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Backgroud: The relationship between serum uric acid (SUA) and 25-hydroxyvitamin D (25(OH)D) has been variably characterized in existing literature, with inconsistent results regarding its nature and implications in the Chinese population. This study aims to clarify this association, considering the potential impact of vitamin D levels on SUA. Methods: This cross-sectional study involved 7,086 individuals from the Second Affiliated Hospital of Zhejiang University School of Medicine, screened throughout 2020. We collected data on 25(OH)D, SUA, and other metabolic markers. Logistic regression models adjusted for confounding factors were utilized to analyze the relationships. Results: Our findings illustrate a statistically significant inverted U-shaped relationship between 25(OH)D and SUA. The identified threshold effect at 28.82 ng/ml is pivotal; with 25(OH)D levels below this point associated with an increased risk of hyperuricemia (odds ratio: 1.0146, p = 0.0148), and levels above it offering protective benefits (odds ratio: 0.9616, p = 0.0164). Conclusions: Our findings confirm a nonlinear, inverted U-shaped correlation between 25(OH)D and SUA, emphasizing the importance of maintaining vitamin D levels within a specific range to effectively manage hyperuricemia. These results support the implementation of personalized vitamin D supplementation strategies to optimize metabolic health outcomes, highlighting the complex interplay between vitamin D status and uric acid levels. [ABSTRACT FROM AUTHOR]

Abstract Backgroud The relationship between serum uric acid (SUA) and 25-hydroxyvitamin D (25(OH)D) has been variably characterized in existing literature, with inconsistent results regarding its nature and implications in the Chinese population. This study aims to clarify this association, considering the potential impact of vitamin D levels on SUA. Methods This cross-sectional study involved 7,086 individuals from the Second Affiliated Hospital of Zhejiang University School of Medicine, screened throughout 2020. We collected data on 25(OH)D, SUA, and other metabolic markers. Logistic regression models adjusted for confounding factors were utilized to analyze the relationships. Results Our findings illustrate a statistically significant inverted U-shaped relationship between 25(OH)D and SUA. The identified threshold effect at 28.82 ng/ml is pivotal; with 25(OH)D levels below this point associated with an increased risk of hyperuricemia (odds ratio: 1.0146, p = 0.0148), and levels above it offering protective benefits (odds ratio: 0.9616, p = 0.0164). Conclusions Our findings confirm a nonlinear, inverted U-shaped correlation between 25(OH)D and SUA, emphasizing the importance of maintaining vitamin D levels within a specific range to effectively manage hyperuricemia. These results support the implementation of personalized vitamin D supplementation strategies to optimize metabolic health outcomes, highlighting the complex interplay between vitamin D status and uric acid levels.

Financial markets are increasingly interlinked. Therefore, this study explores the complex relationships between the Tadawul All Share Index (TASI), West Texas Intermediate (WTI) crude oil prices, and Bitcoin (BTC) returns, which are pivotal to informed investment and risk-management decisions. Using copula-based models, this study identified Student's t copula as the most appropriate one for encapsulating the dependencies between TASI and BTC and between TASI and WTI prices, highlighting significant tail dependencies. For the BTC–WTI relationship, the Frank copula was found to have the best fit, indicating nonlinear correlation without tail dependence. The predictive power of the identified copulas were compared to that of Long Short-Term Memory (LSTM) networks. The LSTM models demonstrated markedly lower Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Scaled Error (MASE) across all assets, indicating higher predictive accuracy. The empirical findings of this research provide valuable insights for financial market participants and contribute to the literature on asset relationship modeling. By revealing the most effective copulas for different asset pairs and establishing the robust forecasting capabilities of LSTM networks, this paper sets the stage for future investigations of the predictive modeling of financial time-series data. The study highlights the potential of integrating machine-learning techniques with traditional econometric models to improve investment strategies and risk-management practices. [ABSTRACT FROM AUTHOR]

For the analysis of color images, the single-channel processing method fails to consider the internal correlation between color components, while the quaternion matrix representation is not compact enough. To avoid these, this paper introduces trinion gyrator transform for color face image and develop a cancelable recognition scheme by jointing with randomized nonlinear PCANet. Firstly, color face images are precoded into trinion matrices and followed by a random binary amplitude mask for non-reversible. The nonlinear trinion correlation is proposed for selecting the optimal ratio. Next, the sampled matrix is modulated by using trinion gyrator transform and logistic-based random phase mask for increasing discriminability. Afterwards, the randomized nonlinear principal component analysis network is employed for extracting features. The recognition accuracy of the proposed algorithm on VIS, Aberdeen, GT and YMU datasets are up to 99.00%, 99.23%, 99.68% and 97.88%, which outperforms several existed methods. On top of that, the correlation index of generated face templates is no more than 0.26, indicating the revocability and security of the proposal. [ABSTRACT FROM AUTHOR]

Variable selection involves selecting truly important predictors from p-dimensional multivariate functional predictors in functional predictive models. In this paper, a variable selection method is designed for scalar-on-function predictions entangled with nonlinear joint associations among scalar response and multiple functional predictors. First, a nonparametric functional nonlinear conditional correlation coefficient, namely, the FunNCC coefficient, is proposed to measure complex dependencies, including the nonmonotonic marginal dependence, along with the conditional associations of redundancy, complement, and interaction. Then, a model-free feature ordering and selection method is designed, where the FunNCC is utilized to rank relevance, enabling the selection of a subset of predictors with the strongest joint dependence. Since this method allows for quantitatively evaluating the contributions of predictors in explaining responses, it achieves moderate model interpretability. Finally, extensive simulation studies and two real-data cases involving air pollution regression and hand gesture recognition are conducted to evaluate the finite sample performance of the proposed method, and the results show that the proposed FunNCC and variable selection methods outperform state-of-the-art baselines. [ABSTRACT FROM AUTHOR]

