The rapid and accurate short-term forecasting (nowcasting) of wildfire spread is a critical challenge for emergency response and public safety. Traditional physics-based models, while grounded in established principles, often lack fine-scale realism and produce overly smooth predictions. Conversely, purely data-driven deep learning models can capture complex patterns but may violate fundamental physical constraints, leading to unrealistic or untrustworthy forecasts. This paper introduces FireCast, a novel, original hybrid algorithm that synergizes both approaches for high-fidelity nowcasting of wildfire perimeters for up to two hours.

FireCast employs a two-stage hybrid framework. First, a Deterministic Forecast Module uses a physics-informed cellular automaton (CA) to generate a coarse, low-resolution forecast. This CA is guided by meteorological data (wind, humidity) from ERA5 and topography from a DEM. Second, this physically-grounded prediction serves as a strong condition for a Stochastic Refinement Module. This module uses a generative diffusion model, based on the CasFormer architecture, to refine the coarse forecast. It adds realistic, high-frequency details learned from historical fire events observed in Himawari-8/9 satellite imagery.

FireCast was trained and validated on a curated dataset of 50 major wildfire events, comprising approximately 4,000 spatiotemporal sequences from the Asia-Pacific region. In a comparative analysis for a 120-minute forecast, FireCast (Dice Similarity Coefficient: 0.84, Hausdorff Distance: 3.21 pixels) significantly outperformed both the baseline Deterministic CA (DSC: 0.72, AHD: 8.45 pixels) and a purely data-driven U-Net (DSC: 0.75, AHD: 5.12 pixels). Qualitative results confirm that FireCast forecasts are not only quantitatively more accurate but also visually more realistic, capturing the complex, intricate perimeters of real fire fronts.

This work validates the power of a hybrid deterministic–stochastic approach for complex environmental forecasting. FireCast offers a viable path toward creating trustworthy, high-fidelity AI tools, providing a significant advancement for operational wildfire management and disaster response.

Variable-rate spraying (VRS) is an essential component of precision agriculture, enabling targeted agrochemical application according to spatial and canopy variability. This work introduces a mathematics-informed deep learning framework that integrates lightweight U-Net architectures, such as U-Net Mini, with optimization-based spray allocation strategies for UAV spraying systems. The encoder–decoder design of U-Net, grounded in variational principles of image analysis, is employed to segment UAV-acquired imagery into canopy and non-canopy regions. From these segmentation masks, geometric measures of canopy area and density are computed to characterize crop heterogeneity. A constrained optimization model is then applied to allocate spray volumes proportionally to canopy demand, ensuring efficiency under limited resource budgets. To enable practical deployment on UAV platforms, parameter-reduced variants of U-Net are explored, demonstrating significant reductions in computational cost while maintaining high segmentation accuracy (IoU > 0.85). When combined with optimization-based variable-rate control, the proposed system reduces chemical usage and spray drift compared to fixed-rate application. The study highlights how mathematical concepts—variational modeling, optimization theory, and geometric analysis—can be embedded within AI architectures to provide efficient, interpretable, and sustainable solutions for UAV-based precision spraying. This fusion of mathematical modeling with lightweight deep learning offers a promising pathway for scalable field applications and environmentally responsible agriculture.

This study presents a hybrid approach for analyzing animal behavior in T-maze tasks, combining traditional analytical modeling with advanced machine learning techniques. T-maze experiments are a well-established paradigm used to investigate decision-making processes in animals, where they must select one of two paths based on reinforcement feedback. To better understand the underlying cognitive mechanisms behind this, the proposed approach integrates conventional methods, such as decision theory and cognitive modeling, with cutting-edge machine learning algorithms, including deep learning models. This combination enables a more comprehensive analysis of the complexity inherent in animal behavior during decision-making tasks. Furthermore, we model the problem mathematically and apply fixed-point results to establish the existence and uniqueness of solutions to the proposed problem. This hybrid methodology not only improves the accuracy of behavioral predictions but also offers deeper insights into the decision-making process. The results show that integrating analytical methods with machine learning techniques leads to more robust and complex analyses compared to traditional approaches. This framework has significant implications for computational ethology, as it advances our understanding of animal cognition. Additionally, the study sets the foundation for future research in behavioral neuroscience, providing a valuable tool for modeling complex animal behaviors in various experimental settings. By bridging the gap between theory and data-driven approaches, this work paves the way for further interdisciplinary studies in the field of cognitive science.

