Fog computing is one of the rapidly growing platforms with an exponentially increasing demand for real-time data processing. The fog computing market is expected to reach USD 8358 million by the year 2030 with a compound annual growth of 50%. The wide adaptation of fog computing by the industries worldwide is due to the advantages like reduced latency, high operational efficiency, and high-level data privacy. The highly distributed and heterogeneous nature of fog computing leads to significant challenges related to resource management, data security, task scheduling, data privacy, and interoperability. The task typically represents a job generated by the IoT device. The action indicates the way of executing the tasks whose decision is taken by the scheduler. Task scheduling is one of the prominent issues in fog computing which includes the process of effectively scheduling the tasks among fog devices to effectively utilize the resources and meet the Quality of Service (QoS) requirements of the applications. Improper task scheduling leads to increased execution time, overutilization of resources, data loss, and poor scalability. Hence there is a need to do proper task scheduling to make optimal task distribution decisions in a highly dynamic resource-constrained heterogeneous fog computing environment. Flow Q learning (FQL) is a potential form of reinforcement learning algorithm which uses the flow matching policy for action distribution. It can handle complex forms of data and multimodal action distribution which make it suitable for the highly volatile fog computing environment. However, flow Q learning struggles to achieve a proper trade-off between the expressive flow model and a reduction in the Q function, as it relies on a one-step optimization policy that introduces bias into the estimated Q function value. The Tiny Language Model (TLM) is a significantly smaller form of a Large Language Model (LLM) which is designed to operate over the device-constrained environment. It can provide fair and systematic guidance to disproportionally biased deep learning models. In this paper a novel TLM guided flow Q learning framework is designed to address the task scheduling problem in fog computing. The neutrality and fine-tuning capability of the TLM is combined with the quick generable ability of the FQL algorithm. The framework is simulated using the Simcan2Fog simulator considering the dynamic nature of fog environment under finite and infinite resources. The performance is found to be good with respect to parameters like execution time, accuracy, response time, and latency. Further the results obtained are validated using the expected value analysis method which is found to be satisfactory.

Facial Expression Recognition (FER) is a critical component of affective computing, with deep learning models dominating performance metrics. In contrast, geometric approaches based on the Facial Action Coding System (FACS) offer explainability through using triangles aligned to facial landmarks. The notable points of these triangles capture the deformation of muscles. However, restricting the feature extraction to notable points may be suboptimal. This paper introduces a novel method for optimizing the extraction of features by searching for optimal inner points in 22 facial triangles applying three metaheuristics: Differential Evolution (DE), Particle Swarm Optimization (PSO), and Convex Partition (CP). This results in a set of 59 geometric-based descriptors that capture muscle deformation more accurately. The proposed method was evaluated using five machine learning classifiers on two benchmark databases: the Karolinska Directed Emotional Faces (KDEF) and the Japanese Female Facial Expression (JAFFE). Experimental results demonstrate significant performance improvements. The combination of DE with a Multi-Layer Perceptron (MLP) achieved an accuracy of 0.91 on the KDEF database, while Support Vector Machine (SVM) optimized via CP attained an accuracy of 0.81 on the JAFFE database. Statistical analysis confirms that optimized descriptors yield higher accuracy than previous geometric methods.

To address the limitations of the standard Sparrow Search Algorithm (SSA) in complex optimization problems—such as insufficient convergence accuracy and susceptibility to local optima—this paper proposes a Composite Strategy Sparrow Search Algorithm (CSSA) for multidimensional optimization. The algorithm first employs chaotic mapping during initialization to enhance population diversity; second, it integrates coordinate axis pattern search to strengthen local exploitation capabilities; third, it applies intelligent crossover operations to promote effective information exchange among individuals; and finally, it introduces an adaptive vigilance mechanism to dynamically balance exploration and exploitation throughout the optimization process. Compared with seven state-of-the-art algorithms, CSSA demonstrates superior performance in both 30-dimensional low-dimensional and 100-dimensional high-dimensional test scenarios. It achieves optimal solutions in three real-world engineering applications: thermal management of electric vehicle battery packs, photovoltaic power system configuration, and data center cooling systems. Wilcoxon rank-sum tests further confirm the statistical significance of these improvements. Experimental results show that CSSA significantly outperforms mainstream optimization methods in terms of convergence accuracy and speed, demonstrating substantial theoretical value and practical engineering significance.