Summary: Background: The precise associations between common clinical biomarkers and hepatocellular carcinoma (HCC) risk remain unclear but hold valuable insights for HCC risk stratification and prediction. Methods: We examined the linear and nonlinear associations between the baseline levels of 32 circulating biomarkers and HCC risk in the England cohort of UK Biobank (UKBB) (n = 397,702). The participants were enrolled between 2006 and 2010 and followed up to 31st October 2022. The primary outcome is incident HCC cases. We then employed random survival forests (RSF) to select the top ten most informative biomarkers, considering their association with HCC, and developed a point-based risk score to predict HCC. The performance of the risk score was evaluated in three validation sets including UKBB Scotland and Wales cohort (n = 52,721), UKBB non-White-British cohort (n = 29,315), and the Taizhou Longitudinal Study in China (n = 17,269). Findings: Twenty-five biomarkers were significantly associated with HCC risk, either linearly or nonlinearly. Based on the RSF model selected biomarkers, our point-based risk score showed a concordance index of 0.866 in the England cohort and varied between 0.814 and 0.849 in the three validation sets. HCC incidence rates ranged from 0.95 to 30.82 per 100,000 from the lowest to the highest quintiles of the risk score in the England cohort. Individuals in the highest risk quintile had a 32–73 times greater risk of HCC compared to those in the lowest quintile. Moreover, over 70% of HCC cases were detected in individuals within the top risk score quintile across all cohorts. Interpretation: Our simple risk score enables the identification of high-risk individuals of HCC in the general population. However, including some biomarkers, such as insulin-like growth factor 1, not routinely measured in clinical practice may increase the model's complexity, highlighting the need for more accessible biomarkers that can maintain or improve the predictive accuracy of the risk score. Funding: This work was supported by the National Natural Science Foundation of China (grant numbers: 82204125) and the Science and Technology Support Program of Taizhou (TS202224).

We propose the Jaccard matrix (JM) and the Jaccard cell (JC), define them as the extended concepts of the Jaccard index, and theoretically and numerically analyze them. The data on the Euclidean plane can derive the JM as a sparse matrix. We show the JC inherits the feature of similarity of the Jaccard index as the exponential function of mutual information. We theoretically and numerically confirm that the local correlation coefficient of the data on the Euclidean plane relates the JC to the mutual information. Although one could potentially select an arbitrary cell size of the grid to make the JM, the knowledge we can obtain from the matrix decreases if the cell size is too big or too small to distinguish the data clusters appropriately. Therefore, the JM needs a computational procedure to determine the cell size within the appropriate scale. Maximizing the variance of the JCs supports determining the unique cell size, which value locates in the middle range of the parabolic function of the cell-size parameter. The JM could derive an index extracting nonlinear correlation of the data. The maximized standard deviation of the JCs as such an index is a decreasing function of the noise scale of the data under the constraint conditions. The ability to determine the homogeneous rectangular grid pattern of the JM might be a significant feature for finding nonlinear correlation. We would summarize this study as that of a nonlinear filter working as an efficient component of explainable AI and statistics.

Introduction: The ratio of Triglyceride (TG) to high-density lipoprotein cholesterol (HDL-C) is a crucial indicator for diabetes diagnosis. Methods: This study utilizes the Copula function to model and fit the non-linear correlation among fasting blood glucose (Glu), glycosylated hemoglobin (HbA1C), and TG/HDL-C in patients with diabetes. The Copula function chosen for this study includes the two-dimensional Archimedes and Elliptical distribution family, as well as the multidimensional Vine Copula function, for fitting the data. The evaluation of the fitting effect is performed using the mean absolute error (MAE) and mean square error (MSE). Results: The results indicate that the Clayton Copula exhibits the highest effectiveness in fitting the pairwise relationship between Glu and TG/HDL-C, as well as HbA1C and TG/HDL-C, displaying the smallest fitting error. Additionally, the Vine Copula function produces a satisfactory fit for the relationship among all three indicators. Compared to linear analysis methods, the Copula function more accurately depicts the correlation among these three types of indicators. Discussion: Moreover, our findings indicate a stronger correlation in the lower tail between Glu and HbA1C, as well as TG/HDL-C, suggesting that the Copula function provides greater accuracy and applicability in depicting the relationship among these indicators. As a result, it can offer a more precise auxiliary diagnosis and serve as a valuable reference in clinical judgment. [ABSTRACT FROM AUTHOR]

Both digital currencies and traditional financial markets are affected by inflation, interest rates, money supply, etc. In terms of price volatility factors, there are cross-asset linkages and risk transfer problems. In this paper, we use the DCCGARCH model to calculate the time-varying nonlinear correlations between different financial markets during different periods. Firstly, we construct a GARCH model for univariate return series and derive standardized residual estimates to determine the conditional insured value and spillover risk that financial markets encounter when the risk materializes. The linkage and shock relationships of BTC with the stock and spot gold markets over ten years are analyzed, as well as the impact of unanticipated events on financial markets. It is found that the short-term impact of digital currency price volatility on the stock market is much larger than the short-term impact of stocks on the gold market and that risks in the digital currency market may be rapidly transmitted to the stock market in the short term. Bitcoin and stocks have a dynamic correlation coefficient that fluctuates between -0.075 and 0.085, with little correlation. Stocks and Bitcoin have a positive correlation of 0.021, meaning that when the price of Bitcoin rises, it can lead to a rise in the price of stocks to some extent. The dynamic correlation coefficient between bitcoin and gold, on the other hand, fluctuates in the range of -0.275 to 0.175, which may produce large fluctuations. During the Cyprus crisis, gold and bitcoin demonstrated a significant investment transfer effect, and there was a contagion and linkage between market risk, the UK’s exit from the European Union, and the new crown epidemic. This paper provides a useful exploration of cross-market financial risk regulation and professional investor risk control.

