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, as well as 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.

Context: The rapid evolution of Generative AI is transforming software engineering, enabling Large Language Models (LLMs) to generate code from natural-language prompts. This capability is increasingly applied to security-critical programming tasks, such as penetration testing, forensic analysis, traffic analysis, and OSINT. However, it remains unclear which prompt engineering strategies security analysts should adopt to obtain reliable and correct code in these scenarios. Objectives: This paper aims to systematically evaluate the impact of different prompting strategies on the quality of LLM-generated code for security-oriented tasks, assessing both functional correctness and robustness. Methods: We present a systematic evaluation of 12 prompting strategies across 4 state-of-the-art LLMs. Our evaluation framework combines textual similarity metrics with execution-based analysis conducted in a Docker-based environment, measuring correctness against ground truth on valid inputs and robustness on edge and invalid inputs. Results: Reasoning-oriented strategies, such as Chain-of-Thought and Few-Shots Prompting, consistently improve the generated code, achieving up to ＋24.6% improvement in ROUGE-L, average correctness rates of 63%–64%, and robustness rates of 50%. In contrast, refinement-based strategies such as Iterative Prompting and Question Refinement degrade structural similarity by up to -50% in BLEU-4, reducing correctness and robustness to 33% and 26%, respectively. Models producing more functionally correct code also exhibit broader behavioral coverage, reaching up to 78.24% average statement coverage. Furthermore, textual similarity alone proves insufficient to predict functional behavior. Conclusion: These findings highlight that prompt design substantially influences the reliability of LLM-generated code in security-critical scenarios, and that execution-based evaluation is essential to complement textual metrics. Reasoning-oriented prompting strategies are recommended for security analysts working with LLM-based code generation tools.

In an era where AI code generators are reshaping software development, the risk of introducing vulnerabilities is a growing concern. With the increasing reliance on machine learning-driven tools, it is essential to support developers with effective automated vulnerability patching while prioritizing the reliability and security of AI. However, current methods face significant challenges, including a high rate of false positives and difficulties in generating high-quality patches. This paper presents PatchitPy, a new patching solution that leverages a pattern-matching approach to detect and patch Python vulnerabilities. We generated 609 Python code using three popular AI code generators (i.e., GitHub Copilot, Claude-3.7-Sonnet, and DeepSeek- V3)and evaluated our solution's performance on these samples. The results demonstrate the effectiveness of PatchitPy, which outperforms state-of-the-art solutions in both detection and patching. PatchitPy achieved an F1 score of 93% and an Accuracy of 89% for vulnerability detection, and produced high-quality patches with a 80% repair rate for identified vulnerabilities. Furthermore, the patches preserve code quality with minimal impact on complexity, ensuring long-term code maintainability.

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. Methods: 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 F 1 Score and Accuracy of 94% while maintaining a low computational cost of 0.14 s per code snippet, on average. Conclusions: The proposed tool provides a lightweight and efficient solution for vulnerability detection even on incomplete code.

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 stability 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 & eacute;nard 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.

An investigation of the basic nanoconvective flow to be applied in evaluating the limit of validity of the transient hot wire experimental (THW) method for nanofluids is presented. Analytical solutions for the basic temperature, basic nanoparticles volume fraction, and basic natural convection velocity are being derived and analyzed. These basic solutions are needed in follow-up linear and nonlinear stability analyses aiming to establish the time required for natural convective heat flux to develop and invalidate transient hot wire experimental results. While the first part of the paper presents the current status of knowledge related to the transient hot wire experimental method and the theoretical aspects governing the validity of the method, the second part aims at presenting new results that can provide additional and more accurate conditions for the validity of that experimental method.

The aim of this paper is to investigate a reaction-diffusion Leslie–Gower predator–prey model, incorporating the intraguild predation and both self and cross-diffusion. The longtime behaviour of the solutions is analysed, proving the existence of an absorbing set. The existence of patterns is investigated by looking for conditions guaranteeing that an equilibrium, stable in the absence of diffusion, becomes unstable when diffusion is allowed.

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.

In this paper, a predator–prey model with intraguild predation describing the evolution between three interacting species—namely prey, mesopredator and top predator—is investigated, with the aim to model a complete food web. In particular, the longtime behaviour of the solutions is analysed, proving the existence of an absorbing set, and the linear and nonlinear stability analyses of the coexistence equilibrium are performed.

