develop the joint asymptotics of kernel-based estimators for MCDs, which can be applied to determine whether two randomly generated variables exhibit symmetric conditional dependence in the presence of confounding variables. In the simulation, we verify the efficacy of the proposed MCDs. Then we use real data to analyze the asymmetric impact of MCDs on stock market movements.

Machine learning motivated data imputation of storm data used in coastal hazard assessments

In the Coastal Hazards System's (CHS) Probabilistic Coastal Hazard Analysis (PCHA) framework developed by the United States Army Corps of Engineers (USACE), historical records of tropical cyclone parameters have been used as data sources for statistical analysis, including fitting marginal distributions and measuring correlations between storm parameters. One limitation of the available historical databases is that observations of central pressure and radius of maximum winds are not available for a large number of storms. This may adversely affect the results of statistical analyses used to develop hazard curves. This study uses machine learning techniques to develop a data imputation method to “fill in” missing storm parameter records in historical datasets used for Joint Probability Method (JPM)-based coastal hazard analysis such as the USACE's CHS-PCHA. Specifically, Gaussian process regression (GPR) and artificial neural network (ANN) models are investigated as candidate machine learning-derived data imputation models, and the performance of different model parameterizations is assessed. Candidate imputation models are compared against existing statistical relationships. The effect of the data imputation process on statistical analyses (marginal distributions and correlation measures) is also evaluated for a series of example coastal reference locations.

A robust correlation coefficient for fermatean fuzzy sets based on spearman’s correlation measure with application to clustering and selection process

A robust correlation coefficient for fermatean fuzzy sets based on spearman’s correlation measure with application to clustering and selection process