In this paper, the affine-invariant Gini distance correlation/covariance is put forward to characterize the dependence between categorical and numerical variables more effectively. Furtherly, the useful features from analyzing subjects are extracted for the establishment of a reliable discrimination model, and proper measurement of correlation is built. The affine-invariant Gini distance measures are not only orthogonal invariant, but also affine invariant, which is important when considering the preservation of the equivalent statistical inference. More importantly, the Gini distance measurements capture nonlinear dependence as well as independence, which is more superb than the existing methods. The affine-invariant Gini distance estimators are easy to calculate, and the estimation of probability density of variables is not required. Besides, it can be easily extended to the reproducing kernel Hilbert spaces. The simulation- and reality-based experiments illustrate that the improved nonlinear correlation method is more effective in measuring dependencies and selecting useful features when compared to other methods. [ABSTRACT FROM AUTHOR]

We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance covariance matrix when the dimensions of the vectors and the sample size tend to infinity simultaneously. This limit is valid when the vectors are independent or weakly dependent through a finite-rank perturbation. It is also universal and independent of the details of the distributions of the vectors. Furthermore, the top eigenvalues of this distance covariance matrix are shown to obey an exact phase transition when the dependence of the vectors is of finite rank. This finding enables the construction of a new detector for such weak dependence where classical methods based on large sample covariance matrices or sample canonical correlations may fail in the considered high-dimensional framework. [ABSTRACT FROM AUTHOR]

Applying bionic airfoils is essential in enlightening the design of rotating machinery and flow control. Dynamic mode decomposition was used to reveal the low dimensional flow structure of Riblets, Seagull, and Teal bionic airfoils at low Reynolds numbers 1 × 105 and is compared with NACA4412 airfoils. The attack angle of the two-dimensional airfoil is 19°, and the SST k-ω turbulence model and ANSYS fluent were used to obtain the transient flow field data. The sparse identification of nonlinear dynamics reveals the nonlinear correlation between modal coefficients and establishes manifold dynamics. The results show that the bionic airfoil and NACA4412 airfoil have the same type of nonlinear correlation, and the dimension and form of the minimum reduced-order model are consistent. The modal coefficients always appear in the manifold equation in pairs with a phase difference of 90°. The dimension of the manifold equation is two-dimensional, and the absolute value of the coefficient corresponds to the fundamental frequency of airfoil vortex shedding. The reconstructed flow field based on the manifold equation is highly consistent with the numerical simulation flow field, which reveals the accuracy of the manifold equation. The relevant conclusions of this study emphasize the unity of the nonlinear correlation of bionic airfoils. [ABSTRACT FROM AUTHOR]

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The purpose of this study was to obtain synergistic information and details in the time–frequency domain of the relationships between the Palmer drought indices in the upper and middle Danube River basin and the discharge (Q) in the lower basin. Four indices were considered: the Palmer drought severity index (PDSI), Palmer hydrological drought index (PHDI), weighted PDSI (WPLM) and Palmer Z-index (ZIND). These indices were quantified through the first principal component (PC1) analysis of empirical orthogonal function (EOF) decomposition, which was obtained from hydro-meteorological parameters at 15 stations located along the Danube River basin. The influences of these indices on the Danube discharge were tested, both simultaneously and with certain lags, via linear and nonlinear methods applying the elements of information theory. Linear connections were generally obtained for synchronous links in the same season, and nonlinear ones for the predictors considered with certain lags (in advance) compared to the discharge predictand. The redundancy–synergy index was also considered to eliminate redundant predictors. Few cases were obtained in which all four predictors could be considered together to establish a significant information base for the discharge evolution. In the fall season, nonstationarity was tested through wavelet analysis applied for the multivariate case, using partial wavelet coherence (pwc). The results differed, depending on the predictor kept in pwc, and on those excluded. [ABSTRACT FROM AUTHOR]

Several studies have revealed that serum vitamin D is an important factor for metabolic associated fatty liver disease (MAFLD), but there had been no consistent conclusion. Of 427,507 subjects who underwent health examination, 83,625 who met the inclusion criteria were included in a cross-sectional analysis. Clinical and laboratory data were collected for analysis. MAFLD was diagnosed by abdominal imaging. Multivariate linear regression models discovered a negative association between serum vitamin D and MAFLD (OR: 0.92, 95% CI: 0.90 to 0.94, p =.001), after adjusting for other well-identified risk factors. The same result was found when serum vitamin D was handled as a categorical variable (quartile, Q1–Q4) (Q4 vs. Q1, OR: 0.82, 95% CI: 0.77 to 0.87, p <.001), and a significant linear trend was observed (p for trend <.001). After analysis, a nonlinear relationship was detected between serum vitamin D and MAFLD, with an inflection point of 2.23 (44.6 nmol/L or 17.84 ng/mL). The effect sizes and the confidence intervals on the left and right sides of the inflection point were 1.16 (1.06 to 1.28) and 0.89 (0.86 to 0.91), respectively. All interactions with MAFLD were not significant for age, sex, diabetes, hypertension, smoking and body mass index (p for interaction =.110,.558,.335,.195,.616 and.401, respectively). There was a nonlinear relationship between serum vitamin D and MAFLD. When the serum vitamin D level was ≥44.6 nmol/L (17.84 ng/mL), a negative correlation between serum vitamin D and MAFLD was detected. Below this level, serum vitamin D might promote the progression of MAFLD. [ABSTRACT FROM AUTHOR]

