We develop and analyze a nonlinear stage-structured model for diabetes progression that distinguishes uncontrolled and controlled diabetes and incorporates bidirectional management-relapse transitions together with bounded prevalence-weighted deterioration effects. We establish local and global well-posedness, positivity, boundedness, and the existence of a positively invariant feasible region. We also characterize the equilibrium structure, derive conditions for the existence of a positive equilibrium, and prove persistence of the downstream disease classes. A central analytical feature is the decomposition of the system into an upstream linear subsystem and a downstream nonlinear subsystem, which clarifies the mechanism governing the long-term dynamics. Local asymptotic stability of the positive equilibrium is established through Jacobian analysis and the Routh-Hurwitz criterion, while a Lyapunov-LaSalle argument yields a sufficient condition for global asymptotic stability. As an extension, we formulate an optimal-control version of the model with prevention, management, and relapse-prevention interventions and solve the resulting system numerically over a 10-year horizon. The simulations show that combining all three controls yields the largest reduction in uncontrolled diabetes and severe-complication burden, while sensitivity analysis identifies the progression-related parameters with the strongest influence on severe outcomes. These results show that the proposed framework is mathematically tractable and biologically relevant for studying long-term diabetes complication dynamics.
Resting state functional connectivity is identified to reflect the intrinsic organization of the brain's cognitive characteristics. One key property of such biological networks is modularity. In this paper, an open dataset ABIDE of which a total of 45 ASD (Autism Spectrum Disorder) and 53 TD (Typical Development) participants from KKI and PITT sites was considered. Graph Theoretic measures involving Degree Centrality, Clustering Coefficient and Modularity were calculated at different thresholds of network connectivity. Linear SVM classifiers were used to distinguish between ASD and TD. The classifier was applied to each of these graph measures at individual threshold levels. Further, ComBat harmonization across both sites was performed to which the above classification model was applied. Experimental results show that participants from KKI sites showed a difference in Newman modularity at 0.3 threshold with 76.1% accuracy with specificity and sensitivity of 73.08% and 81.25% respectively. Although the accuracy of the site-specific TD vs ASD classifiers were comparable, the sensitivity of the KKI classifier was less, which improved post harmonization. Similar performance was observed in degree centrality and clustering coefficient measures. Therefore, the harmonization process plays a significant role in classifier performance and in model selection.
This research introduces a compartmental mathematical model, inspired by epidemiology, to analyze crime dynamics and design reduction strategies. The population is divided into four groups: susceptible individuals, active criminals, prisoners, and rehabilitated individuals. Two control functions are incorporated: one aimed at deterrence through sanction policies, and the other focused on social reintegration via educational, psychological, and professional support programs. Based on optimal control theory, the model identifies relevant intervention strategies to prevent crime and improve its management. The theoretical findings are validated through numerical simulations using MATLAB, comparing the system's evolution with and without intervention. This approach offers a solid analytical framework to support the development of integrated, flexible, and adaptive public policies addressing contemporary crime-related challenges.
Domestic wastewater flowing from residential areas to wastewater stabilization ponds generally contains various pollutants. In this study, research was conducted to investigate the distribution of pollutants in wastewater ponds by observing changes in biochemical oxygen demand (BOD) parameters. The concentration of pollutant tested was same as the concentration of BOD. The phenomenon of waste particle distribution in domestic wastewater stabilization ponds is viewed as an advection-diffusion scheme. The advection-diffusion scheme can be developed into a mathematical model, specifically a two-dimensional partial differential equation. In this study, numerical methods were used to solve these equations. The Crank-Nicolson method was used to discretize partial differential equations in time and space. The purpose of this study was to determine the points of pollutant dispersion in liquid wastewater stabilization ponds. The dispersion of wastewater pollutants is displayed in simulations performed using Python 3.14.0. The stability analysis of the Crank-Nicolson method is investigated using the Von Neumann method. The results of the analysis show that the Crank-Nicolson method is convergent and unconditionally stable.
