Search Results (358)

We develop SAFIRE (Self-Attention Fuzzy-Inspired Rule Estimator), a differentiable fuzzy-inspired rule-scoring surrogate for binary medical tabular classification coupling multi-head self-attention, Gaussian membership functions, and Hard Concrete gates for continuous rule scoring. We position SAFIRE as a smooth surrogate of the discrete $L_0$-regularised rule-selection problem and establish five mathematical results and one complexity remark: (1) the relaxed objective is differentiable almost everywhere under positive Gaussian widths (enforced by a Softplus reparameterisation) and fixed batch-normalisation statistics; (2) the deterministic-inference active threshold is strictly stricter than the expected-nonzero training threshold, identifying Hard Concrete gates as continuous rule-scoring devices rather than automatic pruning mechanisms; (3) per-sample forward complexity identifies attention and rule layers as the dominant terms; (4) the Softplus–BatchNorm–linear rule operator violates all four triangular-norm axioms—with necessary and sufficient conditions per axiom and a no-finite-parameterisation impossibility result—while a Softplus reparameterisation restores coordinate-wise monotonicity; (5) a margin-based upper bound characterises disagreement between the full classifier and a top-k rule-only surrogate; and (6) the Softplus-reparameterised constrained variant is provably coordinate-wise monotone with explicit asymptotic regimes. Evaluated on four University of California, Irvine (UCI), medical binary tabular benchmarks under repeated stratified cross-validation, SAFIRE-Prog is statistically competitive with strong interpretable, modern, and gradient-boosting baselines, with one Bonferroni-significant gain over RuleFit on the Diabetic Retinopathy Debrecen corpus. The 48-configuration Hard Concrete sweep, constrained-variant comparison, and a top-k fidelity analysis (per-fold range 0.73–0.95) provide quantitative companion measurements for the mathematical framework. A supplementary large-scale hospital electronic health record (EHR) benchmark (Diabetes 130-US Hospitals, $n=101,766$) shows the rule-scoring mechanism scales to ∼${10}^5$ records and, under severe class imbalance, statistically matches gradient boosting on accuracy while significantly exceeding it on macro-F1. The results offer a mathematically auditable pathway towards interpretable, auditable rule scoring for medical tabular classification, with rule signatures defined in a projected latent space rather than over raw clinical variables. Full article

The mineral system model formalizes the critical geological processes and mappable parameters that control ore formation, which can then be translated into spatial predictors used as input features in machine learning (ML)-based mineral prospectivity mapping (MPM). In most MPM studies, exploration evidence features are indeed derived from the mineral system model of the targeted deposit type. However, not all features produced in this way are necessarily informative or favorable for prospectivity analysis. This challenge can be addressed by using feature selection frameworks to identify the most relevant features before applying ML and deep learning (DL) algorithms for mathematical integration. To address this need, this study employs an unsupervised variational autoencoder (VAE) framework to evaluate and rank exploration evidence layers. The VAE quantifies feature importance through a systematic strategy that measures the sensitivity of reconstruction-error components, mean squared error (MSE), mean absolute error (MAE), and Kullback–Leibler (KL) divergence, to individual feature variations. In this way, the VAE ranks the exploration features and helps to identify those that are the most useful for prospectivity mapping. The proposed approach was applied to a real geo-dataset from a porphyry copper district in Iran. Based on the conceptual model of porphyry copper mineralization, 15 evidence layers were generated, including proximity to phyllic, argillic, propylitic, iron oxide, and silicification alteration zones; proximity to intrusive rocks, faults, and fault intersections; and geochemical maps of Cu, Mo, Sb, Pb, Zn, As, and W. The VAE-based ranking indicated that evidence layers related to hydrothermal alterations, intrusive rocks, and faults were the most influential exploration features, whereas geochemical evidence layers showed lower relative importance. Based on this evaluation, two modeling scenarios were considered: in the first, all available features were used, and in the second, only the features selected by the VAE framework were included. In both cases, the final prospectivity model was produced by an autoencoder (AE). For comparison, the prediction-area (P–A) plots of the two prospectivity models were generated using 14 known mineral occurrences as positive ground-truth labels, indicating that the model based on the selected features achieved a higher prediction rate (80%) than the model based on all features (72%). These results demonstrate that the evidence layers derived from the mineral system approach can benefit from unsupervised VAE-based evaluation, leading to improved performance of the prospectivity modeling. Full article

