AppliedMath

Tumor angiogenesis models based on coupled nonlinear parabolic partial differential equations require solving stiff systems where explicit time-stepping methods impose severe stability constraints on the time step size. Implicit–Explicit (IMEX) schemes relax this constraint by treating diffusion terms implicitly and reaction–chemotaxis terms explicitly, reducing each time step to a single linear system solution. However, standard Gaussian elimination with partial pivoting exhibits cubic complexity in the number of spatial grid points, dominating computational cost for realistic discretizations in the range of 400–800 grid points. This work presents a CUDA-based parallel algorithm that accelerates the IMEX scheme through GPU implementation of three core computational kernels: pivot finding via atomic operations on double-precision floating-point values, row swapping with coalesced memory access patterns, and elimination updates using optimized two-dimensional thread grids. Performance measurements on an NVIDIA H100 GPU demonstrate speedup factors, achieving speedup factors from 3.5× to 113× across spatial discretizations spanning $M\in [25,800]$ grid points relative to sequential CPU execution, approaching 94.2% of the theoretical maximum speedup predicted by Amdahl’s law. Numerical validation confirms that GPU and CPU solutions agree to within twelve digits of precision over extended time integration, with conservation properties preserved to machine precision. Performance analysis reveals that the elimination kernel accounts for nearly 90% of total execution time, justifying the focus on GPU parallelization of this component. The method enables parameter studies requiring $\sim {10}^4$ PDE solves, previously computationally prohibitive, facilitating model-driven investigation of anti-angiogenic therapy design. Full article

A novel statistical model, the Bounded Gamma–Gompertz Distribution (BGGD), is presented alongside a full characterization of its properties. Our investigation identifies maximum-likelihood estimation (MLE) as the most effective fitting procedure, proving it to be more consistent and efficient than alternative approaches like L-moments and Bayesian estimation. Empirical validation on Tesla (TSLA) financial records—spanning open, high, low, close prices, and trading volume—showcased the BGGD’s superior performance. It delivered a better fit than several competing heavy-tailed distributions, including Student-t, Log-Normal, Lévy, and Pareto, as indicated by minimized AIC and BIC statistics. The results substantiate the distribution’s robustness in capturing extreme-value behavior, positioning it as a potent tool for financial modeling applications. Full article

Forecasting stock prices remains a central challenge in financial modelling, as markets are influenced by market sentiment, firm-level fundamentals and complex interactions between macroeconomic and microeconomic factors, for example. This study evaluates the predictive performance of both classical statistical models and advanced attention-based deep learning architectures for daily stock price forecasting. Using a dataset of major U.S. equities and Exchange Traded Funds (ETFs) covering 2012–2024, we compare traditional statistical approaches, Seasonal Autoregressive Integrated Moving Average (SARIMA) and Exponential Smoothing (ES) in the Error, Trend, Seasonal (ETS) framework, with deep learning architectures such as the Temporal Fusion Transformer (TFT), and a novel hybrid model, the TFT-Graph Neural Network (TFT-GNN), which incorporates relational information between assets. All models are assessed under consistent experimental conditions in terms of forecast accuracy, computational efficiency, and interpretability. Our results indicate that while statistical models offer strong baselines with high stability and low computational cost, the TFT outperforms them in capturing short-term nonlinear dependencies. The hybrid TFT-GNN achieves the highest overall predictive accuracy, demonstrating that relational signals derived from inter-asset connections provide meaningful enhancements beyond traditional temporal and technical indicators. These findings highlight the advantages of integrating relational learning into temporal forecasting frameworks and emphasise the continued relevance of statistical models as interpretable and efficient benchmarks for evaluating deep learning approaches in high-frequency financial prediction. Full article

In this paper, we incorporate a new type of fear effect into a predator–prey time-delay model to study their combined impact on the system’s dynamics. Without time delay, our results show that the prey-only and coexistence equilibrium points are globally asymptotically stable under certain conditions. We also find that a transcritical bifurcation occurs near the prey-only equilibrium, while a Hopf bifurcation arises near the coexistence equilibrium. The fear effect plays a crucial role in the system’s behavior, as it can lead to predator extinction or near-extinction of the prey. Moreover, the inclusion of time delay influences the coexistence equilibrium, potentially destabilizing it and giving rise to a stable limit cycle. Full article

