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A polarity identification is very important for operation of transformers, measurement and protection equipment, where it is useful in analyzing of transformer connections and operation as well as testing of protective systems. Moreover, it's essential in assessment of power systems performance during both normal and abnormal operation. Ensuring the correct polarity of the primary and secondary windings in voltage and current transformers is of paramount importance for various measurement and protection schemes in power networks. This paper proposes a digital polarity detector and tester using correlation coefficients and nine polarity indices calculated for instrument transformer signals. In order to test the performance of the proposed polarity tester algorithm, MATLAB code is imported to the LABVIEW model, and the numerical data obtained from the synchronous generator terminals via instrument transformers are interfaced with the computer through the Data Acquisition Card (DAC). The experimental system consists of a motor-generator set supplying a three-phase inductive load with instrument transformers connected to measure each phase voltage and current. The obtained results for various operating conditions and different types of abnormal conditions prove that the suggested algorithm is accurate, reliable and applicable to smart grids and substation automation systems. It can be considered as an integrated system incorporated with digital fault recorders, relays and meters. [ABSTRACT FROM AUTHOR]

As an effective tool to show the fuzziness of qualitative information, the probabilistic hesitant fuzzy set (PHFS) can utilize a group of membership degrees with a clear probability distribution to show the opinions of decision-maker (DM). Given this merit, many probabilistic hesitant fuzzy multi-criteria group decision-making (PHF-MCGDM) methods have been designed. However, most of the existing PHF-MCGDM methods have some limitations, including the difficulty of reflecting DMs' ambiguous and hesitant preferences for criteria weights and the inability to comprehensively show the impacts of DMs' irrational behaviors. To address these limitations, this paper develops a novel PHF-MCGDM method that integrates the defining interrelationships between ranked criteria (DIBR) approach and tri-reference point (TRP) theory. First, the PHF-DIBR approach is constructed to determine criteria weights by fully expressing DMs' ambiguous and hesitant preferences for the importance of criteria. Second, the novel probabilistic hesitant fuzzy correlation coefficient (NPHFCC) is developed for deriving the weights of DMs, which remedies the flaws of the existing correlation coefficients (CC). Moreover, TRP theory is used to describe the psychological behavior effects of DMs and derive the order of alternatives. Finally, the applicability of the proposed method is validated by the case about office flooring material selection, while the sensitivity and comparison analyses are also conducted to further prove its advantages and effectiveness. [ABSTRACT FROM AUTHOR]

In the ABL wind tunnel, three inverted umbrella-shaped membrane structure groups were subjected to simultaneous pressure measurement model test. Time series of the fluctuating wind pressure were collected from 24 different wind angles. Upon examining the correlation coefficient of the fluctuating wind pressure between the upper and lower surfaces at the same pressure tap, it was discovered that the fluctuating wind pressure of the upwind roof exhibited asynchronous changes, which is a characteristic of a negative correlation area and has detrimental effects on the structure's wind resistance. The local areas with non-Gaussian properties were evaluated by analyzing the probability density function of representative pressure taps. The mechanism behind non-Gaussian wind pressure was elucidated through considerations of the central limit theorem and spatial correlation of fluctuating wind pressure. This study introduces a quantitative classification criterion for identifying the non-Gaussian distribution area of fluctuating wind pressure, setting the threshold at an 80% cumulative probability for both skewness and kurtosis. The analysis showed that the steady airflow of the structure corresponds to the Gaussian distribution area, while the non-Gaussian distribution area is primarily concentrated at the front edge of the upwind roof and the rear edge of the downwind roof. To ascertain the peak factor for the non-Gaussian distribution, the improved peak factor method was utilized, providing insights into the range of peak factor in the non-Gaussian distribution area of this particular roof configuration. This information serves as a foundation for the wind resistance design of this structure. [ABSTRACT FROM AUTHOR]

Background The psychological disorders like depression, anxiety, and stress seem significantly more prevalent in medical students than in general people nowadays. The medical courses with tedious academic activities raise this mental distress among them. In addition, demographic and biological factors have a citable impact on mental illness. Thus, to analyze these health issues, many studies have been done based on the DASS- Depression Anxiety Stress Scale, where DASS21 comprises 21 questionnaires. Objectives To highlight the correlation between demographic features and DASS21 attributes. Determining the severity of depression, anxiety, and stress in medical students, and observing the percentage-wise relation between preferred features - BMI, Blood Pressure, and Blood Group - and DASS21 attributes. Methods An online survey was conducted on Uttara Adhunik Medical College undergraduate students in November 2023. Students' demographic data, biological factors information, and responses from DASS21 questionnaires were taken in this survey. Further analysis of results and visual observation has been done through online and offline spreadsheets. Result Following the correlation coefficient test, students' age and blood pressure negatively relate to DASS attributes; however, BMI is correlated positively with depression, anxiety, and stress. The severe prevalence rate of depression- 59%, anxiety- 72%, and stress- 53%, where females are more affected. The students who belong to the O and B blood groups as well as the overweight and obese students are more affected although most of them are healthier; nevertheless, depressed, anxious, and stressed students are mostly normotensive. Conclusion The present study highlights that most of the undergraduate medical students of UAMC, especially females are suffering from depression, anxiety, and stress issues. These psychological disorders are highly associated with their BMI, Blood Pressure, and Blood Groups. [ABSTRACT FROM AUTHOR]

The aim of this study is to compare the results of correlation coefficient estimation of reliability with those obtained through the Bland–Altman plot technique. The scale was first divided into two halves using three different approaches. A linear and high-level relationship was found between the scale scores obtained from the halved forms. However, there was disagreement between the scores obtained from Form A and B, as well as between Form C and D. Agreement was found between the scores obtained from Form E and F. [ABSTRACT FROM AUTHOR]

This scientific paper explores the use of correlation coefficients of vibration signals and machine learning algorithms for structural damage assessment in beams under moving loads. The paper discusses the challenges of maintaining structural integrity and the importance of automated, nondestructive monitoring techniques. Preprocessing techniques, such as the random decrement technique (RDT), are highlighted for improving data analysis. Machine learning algorithms are identified as valuable tools for structural damage assessment. The paper concludes by emphasizing the potential of machine learning in safeguarding critical infrastructures. The text also discusses trigger points and the vibration response of a slender beam under a moving load. An artificial neural network (ANN) is proposed as a computational model for identifying non-linear features. Experimental testing on a simulated bridge girder using accelerometers collected data to identify and locate damage in the beam. The ANN achieved high accuracy in detecting damage appearance and location, but further research is needed to improve accuracy in real-world situations. [Extracted from the article]

Analyzing correlated parameters can help water managers find and prove the cause of a water quality change. [ABSTRACT FROM AUTHOR]