Understanding animal decision-making processes in controlled environments is crucial for gaining insights into cognitive functions and behavior. T-maze tasks, commonly used in behavioral experiments, provide a valuable framework for studying binary decision-making, where animals must choose between two distinct paths. This study presents a comprehensive computational analysis of animal behavior in T-maze tasks, where animals are required to make binary decisions between two paths. By integrating both analytical modeling and machine learning techniques, we aim to explore the decision-making processes involved in such behavioral tasks. In particular, we focus on enhancing our understanding of the cognitive mechanisms that guide these decisions by employing advanced deep learning models. Specifically, we apply Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) and Convolutional Neural Network-Gated Recurrent Unit (CNN-GRU) architectures to analyze the data. These models achieved impressive classification accuracies of 92.3% and 95.6%, respectively, demonstrating their superior predictive capabilities compared to traditional machine learning methods such as Support Vector Machines and Random Forests. In addition to machine learning, we employed analytical methods to model and interpret the decision-making behavior of animals, providing deeper insights into their cognitive processes during navigation. The results of this research contribute to the field of computational ethology by showcasing the potential of combining analytical solutions with machine learning techniques to model complex biological systems. This approach offers new avenues for understanding animal decision-making in T-maze tasks and similar behavioral experiments.

Individual aspiration plays a central role in shaping vaccination decisions and epidemic outcomes. Recent studies have shown that higher aspiration toward immunity can increase vaccine uptake and reduce the social efficiency deficit (SED) [1–4]. However, aspiration in reality is rarely constant. People’s motivation to vaccinate can rise during outbreaks when the risk of infection becomes salient, and decline when cases fall or vaccine fatigue develops. To address this limitation, we extend the aspiration-based vaccination model of Khatun et al. [1] within a SEIRS epidemic framework by incorporating time-varying aspiration. Two simple mechanisms are considered: (i) prevalence-driven aspiration, where aspiration increases with the number of infectious cases, and (ii) time-decaying aspiration, where aspiration gradually declines in the absence of strong risk perception. Using mean-field analysis and numerical simulations, we investigate how dynamic aspiration influences epidemic prevalence, vaccination coverage, and the social efficiency deficit (SED) compared to fixed aspiration levels. Our findings reveal that prevalence-driven aspiration can generate rapid increases in vaccination during outbreaks, effectively suppressing infection peaks, while time-decaying aspiration may lead to delayed responses and higher long-term infection burdens. These results highlight the importance of incorporating dynamic behavioral motivation into vaccination game models and suggest that public health strategies could benefit from actively sustaining aspiration levels over time.

References :

1. Khatun, K., Khan, M. M. U. R., & Tanimoto, J. (2025). Aspiration can decline epidemic disease. Alexandria Eng. J., 112, 151–160. https://www.sciencedirect.com/science/article/pii/S111001682401250X

2. Lyu, Z., Su, Y., & Zhuo, X. (2024). Vaccination games and imitation dynamics with age structure. Chaos Solitons Fractals, 183, 114929. https://doi.org/10.1016/j.chaos.2024.114929

3. Kulsum, U., Alam, M., & Kamrujjaman, M. (2024). Early vs. delayed vaccination under imitation and aspiration dynamics. Chaos Solitons Fractals, 178, 114364. https://doi.org/10.1016/j.chaos.2023.114364

4. Schimit, P. H. T. (2025). Vaccination as a Game: Behavioural Dynamics, Network Effects, and Policy Implications. Mathematics, 13(14), 2242. https://www.mdpi.com/2227-7390/13/14/2242

Introduction: Higher order boundary value problems model several physical phenomena in fluid dynamics, astrophysics, hydrodynamics, beam theory, astronomy, hydromagnetic stability, and engineering. Eighth-order boundary value problems arise in the physics of various hydrodynamic stability problems. This paper applies an efficient collocation method based on the shifted Horadam polynomials to obtain approximate solutions of an eight-order boundary value problem in ordinary differential equation.
Methodology: The Horadam collocation method expresses the solution of the proposed problem as a shifted Horadam polynomial series. Using the zeros of the shifted Horadam polynomials as the collocation points, the proposed boundary value problem is reduced to a set of algebraic equations in the expansion coefficients of the series solution. The obtained algebraic equations are then solved for the unknown expansion coefficients using Newton's iterative method. Two illustrative examples of the proposed boundary value problem are considered for the purpose of accuracy, efficiency, and reliability of the proposed method.
Results: Numerical solutions obtained are compared with the exact solutions and other existing solutions. The comparisons of results are demonstrated in tables and graphs. It is observed that the proposed method outperforms other existing methods under comparison.
Conclusion: This research work shows that the Horadam polynomial-based collocation method is an efficient method for obtaining accurate and reliable approximate solutions of higher order boundary value problems.

