Search Results (3,084)

Non-convex stochastic optimization presents fundamental mathematical challenges across machine learning, wireless networks, data center resource allocation, and optical wireless communication systems, where complex loss landscapes with multiple local minima and saddle points impede classical variational inference methods. This paper introduces the Quantum-Inspired Variational Inference (QIVI) framework, which systematically integrates quantum mechanical principles (superposition, entanglement, and measurement operators) into classical variational inference through rigorous mathematical formulations grounded in Hilbert space theory and operator algebras. We develop a unified optimization framework that encodes classical parameters as quantum-inspired states within finite-dimensional complex Hilbert spaces, employing unitary evolution operators and adaptive basis selection governed by gradient covariance eigendecomposition. The core mathematical contribution establishes that QIVI achieves a convergence rate of $\mathit{O}({log}^{2}T/T^{1/2})$ for $\sigma$-strongly non-convex functions, provably improving upon the classical $\mathit{O}\left(T^{-1/4}\right)$ rate, yielding a theoretical speedup factor of $1.85$–$1.96\times$. Comprehensive experiments across synthetic benchmarks, Bayesian neural networks, and real-world applications in network optimization and financial portfolio management demonstrate 23–$47\%$ faster convergence, 15–$35\%$ superior objective values, and 28–$46\%$ improved uncertainty calibration. The principal contributions include: (i) a rigorous Hilbert space-based mathematical framework for quantum-inspired variational inference grounded in operator algebras, (ii) a novel hybrid quantum–classical algorithm (QIVI) with adaptive basis selection via gradient covariance eigendecomposition, (iii) formal convergence proofs establishing provable improvement over classical methods, (iv) comprehensive empirical validation across diverse problem domains relevant to machine learning and network optimization, and (v) demonstration of the framework’s applicability to optimization problems arising in wireless networks, data center resource allocation, and network system design. Statistical validation using the Friedman test (${\chi }^2=847.3$, $p<0.001$) and post hoc Wilcoxon signed-rank tests with Holm–Bonferroni correction confirm that QIVI’s improvements over all baseline methods are statistically significant at the $\alpha =0.05$ level across all benchmark categories. The framework discovers $18.1$ out of 20 true modes in multimodal distributions versus $9.1$ for classical methods, demonstrating the potential of quantum-inspired optimization approaches for challenging stochastic problems arising in machine learning, wireless communication, and network optimization. Full article

Different methodologies have been developed for the analysis and study of dynamical systems, including both theoretical models and natural systems. Examples span a wide range of applications, such as astronomy, financial and economic time series, biophysical systems, physiological phenomena, and Earth sciences, including seismicity and climatic processes. The study of these complex systems is commonly based on the analysis of the signals they generate, using mathematical tools to extract relevant information. A broad spectrum of mathematical disciplines converges in this context, including stochastic, probability and statistical theory, entropic and informational measures, fractal and multifractal analysis, natural time analysis, modeling of non-linearity and recurrence methods, generalized entropies, non-extensive systems, machine learning, and high-dimensional and multivariate complexity. Research in this area is largely focused on the characterization of complex systems, providing indicators of determinism or stochasticity, distinguishing between regularity, chaos, and noise, and identifying topological as well as disorder-regularity features. In addition, short- and long-term forecasting, together with the identification of short- and long-range correlations, play a central role in such characterization. To address these objectives, numerous mathematical tools have been developed for the analysis of time series and point processes, each designed to capture specific signal properties. In this work, many of the most important tools used in time series analysis are compiled and reviewed, highlighting their main characteristics and the different types of complex systems to which they have been applied. Full article

