Correlation Measures Research Articles

Mutual information sums and relations with interaction energies in N-particle quantum systems.

The sums of position- and momentum-space mutual information measures are used to examine the pairwise and higher-order statistical correlation in the ground states of N-particle coupled oscillators. Analytical expressions for these measures are shown to be related to the logarithmic interaction energies of these states, plus those of mirror states where the intensities of the one- and two-body potentials are interchanged, and the nature of the attractive or repulsive interaction is opposite to that in the original state. The measures separate the contributions from the interactionsand those from the effective interactions due to marginalization into different terms. The pairwise mutual information sum is linearly related to the Shannon entropy sum in two particle systems, while the total correlation sum exhibits a similar relationship in three particle ones. In the latter instance, the interaction information sum can be related to entropy differences. This illustrates how entropy sums are connected to correlation measure sums in these systems. All measures approach zero with large N, when the magnitudes of the one- and two-body potentials are fixed. The pair mutual information and total correlation sums decay monotonically with N in the presence of an attractive potential and monotonically increase with a repulsive potential. On the other hand, the interaction information sum exhibits a minimum at small N, with an attractive potential. This is a consequence of the higher-order correlations governing behavior at smaller N while the pairwise ones dominate at larger N. Results are presented when the magnitude of the one-body potential is set to N.

Holographic entropy inequalities and multipartite entanglement

We study holographic entropy inequalities and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much simpler ones which share interestingly rigid structures. By performing a systematic search over some of these structures, we are able to discover more than 1800 novel entropy inequalities for six parties, thereby demonstrating that these recastings provide a fruitful generating technique for uncovering new holographic entropy inequalities. In attempting to interpret the corresponding sign-definite quantities as correlation measures, we also obtain a no-go result: the superbalance property of holographic entropy inequalities turns out to preclude them from being monotonic under partial tracing. In the process, we also comment on the geometrical significance of multipartite information quantities and present various structural relations amongst them.

Test and Measure for Partial Mean Dependence Based on Machine Learning Methods

It is of importance to investigate the significance of a subset of covariates W for the response Y given covariates Z in regression modeling. To this end, we propose a significance test for the partial mean independence problem based on machine learning methods and data splitting. The test statistic converges to the standard Chi-squared distribution under the null hypothesis while it converges to a normal distribution under the fixed alternative hypothesis. Power enhancement and algorithm stability are also discussed. If the null hypothesis is rejected, we propose a partial Generalized Measure of Correlation (pGMC) to measure the partial mean dependence of Y given W after controlling for the nonlinear effect of Z. We present the appealing theoretical properties of the pGMC and establish the asymptotic normality of its estimator with the optimal root-N convergence rate. Furthermore, the valid confidence interval for the pGMC is also derived. As an important special case when there are no conditional covariates Z, we introduce a new test of overall significance of covariates for the response in a model-free setting. Numerical studies and real data analysis are also conducted to compare with existing approaches and to demonstrate the validity and flexibility of our proposed procedures. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Center vortex geometry at finite temperature

The geometry of center vortices is studied in SU(3) gauge theory at finite temperature to capture the key structural changes that occur through the deconfinement phase transition. Visualizations of the vortex structure in temporal and spatial slices of the lattice reveal a preference for the vortex sheet to align with the temporal dimension above the critical temperature. This is quantified through a correlation measure. A collection of vortex statistics, including vortex and branching point densities, and vortex path lengths between branching points, are analyzed to highlight internal shifts in vortex behavior arising from the loss of confinement. We find the zero-temperature inclination of branching points to cluster at short distances vanishes at high temperatures, embodying a rearrangement of branching points within the vortex structure. These findings establish the many aspects of center vortex geometry that characterize the phase transition in pure gauge theory. Published by the American Physical Society 2024

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A hybrid multi-measure and improved UMAP approach for train traction motor bearing protection state assessment

