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This work investigates the influence of a generic anomalous diffusion model on mass convection in a fluid-saturated porous medium, focusing on superdiffusive regimes. A mathematical model is developed, and tability analyses - both linear and nonlinear - are performed. Results demonstrate that the specific form of the time function describing anomalous diffusion significantly affects system stability, allowing stability to persist beyond the classical Rayleigh-B\'enard neutral threshold. Furthermore, transient perturbation growth is observed under certain conditions, followed by eventual decay. The paper systematically examines various memory functions, including power-law, exponential, and logarithmic forms, highlighting their impact on the dynamics of disturbances. The findings underscore the importance of anomalous diffusion in modulating stability and provide new insights into the transient behaviours induced by non-Fickian mass transport., Comment: 20 pages, 7 figures

A ternary reaction-diffusion model for early HIV infection dynamics, incorporating logistic growth of target cells, is introduced. According to in vitro and in vivo studies, random movement of target cells, infected cells, and virions and a chemotactic attraction of target cells by cytokines, are included. The research explores the existence of disease-free and coexistence equilibria, conducting linear stability analyses for homogeneous and heterogeneous scenarios. Specifically, conditions for chemotactic-self diffusion instability of the endemic equilibrium are found, indicating that Turing patterns may emerge when the chemotactic effect surpasses a critical threshold. This threshold is lower than in models without logistic growth of target cells, suggesting that the logistic model provides better insights into infection hot spots in the early stages. The location and shape of these patterns, crucial for developing infection control strategies, are investigated using weakly nonlinear analysis and demonstrated through numerical simulations., Comment: 13 pages, preprint version

Context: AI code generators are revolutionizing code writing and software development, but their training on large datasets, including potentially untrusted source code, raises security concerns. Furthermore, these generators can produce incomplete code snippets that are challenging to evaluate using current solutions. Objective: This research work introduces DeVAIC (Detection of Vulnerabilities in AI-generated Code), a tool to evaluate the security of AI-generated Python code, which overcomes the challenge of examining incomplete code. Method: We followed a methodological approach that involved gathering vulnerable samples, extracting implementation patterns, and creating regular expressions to develop the proposed tool. The implementation of DeVAIC includes a set of detection rules based on regular expressions that cover 35 Common Weakness Enumerations (CWEs) falling under the OWASP Top 10 vulnerability categories. Results: We utilized four popular AI models to generate Python code, which we then used as a foundation to evaluate the effectiveness of our tool. DeVAIC demonstrated a statistically significant difference in its ability to detect security vulnerabilities compared to the state-of-the-art solutions, showing an F1 Score and Accuracy of 94% while maintaining a low computational cost of 0.14 seconds per code snippet, on average. Conclusions: The proposed tool provides a lightweight and efficient solution for vulnerability detection even on incomplete code., Comment: Accepted for publication in the Information and Software Technology (IST) journal

A reaction-diffusion Leslie-Gower predator-prey model, incorporating the fear effect and prey refuge, with Beddington-DeAngelis functional response, is introduced. A qualitative analysis of the solutions of the model and the stability analysis of the coexistence equilibrium, are performed. Sufficient conditions guaranteeing the occurrence of Turing instability have been determined either in the case of self-diffusion or in the case of cross-diffusion. Different types of Turing patterns, representing a spatial redistribution of population in the environment, emerge for different values of the model parameters.

Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variation. In this paper the linear analysis of the Darcy-B\'enard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor $\beta$ which describes the compressibility of the fluid and plays an essential role in the instability results. In particular, in the Oberbeck-Boussinesq approximation, a more realistic constitutive equation for the fluid density is employed in order to obtain more thermodynamic consistent instability results. Via linear instability analysis of the conduction solution, the critical Rayleigh-Darcy number for the onset of convection is determined as a function of a dimensionless parameter $\widehat{\beta}$ proportional to the compressibility factor $\beta$, proving that $\widehat{\beta}$ enhances the onset of convective motions.

In the present paper double-diffusive convection, taking into account Coriolis effects, in a horizontal layer of Brinkman-anisotropic bi-disperse porous medium is analysed. Via linear instability analysis, we found that convection can set in through stationary or oscillatory motions and the critical Rayleigh numbers for the onset of stationary secondary flow (steady convection) and overstability (oscillatory convection) are determined.