Software evolution is an essential foundation in delivering technology that adapts to user needs and industry dynamics. In an era of rapid technological development, software evolution is not just a necessity, but a must to ensure long-term relevance. Developers are faced with major challenges in maintaining and improving software quality over time. This research aims to investigate the correlation between feature volatility and bug occurrence rate in software evolution, to understand the impact of dynamic feature changes on software quality and development process. The research method uses commit analysis on the dataset as a marker of bug presence, studying the complex relationship between feature volatility and bug occurrence rate to reveal the interplay in software development. Validated datasets are measured by metrics and correlations are measured by Pearson-productmoment analysis. This research found a strong relationship between feature volatility and bug occurrence rate, suggesting that an increase in feature changes correlates with an increase in bugs that impact software stability and quality. This research provides important insights into the correlation between feature volatility and bug occurrence rates, guiding developers and quality practitioners to develop more effective testing strategies in dynamic development environments. [ABSTRACT FROM AUTHOR]

To fulfill the demand for high-precision underwater acoustic positioning at full sea depth, an ultra-short baseline (USBL) positioning method with the square array based on the least squares estimating signal parameters via rotational invariance techniques (LS-ESPRIT) algorithm is presented in this paper. A combination of beam tracking and beamforming is employed to improve the accuracy of direction-of-arrival (DOA) estimation and, consequently, enhance overall positioning accuracy. In order to mitigate the issue of position jumping resulting from phase ambiguity in traditional four-element cross arrays, we have improved the stability of the positioning algorithm by utilizing a multi-element square array and employing the LS-ESPRIT algorithm for DOA estimation. Furthermore, the signal detection method integrating the correlation coefficient and ascending/descending chirp signals is employed to enhance the reliability of the location algorithm. Simulation analysis and experimental results demonstrate that the proposed algorithm effectively enhances positioning accuracy and improves the problem of jumping in positioning results. [ABSTRACT FROM AUTHOR]

The primary design property necessary to ensure the longevity and durability of manufactured materials is the material hardness. The primary objective of this study was to investigate the effect of cutting parameters, namely feed rate, cutting speed, and depth of cut, on the surface hardness generated during the turning process of aluminum alloy 6061. The turning experiments were conducted using a Taguchi L27 orthogonal array arranged for three-level cutting parameters. The Analysis of Variance (ANOVA) was employed to determine the relative importance of each parameter on surface hardness. Additionally, an Artificial Nural Network (ANN) predictive model using the back-propagation learning algorithm was created to predict surface hardness levels at each level of the cutting parameters. The results revealed that increasing the values of all the turning parameters resulted in an increase in hardness, and it was concluded that the feed rate was the most critical factor (53.41%) in achieving high surface hardness, followed by the depth of cut (27.89%), whereas cutting speed had a lower impact (18.7%). This study also suggests a simple equation for estimating the surface hardness from the cutting parameters. The ANN model could accurately estimate the surface hardness with a coefficient of correlation (R) higher than 0.98 between the predicted and experimental values. The predicted values of hardness by ANN were more precise (R² =0.973839) than those predicted by ANOVA (R²=0.893). [ABSTRACT FROM AUTHOR]

By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models. [ABSTRACT FROM AUTHOR]

To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

The evaluation methods for shale gas resources and the key parameters involved are diverse. The main research object of this article is the key parameters in shale gas resource evaluation, and this study aims to quantitatively evaluate the required key parameters for calculation, thereby improving the credibility of shale gas resource evaluation results. This article mainly analyzes the weight analysis of the key parameters used in the resource evaluation process, focusing on the analysis and determination of key parameters controlling the generation, enrichment, and preservation of shale gas. The key parameters are graded and evaluated layer by layer, and the common key parameters that participate in the determination are extracted. Based on the above analysis, a weight conversion model is proposed to quantitatively evaluate the actual importance of key parameters in resource evaluation. By combining statistical research, the partial correlation coefficients in the correlation coefficients are applied to estimate the resource quantities in the exploration field in order to quantitatively evaluate the credibility of the resource evaluation results. This article focuses on the weight assignment of key parameters for calculating the resource quantity of the Jiaoshiba shale gas field in the Fuling area of Chongqing and obtains different weight results for different parameters. Using this method to assign key parameter weights to the target block can provide reliable parameter support for shale gas resource evaluation and provide strong support for shale gas resource estimation. [ABSTRACT FROM AUTHOR]

In the context of growing concerns related to the impact of mining activities on the environment, the present study focuses on the analysis of the correlations between the concentrations of heavy metals in Branch 1 and 2 tailing dumps in Lupeni, using Pearson correlation coefficient matrix. Tailing dumps from mining activity can be significant sources of soil contamination with heavy metals. In this work, the waste dumps Branch 1 and 2 were taken as a case study. This dump has been inactive for about 7 years and is the result of the exploitation of the waste from Lupeni mine located in the Jiu Valley. In this study, soil samples from the two branches of the tailing dump were collected and analyzed to determine heavy metal concentrations. Using Pearson correlation coefficient, statistical relationships between the concentrations of these heavy metals were calculated, providing a detailed matrix of correlations between them. This statistical analysis can help develop more effective remediation and management strategies, lessening the long-term impact of mining activities on the environment and human health. [ABSTRACT FROM AUTHOR]

The relevance of this research is due to the need to stabilize the composition of the melting products of copper–nickel sulfide raw materials. Statistical methods of analyzing the historical data of the real technological object and the correlation analysis of process parameters are described. Factors that exert the greatest influence on the main output parameter (the fraction of copper in a matte) and ensure the physical–chemical transformations are revealed: total charge rate, overall blast volume, oxygen content in the blast (degree of oxygen enrichment in the blowing), temperature of exhaust gases in the off-gas duct, temperature of feed in the smelting zone, copper content in the matte. An approach to the processing of real-time data for the development of a mathematical model for control of the melting process is proposed. The stages of processing of the real-time information are considered. The adequacy of the models was assessed by the value of the mean absolute error (MAE) between the calculated and experimental values. [ABSTRACT FROM AUTHOR]

