Mathematics

This paper investigates the general decay stability of the stochastic linear theta (SLT) method and the split-step theta (SST) method for stochastic delay Hopfield neural networks. The definition of general decay stability for numerical solutions is formulated. Sufficient conditions are derived to ensure the general decay stability of the SLT and SST methods, respectively. The key findings reveal that, under the derived sufficient conditions, both the SLT and SST methods can achieve general decay stability when $\theta \in \left[{\displaystyle \frac{1}{2}},1\right]$, while for the case of $\theta \in \left[0,{\displaystyle \frac{1}{2}}\right)$, the stability can also be guaranteed, which requires a stronger constraint on the step size. Finally, numerical examples are provided to demonstrate the effectiveness and validity of the theoretical results. Full article

Despite widespread adoption, traditional Agile project management practices often fail to ensure successful delivery of enterprise-scale software projects. One key limitation lies in the absence of a conceptually defined structure for the various types of Agile activities and their interactions. As a result, Agile methodologies typically lack formal indicators for evaluating the semantic content and progress status of project activities. Although widely used tools for Agile project management, such as Atlassian Jira, capture operational data, project status assessment interpretation remains largely subjective—relying on the experience and judgment of managers and team members rather than on a formal knowledge model or well-defined semantic attributes. As Agile project activities continue to grow in complexity, there is a pressing need for a modeling approach that captures their causal structure in order to describe the essential characteristics of the processes and ensure systematic monitoring and evaluation of the project. The complexity of the corresponding model must correlate with the causality of processes to avoid losing essential properties and to reveal the content of causal interactions. To address these gaps, this paper introduces a causal Agile process model that formalizes the internal structure and transformation pathways of Agile activity types. To our knowledge, it is the first framework to integrate a recursive, causally grounded structure into Agile management, enabling both semantic clarity and quantitative evaluation of project complexity and progress. The aim of the article is, first, to describe conceptually different Agile activity types from a causal modeling perspective, its internal structure and information transformations, and, second, to formally define the causal Agile management model and its characteristics. Each Agile activity type (e.g., theme, initiative, epic, user story) is modeled using the management transaction (MT) framework—an internal model of activity that comprises a closed-loop causal relationship among management function (F), process (P), state attribute (A), and control (V) informational flows. Using this framework, the internal structure of Agile activity types is normalized and the different roles of activities in internal MT interactions are defined. An important feature of this model is its recursive structure, formed through a hierarchy of MTs. Additionally, the paper presents classifications of vertical and horizontal causal interactions, uncovering theoretically grounded patterns of information exchange among Agile activities. These classifications support the derivation of quantitative indicators for assessing project complexity and progress at a given point in time, offering insights into activity specification completeness at hierarchical levels and overall project content completeness. Examples of complexity indicator calculations applied to real-world enterprise application system (EAS) projects are included. Finally, the paper describes enhancements to the Jira tool, including a causal Agile management repository and a prototype user interface. An experimental case study involving four Nordic EAS projects (using Scrum at the team level and SAFe at the program level) demonstrates that the Jira tool, when supplemented with causal analysis, can reveal missing links between themes and initiatives and align interdependencies between teams in real time. The causal Agile approach reduced the total number of requirements by an average of 13% and the number of change requests by 14%, indicating a significant improvement in project coordination and quality. Full article

This work investigates the solutions of fractional integro-differential equations (FIDEs) using a unique kernel operator within the Caputo framework. The problem is addressed using both analytical and numerical techniques. First, the two-step Adomian decomposition method (TSADM) is applied to obtain an exact solution (if it exists). In the second part, numerical methods are used to generate approximate solutions, complementing the analytical approach based on the Adomian decomposition method (ADM), which is further extended using the Sumudu and Shehu transform techniques in cases where TSADM fails to yield an exact solution. Additionally, we establish the existence and uniqueness of the solution via fixed-point theorems. Furthermore, the Ulam–Hyers stability of the solution is analyzed. A detailed error analysis is performed to assess the precision and performance of the developed approaches. The results are demonstrated through validated examples, supported by comparative graphs and detailed error norm tables ($L_{\infty }$, $L_2$, and $L_1$). The graphical and tabular comparisons indicate that the Sumudu-Adomian decomposition method (Sumudu-ADM) and the Shehu-Adomian decomposition method (Shehu-ADM) approaches provide highly accurate approximations, with Shehu-ADM often delivering enhanced performance due to its weighted formulation. The suggested approach is simple and effective, often producing accurate estimates in a few iterations. Compared to conventional numerical and analytical techniques, the presented methods are computationally less intensive and more adaptable to a broad class of fractional-order differential equations encountered in scientific applications. The adopted methods offer high accuracy, low computational cost, and strong adaptability, with potential for extension to variable-order fractional models. They are suitable for a wide range of complex systems exhibiting evolving memory behavior. Full article