Under the goal of a "new development pattern", it is of great practical significance to accurately identify the economic growth effect of fiscal and tax policies. This paper constructs a TVP-FAVAR model to measure the economic effects of China's fiscal and tax policies at the aggregate and structural levels. The results show that the reduction in total tax has a positive effect on real variables such as output and consumption; especially at the present stage, the promotion effect of total tax reduction on economic growth is relatively strong, but the stimulation effect on price is relatively weak. Further, the tax structure in which the ratio of direct tax to total tax increases and the ratio of indirect tax to total tax decreases is more conducive to the increase in output and consumption, and will not strongly stimulate the rise of price level. Therefore, at this stage, China should continue to vigorously implement the tax reduction policy and ensure the continuity of the tax reduction policy. At the same time, we should continue to optimize the tax structure and give better play to the regulatory role of fiscal and tax policies in income redistribution, so as to achieve the goal that fiscal and tax policies help build a "new development pattern" and promote high-quality economic development. [ABSTRACT FROM AUTHOR]

Summary: Correlation analysis has long been a question of great interest in measuring the relationship among different variables and has been applied in many fields, such as dimension reduction, classification, and so on. However, current methods of correlation analysis take into account the linear relationship between multiple variables and only few works on nonlinear interaction of two variables have been considered. In this article, we first present a nonlinear analysis method of multiple (two or more) variables based on mutual information for tensor analysis (MITA). In addition, we extend the mutual‐information matrix analysis directly to MITA and show the multivariable mutual information formula based on Venn diagram. Experiments on multiview dimension reduction, including attacking internet traffic prediction, advertisement classification, and biometric structure prediction illustrate the effectiveness of the proposed method, especially in the case of low‐dimensional subspace. [ABSTRACT FROM AUTHOR]

• Gaussian Copula is limited for nonlinearly correlation of substation equipment. • Archimedean Copula is qualified for response simulation of substation equipment. • Existing non-correlation method significantly underestimate failure probabilities. • The Copula evaluation is stable with selections of sample ground motions. Seismic vulnerability evaluations of substation equipment under multiple correlated failure modes are urgently needed. The Copula method, an efficient tool for considering the correlation between variables, holds significant potential application value. However, due to the evident nonlinear correlation between structural and functional responses of substation equipment, the effectiveness of the Copula method is adversely affected. Therefore, this study takes four seismic intensity levels, investigates the distribution and correlation characteristics of seismic responses of typical substation equipment at different levels, and demonstrates the feasibility of the Copula method. The results indicate that the nonlinear correlation features of equipment responses have a significant impact on the choice of Copula functions. The widely used Gaussian Copula exhibits evident limitations, while the Archimedean family Copula is more suitable for substation equipment assessment. Traditional methods that do not consider multiple failure modes or neglect correlation between different modes yield significantly lower seismic vulnerability compared to the Copula-based method that considers correlations. Additionally, compared to traditional non-correlation assessment methods, the Copula method demonstrates better stability, with assessment results less affected by variations in the selection of sample ground motions. Therefore, the Copula method is suitable for assessing the seismic vulnerability of substation equipment and merits widespread application. [ABSTRACT FROM AUTHOR]

The increase in the share of motorization in short-distance trips is a significant contributor to the decline in the share of active travel (AT) and will further pose a challenge to sustainable transport. While many studies have explored the relationship between the built environment (BE) and AT, few have focused on short trips. Additionally, most studies have ignored the important role of the streetscape. To address these gaps, this study utilizes street view big data to quantify street view elements and applies extreme gradient boosting decision trees (XGBoost) to 2020 household travel data in Wuhan. The results indicate that streetscape attributes are more important than land use in predicting short-distance AT, with streetscape being more than 40% relative importance in both models. The contribution of almost all streetscape elements cannot be ignored. Among them, the percentage of driveways showed the highest predictive power. Among land use attributes, population density has the highest relative importance. In addition, most of the independent variables are nonlinearly correlated with the explanatory variables, and this study quantified these association thresholds. These results suggest that optimizing the street built environment has the potential to promote a shift from short-distance driving to AT. The quantification of correlation thresholds provides precise empirical evidence for built environment interventions that promote short-distance AT. [ABSTRACT FROM AUTHOR]

Streamflow similarity regionalization is significant for interpolating and transferring streamflow data and regional flood frequency analysis. To accurately identify the similarities and differences of streamflow characteristics of different hydrological stations in a hydrometric network and improve the accuracy of streamflow similarity regionalization results, we introduce the copula entropy method to estimate the mutual-information-based R statistics, aiming at measuring the nonlinear correlations between streamflow series. Subsequently, the complex network theory was applied to construct the streamflow similarity regionalization model, where the hydrological stations were set as nodes and the condition whether the R statistics of corresponding streamflow series were higher than the specified R-statistic threshold was considered as the basis for judging the existence of the linked edges between node pairs. The GN algorithm was used to conduct the streamflow similarity regionalization. Taking the hydrometric network of the Poyang Lake basin as an example, the research results showed that the streamflow similarity regionalization model was characterized by high stability and efficiency. When the R statistic was 0. 8, the streamflow similarity regionalization result was the best, the hydrometric network was generally divided into two parts, i. e., north and south, and in total 12 types of regions, where the north part contained only one type of region. Compared with the K-means clustering method, the complex network method performs better, and its optimal partitioning result is more reasonable. [ABSTRACT FROM AUTHOR]