Due to the rapidly increasing number of studies conducted using SFO in recent years, a comprehensive and systematic review of the existing literature has become necessary. SFO is a bio-inspired metaheuristic optimization algorithm developed based on the sun-tracking behavior of sunflower plants. Owing to its simple mathematical structure and flexible search capability, SFO has been increasingly applied to various engineering and AI problems. This review study presents a systematic and comprehensive analysis of SFO-based studies published in the literature. The literature search was performed using the Scopus database, and a total of 192 studies were included in the final evaluation process. The reviewed studies were classified into eight major application domains, including engineering design, energy systems, machine learning, image processing, communication systems, robotics, forecasting, and multi-objective optimization. In addition, the distributions of standard, hybrid, and modified SFO approaches were comparatively analyzed. The temporal evolution of SFO studies, hybridization tendencies, application diversity, strengths, limitations, and future research directions were also systematically evaluated. The findings indicate that hybrid and modified SFO structures have become increasingly dominant in recent years, particularly in AI and data-driven optimization applications. Overall, this review provides a broad understanding of the current state and future research potential of SFO-based optimization studies. Full article

Supplier selection in healthcare is a complex multi-criteria decision-making (MCDM) challenge requiring a balance of sustainability, resilience, and operational efficiency. Traditional methods struggle with scalability and subjectivity when applied to large administrative datasets. This study introduces a transparent hybrid Machine Learning–MCDM (ML–MCDM) framework, validated using a U.S. Medicare dataset of 661 suppliers. The framework integrates eXtreme Gradient Boosting (XGBoost) and SHapley Additive exPlanations (SHAP) for criterion prioritization, the Full Consistency Method (FUCOM) for mathematically consistent weighting, and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for final ranking. As the dataset lacks direct sustainability metrics, seven indicators were synthetically generated; thus, the results serve as proof-of-concept demonstration of the framework’s architecture. Specifically, XGBoost–SHAP is trained to predict a synthetically constructed Overall Performance Score (OPS), meaning that the resulting feature importance output constitutes an algorithmic consistency check—confirming that the pipeline correctly recovers importance signals deliberately embedded in the training target. For interpretability, suppliers were segmented into five performance profiles via K-Means: Strategic Partners (17.7%), Green Leaders (18.6%), Reliable Emergency Suppliers (18.2%), Balanced Performers (20.4%), and Developing Suppliers (25.1%). Carbon Footprint Score (0.408) and Emergency Response Capability (0.316) achieved the highest feature importance. FUCOM-derived weights prioritized On-Time Delivery Rate (0.272), Carbon Footprint Score (0.222), and Emergency Response Capability (0.220). The top supplier attained a TOPSIS closeness coefficient of 0.800, showing strong discrimination. Sensitivity analysis across four scenarios confirmed ranking robustness, maintaining Spearman correlations ρ ≥ 0.977. This ML–FUCOM–TOPSIS approach provides an auditable, scalable, and policy-relevant decision-support tool, enabling procurement managers to navigate high-dimensional data while ensuring operational continuity and environmental responsibility in healthcare supply chains. Full article

Topological data analysis (TDA) has evolved into a flexible and robust paradigm for obtaining qualitative, geometry-inspired insights from high-dimensional, noisy, and complex data. Grounded in algebraic topology, geometry, statistics, and machine learning (ML), TDA provides multiscale descriptions through persistent homology, Mapper (a graph-based method that summarizes the shape of high-dimensional data), and related topological signatures that are often inaccessible to standard linear and metric methods. In recent years, and especially during 2024–2025, TDA has expanded rapidly across science, engineering, biomedical research, and socio-economic studies, while also being integrated with modern learning paradigms such as deep learning (DL) and graph learning. This survey summarizes recent developments in TDA using a carefully selected set of articles, with emphasis on 2024–2025. We first present the mathematical and computational foundations of TDA, covering simplicial complexes, filtrations, persistent homology, the Mapper algorithm, and computational advances such as data simplification, stability, and efficiency. We then review applications in time series and dynamical systems, biomedical imaging and precision medicine, engineering and physical sciences, finance and risk analysis, DL and interpretability, and security and critical infrastructure systems. Throughout, we highlight how TDA can extract informative features, function as a model component, and provide a conceptual lens for studying complex systems. However, the survey also emphasizes recurrent failure patterns: TDA performance is highly sensitive to filtration, embedding, and vectorization choices; aggressive simplification can dilute or remove informative topological signals; and integration into standard ML workflows still lacks uniform validation and reporting protocols. We conclude by outlining key challenges—including scalability, statistical foundations, interpretability, and compatibility with rapidly evolving artificial intelligence (AI) paradigms—and by identifying directions for future research. The survey also provides a unifying design perspective for TDA systems, highlighting methodological trade-offs and emerging research directions for integrating topology with modern ML. Full article