This paper considers a continuous review inventory system for two interconnected product types, 1 and 2. Product type 1 is purchased from an external agency, whereas type 2 is manufactured in-house through a sequential batching process. The maximum stock position attainable by type 1 is $S_1$ and that of type 2 is $S_2$. Unit demands arise independently for the two products, where type 1 demand arrives following a Poisson process with rate ${\lambda }_1$ and that for product B also follows a Poisson process with rate ${\lambda }_2$. At the instance of the stock level of type 1 dropping to zero, it is replenished instantaneously to the maximum level $S_1$, such that the stock level is never zero, and hence all demands for type 1 product are satisfied. The production machine attached to type 2 stops manufacturing immediately when its stock level reaches $S_2$, and resumes immediately when the stock level drops to $S_2-1$. In the event of the type 2 product not being available when demand arrives, it is substituted with the type 1 product with probability p. The production time for a single unit of type 2 is exponentially distributed with mean ${\displaystyle \frac{1}{\gamma }}$. We identify the underlying Markov process and analyse the performance of the interconnected inventory system. Full article

Based on noncommutative relations and the Dirac canonical dequantization scheme, I generalize the canonical Poisson bracket to a deformed Poisson bracket and develop a non-canonical formulation of the Poisson, Hamilton, and Lagrange equations in the deformed Poisson and symplectic spaces. I find that both of these dynamical equations are the coupling systems of differential equations. The noncommutivity induces the velocity-dependent potential. These formulations give the Noether and Virial theorems in the deformed symplectic space. I find that the Lagrangian invariance and its corresponding conserved quantity depend on the deformed parameters and some points in the configuration space for a continuous infinitesimal coordinate transformation. These formulations provide a non-canonical framework of classical mechanics not only for insight into noncommutative quantum mechanics, but also for exploring some mysteries and phenomena beyond those in the canonical symplectic space. Full article

Background: Realistic simulation of ECG signals is essential for validating signal-processing algorithms and training artificial intelligence models in cardiology. Many existing approaches model either waveform morphology or heart rate variability (HRV), but few achieve both with high accuracy. This study proposes a hybrid method that combines morphological accuracy with physiological variability. Methods: We developed a mathematical model that integrates Gaussian mesa functions (GMF) for waveform generation and a chaotic Rössler attractor to simulate RR-interval variability. The GMF approach allows fine control over the amplitude, width, and slope of each ECG component (P, Q, R, S, T), while the Rössler system introduces dynamic modulation through the use of seven parameters. Spectral and statistical analyses were applied, including power spectral density (PSD) computed via the Lomb–Scargle, STFT, CWT, and histogram analyses. Results: The synthesized signals demonstrated physiological realism in both the time and frequency domains. The LF/HF ratio was 1.5–2.0 when simulating a normal rhythm and outside these limits in a simulated stress rhythm, consistent with typical HRV patterns. PSD analysis captured clear VLF (0.003–0.04 Hz), LF (0.04–0.15 Hz), and HF (0.15–0.4 Hz) bands. Histogram distributions showed amplitude ranges consistent with real ECGs. Conclusions: The hybrid GMF–Rössler approach enables large-scale ECG synthesis with controllable morphology and realistic HRV. It is computationally efficient and suitable for artificial intelligence training, diagnostic testing, and digital twin modeling in cardiovascular applications. Full article

Early and accurate diagnosis of Alzheimer’s disease is critical for effective clinical intervention, particularly in distinguishing it from mild cognitive impairment, a prodromal stage marked by subtle structural changes. In this study, we propose a hybrid deep learning ensemble framework for Alzheimer’s disease classification using structural magnetic resonance imaging. Gray and white matter slices are used as inputs to three pretrained convolutional neural networks: ResNet50, NASNet, and MobileNet, each fine-tuned through an end-to-end process. To further enhance performance, we incorporate a stacked ensemble learning strategy with a meta-learner and weighted averaging to optimally combine the base models. Evaluated on the Alzheimer’s Disease Neuroimaging Initiative dataset, the proposed method achieves state-of-the-art accuracy of 99.21% for Alzheimer’s disease vs. mild cognitive impairment and 91.02% for mild cognitive impairment vs. normal controls, outperforming conventional transfer learning and baseline ensemble methods. To improve interpretability in image-based diagnostics, we integrate Explainable AI techniques by Gradient-weighted Class Activation Mapping, which generates heatmaps and attribution maps that highlight critical regions in gray and white matter slices, revealing structural biomarkers that influence model decisions. These results highlight the framework’s potential for robust and scalable clinical decision support in neurodegenerative disease diagnostics. Full article

