This study introduces a novel one-parameter probability distribution called the QGamma distribution (QGaD), constructed through a specific mixture of the exponential and Chris–Jerry distributions. The mathematical properties of the QGaD are thoroughly investigated, including its probability density function, cumulative distribution function, moments, variance, mean residual life function, order statistics, and hazard rate function. Fifteen classical estimation methods are employed to estimate its parameter, with their performance evaluated through a Monte Carlo simulation. The flexibility and modeling capability of the proposed distribution are assessed by comparing it with several well-known distributions, including the exponential, Chris–Jerry, gamma, sine exponential, Shanker, Lindley, and X-Lindley distributions. The empirical results reveal that the QGaD provides superior fits to real-world data based on standard goodness-of-fit measures. Overall, the findings highlight the potential of the QGaD as a robust and flexible tool for modeling lifetime and reliability data. The study concludes that QGaD makes a valuable contribution to the development of statistical models, particularly in contexts that require a parsimonious yet versatile distribution.
Randomized controlled trials (RCTs) are often considered the gold standard for causal inference, but their implementation can be costly, time-consuming, and sometimes infeasible due to ethical or practical constraints. The so-called target trial emulation framework introduced the systematic use of observational data for treatment effect. This approach necessitates the detailed specification of a hypothetical trial protocol including eligibility criteria, treatment strategies, and outcome measures, which are then emulated by utilizing observational data. We expanded the target trial framework by integrating drug pathway embeddings and causal modeling, enabling prediction of treatment outcomes for unseen or held-out mechanisms of action based on the embedding relationships among existing therapies. We demonstrate that embedding-based models can reliably predict the direction of observed clinical outcomes across diverse therapeutic classes (e.g., small molecules, biologics), even when masking the observational data for the particular mechanism being estimated, though the precise magnitude of treatment effect remains hard to recover. This approach illustrates the potential to estimate the clinical efficacy of new drug mechanisms and to enhance the precision of future trial design and operations.
This paper explores the dynamic behavior and control of a novel 4D fractional-order hyperchaotic Yan system, characterized by transitions between stability, periodicity, and chaos, driven by fractional-order parameters and initial conditions. The system’s complex nonlinear dynamics are comprehensively analyzed using phase portraits, bifurcation diagrams, Lyapunov exponents, Poincaré maps, and the 0–1 test, revealing a broad spectrum of behaviors influenced by variations in system parameters and fractional-order effects. A robust backstepping control strategy is implemented to achieve synchronization and ensure system stability. Additionally, a radial basis function neural network (RBFNN) is used to model the system dynamics with high accuracy, as shown by a minimal root mean square error. This study presents an innovative approach that combines data-driven modeling with the Yan system, offering enhanced insights into their intricate dynamics. The results align closely with numerical solutions based on the Caputo derivative, underscoring the accuracy and reliability of the RBFNN methodology.
Subdivision schemes are widely used in computer-aided geometric design and computer graphics for generating smooth curves from discrete control polygons. This paper presents a general transformation framework for constructing the corresponding 4-point relaxed quaternary subdivision schemes from 3-point relaxed binary subdivision schemes. The proposed framework requires only the subdivision mask of the binary scheme and is applicable to both parametric and non-parametric subdivision schemes. The resulting quaternary schemes preserve the fundamental properties of their binary counterparts, including continuity, polynomial generation, polynomial reproduction, and shape-preserving characteristics. In many cases, they also possess an enlarged continuity parameter range and increased Hölder regularity. Several examples are presented to demonstrate the applicability of the proposed framework and to illustrate the relationship between the binary subdivision schemes and their corresponding quaternary subdivision schemes. The graphical results show that the transformed quaternary schemes preserve the geometric behavior of their binary counterparts while producing smoother limit curves with fewer subdivision iterations. The proposed framework provides a systematic and efficient approach for establishing the connection between binary and quaternary subdivision schemes and for constructing quaternary schemes directly from existing binary schemes.
Delay differential equations form a distinct class of differential equations in which the derivative of the dependent variable depends on its value at an earlier time. This unique structure makes them particularly suitable for modeling phenomena in areas such as population dynamics, epidemiology, and the spread or control of diseases. In this study, a high-order Haar wavelet collocation method (HoHWCM) is proposed for the numerical solution of second-order delay differential equations (SoDDEs). The delay term is approximated using a Taylor expansion, transforming the SoDDE into a standard second-order differential equation (SoDE). The nonlinear terms are linearized through an innovative Taylor series-based approach, which also serves as an efficient iterative scheme. The resulting SoDE is then discretized using Haar wavelet basis functions, yielding a system of linear algebraic equations that is solved iteratively. This strategy eliminates the need for Newton’s or Broyden’s methods, thereby reducing computational cost and improving time efficiency. A variety of linear and nonlinear benchmark problems are solved to evaluate the accuracy and efficiency of the proposed method. Comparative results with established approaches from the literature demonstrate that the HoHWCM achieves higher accuracy, faster convergence, and reduced computational time, making it a highly effective alternative for solving such problems.