With today's changing dietary demands and agricultural constraints, millets have become essential crops with significant agronomic and nutritional benefits. Among these, barnyard millet stands out for its resilience and nutritional richness. Despite its considerable nutritional and agronomic benefits, Barnyard millet suffers from a lack of recognition, relegating it to the status of a neglected and underutilized crop. The present study ventures into barnyard millet cultivation, utilizing correlation and path coefficient analysis to elucidate the complex interplay influencing its productivity and attributes. The study was conducted over two consecutive years and involved 172 genotypes with 23 yield-contributing traits under scrutiny. Panicle weight per plant (PWPP) (0.98), single panicle weight (0.81), biological yield per plant (0.79) and harvest index (0.71) exhibited strong positive correlations with grain yield per plant. While PWPP (0.82), PL (0.36), DSYPP (0.31) and HI (0.30) demonstrated high direct positive effects on grain yield per plant in the path coefficient analysis, emphasizing their significance in breeding programs. By improving these traits through selective breeding or genetic manipulation, researchers can potentially develop high-yielding varieties better adapted to varying environmental conditions. Conversely, days to maturity had a significant negative correlation with grain yield (-0.28) focusing on selecting early maturity genotypes. Panicle exertion (-0.30), biological yield per plant (-0.21) and flag leaf sheath length (-0.18) had the highest negative direct effects in the path analysis, suggesting their potential role as limiting factors in barnyard millet cultivation. Overall, these findings provide a roadmap for future research endeavours aimed at enhancing the productivity and resilience of barnyard millet, ultimately contributing to food security and agricultural sustainability in regions where this crop plays a vital role. [ABSTRACT FROM AUTHOR]

When analyzing GPS time series, common mode errors (CME) often obscure the actual crustal movement signals, leading to deviations in the velocity estimates of station coordinates. Therefore, mitigating the impact of CME on station positioning accuracy is crucial to ensuring the precision and reliability of GNSS time series. The current approach to separating CME mainly uses signal filtering methods to decompose the residuals of the observation network into multiple signals, from which the signals corresponding to CME are identified and separated. However, this method overlooks the spatial correlation of the stations. In this paper, we improved the Independent Component Analysis (ICA) method by introducing correlation coefficients as weighting factors, allowing for more accurate emphasis or attenuation of the contributions of the GNSS network's spatial distribution during the ICA process. The results show that the improved Weighted Independent Component Analysis (WICA) method can reduce the root mean square (RMS) of the coordinate time series by an average of 27.96%, 15.23%, and 28.33% in the E, N, and U components, respectively. Compared to the ICA method, considering the spatial distribution correlation of stations, the improved WICA method shows enhancements of 12.53%, 3.70%, and 8.97% in the E, N, and U directions, respectively. This demonstrates the effectiveness of the WICA method in separating CMEs and provides a new algorithmic approach for CME separation methods. [ABSTRACT FROM AUTHOR]

Aim: This study aimed to establish the shear wave measurement (SWM) cut‐off value for each fibrosis stage using magnetic resonance (MR) elastography values as a reference standard. Methods: We prospectively analyzed 594 patients with chronic liver disease who underwent SWM and MR elastography. Correlation coefficients (were analyzed, and the diagnostic value was evaluated by the area under the receiver operating characteristic curve. Liver stiffness was categorized by MR elastography as F0 (<2.61 kPa), F1 (≥2.61 kPa, <2.97 kPa, any fibrosis), F2 (≥2.97 kPa, <3.62 kPa, significant fibrosis), F3 (≥3.62 kPa, <4.62 kPa, advanced fibrosis), or F4 (≥4.62 kPa, cirrhosis). Results: The median SWM values increased significantly with increasing fibrosis stage (p < 0.001). The correlation coefficient between SWM and MR elastography values was 0.793 (95% confidence interval 0.761–0.821). The correlation coefficients between SWM and MR elastography values significantly decreased with increasing body mass index and skin–capsular distance; skin–capsular distance values were associated with significant differences in sensitivity, specificity, accuracy, or positive predictive value, whereas body mass index values were not. The best cut‐off values for any fibrosis, significant fibrosis, advanced fibrosis, and cirrhosis were 6.18, 7.09, 8.05, and 10.89 kPa, respectively. Conclusions: This multicenter study in a large number of patients established SWM cut‐off values for different degrees of fibrosis in chronic liver diseases using MR elastography as a reference standard. It is expected that these cut‐off values will be applied to liver diseases in the future. [ABSTRACT FROM AUTHOR]

Copyright of Laser Technology is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The Federal Open Market Committee (FOMC) is a component of the Federal Reserve System responsible for overseeing open market operations. The FOMC meets roughly eight or more times per year to assess the economy of the United States. After each meeting, the FOMC releases a statement to the press outlining its assessment of the US economy and its monetary policy stance. The sentiment of these statements may have an influence on the US economy and financial markets. Using sentiment and correlational analyses, this research examines how the sentiment of these statements affects the US economy and financial markets by analyzing how FOMC statement sentiment is correlated with the Consumer Price Index (CPI), the National Financial Conditions Index (NFCI), and the Adjusted National Financial Conditions Index (ANFCI). We find evidence to suggest that there is a moderate negative correlation between an FOMC statement's sentiment and the US City Average CPI value associated with the month before and the month after the statement's release. We also find that there is no evidence to suggest there exists a correlation between an FOMC statement's sentiment and the NFCI value associated with the week before or the week after the statement's release. However, we do find evidence to suggest that there is a moderate negative correlation between an FOMC statement's sentiment and the ANFCI value associated with the week before and the week after the statement's release. We also found that out of the three models we tested (linear regression, vine copula regression, and Gaussian copula regression), the Gaussian copula regression model performs the best when forecasting the CPI and the ANFCI. Additionally, we find that when forecasting CPI values, the models that include FOMC statement sentiment are more accurate than the models that exclude FOMC statement sentiment. [ABSTRACT FROM AUTHOR]

Abstract A polarity identification is very important for operation of transformers, measurement and protection equipment, where it is useful in analyzing of transformer connections and operation as well as testing of protective systems. Moreover, it’s essential in assessment of power systems performance during both normal and abnormal operation. Ensuring the correct polarity of the primary and secondary windings in voltage and current transformers is of paramount importance for various measurement and protection schemes in power networks. This paper proposes a digital polarity detector and tester using correlation coefficients and nine polarity indices calculated for instrument transformer signals. In order to test the performance of the proposed polarity tester algorithm, MATLAB code is imported to the LABVIEW model, and the numerical data obtained from the synchronous generator terminals via instrument transformers are interfaced with the computer through the Data Acquisition Card (DAC). The experimental system consists of a motor-generator set supplying a three-phase inductive load with instrument transformers connected to measure each phase voltage and current. The obtained results for various operating conditions and different types of abnormal conditions prove that the suggested algorithm is accurate, reliable and applicable to smart grids and substation automation systems. It can be considered as an integrated system incorporated with digital fault recorders, relays and meters.