This scoping review critically synthesizes 34 studies (2015–2026) examining the metaverse’s role in fostering six core STEM competencies, moving beyond descriptive reporting to interrogate whether these technologies constitute genuine pedagogical transformation, whose learners are served or excluded, and how isolated interventions connect into lifelong learning pathways. Following PRISMA-ScR guidelines, our analysis reveals that while technology literacy and collaboration appear in 91.2% of our selected studies, mathematical application is addressed in fewer than half (44.1%), raising unanswered questions about whether this pattern reflects an equitable distribution of mathematical learning opportunities across diverse learner populations—a question the current evidence base cannot answer but one that warrants urgent investigation. The evidence demonstrates substantial immediate learning gains through embodied presence and risk-free experimentation, yet a deeper reading suggests this often represents technological optimization of traditional goals rather than epistemological transformation. More troublingly, the concentration of inclusivity evidence on select populations—while rendering students with physical disabilities, Indigenous learners, and refugee students entirely invisible—reveals an equity paradox where immersive technologies may inadvertently amplify existing disparities. The absence of any longitudinal data linking short-term engagement to sustained STEM participation leaves the field’s claim to transformative impact unsubstantiated. This review argues for moving beyond fragmented interventions toward designing coherent, equitable learning pathways that fulfill the metaverse’s potential for all learners. Full article

In Vietnamese primary mathematics education, geometry instruction often emphasizes rote calculation and formula memorization rather than meaningful contextualization, leaving students disconnected from abstract concepts and lacking opportunities to connect learning with cultural identity. This quasi-experimental study investigates how integrating generative AI tools (ChatGPT, DALL·E, Canva) with the culturally grounded Vietnamese folktale Bánh Chưng—Bánh Giầy can support Grade 5 students’ understanding of circle geometry. Employing a mixed-methods design with 30 students divided into experimental (AI + storytelling) and control (traditional instruction) groups, the study measured cognitive and affective learning outcomes through pre/post-tests, a validated 25-item questionnaire, interviews, and classroom observations. Quantitative results revealed significant improvements in the experimental group across all measured dimensions, learning interest, attentional focus, conceptual understanding, mathematics passion, and cultural preservation awareness, with large effect sizes. Qualitative findings confirmed enhanced engagement, multimodal conceptual clarity, and cultural affective resonance. The study demonstrates that low-cost, teacher-mediated generative AI can effectively support learning in resource-constrained primary settings when anchored in local narratives. Implications for ethical AI integration and teacher professional development in Vietnamese contexts are discussed. Full article

Mathematical knowledge is essential for adult learners’ advancement in academic and professional settings; however, instructional strategies for adult learners in higher education often emphasize memorizing procedures while neglecting their personal and professional experiences. Such approaches limit opportunities to leverage these experiences for developing meaningful mathematical understanding. Grounded in the Models and Modeling Perspective, this exploratory qualitative case study examines how a Model Development Sequence (MDS) supports the development of mathematical knowledge of adult learners returning to higher education. The participants were a group of seven first-year business adult learners enrolled in the Applied Mathematics in Business course at a higher education institution. Data were analyzed using protocol coding to describe the types of mathematical models the participants constructed. Findings indicate that participants progressed from creating models requiring redirection, grounded in proportional reasoning, to developing more sophisticated models based on linear and exponential functions. The MDS supported learners in refining, extending, and adapting their models, strengthening their conceptual understanding of variation, linear and exponential functions, and covariational reasoning. Moreover, the participants’ personal and professional experiences were central to model development. This study contributes to research on adult mathematics education by demonstrating the potential of MDS to support meaningful mathematical learning. Full article

