Radial Basis Functions (RBFs) have gained significant attention in various machine learning applications, including regression modeling, due to their ability to approximate complex, nonlinear relationships. RBFs offer a flexible approach to capturing intricate dependencies between input features and the target variable, making them particularly useful in high-dimensional and nonparametric settings. This paper investigates the use of a specific class of compactly supported RBFs, known as Wendland functions, within the framework of kernel ridge regression (KRR). We discuss their theoretical advantages—such as sparsity enforcement and computational efficiency as well as practical challenges, including parameter selection and scalability. A comprehensive overview of RBFs is provided, along with their mathematical formulation and a comparison of different RBF kernels in terms of smoothness and locality. We detail the integration of Wendland functions into KRR models, emphasizing their suitability for problems requiring robustness and interpretability. Through extensive simulation studies, the performance of the proposed approach is evaluated against conventional RBF kernels and other widely used regression techniques. Our results demonstrate that Wendland-based KRR achieves competitive accuracy while offering improved stability in the presence of noise and outliers. Furthermore, real-world case studies illustrate the effectiveness of Wendland functions in handling datasets with high collinearity, where traditional kernels often struggle. The practical implications of our findings are discussed, along with guidelines for implementation and potential extensions to large-scale or sparse data scenarios. This work contributes to the growing body of research on interpretable and efficient kernel methods, providing insights for both theoretical and applied machine learning practitioners.

Background and objectives: Precise forecasting of water quality (WQ) parameters, specifically PS (potential salinity), is critical for sustainable water utilization. In water-stressed regions like the Karun River in Iran, effective monitoring and prediction of the PS is not only important but also critical because of anthropogenic activities, climate change, and reduced inflows of freshwater. Therefore, effective machine learning (ML) models and appropriate input data is very important for monitoring and predicting WQ parameters. However, the influencing factors exhibit complex and non-linear relationships, and multicollinearity in the datasets makes it challenging for traditional ML models to address the problem. Limitations, thus, can result in inaccurate predictions, which obstruct the establishment of sustainable water management strategies. As mentioned above, accurate forecasting of PS is essential for water and soil conservation, because PS helps mitigate salinity-related degradation of agricultural lands and ensure the sustainability of vital ecosystems. This study supports the development of effective conservation strategies to maintain soil productivity and WQ in vulnerable regions by providing reliable predictions. To address these issues, the present study introduces a new hybrid model, IKRidge-GRM, which inherits the advantages of improved kernel ridge regression (IKRidge) and generalized ridge regression (GRM). The hybrid model integrates IKRidge's improved capacity to identify non-linearity with GRM's resilience against multicollinearity problems to improve the predictive performance of the PS prediction. This unique framework offers improved stability and interpretability of results, as well as increases forecast accuracy, making it a helpful tool for environmental monitoring and decision-making. The proposed strategy could aid policymakers and water resource managers in designing reasonable strategies to alleviate salinity issues, protect aquatic ecosystems, and ensure the long-term survival of vital water sources like the Karun River.Materials and methods: This study introduces a novel hybrid ML model based on two regression techniques, namely: generalized ridge regression (GRM) and improved kernel ridge regression (IKRidge), called IKRidge-GRM. The GRM effectively addresses multicollinearity and overfitting issues using the iteratively reweighted least squares (IRLS) process. On the other hand, IKRidge incorporates a wavelet kernel function, optimized through the INFO algorithm, and the regularized locally weighted (RLW) approach, enabling it to capture complex, non-linear patterns in the data with high precision. This combination of techniques allows the hybrid model to overcome the limitations of traditional ML methods, making it particularly suitable for handling the intricate relationships inherent in WQ datasets. To further enhance the model's predictive accuracy, the IKRidge-GRM framework integrates a light gradient boosting machine (LGBM) for feature selection. It reduces dimensionality by identifying the most relevant input variables while eliminating redundant or irrelevant features.Additionally, the model employs multivariate variational mode decomposition (MVMD) to decompose the input data into high- and low-frequency components, allowing it to capture both short-term fluctuations and long-term trends in WQ parameters. The study utilized an extensive dataset comprising 48 years of monthly WQ data collected from the Farisat station on the Karun River. Nine keys WQ parameters, including magnesium (Mg), sulfate (SO42−), calcium (Ca), discharge (Q), sodium (Na), bicarbonate (HCO3), chloride (Cl), electrical conductivity (EC), total dissolved solids (TDS) and pH, were used as inputs to forecast the PS three months ahead. Results: The proposed IKRidge-GRM model accurately predicted PS values at the Farisat station, significantly outperforming baseline models (Ridge, DELM, and LSSVM) and their MVMD-enhanced versions. By leveraging its hybrid architecture and advanced feature extraction techniques, the MVMD-IKRidge-GRM model achieved remarkable results during the testing phase, with the highest correlation coefficient (R = 0.977), the lowest RMSE (0.956), and the lowest MAPE (4.521). These metrics indicate the model's superior predictive accuracy and reliability in handling complex, non-linear relationships. The model also achieved high IA (0.988) and KGE (0.948) scores, underscoring its robustness and effectiveness in capturing the intricate dynamics of the PS variations. These results highlight the model's ability to uncover hidden patterns in the data and provide highly accurate predictions, even in challenging scenarios involving multicollinearity and non-linear dependencies. The model's exceptional performance was further confirmed by visual evaluations such as scatter plots, relative error plots, and Taylor diagrams. Scatter plots demonstrated that the MVMD-IKRidge-GRM model's predictions closely aligned with measured values, with minimal prediction intervals and narrow error distributions, reflecting its precision and consistency. Relative error plots revealed that the model exhibited the most compact and symmetric error distribution, with minimal bias and variability. Relative error plots also indicated the models’ ability to generalize well across different data points. Taylor diagrams provided evidence of the model's strong agreement with reference data, showcasing its ability to balance accuracy, variability representation, and error minimization effectively. Residual analysis further confirmed the model's precision and reliability. Among all the models tested, the MVMD-IKRidge-GRM model achieved the smallest mean residual (-0.0073) and the lowest standard deviation (0.0613), demonstrating its ability to minimize prediction errors consistently. This level of precision is critical for practical applications, as it ensures that the model can provide reliable forecasts for decision-making in water resource management. The model's ability to integrate advanced regression techniques, feature selection, and frequency decomposition enhances its predictive capabilities. The ability also establishes the proposed model as a robust framework for addressing complex environmental challenges. These findings emphasized the potential of the MVMD-IKRidge-GRM model as a powerful tool for sustainable water resource management, particularly in regions like the Karun River basin, where accurate and reliable predictions are essential for mitigating environmental degradation and ensuring long-term ecological balance.Conclusion: The IKRidge-GRM model predicted PS values at the Farisat station on the Karun River. The findings demonstrated high accuracy and reliability across all evaluation metrics. The IKRidge-GRM model has the ability to uncover hidden patterns in complex, non-linear datasets. Its capacity to deliver precise predictions also highlights its potential as a valuable tool for environmental monitoring and management. By integrating advanced regression techniques, such as improved kernel ridge regression (IKRidge) and generalized ridge regression (GRM), with innovative feature selection and decomposition methods like light gradient boosting machine (LGBM) and multivariate variational mode decomposition (MVMD), the model effectively addresses challenges such as multicollinearity, overfitting, and non-linear relationships. This comprehensive framework ensures that the IKRidge-GRM model achieves superior predictive performance and maintains robustness and adaptability across diverse environmental conditions. This study emphasizes the importance of combining advanced ML techniques with effective preprocessing methods to develop reliable models for analyzing and forecasting complex environmental data. Integrating feature selection and frequency decomposition enhances the model's ability to extract meaningful information from high-dimensional datasets. This integration also enable the models to capture both short-term fluctuations and long-term trends in WQ parameters better. Such capabilities are essential for addressing the multifaceted challenges posed by environmental degradation, particularly in regions like the Karun River basin, where water resources are under significant stress due to anthropogenic activities and climate change.