Longitudinal data, characterized by repeated measurements on the same subjects over time, are ubiquitous in biomedical sciences, economics, social sciences, and engineering. Analyzing such data presents unique statistical and computational challenges, including within-subject correlation, time-varying covariates, irregular observation times, informative dropout, and high dimensionality. While traditional statistical methods, such as linear mixed-effects models and generalized estimating equations, remain foundational, they often struggle with complex nonlinear dynamics, ultra-high-dimensional feature spaces, and very large sample sizes. Over the past two decades, machine learning (ML) and artificial intelligence (AI) methods have emerged as powerful complementary approaches to address these limitations. This review provides a comprehensive survey of mathematical and computational methods for longitudinal data analysis. We cover classical statistical models, penalized regression techniques, tree-based ensemble methods, kernel machines, Bayesian hierarchical models, and modern deep learning architectures, including recurrent neural networks, temporal convolutional networks, attention-based Transformers, neural ordinary differential equations, and generative models. We propose a unified taxonomy that organizes existing methods along two primary axes: the underlying mathematical framework and the analytical objective. For each category, we present detailed mathematical formulations, discuss key theoretical properties, examine computational considerations, and summarize representative reported applications drawn from the published literature. To increase the practical value of this review, we provide a cross-cutting comparison of method families against five key challenges (within-subject correlation, irregular sampling, missing data, high dimensionality, and scalability) and offer concrete guidance on method selection according to sample size, dimensionality, and analytical objective. Finally, we critically evaluate the strengths and limitations of these approaches, with particular emphasis on interpretability, scalability, handling of missing data, robustness to covariance misspecification, and uncertainty quantification. Full article

In this study, a layer-wise point cloud representation of CT scan images is proposed, from which persistence diagrams are constructed and persistent entropy is computed as a compact topological feature for three-class lung tumor classification. Two parallel approaches are investigated: the direct computation of persistence diagrams from CT images, and computation from subsampled point clouds derived from image intensity layers. The proposed method is evaluated on the publicly available IQ-OTH/NCCD lung cancer dataset, comprising 1097 CT scan images from 110 individuals, annotated by expert oncologists and radiologists. Classification is performed using K-Nearest Neighbors (KNN), Random Forest, Support Vector Machine, and eXtreme Gradient Boosting, and compared against Convolutional Neural Network (CNN) and traditional image feature-based methods. The persistent entropy approach applied to layer-wise subsampled point clouds achieves 97.67% accuracy, a Precision–Recall AUC of 96.63%, and a ROC-AUC of 99.46% using KNN, outperforming direct image-based analysis (95.91%) and achieving comparable accuracy to the CNN method (97.21%) with a computational speedup of approximately $478\times$. These results demonstrate that persistent homology applied to subsampled point clouds provides an accurate, mathematically interpretable, and computationally efficient alternative to deep learning for lung tumor classification. Full article

Cardiovascular disease (CVD) remains the leading global cause of death, with approximately 17.9 million mortalities annually. Studies have shown that adopting healthy behaviors, i.e., a balanced diet, regular physical activity, and weight management, can reduce CVD risk. However, evaluating their long-term impact requires extensive data collection and analysis, which are both time-consuming and challenging. This study developed a novel mathematical framework integrating an agent-based model (ABM) to simulate CVD risk progression and established clinical guidelines into synthetic training data for machine learning (ML) classification. The ML model was trained entirely on synthetic data generated from World Health Organization/International Society of Hypertension cardiac risk indications, and validated using outcomes from a NetLogo simulation. The workflow does not use real patient data; instead, the expected simulation results serve as a reference to assess the ML model and synthetic data. The ABM, designed in NetLogo, exchanges agent characteristics with a trained ML model to classify individuals into appropriate CVD risk levels based on lifestyle and clinical parameters. The simulation indicated measurable risk progression (5–12%) by year 20 in individuals with both smoking and diabetes. A combined effect of high dietary intake and low physical activity showed over 20% risk increase, demonstrating the model’s capacity to capture dynamic risk interactions. The relationship between CVD risk and systolic blood pressure was also effectively reproduced. Additional scenarios confirmed the alignment of model outcomes with real-world trends, showing model self-consistency, identifying critical thresholds and population-level risk shifts through detailed tabular analysis. Beyond confirming known associations, the findings support the internal consistency of the model, highlighting its potential as a simulation based tool for studying cardiovascular risk patterns and supporting risk monitoring within controlled settings. Full article

