Predicting wildland fire spread requires numerical schemes that can resolve sharp gradients at the fireline while remaining stable and efficient on practical grids. We develop a compact high-order finite-difference scheme for Hamilton–Jacobi level-set formulations of wildfire propagation, based on the anisotropic spread law of Mallet and co-authors. The spatial discretization employs a compact finite-difference derivative scheme to achieve spectral-like resolution with narrow stencils, improving accuracy and boundary robustness compared with wide-stencil ENO/WENO reconstructions. To control high-frequency artifacts intrinsic to non-dissipative compact schemes, an implicit high-order low-pass filter is incorporated and activated after each Runge–Kutta stage. Convergence is verified on the eikonal expanding-circle benchmark, where the method attains the expected high-order spatial accuracy as the grid is refined. The proposed scheme is then applied to wind-driven wildfire simulations governed by Mallet’s non-convex Hamiltonian, including a single ignition under moderate and strong wind. A complex topology test case is also considered, involving two ignitions that merge into a single front with the evolution of an internal unburnt island. The results demonstrate that the proposed method accurately reproduces fireline evolution even on coarse grids, achieving accuracy comparable to fifth-order WENO while maintaining superior fidelity in complex fireline topologies, where it better resolves multi-front interactions and topological changes in the fireline. This makes the method an efficient, accurate alternative for level-set wildfire modeling and readily integrable into existing frameworks.

The analysis of multivariate data is a central issue in biomedical research, where the accurate classification of patients and the extraction of reliable conclusions are of critical importance. Linear Discriminant Analysis (LDA) remains one of the most established methods for both dimensionality reduction and classification of data. In this paper, we examine in detail the theoretical foundations, assumptions, and statistical properties of LDA, and apply the method step by step to real data from the Breast Cancer Wisconsin (Diagnostic) database, which includes cellular features from breast biopsy samples with the aim of distinguishing benign from malignant tumors. Emphasis is placed on the importance of the method’s assumptions, such as multivariate normality, equality of covariance matrices, and absence of multicollinearity, demonstrating that their fulfillment leads to significant improvements in model performance. Specifically, careful preprocessing and strict adherence to these assumptions increase classification accuracy from $95.6\%$ ($94.7\%$ cross-validated) to $97.8\%$ ($97.4\%$ cross-validated). To our knowledge, this study is the first to demonstrate the dual use of LDA as both a dimensionality-reduction tool and a predictive classification model for this medical database within the same biomedical analysis framework. Moreover, we provide, for the first time, a systematic comparison between our assumption-aware LDA model and related studies employing the most accurate machine-learning classifiers reported in the literature for this dataset, showing that classical LDA achieves accuracy comparable to these more complex methods. The resulting discriminant model, which uses 13 variables out of the original 30, can be applied easily by clinical researchers to classify new cases as benign or malignant, while simultaneously providing interpretable coefficients that reveal the underlying relationships among variables. The implementation is carried out in the SPSS environment, following the theoretical steps described in the paper, thus offering a user-friendly and reproducible framework for reliable application. In addition, the study establishes a structured and transparent workflow for the proper application of LDA in biomedical research by explicitly linking assumption verification, preprocessing, dimensionality reduction, and classification.

Energy-efficient wireless sensor networks (WSNs) rely on complex mathematical models to optimize critical operations such as coverage, routing, and energy harvesting. However, these equations impose diverse computational requirements: some demand rapid approximate methods to minimize overhead, while others require high-accuracy or even analytical solutions for precise optimization. This diversity introduces a key challenge: selecting the most suitable solving method for each equation type. This paper introduces the Argumentation-Based Equation-Solver Selector (ABESS), a decision-making framework that chooses a solver based on user-provided descriptors and also provides justification, by encoding rules, preferences, and contextual priorities. By leveraging computational argumentation, ABESS provides an adaptive and explainable approach to managing the resource-constrained nature of WSNs. Another contribution is a detailed functional behavior analysis of characteristic formulas in the WSN domain. This analysis on the one hand derives the descriptors for ABESS reasoning, e.g., verified localization intervals for design solutions, and on the other hand, cross-validates its performance. Thus, ABESS helps to avoid the use of failure-prone numerical methods and significantly improves computational efficiency. Empirical results across three core WSN models demonstrate the framework’s efficacy, including a 870× speedup in integer thresholding compared to uninformed exhaustive scanning.