This article establishes new retarded nonlinear integral inequalities that extend and generalize several known results in the literature, including recently reported estimates. These inequalities are used to derive explicit bounds for the unknown functions. These bounds are shown to be sharper and more general than existing ones, recovering earlier results as special cases. As an application, the derived inequalities are used to study the boundedness, uniqueness, and global existence of solutions to an initial value problem for a class of nonlinear integro-differential equations with delay. An illustrative example is presented to illustrate the applicability and effectiveness of the results.
This study investigates the influence of liner elastic deformation on the static performance and dynamic stability of grooved rubber journal bearings (GRJBs) using the finite element method (FEM) in conjunction with a Winkler elastic foundation model. The formulation is validated through comparison with the limiting case of a plain circular bearing. Increasing the effective liner stiffness (k^) reduces liner compliance and consequently shifts the overall system response toward that of a rigid bearing. For configurations with 6, 9, and 12 grooves, raising the effective liner stiffness from 0.4 to 4 GPa/mm increases the maximum hydrodynamic pressure by approximately 8–15% and enhances the load-carrying capacity by about 5–8%. The variation in key performance indicators becomes progressively less sensitive beyond an approximate threshold, entering a low-sensitivity region near 1.5 GPa/mm. Dynamic stability is assessed through linear perturbation of the journal center about its static equilibrium position. The stiffness and damping matrices are derived from the perturbed lubricant-film pressure response, capturing both restoring forces and squeeze-film effects. The results indicate that increasing effective liner stiffness generally strengthens the direct stiffness and damping behavior and raises the dimensionless critical mass, suggesting an improved stability margin under the investigated conditions. The influence of groove number on dynamic response is also significant. Fewer grooves tend to promote a more favorable balance between restoring and damping actions, whereas higher groove counts can reduce the stability margin despite improvements in lubricant supply characteristics. Among the studied cases, the 6-groove bearing yields the highest predicted critical mass and linear stability margin, while the 9-groove configuration provides the highest vertical direct stiffness coefficient. Overall, the findings emphasize that the groove number and effective liner stiffness should be optimized jointly, as static performance improvements do not necessarily translate into proportional gains in dynamic stability.
Encoder-decoder segmentation networks use skip connections to recover spatial detail, but direct feature transfer can also propagate irrelevant high-frequency responses into the decoder. This problem is pronounced at weak or irregular tumor margins, where contour evidence is useful but should not modify semantically reliable features indiscriminately. We propose Bridge-Net, a boundary-ambiguity guided residual injection framework for two-dimensional brain tumor MRI segmentation. Bridge-Net formulates boundary enhancement as a conditional feature-correction problem. A structural boundary prior is coupled multiplicatively with an ambiguity map obtained from an auxiliary foreground logit. The ambiguity cue is deterministic and probability-based, rather than a Bayesian or calibrated uncertainty estimate. The overlap between the two cues identifies locations that are both boundary-like and prediction-ambiguous. A level-specific gated residual branch then injects the resulting cue into each skip feature, while a zero-initialized bounded scaling factor preserves an identity-like main pathway at the start of optimization. Experiments were conducted on TCGA-LGG and BRISC2025 under dataset-specific protocols, including patient-level partitioning for TCGA-LGG and the official image-level split for BRISC2025. Bridge-Net achieved Dice/IoU/HD95 values of 84.16%/73.65%/15.38 on TCGA-LGG and 87.26%/77.63%/8.68 on BRISC2025. Patient-level paired analysis on TCGA-LGG and image-level paired analysis on BRISC2025 further supported the improvements over UCTransNet. Ablation results support the complementary roles of structural boundary and probability-ambiguity cues, and a same-seed repeated-run comparison across reproduced models supports the stability of the observed performance trend under the tested setting. Relative to UCTransNet, the proposed mechanism increases the parameter count from 7.982 M to 7.988 M and FLOPs from 24.083 G to 24.196 G at 256×256 resolution. These results indicate that ambiguity-filtered boundary residual fusion introduces only a small increase in parameter count and FLOPs for boundary-ambiguous MRI segmentation, although broader patient-level and volumetric validation remains necessary.