Pipes conveying fluids are important fluid–structure interaction systems encountered in aerospace, energy, marine, and industrial applications. Their dynamic behavior is strongly influenced by the interaction between structural motion and internal or external flow, leading to complex phenomena such as divergence, flutter, and flow-induced vibration. This review presents a comprehensive assessment of the dynamics and stability of pipes conveying fluids by integrating classical theories with recent developments in modeling, computation, materials, and control. The review covers mathematical formulations based on Euler–Bernoulli, Rayleigh, Timoshenko, and shell theories, together with analytical and numerical solution methods used for stability and vibration analysis. The effects of geometry, boundary conditions, flow configuration, damping, and material properties on dynamic response and instability thresholds are discussed. Special attention is given to composite, viscoelastic, functionally graded, and smart materials, as well as micro- and nanoscale pipe systems. Recent advances in vibration suppression, reduced-order modeling, machine learning, and physics-informed computational approaches are also reviewed. Finally, the paper identifies current challenges and future research directions, including multiphysics coupling, experimental validation, digital twins, and AI-assisted predictive modeling for fluid-conveying pipe systems. Full article

Many methods have been proposed for visualizing and interpreting the results of artificial intelligence (AI) algorithms. AI explainability (XAI) methods vary in mathematical basis, effectiveness, and scope of application. Knowing this, an important question arises: how do their results differ from a statistical point of view, and are some of them more useful than the others in certain scenarios? Our article aims to assess the robustness of the most popular AI models’ explainability visualization methods and to identify differences in the results obtained. We did this by analyzing fundamental convolutional neural network models that classified 598 cat images from the Oxford III-T Pet database and 580 filtered pictures of Boeing planes from the Aircraft Images Dataset. We performed a comparative analysis of the similarities between methods based on Class Activation Mapping (CAM), gradients, and Local Interpretable Model-agnostic Explanations (LIME). To evaluate them, we used Pearson Correlation Coefficient (CC), Matthews Correlation Coefficient (MCC), Spearman’s Rank, Structural Similarity Index Measure (SSIM), Kullback–Leibler divergence, Intersection over Union (IoU), and Soft IoU. To check the fidelity and robustness of the XAI methods, we used RandomCAM and ran an ablation test, checking for a decrease in prediction confidence as we gradually removed the least significant regions. Our results provide an up-to-date and broad comparative analysis of this field. They can serve as a reference point for machine learning scientists and engineers. Full article

This study proposes a condition-based maintenance monitoring method based on Geometry-based Optical Focus Metrology (GOFM) to detect wafer table edge deterioration early and enable proactive interventions before actual Critical Dimension (CD) bridge defects occur. In advanced Deep Ultraviolet (DUV) immersion photolithography, prolonged equipment operation mechanically wears the wafer table, inducing Edge-Roll-Off (ERO). Because conventional optical metrology struggles to separate this localized defocus from process noise, this work utilizes the existing GOFM technique to isolate the pure focus residual within the 140–147 mm radius region. To quantify this hardware-specific degradation, a mathematical dual-indicator system was constructed. This framework integrates a statistical threshold, the Range Percentile 97%, to reject baseline measurement noise, and a geometric variable, Slope × 3, to capture the topographical drop in the outermost 3 mm. Analysis of long-term time-series data from multiple High-Volume Manufacturing (HVM) scanners confirmed a strong correlation ($R^2=0.93$) between these indicators. Furthermore, we proved that the drift trajectory of Slope × 3 deterministically predicts mechanical failure prior to defect occurrence on production wafers. Based on these findings, an automated condition-based maintenance architecture was designed using an OR-logic decision gate. By triggering a preemptive table replacement at a quality-based critical warning threshold, this system converts routine time-based scheduling into a data-driven paradigm, maximizing both edge yield and equipment uptime. Furthermore, this proposed framework establishes a solid foundation for future extensions toward machine learning-based predictive maintenance. Full article