Neuronal circuits arise as axons and dendrites extend, navigate, and connect to target cells. Axonal growth, in particular, integrates deterministic guidance from substrate mechanics and geometry with stochastic fluctuations generated by signaling, molecular detection, cytoskeletal assembly, and growth cone dynamics. A comprehensive quantitative description of this process remains incomplete. We review stochastic models in which Langevin dynamics and the associated Fokker–Planck equation capture axonal motion and turning under combined biases and noise. Paired with experiments, these models yield key parameters, including effective diffusion (motility) coefficients, speed and angle distributions, mean-square displacement, and mechanical measures of cell–substrate coupling, thereby linking single-cell biophysics and intercellular interactions to collective growth statistics and network formation. We further couple the Fokker–Planck description to a mechanochemical actin–myosin–clutch model and perform a linear stability analysis of the resulting dynamics. Routh–Hurwitz criteria identify regimes of steady extension, damped oscillations, and Hopf bifurcations that generate sustained limit cycles. Together, these results clarify the mechanisms that govern axonal guidance and connectivity and inform the design of engineered substrates and neuroprosthetic scaffolds aimed at enhancing nerve repair and regeneration. Full article

Material failure by adiabatic shear is analyzed in viscoplastic metals that can demonstrate up to three distinct softening mechanisms: thermal softening, ductile fracture, and melting. An analytical framework is constructed for studying simple shear deformation with superposed static pressure. A continuum power-law viscoplastic formulation is coupled to a ductile damage model and a solid–liquid phase transition model in a thermodynamically consistent manner. Criteria for localization to a band of infinite shear strain are discussed. An analytical–numerical method for determining the critical average shear strain for localization and commensurate stress decay is devised. Averaged results for a high-strength steel agree reasonably well with experimental dynamic torsion data. Calculations probe possible effects of ductile fracture and melting on shear banding, and vice versa, including influences of cohesive energy, equilibrium melting temperature, and initial defects. A threshold energy density for localization onset is positively correlated to critical strain and inversely correlated to initial defect severity. Tensile pressure accelerates damage softening and increases defect sensitivity, promoting shear failure. In the present steel, melting is precluded by ductile fracture for loading conditions and material properties within realistic protocols. For this steel, if conduction, fracture, and damage softening are artificially suppressed, melting is confined to a narrow region in the core of the band. However, for other metals with vastly different physical properties, or for more diverse loading conditions, melting has not been unequivocally ruled out, even if fracture and conduction are permitted. Full article

This study introduces and analyzes several new functionals defined on the interval $[0,1]$, which are associated with weighted integral inequalities for geometrically–arithmetically ($GA$) convex functions. Building upon the classical Hermite–Hadamard and Fejér inequalities, we define mappings such as $\mathcal{G}\left(u\right)$, ${\mathcal{H}}_y\left(u\right)$, ${\mathcal{K}}_y\left(u\right)$, $\mathcal{N}\left(u\right)$, $\mathcal{L}\left(u\right)$, ${\mathcal{L}}_y\left(u\right)$, and ${\mathcal{S}}_y\left(u\right)$, which incorporate a $GA$-convex function x and a non-negative, integrable weight function y that is symmetric about the geometric mean $\sqrt{s_1{s}_2}$. Under these conditions, we establish novel Fejér-type inequalities that connect these functionals. Furthermore, we investigate essential properties of these mappings, including their $GA$-convexity, monotonicity, and symmetry. The validity of our main results is demonstrated through detailed examples. The findings presented herein provide significant refinements and weighted generalizations of known results in the literature. Full article