Predicting systemic stress in high-dimensional equity markets remains challenging, owing to non-stationarity, heavy tails, and regime shifts. This paper introduces GWS-STNet (Gaussian-Weighted Swin Spatio-Temporal Network), a deep learning architecture grounded in functional analysis and thermodynamic analogy. A Gaussian-Weighted Swin Operator (Gσ) replaces the standard shifted-window attention mechanism with a kernel-regularised counterpart on the Hilbert space (H) of financial spatio-temporal voxels. The principal theoretical contribution is a proof, via the Banach Fixed-Point Theorem, that the window-level attention operator (Gσ) is a strict contraction (Lipschitz constant of κ<1) under a bandwidth of σ<(2π)−1/2, guaranteeing convergence of internal network representations to a unique fixed point. Metabolic Saliency (Sms), derived from the exact Jacobian of the Power Mapping Network (PMNet) weighted by pairwise transfer entropy, provides intrinsic, post hoc-free attribution of sector-level stress contributions. Empirical validation on 15 large-capitalisation JSE securities (T=2857 trading days, January 2015–December 2025) with Eskom load-shedding stages as exogenous stress injectors shows that GWS-STNet outperforms nine baselines, including classical benchmarks (Random Walk and AR(1)) and state-of-the-art Transformers across RMSE, MAE, the Gaussian Calibration Score (GCS), and the Metabolic Efficiency Ratio (MER), with Diebold–Mariano p<0.001.
This paper addresses adaptive fuzzy tracking control for fractional-order nonlinear systems (FONSs) subject to asymmetric state constraints without imposing separate feasibility conditions on intermediate virtual controllers. Fuzzy logic systems are used to approximate the unknown nonlinear functions. By exploiting the boundedness of the hyperbolic tangent function, a coordinate transformation and an asymmetric fractional barrier Lyapunov function (AFBLF) are developed to construct bounded virtual control signals. Within a backstepping framework, an adaptive fuzzy controller is designed. Fractional-order Lyapunov analysis establishes semi-global uniform ultimate boundedness of all closed-loop signals and preservation of the prescribed asymmetric constraints. Comparative and benchmark simulations demonstrate constraint satisfaction, moderate control effort, and suppression of high-frequency chattering-like oscillations.
Volatility regime identification underpins risk management and portfolio allocation in quantitative finance, yet standard mixture models fail in heavy-tailed environments: components are consumed by outliers rather than genuine persistent regimes. We propose the Bayesian Spike-and-Slab Finite Mixture with Adaptive Tail Regularisation (BSS-FM-ATR), which resolves this at the component level via a spike-and-slab prior on the degrees-of-freedom parameter νk. A latent binary indicator assigns each component to a slab state (data-driven tail adaptation for genuine regimes) or a spike state (inert heavy-tail absorber for artefacts). Applied to 19 JSE blue-chip securities over December 2019 to December 2025—spanning the COVID-19 crash and Eskom load-shedding episodes—BSS-FM-ATR achieves the highest silhouette score (0.3809 on the full dataset), regime persistence (0.9391), and interpretability (0.800) across nine standard baselines, including Gaussian HMM, MS-AR, MS-GARCH(1,1), and Bayesian Changepoint detection, plus three outlier-component comparators (Contaminated–Normal Mixture, TCLUST, and robust Bayesian mixture). A complete rerun after removing the contaminated observations confirms that ARI (Δ=−0.0283) and persistence (Δ=+0.0105) remain stable; the silhouette reduction (from 0.3809 to 0.3773) is a positive finding: it confirms that the spike-state component R3 was correctly identified as a compact, well-separated artefact cluster whose removal reveals the genuine regime structure. This dual validation establishes BSS-FM-ATR’s role as both a regime identifier and a data quality filter. The method isolates a Yahoo Finance data-contamination artefact (n=21, January–February 2025) through a principled spike-and-slab mechanism, providing an explicit posterior probability p(γ3=0∣X)>0.99 of artefact status: a structural identifier that contaminated-normal and robust Bayesian alternatives cannot supply, establishing its value as both a regime identifier and a data quality filter for financial monitoring systems.
