Accurately predicting protein subcellular localization is essential for understanding biological function and informing medical research. To address the limitations of traditional laboratory techniques, this study introduces two deep learning frameworks-ML-FGAT and ML-GRat-for multi-label protein subcellular localization (ML-PSL). ML-FGAT integrates seven diverse feature encoding schemes-DC, PsePSSM, CTD, GO, CT, DDE, and EBGW [5]-followed by Differential Evolution (DE)-based feature fusion and entropy-guided selection. To enhance representation quality, a self-attention-based feature recalibration (SAFR) module is introduced to emphasize biologically relevant features. A Feature-Generative Adversarial Network (F-GAN) then balances class distributions, and classification is performed using a Graph Attention Network (GAT). ML-FGAT achieved OAA scores ranging from 93.5% to 98.8% across five test datasets. ML-GRat uses DE for feature weighting and Canonical Correlation Analysis (CCA) for dimensionality reduction, followed by SAFR and a hybrid GAT-ResNet classifier. This model achieved OAA scores between 94.0% and 98.9% on six independent datasets, including SARS-CoV-2 and human proteins [6]. The proposed models demonstrate robust generalization, high predictive performance, and improved interpretability for ML-PSL tasks in computational biology.

As global living standards improve and medical technology advances, many infectious diseases have been effectively controlled. However, certain diseases, such as the recent COVID-19 pandemic, continue to pose significant threats to public health. This paper explores the evolution of infectious disease modeling, from early ordinary differential equation-based models like the SIR framework to more complex reaction-diffusion models that incorporate both temporal and spatial dynamics. The study highlights the importance of numerical methods, such as the Runge-Kutta method, implicit-explicit time-discretization techniques, and finite difference methods, in solving these models. By analyzing the development and application of these methods, this research underscores their critical role in predicting disease spread, informing public health strategies, and mitigating the impact of future pandemics.

In our research, we focus on the existence, non-existence, and multiplicity of positive solutions to a Quasilinear Schrödinger equation in the form: −∆𝑢 + 𝜆𝑢 + 𝑘 2 [∆(𝑢 2)]𝑢 = 𝑓(𝑢), 𝑢 ∈ 𝐻 1 (ℝ 𝑵) With prescribed mass: ∫ ℝ 𝑁 |𝑢| 2 𝑑𝑥 = 𝑐, Here 𝑁 ≥ 3, The dual approach is used to transform this equation into a corresponding semilinear form. Then, we implement a global branch approach, adeptly handling nonlinearities 𝑓(𝑠) that fall into mass subcritical, critical, or supercritical categories. Key aspects of this study include examining the positive solutions' asymptotic behaviors as 𝜆 → 0 + 𝑜𝑟 𝜆 → +∞ and identifying a continuum of unbounded solutions in (0, +∞) × 𝐻 1 (ℝ 𝑵).

In this article, we investigate the presence of standing wave solutions for the given quasilinear Schrödinger system. { −𝜀 2 Δ𝑢 + 𝑊(𝑥)𝑢 − 𝜅𝜀 2 Δ(𝑢 2)𝑢 = 𝑄 𝑢 (𝑢, 𝑣) 𝑖𝑛 ℝ 𝑁 −𝜀 2 Δ𝑣 + 𝑉(𝑥)𝑣 − 𝜅𝜀 2 Δ(𝑣 2)𝑣 = 𝑄 𝑣 (𝑢, 𝑣) 𝑖𝑛 ℝ 𝑁 𝑢, 𝑣 > 0 in ℝ 𝑁 , 𝑢, 𝑣 ∈ 𝐻 1 (ℝ 𝑁).