This study introduces the Quantum-Resistant Federated Anomaly Detection (QRFAD) framework, a novel approach for addressing the challenges of anomaly detection in Identity and Access Management (IAM) systems in the face of evolving cyber threats and emerging quantum computing risks. By combining federated learning, quantum-resistant cryptography, and Agentic AI, QRFAD overcomes the limitations of traditional anomaly detection models, such as LSTM and SVM. The framework ensures a scalable, secure, and privacy-preserving solution that enables multiple organizations to collaboratively train models without sharing sensitive data. Key performance metrics, including precision, recall, F1-score, latency, and scalability, were evaluated on the ICS-Flow dataset, demonstrating that QRFAD significantly outperformed the LSTM and SVM models. Specifically, QRFAD achieved a precision of 0.94, recall of 0.91, and F1-score of 0.92, all higher than the LSTM (0.85, 0.83, 0.84) and SVM models (0.78, 0.75, 0.76). Moreover, QRFAD reduced the latency by 35.71\% (75 ms vs. 120 ms) and improved the model update overhead by 50\% (1.2s vs. 2.5s). This work addresses key gaps in the literature related to scalability, quantum threats, and autonomous decision-making, providing an adaptive and secure IAM solution capable of evolving with emerging cyber threats.
This paper presents a novel approach to cybersecurity risk management through the development of a cascading risk model that simulates the propagation of risks across interconnected systems and evaluates mitigation strategies. Unlike traditional linear risk models, the proposed model integrates nonlinear wave decomposition and adaptive control mechanisms to capture the dynamic and evolving nature of cybersecurity threats. The model was validated using data from both the Kaggle Cyberattack Dataset and the National Vulnerability Database (NVD), demonstrating its ability to accurately model cascading risks and assess the effectiveness of mitigation measures. The simulation results show significant reductions in risk propagation, with mitigation strategies reducing the overall risk by up to 42% for certain attack types. The findings underscore the model’s ability to address gaps in existing cybersecurity frameworks by providing real-time adaptive risk management in complex, interdependent environments. This work offers a scalable solution for improving cybersecurity resilience in modern infrastructure and IoT ecosystems.
This study presents a mathematical model using non-homogeneous heat equations with dynamic boundary conditions to simulate the spread and mitigation of cybersecurity threats. Our results demonstrate that incorporating adaptive boundary conditions, which represent real-time adjustments to defense mechanisms, improves the robustness of cybersecurity systems against evolving threats. Stability analysis using the Lyapunov criterion shows that the system remains stable over time, with the vulnerability (represented by the Lyapunov function) decreasing as time progresses. Numerical simulations indicate that varying the intensity of cyber-attacks and adjusting boundary conditions dynamically leads to more efficient and effective defense strategies, optimizing both computational load and system security. The mathematical model, validated through several test cases, reveals that dynamic adaptation of defense mechanisms significantly outperforms traditional static models, offering scalable solutions for real-time cyber defense. Furthermore, our results demonstrate the model's ability to simulate the impact of network topology changes and varying attack intensities, providing insights into how network configurations influence the propagation of vulnerabilities.
This paper presents a novel framework for addressing code-level vulnerabilities in critical applications by combining formal verification with risk scoring systems. It ensures the correctness and reliability of code while prioritizing vulnerabilities based on exportability and impact. The approach is applied to high-stakes industries such as healthcare, aerospace, and industrial control, where system failures can have catastrophic consequences. A numerical example demonstrates a 22% reduction in risk (from 1.905 to 1.485) within budgetary constraints. Results show that this combined method offers a robust, cost-efficient solution for improving security, making it practical for real-world deployment. The framework emphasizes risk reduction and cost optimization in resource-constrained environments.
This study addresses an inverse problem for a time-fractional heat equation involving the Caputo derivative, where the objective is to determine an unknown time-dependent thermal coefficient. The governing equation incorporates a fractional order time derivative, a spatially dependent diffusion term, and a known source term. To solve the inverse problem, we employ the Laplace Homotopy Analysis Method (LHAM)—a semi-analytical approach that combines the Laplace transform with the Homotopy Analysis Method. This technique allows for the construction of a convergent series solution for both the temperature distribution and the unknown coefficient . By appropriately selecting the initial guess , the convergence-control parameter h becomes embedded in the solution process, reducing com-computational effort. The proposed method is validated through an illustrative example, demonstrating the effectiveness and accuracy of LHAM in solving time-fractional inverse problems with a source term.
