University of Szczecin

In this paper, we present mathematical geometric models and recursive algorithms to generate and design complex patterns using fractal structures. By applying analytical, iterative methods, iterative function systems (IFS), and L-systems to create geometric models of complicated fractals, we developed fractal construction models, visualization tools, and fractal measurement approaches. We introduced a novel recursive fractal modeling (RFM) method designed to generate intricate fractal patterns with enhanced control over symmetry, scaling, and self-similarity. The RFM method builds upon traditional fractal generation techniques but introduces adaptive recursion and symmetry-preserving transformations to produce fractals with applications in domains such as medical imaging, textile design, and digital art. Our approach differs from existing methods like Barnsley’s IFS and Jacquin’s fractal coding by offering faster convergence, higher precision, and increased flexibility in pattern customization. We used the RFM method to create a mathematical model of fractal objects that allowed for the viewing of polygonal, Koch curves, Cayley trees, Serpin curves, Cantor set, star shapes, circulars, intersecting circles, and tree-shaped fractals. Using the proposed models, the fractal dimensions of these shapes were found, which made it possible to create complex fractal patterns using a wide variety of complicated geometric shapes. Moreover, we created a software tool that automates the visualization of fractal structures. This tool may be used for a variety of applications, including the ornamentation of building items, interior and exterior design, and pattern construction in the textile industry.

Background/Objectives: The early and accurate detection of Coronary Artery Disease (CAD) is crucial for preventing life-threatening complications, particularly among athletes engaged in high-intensity endurance sports. This demographic faces unique cardiovascular risks, as prolonged and intense physical exertion can exacerbate underlying CAD conditions. Studies indicate that while athletes typically exhibit enhanced cardiovascular health, this demographic is not immune to Coronary Artery Disease (CAD) risks. Research has shown that approximately 1–2% of competitive athletes suffer from CAD-related complications, with sudden cardiac arrest being the leading cause of mortality in athletes over 35 years old. High-intensity endurance sports can exacerbate underlying CAD conditions due to the prolonged physical stress placed on the cardiovascular system, making early detection crucial. This study aimed to develop and evaluate a lightweight deep learning model for CAD detection tailored to the unique challenges of diagnosing athletes. Methods: This study introduces a lightweight deep learning model specifically designed for CAD detection in athletes. By integrating ResNet-inspired residual connections into the VGG16 architecture, the model achieves a balance of high diagnostic accuracy and computational efficiency. By incorporating ResNet-inspired residual connections into the VGG16 architecture, the model enhances gradient flow, mitigates vanishing gradient issues, and improves feature extraction of subtle morphological variations in coronary lesions. Its lightweight design, with only 1.2 million parameters and 3.5 GFLOPs, ensures suitability for real-time deployment in resource-constrained clinical environments, such as sports clinics and mobile diagnostic systems, where rapid and efficient diagnostics are essential for high-risk populations. Results: The proposed model achieved superior performance compared to state-of-the-art architectures, with an accuracy of 90.3%, recall of 89%, precision of 90%, and an AUC-ROC of 0.912. These metrics highlight its robustness in detecting and classifying CAD in athletes. The model lightweight architecture, with only 1.2 million parameters and 3.5 GFLOPs, ensures computational efficiency and suitability for real-time clinical applications, particularly in resource-constrained settings. Conclusions: This study demonstrates the potential of a lightweight, deep learning-based diagnostic tool for CAD detection in athletes, achieving a balance of high diagnostic accuracy and computational efficiency. Future work should focus on integrating broader dataset validations and enhancing model explainability to improve adoption in real-world clinical scenarios.

This study explored the relationship between muscle fatigue and changes in sEMG amplitude during isometric exercises. Using the FREEEMG 1000 hardware and software system, we monitored muscle activity biosignals in a cohort of healthy schoolchildren. Our findings suggest a correlation between fluctuations in sEMG amplitude and indications of muscle fatigue. However, the potential of fatigue indices rooted in sEMG amplitude as an objective metric for evaluating the efficacy of endurance training requires investigation that is more comprehensive.

This article explores the possibility of preparing athletes for Paralympic competitions based on kinematic tests grounded in computer information systems. The study examines the effectiveness of adjusting training load volumes in athletes’ physical preparation and diagnosing based on specific indicators. One of the primary objectives for domain experts is to integrate methods and tools into the training process that yield significant results in a short timeframe. The outcomes of this research reveal the potentialities of kinematic analysis concerning the volume and intensity of selected loads for each phase of para-athletes’ preparation, as well as the methodology chosen for executing these loads.