Mathematics is a diverse discipline that requires a variety of cognitive abilities and presents varying levels of difficulty. Understanding how different cognitive profiles relate to specific patterns of mathematical performance is important for developing effective educational interventions. This study extends our previous research, in which we identified subgroups of children with mathematical difficulties based on their cognitive abilities. We examined 146 Israeli elementary school children in grades 3 and 4, classified into four subgroups: Reading Accuracy Difficulties (RAD), Mild Mathematical Difficulties (MMD), Non-Verbal Reasoning Difficulties (NVRD), and Typically Developing children (TD). Participants were assessed on arithmetic facts, computational fluency, procedural skills, estimation, and numeration. We observed varied performance patterns among subgroups. The RAD group showed the most severe impairments across all mathematical domains, along with reading comorbidity and cognitive difficulties. The MMD group, which maintained intact cognitive skills, faced notable challenges in computation, performing significantly below the TD group but better than the RAD group. The NVRD group, despite limitations in nonverbal reasoning, outperformed other difficulty groups on fact retrieval and estimation. Performance on multiplication and division tasks consistently followed a hierarchical pattern across all difficulty groups, with the RAD group facing the greatest challenges. These findings demonstrate that mathematical difficulties vary across cognitive profiles and that distinguishing between profiles through targeted assessment enables the development of differentiated interventions tailored to each learner’s specific cognitive profile. Full article

This study investigates the relationship between creative personality and academic achievement in first-year secondary education students, as well as the predictive capacity of creative personality on performance across different subject areas. The sample comprised 125 students who completed Garaigordobil’s Creative Personality Scale, and their academic grades were collected as performance indicators. Academic achievement was analyzed by distinguishing between STEM subjects (biology, technology, and mathematics) and non-STEM subjects (Spanish language, geography, arts, physical education, French, and English). The findings saw a positive association between creative personality and academic achievement in both STEM and non-STEM domains. Moreover, statistically significant sex differences emerged: female students obtained higher scores than male students on creative personality traits associated with problem identification and problem solving, as well as on dimensions related to enjoyment of diverse games and openness to new experiences. These results underscore the relevance of creative personality as a determinant of academic achievement across both scientific and non-scientific areas. They also highlight the importance of fostering creativity as an educational strategy aligned with sustainability goals. This study offers practical implications for the design of evidence-based psycho-pedagogical interventions that incorporate creativity as a means to promote responsible, equitable, and sustainable learning. Full article

Digital signal processing (DSP) methods and artificial intelligence (AI) serve as a unifying platform across diverse research areas and educational courses based on analysis of signals acquired by appropriate sensors and their time-synchronized systems. Autonomous sensor systems having their own batteries, memories, and possibilities of wireless communication form the core of modern technological systems. The interconnection of sensors for data acquisition, methods for advanced analysis of signal features, and collaborative evaluation promotes both theoretical learning and practical problem solving in professional practice. This paper emphasizes a common mathematical foundation for the processing of data acquired by different sensor systems, and it presents the integration of DSP and AI, enabling the use of similar theoretical methods in different applications, including robotics, digital twins, neurology, augmented reality, and energy optimization. Through selected case studies, it shows how a combination of sensor technology for data acquisition and the use of similar computational methods, visualization, and real-world case studies strengthens interdisciplinary collaboration. Findings of this paper demonstrate how integrating AI with DSP supports innovative research and teaching strategies, redefines the field’s educational role in the digital era, and points to the development of new digital technologies. Full article

MOS gas sensors have proven to be useful in electronic noses, which utilize these sensors to detect volatile organic compounds in human breath to detect various lung diseases. Unfortunately, the long settling time of MOS gas sensors is ill-suited to measuring human breath, where complete breathing cycles are often shorter than 5 s. Existing studies circumvent this limitation by collecting gas samples and injecting them into a sealed chamber to react with the sensors. However, it would be convenient if breath-by-breath analysis could be conducted without the need to store breath samples. To accomplish this, we present a novel forecasting methodology to predict the final value $t_{\infty }$ of a gas sensor’s response based on its initial transient behavior. To do this, we present and validate a second-order mathematical model of the sensors’ response characteristics, which we then use in our preliminary work using neural networks to predict the final sensor value. Although some challenges were encountered, the initial results are encouraging, and we plan to extend our study in the future to collect a more expansive dataset and explore the use of other types of machine learning algorithms for this application. Full article

