The key step in classical convolution and correlation algorithms, the componentwise multiplication of vectors after initial Fourier Transforms, is shown to be physically impossible to do on quantum states. Then this is used to show that computing the convolution or correlation of quantum state coefficients violates quantum mechanics, making convolution and correlation of quantum coefficients ph...

Pearson product-moment correlation coefficients are a wellpracticed quantification of linear dependence seen across many fields. When calculating a sample-based correlation coefficient, the accuracy of the estimation is dependent on the quality and quantity of the sample. Like all statistical models, these correlation coefficients can suffer from overfitting, which results in the representation...

This research reports an investigation of the use of standardized regression (beta) coefficients in meta-analyses that use correlation coefficients as the effect-size metric. The investigation consisted of analyzing more than 1,700 corresponding beta coefficients and correlation coefficients harvested from published studies. Results indicate that, under certain conditions, using knowledge of co...

BACKGROUND The food frequency questionnaire (FFQ) is the most efficient and cost-effective method to investigate the relationship between usual diet and disease in epidemiologic studies. Although FFQs have been validated in many adult populations worldwide, the number of valid FFQ in preschool children is very scarce. The aim of this study was to evaluate the reproducibility and validity of a s...

Population structure can be described by genotypic-correlation coefficients between groups of individuals, the most basic of which are the pairwise relatedness coefficients between any two individuals. There are nine pairwise relatedness coefficients in the most general model, and we show that these can be reduced to seven coefficients for biallelic loci. Although all nine coefficients can be e...

BACKGROUND Cluster sample study designs are cost effective, however cluster samples violate the simple random sample assumption of independence of observations. Failure to account for the intra-cluster correlation of observations when sampling through clusters may lead to an under-powered study. Researchers therefore need estimates of intra-cluster correlation for a range of outcomes to calcula...

Extended hesitant fuzzy sets (EHFSs), which allow the membership degree of an element to a set represented by several possible value-groups, can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we derive some correlation coefficients between EHFSs, which contain two cases, the correlation coefficients taking into account the l...

Abstract—Correlation matrices are ubiquitous throughout signal processing, networking and in many areas of science [1][2][3]. However, our study of the literature found that there is limited research on the structure of the indices in correlation matrix of wavelet coefficients, and in the exploitation of that structure to improve its computational efficiency. This article seeks to make a contri...

Extended hesitant fuzzy sets (EHFSs), which allow the membership degree of an element to a set represented by several possible value-groups, can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we derive some correlation coefficients between EHFSs, which contain two cases, the correlation coefficients taking into account the l...

Figure 1: Visualizations of correlation for a dataset containing 22,000 variables. The left two images show the correlation coefficients using a heatmap, clustered with (a) average linkage, and (b) complete linkage. The visible patterns in the heatmap are highly dependent on the clustering algorithm. In (c), our novel s-CorrPlot spatially encodes correlation coefficients, highlighting very diff...