Correlation Measures Research Articles

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.

Operator growth hypothesis in open quantum systems

The operator growth hypothesis (OGH) is a technical conjecture about the behavior of operators—specifically, the asymptotic growth of their —under repeated action by a Liouvillian. It is expected to hold for a sufficiently generic closed many-body system. When it holds, it yields bounds on the high-frequency behavior of local correlation functions and measures of chaos (like OTOCs). It also gives a route to numerically estimating response functions. Here we investigate the generalization of OGH to open quantum systems, where the Liouvillian is replaced by a Lindbladian. For a quantum system with local Hermitian jump operators, we show that the OGH is modified: we define a generalization of the Lanczos coefficient and show that it initially grows linearly as in the original OGH, but experiences exponentially growing oscillations on scales determined by the dissipation strength. We see this behavior manifested in a semi-analytically solvable model (large-q SYK with dissipation), numerically for an ergodic spin chain, and in a solvable toy model for operator growth in the presence of dissipation (which resembles a non-Hermitian single-particle hopping process). Finally, we show that the modified OGH connects to a fundamental difference between Lindblad and closed systems: At high frequencies, the spectral functions of the former decay algebraically, while in the latter they decay exponentially. This is an experimentally testable statement, which also places limitations on the applicability of Lindbladians to systems in contact with equilibrium environments. Published by the American Physical Society 2024

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

Quantile generalized measures of correlation

Quantile generalized measures of correlation

Geometric interpretation and experimental test of Leggett inequalities with nonmaximally entangled states.

Leggett inequality states that nonlocal hidden-variable models might still be incompatible with the predictions of quantum physics. However, its theoretical and experimental demonstration is only in the scenario of 2-dimensional maximally entangled systems. An open question remains as to whether the Leggett inequality can be violated by nonmaximally entangled states. Here, we answer this question both in theory and experiment. Specifically, from the point of view of geometry, we theoretically map the problem of maximizing the correlation measure in the Leggett inequality to maximizing the sum of an ellipse's diameter and semi-diameter axes, accordingly, demonstrating that the violation of the Leggett inequality requires a more robust entanglement than that of Bell's theory. Experimentally, by leveraging the controllable photonic orbital angular momentum entanglement, we demonstrate the violation of Leggett-type inequalities by more than 8.7 and 4.5 standard deviations under concurrence C = 0.95 and 0.9, respectively. Our observations indicate that, the requirement for quantum correlation should be increased to exclude a particular class of non-local hidden variable theories that abide by Leggett's model, providing insights into the boundaries of quantum correlation and the limitations imposed by non-local hidden variables.

A comprehensive study on non-governmental actors in shaping grassland ecological compensation within legal frameworks

Ecological compensation has emerged as a crucial institutional framework for managing the interplay between ecological preservation and economic development in China. This study focuses on the specific case of grassland ecological compensation to investigate the protection of rights and interests of non-governmental subjects. By utilizing data derived from questionnaire responses, this study examines the legal rights, obligations, and responsibilities associated with grassland ecological compensation. Statistical techniques such as Z-distribution, chi-square test, and non-parametric measures of correlation are employed to analyze the collected data, which are presented using tables and graphs. Furthermore, this research evaluates the current state of rights and interests of compensation subjects engaged in ecological compensation practices, aiming to enhance our comprehension and assessment of the extent to which the ecological compensation system safeguards the rights and interests of individuals. The findings show that a substantial number of respondents see current grassland ecological compensation methods in China as reasonable but insufficient, indicating a need for method diversification. There’s a clear preference for a shared responsibility model over government-only funding, especially in regions with large grassland areas. This highlights the necessity for adaptable laws and a legal framework that accommodates diverse stakeholder needs. Additionally, the importance of clear property rights is emphasized for sustainable land use. The study suggests legislative reform towards a more equitable and effective approach to grassland conservation, providing valuable recommendations for refining and advancing the ecological compensation system.Author name 1 (Ziqi Liu) mismatch between ms and metadata. We have foolowed metadata. Kindly check and confirm.The metadata is right. Thank you.

