M. Usman

Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman

In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.

Muhammad Usman, Yugyung Lee

Dynamic trust evaluation in large, rapidly evolving graphs requires models that can capture changing relationships, express calibrated confidence, and resist adversarial manipulation. DGTEN (Deep Gaussian-based Trust Evaluation Network) introduces a unified graph framework that achieves all three by combining uncertainty-aware message passing, expressive temporal modeling, and built-in defenses against trust-targeted attacks. It represents nodes and edges as Gaussian distributions so that both semantic signals and epistemic uncertainty propagate through the graph neural network, enabling risk-aware trust decisions rather than overconfident guesses. To model how trust evolves, it employs hybrid Absolute-Gaussian-Hourglass (HAGH) positional encoding with Kolmogorov-Arnold network-based unbiased multi-head attention, followed by an ordinary differential equation (ODE)-based residual learning module to jointly capture abrupt shifts and smooth trends. Robust adaptive ensemble coefficient analysis prunes or down-weights suspicious interactions using complementary cosine and Jaccard similarity measures, mitigating reputation laundering, sabotage, and on/off attacks. On two signed Bitcoin trust networks, DGTEN delivers significant improvements: in single-timeslot prediction on Bitcoin-Alpha, it improves MCC by 10.77% over the best dynamic baseline; in the cold-start scenario, it achieves a 16.41% MCC gain - the largest across all tasks and datasets. Under adversarial on/off attacks, it surpasses the baseline by up to 11.63% MCC. These results validate the effectiveness of the unified DGTEN framework.