Food shortages in most countries are not only associated with unfavorable weather conditions, but are also significantly blamed on ineffective post-harvest handling of food. Eminent threats caused by post-harvest losses due to inadequate drying and poor storage is responsible for up to 40-60% losses of agricultural produce each season. One of the mitigation strategies is the provision of sustainable and affordable food drying facilities. The most suitable solution is the use of solar food driers, which can be accessed locally. The optimal performance of a solar food drier depends on the consideration of design parameters and operation guidelines. This research paper models a solar drier to identify significant parameters and simulates to determine their optimal threshold values for the purpose of designing an effective solar drier suitable for dehydrating a variety of agricultural products. The model was formulated using a system of differential equations, to describe dynamics in four distinct compartments of a solar drier, namely; the solar heat collector, the closed loop pipe network circulating thermal fluid, the set of heat exchanger where heat is extracted from the hot liquid to hot drying air, and lastly is the dying chamber with controls of humidity, temperature, mass flow rate and energy balance. The set of solar dryer mathematical model equations was transformed to a MATLAB–SIMULINK model for simulation and parameter estimation. It was found that exposing a solar collector of ηc=0.8 efficiency, with aperture area of Ac=14.4m2 and a fluid capacity of Vc=500l, to solar irradiation of average Ic=5.6637KW/m2 can heat 5000 liters of water from Tin=220C to Tco=700C in 12 hours at a collector’s flow rate of v ̇c=1.128l/s. This heat energy in the thermal fluid can be extracted using a 5m2 heat exchanger to obtain hot air of up to 700C, which can be regulated to the desired temperature depending on the food to be dried.
This study paper uses advanced Artificial Intelligence (AI) analytical tools to enhance cryptographic systems and counter evolving security threats. The proposed approach integrates traditional cryptographic techniques with Machine Learning (ML) to improve key management, encryption algorithms, and overall system security. This methodology is further strengthened by integrating the Cyber-Kill Chain (CKC) and the National Institute of Standards and Technology (NIST ) Cybersecurity Framework. In CKC’s stage model, Reconnaissance, Weaponization, and Exploitation are related to the NIST phases of Identifying, Protecting, Detecting, Responding, and Recovering as a comprehensive cybersecurity plan. Bayesian networks, Markov Decision Processes, and Partial Differential Equations (PDE) are referenced for threat detection, temporal modeling of vulnerabilities, and mathematical correctness, respectively. Introducing such optimizations promoted by AI into the CKC and NIST frameworks helps the proposed system achieve better flexibility, robustness, and extensibility. Additionally, reinforcement learning is explored to dynamically adjust security measures based on real-time threats. Experimental validation supports the efficiency of integrating AI-driven analytics into cryptographic frameworks. In this context, the work suggests a forward-looking plan for cybersecurity in contemporary society, mapping between theory development and applications that produce sound and secure cryptographic systems that neutralize cutting-edge security risks.
This article explores the application of Forward-Backward Stochastic Differential Equations (FBSDEs) to cash flow optimization in uncertain financial environments. FBSDE provide a rigorous framework for modeling investment and payment dynamics, enabling the maximization of investor preferences while minimizing financial risks. The model considers a portfolio composed of both risky and risk-free assets, incorporating constraints such as the balance between discounted payments and accumulated premiums. The analysis includes solving the optimization problem using the stochastic maximum principle and Lagrange multipliers. Optimal admissible strategies are defined as stochastic processes satisfying integrability conditions and backward differential equations. Numerical simulations assess the impact of key parameters, such as initial wealth, discount rate, volatility, and risk aversion, on investment and consumption decisions. The results demonstrate that the FBSDE approach effectively captures complex dynamics and facilitates the development of robust strategies under uncertainty. In conclusion, this article highlights the potential of FBSDEs for portfolio management, financial product pricing, and decision optimization in uncertain environments. Future research could expand this framework by integrating exogenous factors, such as macroeconomic conditions, thereby broadening its applicability and relevance.
This study presents a novel partial differential equation (PDE)-based model for neural stem cell (NSC) therapy in spinal cord injury (SCI) treatment. Existing models often fail to accurately represent NSC migration, differentiation, and interaction with biomaterials and immune responses. By integrating scaffold-mediated diffusion and immune response dynamics, the proposed model offers a more realistic framework for regenerative therapy optimization. The model improves upon previous approaches by providing precise control overgrowth factor distribution, ensuring sustained bioavailability for enhanced NSC survival and functional integration. Applications of this framework extend beyond SCI treatment, with potential implications for neurodegenerative diseases, brain injury repair, and personalized medicine. Future research will focus on experimental validation and machine learning-driven optimization to refine the predictive capabilities of the model.