In subway stations constructed using the cut-and-cover method, an increasing number of projects are adopting the form of precast components combined with on-site assembly. However, analysis of the novel structural elements within such overlapped subway stations remains inadequate. To simulate the shear failure mechanism at slab–wall joints, the structural behavior of these joints in overlapped subway stations is idealized as a rigid die stamping problem. An admissible failure mechanism is constructed, comprising a rigid wedge zone and a vertical tensile fracture perpendicular to a smooth base. The limit analysis approach is adopted, a two-dimensional velocity field is constructed, and the upper-bound theorem is applied to determine the bearing capacity of these joints under strip loading, utilizing a modified Coulomb yield criterion incorporating a small tensile stress cutoff. The failure mechanism proposed on the basis of an engineering case is validated through analytical calculations and parametric studies. Finally, a parametric analysis is conducted to investigate the influence of factors such as the geometric configuration of the slab–wall joints and the tensile and compressive strengths of concrete on their ultimate bearing capacity. The results obtained can provide an effective reference for the design and construction of precast slab–wall joints in future overlapped subway station projects. Full article

Urban rail transit (URT) systems are essential to ensuring efficient and sustainable urban mobility. However, the core components of operational planning, service frequency setting, train timetabling, and train allocation are often optimized separately, leading to fragmented decision-making and suboptimal system performance. This study addresses that gap by proposing an integrated optimization framework that simultaneously considers all three planning layers under time-dependent passenger demand conditions. The problem is formulated as a bi-objective Integer Nonlinear Programming (INLP) model, aiming to jointly minimize passenger waiting time and total operational cost. To solve this large-scale, combinatorial problem, a tailored Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is developed. The algorithm incorporates discrete variable handling, constraint-preserving mechanisms, and a customized encoding scheme that aligns with the structural characteristics of URT operations. The proposed framework is applied to real-world data from the Addis Ababa Light Rail Transit (AALRT) system. The results demonstrate that the MOPSO-based approach offers a more diverse and operationally feasible set of trade-off solutions compared to a widely used benchmark algorithm, NSGA-II. Specifically, it provides transit planners with a flexible decision-support tool capable of identifying schedules that balance service quality and cost, based on varying strategic or budgetary priorities. By integrating interdependent planning decisions into a unified model and leveraging the strengths of a customized metaheuristic algorithm, this study contributes a scalable, adaptable, and practically relevant methodology for improving the performance of urban rail systems. Full article

This paper addresses the stabilization problem in Boolean networks with time delays (TBNs) under state-flipped control. First, the algebraic form of TBNs under state-flipped control is derived utilizing the semi-tensor product (STP) of matrices. Based on their periodic properties, the TBNs are then partitioned into subsystems. Subsequently, leveraging these developments, the equivalence between the stabilization of the original TBNs and that of the derived subsystems under state-flipped control is established. Furthermore, an equivalent stabilization criterion for the TBNs under state-flipped control is provided. An algorithm is also presented for constructing a flipped-set sequence to achieve stabilization. Finally, illustrative examples are provided to demonstrate the effectiveness of the theoretical results. Full article

Generative video diffusion models (GVDs) generate high-fidelity, text-conditioned videos but risk producing unsafe or copyrighted content due to training on large, uncurated datasets. Concept erasure techniques aim to remove such harmful concepts from pre-trained models while preserving overall generative performance. However, existing methods mainly target single-concept erasure and thus cannot satisfy the demand for simultaneously eliminating multi-concept in real-world scenarios. On the one hand, naively applying single-concept erasure sequentially to multi-concept often yields suboptimal results due to conflicts among target concepts; on the other hand, methods that alter concept mappings exhibit very poor adaptability and fail to accommodate the dynamic concept changes. To address these, we propose ConceptVoid, a scalable multi-concept erasure framework formulated as a constrained multi-objective optimization problem. For each target concept, an erasure loss is defined as the discrepancy between noise predictions conditioned and unconditioned on the concept. Non-target generation capabilities are preserved via output-distribution alignment regularization. We apply the multiple gradient descent algorithm (MGDA) to obtain Pareto-optimal solutions, aiming to minimize conflicts among different concept erasure objectives. In addition, we improve MGDA by introducing an importance-weighting mechanism, which adjusts the weights of gradients corresponding to each erasure objective, enabling flexible control over the priority and intensity of erasing different concepts, thereby enhancing the scalability of ConceptVoid. Extensive experiments demonstrate the effectiveness of ConceptVoid, validating our key contributions: (1) a scalable framework for multi-concept erasure in GVDs; (2) the integration of per-concept erasure with distribution alignment to retain non-target quality; and (3) an enhanced MGDA for conflict-aware, controllable erasure. Full article