Abstract Different protection states have different protection effects on bogie traction motor bearings under road transportation conditions, which directly affects the stability and safety of later vehicle operations. The motor bearing monitoring system usually adopts the time-frequency domain and other indicators to accurately describe its state, and the selection of specific indicators usually originates from the experience of domain experts. To explore the weak and effective features hidden in the data more deeply, this paper researches feature selection and fusion, and proposes a hybrid multi-measure and improved UMAP approach for train traction motor bearing protection state assessment. Firstly, a platform is built to collect multiple sensor signals of traction motor vibration during road transportation and the time-frequency domain feature set is extracted. Then, by comparing the feature extraction effects of 10 single-measure models, a hybrid multi-measure feature selection model and its evaluation indexes, which comprehensively consider the combined distance measure, correlation, and information measure, are constructed to optimize the best hybrid multimetric and the feature set corresponding to the optimal strategy. To perform multi-sensor feature fusion, the PSO-optimized UMAP algorithm is used for feature fusion of the feature set and compared with eight other algorithms. Finally, the results of feature selection and fusion are input into eight classifiers for performance comparison, and the method achieves more than 85% accuracy in distinguishing different protection states, obviously due to the original feature subset. The experimental results prove the effectiveness of the method proposed in this paper, and it provides a theoretical basis and technical reference for the protection scheme of the traction motor and the design and selection of bearings.

(Invited) On the Definition of Velocity in Statistically Accurate, Discrete-Time Simulations of Thermodynamics

One of the most basic struggles in simulations of statistical and dynamical systems is how to appropriately balance the desire for simulation accuracy, obtained in the small time step limit, with simulation efficiency, obtained for large time steps. Obviously, we would like to have the benefits of both limits of accuracy and efficiency. Thus, understanding the influence of discrete time on the behavior of equations of motion is crucial for the understanding and optimization of numerical simulations in physical science and engineering. There are two different types of crucial discretization errors. One is that the simulated, discrete-time trajectory increasingly deviates from the true, continuous-time trajectory as the time step is increased. Another is that the simulated discrete-time velocity increasingly deviates from the expected velocity of the corresponding simulated trajectory as the time step is increased. While the former error is a signature that the simulated trajectory is not exactly the intended one, the simulation may still be representative of the true system. In contrast, the latter error is a signature of a fundamental internal inconsistency in the simulation, which may greatly complicate physical interpretation of the simulation results, especially when both configurational and kinetic measures are required. It is therefore crucially important to understand the relationship between a discrete-time coordinate and its corresponding velocity.It has previously been shown that, unlike in continuous-time, discrete-time configurational dynamics does not need a discrete-time velocity variable. This realization allowed for the derivation of the complete configurational GJ set of stochastic Verlet-type algorithms for simulating the Langevin equation. This set has the key feature of simultaneously giving exact, time-step independent statistical sampling of damped, noisy harmonic oscillators, and giving exact spatial transport values, drift and Einstein diffusion, on flat surfaces. The apparent fact that a discrete-time velocity is not required to simulate a coordinate trajectory implies that discrete-time velocity is an ambiguous concept, which, in turn, implies that multiple velocity definitions can be entertained in order to avoid internal simulation inconsistencies between configurational and kinetic measures. From the derivation of the stochastic GJ methods it was shown that a statistically correct velocity obtained at the same time as the coordinate (an on-site velocity) cannot be obtained. In contrast, a velocity at the half-step between consecutive configurational time steps (a half-step velocity) was identified to produce exact statistical kinetic response for harmonic oscillators regardless of the applied time step. However, only for a single GJ method does this velocity also give the correct drift value.We here derive new, practical velocity definitions that are optimized for statistical kinetic measures, such that, e.g., measures of kinetic energy and correlations with the configurational coordinate are exact for the noisy harmonic oscillator, while also producing the correct kinetic measure of transport on flat surfaces. We identify and analyze three half-step velocity definitions that fulfill these criteria, and we outline simple and practical Verlet-type algorithms that incorporate these velocities within the statistically desirable GJ format that provides the optimized configurational statistics. The application of the methods are demonstrated through characteristic Molecular Dynamics simulations of both simple and complex systems, illustrating how the resulting methods are able to efficiently and simultaneously simulate configurational and kinetic statistical ensembles in different situations using very large time steps.