This study investigates how stochastic optimization is applied to the management of a company's portfolio in order to maximize the expected utility of wealth over a given period. Inspired by Merton's research, this model involves random volatility in the financial markets, while maintaining a constant interest rate to take better account of real economic uncertainties. The aim is to formulate optimal investment and consumption strategies based on Pontryagin's maximum principle. Taking into account key factors such as economic growth and market volatility, as well as risk aversion in our financial considerations, we recommend an approach incorporating a quadratic penalty for excessive investment. This innovative method aims to adjust financial choices in line with economic fluctuations and ensure prudent management of the company's monetary resources. Finally, numerical simulations illustrate the influence of these factors on overall wealth, as well as on investment and consumption, underlining the importance of prudent portfolio management during periods of uncertainty.
In this paper, we establish common fixed point theorems for quadruple weakly compatible mappings satisfying a new generalized contraction condition. Our results generalize the corresponding result of Budi Nurwahyu et al. [6]. Non-trivial examples are further provided to support the hypotheses of our results.
This study analyzes the stability of Lancaster-type ODE models in symmetric warfare situations. In symmetric warfare situations, when the lethality coefficients (K) are equal for both forces in battle, the system exhibits marginal stability, characterized by poles at ± K, indicating that the model is stable in some regions and unstable in others. The present research illustrates a controlled rhythmicity, and these forces show a harmonized balance between the two battling forces in order to develop a strong strategy and decision for military.
In this paper the Adomian decomposition Method (ADM), Regular Pertubation Method (RPM) and the Homotopy Perturbation Method (HPM) are used to study Burgers equation. Then we compare the solutions obtained by these three methods.
In this paper, an age-structured model was used to model population dynamics, and make predictions through simulation using 2019 Kenya population data. The age-structured mathematical model was developed, using partial differential equations on population densities as func-tions of age and time. The population was structured into 20 clusters each of 5 year interval, and assigned different birth and death rate pa-rameters. Crank-Nicolson numerical scheme was used to simulate the model and the 2019 initial population of 38,589,011 was found to increase by 50% to 57,956,100 by 2050. The initial economic dependency ratio was computed to be 1:2, but due to changes in technology and improvement of living standards, the new ratio is lowered to 1:1.14. The graphical presentation showed a trend of transition from ex-pansive to constrictive population pyramid.
This study addresses the one-dimensional non-homogeneous heat equation with non-homogeneous boundary conditions using a transformation method. We introduce a new dependent variable V(x,t) and a function ψ(x) to simplify the PDE into a homogeneous form, solving it analytically. The solution involves separating variables and applying Fourier series, leading to: Numerical simulations confirm the theoretical results, illustrating the method’s robustness for modeling heat conduction problems.
This work presents details of the study of the entire flow inside the facility where the exothermic chemical reaction process in the chemical laser cavity is analyzed. In our paper we will describe the principles of chemical lasers where flow reversal is produced by chemical reactions. We explain the device for converting chemical potential energy laser energy. We see that the phenomenon thus has an explosive trend. Finally, the feasibility and effectiveness of the proposed method is demonstrated by computer simulation.
Symmetry and asymmetry play a crucial role in the stability of the fundamental components of matter. Thus, the main objective of this work is to study the existence of symmetry, this universal geometric property of matter, in certain atoms, in order to provide a classification of the elements of the periodic table based on a symmetry criterion.
The study of epidemiology is often done with an assumption that the population is homogeneously mixed, and the disease dynamics is uniform. However, this is not always true, and cultural beliefs and economic activities significantly contribute to segregation not necessarily in spatial dimension but on the way of life. In this study, the dynamics of HIV/AIDS is studied in four distinct fisher-folk population patches, both individually and under all-to-all diffusive coupling. It was found that, the dynamics of each patch is periodic, and there exist an attracting invariant stable synchronization manifold. The manifold of the coupled system displayed robustness under small perturbation, even with a small coupling strength of k≪1. This guarantees uniformity of long term metapopulation disease dynamics.
The study, based on available data on the Congolese banking sector has succeeded in establishing a benchmark of the ideal distribution of a bank’s credit portfolio by sector in order to improve its profitability while reducing the risk of default. This benchmark has been established on an exclusively quantitative basis on the results of three distinct methods of multi-criteria decision aid: AHP and TOPSIS. It can help banks to assess of the quality of their credit portfolio (or, at least, their sectorial allocation) relative to the latter, which is derived from the aggregates of the entire banking sector. It would benefit from being usefully combined with a more qualitative analysis that escapes the spectrum of this study taking into account the quality and availability of the guarantee, track record, etc. The Student t-test, as the correlation coefficient has shown that the results of our different methods are in perfect correlation with the data of the bank, and the difference of the discrepancies between our methods and the data of the bank are random, that is to say not significant.
The aim of this paper is to prove some common fixed point theorems for four pair of weakly commuting mappings using multiplicative b-metric spaces. Our results obtained in this paper improve, extend and unify some related results in the literature.