Objective: This paper aims to introduce a modified kernel-type ridge estimator for partially linear models under randomly-right censored data. Such models include two main issues that need to be solved: multi-collinearity and censorship. To address these issues, we improved the kernel estimator based on synthetic data transformation and kNN imputation techniques. The key idea of this paper is to obtain a satisfactory estimate of the partially linear model with multi-collinear and right-censored using a modified ridge estimator. Results: To determine the performance of the method, a detailed simulation study is carried out and a kernel-type ridge estimator for PLM is investigated for two censorship solution techniques. The results are compared and presented with tables and figures. Necessary derivations for the modified semiparametric estimator are given in appendices.

This paper considers an extension of the linear mixed model, called semiparametric mixed effects model, for longitudinal data, when multicollinearity is present. To overcome this problem, a new mixed ridge estimator is proposed while the nonparametric function in the semiparametric model is approximated by the kernel method. The proposed approache integrates ridge method into the semiparametric mixed effects modeling framework in order to account for both the correlation induced by repeatedly measuring an outcome on each individual over time, as well as the potentially high degree of correlation among possible predictor variables. The asymptotic normality of the exhibited estimator is established. To improve efficiency, the estimation of the covariance function is accomplished using an iterative algorithm. Performance of the proposed estimator is compared through a simulation study and analysis of CD4 data.