The presented research covers a significant part of the period of the COVID-19 pandemic and studies the role of environmental factors in formation of population mortality from main causes. The main causes of mortality among the population of Odesa Region during the studied period include diseases of circulatory system, COVID-19, neoplasms, external causes, diseases of digestive organs and diseases of respiratory organs. The aforesaid causes constitute 94-95% of all causes of mortality in Odesa Region. However, out of these six classes of diseases, only diseases of circulatory system, COVID-19 and diseases of respiratory organs and some of their nosological forms have simultaneous peaks in mortality, during which mortality of the Odesa Region population from all causes almost doubles. Over time, there is a certain redistribution of frequency of the causes of mortality among the six main causing diseases of the population`s mortality in the region. But this does not explain occurrence of simultaneous peaks in mortality from diseases of circulatory system, COVID-19, and diseases of respiratory organs. Formation of simultaneous peaks in mortality from non-infectious and infectious diseases cannot be explained by the influence of social or anthropogenic factors. This indicates the need to address a number of environmental factors of natural origin – meteorological, biometeorological and heliocosmic. The study shows the possibility of an existing linear statistical connection between these environmental factors and the mortality of the Odesa Region population from such classes of diseases as diseases of circulatory system, COVID-19 and diseases of respiratory organs, as well as the relevant nosological forms. The results of the correlation analysis between mortality rates from major diseases and the environmental factors studied showed weak correlations between them. It is fully consistent with the World Health Organization's view of the role of environmental conditions in shaping public health.

Utilizing the European Centre for Medium-Range Weather Forecast (ECMWF) Reanalysis v5 (ERA5), for the first time, we have confirmed close links among Sudden Stratospheric Warmings (SSWs) in the Northern Hemisphere (NH), the polar vortices, and stratospheric Planetary Waves (PWs) by analyzing and comparing their trends. Interestingly, within overall increasing trends, the duration and strength of SSWs exhibit increasing and decreasing trends before and after the winter of 2002, respectively. To reveal possible physical mechanisms driving these trends, we analyzed the long-term trends of the winter (from December to February) polar vortices and of stratospheric PWs with zonal wave number 1. Notably, our results show that in all three time periods (the entire period of 41 winters, 1980 to 2020, and the two subperiods — 1980−2002 and 2002−2020) enhancing SSWs were always accompanied by weakening winter polar vortices and strengthening polar PWs like Stationary Planetary Waves (SPWs) and 16-day waves, and vice versa. This is the first proof, based on ERA5 long-term trend data, that weakening polar vortices and enhancing stratospheric PWs (especially SPWs) could cause an increase in SSWs.

The opinion of r,s,t spherical fuzzy set (r,s,t-SFS) revealed by Ali and Naeem (IEEE Access 11:46454-46475, 2023a) is one of the significant spreads of picture fuzzy set which is developed to define ambiguous, undefined information in multi criteria decision making (MCDM) problems, machine learning, data mining and medical diagnosis so on. This paper aims to present a new tool called as r,s,t spherical hesitant fuzzy set (r,s,t-SHFS) by extending to r,s,t-SFS to overcome uncertainness and impreciseness encountered in daily life scenes. This construction puts forward many advantages for experts as extract parameters, carrying more information, hosting to several clusters in its own structure, being more flexible concept. The framework of r,s,t-SHFS is a generalization of hesitant fuzzy set, spherical hesitant fuzzy set, picture hesitant fuzzy set and t-spherical hesitant fuzzy set having a gorgeous potential of overcoming with uncertain and vagueness events. When examined from this perspective, the proposed cluster may present a more flexible structure for decision makers. Further, the correlation coefficient (CC) is often used to predict how a particular factor will fluctuate relative to another. The existing work investigates CC and weighted CC for r,s,t spherical hesitant fuzzy set and some set-theoretical operations. Moreover, we build a MCDM algorithm known as clustering based on the introduced correlation coefficients. Then, we solve another example by finding ideal and non-ideal solutions based on union and intersection operations through the technique for order preference by similarity to ideal solution method. Moreover, we determine the usefulness and limited sides of the new concept by comparing with some existing instructions. Some graphical presentations are given to demonstrate the credibility and effectiveness of the defined measures. [ABSTRACT FROM AUTHOR]

The relevance of this research is due to the need to stabilize the composition of the melting products of copper–nickel sulfide raw materials. Statistical methods of analyzing the historical data of the real technological object and the correlation analysis of process parameters are described. Factors that exert the greatest influence on the main output parameter (the fraction of copper in a matte) and ensure the physical–chemical transformations are revealed: total charge rate, overall blast volume, oxygen content in the blast (degree of oxygen enrichment in the blowing), temperature of exhaust gases in the off-gas duct, temperature of feed in the smelting zone, copper content in the matte. An approach to the processing of real-time data for the development of a mathematical model for control of the melting process is proposed. The stages of processing of the real-time information are considered. The adequacy of the models was assessed by the value of the mean absolute error (MAE) between the calculated and experimental values.

Abstract The Dunhuang murals are a precious treasure of China’s cultural heritage, yet they have long been affected by salt damage. Traditional methods for detecting salt content are costly, inefficient, and may cause physical harm to the murals. Among current techniques for measuring salt content in murals, hyperspectral remote sensing technology offers a non-invasive, circumventing issues of high costs, low efficiency. Building on this, the study constructs an inversion model for the Electrical Conductivity (EC) values of mural plaster subjected to phosphate erosion, through the integration of Fractional Order Differentiation (FOD), a novel three-band spectral index, and the Partial Least Squares Regression algorithm. The specific research contents include: (1) Initially, in preparation for the experiments, the materials used to create the samples underwent a rigorous desalting process, and phosphate solutions were prepared using deionized water to ensure uniform experimental conditions and the accuracy of the results. These meticulous preprocessing steps guaranteed that the measured EC values exhibited a clear correlation with the phosphate content. Subsequently, by employing qualitative experimental analysis techniques, this study was able to more accurately simulate the real-world scenarios of mural plaster affected by salt damage, enabling a deeper investigation into the mechanisms by which salts inflict microscopic damage to murals. (2) Explores the absorption mechanisms and characteristic spectral bands of the Electrical Conductivity (EC) values measured after the phosphate erosion of mural plaster. By integrating the optimal spectral indices, a univariate linear regression model is constructed, providing a basis for the rapid quantitative measurement of electrical conductivity in murals. (3) By comparing the accuracy of the Phosphate Simple Ratio (PSR) and Phosphate Normalized Difference Index (PNDI) spectral indices based on the linear regression model, the first six orders of the highest accuracy spectral index were selected as the optimal three-band spectral index combination, used as explanatory variables, with mural plaster electrical conductivity as the response variable, employing the PLSR method to construct the mural phosphate content high-spectral feature inversion model. The study’s findings include: (1) Surfaces of samples deteriorated by phosphate erosion formed numerous irregularly shaped crystal clusters, exhibiting uneven characteristics. (2) By comparing the outcomes of different orders of fractional differentiation, it was found that the model performance reached its optimum at a 0.3 order of differentiation for both PSR and PNDI data, with a determination coefficient (Q2) of 0.728. (3) Utilizing PLSR, this study employed the previously determined optimal six-order three-band spectral index combination as explanatory variables, with salt content as the response variable, successfully constructing the high-spectral feature inversion model for mural electrical conductivity with a determination coefficient (Q2) of 0.815. This provides an effective technical means for monitoring the salt damage conditions of precious cultural heritage such as murals.