Wasserstein Generative Adversarial Networks (WGANs) have gained significant attention due to their theoretical foundations and effectiveness in generative modeling. However, training stability remains a major challenge, typically addressed through fixed gradient penalty (GP) techniques. In this paper, we propose an Adaptive Gradient Penalty (AGP) framework that employs a Proportional–Integral (PI) controller to adjust the gradient penalty coefficient ${\lambda }_t$ based on real-time training feedback. We provide a comprehensive theoretical analysis, including convergence guarantees, stability conditions, and optimal parameter selection. Experimental validation on MNIST and CIFAR-10 datasets demonstrates that AGP achieves an 11.4% improvement in FID scores on CIFAR-10 while maintaining comparable performance on MNIST. The adaptive mechanism automatically evolves penalty coefficients from 10.0 to 21.29 for CIFAR-10, appropriately responding to dataset complexity, and achieves superior gradient norm control with only 7.9% deviation from the target value compared to 18.3% for standard WGAN-GP. This work represents the first comprehensive investigation of adaptive gradient penalty mechanisms for WGANs, providing both theoretical foundations and empirical evidence for their advantages in achieving robust and efficient adversarial training. Full article

Unmanned Aerial Vehicles (UAVs) are known to have limited payloads, which challenges their widespread use in transporting heavy goods. Meanwhile, collaboration between multiple UAVs in performing such a task may be a promising solution. To address the issues associated with the simultaneous use of UAVs, this paper presents a formation control system for transporting a payload suspended via a cable using two UAVs. The control structure is based on a layered scheme that combines a null-space-based kinematic controller with a PID controller associated with each UAV (quadcopters) with a neural correction system. The null-space supervisor controller is designed to generate the desired velocity for the UAV system to maintain formation. This proposal aims to avoid obstacles, balance the weight distribution across each vehicle, and also reduce the payload trajectory tracking error. The PID controller associated with the neural correction system receives these desired speeds and performs dynamic compensation, taking into account parametric uncertainties and dynamic disturbances caused by the movement of the payload coupled to the UAV systems. The stability analysis of the entire control system is performed using Lyapunov theory. Detailed dynamic models of each UAV in the system, the flexible cables, and the payload are presented in a realistic scenario. Finally, numerical simulations demonstrate the good performance of the UAV system control in formation. Full article

Seismic retrofitting of reinforced concrete (RC) structures is essential for improving resilience and extending service life, particularly in regions with outdated building codes. However, selecting the optimal retrofitting strategy requires balancing multiple interdependent sustainability criteria—economic, environmental, and social—under expert-based uncertainty. This study presents a fuzzy hybrid multi-criteria decision-making (MCDM) approach that combines DEMATEL, DANP, and TOPSIS to represent causal interdependencies, derive interlinked priority weights, and rank retrofit alternatives. The assessment applies three complementary life cycle-based tools—cost-based, environmental, and social sustainability analyses following LCCA, LCA, and S-LCA frameworks, respectively—to evaluate three commonly used retrofitting strategies: RC jacketing, steel jacketing, and carbon fiber-reinforced polymer (CFRP) wrapping. The fuzzy-DANP methodology enables accurate modeling of feedback among sustainability dimensions and improves expert consensus through causal mapping. The findings identify CFRP as the top-ranked alternative, primarily attributed to its enhanced performance in both environmental and social aspects. The model’s robustness is confirmed via sensitivity analysis and cross-method validation. This mathematically grounded framework offers a reproducible and interpretable tool for decision-makers in civil infrastructure, enabling sustainability-oriented retrofitting under uncertainty. Full article