Abstract Background With the advance of high throughput sequencing, high-dimensional data are generated. Detecting dependence/correlation between these datasets is becoming one of most important issues in multi-dimensional data integration and co-expression network construction. RNA-sequencing data is widely used to construct gene regulatory networks. Such networks could be more accurate when methylation data, copy number aberration data and other types of data are introduced. Consequently, a general index for detecting relationships between high-dimensional data is indispensable. Results We proposed a Kernel-Based RV-coefficient, named KBRV, for testing both linear and nonlinear correlation between two matrices by introducing kernel functions into RV2 (the modified RV-coefficient). Permutation test and other validation methods were used on simulated data to test the significance and rationality of KBRV. In order to demonstrate the advantages of KBRV in constructing gene regulatory networks, we applied this index on real datasets (ovarian cancer datasets and exon-level RNA-Seq data in human myeloid differentiation) to illustrate its superiority over vector correlation. Conclusions We concluded that KBRV is an efficient index for detecting both linear and nonlinear relationships in high dimensional data. The correlation method for high dimensional data has possible applications in the construction of gene regulatory network.

Applying bionic airfoils is essential in enlightening the design of rotating machinery and flow control. Dynamic mode decomposition was used to reveal the low dimensional flow structure of Riblets, Seagull, and Teal bionic airfoils at low Reynolds numbers 1 × 105 and is compared with NACA4412 airfoils. The attack angle of the two-dimensional airfoil is 19°, and the SST k-ω turbulence model and ANSYS fluent were used to obtain the transient flow field data. The sparse identification of nonlinear dynamics reveals the nonlinear correlation between modal coefficients and establishes manifold dynamics. The results show that the bionic airfoil and NACA4412 airfoil have the same type of nonlinear correlation, and the dimension and form of the minimum reduced-order model are consistent. The modal coefficients always appear in the manifold equation in pairs with a phase difference of 90°. The dimension of the manifold equation is two-dimensional, and the absolute value of the coefficient corresponds to the fundamental frequency of airfoil vortex shedding. The reconstructed flow field based on the manifold equation is highly consistent with the numerical simulation flow field, which reveals the accuracy of the manifold equation. The relevant conclusions of this study emphasize the unity of the nonlinear correlation of bionic airfoils.

Background: The precise associations between common clinical biomarkers and hepatocellular carcinoma (HCC) risk remain unclear but hold valuable insights for HCC risk stratification and prediction., Methods: We examined the linear and nonlinear associations between the baseline levels of 32 circulating biomarkers and HCC risk in the England cohort of UK Biobank (UKBB) (n = 397,702). The participants were enrolled between 2006 and 2010 and followed up to 31st October 2022. The primary outcome is incident HCC cases. We then employed random survival forests (RSF) to select the top ten most informative biomarkers, considering their association with HCC, and developed a point-based risk score to predict HCC. The performance of the risk score was evaluated in three validation sets including UKBB Scotland and Wales cohort (n = 52,721), UKBB non-White-British cohort (n = 29,315), and the Taizhou Longitudinal Study in China (n = 17,269)., Findings: Twenty-five biomarkers were significantly associated with HCC risk, either linearly or nonlinearly. Based on the RSF model selected biomarkers, our point-based risk score showed a concordance index of 0.866 in the England cohort and varied between 0.814 and 0.849 in the three validation sets. HCC incidence rates ranged from 0.95 to 30.82 per 100,000 from the lowest to the highest quintiles of the risk score in the England cohort. Individuals in the highest risk quintile had a 32-73 times greater risk of HCC compared to those in the lowest quintile. Moreover, over 70% of HCC cases were detected in individuals within the top risk score quintile across all cohorts., Interpretation: Our simple risk score enables the identification of high-risk individuals of HCC in the general population. However, including some biomarkers, such as insulin-like growth factor 1, not routinely measured in clinical practice may increase the model's complexity, highlighting the need for more accessible biomarkers that can maintain or improve the predictive accuracy of the risk score., Funding: This work was supported by the National Natural Science Foundation of China (grant numbers: 82204125) and the Science and Technology Support Program of Taizhou (TS202224)., Competing Interests: All authors declare no conflict of interests., (© 2024 The Author(s).)

Due to the influence of multiple environmental factors, bridge frequencies can vary with time, which can affect the frequency variations that cause structural damage. However, the nonlinear effects of multiple environmental factors and other uncertain effects on structural frequencies cannot be properly considered, which is a major obstacle to achieving bridge damage detection based on structural frequency variations. Therefore, this paper focuses on establishing an appropriate mapping model between modal frequencies and multiple environmental factors, which can consider such nonlinear and uncertain effects simultaneously. Principal component analysis integrates the features of long-term environmental monitoring data into several principal components. To address nonlinearity and uncertainty in modeling, a Gaussian process regression model with principal components as inputs is developed to estimate the modal frequency distributions. Four groups of models with different inputs are validated in a cable-stayed bridge case. The proposed modeling method can map multiple environmental factors onto modal frequencies by considering both nonlinearity and uncertainty and accurately describe the environmental impacts on frequencies based on monitoring data. [ABSTRACT FROM AUTHOR]

