AppliedMath

Robust mean-geometric mean (MGM) linking methods enable reliable group comparisons in item response theory models under fixed and sparse differential item functioning. This article evaluates six alternative standard error and confidence interval (CI) estimation methods across four MGM linking approaches. Our Simulation Study demonstrates that CIs based on the delta method or bootstrap procedures using the normal distribution or empirical quantiles exhibit highly inflated coverage rates. In contrast, CIs derived from a weighted least squares estimation problem, as well as basic and bias-corrected bootstrap methods, yield satisfactory coverage rates in most simulation conditions for robust MGM linking. Full article

This work explores the morphogenesis of the skeletal mineral component, with a specific emphasis on hydroxyapatite (HAp) crystal assembly. Bone is fundamentally a triphasic biomaterial, consisting of an inorganic mineral phase, an organic matrix, and an aqueous component. The inorganic phase (hydroxyapatite), is characterized by its hexagonal prismatic nanocrystalline structure. We leverage a cellular automata (CA) paradigm to computationally simulate the mineralization process, leading to the formation of the bone’s hydroxyapatite framework. This model exclusively considers the physicochemical aspects of bone formation, intentionally excluding the biological interactions that govern in vivo skeletal development. To optimize computational efficiency, a simplified anatomical segment of a long bone (e.g., the femur) is modeled. This geometric simplification encompasses an outer ellipsoidal cylindrical boundary (periosteal envelope), an inner ellipsoidal surface defining the interface between cortical and cancellous bone, and a central circular cylindrical lumen representing the medullary cavity, which accommodates the bone marrow and primary vasculature. The CA methodology is applied to generate the internal bone microarchitecture, while deliberately omitting the design of smaller, secondary vascular channels. Full article

This research delves into the assessment of students’ perspectives regarding virtual internships within Brazilian organizations, a phenomenon accelerated by the global pandemic. Evaluating 78 students’ virtual internships via a survey, the study employs the Fuzzy TOPSIS Class method for analysis. Additionally, a sensitivity analysis was conducted to assess the robustness of the results. Key insights for enhancing virtual internships encompass: emphasizing application and deeper understanding of topics learned during the undergraduate course, enhancing understanding about how organizations work, and fostering comprehension of market dynamics. Among the points best rated by students are the opportunity to explore new subjects, development of soft skills, and supervisors’ competence in managing teams in virtual environments. This paper contributes methodologically by proposing a multicriteria decision-making approach to assess virtual internships. The findings serve as a valuable resource for internship supervisors in companies and higher education institutions, aiding them in guiding students through this pivotal developmental phase that shapes their future careers. Full article

Given a triangular mesh in ${\mathbb{R}}^3$ with a family of points associated with its vertices along with vectors associated with its edges, we propose a novel technique for the construction of locally generated fitting parametrized G1-spline interpolation surfaces. The method consists of a G1 correction over the mesh edges of the mesh triangles, produced using reduced side derivatives (RSDs) introduced earlier by the author in terms of the barycentric weight functions. In the case of polynomial RSD shape functions, we establish polynomial edge corrections via an algorithm with an independent interest in determining the optimal GCD cofactors with the lowest degree for arbitrary families of polynomials. Full article

Glaucoma is a leading cause of irreversible blindness globally, with early diagnosis being crucial to preventing vision loss. Traditional diagnostic methods, including fundus photography, OCT imaging, and perimetry, often fall short in sensitivity and fail to integrate structural and functional data. This study proposes a novel multi-modal diagnostic framework that combines convolutional neural networks (CNNs), vision transformers (ViTs), and quantum-enhanced layers to improve glaucoma detection accuracy and efficiency. The framework integrates fundus images, OCT scans, and clinical biomarkers, leveraging their complementary strengths through a weighted fusion mechanism. Datasets, including the GRAPE and other public and clinical sources, were used, ensuring diverse demographic representation and supporting generalizability. The model was trained and validated using cross-entropy loss, L2 regularization, and adaptive learning strategies, achieving an accuracy of 96%, sensitivity of 94%, and an AUC of 0.97—outperforming CNN-only and ViT-only approaches. Additionally, the quantum-enhanced architecture reduced computational complexity from O(n²) to O (log n), enabling real-time deployment with a 40% reduction in FLOPs. The proposed system addresses key limitations of previous methods in terms of computational cost, data integration, and interpretability. The proposed system addresses key limitations of previous methods in terms of computational cost, data integration, and interpretability. This framework offers a scalable and clinically viable tool for early glaucoma detection, supporting personalized care and improving diagnostic workflows in ophthalmology. Full article