Mosquito-borne diseases pose a significant public health challenge, and effective prevention requires accurate forecasting of mosquito populations. In this study, we developed a statistical forecasting framework that leverages climate factors, such as temperature and precipitation, to improve mosquito population predictions in Maricopa County, Arizona. Our approach combines adaptive modeling techniques and filtering methods to infer precise model parameters and address previously observed limitations, particularly the inability to capture spring dynamics in the mosquito population data. By incorporating an Ensemble Kalman Filter (EnKF) method, we estimated time-varying parameters (baseline population growth rate) and static parameters while resolving the spring problem observed in prior models. Using generalized additive models (GAM), we forecasted the baseline population growth rate on a two-week basis and its quantiles, integrating precipitation and temperature data as covariates. These forecasts were further used to run a mechanistic ordinary differential equation (ODE) model to predict mosquito abundance and estimate associated uncertainties. Our iterative framework was applied over a 52-week period, successfully capturing seasonal variations in mosquito populations from 2014 to 2016. The EnKF demonstrated superior performance compared to traditional Markov Chain Monte Carlo (MCMC) approaches for fitting mosquito abundance data. This enhanced methodology provides actionable insights for public health decision-makers, supporting resource allocation and improving outcomes in mosquito-borne disease prevention. Our findings underscore the value of integrating climate data and adaptive filtering techniques to address forecasting challenges, ultimately enabling more effective responses to emerging or reemerging pathogens of mosquito-borne disease risks, which can be driven by human behavior to become a pandemic.

Introduction. Multiplication tables, traditionally used in foundational mathematics education, also harbor rich arithmetic structures when analyzed through operations of sum, difference, and product. This study introduces a novel, deterministic prime-detection methodology derived from the structural patterns in these tables, adapted for large numbers via a logarithmic framework.

Methods. We formalize three operations on the multiplication table T(n) of a fixed integer n: the tabular sum (∑), difference (δ), and product (∏). We derive closed-form expressions for ∑ (linking to triangular numbers), δ (relating to arithmetic sequences), and ∏ (corresponding to factorial constructs), leading to the Kadouno Primality Test. A logarithmic adaptation exploits Stirling’s approximation and a dynamic scaling regulated by decimal thresholds to maintain computational tractability for very large integers. Further refinement replaces the factorial structure with a primorial-based test that preserves small-prime exclusion and enhances algorithmic efficiency.

Results. The primality test reliably distinguishes prime from composite numbers across multiple ranges. With the logarithmic version, the method remains accurate and efficient even as input size grows, thanks to a dynamically adjusted depth parameter. Incorporating the primorial variant secures robust rejection of Carmichael numbers—a significant advantage over probabilistic Fermat-type tests.

Conclusions. This research presents a deterministic, scalable, and pedagogically intuitive primality test grounded in elementary tabular analysis. Its dual utility in both computational number theory and mathematics education positions it as a valuable contribution with practical and theoretical impact. Future work will explore integration with educational software and further extension to cryptographic applications.

We investigated the behavior of the diffusion coefficient in a time-dependent oval-shaped billiard, focusing on the connection between this quantity and the system’s transition from unbounded to bounded diffusion caused by inelastic collisions with the boundary. The diffusion coefficient plays a key role in describing the scaling invariance characteristic of this transition. For short times, the low-action regime is characterized by a constant diffusion coefficient, which begins to decay after a crossover iteration, thereby suppressing the unlimited growth of velocity. We demonstrate that this behavior is scaling-invariant concerning the control parameters and can be described by a homogeneous generalized function and its associated scaling laws. This universal function effectively collapses all numerical data onto a single curve, confirming the self-similar nature of the dynamical crossover. The critical exponents governing this scaling were determined both phenomenologically, through extensive numerical simulations, and analytically, by examining the system's equations of motion near the critical point. This analysis confirmed the decay exponent β = -1 for the diffusion coefficient, a value previously identified in related low-dimensional dissipative systems like the dissipative standard map. The consistency between our analytical derivations and numerical results strongly validates the universal framework we propose for describing transport phenomena in open Hamiltonian systems subject to dissipation.

This research describes a compartmental epidemic model of Hepatitis B virus (HBV) transmission that includes vertical transmission and spontaneous recovery in acute patients. The model incorporates a saturated treatment response for persistently infected populations and a vaccination mechanism for susceptible populations. The basic reproduction number, R0, is calculated using the next-generation matrix approach, which provides important information on disease dynamics. To find out the most influential parameter of the model dynamics, a sensitivity analysis is carried out with the help of Latin Hypercube Sampling (LHS) along with the Partial Rank Correlation Coefficient (PRCC). The qualitative behavior of the model is investigated using stability analysis of disease-free and endemic equilibria. It is established that the disease-free equilibrium is globally asymptotically stable when R0 < 1, but the endemic equilibrium achieves global stability when R0 > 1. Pontryagin’s Maximum Principle is used to optimize public health initiatives, resulting in three optimal control techniques that attempt to reduce the combined cost of treatment and immunization. The results provide a rigorous theoretical foundation for designing cost-effective interventions against HBV transmission. This work contributes a more biologically accurate and analytically rich model to the literature, offering new insights into the strategic control of HBV infection, particularly in regions where vaccination and treatment resources are limited.