Recommender systems are essential tools across numerous digital platforms, helping users discover relevant products, content, and services. Research has traditionally focused on prediction accuracy and relevance, relying primarily on collaborative filtering and matrix factorization techniques. With the increasing complexity of user behavior and data modalities, modern systems have moved beyond simple rating prediction to address additional objectives, including fairness, transparency, privacy, long-term engagement, and trustworthiness. This article systematically reviews the evolution of recommender systems, covering key stages from early predictive models to modern human-centered and trust-aware systems. Each stage is discussed in terms of methodological advances and practical applications. Emerging paradigms, including causal reasoning for bias mitigation, reinforcement learning for long-term optimization, federated and privacy-preserving learning, explainable recommendation techniques, and blockchain-based trust mechanisms, are analyzed. These developments illustrate a broader shift from static, correlation-driven predictions toward adaptive, context-aware, and human-centered intelligence. By organizing research into coherent clusters, this review provides a unified perspective on the field, highlights the connections between past and current approaches, and identifies promising directions for next-generation recommender systems that balance accuracy, user satisfaction, ethical considerations, and long-term system effectiveness.
This paper mainly presents upper bounds for the singular values and unitarily invariant norms of the product of two complex matrices. The obtained bounds refine many celebrated results in the literature, such as the celebrated matrix arithmetic-geometric mean inequality and its variants.
A fractional vaccination model for monkeypox infection with two strains, based on real data, is proposed. We consider monkeypox case data for the period January 1, 2025, to July 31, 2025. The model is first formulated using an integer-order derivative and then extended to a fractional-order derivative. It is shown that the fractional model exists and has a unique solution. Equilibrium points are obtained, and their stability is analyzed; the model is found to be locally asymptotically stable whenever [Formula: see text]. Multiple equilibria are identified, and under certain conditions, the existence of a positive endemic equilibrium and the possibility of backward bifurcation are demonstrated. A nonlinear least-squares approach is used for the estimation of model parameters, and sensitivity analysis identifies parameters with high potential for disease control. The numerical values estimated for the parameters give [Formula: see text]. A numerical scheme is proposed to accurately solve the two-strain mpox model, and graphical results illustrate how disease elimination can be achieved based on the fractional-order parameter and contact rates.
Context: Cross-project defect prediction (CPDP) aims to predict software defects in a target project using data from related source projects, especially when defect data for the target project is limited or unavailable. A key challenge in CPDP is data heterogeneity and distributional differences across projects, which often lead to poor performance and unreliable predictions. Objectives: This study proposes a new CPDP model that improves prediction accuracy and robustness by introducing fuzzy embedding and deep learning to better capture similarities and differences across projects. The method is designed to mitigate mismatches in data distribution that hinder existing transfer learning and transformation-based approaches. Methods: The fuzzy embedding technique is built on fuzzy clustering and fuzzy set theory, which map each data point into a two-dimensional space of membership degrees across clusters. This representation models complex relationships with partial memberships and preserves contextual information that is often lost in conventional transformations. A deep learning model based on convolutional neural networks (CNN) processes the embedding matrices to learn discriminative defect patterns. The framework is evaluated against state-of-the-art CPDP models across multiple datasets, and sensitivity analysis is conducted on the number of clusters used in fuzzy embeddings. Results: Empirical evaluation shows that the proposed model consistently outperforms advanced CPDP approaches that rely on standard transformation or weighting methods. Improvements are observed in AUC and other key metrics across diverse datasets, demonstrating that fuzzy embeddings enhance the ability of deep learning to generalize knowledge across projects with varying characteristics. Conclusion: This work contributes a practical and effective solution for addressing heterogeneity in CPDP. By combining fuzzy embeddings with deep learning, the model not only achieves higher predictive accuracy but also improves reliability in real-world scenarios where project data distributions differ significantly. These findings highlight the potential of fuzzy embedding to support more resilient software quality assurance practices and provide actionable insights for practitioners dealing with limited or imbalanced defect data.
The design of robust, scalable, and web-accessible engineering platforms is essential for modern computational workflows. This work addresses these needs by presenting a robust, API-first system that enables remote execution of MATLAB scripts and Simulink models within a cloud-based digital engineering framework. By exposing MATLAB functionalities through RESTful APIs and structured JSON exchanges, the system supports function parsing, simulation control, and result extraction with high precision. A React-based user interface enhances accessibility and user control, while backend modules ensure secure execution, cloud storage integration, and compatibility with diverse applications. The architecture effectively overcomes interoperability challenges between MATLAB and other tools, enabling seamless inclusion in digital threads. Performance evaluations confirm minimal overhead and real-time responsiveness, reinforcing the platform’s suitability for scalable deployment in advanced intelligent systems and applications.