Functional segregation in brain networks refers to the division of specialized cognitive functions across distinct regions, enabling efficient and dedicated information processing. This paper explores the significance of functional segregation in shaping brain network architecture, highlighting methodologies such as modularity and local efficiency that quantify the degree of specialization and intra-regional communication. We examine how these metrics reveal the presence of specialized modules underpinning various cognitive processes and behaviors and discuss the implications of disruptions in functional segregation in neurological and psychiatric disorders. Our findings underscore the fact that understanding functional segregation is crucial for elucidating normal brain function, identifying biomarkers, and developing therapeutic interventions. Overall, functional segregation is a fundamental principle governing brain organization, and ongoing research into its mechanisms promises to advance our comprehension of the brain’s complex architecture and its impact on human health. Full article

A two-dimensional time-dependent model is presented for upward-propagating internal gravity waves generated by an imposed thermal forcing in a layer of fluid with uniform background velocity and stable stratification under the anelastic approximation. The configuration studied is representative of a situation with deep or shallow latent heating in the lower atmosphere where the amplitude of the waves is small enough to allow linearization of the model equations. Approximate asymptotic time-dependent solutions, valid for late time, are obtained for the linearized equations in the form of an infinite series of terms involving Bessel functions. The asymptotic solution approaches a steady-amplitude state in the limit of infinite time. A weakly nonlinear analysis gives a description of the temporal evolution of the zonal mean flow velocity and temperature resulting from nonlinear interaction with the waves. The linear solutions show that there is a vertical variation of the wave amplitude which depends on the relative depth of the heating to the scale height of the atmosphere. This means that, from a weakly nonlinear perspective, there is a non-zero divergence of vertical momentum flux, and hence, a non-zero drag force, even in the absence of vertical shear in the background flow. Full article

As cities grow denser, the demand for efficient parking systems becomes more critical to reduce traffic congestion, fuel consumption, and environmental impact. This paper proposes a smart parking solution that combines deep learning and algorithmic sorting to identify the nearest available parking slot in real time. The system uses several pre-trained convolutional neural network (CNN) models—VGG16, ResNet50, Xception, LeNet, AlexNet, and MobileNet—along with a lightweight custom CNN architecture, all trained on a custom parking dataset. These models are integrated into a mobile application that allows users to view and request nearby parking spaces. A merge sort algorithm ranks available slots based on proximity to the user. The system is validated using benchmark datasets (CNR-EXT and PKLot), demonstrating high accuracy across diverse weather conditions. The proposed system shows how applied mathematical models and deep learning can improve urban mobility through intelligent infrastructure. Full article

Stokes wave is a classical problem in physics. Various Stokes wave theories in different forms have been developed to help us better understand their characteristics and for engineering applications. Exploring whether these Stokes wave theories can be converted into each other is a mathematical issue. We select three Stokes wave theories with different expansion parameters, all expressed in terms of water depth measured from the mean water level (MWL). Using series reversion to convert between the different expansions, we successfully transform the expressions for the velocity potential, wave profile, and dynamic properties between two of the Stokes wave theories. Through this conversion, we identify an incorrect expression for the water level in one Stokes wave theory. Full article

Psychological momentum dynamics in tennis have triggered interest for a long time, but measuring their impact presents substantial obstacles. In this paper, we present an approach to quantify momentum that combines real-time winning probabilities, leverage, and an exponentially weighted moving average (EWMA). We test the method on a high-profile match between Carlos Alcaraz and Novak Djokovic, demonstrating how changes in leverage affect momentum. Furthermore, we use feature extraction methods from time series analysis to derive momentum-related characteristics, which are critical inputs for creating an eXtreme Gradient Boosting (XGBoost) binary classification model to predict game winners. The algorithm has an average accuracy of 84% and provides real-time predictions of each player’s chances of winning the match. Our findings indicate that momentum is a somewhat relevant element in forecasting match outcomes, highlighting its potential value in improving match prediction systems. Full article

