Feature Paper Collection of Mathematical and Computational Applications—2025

This Special Issue comprises the fifth collection of papers submitted by both the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA) and the outstanding scholars working in the core research fields of MCA. Therefore, this collection typifies the most insightful and influential original articles that discuss key topics in these fields. More precisely, this issue contains 16 research articles published in MCA between February and December 2025. All papers are briefly outlined below, organized chronologically by publication.

Gandomirouzbahani et al. [1] developed a patient-specific head model to address the impact of the brain’s constitutive model and loading location on head impact. More precisely, two hyperelastic constitutive models and one hyper-viscoelastic constitutive model were developed for brain tissue. The results regarding the impact on the head and critical regions can help in the development of protective features, such as helmets and airbags.

Lau et al. [2] developed and analyzed machine learning (ML) models that can identify patients at risk of requiring red blood cell transfusion. The retrospective cohort study was conducted at a tertiary northern Portuguese hospital between 2018 and 2023. The considered ML models demonstrate the potential to improve the accuracy of transfusion prediction at hospital admission, despite the absence of key variables such as surgeon identity and anaemia diagnosis.

Sarfraz et al. [3] investigated how regime shifts during the COVID-19 pandemic influenced variable annuity pricing in the Indian stock market. Advanced methodologies, including regime-switching hidden Markov models, artificial neural networks, and Monte Carlo simulations, were applied to analyze pre- and post-COVID-19 market behavior. The regime-switching hidden Markov models can effectively capture latent market regimes and their transitions, which traditional models often overlook, while neural networks can provide flexible functional approximations that enhance pricing accuracy in highly non-linear environments. The findings highlight the effectiveness of regime-switching models in capturing market dynamics, particularly during periods of economic uncertainty and turbulence.

Rocha et al. [4] studied risk factors that lead to psychological problems, using data from primary health care centers in the region of Aveiro. A significant increase in number of appointments was observed in 2021 and 2022, revealing an increase in mental health problems, resulting in more medical consultations for psychological reasons. Risk factors included being female and having chronic conditions such as cancer. The findings provide insights into the burden of mental health issues in the region, highlighting the need for effective mental health interventions and resources to address health inequalities and support at-risk groups.

López-Lobato et al. [5] proposed a generalization of the induction process of a Convolutional Decision Tree (CDT) with the Differential Evolution (DE) algorithm for image segmentation. More precisely, this new approach considered color images, while previous methods were restricted to grayscale images due to the higher computational cost. The efficacy of the novel techniques were evaluated using two datasets, resulting in favorable outcomes in terms of the segmentation performance of the induced CDTs, and the processing time and memory required for the induction process.

Herrera-Sánchez et al. [6] proposed an automated multiple-feature construction approach for image segmentation, working with magnetic resonance images, computed tomography, and RGB digital images. Genetic programming is used to automatically create and construct pipelines to extract meaningful features for segmentation tasks. Additionally, a co-evolution strategy is proposed within the evolution process to increase diversity without affecting segmentation performance. Numerical results on some benchmark problems show that the novel method is highly competitive with state of the art algorithms.

López-Lobato et al. [7] proposed a procedure to identify the colors of heterogeneous color bean landraces based on the information from their digital images. This classification is of particular interest since the color of these plants is associated with the nutritional components present in their seeds. The novel approach facilitates the acquisition of representative information for the colors of a bean landrace. Furthermore, the method can be trained with these punctual representations to identify colors, yielding satisfactory results on landraces with homogeneous and heterogeneous seeds.

Morales-Reyes et al. [8], propose a methodology for classifying bean landrace samples using three two-dimensional histograms with data in the CIE L*a*b* color space while additionally integrating chroma (C*) and hue (h°) to develop a new proposal from histograms, employing deep learning for the classification task. It is shown that the new color characterization approach presents a viable solution for classifying common bean landraces of both homogeneous and heterogeneous colors.

Temizel et al. [9] addressed the problem of accurate permeability predictions for the understanding of fluid flows in porous media. To this end, they introduced a new paradigm, employing vision transformers (ViTs)—a recent advancement in computer vision—for this crucial task. The prediction results suggest that, with adequate training data, ViTs can match or surpass the predictive accuracy of CNNs, especially in rocks exhibiting significant heterogeneity. The study underscores the potential of ViTs as an innovative tool in permeability prediction, paving the way for further research and integration into mainstream reservoir characterization workflows.

Barradas-Palmeros et al. [10] tested various efficient evaluation methods (EEMs) in the Deep Genetic Algorithm (DeepGA), including early stopping, population memory, and training-free proxies. This is carried out with the aim of reducing the computational resources for Neural Architecture Search (NAS). A comparison of the architectures and hyperparameters obtained with the different algorithm configurations is presented. The training-free search processes resulted in deeper architectures with more fully connected layers and skip connections than the ones obtained with accuracy-guided search configurations.

Bertolo et al. [11] developed a second-order Kurganov–Tadmor scheme in curvilinear coordinates to analyze the external supersonic flow over bodies of various shapes. This scheme is capable of handling interfaces across different regions of the domain. A fourth-order Runge–Kutta temporal integrator is used and several test cases are conducted to validate the performance of the new scheme. The results indicate that the new method produces highly accurate outcomes.

Ratner et al. [12] presented a systematic literature review of data envelopment analysis (DEA) models used to evaluate circular economy (CE) practices. The analysis shows that DEA models provide valuable insights when assessing circular strategies. Over 40% of the surveyed literature focuses on China, with nearly 20% on the European Union. Other regions are sparsely represented within the sample, highlighting a potential gap in the current research landscape.

Martines-Arano et al. [13] examined the contrast in the nonlinear dynamics of Thrinax radiata Lodd. ex Schult. & Schult. f. (known as chit palm in the Yucatán Peninsula). Simulations reveal heat transfer of approximately 1 °C in central regions, closely correlating with observed changes in chaotic attractor morphology. These findings pave the way for future applications and highlight the potential of chaos theory for the early detection of structural and bioelectrical changes induced by external energy inputs, thereby contributing to sample protection.

Bolle et al. [14] utilized $\kappa$-mathematics for the analysis of complex systems. Specifically, the mathematical framework in the context of a first-order decay $\kappa$-differential equation was investigated, facilitating an in-depth examination of the $\kappa$-mathematical structure. This framework serves as a foundational platform, representing the simplest non-trivial setting for such inquiries, which are demonstrated for the first time in the literature. In conclusion, possible paths of future research are discussed.

Kamran et al. [15] presented a comparative analysis of tumor growth models based on logistic, exponential, and Gompertz formulations. Their response to therapeutic intervention was examined to identify which model shows better behavior with minimal decline of immune cells. Numerical simulations indicate that the logistic model provides more favorable treatment outcomes compared to the exponential and Gompertz models. The results also show a faster decline of immune cell populations in the exponential and Gompertz models than in the logistic model under varying drug flux.

Finally, Tavakoli et al. [16] presented an integrative framework based on Evolutionary Stackelberg Game Theory to model the strategic interaction between a physician, acting as a rational leader, and a heterogeneous population of treatment-sensitive and treatment-resistant breast cancer cells. It is shown that this framework offers a biologically interpretable tool for guiding evolution-aware, patient-tailored cancer therapies toward improved long-term outcomes.