We establish a modular-space framework for the study of tripled fixed points and tripled best proximity points. Under suitable assumptions on the underlying modular (convexity, the ${\Delta }_2$ property, uniform continuity, and uniform convexity-type properties), we prove that Banach theorems guarantee the existence, uniqueness, and convergence of modular iterative schemes. In particular, we develop results for cyclic $\rho$–Kannan contraction maps and pairs, showing that both tripled fixed points and tripled best proximity points arise uniquely and attract all iterative trajectories. An illustrative example in the space $L^2[0,1]$ with integral operators demonstrates the applicability of the theory and the predicted rate of convergence. These results extend classical fixed point methods to a broader modular setting and open the way for applications in nonlinear functional equations. Full article

Geospatial–statistical integration remains a persistent bottleneck for official statistics and applied spatial analysis. The GISINTEGRATION R package provides a modular, reproducible workflow for preprocessing, harmonizing, and linking heterogeneous GIS and non-GIS datasets, with export utilities that are compatible with common desktop GIS. This paper outlines the package architecture and demonstrates its use in two applications. The first integrates population statistics with newly introduced statistical output geographies for Northern Ireland, enabling rapid preparation of analysis-ready layers such as all usual residents and population density at Super Data Zones. The second links daily PM_2.5 measurements from the U.S. EPA Air Quality System with county boundaries for California (July 2020) to produce policy-relevant indicators; spatial aggregation yielded valid monthly means for 46 of 58 counties (79.31%) and reduced variance from 40.716 (monitor level) to 5.777 (county means), improving signal stability and comparability. Across both cases, the workflow standardizes variable names, supports user-controlled overrides, identifies common keys, and performs quality checks, thereby reducing manual effort while increasing transparency and reproducibility. The results illustrate how standardized integration facilitates official statistical production, environmental monitoring, and evidence-based decision-making. Full article

The design of a control system becomes more complex with the advancement of technology, and this requires optimization techniques to be developed. In particular, multi-objective optimal control (MOC) is a method that can be used to achieve a scheme for control system that coordinates several design objectives that can be in conflict with each other. In this study, a new hybrid scheme is presented that is a combination of non-dominated sorting genetic algorithm-II (NSGA-II) and the simple cell mapping (SCM) method. The combined method first starts a random search using the genetic algorithm and then proceeds by using the SCM method for a neighborhood-based search and recovery algorithm. An evaluation of the proposed method’s efficiency and performance was conducted on two benchmark problems and two multi-objective optimal control problems. We utilized two performance indicators (generational distance (GD) and a diversity metric) to assess the convergence to the Pareto front and the diversity of the solution set, respectively. The results demonstrated that the proposed method not only achieved superior efficiency but also produced a more uniform distribution of solutions along the Pareto front compared to the SCM and NSGA-II algorithms. Full article

Fisheries worldwide exhibit puzzling boom-and-bust cycles despite regulatory efforts, raising questions about what drives these oscillations. We investigate whether temporal delays in monitoring and decision-making contribute to system instability. Our model uses delay differential equations to track an exploiting population and its renewable resources, incorporating two distinct delays: one for perceiving resource status (${\tau }_2$) and another for implementing management responses (${\tau }_1$). We establish the existence, uniqueness, and positivity of solutions, then analyze equilibrium stability through linearization and Lyapunov–Razumikhin functions. The characteristic equation reveals Hopf bifurcations at critical delay thresholds. Numerical simulations across 1600 parameter combinations using MATLAB R2023b’s DDE23 algorithm quantify these transitions. The results show a critical threshold near 1.64 years (20 months): below this value, systems converge to a stable equilibrium, while above it, persistent oscillations emerge within 20–26 year periods. Unexpectedly, one large delay destabilizes less than two moderate delays summing to the same total, contradicting uniform improvement strategies. Convergence to limit cycles requires roughly 40 years, exceeding typical management horizons and potentially masking true system dynamics. The critical threshold lies within realistic administrative timescales, suggesting that institutional delays may substantially contribute to observed population fluctuations. These findings indicate that accelerating either monitoring or decision processes rather than providing modest improvements to both could better stabilize exploited resources. Full article