Accurate prediction of Blood Glucose (BG) levels is essential for effective diabetes management and the prevention of adverse glycemic events. This study introduces a novel designed hybrid Gated Recurrent Unit-Transformer (GRU-Transformer) model tailored to forecast BG levels at 15, 30, 45, and 60 min horizons using only Continuous Glucose Monitoring (CGM) data as input. The proposed approach integrates advanced CGM feature extraction step. The extracted features are statistically the mean, the median, the maximum, the entropy, the autocorrelation and the Detrended Fluctuation Analysis (DFA). In addition, in order to define more enhanced and specific features, the custom 3-points monotonicity score, the sinusoidal time encoding, and the workday/weekend binary features are proposed in this work. This approach enables the model to capture physiological dynamics and contextual temporal patterns of Type 1 Diabetes (T1D) with great accuracy. To thoroughly assess the performance of the proposed method, we relied on several well-established metrics, including Root Mean Squared Error (RMSE), Coefficient of Determination (R2), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Root Mean Squared Percentage Error (RMSPE). Experimental results demonstrate that the proposed method achieves superior predictive accuracy for both short-term (15–30 min) and long-term (45–60 min) forecasting. Specifically, the model attained the lowest average RMSE values, with 4.00 mg/dL, 6.65 mg/dL, 7.96 mg/dL, and 8.91 mg/dL and yielding consistently high R2 scores for the respective prediction horizons. This new method distinguishes itself by continuously exceeding current prediction models, reinforcing its potential for real-time CGM and clinical decision support. Its high accuracy and adaptability make it a favorable tool for improving diabetes management and personalized glycemic control.

The aim of this article is to study duality results for nonsmooth mathematical programs with equilibrium constraints in terms of tangential subdifferentials. We study the Wolfe-type dual problem under the convexity assumptions and a Mond–Weir-type dual problem is also formulated under convexity and generalized convexity assumptions for MPEC by using tangential subdifferentials. We establish weak duality and the two dual programs by assuming tangentially convex functions and also obtain strong duality theorems by assuming generalized standard Abadie constraint qualification.

This paper presents research aimed at detecting and quantifying backlash in the feed motion subsystem of machine tools using positioning accuracy test results. By applying shallow neural networks, we not only estimate backlash magnitude but also analyse the impact of key parameters on its occurrence. This approach enables continuous, data-driven monitoring and prediction of backlash variation while reducing machine tool calibration time in industrial settings. The experimental study used two standard motion methods while monitoring machine and ambient temperature, atmospheric pressure, and humidity. The results show how experimental parameters affect detected backlash. A feed-forward neural network predicts current backlash at specific measurement points. The results demonstrate high accuracy in backlash estimation, significantly simplifying machine calibration during maintenance and providing a foundation for real-time error compensation.

The theory underlying non-linear dynamical systems remains essential for understanding complex behaviors in science and engineering. In this study, we propose a new chaotic dynamical system that exhibits a butterfly-shaped attractor without any equilibrium point. Despite its compact structure comprising only five terms, the system demonstrates rich chaotic behavior distinct from conventional oscillator models. Detailed modeling and dynamical analyses are conducted to confirm the presence of chaos and to characterize the system’s sensitivity to initial conditions. Furthermore, synchronization of the proposed dynamical system is investigated using both identical and non-identical control algorithms. In the identical case, the activation function of the neural network is governed by the butterfly oscillator dynamics, whereas in the non-identical case, a sigmoidal activation function is employed. The proposed synchronization algorithms enable faster convergence by pinning a subset of nodes in the network. Finally, a practical implementation of the conceived dynamical system in an encryption framework is presented, with the aim to demonstrate its feasibility and potential application in secure communication systems. The results highlight the effectiveness of the proposed approach for both theoretical exploration and engineering applications involving chaotic dynamical systems.