Reliable electricity supply in educational facilities demands predictive frameworks that reflect usage patterns and consumption variability. This study investigates electricity-consumption forecasting in lower-to-middle-income pre-tertiary institutions in Western Cape, South Africa, using adaptive neuro-fuzzy inference systems (ANFISs) optimized by evolutionary algorithms. Using genetic algorithm (GA) and particle swarm optimization (PSO) algorithms, the impact of two clustering techniques, Subtractive Clustering (SC) and Fuzzy C-Means (FCM), along with their cogent hyperparameters, were investigated, yielding several sub-models. The efficacy of the proposed models was evaluated using five standard statistical metrics, while the optimal model was also compared with other variants and hybrid models. Results obtained showed that the GA-ANFIS-FCM with four clusters achieved the best performance, recording the lowest Root Mean Square Error (RMSE) of 3.83, Mean Absolute Error (MAE) of 2.40, Theil’s U of 0.87, and Standard Deviation (SD) of 3.82. The developed model contributes valuable insights towards informed energy decisions. Full article

This study demonstrates the effectiveness of the differential transform method (DTM) in solving complex solid mechanics problems, focusing on static analysis of beams under various loads and boundary conditions. For cantilever beams (BSM1), DTM provided exact polynomial solutions for deflections and slopes: a cubic solution for concentrated end loads, a quadratic distribution for applied moments, and a fourth-degree polynomial for uniformly distributed loads, all matching established theoretical results. For simply supported beams (BSM2), DTM yielded solutions across two intervals for midspan concentrated forces, though required corrective terms for applied moments due to discontinuities. Under uniform loading, the method produced precise polynomial solutions with maximum deflection at midspan. Key advantages include DTM’s high-precision analytical solutions without additional approximations and its adaptability to diverse loading scenarios. However, for cases with pronounced discontinuities like concentrated moments, supplementary methods (e.g., Green’s functions) may be needed. The study highlights DTM’s potential for extension to nonlinear or dynamic problems, while software integration could broaden its engineering applications. This study demonstrates, for the first time, how DTM yields exact polynomial solutions for Euler–Bernoulli beams under discontinuous loads (e.g., concentrated moments), overcoming limitations of traditional numerical methods. The method’s analytical precision and avoidance of discretization errors are highlighted. Traditional methods like FEM require mesh refinement near discontinuities (e.g., concentrated moments), leading to computational inefficiencies. DTM overcomes this by providing exact polynomial solutions with corrective terms, achieving errors below 0.5% with only 4–5 series terms. Full article

The emergence of deep vision models such as convolutional neural networks and vision transformers has revolutionized computer vision, enabling significant advancements in image classification, object detection, and segmentation. In parallel, the rapid development of quantum computing has spurred interest in quantum machine learning (QML), which integrates the strengths of quantum computation with the representational power of deep learning. In QML, parameterized quantum circuits offer the potential to capture complex image features, define complex decision boundaries, and provide other computational advantages. This paper investigates hybrid quantum-classical vision architectures, with a focus on hybrid quantum-classical convolutional neural networks and hybrid quantum-classical vision transformers. These hybrid models explore both quantum pre-processing and post-processing of data, respectively, where quantum circuits are strategically integrated into the data pipeline to enhance model performance. Our results suggest that these hybrid models can enhance accuracy and computational efficiency in vision-related tasks, even with the constraints of current noisy intermediate-scale quantum devices. Full article

High dynamic range (HDR) tone mapping techniques have been widely studied to effectively represent the broad dynamic range of real-world scenes. However, generating an HDR image from multiple low dynamic range (LDR) images captured at different exposure levels can introduce ghosting artifacts in dynamic scenes. Moreover, methods that estimate HDR information from a single LDR image often suffer from inherent accuracy limitations. To overcome these limitations, this study proposes a novel image processing technique that extends the dynamic range of a single LDR image. This technique achieves the goal through leveraging a Convolutional Neural Network (CNN) to generate a synthetic Near-Infrared (NIR) image—one that emulates the characteristic of real NIR imagery being less susceptible to diffraction, thus preserving sharper outlines and clearer details. This synthetic NIR image is then fused with the original LDR image, which contains color information, to create a tone-distributed HDR-like image. The synthetic NIR image is produced using a lightweight U-Net-based autoencoder, where the encoder extracts features from the LDR image, and the decoder synthesizes a synthetic NIR image that replicates the characteristics of a real NIR image. To enhance feature fusion, a cardinality structure inspired by Extended-Efficient Layer Aggregation Networks (E-ELAN) in You Only Look Once Version 7 (YOLOv7) and a modified convolutional block attention module (CBAM) incorporating a difference map are applied. The loss function integrates a discriminator to enforce adversarial loss, while VGG, structural similarity index, and mean squared error losses contribute to overall image fidelity. Additionally, non-reference image quality assessment losses based on BRISQUE and NIQE are incorporated to further refine image quality. Experimental results demonstrate that the proposed method outperforms conventional HDR techniques in both qualitative and quantitative evaluations. Full article