Currently, in pork auctions in Korea, only carcass weight and backfat thickness provide information on meat quantity, while the production volume of primal cuts and fat contents remains largely unknown. This study aims to predict the production of primal cuts in pigs and investigate how these carcass traits affect pricing. Using the VCS2000, the production of shoulder blade, loin, belly, shoulder picnic, and ham was measured for gilts (17,257 pigs) and barrows (16,365 pigs) of LYD (Landrace × Yorkshire × Duroc) pigs. Single and multiple regression analysis were conducted to analyze the relationship between the primal cuts and carcass weight. The study also examined the correlation between each primal cut, backfat thickness (1st thoracic vertebra backfat thickness, grading backfat thickness, and Multi-brached muscle middle backfat thickness), pork belly fat percentage, total fat yield, and auction price. A multiple regression analysis was conducted between the carcass traits that showed a high correlation and the auction price. After conducting a single regression analysis on the primal cuts of gilt and barrow, all coefficients of determination (R2) were 0.77 or higher. In the multiple regression analysis, the R2 value was 0.98 or higher. The correlation coefficient between the carcass weights and the auction price exceeded 0.70, while the correlation coefficients between the primal cuts and the auction prices were above 0.65. In terms of fat content, the backfat thickness of gilt exhibited a correlation coefficient of 0.70, and all other items had a correlation coefficient of 0.47 or higher. The correlation coefficients between the Forequarter, Middle, and Hindquarter and the auction price were 0.62 or higher. The R2 values of the multiple regression analysis between carcass traits and auction price were 0.5 or higher for gilts and 0.4 or higher for barrows. The regression equations between carcass weight and primal cuts derived in this study exhibited high determination coefficients, suggesting that they could serve as reliable means to predict primal cut production from pig carcasses. Elucidating the correlation between primal cuts, fat contents and auction prices can provide economic indicators for pork and assist in guiding the direction of pig farming.

Abstract The multi-criteria decision-making (MCDM) field has long sought tools capable of adeptly capturing the intricacies of human decision-making amidst uncertainty. Hesitant fuzzy sets (HFS) have become a cornerstone in the MCDM field due to their ability to capture the intricacies of human decision-making under uncertainty. Nonetheless, we identified a significant gap in traditional HFS formulations, which often fail to fully harness the nuanced and implicit preferences of decision-makers (DMs). This shortcoming can lead to suboptimal decision outcomes in complex and uncertain environments. We introduce the normal wiggly hesitant fuzzy set (NWHFS), a novel construct that encapsulates both explicit and implicit preferences within a more representative framework. This study pioneers the development of new correlation coefficients for NWHFSs, offering a robust quantitative measure to elucidate the intricate relationships between variables. Our findings demonstrate that NWHFSs significantly enhance the MCDM process, providing a nuanced perspective that traditional HFS models cannot match. The proposed correlation coefficients not only reveal the concealed preferences of DMs but also broaden the decision-making spectrum, offering a more profound understanding of the relationships between alternatives and criteria. We illustrate the superiority of our approach through comparative analysis with existing methods, highlighting its ability to discern subtleties that other models overlook. Moreover, we integrate NWHFSs into clustering analysis, showcasing their potential to classify data sources with shared attributes effectively. This integration is particularly noteworthy for its ability to navigate complex datasets, offering a new dimension in data mining and resource retrieval. In essence, our study redefines the MCDM paradigm by introducing NWHFSs and their correlation coefficients, setting a new standard for decision-making accuracy and insight. The implications of our work extend beyond theory, offering practical solutions to real-world decision-making challenges.

Breast cancer is perceived as the most common cause of mortality among women globally. Early detection of this disease is critical to reduce significantly the possibility of death. Machine learning techniques have been proved to be efficient and very successful for an accurate breast cancer diagnosis. In this paper, an efficient hybrid Feature Selection (FS) method named a Correlation technique-Modified Grey Wolf Optimizer (CMGWO) was proposed for accurate breast cancer classification based on dimensionality reduction. The suggested technique is based on two stages: the feature selection step and the classification step. Feature selection is the process of picking the most significant characteristics from a dataset. This stage is crucial in machine learning. Firstly, we focus on the filter method by using a Correlation technique for dimensionality reduction. This technique is intended to eliminate and reduce the number of features by selecting one feature from the other correlated features. Secondly, we use the Modified Grey Wolf Optimization algorithm (MGWO) to locate and determine the most significant features from uncorrelated features. After that, we use multiple classifiers to classify breast cancer disease based on the selected features. The Wisconsin Diagnostic Breast Cancer (WDBC) database was used to prove the performance of our proposed work. The experimental results show that the combination of the correlation method and MGWO for feature selection increases the accuracy rate of classification with a minimum number of features. The performances of different machine learning algorithms were evaluated, including Random Forest classifier (RF), Support Vector Machine (SVM) Classifier, and Naïve Bayes (NB) Classifier for the classification step. The suggested technique proves to be the best approach and reliable one among all studied approaches since it increases classification accuracy to 99.12\% obtained by CMGWO using Random Forest classifier and demonstrates its significance in detecting breast cancer.

Abstract Most current algorithms for multivariate time series classification tend to overlook the correlations between time series of different variables. In this research, we propose a framework that leverages Eigen-entropy along with a cumulative moving window to derive time series signatures to support the classification task. These signatures are enumerations of correlations among different time series considering the temporal nature of the dataset. To manage dataset’s dynamic nature, we employ preprocessing with dense multi scale entropy. Consequently, the proposed framework, Eigen-entropy-based Time Series Signatures, captures correlations among multivariate time series without losing its temporal and dynamic aspects. The efficacy of our algorithm is assessed using six binary datasets sourced from the University of East Anglia, in addition to a publicly available gait dataset and an institutional sepsis dataset from the Mayo Clinic. We use recall as the evaluation metric to compare our approach against baseline algorithms, including dependent dynamic time warping with 1 nearest neighbor and multivariate multi-scale permutation entropy. Our method demonstrates superior performance in terms of recall for seven out of the eight datasets.