While outlier detection and control are not fundamental to the estimation of Bayesian Vector Autoregressive (BVAR) models, they represent a significant improvement that may enhance the robustness and reliability of estimation and forecasting. The increasing prevalence of big data pose challenges for monitoring and maintaining data quality for estimation. In this paper, the standard BVAR model is extended through Outlier Detection and Control (ODC), known as Extended BVAR-ODC model. The Extended BVAR-ODC decomposes the data generating process into three explicit components: a core VAR process with coefficient matrices and Gaussian innovations, an outlier component, and a multivariate normal-tempered innovation structure. Also, the ODC mechanism operates through a two-stage Bayesian procedure: posterior inference on outlier indicators, and simultaneous estimation of outlier impact coefficients and VAR parameters. It is shown in simulation that the Extended BVAR-ODC provides superior fit compared to the standard BVAR. Across all diagnostics, including parameter recovery, posterior trace convergence, mixing and predictive calibration, the Extended BVAR-ODC consistently outperforms the standard BVAR. Particularly, the posterior estimates of intercepts, lagged coefficients, and covariance matrices exhibit higher stability and smaller posterior dispersion. Additionally, residual analyses and goodness-of-fit confirm that the Extended BVAR-ODC effectively mitigates distortions induced by outliers. All performance measures favour the Extended BVAR-ODC, highlighting its superior generalization performance. Therefore, the Extended BVAR-ODC would be very useful in modeling financial systems that are subject to structural breaks or extreme events. Its outlier-induced specification ensures more robust inference under contaminated data distributions.
The increasing complexity of medical data in modern healthcare environments necessitates intelligent frameworks that not only deliver accurate predictions but also support effective knowledge generation and decision-making. In the context of brain tumor analysis using multi-modal magnetic resonance imaging (MRI), challenges such as tumor heterogeneity, variability in imaging protocols, and limited interpretability of deep learning models hinder their integration into clinical knowledge workflows. This study proposes an explainable, knowledge-driven hybrid CNN-Transformer-Radiomics (HCTR) framework designed to facilitate both predictive performance and clinical knowledge extraction. The framework integrates convolutional neural networks for localized feature learning, transformer-based architectures for global contextual understanding, and radiomic descriptors for structured, domain-relevant feature representation. A cross-attention-based fusion mechanism is employed to combine these heterogeneous knowledge sources into a unified representation. Beyond detection and analysis, the proposed system emphasizes interpretability through Grad-CAM visualizations and feature attribution methods, enabling the transformation of model outputs into clinically meaningful insights. This supports enhanced transparency, trust, and knowledge dissemination within clinical decision-making processes. The proposed framework contributes to the development of intelligent decision support systems by bridging data-driven modeling with knowledge-centric interpretation. It provides a scalable approach for integrating explainable AI into healthcare knowledge management environments, facilitating improved diagnostic reasoning and informed clinical decisions.
Modeling HbA1c levels in patients with diabetes mellitus is commonly conducted using parametric regression; however, this approach is often inadequate in capturing nonlinear relationships with metabolic predictors. This study aims to develop a multipredictor quadratic spline regression model with confidence interval estimation to model HbA1c levels flexibly. The model incorporates five predictor variables: body weight, fasting blood glucose, HDL cholesterol, LDL cholesterol, and triglycerides, and is implemented using RStudio version 2024.12.0. The results clearly demonstrate nonlinear relationships between HbA1c levels and all predictors. LDL cholesterol shows the strongest influence. Threshold effects are observed for body weight and HDL cholesterol, while glucose and triglycerides exhibit moderate nonlinear patterns. The visualization of the fitted curves and confidence bands supports a more interpretable representation of the model. Overall, the quadratic spline regression with confidence intervals provides a flexible and informative framework for modeling HbA1c levels, particularly when nonlinear associations are present.