Maritime mobile edge computing (MMEC) technology enables the deployment of high-precision, computationally intensive object detection tasks on resource-constrained edge devices. However, dynamic network conditions and limited communication resources significantly degrade the performance of static offloading strategies, leading to increased task blocking probability and delays. This paper proposes a scheduling and offloading strategy tailored for MMEC scenarios driven by object detection tasks, which explicitly considers (1) the hierarchical structure of object detection models, and (2) the sporadic nature of maritime observation tasks. To minimize average task completion time under varying task arrival patterns, we formulate the average blocking delay minimization problem as a Markov Decision Process (MDP). Then, we propose an Orthogonalization-Normalization Proximal Policy Optimization (ON-PPO) algorithm, in which task category states are orthogonally encoded and system states are normalized. Experiments demonstrate that ON-PPO effectively learns policy parameters, mitigates interference between tasks of different categories during training, and adapts efficiently to sporadic task arrivals. Simulation results show that, compared to baseline algorithms, ON-PPO maintains stable task queues and achieves a $22.9\%$ reduction in average task latency. Full article

We propose a novel Bayesian wavelet regression approach using a three-component spike-and-slab prior for wavelet coefficients, combining a point mass at zero, a moment (MOM) prior, and an inverse moment (IMOM) prior. This flexible prior supports small and large coefficients differently, offering advantages for highly dispersed data where wavelet coefficients span multiple scales. The IMOM prior’s heavy tails capture large coefficients, while the MOM prior is better suited for smaller non-zero coefficients. Further, our method introduces innovative hyperparameter specifications for mixture probabilities and scale parameters, including generalized logit, hyperbolic secant, and generalized normal decay for probabilities, and double exponential decay for scaling. Hyperparameters are estimated via an empirical Bayes approach, enabling posterior inference tailored to the data. Extensive simulations demonstrate significant performance gains over two-component wavelet methods. Applications to electroencephalography and noisy audio data illustrate the method’s utility in capturing complex signal characteristics. We implement our method in an R package, NLPwavelet (≥1.1). Full article

This paper presents a novel adaptive fixed-time sliding mode control (AFxTSMC) framework for industrial manipulators. The proposed adaptive reaching law (ARL) enables rapid and stable gain reduction by leveraging the current parameter values to maintain positivity and prevent sign reversals, thereby reducing chattering. Additionally, the ARL guarantees fixed-time convergence. A singularity-free fixed-time sliding function (SF-FxTSF) ensures fast, robust, and singularity-free convergence. To enhance robustness, a modified third-order sliding mode observer (TOSMO) is integrated into the control framework. This observer estimates both internal uncertainties and external disturbances with improved estimation speed, enabling effective compensation while maintaining convergence performance. A Lyapunov-based analysis rigorously confirms the stability of the proposed method. Simulations of the SAMSUNG FARA AT2 manipulator indicate superior tracking accuracy, faster convergence, and smoother control performance compared to the three state-of-the-art methods. These results underscore the proposed method’s advantages as a robust, scalable, and high-performance control solution for industrial robotic systems. Full article

Distributed permutation flowshop scheduling is an NP-hard problem that has become a hot research topic in the fields of optimization and manufacturing in recent years. Multimodal optimization finds multiple global and local optimal solutions of a function. This study proposes a harmony search algorithm with iterative optimization operators to solve the NP-hard problem for multimodal optimization with the objective of makespan minimization. First, the initial solution set is constructed by using a distributed NEH operator. Second, after generating new candidate solutions, efficient iterative optimization operations are applied to optimize these solutions, and the worst solutions in the harmony memory (HM) are replaced. Finally, the solutions that satisfy multimodal optimization of the harmony memory are obtained when the stopping condition of the algorithm is met. The constructed algorithm is compared with three meta-heuristics: the iterative greedy meta-heuristic algorithm with a bounded search strategy, the improved Jaya algorithm, and the novel evolutionary algorithm, on 600 newly generated datasets. The results show that the proposed method outperforms the three compared algorithms and is applicable to solving distributed permutation flowshop scheduling problems in practice. Full article