Background: Forecasting petroleum prices in state-administered markets presents unique challenges distinct from liberalized commodity exchanges. Algeria's hydrocarbon sector, accounting for 95% of export earnings, operates under administered pricing by the national oil company, creating irregular temporal dynamics, regime-dependent policy inertia, and geopolitical risk endogeneity that violate classical forecasting assumptions. Existing neural architectures fail to capture the institutional constraints and network effects of OPEC+ coordination.

Methods: We developed a novel three-tiered deep learning framework integrating: (1) a Phased Bidirectional Gated Recurrent Unit (GRU) encoder handling irregular policy sampling intervals through learnable temporal gates; (2) a conflict-gated graph convolution layer modeling Algeria as a node in a dynamic OPEC+ network with edge weights modulated by geopolitical instability and compliance correlation; and (3) a regime-aware Mixture Density Network (MDN) for uncertainty quantification during high-volatility episodes. The model was trained on proprietary daily Official Selling Prices (2010--2023) augmented with conflict intensity and shipping logistics data, using curriculum learning and multi-objective optimization combining negative log-likelihood with quantile calibration.

Results: The proposed architecture achieved a Mean Absolute Percentage Error (MAPE) of 2.48% and coefficient of determination (R^2) of 0.92 on out-of-sample testing (2022--2023), representing a 22.7% improvement over Temporal Fusion Transformer baselines. During high-intensity conflict periods, error metrics improved by 43% compared to conventional models. Ablation studies confirmed that each architectural component significantly contributes to robustness, with the conflict gate preventing error cascade during domestic instability episodes.

Conclusions: This work establishes a new benchmark for forecasting in administered energy markets by explicitly encoding institutional rigidity and geopolitical constraints. The framework provides actionable intelligence for fiscal planning, demonstrating potential annual revenue forecasting error reduction of 91 million dollars. The approach is transferable to other state-administered commodity markets facing similar structural challenges.

Biological issues are often subjected to forces. In many cases, such as tumor growth or skin contraction, it is crucially important to model the state of tissues that are exposed to forces in order to improve or optimize therapies for different pathologies. The simplest models use linear elasticity as a constitutive law. This linearity enables the use of the superposition principle and the use of fundamental solutions to analyze the influence of multiple points of action of forces. A clear illustration of this principle is the immersed interface method. In this presentation, we discuss this principle in terms of convergence properties.

However, in real-life tissues, the use of linear elasticity is too restrictive due to the presence of moisture and the porous structure of biological tissues. Furthermore, in various biomedical cases, the microstructure of the tissue changes due to cellular activity. For this reason, we construct and use a model that consists of elasticity, porosity and microstructural changes. The mathematical framework is referred to as morpho-visco-poroelasticity. This framework is original and for this reason, we analyze this framework in terms of stability around equilibria. Since numerical solutions can be characterized by spurious oscillations, we provide conditions for monotonicity by mathematical analysis. Furthermore, we propose a numerical stabilization method to avoid spurious oscillations on the forehand.

We investigate a class of conditional McKean–Vlasov stochastic differential equations with jump components and Markovian regime-switching, thereby extending classical mean-field frameworks to encompass discontinuous perturbations and environment-dependent dynamics. The models describe interacting particle systems whose evolution depends not only on the individual state and stochastic perturbations, but also on the conditional distribution of the system given an underlying filtration, providing a mathematically natural setting for partial information, common noise effects, and regime-driven interactions.

A comprehensive analysis of well-posedness, stability, and regularity is developed, revealing the delicate interaction between Poisson jump mechanisms, regime-switching dynamics, and conditional mean-field effects. A central contribution is the derivation of first- and second-order differentiability properties of the solution flow with respect to the probability measure, carried out through Lions’ differential calculus on the Wasserstein space.

Furthermore, we show that the conditional McKean–Vlasov dynamics induce a novel class of nonlocal systems of partial integro-differential equations with terminal conditions. Under appropriate structural and regularity assumptions, we establish a probabilistic representation of the unique classical solutions of these systems via an extended Feynman–Kac-type formula.

These results provide a rigorous and unified connection between conditional stochastic particle systems and their associated analytical equations, significantly enriching the theory of mean-field models with jumps and switching. The framework opens new avenues for applications in areas such as systemic risk, neural network modeling, and controlled interacting systems under uncertainty.

Energy consumption has become a critical issue in modern distributed manufacturing systems due to increasing production complexity and sustainability requirements. This paper addresses the Distributed Flow Shop Scheduling Problem (DFSP) with the objective of minimizing Total Energy Consumption (TEC), which is known to be a challenging NP-hard combinatorial optimization problem.