Accurate forecasting of financial market volatility remains a central challenge due to nonlinear dynamics, volatility clustering, and regime-dependent behavior in financial time series. While econometric volatility models capture conditional heteroskedasticity, deep learning architectures provide flexible nonlinear modeling capabilities. However, existing approaches often treat these paradigms independently or combine them post hoc, limiting their ability to jointly exploit statistical structure and representation learning. This study addresses this gap by proposing a hybrid architecture that integrates GARCH-family models directly within an attention-based Transformer through representation-level learning. We develop a Multi-GARCH Transformer architecture that embeds conditional variance estimates from multiple GARCH-family models into the input representation of a Transformer encoder. This hybrid architecture functions as a heterogeneous ensemble in which complementary volatility dynamics are integrated at the feature level and adaptively weighted through self-attention. The analysis uses daily stock returns of Safaricom from 2015 to 2024.The study combines descriptive statistics, econometric modeling, and transformer-based hybrid forecasting. Model performance is evaluated using quasi-likelihood (QLIKE), RMSE, and MAE, alongside statistical comparison using the Diebold-Mariano test. Empirical findings confirm that the Multi-GARCH-Transformer ensemble achieves superior out-of-sample volatility forecasting performance by embedding complementary econometric signals within an attention-based architecture. This hybrid model delivers the strongest performance under QLIKE and exhibits statistically significant improvements validated through Diebold-Mariano testing. The observed training behavior indicates more stable convergence and stronger generalization than non-hybrid architectures, reinforcing the effectiveness of representation-level ensemble learning. The results highlight the advantages of integrating econometric theory with attention-based deep learning through feature-level hybridization. By jointly modeling structured volatility dynamics and nonlinear temporal dependencies, the approach improves forecasting robustness, interpretability, and predictive accuracy. This study contributes to the intersection of financial econometrics and deep learning by introducing a hybrid ensemble modeling strategy for complex and evolving market environments.
Heart disease is a wide phrase that covers a variety of disorders affecting the heart and blood arteries. It's one of the leading causes of death globally. In some cases, heart disease develops silently over years, showing no symptoms until a major event like heart attack or stroke occurs. It results from a complex interplay of lifestyle, genetic, metabolic, and environmental factors. The growing prevalence and complexity of heart disease highlight the urgent need for intelligent, data driven early prediction systems. Healthcare, which has been transformed by machine learning, a branch of Artificial Intelligence, allows computers to learn and make precise predictions. Unlike traditional statistical techniques, Machine learning algorithms can model complex, non-linear relationships and capture subtle patterns in medical data, making them highly suitable for heart disease prediction. These models exposed to more data, so they improve over time, this makes them more accurate with continuous retaining. This work uses Bald Eagle Search optimization, a metaheuristic algorithm for feature selection. For classification, ensemble methods such as Random Forest, Voting, Bagging, Stacking, and various boosting techniques are used. The dataset for this work has 1025 instances and 14 features which is obtained from Kaggle. The result shows that Stacking has achieved highest accuracy of 95.61%.
The impact of parameters on influenza dynamics deeper insights to understand and control the spread of the disease. The present study examines the impact of parameters on the transmission dynamics of the influenza virus through a nonlinear SVITR (Susceptible-Vaccinated-Infected-Treated-Recovered) model. The Basic Reproduction Number R0 is studied using Next Generation Metrix. Furthermore, the model exhibits transcritical bifurcation, where stability shifts between equilibria as critical parameter thresholds, particularly the transmission rate, are crossed. Numerical simulations validate the theoretical results, demonstrating the sensitivity of disease dynamics to variations in the model and identifying key parameters that significantly influence disease spread. Based on different parameter values, stability analysis is performed for disease-free and endemic equilibria. The model's positivity, boundedness, and uniqueness are also established to ensure biological feasibility. These findings offer valuable insights for designing effective control strategies against influenza outbreaks.
The application of the M-polynomial to chemical networks, particularly to chemical compounds, is a relatively recent development in chemical graph theory. Despite its novelty, this approach has proven to be a powerful and effective tool for deriving degree-based topological indices. These indices playAa crucial role in modeling and predicting various physicochemical properties as well as biological activities of chemical substances and nanostructured systems. The M-polynomial offers a unified and systematic framework by establishing mathematical relationships between molecular structure and chemical behavior. In this work, we focus on computing the general form of M-polynomials for Hierarchical Hypercube Networks (HHNs). AThe selected HHNs exhibit a high degree of structural symmetry, which significantly simplifies the analytical computations and enables the exact determination of the corresponding M-polynomials. By exploiting these symmetries, we derive closed-form expressions that describe the underlying degree distributions of the considered nanostructures. Furthermore, several important degree-based topological indices are obtained from the derived M-polynomials. AThese indices provide valuable insights into the structural complexity and potential chemical dynamics of the studied Hierarchical Hypercube Networks. Finally, the M-polynomials are presented graphically to highlight and visualize the structural characteristics of the HHNs.
