Background/Objectives: In the modern healthcare landscape, breast cancer remains one of the most prevalent malignancies and a leading cause of mortality among women worldwide. Early and accurate prediction of breast cancer plays a pivotal role in effective diagnosis, treatment planning, and improving survival outcomes. However, due to the complexity and heterogeneity of medical data, achieving high predictive accuracy remains a significant challenge. This study proposes an intelligent hybrid system that integrates traditional machine learning (ML), deep learning (DL), and ensemble learning approaches for enhanced breast cancer prediction using the Wisconsin Breast Cancer Dataset. Methods: The proposed system employs a multistage framework comprising three main phases: (1) data preprocessing and balancing, which involves normalization using the min–max technique and application of the Synthetic Minority Over-sampling Technique (SMOTE) to mitigate class imbalance; (2) model development, where multiple ML algorithms, DL architectures, and a novel ensemble model are applied to the preprocessed data; and (3) model evaluation and validation, performed under three distinct training–testing scenarios to ensure robustness and generalizability. Model performance was assessed using six statistical evaluation metrics—accuracy, precision, recall, F1-score, specificity, and AUC—alongside graphical analyses and rigorous statistical tests to evaluate predictive consistency. Results: The findings demonstrate that the proposed ensemble model significantly outperforms individual machine learning and deep learning models in terms of predictive accuracy, stability, and reliability. A comparative analysis also reveals that the ensemble system surpasses several state-of-the-art methods reported in the literature. Conclusions: The proposed intelligent hybrid system offers a promising, multidisciplinary approach for improving diagnostic decision support in breast cancer prediction. By integrating advanced data preprocessing, machine learning, and deep learning paradigms within a unified ensemble framework, this study contributes to the broader goals of precision oncology and AI-driven healthcare, aligning with global efforts to enhance early cancer detection and personalized medical care.

Accurate estimation of population distribution characteristics is a fundamental task in survey sampling and statistical inference. This paper introduces a new family of estimators for the cumulative distribution function (CDF) under probability proportional to size (PPS) sampling, incorporating auxiliary information to enhance efficiency. The proposed approach employs dual auxiliary variables in the estimation phase, while the sampling design relies on a single auxiliary variable. Theoretical properties, including bias and mean squared error (MSE), are rigorously derived to establish the efficiency of the new class. An extensive empirical evaluation using three distinct populations—fisheries data, wine chemistry data, and demographic records—demonstrates the superiority of the proposed estimators. In terms of accuracy, the best-performing proposed estimator achieves an MSE of 0.0012, compared to 0.0127 for the widely used GK estimator. Percentage relative efficiency (PRE) values further underscore these improvements, with gains ranging from 123% to over 328% across the three populations. Graphical comparisons confirm these trends, illustrating that the proposed estimators consistently dominate conventional approaches. Overall, the findings highlight both the theoretical soundness and practical utility of the proposed family, offering robust and computationally efficient improvements for CDF estimation in complex survey designs.

The inherent non-linear, non-stationary, multi-scale nature of financial time-series data makes the task of financial forecasting exceptionally difficult. While deep learning models incorporating decomposition techniques have achieved significant progress in forecasting, their performance heavily relies on the signal’s quality during decomposition and the setting of parameters. To this end, this study presents a forecasting framework for the S&P 500 index using RFEO–VMD–PatchTST (RIME and Fuzzy Entropy Optimized Variational Mode Decomposition with PatchTST). We utilized the RIME optimization algorithm to autonomously obtain VMD’s optimal number of modes K and penalty term. To identify which is the best-performing model among the evaluated models under the reported test protocol, i.e., Sample Entropy (SE), Fuzzy Entropy (FE), and Permutation Entropy (PE), were discussed and used as objectives for optimization. In particular, the experimental analysis showed that Fuzzy Entropy achieves better decomposition quality with K = 2, producing two adaptive IMFs and yields the optimal decomposition that represents the primary driving forces of market trends. Subsequently, we independently model each IMF using the Patch Time Series Transformer (PatchTST) and then combine the IMF forecasts to obtain the final prediction. Experiments with various evaluation criteria were conducted on S&P 500 index data, and the results show that our framework consistently outperforms conventional methods, including statistical, machine learning, deep learning, and decomposition-based approaches. Additionally, to verify that our framework is robust, stable, and statistically significant, we provide ablation studies, multi-horizon forecasting, rolling-window analysis, random-seed experiments, and Diebold–Mariano tests.

Leadership styles are increasingly recognised as strategic organizational resources for faculty well-being, yet the evidence remains fragmented: prior stud

Optimizing coagulant dosages in Drinking Water Treatment Plants (DWTPs) is critical for reducing operational costs, minimizing chemical waste, mitigating environmental impacts, and ensuring consistent water quality, particularly in resource-constrained settings where conventional jar tests are labor-intensive and poorly suited to real-time demands. This study develops and validates a Random Forest (RF) machine learning model to predict optimal dosages of aluminum sulfate, polyaluminum chloride, and a polymer flocculant at the Miguel de la Cuba Ibarra DWTP in Peru, addressing the need for an efficient, real-time decision support system. Using a historical dataset of 2556 jar tests, a univariate RF model was developed to predict settled water turbidity, tailored to the plant’s typical operational range. The model demonstrated robust predictive performance, achieving a coefficient of determination (R²) of 0.92 during training and 0.76 during validation with unseen data, alongside a Root Mean Square Error (RMSE) of 0.11 NTU and a Mean Absolute Percentage Error (MAPE) of 0.11 in the training phase. Integrated into a digital platform, the model generates real-time NTU ppm dosing curves, providing a practical and responsive tool to enhance operational efficiency for DWTP operators. This work offers a scalable, data-driven solution to improve water treatment processes in resource-limited contexts.