The purpose of this study was to obtain synergistic information and details in the time–frequency domain of the relationships between the Palmer drought indices in the upper and middle Danube River basin and the discharge (Q) in the lower basin. Four indices were considered: the Palmer drought severity index (PDSI), Palmer hydrological drought index (PHDI), weighted PDSI (WPLM) and Palmer Z-index (ZIND). These indices were quantified through the first principal component (PC1) analysis of empirical orthogonal function (EOF) decomposition, which was obtained from hydro-meteorological parameters at 15 stations located along the Danube River basin. The influences of these indices on the Danube discharge were tested, both simultaneously and with certain lags, via linear and nonlinear methods applying the elements of information theory. Linear connections were generally obtained for synchronous links in the same season, and nonlinear ones for the predictors considered with certain lags (in advance) compared to the discharge predictand. The redundancy–synergy index was also considered to eliminate redundant predictors. Few cases were obtained in which all four predictors could be considered together to establish a significant information base for the discharge evolution. In the fall season, nonstationarity was tested through wavelet analysis applied for the multivariate case, using partial wavelet coherence (pwc). The results differed, depending on the predictor kept in pwc, and on those excluded.

For steel bridge girders, several control sections usually exist. If one or more sections fail, then the bridge girder might fail. Therefore, the failure probability analysis of each control section is important for bridge girder safety assessment. To make a reasonable failure probability analysis for bridge girder sections that have structural health monitoring data, first, vine copula models that consider the nonlinear correlation of multiple monitored variables will be established based on the extreme stress data of bridge girder sections, which mean that the extreme stress data fusion will be achieved; second, the vine copula models that consider the nonlinear correlation of failure modes of the multiple monitored points from bridge girder sections that were constructed with the corresponding performance functions, further, by combining the built vine copula models with the first-order second-moment (FOSM) method, the failure probability of the bridge girder section that considers the nonlinear correlation of failure modes at the multiple monitored points will be analyzed; finally, the monitored data of an existing bridge will be provided to illustrate the proposed model and method. The results show that: (1) the C-vine structure-based failure probability of a bridge girder is smaller than the D-vine structure-based failure probability; (2) the obtained bridge girder section failure probability that considered the nonlinear correlation of the failure modes is smaller than when the correlation of the failure modes is not considered. It was illustrated that the obtained C-vine structure-based failure probability was the most reasonable. [ABSTRACT FROM AUTHOR]

Abstract The Equatorial Indian Ocean Oscillation (EQUINOO) and El Niño Southern Oscillation (ENSO) are important climatic oscillations over the Indian and Pacific oceans influencing the inter‐annual variation of the Indian monsoon. The study of these indices, including their relationship and influence over various climatic phenomena, is the main focus in the literature. However, an attempt is made here to predict the indices for different temporal periods. Though ENSO prediction is established by many statistical and numerical models, the prediction of the EQUINOO index is not much studied. A deep‐learning method using an autoencoder is proposed for the prediction of the EQUINOO and ENSO. An autoencoder assists in feature learning. The learned features are ranked using linear and nonlinear correlation studies. This assists in identifying a set of potential predictors, used for indices prediction, with an ensemble of regression trees and decision forest models. Predictors identified by nonlinear correlation are observed to predict with better accuracy as compared with linear correlation. The predicted indices show high correlation against the observed values. The EQUINOO prediction is provided with a high lead of 7 months with a 0.88 correlation co‐efficient (p

Characterizing the relationship between time series is an important issue in many fields, in particular, in many cases there is a nonlinear correlation between series. This paper provides a new method to study the relationship between time series using the perspective of complex networks. This method converts a time series into a distance matrix and constructs a sequence of nearest neighbor networks, so that the nonlinear relationship between time series is expressed as similarity between networks. In addition, based on the surrogate series, we applied Z -score to characterize the level of significance and analyzed some benchmark models. We not only use the artificial dataset and the real dataset to verify the effectiveness of the proposed method, but also analyze its robustness, which provides an alternative method for detecting nonlinear relationships. [ABSTRACT FROM AUTHOR]

Vehicle body crashworthiness is crucial in a traffic accident. It can protect passengers from serious injury or death and reduce vehicle damage. To provide a more effective design framework for ensuring crash safety, a reliability-based design optimization (RBDO) method for vehicle body crashworthiness considering complex parametric correlation is developed by integrating copula functions. An RBDO model is formulated for the vehicle body crashworthiness problem based on a finite element model of a vehicle crash. Taking into account the correlation of random parameters, the optimal copula function is selected by the Bayesian method to model parametric correlation and build the joint probability distribution function. An efficient solution strategy is provided to perform the reliability analysis and optimization design of crashworthiness. The results demonstrate that the proposed method is reliable and has a high accuracy for crashworthiness design. [ABSTRACT FROM AUTHOR]

The Equatorial Indian Ocean Oscillation (EQUINOO) and El Niño Southern Oscillation (ENSO) are important climatic oscillations over the Indian and Pacific oceans influencing the inter‐annual variation of the Indian monsoon. The study of these indices, including their relationship and influence over various climatic phenomena, is the main focus in the literature. However, an attempt is made here to predict the indices for different temporal periods. Though ENSO prediction is established by many statistical and numerical models, the prediction of the EQUINOO index is not much studied. A deep‐learning method using an autoencoder is proposed for the prediction of the EQUINOO and ENSO. An autoencoder assists in feature learning. The learned features are ranked using linear and nonlinear correlation studies. This assists in identifying a set of potential predictors, used for indices prediction, with an ensemble of regression trees and decision forest models. Predictors identified by nonlinear correlation are observed to predict with better accuracy as compared with linear correlation. The predicted indices show high correlation against the observed values. The EQUINOO prediction is provided with a high lead of 7 months with a 0.88 correlation co‐efficient (p < 0.001) and the ENSO with a lead of 1 month with a 0.87 correlation co‐efficient (p < 0.001) between the observed and predicted indices. Moreover, the proposed method proves efficient in predicting the positive or negative index values with an appropriate sign. The ENSO prediction by the proposed approach is observed to be comparable with the existing models. [ABSTRACT FROM AUTHOR]