Cardiorespiratory fitness and muscular fitness correlates in youth: A hierarchy of behavioral, contextual, and health-related outcomes

ObjectivesDespite the health importance of identifying correlates of physical fitness in youth, no investigation to date has explored the influence of behavioral, health-related, and contextual correlates simultaneously. We investigated the hierarchical relationship of multiple modifiable correlates favoring or diminishing cardiorespiratory and muscular fitness in youth. DesignCross-sectional investigation. MethodsIn a sample of 5174 children and adolescents, 31 correlates were hierarchized according to their impact on cardiorespiratory and muscular fitness assessed using the FITESCOLA® fitness battery. A Chi-squared Automatic Interaction Detection approach was employed and measures of correlation and association were used to investigate the relationship between physical fitness and correlates. ResultsIn children, body mass index was the most relevant factor to discriminate between high and low cardiorespiratory and muscular fitness of the upper, middle, and lower body. While body mass index was more important than any other correlate to differentiate levels of upper and lower body muscular fitness during adolescence, specific characteristics of sports participation emerged as key factors to discriminate between high and low cardiorespiratory fitness and middle body muscular fitness. Other correlates, including the self-report of active recess time, active commuting to school, favorable neighborhood conditions, and limited time on screens and cellphones, were demonstrative of favorable physical fitness levels. ConclusionsBoth body composition and sports-related characteristics emerged as the two most relevant factors of physical fitness in youth. Additional health benefits may be obtained from building supportive environments for sports and healthy exercise habits within the household and at different school education levels.

Radiographic Union Assessment in Surgically Treated Distal Femur Fractures: A Systematic Review.

Distal femur fractures are known to have challenging nonunion rates. Despite various available treatment methods aimed to improve union, optimal interventions are yet to be determined. Importantly, there remains no standard agreement on what defines radiographic union. Although various proposed criteria of defining radiographic union exist in the literature, there is no clear consensus on which criteria provide the most precise measurement. The use of inconsistent measures of fracture healing between studies can be problematic and limits their generalizability. Therefore, this systematic review aims to identify how fracture union is defined based on radiographic parameters for surgically treated distal femur fractures in current literature. In accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines, Medline, EMBASE, Cochrane Central Register of Controlled Trials, and Web of Science Core Collection databases were searched from inception to October 2022. Studies that addressed surgically treated distal femur fractures with reported radiographic union assessment were included. Outcomes extracted included radiographic definition of union; any testing of validity, reliability, or responsiveness; reported union rate; reported time to fracture union; and any functional outcomes correlated with radiographic union. Sixty articles with 3,050 operatively treated distal femur fractures were included. Operative interventions included lateral locked plate (42 studies), intramedullary nail (15 studies), dynamic condylar screw or blade plate (7 studies), dual plate or plate and nail construct (5 studies), distal anterior-posterior/posterior-anterior screws (1 study), and external fixation with a circular frame (1 study). The range of mean follow-up time reported was 4.3 to 44 months. The most common definitions of fracture union included "bridging or callus formation across 3 of 4 cortices" in 26 (43%) studies, "bony bridging of cortices" in 21 (35%) studies, and "complete bridging of cortices" in 9 (15%) studies. Two studies included additional assessment of radiographic union using the Radiographic Union Scale in Tibial fracture (RUST) or modified Radiographic Union Scale in Tibial fracture (mRUST) scores. One study included description of validity, and the other study included reliability testing. The reported mean union rate of distal femur fractures was 89% (range 58%-100%). The mean time to fracture union was documented in 49 studies and found to be 18 weeks (range 12-36 weeks) in 2,441 cases. No studies reported correlations between functional outcomes and radiographic parameters. The current literature evaluating surgically treated distal femur fractures lacks consistent definition of radiographic fracture union, and the appropriate time point to make this judgement is unclear. To advance surgical optimization, it is necessary that future research uses validated, reliable, and continuous measures of radiographic bone healing and correlation with functional outcomes. Level IV. See Instructions for Authors for a complete description of levels of evidence.

