Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1]....Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.展开更多
Effectively handling imbalanced datasets remains a fundamental challenge in computational modeling and machine learning,particularly when class overlap significantly deteriorates classification performance.Traditional...Effectively handling imbalanced datasets remains a fundamental challenge in computational modeling and machine learning,particularly when class overlap significantly deteriorates classification performance.Traditional oversampling methods often generate synthetic samples without considering density variations,leading to redundant or misleading instances that exacerbate class overlap in high-density regions.To address these limitations,we propose Wasserstein Generative Adversarial Network Variational Density Estimation WGAN-VDE,a computationally efficient density-aware adversarial resampling framework that enhances minority class representation while strategically reducing class overlap.The originality of WGAN-VDE lies in its density-aware sample refinement,ensuring that synthetic samples are positioned in underrepresented regions,thereby improving class distinctiveness.By applying structured feature representation,targeted sample generation,and density-based selection mechanisms strategies,the proposed framework ensures the generation of well-separated and diverse synthetic samples,improving class separability and reducing redundancy.The experimental evaluation on 20 benchmark datasets demonstrates that this approach outperforms 11 state-of-the-art rebalancing techniques,achieving superior results in F1-score,Accuracy,G-Mean,and AUC metrics.These results establish the proposed method as an effective and robust computational approach,suitable for diverse engineering and scientific applications involving imbalanced data classification and computational modeling.展开更多
This study demonstrates the complexity and importance of water quality as a measure of the health and sustainability of ecosystems that directly influence biodiversity,human health,and the world economy.The predictabi...This study demonstrates the complexity and importance of water quality as a measure of the health and sustainability of ecosystems that directly influence biodiversity,human health,and the world economy.The predictability of water quality thus plays a crucial role in managing our ecosystems to make informed decisions and,hence,proper environmental management.This study addresses these challenges by proposing an effective machine learning methodology applied to the“Water Quality”public dataset.The methodology has modeled the dataset suitable for providing prediction classification analysis with high values of the evaluating parameters such as accuracy,sensitivity,and specificity.The proposed methodology is based on two novel approaches:(a)the SMOTE method to deal with unbalanced data and(b)the skillfully involved classical machine learning models.This paper uses Random Forests,Decision Trees,XGBoost,and Support Vector Machines because they can handle large datasets,train models for handling skewed datasets,and provide high accuracy in water quality classification.A key contribution of this work is the use of custom sampling strategies within the SMOTE approach,which significantly enhanced performance metrics and improved class imbalance handling.The results demonstrate significant improvements in predictive performance,achieving the highest reported metrics:accuracy(98.92%vs.96.06%),sensitivity(98.3%vs.71.26%),and F1 score(98.37%vs.79.74%)using the XGBoost model.These improvements underscore the effectiveness of our custom SMOTE sampling strategies in addressing class imbalance.The findings contribute to environmental management by enabling ecology specialists to develop more accurate strategies for monitoring,assessing,and managing drinking water quality,ensuring better ecosystem and public health outcomes.展开更多
This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression model...This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.展开更多
Let Lk= （-△）k ＋ Vk be a SchrSdinger type operator, where k ≥1 is a positive integer and V is a nonnegative polynomial. We obtain the Lp estimates for the operators △2kLk-1 and △kLk-1/2
基金supported by the NSFC(12071437)the National Key R&D Program of China(2022YFA1005700).
文摘Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.
基金supported by Ongoing Research Funding Program(ORF-2025-488)King Saud University,Riyadh,Saudi Arabia.
文摘Effectively handling imbalanced datasets remains a fundamental challenge in computational modeling and machine learning,particularly when class overlap significantly deteriorates classification performance.Traditional oversampling methods often generate synthetic samples without considering density variations,leading to redundant or misleading instances that exacerbate class overlap in high-density regions.To address these limitations,we propose Wasserstein Generative Adversarial Network Variational Density Estimation WGAN-VDE,a computationally efficient density-aware adversarial resampling framework that enhances minority class representation while strategically reducing class overlap.The originality of WGAN-VDE lies in its density-aware sample refinement,ensuring that synthetic samples are positioned in underrepresented regions,thereby improving class distinctiveness.By applying structured feature representation,targeted sample generation,and density-based selection mechanisms strategies,the proposed framework ensures the generation of well-separated and diverse synthetic samples,improving class separability and reducing redundancy.The experimental evaluation on 20 benchmark datasets demonstrates that this approach outperforms 11 state-of-the-art rebalancing techniques,achieving superior results in F1-score,Accuracy,G-Mean,and AUC metrics.These results establish the proposed method as an effective and robust computational approach,suitable for diverse engineering and scientific applications involving imbalanced data classification and computational modeling.
文摘This study demonstrates the complexity and importance of water quality as a measure of the health and sustainability of ecosystems that directly influence biodiversity,human health,and the world economy.The predictability of water quality thus plays a crucial role in managing our ecosystems to make informed decisions and,hence,proper environmental management.This study addresses these challenges by proposing an effective machine learning methodology applied to the“Water Quality”public dataset.The methodology has modeled the dataset suitable for providing prediction classification analysis with high values of the evaluating parameters such as accuracy,sensitivity,and specificity.The proposed methodology is based on two novel approaches:(a)the SMOTE method to deal with unbalanced data and(b)the skillfully involved classical machine learning models.This paper uses Random Forests,Decision Trees,XGBoost,and Support Vector Machines because they can handle large datasets,train models for handling skewed datasets,and provide high accuracy in water quality classification.A key contribution of this work is the use of custom sampling strategies within the SMOTE approach,which significantly enhanced performance metrics and improved class imbalance handling.The results demonstrate significant improvements in predictive performance,achieving the highest reported metrics:accuracy(98.92%vs.96.06%),sensitivity(98.3%vs.71.26%),and F1 score(98.37%vs.79.74%)using the XGBoost model.These improvements underscore the effectiveness of our custom SMOTE sampling strategies in addressing class imbalance.The findings contribute to environmental management by enabling ecology specialists to develop more accurate strategies for monitoring,assessing,and managing drinking water quality,ensuring better ecosystem and public health outcomes.
文摘This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.
基金Supported by the National Natural Science Foundation of China(10901018,11001002)the Beijing Foundation Program(201010009009,2010D005002000002)the Fundamental Research Funds for the Central Universities
文摘Let Lk= （-△）k ＋ Vk be a SchrSdinger type operator, where k ≥1 is a positive integer and V is a nonnegative polynomial. We obtain the Lp estimates for the operators △2kLk-1 and △kLk-1/2