Introduction: The ratio of Triglyceride (TG) to high-density lipoprotein cholesterol (HDL-C) is a crucial indicator for diabetes diagnosis., Methods: This study utilizes the Copula function to model and fit the non-linear correlation among fasting blood glucose (Glu), glycosylated hemoglobin (HbA1C), and TG/HDL-C in patients with diabetes. The Copula function chosen for this study includes the two-dimensional Archimedes and Elliptical distribution family, as well as the multidimensional Vine Copula function, for fitting the data. The evaluation of the fitting effect is performed using the mean absolute error (MAE) and mean square error (MSE)., Results: The results indicate that the Clayton Copula exhibits the highest effectiveness in fitting the pairwise relationship between Glu and TG/HDL-C, as well as HbA1C and TG/HDL-C, displaying the smallest fitting error. Additionally, the Vine Copula function produces a satisfactory fit for the relationship among all three indicators. Compared to linear analysis methods, the Copula function more accurately depicts the correlation among these three types of indicators., Discussion: Moreover, our findings indicate a stronger correlation in the lower tail between Glu and HbA1C, as well as TG/HDL-C, suggesting that the Copula function provides greater accuracy and applicability in depicting the relationship among these indicators. As a result, it can offer a more precise auxiliary diagnosis and serve as a valuable reference in clinical judgment., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Liu, Yang, Yang and Wang.)

Botulinum toxin (BoTX) is the standard treatment for task-specific dystonias (TSDs) such as musician’s dystonia (MD). Our aim was to assess the long-term changes in BoTX treatment in a highly homogeneous and, to our knowledge, largest group of MD patients with respect to the following parameters: (1) absolute and (2) relative BoTX dosage, (3) number of treated muscles, and (4) inter-injection interval. We retrospectively assessed a treatment period of 20 years in 233 patients, who had received a cumulative dose of 68,540 MU of BoTX in 1819 treatment sessions, performed by two neurologists. Nonlinear correlation was used to analyze changes in the parameters over the course of repeated treatments. Post-hoc we applied a median-split to classify two subgroups (high-BoTX, low-BoTX) depending on the total amount of BoTX needed during treatment. Across all patients, we found a decrease of dosage for the first approximately 25 treatments with an increase afterwards. The number of muscles and inter-injection intervals increased with time with a discrete decrease of inter-injection intervals after about 35 treatments. Subgroup differences were observed in the amount of BoTX and inter-injection intervals, with continuously increasing inter-injection intervals and decreasing BoTX dosage in the low-BTX group. Both groups showed a continuously increasing number of injected muscles. In summary, we found nonlinear changes of BoTX dosage and inter-injection intervals and a continuously increasing number of injected muscles with treatment duration in TSD-patients. Furthermore, we, for the first time, identified two subgroups with distinct differences. Increasing inter-injection intervals and decreasing BoTX dosages in the low-BoTX group indicated improvement of symptoms with continued treatment. Continually increasing BoTX dosages with unchanged inter-injection intervals in the high-BoTX group indicated deterioration.

Background: Non-small cell lung cancer (NSCLC) is the first cause of cancer-related mortality for men and women in the United States. In spite of curative resection in early-stage, patient survival is not optimal and recurrence rate is high. Consequently, early detection and staging is essential to increase the patient's survival.Methods: Copy number (CN) changes in cancer populations have been broadly investigated to identify CN gains and deletions associated with cancer. In contrast, in this research, we quantify the similarities and disparities between cancer and paired peripheral blood samples using maximal information coefficient (MIC). We then detect the spatial locations with substantially high and the spatial locations with very low MICs in each chromosome. These locations can potentially help with early diagnosis, treatment, and prevention of cancer by identifying the similarities and disparities between cancer and healthy tissues.Results: Lung cancer data used in this project contains CN pairs for cancer and blood (non-involved) samples for 63 subjects. MIC was obtained to quantify the relation (linear or nonlinear) between cancer-blood pair samples for 63 subjects at each location for each chromosome. MIC values above a high threshold and MIC values below a low threshold were located. Among them top five (with lowest MIC's and with highest MIC's) were identified for each chromosome. For these identified locations, a high MIC score indicates high similarity between blood (non-involved) and cancer samples, while a low MIC score shows lack of similarity between the two samples.Conclusions: The results showed that a few chromosomes have a large number of MICs exceeding a high threshold. These locations can potentially be used to identify early indicators of NSCLC. In contrast, second group of chromosomes have several locations with small MICs which are potential candidates to develop biomarkers for discriminating cancer from the matched blood sample. Moreover, there is a third group of chromosomes with a large number of MICs exceeding a high threshold and a large set of MICs below a low threshold. These locations can help with both finding early indicators of cancer and developing biomarkers for discriminating cancer from non-involved tissue. [ABSTRACT FROM AUTHOR]

