Takagi–Sugeno–Kang (TSK) fuzzy classifiers have achieved notable success in pattern recognition and data mining due to their combination of approximation capability and model interpretability. However, existing TSK classifiers predominantly rely on batch training, which becomes impractical in streaming environments characterized by continuous sample arrival, limited memory, and evolving data distributions. To address these challenges, this paper proposes the Online Adaptive TSK (OA-TSK) fuzzy classifier with an incremental–decremental update protocol for non-stationary data streams. First, we develop the Decremental Adaptive TSK Fuzzy Classifier (DA-TSK), whose update procedure applies the Sherman–Morrison formula to a symmetric rank-one downdate, enabling precise sample removal while maintaining exact equivalence to batch least-squares retraining. Building upon DA-TSK and our prior Dynamic Incremental Adaptive TSK Fuzzy Classifier (DIA-TSK), we then propose OA-TSK, which integrates incremental and decremental updates within a sliding-window mechanism to achieve continuous adaptation with bounded memory. The key theoretical contribution is that, in exact arithmetic, OA-TSK produces at every time step the same ridge-regularized least-squares solution as batch retraining on the active window. To further handle severe shifts in the input distribution, which can cause fixed rule centers to become poorly aligned with newly arriving samples, we propose Online Adaptive TSK with Antecedent Reclustering (OA-A-TSK), which incorporates an adaptive antecedent reclustering mechanism. Comprehensive experiments on synthetic and real-world data streams demonstrate that OA-TSK achieves classification accuracy comparable to that of ridge-regularized batch retraining while substantially reducing per-sample computational complexity. An analysis of average ranks shows that OA-TSK and OA-A-TSK rank among the top-performing methods across diverse drift scenarios while preserving the intrinsic interpretability of TSK fuzzy systems.
Effective transportation of heat and mass in nanofluids is vital for enhancing energy transfer and thermal management. In this study, the Cattaneo–Christov double-diffusive MHD flow of a Maxwell ternary hybrid nanofluid through a porous medium is examined, taking into account activation energy and nonlinear thermal effects. The aim of this work is to investigate the effects of the magnetic field, porous medium, thermal and concentration relaxation, radiation, viscous dissipation, chemical reaction, and activation energy on the fluid flow. The momentum, energy, and concentration equations are modeled using nonlinear partial differential equations. Suitable similarity transformations are used to reduce the nonlinear PDEs to nonlinear ODEs. The extra stress is described by the upper-convected Maxwell model, and the similarity transformation is derived from a one-parameter Lie scaling group under which the governing equations and boundary conditions are invariant; the resulting invariants identify the parametric groupings that govern heat transfer and nanoparticle concentration. The resulting nonlinear boundary value problem is then solved numerically using the built-in MATLAB solver bvp4c. The numerical solutions are presented in graphs and tables and are validated against results reported in the literature. The results show that the velocity profile decreases with increasing magnetic field, porous medium parameter, and Maxwell parameter. The temperature profile, on the other hand, increases with the nanoparticle volume fraction, heat generation, Eckert number, and thermal relaxation parameter, but decreases with increasing radiation parameter and Biot number.
Financial time series are characterized by high volatility, nonstationarity, nonlinear dynamics, and multiscale fluctuations, which pose significant challenges to accurate stock price forecasting. In multivariate financial forecasting, financial variables may exhibit symmetric and asymmetric characteristics in their temporal fluctuations and structural dependencies across different time scales. Understanding these characteristics is relevant to the analysis of symmetry and asymmetry in financial time series. Modeling multiscale temporal patterns and inter-variable dependencies is therefore important for improving forecasting performance. To address these challenges, this study proposes a hybrid CEEMDAN–IGOA–TCN–iTransformer framework for multivariate stock price prediction. First, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is employed to decompose financial time series into intrinsic mode functions and residual components, facilitating multiscale feature extraction. Second, a population-based hyperparameter optimization procedure is employed to select key model hyperparameters based on validation performance. Third, a TCN–iTransformer architecture is constructed, in which the Temporal Convolutional Network (TCN) extracts local temporal features and multiscale patterns, while the iTransformer models dependencies among financial input variables through its inverted attention mechanism. Finally, the extracted features are integrated to generate the predicted stock closing price. Experiments were conducted on three Chinese A-share stock datasets, representing Ping An Insurance, BOE Technology Group, and Arcplus Group. The proposed framework achieved test-set RMSE values of 0.8987, 0.0656, and 0.6717, respectively, with a corresponding arithmetic mean RMSE of 0.5453 across the three datasets. Comparative experiments and ablation studies were conducted to evaluate the forecasting performance and contributions of the framework’s components. The findings indicate that the proposed approach can provide accurate one-step-ahead closing-price predictions under the investigated experimental conditions, while its performance and generalizability remain dependent on the characteristics of the evaluated datasets.
We study the undirected power congruence graph Gnk({p,q}) on vertex set V={0,1,…,n−1} in which two distinct vertices a,b are adjacent whenever ak≡bk(modp) or ak≡bk(modq), where p,q are distinct primes with pq
Airfoil profiles form the foundation of flight performance by determining the balance between lift and drag forces. Computational Fluid Dynamics (CFD) analyses enable a detailed examination of the velocity and pressure distributions around these profiles. Interpolation methods enhance the accuracy of simulations by allowing for the precise definition of wing geometry. These methods make it possible to compare different profile types and achieve an optimal aerodynamic design. Accurate geometric representation of airfoil profiles is critically important for achieving reliable aerodynamic predictions in computational fluid dynamics, particularly under low-Reynolds-number flow conditions where pressure-gradient sensitivity and flow separation behavior become highly geometry-dependent. In this study, the aerodynamic behavior of Clark Y, Eppler 205, FX 63-137, NACA series, RAE 2822, and S1223 airfoil sections under low-Reynolds-number (Re≈1×105) conditions was investigated using CFD analyses. It was observed that the leading-edge suction peak became more pronounced in all profiles with increasing angle of attack, while the lift and drag responses exhibited airfoil-dependent variations across the investigated angles of attack. Differences in the lift and drag responses became more pronounced among the investigated profiles at the higher evaluated angles of attack, reflecting their different geometric and aerodynamic characteristics. Hermite interpolation-based geometric modeling, which forms the basis of this study, improved geometric continuity and reduced interpolation-induced surface irregularities, thereby providing a more consistent geometric representation for the subsequent CFD analyses. It should be emphasized that geometric or numerical stability alone does not establish physical aerodynamic accuracy, which requires independent validation against appropriate reference or experimental data. The results indicate the variations in pressure distributions and aerodynamic coefficients across the examined angles of attack, depending on the airfoil profile, specifically, suction performance becomes more pronounced as the angle of attack increases, while lift and drag characteristics vary among the profiles studied, establishing optimized Hermite airfoil profiles as a basis for CFD aerodynamic evaluation under low-Reynolds-number conditions.