This paper identifies and characterizes the background driving Lévy process (BDLP) associated with the Generalized Tempered Stable (GTS) distribution, a flexible seven-parameter family of infinitely divisible distributions with applications in physics and quantitative finance. We show that the corresponding BDLP is a finite-variation, infinite-activity Type B Lévy process and derive its explicit background driving characteristic exponent function (BDCEF). The resulting BDLP provides a unified representation that encompasses several important special cases, including the bilateral stable, bilateral Gamma, and Variance Gamma distributions. Building on these results, we develop a simulation framework based on a stationary Ornstein–Uhlenbeck (OU)-type process driven by the GTS BDLP. The mean-reversion speed parameter of the OU process is calibrated using maximum likelihood estimation applied to daily return data from the SPY ETF and Ethereum over the period 2010–2024. The proposed simulation methodology produces realistic daily cumulative return trajectories, and comprehensive numerical error analyses demonstrate the accuracy and efficiency of the resulting discretization scheme. These findings provide both a theoretical extension of Lévy-driven OU models and a practical framework for simulating complex financial return dynamics.
Rotary and vibro-rotary burnishing create regular arrays of imprints whose geometric interaction depends on the pitch, indentation depth, and relative curvature of the tool–workpiece pair. This paper develops a unified kinematic–curvature model that maps machine settings to an imprint layout on the unwrapped cylindrical surface and constructs the relative curvature tensor. The tensor state and full normalized neighbor metric assign the contact state to one of four mutually exclusive categories: non-elliptic, cell-limited, near-conformal (warning), or isolated elliptic. The tensor formulation is invariant under rotation of the tangent basis and provides a common geometric mapping for external cylinders and internal tubes. The kinematic map and tensor classification are independent of the rigid-plastic mean-pressure approximation and are verified by the factor relation between the center-line slope and imprint orientation, tensor invariance, limiting cases, and a closed-form identity. The calibrated approximation is used solely to estimate the maximum-load penetration and an equivalent projected footprint. At a fixed normal force and effective hardness, the projected area is identical in all curvature cases, whereas the curvature changes the penetration and footprint aspect ratio. Neglecting the workpiece curvature underestimates the external cylinder indentation depth by about 5.8% relative to the full tensor calculation; this ratio is independent of the force and effective hardness within the approximation. For the stated internal tube row pitch and hardness, the axis-aligned cell-limited transition force is 5–8 N. Evaluation with the full metric shows that the consecutive-event vectors are separated well; the periodic-row neighbor nevertheless places the reference case in the cell-limited class. A closed-form expression for this transition force is derived. The model provides a transition criterion verified by analytical identity and consistency checks; residual geometry and post-threshold pressure redistribution require unloading calibration and a periodic unilateral contact formulation, respectively.
Multiscale models for infectious disease systems are highly nonlinear. This presents substantial difficulties for both analysis and computation. Consequently, there is a continuous demand for the development of efficient numerical methods that provide reliable solutions. Over time, various numerical techniques have been developed for single-scale models. However, multiscale models have increasingly relied on built-in solvers and, more recently, the nonstandard finite difference method. The primary aim of this study is to offer an in-depth examination of the multistage spectral relaxation method (MSRM) applied to the multiscale model characterising norovirus infection. This study also provides a comprehensive comparison with the nonstandard finite difference method (NSFDM) in terms of convergence and accuracy, as well as their handling of highly nonlinear systems of ordinary differential equations. Both schemes were validated against an adaptive ODE45 scheme in MATLAB2025a, which served as the reference solver. The numerical outcomes indicate that the MSRM achieves a better accuracy level, with relative L2 errors ranging from 10−9 to 10−7 for Δτ≤0.10 and Nch=8. In contrast, the NSFDM provides solid first-order accuracy, yielding L2 errors around 10−4, while ensuring strict unconditional positivity and stability across all tested step sizes from h=0.01 to 2.0. This study features a parameter sensitivity analysis that varies βH,δH,αh,μV,μH, as well as semi-log error graphs, convergence rate visuals, and CPU performance benchmarks. The MSRM costs about 24 times more per run, but it offers better accuracy for between-host variables. This makes it the preferred method for high-fidelity applications. In contrast, the NSFDM is the best option for quick parameter sweeps and long simulations that require guaranteed positivity.
Urban traffic congestion remains a major challenge for modern cities, requiring intelligent traffic signal control (TSC) strategies capable of adapting to dynamic traffic conditions. This paper proposes a hybrid reinforcement learning approach for traffic signal control that combines the complementary learning mechanisms of Q-learning, SARSA, and Monte Carlo algorithms to improve both learning efficiency and control performance. The proposed approach is implemented and evaluated using the Simulation of Urban MObility (SUMO) simulator on a realistic road network corresponding to the “Route de Sefrou” in Fez, Morocco. The traffic signal controller is trained through continuous interaction with the simulated environment and compared with the three individual reinforcement learning algorithms under identical experimental conditions. The experimental results demonstrate that the proposed hybrid approach provides more efficient traffic management, faster convergence, and greater learning stability than the individual algorithms. These findings demonstrate the potential of hybrid reinforcement learning as an effective solution for adaptive traffic signal control in realistic urban environments.