Characterizing nonclassical correlation via local channels

Local operation is an important tool to characterize the nonlocal aspects of multipartite quantum system. Exploiting the notion of resource theory of coherence, in this article, we establish a quantum correlation measure as the difference between the bipartite coherence and marginal state coherence. We study the Tsallis α-entropy (TαE) coherence based quantum correlation of bipartite state relative to different channels such as unitary channel, the twirling (unitary-induced) channel, projective measurements and weak measurements. It is shown that the quantum channel helps us to discriminate the product and classical-quantum states. We provide the operational interpretation of the correlation measure relative to the measurement in terms of classical uncertainty of channel. A closer connection between the correlation relative to the projective measurements and weak measurements is obtained in terms of measurement strength. As an illustration, we have studied the quantum correlations of well-known two-qubit states.

Rethinking the Effectiveness of Objective Evaluation Metrics in Multi-Focus Image Fusion: A Statistic-Based Approach.

As an effective technique to extend the depth-of-field (DOF) of optical lenses, multi-focus image fusion has recently become an active topic in image processing community. However, a major problem remaining unsolved in this field is the lack of universal criteria in selecting objective evaluation metrics. Consequently, the metrics utilized in different studies often vary significantly, leading to high difficulties in achieving unbiased evaluation. To address this problem, this paper proposes a statistic-based approach for verifying the effectiveness of objective metrics in multi-focus image fusion. The core idea is to adopt statistical correlation measures to evaluate the performance consistency between a certain fusion metric and some popular full-reference image quality assessment models. In addition, a convolutional neural network (CNN)-based fusion metric is presented to measure the similarity between the source images and the fused image based on the semantic features at multiple abstraction levels. A comparative study is conducted to evaluate 20 existing fusion metrics using the proposed statistic-based approach on a large-scale, realistic and with-ground-truth multi-focus image fusion dataset recently released. Experimental results demonstrate the feasibility of the proposed approach in evaluating the effectiveness of objective metrics and the advantage of our CNN-based metric.

Applying Sequential Correlation to Identify Order Dependent Activity Pairs

Mining sequential patterns has been one of the most useful fields in data mining. For example, one recent application of sequential pattern mining is analyzing logs of activity to predict and recognize activities. This is used for both daily life activities and virtual activities. However, only patterns are not always enough to represent the truly interesting information to the end user, especially when the support threshold is low and the number of frequent patterns is huge. A correlation measure is necessary to decipher the relationship between the logged activities. This data is generally collected as a sequence and there is no widely popular correlation measure for elements in sequential patterns. Therefore, we define Sequential Correlation, a novel correlation measure, for discovering important knowledge in sequential patterns and the corresponding full method, SCMine, to classify patterns based on the measure. We employed the measure to establish either a unidirectional or bidirectional association among the activities within a sequence and subsequently classified the sequences based on order dependency. Moreover, an efficient implementation approach for our measure is also discussed. Our performance study shows that, a significant number of activity patterns can be pruned when degree of order among the activities is important. So, it is also useful for classifying or pruning less significant activity patterns from a vast number of frequent sequential patterns. DUJASE Vol. 8 (1) 51-61, 2023 (January)

Portfolio Selection Based on Mean-Generalized Variance Analysis: Evidence from the G20 Stock Markets

Modern finance theories have been increasingly paying attention to nonlinear and asymmetric features of stock returns. In this paper, we extend the concept of covariance to generalized covariance by using Generalized Measure of Correlation (GMC). Based on the generalized covariance which is capable of catching the nonlinearity and asymmetry in stock (index) returns, we propose a mean-generalized variance portfolio selection model which considers the gross-exposure constraint. Furthermore, we propose the corresponding nonparametric estimation approach and the global optimization algorithm to enhance the applicability of our new model. Empirical studies on G20 stock markets support that a portfolio considering nonlinear and asymmetric features among the international markets would outperform traditional ones based on mean-variance optimization and equal weighting strategy in terms of return and flexibility.