The rapid advancement of machine learning and deep learning techniques has revolutionized stock market prediction, providing innovative methods to analyze financial trends and market behavior. This review paper presents a comprehensive analysis of various machine learning and deep learning approaches utilized in stock market prediction, focusing on their methodologies, evaluation metrics, and datasets. Popular models such as LSTM, CNN, and SVM are examined, highlighting their strengths and limitations in predicting stock prices, volatility, and trends. Additionally, we address persistent challenges, including data quality and model interpretability, and explore emerging research directions to overcome these obstacles. This study aims to summarize the current state of research, provide insights into the effectiveness of predictive models. Full article

Artificial intelligence (AI) has found applications across diverse sectors in recent years, significantly enhancing operational efficiencies and user experiences. Educational data mining (EDM) has emerged as a pivotal AI application to transform educational environments by optimizing learning processes and identifying at-risk students. This study leverages EDM within a Moroccan university (Hassan First, University Settat, Morocco) context to augment educational quality and improve learning. We introduce a novel “Hybrid approach” that synthesizes students’ historical academic records and their in-class behavioral data, provided by instructors, to predict student performance in initial coding courses. Utilizing a range of machine learning (ML) algorithms, our research applies multi-classification, data augmentation, and binary classification techniques to evaluate student outcomes effectively. The key performance metrics, accuracy, precision, recall, and F1-score, are calculated to assess the efficacy of classification. Our results highlight the long short-term memory (LSTM) algorithm’s robustness achieving the highest accuracy of 94% and an F1-score of 0.87 along with a support vector machine (SVM), indicating high efficacy in predicting student success at the onset of learning coding. Furthermore, the study proposes a comprehensive framework that can be integrated into learning management systems (LMSs) to accommodate generational shifts in student populations, evolving university pedagogies, and varied teaching methodologies. This framework aims to support educational institutions in adapting to changing educational dynamics while ensuring high-quality, tailored learning experiences for students. Full article

Vector-borne diseases pose a significant public health challenge in tropical regions, where complex interactions between hosts, vectors, and the environment drive epidemic dynamics. In this study, we develop a spatio-temporal mathematical model to describe the spread of such diseases, incorporating population dynamics and spatial–temporal factors affecting pathogen transmission. We conduct a theoretical analysis of the model, proving the existence, uniqueness, and positivity of solutions. Additionally, we examine equilibrium states and key epidemiological parameters, including the basic reproduction number. Our findings provide mathematical insights into epidemic propagation and offer a foundation for designing effective control strategies. Full article

The aim of this paper is to propose mathematical models to predict and optimize the cost of wastewater treatment using bacteria and oxygen under fluctuating resource and cultivation conditions. We have thus developed deterministic mathematical models based on dynamic systems and applied optimal control theory to reduce treatment costs. Two wastewater treatment models are proposed: one using only one type of aerobic bacteria, thermophilic bacteria; and the second using two types of aerobic bacteria, thermophilic and mesophilic bacteria. For each model, an optimal control problem is solved and numerical simulations illustrate the theoretical results. Full article

In this study, we introduce a novel application of the Smooth Overlap of Atomic Positions (SOAP) descriptor for pixel-wise image feature extraction and classification as a benchmark for SOAP point cloud feature extraction, using MNIST handwritten digits as a benchmark. By converting 2D images into 3D point sets, we compute pixel-centered SOAP vectors that are intrinsically invariant to translation, rotation, and mirror symmetry. We demonstrate how the descriptor’s hyperparameters—particularly the cutoff radius—significantly influence classification accuracy, and show that the high-dimensional SOAP vectors can be efficiently compressed using PCA or autoencoders with minimal loss in predictive performance. Our experiments also highlight the method’s robustness to positional noise, exhibiting graceful degradation even under substantial Gaussian perturbations. Overall, this approach offers an effective and flexible pipeline for extracting rotationally and translationally invariant image features, potentially reducing reliance on extensive data augmentation and providing a robust representation for further machine learning tasks. Full article

