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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]

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]

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]

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]

• 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]

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]

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]

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]

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]

We propose new concepts to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of the time series and robust against small perturbations or measurement errors. Ordinal pattern dependence can be characterized by four parameters. We propose estimators for these parameters, and we calculate their asymptotic distributions. Furthermore, we derive a test for structural breaks within the dependence structure. All results are supplemented by simulation studies and empirical examples. For three consecutive data points attaining different values, there are six possibilities how their values can be ordered. These possibilities are called ordinal patterns. Our first idea is simply to count the number of coincidences of patterns in both time series and to compare this with the expected number in the case of independence. If we detect a lot of coincident patterns, it would indicate that the up-and-down behavior is similar. Hence, our concept can be seen as a way to measure nonlinear “correlation.” We show in the last section how to generalize the concept to capture various other kinds of dependence. [ABSTRACT FROM PUBLISHER]

The coherence method is always used to describe the discontinuity and heterogeneity of seismic data. In traditional coherence methods, a linear correlation coefficient is always used to measure the relationship between two random variables (i.e., between two seismic traces). However, mathematically speaking, a linear correlation coefficient cannot be applied to describe nonlinear relationships between variables. In order to overcome this limitation of liner correlation coefficient. We proposed an improved concordance measurement algorithm based on Kendall's tau. That mainly concern the sensitivity of the liner correlation coefficient and concordance measurements on the waveform. Using two designed numerical models tests sensitivity of waveform similarity affected by these two factors. The analysis of both the numerical model results and real seismic data processing suggest that the proposed method, combining information divergence measurement, can not only precisely characterize the variations of waveform and the heterogeneity of an underground geological body, but also does so with high resolution. In addition, we verified its effectiveness by the actual application of real seismic data from the north of China. [ABSTRACT FROM AUTHOR]

Background: Estrogen receptor alpha36 (ERalpha36), a variant of estrogen receptor alpha (ER) is expressed in about half of breast tumors, independently of the [ER+]/[ER-] status. In vitro, ERalpha36 triggers mitogenic non-genomic signaling and migration ability in response to 17beta-estradiol and tamoxifen. In vivo, highly ERalpha36 expressing tumors are of poor outcome especially as [ER+] tumors are submitted to tamoxifen treatment which, in turn, enhances ERalpha36 expression. Results: Our study aimed to validate ERalpha36 expression as a reliable prognostic factor for cancer progression from an estrogen dependent proliferative tumor toward an estrogen dispensable metastatic disease. In a retrospective study, we tried to decipher underlying mechanisms of cancer progression by using an original modeling of the relationships between ERalpha36, other estrogen and growth factor receptors and metastatic marker expression. Nonlinear correlation analyses and mutual information computations led to characterize a complex network connecting ERalpha36 to either non-genomic estrogen signaling or to metastatic process. Conclusions: This study identifies ERalpha36 expression level as a relevant classifier which should be taken into account for breast tumors clinical characterization and [ER+] tumor treatment orientation, using a generic approach for the rapid, cheap and relevant evaluation of any candidate gene expression as a predictor of a complex biological process. [ABSTRACT FROM AUTHOR]

Background: Estrogen receptor alpha36 (ERalpha36), a variant of estrogen receptor alpha (ER) is expressed in about half of breast tumors, independently of the [ER+]/[ER-] status. In vitro, ERalpha36 triggers mitogenic non-genomic signaling and migration ability in response to 17beta-estradiol and tamoxifen. In vivo, highly ERalpha36 expressing tumors are of poor outcome especially as [ER+] tumors are submitted to tamoxifen treatment which, in turn, enhances ERalpha36 expression. Results: Our study aimed to validate ERalpha36 expression as a reliable prognostic factor for cancer progression from an estrogen dependent proliferative tumor toward an estrogen dispensable metastatic disease. In a retrospective study, we tried to decipher underlying mechanisms of cancer progression by using an original modeling of the relationships between ERalpha36, other estrogen and growth factor receptors and metastatic marker expression. Nonlinear correlation analyses and mutual information computations led to characterize a complex network connecting ERalpha36 to either non-genomic estrogen signaling or to metastatic process. Conclusions: This study identifies ERalpha36 expression level as a relevant classifier which should be taken into account for breast tumors clinical characterization and [ER+] tumor treatment orientation, using a generic approach for the rapid, cheap and relevant evaluation of any candidate gene expression as a predictor of a complex biological process. [ABSTRACT FROM AUTHOR]

The aim of this study is to estimate the state of charge (SOC) of the lithium iron phosphate (LiFePO4) battery pack by applying machine learning strategy. To reduce the noise sensitive issue of common machine learning strategies, a kind of SOC estimation method based on fuzzy least square support vector machine is proposed. By applying fuzzy inference and nonlinear correlation measurement, the effects of the samples with low confidence can be reduced. Further, a new approach for determining the error interval of regression results is proposed to avoid the control system malfunction. Tests are carried out on modified COMS electric vehicles, with two battery packs each consists of 24 50 Ah LiFePO4 batteries. The effectiveness of the method is proven by the test and the comparison with other popular methods. [ABSTRACT FROM AUTHOR]