Mitigating nitrogen dioxide (NO₂) pollution is a critical objective for enhancing urban environmental quality. The spatial structure of urban tree canopies plays a crucial role in influencing NO₂ diffusion and deposition. However, previous studies have focused mainly on the linear relationships between two-dimensional green spaces and NO₂, while the associated nonlinear relationships and threshold effects of three-dimensional urban tree canopy (UTC) spatial structure remain underexplored. To address this gap, we leveraged 1 m resolution satellite-derived data and explainable machine learning (XGBoost, SHAP, PDP) to examine the nonlinear influences and threshold effects of three-dimensional UTC spatial structures on NO₂ in Shenzhen. The results revealed that urban tree canopy spatial structure is associated with NO₂ concentrations. Among the key metrics, the two-dimensional canopy coverage ratio (CCR) emerged as the primary canopy-related correlate of lower NO₂ concentrations, while three-dimensional vertical structure metrics, particularly canopy height variability (CHV) and standard deviation of canopy height (SDCH), acted as critical secondary correlates in modulating the spatial distribution of pollutants. Based on these relationships, we identified potential threshold ranges for key metrics by comparing mathematically identified inflection points with practical urban planning constraints. In summary, this study advances the spatial analysis of “green spaces-NO₂” interactions from a two-dimensional to a three-dimensional perspective. Our findings could provide quantitative guidance for optimizing green space structure in high-density urban areas to inform strategies potentially associated with improved NO₂ outcomes. Full article

Modern machine learning systems can achieve remarkable predictive performance. Nevertheless, in several fields, this is not enough to produce acceptable solutions as we need formal guarantees of robustness, fairness, and interpretability. Most existing approaches treat these properties separately or introduce them through external constraints, which makes their interaction difficult to analyze. In this work, we develop a unified variational perspective that incorporates these requirements directly into the learning objective. Concretely, we model learning as the minimization of a composite functional that combines predictive risk, regularization, and additional terms that capture robustness, fairness, and interpretability. This viewpoint allows us to study these properties within a single mathematical framework. Under standard assumptions, we prove the existence of minimizers and show that the resulting solutions are Pareto-optimal for the associated multi-objective problem. We illustrate the framework using examples based on adversarial and distributional robustness, statistical fairness criteria, and a notion of interpretability. The analysis points out the trade-offs that inevitably arise. We also examine statistical aspects of the proposed objective and show that classical generalization guarantees can still be obtained under appropriate conditions. The resulting framework provides a flexible basis for designing reliable learning systems. Full article

Studies explaining the variation in educational outcomes across countries, when based on “black box” models that provide high accuracy but struggle to present the decision-making mechanism transparently, carry the risk of producing limited interpretations for policy discussions. This study examines the system-level relational patterns through which the subcomponents of the Heritage Foundation Index of Economic Freedom distinguish country-average low–medium–high PISA performance profiles in mathematics, reading, and science, and interprets these patterns using machine learning and explainable artificial intelligence (XAI). The analysis draws on approximately twenty years of nominal country-year records covering 76 countries. The study design proceeds through a classification approach, treating country performance as low–medium–high profiles; thus, model outputs are presented on an interpretable reference plane for cross-country comparisons. The findings indicate that the models demonstrate consistent generalization ability in distinguishing performance profiles and that the XAI layer produces explanations that make the model’s reasoning visible in a verifiable manner. The explanation results indicate that components representing institutional trust (such as government integrity and property rights) produce strong, recurring signals alongside higher performance profiles in all three areas; while components such as public expenditure and tax burden can emerge as balancing/suppressing signals in some scenarios. Rather than offering causal policy implications, these findings transparently reveal the structural areas that stand out in distinguishing performance profiles in cross-country comparisons, thus providing an explainable, replicable evidence base for comparative analysis and further research. Full article

Accurate estimation of lithium-ion battery state of health (SOH) is essential for reliable battery management, although SOH cannot be measured directly during normal operation. This review considers machine-learning methods for SOH estimation from a mathematical and trustworthiness-oriented perspective. The literature is organised by learning the formulation, including supervised regression, sequence learning, multi-task prediction, and weakly physics-guided methods. Attention is given to data representation, evaluation methods, uncertainty estimation, calibration, robustness under distribution shifts, and physical validity of predictions. The reviewed studies indicate that the feature-based models remain effective in small-data settings, whereas deep sequence models show stronger performance when more informative temporal data and stricter evaluation settings are available. Reported results are strongly affected by split design, preprocessing, and differences between training and test conditions, and may be overstated under same-cell evaluation, leakage, or limited cross-condition testing. The reviewed evidence indicates that reliable SOH estimation requires suitable cross-cell or cross-condition evaluation, uncertainty estimates supported by calibration analysis, robustness under operating variation, clear reporting, and agreement with physical battery behaviour. On this basis, benchmark design principles, reporting recommendations, method-selection guidance, and open research problems are presented. Full article