Lancaster correlation: A new dependence measure linked to maximum correlation

AbstractWe suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In contrast to maximum correlation, however, our correlation coefficients allow for rank and moment‐based estimators which are simple to compute and have tractable asymptotic distributions. Confidence intervals resulting from these asymptotic approximations and the covariance bootstrap show good finite‐sample coverage. In a simulation, the power of asymptotic as well as permutation tests for independence based on our correlation measures compares favorably with competing methods based on distance correlation or rank coefficients for functional dependence, among others. Moreover, for the bivariate normal distribution, our correlation coefficients equal the absolute value of the Pearson correlation, an attractive feature for practitioners which is not shared by various competitors. We illustrate the practical usefulness of our methods in applications to two real data sets.

A systematic correlation analysis for regression model selection: Application to bridge response prediction using contact and remote sensor systems

Correlation analysis is a crucial step prior to any regression modeling for data prediction, as it can unveil the relationship between predictors and responses, particularly in terms of linearity and nonlinearity. This step is often mandatory for selecting the most suitable regression model. The major challenge is that linear correlation measures are only appropriate for linear cases and there are limited nonlinear measures for nonlinearity assessment. Apart from these challenges, the demanding issue relates to the influence of unknown and unmeasured predictor data in regression model selection thereby yielding unrealistic and inaccurate outputs from both linear and nonlinear correlation measures. To tackle these challenges, this paper proposes a hierarchical correlation analysis method that initially indicates the influence of unknown predictors and then assists in selecting the best regressor for modeling and forecasting. The proposed method utilizes a linear measure known as canonical correlation analysis and a nonlinear measure known as the maximal information criterion. Based on the correlation values derived from these measures, it is possible to classify them into three levels of correlation: low, moderate, and high. In the first and second scenarios, it is inferred that the response data is linearly or nonlinearly influenced by the measured predictors, respectively. In the third scenario, three conditions are derived from the correlation levels, suggesting that the response data is not influenced by the measured predictors. To validate the proposed hierarchical correlation analysis method's applicability and effectiveness, it is tested with predictor and response data related to real-world long-span bridges. The only measured predictor is air temperature, while the response data comprises limited bridge displacements obtained from synthetic aperture radar images, in line with remote sensing technology. The results indicate that the proposed method is highly effective and applicable for selecting the best regression model for prediction.

CREDIT RISK ASSESSMENT PRACTICES AND FINANCIAL PERFORMANCE OF MICROFINANCE INSTITUTION IN RWANDA A CASE OF COPEDU PLC

Background: This exploration design, with a case study of COPEDU PLC, aimed to assess the influence of credit risk assessment practices on the financial performance of COPEDU PLC in Rwanda. This exploration design was structured around three specific objects originally, to estimate the influence of customer financial status analysis on the financial performance of COPEDU PLC in Rwanda secondly, to examine the effect of the 5Cs of credit on the financial performance of COPEDU PLC in Rwanda and eventually, to assess the influence of credit risk on the financial performance of COPEDU PLC in Rwanda. Materials and Methods: To achieve the exploration objects, a descriptive and correlation exploration design was used. Data was collected through a combination of both quantitative and qualitative styles, exercising interview attendants and questionnaires. Using tale approach in the slice process, an exploration population of comprising of staff population of 65 at COPEDU PLC headquarters were all be regarded as the sample size. Results: The collected data presented compelling findings grounded on numerical data. specially, the analysis of COPEDU PLCs financial pointers revealed positive comprehensions, with crucial numbers similar as a mean credit score of4.49(SD = 0.75) and a mean debt- to- income rate of4.51(SD = 0.73). These pointers demonstrated a predominant agreement among repliers, with49.23 agreeing on the significance of credit scores and47.69 admitting the significance of the debt- to- income rate. The study also explored the relationship between the 5Cs of Credit and financial performance, revealing specific numbers similar as a mean score of4.35 (SD = 1.15) for collateral and4.42 (SD = 1.13) for capacity. In addition, effective credit risk operation strategies were quantified, with mean probabilities indicating strong agreement (SA) from41.85 of repliers on diversifying the loan portfolio and46.15 on effective loan recovery strategies. The correlation analysis further stressed a robust relationship, with a Pearson Correlation measure of0.894 (p- value = .000), italicizing the statistical significance of the positive association between credit risk assessment practices and the financial performance of microfinance institutions. Conclusion:The exploration study concludes grounding of the findings revealed that COPEDU PLCs credit risk assessment practices significantly impact financial performance, with repliers feting the significanceof crucial financial pointers and the 5Cs of credit. In addition, those effective risk operation strategiesare pivotalfor financial success. still, the study recommends microfinance institutions to upgradecredit riskassessment criteria, train staff on the 5Cs of credit, diversify loan portfolios, ameliorate loan recovery strategies, establish a methodical review process, and invest in technology results to enhance credit risk operationand financial sustainability. Eventually, the study made suggestions for farther exploration on credit risk operation in microfinance institutions, including assayingindividual financial pointers, comparing practices across institutions, assessing risk operation strategies, and tracking long- term goodson financial sustainability and growth. It also suggests comparing variations in credit risk assessment practices and enforcing effective recovery strategies.