To tackle this problem, several metaheuristic algorithms are considered, including the Genetic Algorithm (GA), Artificial Bee Colony (ABC), and Iterated Greedy (IG) algorithm, along with their hybrid versions integrating Q-Learning (QL). In the proposed approaches, Q-Learning is embedded within the optimization process to guide the search through the adaptive selection of neighborhood-based operators, such as insertion, swapping, and reconstruction moves. This reinforcement learning mechanism enables the algorithm to dynamically learn the most effective search strategies based on their impact on energy consumption, thus improving the balance between exploration and exploitation.

The performance of the proposed methods is evaluated through extensive computational experiments on different problem instances with varying sizes and configurations. The results demonstrate that integrating Q-Learning significantly enhances the performance of the metaheuristic algorithms, leading to improved solution quality in terms of energy consumption. In particular, the hybrid approaches consistently outperform classical methods, with the HMBOQL-VNS approach achieving the best performance and a dominance rate of 82.1%.

These results highlight the effectiveness of combining reinforcement learning with metaheuristic optimization for developing efficient and sustainable scheduling strategies in distributed manufacturing systems.

Harmonic distortion remains a critical issue in modern single-phase power systems, primarily due to the increasing penetration of nonlinear loads and power-electronic devices. Accurate estimation of harmonic content is essential for maintaining voltage quality, ensuring equipment reliability, and supporting overall grid stability. Existing numerical approaches, including discrete Fourier transform (DFT)-based methods, often face limitations such as high sensitivity to noise, spectral leakage, and increased computational load.

This study introduces a complex-analysis-based mathematical framework for harmonic distortion estimation, offering improved analytical insight and computational efficiency. The distorted voltage waveform is modeled as a complex-valued periodic function, enabling decomposition through Fourier series in the complex plane. Key tools from complex variables—such as contour integration, residue theorem, and analytic continuation—are employed to derive harmonic coefficients with enhanced precision. Linear algebraic formulations and numerical approximation methods from advanced engineering mathematics (including iterative solvers and error minimization techniques) further optimize coefficient extraction and reduce computational overhead.

Simulation results on multiple non-sinusoidal test signals demonstrate that the proposed method achieves higher accuracy in estimating harmonic magnitudes and phases, with up to an 18% improvement in convergence compared to conventional DFT-based approaches. The framework also exhibits strong noise tolerance, providing clearer differentiation between dominant and weak harmonic components.

Overall, this work offers a mathematically rigorous and efficient methodology for real-time harmonic analysis in power systems. The framework bridges complex analysis with power-engineering applications and has strong potential for integration into modern power quality monitoring and control systems.

In classical vaccination game theory, population groups are typically treated as homogeneous, with individuals assumed to share identical disease risks, cost perceptions, and beliefs about vaccine performance. In this talk, we depart from this assumption and introduce a vaccination game model designed for an infinite population whose members exhibit heterogeneous preferences and characteristics. Specifically, we allow individuals to differ in three key dimensions: (1) their susceptibility to infection, (2) their perceived costs associated with both contracting the disease and receiving the vaccine, and (3) their subjective assessment of vaccine efficacy. We encode this heterogeneity using a quantile function that captures the distribution of agents’ net relative vaccination costs, providing a flexible and analytically tractable representation of diverse behavioral responses. Within this framework, we derive an explicit closed-form expression for the Nash equilibrium vaccination rate, offering transparent insights into how population-level behavior emerges from heterogeneous individual incentives. We then demonstrate how our model can be calibrated using real-world survey data to generate empirical predictions about vaccination uptake. A systematic comparison with the standard homogeneous model reveals that our heterogeneous approach yields consistently improved predictive accuracy, particularly in data-sparse settings where only a limited number of survey responses are available. Across a range of scenarios, the heterogeneous model not only reduces prediction error but also exhibits greater robustness to sampling variability and model misspecification. Overall, our results highlight the importance of accounting for preference diversity in vaccination games and illustrate how heterogeneity can significantly enhance the realism and reliability of epidemiological behavior models.