Artificial neural networks, machine learning, and data preparation are normally implemented in a wide range of real-world problems, especially in geotechnical applications with optimistic prospects of accurate procedure outcomes. This technique has been utilized to precisely predict the top settlement of piles with various piles and soil parameters. Generally, the pile settlement is an essential requirement to produce a secure structure and has high-performance services. The current article presents the fitting of the artificial neural network (ANN) outcomes by calculating the coefficient of correlation R 2 between the predicted and the measured or calculated value of pile settlement. The ANN algorithm is developed using Python 3.9 IDLE and open-source libraries such as Keras, sklearn, Numpy, matplotlib, pandas, and Tensorflow. Because of random training and test performance, the model has been run at least ten times. The ANN model score and R 2 are compared for all runs in the testing phase. The higher score and R 2 values are chosen. Moreover, the Multivariate Linear Regression with the sklearn library is also offered in this article and utilized to produce a pile settlement formula by applying the same dataset used in ANN. The score and R 2 for choosing the first run of the ANN are 99.95% and 0.9631, respectively, while the correlation coefficient for the Multivariate Linear Regression in the training and testing phases is 0.972 and 0.919, respectively. Both techniques illustrate considerable results.

Complex interval-valued intuitionistic fuzzy sets not only consider uncertainty and periodicity semantics at the same time but also choose to express the information value with an interval value to give experts more freedom and make the solution to the problem more reasonable. In this study, we used the interval quaternion number space to generalize and extend the utility of complex interval-valued intuitionistic fuzzy sets, analyze their order relation, and offer new operations based on interval quaternion numbers. We proposed a new score function and correlation coefficient under interval quaternion representation. We applied the interval quaternion representation and correlation coefficient to a multi-criterion decision making model and applied the model to enterprise decision-making.

Purpose: Grape (Vitis vinifera L.) is one of the most important horticultural products that are grown in different parts of Iran and has high nutritional values. In this study, the genetic diversity of cultivars and genotypes of some vineyards of Markazi province were investigated for the preliminary selection of superior cultivars and genotypes in terms of morphological and fruit characteristics for use in grape breeding programs. Research method: For this purpose, grouping and comparing 84 grape cultivars and genotypes were carried out using 70 traits including phenological and vegetative traits, trichome and stomata, bunch and berry traits. Findings: Based on the results, the “Sahebi Hazaveh” cultivar with 1000.17 g had highest an average bunch weight to compare other cultivars and genotypes. Results showed that, some traits such as bunch weight, bunch shoulders, fresh weight, rachis weight, the ratio of bunch weight to peduncle weight, the ratio of rachis weight to bunch weight, dry weight of bunch shoulders, length of the tail of bunch, berry weight, pedicel weight, seed weight and length of seed had a high coefficient of variation. Factor analysis reduced the evaluated traits to 10 main factors showed that they justified 78.38% of the total variance. Cluster analysis divided cultivars and genotypes into 4 main groups at five Euclidean distances. Limitations: No limitations were encountered. Originality/Value: This study indicated that grapes germplasm resources in zone are of noticeable diversities and can be promising for the utilization in the breeding programs. Based on the results, cultivars and genotypes of “Khalili Khondab” region, “Yaghouti”, “Sahebi”, “Fakhri”, “Kharvand” and “Kondori” Hazaveh region and “Sahebi” Aghbolagh region in leafing time, late flowering, sugar percentage, bunch and berry characteristics, stomatal density, standing and lying trichome density in leaves were superior to other cultivars and genotypes.

Buckyballs are closed spherical carbon cages which are beneficial in several industries. Their chemical graphs provide structural invariants called topological invariants. This study is devoted to investigating the relation between degree-based topological index called Sombor index and physical properties of buckyballs. The sample contains buckyballs consisting of 54, 58, 60, 70, 74, 76, 78, 80, 82, 84, 86 and 90 carbon atoms.The topological indices with degree bases can be used to display the physical characteristics of buckyballs. The numerical values of topological indices describe the topological structure of a molecule. The physical properties include binding energy, Ramsauer–Townsend effect (RT-1, RT-2), shape resonances (SR-1, SR-2), and heat of formation of buckyballs. [ABSTRACT FROM AUTHOR]

The Dunhuang murals are a precious treasure of China's cultural heritage, yet they have long been affected by salt damage. Traditional methods for detecting salt content are costly, inefficient, and may cause physical harm to the murals. Among current techniques for measuring salt content in murals, hyperspectral remote sensing technology offers a non-invasive, circumventing issues of high costs, low efficiency. Building on this, the study constructs an inversion model for the Electrical Conductivity (EC) values of mural plaster subjected to phosphate erosion, through the integration of Fractional Order Differentiation (FOD), a novel three-band spectral index, and the Partial Least Squares Regression algorithm. The specific research contents include: (1) Initially, in preparation for the experiments, the materials used to create the samples underwent a rigorous desalting process, and phosphate solutions were prepared using deionized water to ensure uniform experimental conditions and the accuracy of the results. These meticulous preprocessing steps guaranteed that the measured EC values exhibited a clear correlation with the phosphate content. Subsequently, by employing qualitative experimental analysis techniques, this study was able to more accurately simulate the real-world scenarios of mural plaster affected by salt damage, enabling a deeper investigation into the mechanisms by which salts inflict microscopic damage to murals. (2) Explores the absorption mechanisms and characteristic spectral bands of the Electrical Conductivity (EC) values measured after the phosphate erosion of mural plaster. By integrating the optimal spectral indices, a univariate linear regression model is constructed, providing a basis for the rapid quantitative measurement of electrical conductivity in murals. (3) By comparing the accuracy of the Phosphate Simple Ratio (PSR) and Phosphate Normalized Difference Index (PNDI) spectral indices based on the linear regression model, the first six orders of the highest accuracy spectral index were selected as the optimal three-band spectral index combination, used as explanatory variables, with mural plaster electrical conductivity as the response variable, employing the PLSR method to construct the mural phosphate content high-spectral feature inversion model. The study's findings include: (1) Surfaces of samples deteriorated by phosphate erosion formed numerous irregularly shaped crystal clusters, exhibiting uneven characteristics. (2) By comparing the outcomes of different orders of fractional differentiation, it was found that the model performance reached its optimum at a 0.3 order of differentiation for both PSR and PNDI data, with a determination coefficient (Q2) of 0.728. (3) Utilizing PLSR, this study employed the previously determined optimal six-order three-band spectral index combination as explanatory variables, with salt content as the response variable, successfully constructing the high-spectral feature inversion model for mural electrical conductivity with a determination coefficient (Q2) of 0.815. This provides an effective technical means for monitoring the salt damage conditions of precious cultural heritage such as murals. [ABSTRACT FROM AUTHOR]

