Signatures of intrinsic decoherence and weak measurement on quantum correlations

In this article, we consider a pair of spin-1/2 particles with squeezing coupling serving as the physical carrier of quantum information. We then examine the dynamics of quantum correlation quantified by the entanglement and measurement-induced nonlocality (MIN) under the intrinsic decoherence. The impact of intrinsic decoherence on the dynamical behaviors of quantum correlations is investigated. We show that the MIN quantities are more robust, while intrinsic decoherence cause sudden death in entanglement. Besides, we highlight the role of spin squeezing coupling and external magnetic field on quantum correlation measures. Finally, we investigate the impact of weak measurement on MIN.

Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance.

Data Processing and Analysis

Data only becomes useful information when it has been analysed and the information has been processed, analysed, and interpreted. Small datasets of 100 or less subjects can be analysed quickly by hand. Data analysis starts with one-, two-, and three-way tables with the analysed data then summarized as percentages, proportions, range, averages, median, and standard deviation. Correlation measures associations between two variables and multiple variables may need to be analysed using regression techniques. Age and sex standardization is usually needed when comparing survey or reported data from two or more different populations. Analysis using computer programmes, such as EpiInfo, is useful for surveys.

Correlation Measures for Cubic m-Polar Fuzzy Sets with Applications

A cubic m -polar fuzzy set (CmPFS) is a new hybrid extension of m -polar fuzzy set and cubic set. A CmPFS is a robust model to express multipolar information in terms of m fuzzy intervals representing membership grades and m fuzzy numbers representing nonmembership grades. In this article, we explore some new operational laws of CmPFSs, produce some related results, and discuss their consequences. We propose relative informational coefficients and relative noninformational coefficients for CmPFSs. These coefficients are analyzed to investigate further properties of CmPFSs. Based on these coefficients, we introduce new correlation measures and their weighted versions for CmPFSs. The value of proposed correlation measures is symmetrical and lies between −1 and 1. Moreover, the applications of the proposed correlation in pattern recognition and medical diagnosis are developed. The feasibility and efficiency of suggested correlation measures is determined by respective illustrative examples.

Entanglement wedge cross section in holographic excited states

We evaluate the entanglement wedge cross section (EWCS) in asymptotically AdS geometries which are dual to boundary excited states. We carry out a perturbative analysis for calculating EWCS between the vacuum and other states for a symmetric configuration consisting of two disjoint strips and obtain analytical results in the specific regimes of the parameter space. In particular, when the states described by purely gravitational excitations in the bulk we find that the leading correction to EWCS is negative and hence the correlation between the boundary subregions decreases. We also study other types of excitations upon adding the extra matter fields including current and scalar condensate. Our study reveals some generic properties of boundary information measures dual to EWCS, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Finally, we discuss how these results are consistent with the behavior of other correlation measures including the holographic mutual information.

Aperiodic order and spherical diffraction, II: translation bounded measures on homogeneous spaces

We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we study auto-correlation measures for large classes of Delone sets in (and even translation bounded measures on) arbitrary locally compact homogeneous metric spaces. We then specialize to the case of weighted model sets, in which we are able to derive more concrete formulas for the auto-correlation. In the case of Riemannian symmetric spaces we also explain how the auto-correlation of a weighted model set in a Riemannian symmetric space can be identified with a (typically non-tempered) positive-definite distribution on $$\mathbb {R}^n$$ R n . This paves the way for a diffraction theory for such model sets, which will be discussed in the sequel to the present article.

Association of intracluster correlation measures with outcome prevalence for binary outcomes in cluster randomised trials

In cluster randomised trials, a measure of intracluster correlation such as the intraclass correlation coefficient (ICC) should be reported for each primary outcome. Providing intracluster correlation estimates may help in calculating sample size of future cluster randomised trials and also in interpreting the results of the trial from which they are derived. For a binary outcome, the ICC is known to be associated with its prevalence, which raises at least two issues. First, it questions the use of ICC estimates obtained on a binary outcome in a trial for sample size calculations in a subsequent trial in which the same binary outcome is expected to have a different prevalence. Second, it challenges the interpretation of ICC estimates because they do not solely depend on clustering level. Other intracluster correlation measures proposed for clustered binary data settings include the variance partition coefficient, the median odds ratio and the tetrachoric correlation coefficient. Under certain assumptions, the theoretical maximum possible value for an ICC associated with a binary outcome can be derived, and we proposed the relative deviation of an ICC estimate to this maximum value as another measure of the intracluster correlation. We conducted a simulation study to explore the dependence of these intracluster correlation measures on outcome prevalence and found that all are associated with prevalence. Even if all depend on prevalence, the tetrachoric correlation coefficient computed with Kirk’s approach was less dependent on the outcome prevalence than the other measures when the intracluster correlation was about 0.05. We also observed that for lower values, such as 0.01, the analysis of variance estimator of the ICC is preferred.