A computable quantification of multi-mode Gaussian coherence and complete monogamy relation

We propose a quantification CνGn of n-mode Gaussian coherence. The value of CνGn only depends on the covariance matrices and displacement vectors of continuous-variable states without any optimization procedures, and thus is easily calculated. For n=1, CνG1 is a proper Gaussian coherence measure of single-mode CV system. For n≥2, CνGn is invariant under any permutation of submodes, nonincreasing under any n-mode local incoherent Gaussian channels, vanishes at incoherent Gaussian states, and, satisfies the unification condition and the hierarchy condition that a multi-partite quantum correlation measure should obey. Thus CνGn is a multi-partite Gaussian correlation measure, which reveals, though the quantum coherence lives in single-partite systems, that the multi-mode coherence for continuous-variable systems can be regarded as a multipartite Gaussian correlation between modes, and such multi-partite Gaussian correlation is also a quantum resource. Moreover, we show that CνGn is completely monogamous as a multipartite Gaussian correlation measure. This means that the n-mode Gaussian coherence subjects to the principles of resource allocation. In addition, CνGn is an upper bound of the geometric-based single-mode Gaussian coherence measure CBu by the Bures distance at pure Gaussian states of mode ≤2 and can be used to detect coherence in any n-mode Gaussian states more efficiently.

Machine learning based software effort estimation using development-centric features for crowdsourcing platform

Crowd-Sourced software development (CSSD) is getting a good deal of attention from the software and research community in recent times. One of the key challenges faced by CSSD platforms is the task selection mechanism which in practice, contains no intelligent scheme. Rather, rule-of-thumb or intuition strategies are employed, leading to biasness and subjectivity. Effort considerations on crowdsourced tasks can offer good foundation for task selection criteria but are not much investigated. Software development effort estimation (SDEE) is quite prevalent domain in software engineering but only investigated for in-house development. For open-sourced or crowdsourced platforms, it is rarely explored. Moreover, Machine learning (ML) techniques are overpowering SDEE with a claim to provide more accurate estimation results. This work aims to conjoin ML-based SDEE to analyze development effort measures on CSSD platform. The purpose is to discover development-oriented features for crowdsourced tasks and analyze performance of ML techniques to find best estimation model on CSSD dataset. TopCoder is selected as target CSSD platform for the study. TopCoder’s development tasks data with development-centric features are extracted, leading to statistical, regression and correlation analysis to justify features’ significance. For effort estimation, 10 ML families with 2 respective techniques are applied to get broader aspect of estimation. Five performance metrices (MSE, RMSE, MMRE, MdMRE, Pred (25) and Welch’s statistical test are incorporated to judge the worth of effort estimation model’s performance. Data analysis results show that selected features of TopCoder pertain reasonable model significance, regression, and correlation measures. Findings of ML effort estimation depicted that best results for TopCoder dataset can be acquired by linear, non-linear regression and SVM family models. To conclude, the study identified the most relevant development features for CSSD platform, confirmed by in-depth data analysis. This reflects careful selection of effort estimation features to offer good basis of accurate ML estimate.

Measuring semantic memory using associative and dissociative retrieval tasks.

Recent theoretical advances highlighted the need for novel means of assessing semantic cognition. Here, we introduce the associative-dissociative retrieval task (ADT), positing a novel way to test inhibitory control over semantic memory retrieval by contrasting the efficacy of associative (automatic) and dissociative (controlled) retrieval on a standard set of verbal stimuli. All ADT measures achieved excellent reliability, homogeneity, and short-term temporal stability. Moreover, in-depth stimulus level analyses showed that the associative retrieval is easier for words evoking few but strong associates, yet such propensity hampers the inhibition. Finally, we provided critical support for the construct validity of the ADT measures, demonstrating reliable correlations with domain-specific measures of semantic memory functioning (semantic fluency and associative combination) but negligible correlations with domain-general capacities (processing speed and working memory). Together, we show that ADT provides simple yet potent and psychometrically sound measures of semantic memory retrieval and offers noteworthy advantages over the currently available assessment methods.