In this paper, we investigate the Ulam stability problem for a second-order discrete matrix difference equation with a single delay. The primary aim of this work is to establish rigorous Ulam-type stability criteria for this class of delayed matrix difference systems. Firstly, we formally define Hyers–Ulam stability (HUS) and Hyers–Ulam–Rassias stability (HURS) tailored to delayed discrete matrix equations, and derive an essential norm estimate for the delayed discrete matrix function (DDMF). Relying on this critical norm inequality, we further derive sufficient conditions to guarantee the Hyers–Ulam and Hyers–Ulam–Rassias stability of the addressed equation, which constitute the core theoretical contributions of this study. Compared with the existing literature, the obtained stability judgments are less conservative and applicable to second-order matrix delayed difference models rarely discussed in previous works. Finally, several numerical examples are presented to demonstrate the correctness and effectiveness of the derived theoretical conclusions.
In this work, we propose an inertial proximal splitting algorithm for the split variational inclusion problem in real Hilbert space, in which a new stepsize rule is provided for avoiding the case that the original stepsize equals to zero, It also helps enlarge the value range of the stepsize parameter. A weak and strong convergence theorem is established under mild conditions. Additionally, our obtained result is extended to split feasibility problems and split minimization problems. Finally, some numerical experiments are conducted to illustrate and compare.
With the rapid deployment of Internet of Things appliances in smart homes, making efficient energy scheduling is a critical necessity to satisfy their exponentially increased residential energy demand. The problem of optimizing appliance operational times in smart homes is known as the Appliance Energy Scheduling Problem, which is a complex, NP-hard multi- objective challenge. Various metaheuristic algorithms have been utilized by researchers to address this problem; existing methods often struggle with slow convergence rates and are trapped in local optima. To overcome these limitations and produce a superior solution, this study proposes a new hybrid framework that integrates the Coronavirus Herd Immunity Optimizer (CHIO) with Lévy Flight (LF). By strategically embedding LF into the CHIO framework, the proposed method effectively balances exploration and exploitation search capabilities to achieve true global optimization. In the evaluation stage, three structural variations in hybrid CHIO models are evaluated against the standard appliance energy scheduling problem to determine the robust model and compare its performance with prominent existing methods in the literature. The experimental results demonstrate the superiority of the optimized CHIOLF-2 approach among other hybrid CHIO models. The CHIOLF-2 successfully navigates the trade-off between grid efficiency and user experience by achieving a reduction in electricity bills and the Peak-to-Average Ratio while maximizing user comfort through minimized appliance waiting times. Eventually, this research produces a highly efficient scheduling framework for modern smart homes and offers a versatile algorithmic design that can be readily adapted to address other complex real-world optimization problems.
For life-threatening events, such as fire hazards, performing real experiments (human-based experiments) to investigate the movement dynamics of occupants is often impractical due to different ethical, safety, and cost constraints. Consequently, realistic crowd movement models are essential for analyzing evacuation behavior. In this work, a modified social force model is proposed to simulate more reasonable movement patterns and prevent the unrealistic behavior of directly moving to and getting close to a fire source. The proposed model considers changes in stress levels caused by exposure to fire and incorporates their effects on escape behavior. Unlike most previous work, the non-homogeneity of occupants’ characteristics and physical abilities are considered. Simulation results show that the proposed model can provide more reasonable movement trajectories to avoid fire sources during emergency evacuation. Furthermore, the impacts of the location of the fire and the width of the exit on the performance of the evacuation process are investigated.
Analyses of electric two-wheeler (E2W) accident causes often overlook individual heterogeneity and non-linear effects among influencing factors, causing risk prediction models to fail. Based on 742 motor vehicle–E2W collisions from the China In-Depth Accident Study (CIDAS) database, we established the correlated random parameter ordered probit model with heterogeneity in means (CRPOPH) and the generalized additive model (GAM) to analyze the effects of discrete and continuous variables on E2W accident severity. The results show that injury severity increases significantly for the following characteristics: male, 51–60 years old, <170 cm, SUV or truck, intersection road, non-asphalt pavement, daytime and side impact accidents. With all other factors held constant, injury severity decreases with increasing seat height and seat–handlebar distance; when the wheelbase is approximately between 1000 mm and 1400 mm, injury severity tends to be the lowest; when the E2W speed is about 15–30 km/h, injury severity is positively correlated with speed; in other speed ranges, E2W speed is negatively correlated with injury severity. Compared with traditional linear models, the proposed method achieves both high interpretability and high fitting accuracy in modeling E2W accident severity.