The aim of this paper is to investigate the effect of a vertical constant throughflow on convective instabilities in a horizontal layer of fluid-saturated bi-disperse porous medium heated from below. Via linear instability and nonlinear stability analyses of the throughflow solution, the linear and nonlinear critical Rayleigh numbers for convective instabilities have been determined and studied as functions of the strength of the throughflow.

The present paper investigates penetrative convection in a bi‐disperse porous medium. In particular, penetrative convection is modeled via a quadratic dependence on the temperature for the fluid density. For the problem under examination, convection can occur only through a secondary stationary motion since the validity of the principle of exchange of stabilities is proved. Via linear instability analysis of the conduction solution, the critical Rayleigh number for the onset of penetrative convection is determined. Moreover, the nonlinear stability is investigated via weighted energy method. In order to analyze the behavior of the stability and instability thresholds, numerical simulations are performed through Chebyshev‐ method, proving the stabilizing effect of the upper boundary layer temperature on the onset of convective motion.

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 variations. In this paper, the linear analysis of the Darcy-Bénard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor β 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 thermodynamically consistent instability results. The critical Rayleigh-Darcy number for the onset of convection is determined, via linear instability analysis of the conduction solution, as a function of a dimensionless parameter β proportional to the compressibility factor β , proving that β enhances the onset of convective motions.

The aim of this paper is the investigation on hydrodynamic stability of an incompressible fluid saturating a horizontal layer of bi-disperse porous medium, heated from below and internally, in order to analyse the effect of the internal heat source on the onset of convective instabilities. The principle of exchange of stabilities is proved, so convection can arise only via stationary motions. Via linear instability and nonlinear stability analyses of the conduction solution, the linear threshold and the nonlinear threshold in the L2−norm for the onset of convective motions are determined and compared.

The onset of thermosolutal convection in a uniformly rotating horizontal nanofluid layer is investigated. By employing an order-1 Galerkin residual method, an approximation of the instability threshold has been determined. A sufficient condition for the onset of steady convection has been found.

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 find 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.

It is well known that when a horizontal layer of fluid is heated from below, a thermal boundary layer of less dense and hot fluid rises up. When this boundary layer becomes unstable, convective motion in the fluid above sets in. Forecasting when instabilities take place is essential. When a salt dissolved in a fluid saturating a porous medium heated from below is considered, simultaneous mass diffusion and thermal diffusion occur. Unlike the diffusion of heat, the diffusion of salt can take place only through the fluid phase, so an additional physical effect has to be considered: the Soret effect, that is the mass flux created by a temperature gradient. In the present paper the onset of convection in a rotating layer of bi-disperse porous medium saturated by a binary fluid mixture, taking into account the Soret effect, is analysed. Linear stability analysis is performed in order to determine the instability thresholds for the onset of convection via a steady state (stationary convection) and via an oscillatory state (oscillatory convection). Nonlinear stability analysis is performed to obtain the global stability threshold with respect to the $$L^2$$ -norm.

In this short paper, some analytical results found in “Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term” by F. Capone, R. De Luca, M. Vitiello, Ricerche Mat. 68, 581–595 (2019), are recalled in order to better explore the dynamic of thermosolutal convection in a horizontal porous layer with the influence of Vadasz and Soret terms.

In this paper, the instability of a vertical fluid motion, or throughflow, is investigated in a horizontal bidisperse porous layer that is uniformly heated from below. By means of the order-1 Galerkin approximation method, the critical Darcy–Rayleigh number for the onset of steady instability is determined in closed form. The coincidence between the linear instability threshold and the global nonlinear stability threshold, in the energy norm, is shown.

Abstract A reaction–diffusion system governing the prey–predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation. Extensive numerical simulations, depicting such complex dynamics, are shown. In order to complete the stability analysis of the coexistence equilibrium, a nonlinear stability result is shown.

Thermal convection in a horizontally isotropic bi-disperse porous medium (BDPM) uniformly heated from below is analysed. The combined effects of uniform vertical rotation and Brinkman law on the stability of the steady state of the momentum equations in a BDPM are investigated. Linear and nonlinear stability analysis of the conduction solution is performed, and the coincidence between linear instability and nonlinear stability thresholds in the L-2-norm is obtained.