This article aims to limit the rule explosion problem affecting market basket analysis (MBA) algorithms. More specifically, it is shown how, if the minimum support threshold is not specified explicitly, but in terms of the number of items to consider, it is possible to compute an upper bound for the number of generated association rules. Moreover, if the results of previous analyses (with different thresholds) are available, this information can also be taken into account, hence refining the upper bound and also being able to compute lower bounds. The support determination technique is implemented as an extension to the Apriori algorithm but may be applied to any other MBA technique. Tests are executed on benchmarks and on a real problem provided by one of the major Italian supermarket chains, regarding more than $500,000$ transactions. Experiments show, on these benchmarks, that the rate of growth in the number of rules between tests with increasingly more permissive thresholds ranges, with the proposed method, is from $21.4$ to $31.8$, while it would range from $39.6$ to $3994.3$ if the traditional thresholding method were applied. Full article

Despite its significance, hysteresis remains underrepresented in mainstream models of plasticity. In this work, we propose a novel framework that explicitly models hysteresis in simple one- and two-neuron models. Our models capture key feedback-dependent phenomena such as bistability, multistability, periodicity, quasi-periodicity, and chaos, offering a more accurate and general representation of neural adaptation. This opens the door to new insights in computational neuroscience and neuromorphic system design. Synaptic weights change in several contexts or mechanisms including, Bienenstock–Cooper–Munro (BCM) synaptic modification, where synaptic changes depend on the level of post-synaptic activity; homeostatic plasticity, where all of a neuron synapses simultaneously scale up or down to maintain stability; metaplasticity, or plasticity of plasticity; neuromodulation, where neurotransmitters influence synaptic weights; developmental processes, where synaptic connections are actively formed, pruned and refined; disease or injury; for example, neurological conditions can induce maladaptive synaptic changes; spike-time dependent plasticity (STDP), where changes depend on the precise timing of pre- and postsynaptic spikes; and structural plasticity, where changes in dendritic spines and axonal boutons can alter synaptic strength. The ability of synapses and neurons to change in response to activity is fundamental to learning, memory formation, and cognitive adaptation. This paper presents simple continuous and discrete neuro-modules with adapting feedback synapses which in turn are subject to feedback. The dynamics of continuous periodically driven Hopfield neural networks with adapting synapses have been investigated since the 1990s in terms of periodicity and chaotic behaviors. For the first time, one- and two-neuron models are considered as parameters are varied using a feedback mechanism which more accurately represents real-world simulation, as explained earlier. It is shown that these models are history dependent. A simple discrete two-neuron model with adapting feedback synapses is analyzed in terms of stability and bifurcation diagrams are plotted as parameters are increased and decreased. This work has the potential to improve learning algorithms, increase understanding of neural memory formation, and inform neuromorphic engineering research. Full article

This article studies the location–price Hotelling game. Numerous studies have been conducted on the Hotelling game with simultaneous decisions; however, in real-life scenarios, decisions are frequently sequential. Unfortunately, studies on the sequential Hotelling (SHOT) game are quite scarce. This article contributes to the study of the SHOT game by considering the case in which the location of one of the players, either the leader or the follower, is externally fixed. The game is studied analytically and by numerical simulation to address scenarios where mathematical analysis is cumbersome due to the discontinuous nature of the game. Simulation is found to be particularly useful in evaluating the subgame perfect equilibrium (SPE) solution of these SHOT games, where the follower outperforms the leader as a very general rule, with very few exceptions. This article complements a previous study of the SHOT game where the two locations are parameterized and paves the way to address the analysis of more sophisticated formulations of the SHOT game, such as those with reservation cost and with elastic demand. Full article

After linear differential systems in the plane, the easiest systems are quadratic polynomial differential systems in the plane. Due to their nonlinearity and their many applications, these systems have been studied by many authors. Such quadratic polynomial differential systems have been divided into ten families. Here, for two of these families, we classify all topologically distinct phase portraits in the Poincaré disc. These two families have already been studied previously, but several mistakes made there are repaired here thanks to the use of a more powerful technique. This new technique uses the invariant theory developed by the Sibirskii School, applied to differential systems, which allows to determine all the algebraic bifurcations in a relatively easy way. Even though the goal of obtaining all the phase portraits of quadratic systems for each of the ten families is not achievable using only this method, the coordination of different approaches may help us reach this goal. Full article