Recent detections of Highly Pathogenic Avian Influenza (HPAI) in dairy cattle have underscored the urgent need to understand within-herd transmission dynamics and potential cross-species spillover risks. This study develops a deterministic $SEI_{s}I_{a}RB$ compartmental model specifically designed to capture the complex interplay between susceptible cattle, multiple infectious states, and environmental reservoirs. By employing the next-generation matrix method, we analytically derive the basic reproduction number ($R_0$) and identify the critical thresholds governing disease extinction and persistence. Rigorous local and global stability analyses of the disease-free and endemic equilibria are provided to characterize long-term herd health outcomes and steady-state behaviour. Numerical simulations validated by comprehensive sensitivity analysis utilising Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCC)---reveal that the transmission rate from asymptomatic infectious cattle ($\beta_a$) is the most influential parameter driving the epidemic curve. Furthermore, our results indicate that the environmental pathogen load significantly sustains the outbreak duration. These findings demonstrate that traditional surveillance focusing solely on symptomatic animals may significantly underestimate the true scale of an outbreak. Consequently, we propose that effective HPAI mitigation strategies must integrate rigorous environmental sanitation protocols with enhanced diagnostic screening for asymptomatic carriers to prevent wide-scale agricultural disruptions and broader public health impacts.

The main objective of a group of decision-makers in a multi-criteria group decision-making (MCGDM) problem is to choose the best option from the available options. Prior to analysis, a number of issues must be resolved to select an appropriate alternative for an MCGDM problem. These issues include quantifying uncertainty in collected data, handling conflicting criteria, evaluating decision makers and criteria weights, properly fusing quantified information, and ultimately choosing the best alternative. The objective of this research is to establish an interactive MCGDM method for evaluating any MCGDM problem while addressing the above-listed challenges. The suggested MCGDM approach employs intuitionistic fuzzy sets (IFSs) to quantify uncertainty in gathered data, assesses decision makers' weights based on their social network, determines criteria weights using the maximizing deviation method, aggregates the data using the Archimedean t-norm and t-conorm (ATT)-based weighted average, and selects the optimal option using the intuitionistic fuzzy Maclaurin symmetric mean and score function. In order to enable manufacturing companies to modify their development strategies for a digital reform in a timely way, the proposed MCGDM technique is used to evaluate the digital reforms of China's manufacturing sector. The results show that the suggested method is practical, flexible, and suitable to assess any MCGDM problem in real life.

Currently, global transportation is increasingly focused on autonomous vehicular systems. However, training traffic systems to rely fully on autonomy remains challenging, as evidenced by numerous Tesla Autopilot accidents. Motivated by this, our study addresses a critical aspect: the driver’s sensitivity in autonomous vehicles, which plays a key role in enhancing their performance. We developed a novel driver sensitivity function responding to real-time traffic dynamics, formulated in two parts: (i) sensitivity depending on the headway gap between the focal and preceding vehicle, and (ii) sensitivity varying with the velocity difference, quantified using the preceding vehicle’s taillight signals.

For the first part, we applied a straightforward formulation inspired by the Optimal Velocity model. Driver awareness increases as the headway shrinks to prevent collisions and decreases with increasing headway due to reduced collision risk. In the second part, sensitivity is modeled using the taillight phenomenon, activated by vehicle acceleration or deceleration. Here, sensitivity escalates with both positive velocity differences, when the preceding vehicle is faster, and negative differences, when the focal vehicle is faster, helping to fill gaps and prevent collisions.

We performed a linear analysis using neutral stability theory, revealing a critical stability line distinct from conventional traffic models. A nonlinear analysis of the headway-based sensitivity produced flow patterns describable by the mKdV wave equation. Finally, numerical simulations were conducted to visualize the internal flow field structures, validating the model’s performance under realistic traffic conditions.

This study demonstrates that incorporating driver sensitivity through velocity and headway dynamics provides a robust framework for improving autonomous vehicle operation, enhancing safety and traffic stability while offering new insights for future autonomous traffic system designs.

Fractional calculus has emerged as a powerful mathematical framework for modeling real-world systems characterized by memory, nonlocality, and complex dynamical behaviors. Unlike classical integer-order models, fractional-order formulations provide a more flexible description of processes with long-term memory and hereditary effects, which are commonly observed in physics, engineering, biology, and information sciences. In particular, fractional-order chaotic and hyperchaotic systems have received considerable attention for their ability to capture richer dynamical features, making them highly relevant in areas such as secure communications, signal encryption, random number generation, and nonlinear control. In this work, we explore a four-dimensional fractional-order chaotic model by integrating the Residual Power Series Method (RPSM) and the Caputo fractional derivative (CFD). The CFD is employed to obtain highly accurate numerical simulations that reveal the sensitivity of chaotic attractors to changes in the fractional order, while the RPSM provides analytical approximations that are computationally efficient, stable, and capable of handling diverse initial conditions. This hybrid framework bridges the gap between purely numerical and purely analytical methods, ensuring both accuracy and mathematical insight. Our findings show that fractional order is a key parameter for tuning system behavior between chaotic and stable regimes. This study contributes new insights into the modeling of hyperchaotic systems, with potential relevance for engineering, cryptography, and nonlinear sciences.