A set of basic structural circuits of control computing facilities (CCF) of data transmission networks (DTN) is defined in the article, the main features of the CCF functioning process are examined, and two classes of algorithms of dispatch program, for which a classification is proposed that makes it possible to formalize the functioning process of CCF of DTN with a limited number of mathematical models are identified.

This paper presents a comprehensive overview of recent advancements in biosignal processing techniques tailored for prosthetic control, specifically focusing on the analysis and classification of electromyography (EMG) signals. EMG signals, derived from muscle electrical activity, play a crucial role in prosthetic devices by enabling intuitive control through the interpretation of muscle behavior. The review begins by elucidating the fundamentals of EMG signal acquisition and processing, with a particular emphasis on preprocessing steps such as noise reduction and feature extraction. Various signal processing methods, including the Fourier transform, wavelet transform, and discrete cosine transform, are elaborated upon, highlighting their applications in analyzing EMG signals in the time–frequency domain.

Background/Objectives: Sports-related bone fractures are a common challenge in sports medicine, requiring accurate and timely diagnosis to prevent long-term complications and enable effective treatment. Conventional diagnostic methods often rely on manual interpretation, which is prone to errors and inefficiencies, particularly for subtle and localized fractures. This study aims to develop a lightweight and efficient deep learning-based framework to improve the accuracy and computational efficiency of fracture detection, tailored to the needs of sports medicine. Methods: We proposed a novel fracture detection framework based on the DenseNet121 architecture, incorporating modifications to the initial convolutional block and final layers for optimized feature extraction. Additionally, a Canny edge detector was integrated to enhance the model ability to detect localized structural discontinuities. A custom-curated dataset of radiographic images focused on common sports-related fractures was used, with preprocessing techniques such as contrast enhancement, normalization, and data augmentation applied to ensure robust model performance. The model was evaluated against state-of-the-art methods using metrics such as accuracy, recall, precision, and computational complexity. Results: The proposed model achieved a state-of-the-art accuracy of 90.3%, surpassing benchmarks like ResNet-50, VGG-16, and EfficientNet-B0. It demonstrated superior sensitivity (recall: 0.89) and specificity (precision: 0.875) while maintaining the lowest computational complexity (FLOPs: 0.54 G, Params: 14.78 M). These results highlight its suitability for real-time clinical deployment. Conclusions: The proposed lightweight framework offers a scalable, accurate, and efficient solution for fracture detection, addressing critical challenges in sports medicine. By enabling rapid and reliable diagnostics, it has the potential to improve clinical workflows and outcomes for athletes. Future work will focus on expanding the model applications to other imaging modalities and fracture types.

ABSTRACTThis article proposes a solution to the factorization problem in cryptographic systems by leveraging the steps of the Toom‐Cook algorithm for large‐number multiplication. This approach can factor a 200‐bit number, with performance varying depending on memory and processing power. Experiments demonstrate that the factorization problem in cryptography can be solved more efficiently by employing algorithms designed for fast and straightforward multiplication of large numbers. Examples include the Schönhage–Strassen algorithm, which is based on polynomials and Fourier transforms, the Fürer algorithm, the second Schönhage–Strassen algorithm using modular arithmetic, and Karatsuba's algorithm. This advancement significantly impacts modern computing and cryptography, enhancing both security and reliability. The proposed technique was extensively tested through simulations using the MATLAB simulator. Experimental results indicate improvements of 91% in efficiency and 95% in accuracy compared to state‐of‐the‐art techniques.

The timely and accurate detection of brain tumors is crucial for effective medical intervention, especially in resource-constrained settings. This study proposes a lightweight and efficient RetinaNet variant tailored for medical edge device deployment. The model reduces computational overhead while maintaining high detection accuracy by replacing the computationally intensive ResNet backbone with MobileNet and leveraging depthwise separable convolutions. The modified RetinaNet achieves an average precision (AP) of 32.1, surpassing state-of-the-art models in small tumor detection (APS: 14.3) and large tumor localization (APL: 49.7). Furthermore, the model significantly reduces computational costs, making real-time analysis feasible on low-power hardware. Clinical relevance is a key focus of this work. The proposed model addresses the diagnostic challenges of small, variable-sized tumors often overlooked by existing methods. Its lightweight architecture enables accurate and timely tumor localization on portable devices, bridging the gap in diagnostic accessibility for underserved regions. Extensive experiments on the BRATS dataset demonstrate the model robustness across tumor sizes and configurations, with confidence scores consistently exceeding 81%. This advancement holds the potential for improving early tumor detection, particularly in remote areas lacking advanced medical infrastructure, thereby contributing to better patient outcomes and broader accessibility to AI-driven diagnostic tools.