Unreinforced masonry walls exhibit limited resistance to lateral loads and, therefore, frequently require strengthening interventions. Carbon fiber reinforced polymer (CFRP) systems provide an efficient retrofit solution; however, current design procedures defined in structural guidelines require repetitive trial calculations to determine the necessary reinforcement amount. This study introduces a hybrid computational process that integrates metaheuristic optimization with symbolic regression to generate direct analytical equations for the estimation of the required CFRP area. First, a comprehensive database containing 1300 optimal strengthening scenarios was generated using the Jaya optimization algorithm under the constraints specified in ACI 440.7R and ACI 530. The resulting dataset was subsequently processed through symbolic regression using the PySR platform to identify explicit mathematical relationships between structural parameters and the optimum CFRP area. Most traditional machine learning approaches operate as black-box predictors. In contrast, the proposed approach generates interpretable closed-form expressions that can be used directly in engineering calculations. Two models were derived from the Pareto-optimal solution set. The first model is a simplified equation emphasizing algebraic simplicity. The second model prioritizes prediction accuracy. The simplified formulation achieved a coefficient of determination of approximately 0.992. The accuracy-focused model achieved a value above 0.997 with very low prediction errors. Validation studies with independent test samples showed that the obtained equations are reliable. The average error for the simplified model is below 4%, and for the high-accuracy model, it is approximately 2%. The results demonstrate that combining the optimization-generated datasets with symbolic regression makes it possible to obtain transparent design equations. These equations eliminate iterative design processes and provide a fast and reliable estimation tool for CFRP strengthening of masonry walls. Full article

This paper develops a rigorous operator-theoretic framework for learning-augmented quasi-gradient methods in constrained optimization. We consider the minimization of an objective function over a closed convex feasible set, where feasibility is enforced via projection and directional updates may incorporate data-driven corrections. Such settings arise naturally in modern optimization algorithms that integrate artificial intelligence components under structural constraints. The proposed formulation introduces an explicit contraction–bias–variance decomposition of the iterative dynamics. Curvature induces deterministic contraction, alignment distortion—quantified by a geometric parameter—modifies the effective contraction margin, and stochastic learning components inject controlled dispersion. Explicit error recursions yield convergence guarantees under strong convexity, the Polyak–Łojasiewicz condition, and smooth nonconvexity. The analysis establishes that stability regions and first-order complexity bounds are preserved whenever alignment distortion remains below unity and bounded second-moment conditions hold. A fully reproducible computational study provides quantitative validation: the empirically observed steady-state error closely matches the theoretical prediction proportional to ${\sigma }^2/\mu (1-\eta )$. Comparative experiments with gradient, stochastic gradient, and momentum methods confirm that the proposed operator retains classical stability margins and conditioning sensitivity while enabling principled integration of learned directional components. The results provide a transparent mathematical bridge between stochastic approximation theory and contemporary AI-enhanced constrained optimization. Full article

The rapid growth of the Internet of Things (IoT) is fundamentally altering industrial and economic landscapes by embedding smart, connected devices into everyday operations. Despite these benefits, significant concerns regarding data protection and user privacy continue to obstruct the widespread use of these technologies, particularly with the looming threat of quantum computing. Implementing post-quantum cryptographic (PQC) solutions is vital for addressing these risks, yet the limited resources found in IoT edge devices present major deployment challenges. Lattice-based cryptography has become a leading solution to these problems, largely because it depends on efficient polynomial multiplication. Enhancing the execution of this mathematical operation is crucial for improving the overall performance of PQC protocols. In this work, we introduce a hybrid serial–parallel systolic architecture specifically engineered for polynomial multiplication within the Binary Ring Learning With Errors (BRLWE) scheme. Designed for the security processors used in IoT hardware, this architecture significantly increases processing speeds while minimizing the use of hardware resources and reducing energy consumption. Such improvements are critical for establishing a secure IoT infrastructure that is resilient against quantum-era attacks and capable of supporting industrial expansion. Moreover, this research aligns with global Sustainable Development Goals (SDGs) 8 and 9 by building trust in innovative systems and fostering a more secure, sustainable, and productive digital economy. Full article