Background and Aims: Overlapping of the proximal surfaces of posterior teeth in the panoramic radiography is a major concern. Therefore, an option has been developed in the panoramic unit of Planmeca Promax, namely improved interproximal mode. This mode causes lower horizental angle with the teeth contact region during the unit rotation decreasing overlapping of the panoramic images of the posterior teeth especially premolar teeth. The present study was done to compare the overlapping of posterior teeth using two techniques of improved interproximal panoramic program and standard panoramic.Materials and Methods: In this diagnostic study, 32 patients requiring panoramic radiographies at their posterior teeth during their routine diagnosis and treatment process with the mean age of 27.3 years were participated. No patients showed crowding of posterior teeth or missed and restored posterior teeth. The participants' panoramic radiographies were randomly taken by two techniques of improved interproximal panoramic and standard panoramic using Planmeca Promax device. The overlapping of the panoramic images was blindly assessed by an oral radiologist. The overlapping in both techniques was reported by frequency and percentage. The comparisons were done by Chi-square test between two techniques and the odds ratio of overlapping was estimated using regression analysis.Results: In standard panoramic techniques, 38.5% (148 contacts of 384 contacts) of the proximal surfaces overlapped while the overlapping of the proximal surfaces was observed in 18.8% (72 contacts of 384 overall contacts) in improved interproximal technique. Significant differences were noted between two techniques regarding overlapping (P<0.001). Also 66.4% and 39.1% of 4-5 teeth contacts overlapped in standard and improved techniques. The values were reported to be 39.1% and 12.5% in contacts of 5-6 teeth and 10.2% and 4.7% in the contacts of 6-7 teeth in both techniques, respectively. The overlapping odds ratio in improved technique as compared to standard techniques was 2.72 more. While the odds ratio of overlapping in the contact regions of 4-5 and 5-6 teeth was 16.4 and 4.61 as compared to the contact region of 6-7 teeth (all: P<0.001). The lower or upper jaw with the patients' mouth side did not significantly influence the overlapping of the proximal surfaces in both panoramic techniques.Conclusion: Under the limitations of this study, improved interproximal panoramic significantly reduced the overlapping of proximal surfaces in the panoramic radiographies of posterior teeth as compared to the standard panoramic technique. Therefore, it can be used to detect proximal caries in the posterior teeth as a diagnostic tool. Using this option may affect other part of panoramic image which should be investigated in other research.

In this paper, a novel LNA design based on improved noise cancellation technique in the frequency range of 27 to 31 GHz.is presented The proposed LNA is suitable for millimeter wave 5G wireless communication. The first stage of this two-stage LNA is designed with noise cancelation approach to decrease the noise figure of the system. In order to improve the design method, we utilizes a negative feedback by implementing a couple inductor with a transformer connection. The negative feedback provides an acceptable input matching and control the gain to increase the band width. The cascode structure is used in the second stage for its higher gain and stability and better reverse isolation at millimeter wave frequency. Furthermore, an inductor is utilized to boost the gain with neutralizing the capacitance of node between two transistors in a cascode structure. The CMOS silicon on insulator (SOI) is utilized to provide a high level of integration and low power consumption with the minimum cost. The proposed LNA is designed with 130 nm CMOS technology and has 22.14 dB gain with 1.86 dB noise figure at 29 GHz. The 3-dB bandwidth of the designed LNA is 4 GHz (14%) and its DC power consumption is 33.4 mW. The IIP3 is -16dBm and input reflection coefficient is better than -10dBm in the frequency range of interest. The proposed LNA is simulated by ADS software.

Controlling of neuroprostheses to restore grasping ability in patients with paralyzed or amputated upper limbs is one of the important applications of BCI systems. The ability to get objects is necessary for daily works so, for a reliable function of the neuroprostheses, it is necessary for the user to control the amount of force needed for grasping. For this reason, increasing the accuracy of continuous force decoding is an important issue for the convenient function of these BCI systems. In most studies in the field of force decoding, linear models such as wiener filter, Kalman filter, PLS, etc. are used to decode force. So far, the effect of using nonlinear models is not investigated on force decoding. The goal of this study is to investigate the effect of using nonlinear regression models based on kernel functions on the accuracy of force decoding in Vistar rats using local field potential signals. To do this, we choose ridge regression, PCR and PLS methods and use the Gaussian kernel function to construct a generalized nonlinear model for the force decoding. Evaluating kernel ridge, kernel PCR and kernel PLS methods shows that considering nonlinear relations between brain signal’ s features improves decoding accuracy. The mean coefficient of determination (R2) improves 12. 7% in kernel ridge toward ridge regression, 25. 5% in kernel PCR toward PCR and 19. 1% in kernel PLS toward PLS method. The best decoding accuracy has been achieved by the kernel ridge regression method and the mean correlation coefficient between the estimated and measured force is 0. 72 and R2 is 0. 62.