Linguistic expressions are widely used to reflect the decision maker's evaluations more easily and clearly in the decision-making problems, The Double Hierarchy Hesitant Fuzzy Linguistic Term Set (DHHFLTS), an extension of linguistic expressions, helps the decision maker to reflect their hesitant evaluations in complex decision making problems using two different sets of linguistic terms. Correlation measurements are used as an important tool in making decisions by making comparative evaluations in complex decision making problems based on common criteria. In this study, a new method is proposed to improve the existing correlation measurement method using DHHFLTSs. The proposed method aims to increase the reflective power of hesitant thoughts in the evaluation process by including fuzzy linguistic expressions in the calculation process. In order to prove the validity of the proposed method, the original problem of choosing the most suitable player for the positions in football sport is considered as a Multi-Attribute Decision Making (MADM) problem. Correlation values and assignment results obtained from the proposed method are compared with the current method values. Consistency of results and values between methods reveals the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Chickpea (Cicer arietinum L.) is one of the crucial legume crops and a primary source of protein for human beings worldwide. The genetically diverse accessions are valuable sources for further improvement in chickpeas through breeding. In the presented study, the 36 chickpea lines from the Chickpea International Elite Nursery-Winter, International Center for Agricultural Research in the Dry Areas (ICARDA), bore assessment for yield-related traits. Determining the effects of various quantitative and yield-attributing traits on the seed yield used linear regression. Simple linear regression models ran separate evaluations for each studied parameter, including plant height, the height of the first pod, the number of secondary branches, the number of pods, the number of seeds per plant, and 100-seed weight. According to analysis for high seed productivity in chickpea cultivation under organic production conditions, the approximate model ensures a high yield as follows: The plant height ranged from 68 to –78 cm, height to the first pod (26–31 cm), number of secondary branches (8–14), number of pods (52–79), number of seeds (64–95), and 100-seed weight (25–45 g). In determining the seed productivity of chickpea genotypes, a direct positive and significant correlation occurred between the 100-seed weight and the number of seeds per plant. These parameters can serve as effective selection criteria for enhancing the chickpea yield. [ABSTRACT FROM AUTHOR]

Cotton is a valuable industrial fiber crop grown in many regions worldwide. Four cotton (Gossypium hirsutum L.) cultivars, i.e., Ishonch, Navbakhor-2, C-6524, and Tashkent-6, and their F1-2 diallel hybrids’ cultivation comprised a randomized complete block design with a factorial arrangement and four replications during 2019–2021 in the Tashkent Region, Uzbekistan. Significant (P ≤ 0.01) differences were notable among the parental genotypes and their F1 hybrids for boll weight and seed cotton yield. The parental cultivars Ishonch and Navbakhor-2 and their F1 diallel hybrids showed more stability and performed better than other genotypes. Broad-sense heritability estimates were the highest for boll weight and seed cotton yield while lowest for bolls per plant. Based on this trait’s yield, heritability, and variability, the inbreeding depression was positive in the F2 populations Ishonch × Navbakhor-2 and Navbakhor-2 × Tashkent-6. According to yield, the cultivars Ishonch, Navbakhor-2, and Tashkent-6 were outstanding as positive donors. [ABSTRACT FROM AUTHOR]

This research work extends the least squares criterion. The regression models which have been treated so far in the literature do not study multilinear relationships between variables. Such relationships are of a nonlinear nature. They take place whenever two or more than two univariate variables are the components of a multiple variable of order 2 or an order greater than 2. A multiple variable of order 2 is not a bivariate variable, and a multiple variable of an order greater than 2 is not a multivariate variable. A multiple variable allows for the construction of a tensor. The α -norm of this tensor gives rise to an aggregate measure of a multilinear nature. In particular, given a multiple variable of order 2, four regression lines can be estimated in the same subset of a two-dimensional linear space over R. How these four regression lines give rise to an aggregate measure of a multilinear nature is shown by this paper. In this research work, such a measure is an estimate concerning the expected return on a portfolio of financial assets. The metric notion of α -product is used to summarize the sampling units which are observed. [ABSTRACT FROM AUTHOR]

Background: The diagnosis and treatment monitoring of hepatitis C is quite challenging. The screening test, i.e. antibody assay, is unable to detect acute cases, while the gold standard hepatitis C virus (HCV) reverse transcriptase polymerase chain reaction (RTPCR) assay is not feasible in resource-limited countries such as India due to high cost and infrastructure requirement. European Association for the Study of the Liver and World Health Organization have approved a new marker, i.e. HCV core antigen (HCVcAg) assay, as an alternative to molecular assay. In this study, we have evaluated HCVcAg assay for diagnosis and treatment monitoring follow-up in Indian population infected with hepatitis C. Methods: Blood specimen of 90 clinically suspected cases of acute hepatitis C were tested simultaneously for anti-HCV antibody assay via ELISA (enzyme-linked immunoassay), HCVcAg assay by chemiluminescence immune assay (CLIA) and HCV RTPCR VL (viral load) assay. Thirty-four HCV RTPCR positive patients were further enrolled in treatment monitoring group whose blood samples were tested at the beginning of treatment, two weeks, four weeks and 12 weeks via HCV core Ag assay and HCV RTPCR Viral Load assay. Results: Considering HCV RTPCR as gold standard, diagnostic performance of HCV core Ag assay and anti-HCV antibody assay was evaluated. The sensitivity and specificity of HCV core Ag assay were higher than that of anti-HCV Antibody assay, i.e. 88.3% and 100% vs. 23.3% and 83.3%, respectively. The overall diagnostic accuracy of HCV core Ag assay was 92.20%. Among treatment follow-up group, HCV core Ag levels correlated well with HCV viral load levels, at the beginning of treatment (baseline) till 12 weeks showing highly significant Spearman rank correlation coefficient of > 0.9 with HCV viral load levels. Conclusions: HCV core Ag assay is a cost-effective, practically feasible substitute of HCV RTPCR viral load assay for diagnosis as well as long duration treatment monitoring of hepatitis C infection in resource-limited settings. [ABSTRACT FROM AUTHOR]

The multi-criteria decision-making (MCDM) field has long sought tools capable of adeptly capturing the intricacies of human decision-making amidst uncertainty. Hesitant fuzzy sets (HFS) have become a cornerstone in the MCDM field due to their ability to capture the intricacies of human decision-making under uncertainty. Nonetheless, we identified a significant gap in traditional HFS formulations, which often fail to fully harness the nuanced and implicit preferences of decision-makers (DMs). This shortcoming can lead to suboptimal decision outcomes in complex and uncertain environments. We introduce the normal wiggly hesitant fuzzy set (NWHFS), a novel construct that encapsulates both explicit and implicit preferences within a more representative framework. This study pioneers the development of new correlation coefficients for NWHFSs, offering a robust quantitative measure to elucidate the intricate relationships between variables. Our findings demonstrate that NWHFSs significantly enhance the MCDM process, providing a nuanced perspective that traditional HFS models cannot match. The proposed correlation coefficients not only reveal the concealed preferences of DMs but also broaden the decision-making spectrum, offering a more profound understanding of the relationships between alternatives and criteria. We illustrate the superiority of our approach through comparative analysis with existing methods, highlighting its ability to discern subtleties that other models overlook. Moreover, we integrate NWHFSs into clustering analysis, showcasing their potential to classify data sources with shared attributes effectively. This integration is particularly noteworthy for its ability to navigate complex datasets, offering a new dimension in data mining and resource retrieval. In essence, our study redefines the MCDM paradigm by introducing NWHFSs and their correlation coefficients, setting a new standard for decision-making accuracy and insight. The implications of our work extend beyond theory, offering practical solutions to real-world decision-making challenges. [ABSTRACT FROM AUTHOR]