Vision-oriented machine learning-assisted seismic energy dissipation estimation for damaged RC beam-column connections

After a seismic event, damage quantification is necessary for safety evaluation, collapse proximity judgment, and measurement of the residual seismic capacity of the joints. Machine learning-based predictive models are developed in this paper aimed at the non-destructive and non-contact estimation of energy dissipation ratio for seismically damaged beam-column joints through surface crack texture complexity indices. For this purpose, the authors collected an experimental dataset comprising 934 images of cracked and/or crushed reinforced concrete-framed joints from 254 specimens under cyclic loading. The associated energy dissipation ratios are then extracted from the lateral load-displacement hysteresis curves for each image by the authors, along with the image-derived fractal indices. Machine learning models with six algorithms, including Linear Regression, Multi-Layer Perceptron, Decision Tree, Random Forest, Gradient Boost, and CatBoost, are trained by 80% of images as a training dataset and validated through the remaining 20% of images in two scenarios. The first scenario develops models by component geometric dimensions and generalized fractal indices calculated for the beams, columns, and joints of seismically damaged connections, while the second scenario adds structural parameters to visual indices to estimate the energy dissipation ratio as the target parameter. Performance evaluation of trained models in the mentioned scenarios via common correlation and accuracy measures, along with the k-fold cross-validation method, indicated that CatBoost-based ML models in both scenarios provide optimal results with R2 = 0.89, RMSE = 0.10 for scenario I and R2 = 0.92, RMSE = 0.09 for scenario II using testing dataset. The first scenario based on the CatBoost algorithm with the R2 variation range of 0.07 and RMSE variation range of 0.03 across the test folds provides a sufficient performance in terms of generalizability and accuracy for estimating the energy dissipation ratio through lower number of input variables.

Scaling Multiobjective Evolution to Large Data With Minions: A Bayes-Informed Multitask Approach.

In an era of pervasive digitalization, the growing volume and variety of data streams poses a new challenge to the efficient running of data-driven optimization algorithms. Targeting scalable multiobjective evolution under large-instance data, this article proposes the general idea of using subsampled small-data tasks as helpful minions (i.e., auxiliary source tasks) to quickly optimize for large datasets-via an evolutionary multitasking framework. Within this framework, a novel computational resource allocation strategy is designed to enable the effective utilization of the minions while guarding against harmful negative transfers. To this end, an intertask empirical correlation measure is defined and approximated via Bayes' rule, which is then used to allocate resources online in proportion to the inferred degree of source-target correlation. In the experiments, the performance of the proposed algorithm is verified on: 1) sample average approximations of benchmark multiobjective optimization problems under uncertainty and 2) practical multiobjective hyperparameter tuning of deep neural network models. The results show that the proposed algorithm can obtain up to about 73% speedup relative to existing approaches, demonstrating its ability to efficiently tackle real-world multiobjective optimization involving evaluations on large datasets.

Adaptive Sampling of 3D Spatial Correlations for Focus+Context Visualization.

Visualizing spatial correlations in 3D ensembles is challenging due to the vast amounts of information that need to be conveyed. Memory and time constraints make it unfeasible to pre-compute and store the correlations between all pairs of domain points. We propose the embedding of adaptive correlation sampling into chord diagrams with hierarchical edge bundling to alleviate these constraints. Entities representing spatial regions are arranged along the circular chord layout via a space-filling curve, and Bayesian optimal sampling is used to efficiently estimate the maximum occurring correlation between any two points from different regions. Hierarchical edge bundling reduces visual clutter and emphasizes the major correlation structures. By selecting an edge, the user triggers a focus diagram in which only the two regions connected via this edge are refined and arranged in a specific way in a second chord layout. For visualizing correlations between two different variables, which are not symmetric anymore, we switch to showing a full correlation matrix. This avoids drawing the same edges twice with different correlation values. We introduce GPU implementations of both linear and non-linear correlation measures to further reduce the time that is required to generate the context and focus views, and to even enable the analysis of correlations in a 1000-member ensemble.