A many objective based feature selection model for software defect prediction

SummaryGiven the escalating magnitude and intricacy of software systems, software measurement data often contains irrelevant and redundant features, resulting in significant resource and storage requirements for software defect prediction (SDP). Feature selection (FS) has a vital impact on the initial data preparation phase of SDP. Nonetheless, existing FS methods suffer from issues such as insignificant dimensionality reduction, low accuracy in classifying chosen optimal feature sets, and neglect of complex interactions and dependencies between defect data and features as well as between features and classes. To tackle the aforementioned problems, this paper proposes a many‐objective SDPFS (MOSDPFS) model and the binary many‐objective PSO algorithm with adaptive enhanced selection strategy (BMaOPSO‐AR2) is proposed within this paper. MOSDPFS selects F1 score, the number of features within subsets, and correlation and redundancy measures based on mutual information (MI) as optimization objectives. BMaOPSO‐AR2 constructs a binary version of MaOPSO using transfer functions specifically for binary classification. Adaptive update formulas and the introduction of the R2 indicator are employed to augment the variety and convergence of algorithm. Additionally, performance of MOSDPFS and BMaOPSO‐AR2 are tested on the NASA‐MDP and PROMISE datasets. Numerical results prove that a proposed model and algorithm effectively reduces feature count while enhancing predictive accuracy and minimizing model complexity.

Not just a pretty picture: Mapping Leaf Area Index at 10 m resolution using Sentinel-2

Achieving the Global Climate Observing System goal of 10 m resolution leaf area index (LAI) maps is critical for applications related to climate adaptation, sustainable agriculture, and ecosystem monitoring. Five strategies for producing 10 m LAI maps from Sentinel-2 (S2) imagery are evaluated: i. bi-cubic interpolation of 20 m resolution S2 LAI maps from the Simplified Level 2 Prototype Processor Version 1 (SL2PV1) as currently performed by the Sentinel Applications Platform (SNAP), ii. applying SL2PV1 to S2 reflectance bands spatially downscaled to 10 m using bi-cubic interpolation (BICUBIC), iii. Applying SL2PV1 to S2 reflectance bands spatially downscaled to 10 m using Area to Point Regression Kriging (ATPRK), iv. using a recalibrated version of SL2PV1 (SL2PV2) requiring only three S2 10m bands, and iv) a novel use of the previously developed Active Learning Regularization (ALR) approach to locally approximate the SL2PV1 algorithm using only 10 m bands.Algorithms were assessed in terms of per-pixel accuracy and spatial metrics when comparing 10 m LAI maps produced using either actual S2 imagery or S2 imagery synthesized from airborne hyperspectral imagery to reference 10 m LAI maps traceable to in-situ fiducial reference measurements at 10 sites across the continental US. ATPRK and ALR algorithms had the lowest precision error of ∼0.15 LAI, compared to 0.19 LAI for SNAP and BICUBIC and 0.35 LAI for SL2PV2, and ranked highest in terms of local correlation and Structural Similarity Index measure as well as qualitative agreement with reference maps. SL2PV2 LAI showed evidence of saturation over forests related to decreased sensitivity of input visible reflectance. All algorithms had a similar uncertainty of ∼0.55 LAI compared to traceable reference maps, due to the trade-off between bias and precision. However, ATPRK and ALR uncertainty reduced to 0.11 LAI and 0.16 LAI, respectively, when compared to reference maps that ignored canopy clumping. These results suggest that both ATPRK and ALR are suitable for producing 10 m S2 LAI maps assuming bias due to local clumping can be corrected in the underlying SL2PV1 algorithm.