Most current algorithms for multivariate time series classification tend to overlook the correlations between time series of different variables. In this research, we propose a framework that leverages Eigen-entropy along with a cumulative moving window to derive time series signatures to support the classification task. These signatures are enumerations of correlations among different time series considering the temporal nature of the dataset. To manage dataset's dynamic nature, we employ preprocessing with dense multi scale entropy. Consequently, the proposed framework, Eigen-entropy-based Time Series Signatures, captures correlations among multivariate time series without losing its temporal and dynamic aspects. The efficacy of our algorithm is assessed using six binary datasets sourced from the University of East Anglia, in addition to a publicly available gait dataset and an institutional sepsis dataset from the Mayo Clinic. We use recall as the evaluation metric to compare our approach against baseline algorithms, including dependent dynamic time warping with 1 nearest neighbor and multivariate multi-scale permutation entropy. Our method demonstrates superior performance in terms of recall for seven out of the eight datasets. [ABSTRACT FROM AUTHOR]

We 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. [ABSTRACT FROM AUTHOR]

This study aimed to explore the nature and characteristics of academic emotions experienced by secondary level students, to investigate the impact of educational emotions on scholarly achievement, to identify factors that contribute to the development of positive academic emotion and to determine the connection between pupil's educational feelings and secondary level accomplishment. An adopted questionnaire, serving as the primary research instrument, was distributed among 1116 participants, selected through random sampling techniques, after obtaining requisite permissions. Data collected through questionnaire was analysed through SPSS. Inferential tools such as the t-test, ANOVA, and correlation coefficient were employed to compare means and discern the impact of variables on academic achievements. In the empirical findings, a significant variance was noted in students' perceptions of academic emotions, specifically between those from Tehsil Multan City or Shujabad and those from Multan City or Jalalpur. The strength of the relationship between cognitive test anxiety, perceived parental expectation, and academic achievement was also assessed. The findings reveal that positive emotions, such as enjoyment and pride, are associated with higher academic achievement, while negative emotions, such as anxiety and frustration, correlate with lower performance. The study emphasizes the importance of emotional well-being in educational contexts and suggests that fostering positive academic emotions can improve student achievement. Additionally, it highlights the need for emotional support and effective teaching strategies to mitigate negative emotions in students. The results provide valuable insights for educators and policymakers to create more emotionally supportive learning environments at the secondary level. [ABSTRACT FROM AUTHOR]

This research paper analyzes satellite altimetry data for the northeastern and middle parts of the Caspian Sea for the period from 1993 to 2023. The verification of altimeter data from the data of marine hydrometeorological stations of nasal observations of the permanent sea at two points was carried out: M Peshnoy and MHP Fort Shevchenko. The results showed that the altimetric data have a high correlation with ground observations (0.89-0.94), with a mean absolute error ranging from 17 cm to 23 cm, and a consistency index above 0.7. The assessment of data applicability according to statistical criteria showed that there are minor deviations. Altimetric data are most accurate for monitoring water levels from April to October and can be used for monitoring sea levels in the open parts of the Caspian Sea. [ABSTRACT FROM AUTHOR]

Aim: This study aimed to evaluate the diagnostic performance of attenuation measurement (ATT; dual‐frequency method) and improved algorithm of ATT (iATT; reference method) for the assessment of hepatic steatosis using magnetic resonance imaging (MRI)‐derived proton density fat fraction (PDFF) as the reference standard. Methods: We prospectively analyzed 427 patients with chronic liver disease who underwent ATT, iATT, or MRI‐derived PDFF. Correlation coefficients were analyzed, and diagnostic values were evaluated by area under the receiver operating characteristic curve (AUROC). The steatosis grade was categorized as S0 (<5.2%), S1 (≥5.2%, <11.3%), S2 (≥11.3%, <17.1%), and S3 (≥17.1%) according to MRI‐derived PDFF values. Results: The median ATT and iATT values were 0.61 dB/cm/MHz (interquartile range 0.55–0.67 dB/cm/MHz) and 0.66 dB/cm/MHz (interquartile range 0.57–0.77 dB/cm/MHz). ATT and iATT values increased significantly as the steatosis grade increased in the order S0, S1, S2, and S3 (p < 0.001). The correlation coefficients between ATT or iATT values and MRI‐derived PDFF values were 0.533 (95% confidence interval [CI] 0.477–0.610) and 0.803 (95% CI 0.766–0.834), with a significant difference between them (p < 0.001). For the detection of hepatic steatosis of ≥S1, ≥S2, and ≥S3, iATT yielded AUROCs of 0.926 (95% CI 0.901–0.951), 0.913 (95% CI 0.885–0.941), and 0.902 (95% CI 0.869–0.935), with significantly higher AUROC values than for ATT (p < 0.001, p < 0.001, p = 0.001). Conclusion: iATT showed excellent diagnostic performance for hepatic steatosis, and was strongly correlated with MRI‐derived PDFF, with AUROCs of ≥0.900. [ABSTRACT FROM AUTHOR]

Grasslands have been increasingly impacted by human activities, gradually becoming one of the most threatened ecosystems globally. Advanced geographic information technology and remote sensing techniques allow for a fresh perspective on studying the response of the grassland degradation index ( G D I ) to climate change. This study utilized remote sensing image data of grasslands to calculate the vegetation coverage and derive the G D I for five grassland regions of China from 2001 to 2019. The results indicate that the national degradation status of grasslands remained at a level of mild degradation. The increasing trend of the G D I in some regions was effectively inhibited by regional climate change, especially in the Northeastern and Northern Plain–Mountain–Hill Grassland regions, where the G D I showed a continuous decreasing trend. G D I was strongly correlated with atmospheric pressure, precipitation, temperature, and wind speed. In the arid northern region, the increasing precipitation and decreasing temperatures predominantly contributed to the depressed G D I . In the Qinghai–Tibetan Plateau Grassland region, the instability of the G D I is attributed to fluctuating atmospheric pressure, with a correlation coefficient ranging from 0.5 to 0.8. Our findings underscore the importance of meteorological factors to evaluate and forecast grassland ecosystem stability. This understanding is vital for developing informed conservation and management strategies to address current and future climate challenges. [ABSTRACT FROM AUTHOR]