Rabab Alharbi

Background: Automated interpretation of 12-lead electrocardiograms (ECGs) remains challenging because multiple abnormalities may coexist and appear in selected leads or brief waveform segments. We developed a compact and interpretable framework for five-superclass multi-label ECG diagnosis. Methods: We evaluated PTB-XL records using the official fold protocol, with folds 1–8 for training, fold 9 for validation monitoring and class-specific threshold selection, and fold 10 for independent internal testing. We then evaluated the frozen 1.33-million-parameter InceptionTime–CNN–BiGRU–Transformer model and validation-derived thresholds on 15,931 Ningbo ECGs without retraining, recalibration, or external threshold adjustment. We also examined calibration, demographic subgroups, computational efficiency, and complementary ECG-domain attribution methods. Results: Macro-AUROC reached 90.83% on PTB-XL fold 10 and 88.85% on Ningbo, indicating generally consistent diagnostic ranking with a modest reduction during external evaluation. Sensitivity analysis showed that CNN-only outperformed the frozen primary model on five of six endpoints. Attribution analyses highlighted qualitatively plausible lead and temporal patterns in representative examples, while calibration and subgroup analyses further characterized model behavior under dataset shift. Conclusions: Our framework integrates leakage-aware development, threshold-controlled testing, frozen external validation, and multimethod interpretability. These findings support its further prospective, locally calibrated evaluation as a potential aid for multi-label ECG interpretation.

Significance: This paper explores the innovative aspect of solving beating cilia related flow with physics informed neural networks (PINNs). PINNs is best way to resolve beating cilia motion without relying on dense meshes or iterative solvers. Purpose: This study explores the beating cilia in confined fluid domains in topological inclined wavy channels. Carreau-Yasuda nanofluid model has been utilized to study such configuration. These features make cilia driven flows valuable for microfluidic cooling systems, particle manipulation and biological transport studies where precise control of near wall dynamics is critical. This study shows how ciliary actuation supports efficient fluid motion without relying on mechanical pumping units. For the velocity control, the inclined magnetic angle has been considered. Methodology: PINNs methodology with a PDFP optimizer has been used to capture physical meaning of beating cilia inside inclined wavy channels. This scheme shows the global view of the solution across space and time. It reduces oscillations in the loss and keeps the network focused on the true physics residuals. Findings: Numerical variation in power-law index parameter reshapes the local shear stiffness of the Carreau-Yasuda nanofluid fluid. When Weissenberg number is increasing, stretching the pressure lobes along the channel and disrupts the phase coherence between the wall motion and the fluid response.

Fractional calculus and distribution theory share a common conceptual origin in the symbolic interpretation of differentiation and integration. Despite this connection, most developments in fractional calculus have traditionally been formulated within the framework of ordinary functions, while the systematic use of distributions remains limited. In this work, a novel distributional framework is developed by constructing a fractional Taylor representation of the product of Euler gamma and Riemann zeta functions in terms of fractional derivatives of the Dirac delta distribution. The proposed formulation enables the derivation of new fractional identities via Laplace transformation and facilitates the analytical solution of fractional differential equations containing such functions. Closed-form solutions are obtained in both classical and generalized distributional senses, allowing the extension of solutions from the positive real axis to the entire real line. Furthermore, the framework is applied to fractional operators of Erdélyi–Kober type, yielding new integral and derivative transforms. Fractional differential and integral equations with singular terms arise naturally in several engineering models involving memory effects, impulsive responses, and anomalous transport phenomena. However, the presence of nonremovable singularities—such as those associated with Euler gamma and Riemann zeta functions—significantly restricts the applicability of classical analytical methods. Overall, the proposed distributional framework bridges the gap between abstract fractional calculus and practical engineering models by enabling analytical solutions of fractional systems with singular memory kernels that were previously inaccessible using classical methods.

On the one hand, convex functions are important to derive rigorous convergence rates, and on the other, synchronous functions are significant to solve statistical problems using Chebyshev inequalities. Therefore, fractional integral inequalities involving such functions play a crucial role in creating new models and methods. Although a large class of fractional operators have been used to establish inequalities, nevertheless, these operators having the Fox-H and the Meijer-G functions in their kernel have been applied to establish fractional integral inequalities for such important classes of functions. Taking motivation from these facts, the primary objective of this work is to develop fractional inequalities involving the Fox-H function for convex and synchronous functions. Since the Fox-H function generalizes several important special functions of fractional calculus, our results are significant to innovate the existing literature. The inventive features of these functions compel researchers to formulate deeper results involving them. Therefore, compared with the ongoing research in this field, our results are general enough to yield novel and inventive fractional inequalities. For instance, new inequalities involving the Meijer-G function are obtained as the special cases of these outcomes, and certain generalizations of Chebyshev inequality are also included in this article.

Fuzzy systems play a crucial role in emerging fields such as artificial intelligence, machine learning, and computer science, drawing significant research interest in fuzzy difference equations. Inspired by this, we analyze the dynamic properties of a fourth-order exponential Riccati-type fuzzy difference equation. The study is further extended to a system of fourth-order fuzzy difference equations. We investigate the boundedness, as well as the local and global stability, of positive solutions. To support the theoretical findings, numerical examples are presented along with graphical and tabular representations.