This paper proposes a multivariate distance nonlinear causality test (MDNC) using the partial distance correlation in a time series framework. Partial distance correlation as an extension of the Brownian distance correlation calculates the distance correlation between random vectors X and Y controlling for a random vector Z. Our test can detect nonlinear lagged relationships between time series, and when integrated with machine learning methods it can improve the forecasting power. We apply our method as a feature selection procedure and combine it with the support vector machine and random forests algorithms to study the forecast of the main energy financial time series (oil, coal, and natural gas futures). It shows substantial improvement in forecasting the fuel energy time series in comparison to the classical Granger causality method in time series. [ABSTRACT FROM AUTHOR]

Workload and fatigue of aircraft pilots represent an argument of great interest in the framework of human factors and a pivotal point to be considered in aviation safety. 75% of aircraft accidents are related to human errors that, in most cases, are due to high level of mental workload and fatigue. There exist several subjective or objective metrics to quantify the pilots’ workload level, with both linear and nonlinear relationships reported in the literature. The main research objective of the present work is to analyze the relationships between objective and subjective workload measurements by looking for a correlation between metrics belonging to the subjective and biometric rating methods. More particularly, the Heart Rate Variability (HRV) is used for the objective analysis, whereas the NASA-TLX questionnaire is the tool chosen for the subjective evaluation of the workload. Two different flight scenarios were considered for the studies: the take-off phase with the initial climb and the final approach phase with the landing. A Maneuver Error Index (MEI) is also introduced to evaluate the pilot flight performance according to mission requirements. Both qualitative and quantitative correlation analyses were performed among the MEI, subjective and objective measurements. Monotonic relationships were found within the HRV indexes, and a nonlinear relationship is proposed among NASA-TLX and HRV indexes. These findings suggest that the relationship between workload, biometric data, and performance indexes are characterized by intricate patterns of nonlinear relationships.

The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences between two statistical systems, and then establish a new Brownian independence test based on fluctuating random paths. We also argue that this result allows revisiting the theory of Brownian covariance from a physical perspective and opens the possibility of engineering nonlinear correlation measures from more general functional integrals.

Evoked cognitive potentials are a promising experimental technique that can be useful in diagnosis of various cognitive disorders, especially connected to the various memory impairments. Of particular interest to researchers is the study of the cognitive evoked potentials' latency when recognition of various stimuli is involved. To study the physiological nature and functional role of evoked cognitive potentials observed during the reaction to stimuli, and to determine the degree of conscious control involved in this reaction, the experimental data were statistically analyzed to determine the numerical correlation between the working memory capacity and the cognitive potential's latency. The cognitive EPs were measured for 166 healthy subjects and 63 others that had some pathological brain condition (discirculatory encephalopathy and other brain discirculatory disorders), varied by the age and gender. Measurements were done with the Neurosoft Neuro-MEP 4 computerized encephalography system, which implemented the standard method of large latency neural response measurement for P300 waves. Measurements were done in the setup where the subject had to recognize the significant stimuli and react to them by pressing a button. The significant stimulus was represented by a 2 kHz tone, while the insignificant stimuli were the frequently repeated 1 kHz tones. The brainwaves were registered in Cz-M1 and Cz-M2 outputs. This method allowed detection and latency measurements of the main response components N2, P3a P3ab and N3. Working memory capacity was determined by the number of words from a 10-15 word sets correctly reproduced shortly after exposures, as outlined by Luria. A statistically significant nonlinear correlation was observed between the memory capacity and the EP's latency, which was fitted by a modified hyperbolic function. Additionally, greater latencies were observed for subjects suffering from the memory disorders, and much shorter latencies were in general noted for the male subjects as opposed to the female ones. One more interesting observation was that in many cases the absolute reaction time was less than the cognitive potential peak taken as a conscious decision, suggesting that it is in many cases an automatic reaction. Cognitive potentials measurements, being an instrumental method, allow a clinical psychologist much greater flexibility in his diagnostic repertory, as it can be used even in the cases where word tests cannot. Also, the reaction times shorter than the latency of conscious reaction to stimuli adds weight to the simultaneous codes theory of automatic reactions. [ABSTRACT FROM AUTHOR]

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A nonparametric statistic, called the roughness of concomitant ranks, is proposed for testing whether 2 quantitative vectors are dependent. The new testing procedure is highly computationally efficient and simple, and exhibits competitive empirical performance in simulations and 2 microarray data analyses. We apply the new method to screen variables for high-dimensional data analysis. For a low signal-to-noise ratio setting, we suggest the use of data binning to increase the power of the test. Simulation results show the fine performance of the proposed method with the existing screening methods. [ABSTRACT FROM AUTHOR]

Cognitive control is of great plasticity. Training programs targeted on improving it have been suggested to yield neural changes in the brain. However, until recently, the relationship between training-induced brain changes and improvements in cognitive control is still an open issue. Besides, although the literature has attributed the operation of cognitive control to interactions between large-scale networks, the neural pathways directly associated with it remain unclear. The current study aimed to examine these issues by focusing on conflict processing. In particular, we employed a training program with a randomized controlled design. The main findings were as follows: 1) In behavior, the training group showed reduced conflict effect after training, relative to the control group; 2) In the pretest stage, the behavioral conflict effect was negatively correlated with a number of neural pathways, including the connectivity from the cingulo-opercular network (CON) to the cerebellum and to sub-regions of the dorsal visual network; 3) increase in the connectivity strength of several network interactions, such as the connectivity from the CON to the cerebellum and to the primary visual network, was associated with behavioral gains; 4) there were also nonlinear correlations between behavioral and neural changes. These findings highlighted a critical role of the modulation of CON on other networks in mediating conflict processing and its plasticity, and raised the significance of investigating nonlinear relationship in the field of cognitive training. [ABSTRACT FROM AUTHOR]