A new adaptive methodology for pattern recognition invariant to scale, rotation and translation is presented. In order to get rotation invariance, this methodology generates an adaptive binary rings mask taking information from the 2D separable scale transform of the target image. With this mask a vectorial signature is generated getting samples from the scale transformation of the target image and it does the same for every problem image. Finally, by the use of a new adaptive nonlinear correlation, the comparison of the signatures of the target and the problem image were done. The performance of this methodology has been experimental verified with a statistical analysis, to know the mean correlation confidence level in the classification of 30 different phytoplankton images in gray scale with rotations from 0° to 180° and ±10% of maximum scale variation with respect to the target image.. [ABSTRACT FROM AUTHOR]

The integration of photon-counting imaging techniques and optical encryption systems can improve information authentication robustness against intruder attacks. Photon-counting imaging generates distributions with far fewer photons than conventional imaging and provides substantial bandwidth reduction by generating sparse encrypted data. We show that photon-limited encrypted distributions have sufficient information for successful decryption, authentication and signal retrieval. Additional compression of the encrypted distribution is applied by limiting the number of phase values used to reproduce the phase information of the complex-valued encrypted data. The validity of this technique--with and without phase compression--is probed through simulated experiments for two types of input images: alphanumerical signs and dithered natural scenes. [ABSTRACT FROM AUTHOR]

We present a nonlinear correlation methodology to recognize objects. This system is invariant to position, rotation, and scale by using vectorial signatures obtained from the target such as those from problem images. Vectorial signatures are calculated through several mathematical transformations such as scale and Fourier transform. In this application, vectorial signatures are compared using nonlinear correlations. Also, experiments were carried out in order to find the noise tolerance. The discrimination coefficient was used as a metric in performance evaluation in presence of noise. In addition, spectral index and vectorial signature index are obtained in order to recognize objects in a simpler way. This technique has low computational cost. The invariance to position, rotation, and scale digital system was tested with 21 different fossil diatoms images. The results obtained are good, and the confidence level is above 95.4%. [ABSTRACT FROM AUTHOR]

The classic template matching directly uses images as templates and correlation coefficients as the measure of matching degree. A novel template matching method for eye localization based on projection coefficient templates and nonlinear correlation is proposed. Unlike classic template matching, the projection coefficients on the basis function of the Karhunen-Loeve transform are used as templates, and the nonlinear correlation is proposed to measure the matching degree. The reduction of computation costs is achieved by taking advantage of the eye symmetry. [ABSTRACT FROM AUTHOR]

Abstract: Objective: The objective of this study is to develop feature selectors based on nonlinear correlations in order to select the most effective and least redundant features from an ECG beat classification system based on higher order statistics of subband components and a feed-forward back-propagation neural network, denoted as HOS-DWT-FFBNN. Methods and materials: Three correlation-based filters (NCBFs) are proposed. Two of them, NCBF1 and NCBF2, apply feature–feature correlation to remove redundant features prior to the feature selection process based on feature–class correlation. The other, SUFCO, skips the redundancy reduction process and selects features based only on feature–class correlation. The performance of these filters is compared to another commonly used nonlinear feature selection method, Relief-F. The discriminality and redundancy of the retained features are evaluated quantitatively. The performance of the most effective NCBF is compared with that of the linear correlation-based filter (LCBF) and other representative heartbeat classifiers in the literature. Results: The results demonstrate that the two NCBFs based on both feature–feature and feature–class correlation methods, i.e. NCBF1 and NCBF2, outperform the other two methods, i.e. SUFCO and Relief-F. An accuracy of as high as 96.34% can be attained with as few as eight features. When tested with statistical methods, the retained features selected by the NCBF1/NCBF2 approach are demonstrated to be more discriminative and less redundant when compared with those features selected by other methods. When compared with LCBF and other heartbeat classifiers in the literature, the proposed NCBF1/NCBF2 approach in conjunction with the HOS-DWT-FFBNN structure outperform them with improved performance that allows discrimination of more beat types and fewer feature dimensions. Conclusion: This study demonstrates the effectiveness and superiority of the proposed approach for ECG beat recognition. [Copyright &y& Elsevier]

We propose a distribution-free approach to detect nonlinear relationships by reporting local correlation. The effect of our proposed method is analogous to piecewise linear approximation although the method does not utilize any linear dependency. The proposed metric, maximum local correlation, was applied to both simulated cases and expression microarray data comparing the rd mouse with age-matched control animals. The rd mouse is an animal model (with a mutation for the gene Pde6b) for photoreceptor degeneration. Using simulated data, we show that maximum local correlation detects nonlinear association, which could not be detected using other correlation measures. In the microarray study, our proposed method detects nonlinear association between the expression of different genes, which could not be detected using the conventional linear methods. The simulation dataset, microarray expression data, and the Nonparametric Nonlinear Correlation (NNC) software library, implemented in Matlab, are included as part of the online supplemental materials. [ABSTRACT FROM AUTHOR]