This study proposes an SVEIR with a reinfection model of tuberculosis disease spread to examine the impact of saturated infection and imperfect vaccination. Vaccinated individuals are considered vulnerable, as they are still likely to be reinfected. As the recovered individuals still have bacteria in their bodies, they are likely to return to their latent class. The dynamic behavior of the proposed model was analyzed to understand both the local and global stability equilibrium points. To analyze the disease-free and endemic equilibrium stability, the Routh–Hurwitz Criterion and Center Manifold theorems were used, respectively. The local and global stability equilibrium state is entirely dependent on the effective reproduction number. If the effective reproduction number is less than one, the disease-free equilibrium point is locally and globally asymptotically stable, whereas if it is greater than one, the endemic equilibrium point is locally asymptotically stable. Numerical simulations show the time series of the solution of the model, phase-plane trajectory, elasticity indices, bifurcation diagram, partial rank correlation coefficients, and the sensitivity of the infected class to variations in the transmission rate represented both in the peak value and a heatmap. Furthermore, the contour plot illustrates that the disease transmission rate affects the effective reproduction number and the stability of equilibrium points. Full article

The stability of energy demand–supply systems is often affected by delayed feedback caused by regulatory inertia, communication lags, and heterogeneous agent responses. Conventional models typically assume discrete delays, which may oversimplify real dynamics and reduce controller effectiveness. This work addresses this limitation by introducing a novel class of nonlinear energy models with distributed delay feedback governed by gamma-distributed memory kernels. Specifically, we consider both weak (exponential) and strong (Erlang-type) kernels to capture a spectrum of memory effects. Using the linear chain trick, we reformulate the resulting integro-differential model into a higher-dimensional system of ordinary differential equations. Analytical conditions for local asymptotic stability and Hopf bifurcation are derived, complemented by Lyapunov-based global stability criteria. The related numerical analysis confirms the theoretical findings and reveals a distinct stabilization regime. Compared to fixed-delay approaches, the proposed framework offers improved flexibility and robustness, with implications for delay-aware energy control and infrastructure design. Full article

In this study, we consider and analyze an inhomogeneous Whittaker-type differential equation of the form ${\displaystyle \frac{d^{2}y\left(x\right)}{d{x}^2}}+{\displaystyle \frac{1}{x}}{\displaystyle \frac{dy\left(x\right)}{dx}}-{\alpha }^2\left(x^2-{\beta }^2\right)y\left(x\right)=g\left(x\right)$, where $\alpha$ and $\beta$ are given parameters. We investigate the analytical structure of its solution through the application of the Whittaker integral representation. The analysis encompasses both initial value problems (IVPs) and boundary value problems (BVPs), wherein appropriate conditions are imposed within a unified analytical framework. Furthermore, a systematic methodology is developed for constructing explicit solutions within the framework of Whittaker function theory. This approach not only elucidates the functional behaviour of the solutions but also provides a foundation for extending the analysis to more general classes of second-order linear differential equations. Full article

Efficient management of heat transfer and entropy generation in nanofluid enclosures is essential for the development of high-performance thermal systems. This study employs the finite element method (FEM) to numerically analyze the effects of wall corrugation and base inclination on magnetohydrodynamic (MHD)-assisted natural convection of Cu–H₂O nanofluid in a trapezoidal cavity containing internal heat-generating obstacles. The governing equations for fluid flow, heat transfer, and entropy generation are solved for a wide range of Rayleigh numbers (10³–10⁶), Hartmann numbers (0–50), and geometric configurations. Results show that for square obstacles, the Nusselt number increases from 0.8417 to 0.8457 as the corrugation amplitude rises (a = 0.025 L–0.065 L) at Ra = 10³, while the maximum heat transfer (Nu = 6.46) occurs at Ra = 10⁶. Entropy generation slightly increases with amplitude (15.46–15.53) but decreases under stronger magnetic fields due to Lorentz damping. Higher corrugation frequencies (f = 9.5) further enhance convection, producing Nu ≈ 6.44–6.47 for square and triangular obstacles. Base inclination significantly influences performance: γ = 10° yields maximum heat transfer (Nu ≈ 6.76), while γ = 20° minimizes entropy (St ≈ 0.00139). These findings confirm that optimized corrugation and inclination, particularly with square obstacles, can effectively enhance convective transport while minimizing irreversibility, providing practical insights for the design of energy-efficient MHD-assisted heat exchangers and cooling systems. Full article