Gurmeet Kaur

Gurmeet Kaur, Randhir Singh, Mehakpreet Singh et al.

In the present work, a new approach is proposed for finding the analytical solution of population balances. This approach is relying on idea of Homotopy Perturbation Method (HPM). The HPM solves both linear and nonlinear initial and boundary value problems without nonphysical restrictive assumptions such as linearization and discretization. It gives the solution in the form of series with easily computable solution components. The outcome of this study reveals that the proposed method can avoid numerical stability problems which often characterize in general numerical techniques related to this area. Several examples including Austin's kernel available in literature are examined to demonstrate the accuracy and applicability of the proposed method.

Saurabh Hinduja, Gurmeet Kaur, Maneesh Bilalpur et al.

Subject-exclusive cross-validation is the standard evaluation protocol for facial Action Unit (AU) detection, yet reported improvements are often small. We show that cross-validation itself introduces measurable stochastic variance. On BP4D+, repeated 3-fold subject-exclusive splits produce an empirical noise floor of $\pm 0.065$ in average F1, with substantially larger variation for low-prevalence AUs. Operating-point metrics such as F1 fluctuate more than threshold-independent measures such as AUC, and model ranking can change under different fold assignments. We further evaluate cross-dataset robustness using a Leave-One-Dataset-Out (LODO) protocol across five AU datasets. LODO removes partition randomness and exposes domain-level instability that is not visible under single-dataset cross-validation. Together, these results suggest that gains often reported in cross-fold validation may fall within protocol variance. Leave-one-dataset-out cross-validation yields more stable and interpretable findings