Monocular depth estimation (MDE) is a critical task in computer vision with applications in autonomous driving, robotics, and augmented reality. However, predicting depth from a single image poses significant challenges, especially in dynamic scenes where moving objects introduce scale ambiguity and inaccuracies. In this paper, we propose the Dynamic Iterative Monocular Depth Estimation (DI-MDE) framework, which integrates an iterative refinement process with a novel scale-alignment module to address these issues. Our approach combines elastic depth bins that adjust dynamically based on uncertainty estimates with a scale-alignment mechanism to ensure consistency between static and dynamic regions. Leveraging self-supervised learning, DI-MDE does not require ground truth depth labels, making it scalable and applicable to real-world environments. Experimental results on standard datasets such as SUN RGB-D and KITTI demonstrate that our method achieves state-of-the-art performance, significantly improving depth prediction accuracy in dynamic scenes. This work contributes a robust and efficient solution to the challenges of monocular depth estimation, offering advancements in both depth refinement and scale consistency.

The one-dimensional quaternion fractional Fourier transform (1DQFRFT) introduces a fractional-order parameter that extends traditional Fourier transform techniques, providing new insights into the analysis of quaternion-valued signals. This paper presents a rigorous theoretical foundation for the 1DQFRFT, examining essential properties such as linearity, the Plancherel theorem, conjugate symmetry, convolution, and a generalized Parseval’s theorem that collectively demonstrate the transform’s analytical power. We further explore the 1DQFRFT’s unique applications to probabilistic methods, particularly for modeling and analyzing stochastic processes within a quaternionic framework. By bridging quaternionic theory with probability, our study opens avenues for advanced applications in signal processing, communications, and applied mathematics, potentially driving significant advancements in these fields.

Accurate segmentation of brain tumors in MRI scans is critical for diagnosis and treatment planning. Traditional segmentation models, such as U-Net, excel in capturing spatial information but often struggle with complex tumor boundaries and subtle variations in image contrast. These limitations can lead to inconsistencies in identifying critical regions, impacting the accuracy of clinical outcomes. To address these challenges, this paper proposes a novel modification to the U-Net architecture by integrating a spatial attention mechanism designed to dynamically focus on relevant regions within MRI scans. This innovation enhances the model’s ability to delineate fine tumor boundaries and improves segmentation precision. Our model was evaluated on the Figshare dataset, which includes annotated MRI images of meningioma, glioma, and pituitary tumors. The proposed model achieved a Dice similarity coefficient (DSC) of 0.93, a recall of 0.95, and an AUC of 0.94, outperforming existing approaches such as V-Net, DeepLab V3+, and nnU-Net. These results demonstrate the effectiveness of our model in addressing key challenges like low-contrast boundaries, small tumor regions, and overlapping tumors. Furthermore, the lightweight design of the model ensures its suitability for real-time clinical applications, making it a robust tool for automated tumor segmentation. This study underscores the potential of spatial attention mechanisms to significantly enhance medical imaging models and paves the way for more effective diagnostic tools.

The generation of synthetic medical data has become a focal point for researchers, driven by the increasing demand for privacy-preserving solutions. While existing generative methods heavily rely on real datasets for training, access to such data is often restricted. In contrast, statistical information about these datasets is more readily available, yet current methods struggle to generate tabular data solely from statistical inputs. This study addresses the gaps by introducing a novel approach that converts statistical data into tabular datasets using a modified Generative Adversarial Network (GAN) architecture. A custom loss function was incorporated into the training process to enhance the quality of the generated data. The proposed method is evaluated using fidelity and utility metrics, achieving “Good” similarity and “Excellent” utility scores. While the generated data may not fully replace real databases, it demonstrates satisfactory performance for training machine-learning algorithms. This work provides a promising solution for synthetic data generation when real datasets are inaccessible, with potential applications in medical data privacy and beyond.

A modern approach to personalized recommendation systems is presented, combining graph neural networks GNN with RL reinforcement learning methods. The GNN model is optimized for recommendation systems and is trained on vector representations of users and products, which are used to generate an initial list of recommendations that are fed into the RL model. Particular attention is paid to the architecture and operation of the integrated GNN-RL model. The results of experimental studies demonstrating the effectiveness of the proposed approach are presented.