Background: Spare parts distribution networks (DNs) play a strategic role in retailers’ profitability. Among DN configuration decisions, selecting the optimal stock deployment policy—centralised, decentralised, or hybrid inventory allocation across distribution centres (DCs)—critically affects service levels and logistics costs. This decision becomes more complex with additive manufacturing (AM) as an alternative to conventional manufacturing (CM). While AM enables production with shorter lead times, its higher costs alter stock deployment cost-effectiveness. Given the complexity of joint stock deployment and manufacturing decisions, retailers require decision support systems (DSSs). Methods: To address this need, we develop a DSS through a three-step methodology: (i) a mathematical model evaluates logistics costs across different stock deployment policies and manufacturing technologies; (ii) parametric analysis tests the model across 2000 realistic scenarios; (iii) Random Forest trained on this dataset predicts optimal solutions, with SHapley Additive exPlanations (SHAP) interpreting post hoc recommendations. Results: The DSS achieves 93.4% prediction accuracy—outperforming (+16.4%) the only comparable literature DSS (77%)—while explaining recommendations. SHAP reveals that AM and CM unit costs dominate decision-making, followed by backorder costs. Conclusions: Beyond individual spare parts recommendations, the DSS provides guidelines enabling retailers to maintain cost-effective DNs aligned with evolving customer needs and to plan valuable investments in AM. Full article

Modeling the complex spatio-temporal dynamics of infectious diseases presents a significant computational challenge due to heterogeneous regional interactions, high-dimensional multimodal data streams, and the critical need for algorithmic fairness. This paper proposes a novel computational framework that unifies graph-based spatio-temporal forecasting, anomaly detection, and retrieval-augmented generation (RAG) into a single mathematical architecture. The predictive backbone employs a graph-augmented Temporal Fusion Transformer to capture non-linear temporal dependencies and spatial disease propagation. By formalizing regional topology and mobility flows as a weighted mathematical graph, the model systematically integrates structured epidemiological counts, continuous environmental covariates, and digital trace signals. To address algorithmic bias, we formulate a fairness-aware optimization problem by embedding a specific regularization term into the training objective, which mathematically penalizes disparities in true-positive rates across diverse socio-demographic strata. Furthermore, the numerical outputs and anomaly scores are processed by a large language model equipped with hybrid dense and sparse retrieval to generate interpretable, computationally grounded decision support. Extensive experiments on a longitudinal dataset comprising 62 administrative regions over 260 weeks validate the mathematical robustness of the proposed framework. The graph-augmented architecture improved forecasting accuracy by up to 24% and anomaly detection F1 scores by over 6% compared to state-of-the-art deep learning baselines, while the fairness-regularized loss function reduced the maximum subgroup recall gap by more than 50%. These findings demonstrate that predictive accuracy and algorithmic fairness can be jointly optimized, providing a rigorous computational methodology for spatio-temporal epidemic modeling and AI-driven surveillance. Full article

Most state-of-the-art machine learning techniques revolve around the optimization of loss functions, making the choice of an objective critical to model performance and reliability. Although recent reviews discuss loss functions in specific domains or in deep learning settings, there is still no single reference that presents widely used losses across major task families within a unified formal setting and with consistent optimization-relevant property annotations. In this survey, we compile and systematize the most widely adopted loss functions for regression, classification, generative modeling, ranking, energy-based modeling, and relational learning. Our selection procedure combines seeding from foundational textbooks and prior surveys with cross-checking of highly cited literature and common implementations in mainstream machine learning frameworks. We introduce 52 loss functions and organize them into an intuitive taxonomy, summarizing their theoretical motivation, key mathematical properties, and typical application contexts, with compact appendix tables for quick lookup. This survey is intended as a resource for undergraduate, graduate, and Ph.D. students, as well as researchers seeking a structured reference for selecting and comparing loss functions. Full article