Many measures have been proposed so far to extract brain functional interactivity from functional magnetic resonance imaging (fMRI) and magnetoencephalography/electroencephalography (MEG/EEG) data sets. Unfortunately, none has been able to provide a relevant, self-contained, and common definition of brain interaction. In this paper, we propose a first step in this direction. We first introduce a common terminology together with a cross- modal definition of interaction. In this setting, we investigate the commonalities shared by some measures of interaction proposed in the literature. We show that temporal correlation, nonlinear correlation, mutual information, generalized synchronization, phase synchronization, coherence, and phase locking value (PLV) actually measure the same quantity (namely correlation) when one is investigating linear interactions between independently and identically distributed Gaussian variables. We also demonstrate that these data-driven measures can only partly account for the interaction patterns that can be expressed by the effective connectivity of structural equation modeling (SEM) . To bridge this gap, we suggest the use of conditional correlation, which is shown to be related to mediated interaction. [ABSTRACT FROM AUTHOR]

In this paper, an optical pattern recognition system with adjustable sensitivity to shape distortions and texture changes of the objects is presented. Application to a recognition task where the information of texture is the most decisive feature for a given object to be detected is provided. We apply the dual nonlinear correlation (DNC) model along with a support function acting in the frequency domain. This support function performs as an additional nonlinearity that enhances the information of some selected frequency bands related to the textural content of the target. A mathematical analysis allows the authors to show the usefulness of the proposed support function in the frame of the DNC model. The recognition system is applied to accomplish different recognition tasks involving model and real textured objects. The proposed optoelectronic correlator has been used to obtain successful experimental optical results, which are in accordance with the simulated results also provided. [Copyright &y& Elsevier]

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we first employ the mean-field variational inference (VI) to maximize the evidence lower bound (ELBO) to obtain informative prior distributions for the hyperparameters in the BNNs, and subsequently we use the Hamiltonian Monte Carlo (HMC) method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fidelity data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem. • Both linear and nonlinear cross-correlation can be discovered adaptively. • Both aleatoric uncertainty and epistemic uncertainty are quantified. • We can easily extend the present method to high-dimensional problems with big data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• A two-stage statistical framework is proposed for drought propagation analysis. • Temporal resolution of drought response time increases from monthly to weekly scale. • Drought response time becomes longer in summer while it is opposite in winter. Meteorological drought propagating to hydrological drought usually occurs with a noticeable time delay due to the catchment buffering effect. Knowledge gain in the delayed hydrological response is indispensable for developing timely drought monitoring systems. In this study, a two-stage statistical framework is proposed for identifying the response time of hydrological droughts to meteorological droughts at a weekly resolution. Candidate response time is initially selected by exclusively evaluating linear or nonlinear correlations between precipitation and streamflow anomalies. In the second stage, the optimal response time is determined, at which the greatest number of streamflow deficits can be monitored by concurrent precipitation deficits. A case study is conducted for the Wei River basin of the Loess Plateau, China to investigate the spatio-temporal variability in drought response time under a changing environment. Results indicate that hydrological droughts respond to meteorological droughts with time lags of 25–39 weeks, exhibiting noticeable spatial variability. The long-time hydrological response is expected where there are sufficient vegetation and loess deposits. Drought response time identification for each calendar month reveals the long-term and short-term hydrological response in winter and summer, respectively. A time-varying baseflow index is found to be positively related to the drought response time, therefore having control on its marked seasonality. In a changing environment, summer hydrological droughts tend to respond to precipitation variability at longer time scales, while decreasing response time is noticed in winter. A preliminary attribution analysis highlights that changes in meteorological drought severity and catchment water storage in combination exert control on the temporal variability in drought response time over the past half-century. Findings of the study may favor hydrological drought monitoring dependent on precipitation deficit information available at large spatial extent. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• The feature indicators are quantitatively extracted from the actual operating data, for the online and comprehensive assessment of the operating condition of circuit breakers. • With the difference in timeliness, the effectiveness of the test indicators and online monitoring indicators is different in the condition assessment. • The correlation between the feature indicators and the operating conditions of circuit breakers is modeled nonlinearly, in line with the complexity of the failure mechanism. • Based on the feature data of the equipment during operation, the panoramic health status is quantitatively graded online, for the selection or development of the optimal maintenance strategy. As the maintenance requirements are changed with the health status of equipment, in order to develop an optimal maintenance strategy, a data-driven nonlinear method is proposed to online assess the operating condition of circuit breakers. From the historical data resources with different timeliness, feature indicators are extracted based on the confidence improved by Bayesian probability. Then, an adaptive error back propagation (BP) neural network is improved to model the nonlinear correlation between the feature indicators and the operating conditions of the circuit breaker, by additional momentum factor, self-adaptive learning rate and improved momentum. Finally, combined with the inspection test and online monitoring data, the panoramic operating condition pf the equipment is objectively graded by the output model. Taking 500kV SF 6 high-voltage circuit breaker as an example, combined with the data provided by China Yunnan Power Grid, the effectiveness of the proposed method is proved by sample tests and method comparison. Image, graphical abstract [ABSTRACT FROM AUTHOR]