Rényi mutual information in quantum field theory, tensor networks, and gravity

We explore a large class of correlation measures called the α − z Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the α − z RMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of α and z, the α − z RMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute the α − z RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography.

Enhanced imaging of electronic hot spots using quantum squeezed light

Detecting electronic hot spots is important for understanding the heat dissipation and thermal management of electronic and semiconductor devices. Optical thermoreflective imaging is being used to perform precise temporal and spatial imaging of heat on wires and semiconductor materials. We apply quantum squeezed light to perform thermoreflective imaging on micro-wires, surpassing the shot-noise limit of classical approaches. We obtain a far-field temperature sensing accuracy of 42 mK after 50 ms of averaging and show that a 256×256 pixel image can be constructed with such sensitivity in 10 min. We can further obtain single-shot temperature sensing of 1.6 K after only 10 μs of averaging, enabling a dynamical study of heat dissipation. Not only do the quantum images provide accurate spatiotemporal information about heat distribution but also the measure of quantum correlation provides additional information, inaccessible by classical techniques, which can lead to a better understanding of the dynamics. We apply the technique to both aluminum and niobium microwires and discuss the applications of the technique in studying electron dynamics at low temperatures.

Momentum-dependent measures of correlations between mean transverse momentum and harmonic flow in heavy-ion collisions

Momentum-dependent measures of correlations between mean transverse momentum and harmonic flow in heavy-ion collisions

Bridging the performance gap between passive and autonomous inflow control devices with a hybrid dynamic optimization technique integrating machine learning and global sensitivity analysis

Wells equipped with flow control devices across their completion intervals have become a proven field development option for geologically complex and/or viscous oil reservoirs. Such wells increase oil recovery, reduce water and gas production, minimize the need for well workover operations, and subsequently lower the wells' carbon footprint. The uncontrolled types of inflow control devices include early-generation passive inflow control devices (ICDs) and later-generation autonomous inflow control devices (AICDs). The superior performance of AICDs over ICDs in managing water and gas production, as well as enhancing the overall well and reservoir performance has been demonstrated in multiple research and case studies. This superiority stems from the AICDs’ ability to self-adjust and increase their flow resistance when undesired fluids (i.e., water and/or gas) flow through them. While ICDs lack this self-adjusting feature, they are more affordable and more readily available on the market.This study aims to reduce the performance gap between passive and autonomous inflow control devices by developing a hybrid dynamic optimization technique. This approach integrates a metaheuristic algorithm, machine learning, global sensitivity analysis, and correlation measures to facilitate the optimization problem by identifying the high-impact control variables. Next, the proposed workflow finds the necessary adjustments to the original well completion design by modifying the high-impact control variables during the optimization process. This results in a modified well completion design that is less influenced by the type of inflow control device (passive or autonomous), thereby bridging the performance gap between these two completion types.The study employs a benchmark ‘Egg field’ model, featuring two multilateral wells (MLWs) producing under a water flooding recovery mechanism. Two different completion designs, utilizing either ICDs or AICDs, are optimized using standard optimization (SO) and the proposed hybrid dynamic optimization techniques. The standard optimization, which employs a standalone Particle Swarm Optimization (PSO) algorithm, highlights, as expected, the superiority of the AICD-based completion, yielding an approximately 13% increase in the net present value (NPV) over the ICD-based completion. However, when applying the hybrid optimization (HO) technique, this difference is significantly reduced to 3.4%. This indicates the potential for the hybrid optimization technique to make ICD-based completions more competitive and economically favourable compared to their AICD-based counterparts.