In constrained nonlinear optimization, we aim to achieve two goals: one is to minimize the objective function, and the other is to satisfy the constraints. A common way to balance these competing targets is to use penalty functions. Suppose that an algorithm generates a descent direction and produces a step that decreases the objective function value but increases the constraint violation—a phenomenon known as the Maratos effect. This leads to the rejection of the full step by the non-smooth penalty function; therefore, superlinear convergence is not preserved. This work leverages a piecewise convexity model to solve the optimal PMU placement. A quadratic objective function is minimized subject to a non-convex equality constraint within box constraints [0, 1] × [0, 1] ⊂ R2. The initial non-convex region is reconsidered as a union of piecewise line segments. This decomposition enables algorithms to converge to a local optimum while preserving superlinear convergence near the solution. An analytical solution is presented using the Karush–Kuhn–Tucker conditions. First-and-second-order optimality conditions are applied to find the local minimum. We show how the Maratos effect is avoided by adopting the piecewise convexity without needing a non-smooth penalty function, second-order corrections or employing the watchdog methods. Simulations demonstrate that the algorithms partially search the space along the line segments—avoiding zig-zag trajectories—and reach (0, 1) or (1, 0), where both feasibility and optimality are satisfied at once.

This study explores the spread of malware within a digital framework by introducing a unique fractional-order model that employs the Atangana–Baleanu–Caputo (ABC) derivative. As cyber threats grow increasingly sophisticated and widespread, traditional models using classical differential equations often prove inadequate, particularly in capturing long-term memory effects and historical dependencies inherent in real-world systems. To address these challenges, the proposed approach utilizes the non-local characteristics of fractional calculus, offering a more comprehensive framework for understanding malware behavior. The model includes the derivation of the basic reproduction number, ℜ0, to evaluate conditions for malware persistence or elimination, sensitivity analysis and examines equilibrium states to assess overall system stability. Theoretical analysis ensures the existence and uniqueness of solutions through fixed-point techniques. Through numerical simulations, the theoretical results are validated, emphasizing the significant impact of antidotal and recovery measures in controlling malware spread. These findings provide essential guidance for enhancing the protection and robustness of sophisticated cyber-physical and humanoid infrastructures.

The objective of the next POI recommendation is using the historical check-in sequences of users to learn the preferences and habits of users, providing a list of POIs that users will be inclined to visit next. Then, there are some limitations in existing POI recommendation algorithms. On the one hand, after obtaining the user’s preferences for the current period, if we consider the entire historical check-in sequence, including future check-in information, it is susceptible to the influence of noisy data, thereby reducing the accuracy of recommendations. On the other hand, the current methods generally rely on modeling long- and short-term preferences within a fixed time window, which possibly leads to an inability to capture users’ behavior characteristics at different time scales. As a result, we proposed a Multimodal Temporal Fusion for Next POI Recommendation(MTFNR). Firstly, to understand users’ preferences and habits at different periods, multiple hypergraph neural networks are constructed to analyze user behavior patterns at different stages, and in order to avoid introducing interference factors, only the check-in sequences visited in the current period are considered to reduce the impact of noise on the model’s recommendation performance. Secondly, modeling the next POI recommendation task through the fusion of time information and long- and short-term preferences in order to gain a more comprehensive understanding of users’ preferences and habits, enhance the timeliness of recommendations, and improve the accuracy of recommendations. Lastly, introducing spatio-temporal interval information into the GRU model, capturing dependencies in sequences to improve the overall performance of the model. Extensive experiments on the real LBSN datasets demonstrated the superior performance of the MTFNR model. The experimental results indicate that Top-10 recall improved 2.81% to 15.97% compared to current methods.