Search Results (108)

This study aims to compare different classifiers in the context of distinguishing two classes of signals: nonlinear electrocardiography (ECG) signals and stochastic artifacts occurring in ECG signals. The ECG signals from a single-lead wearable Movesense device were analyzed with a set of eight features: variance (VAR), three fractal dimension measures (Higuchi fractal dimension (HFD), Katz fractal dimension (KFD), and Detrended Fluctuation Analysis (DFA)), and four entropy measures (approximate entropy (ApEn), sample entropy (SampEn), and multiscale entropy (MSE) for scales 1 and 2). The minimum-redundancy maximum-relevance algorithm was applied for evaluation of feature importance. A broad spectrum of machine learning models was considered for classification. The proposed approach allowed for comparison of classifier features, as well as providing a broader insight into the characteristics of the signals themselves. The most important features for classification were VAR, DFA, ApEn, and HFD. The best performance among 34 classifiers was obtained using an optimized RUSBoosted Trees ensemble classifier (sensitivity, specificity, and positive and negative predictive values were 99.8, 73.7%, 99.8, and 74.3, respectively). The accuracy of the Movesense device was very high (99.6%). Moreover, the multifractality of ECG during sleep was observed in the relationship between SampEn (or ApEn) and MSE. Full article

Objectives: This study evaluated the utility of complex morphometric analyses for predicting radiation pneumonitis (RP) and proposed a quantitative prognostic framework for patients with non-small cell lung cancer (NSCLC) undergoing curative-intent radiotherapy (RT). Imaging biomarkers, including box-counting fractal dimension (BoxFD), lacunarity, and minimum spanning tree fractal dimension (MSTFD), were assessed for their prognostic significance. Materials and Methods: We retrospectively analyzed 166 NSCLC patients who received curative-intent RT and had both pre-treatment and follow-up chest CT scans. Among them, 85 received RT alone and 81 underwent concurrent chemoradiotherapy (CCRT). Fractal features were measured to build a Random Forest model (RFM) predicting RP of grade ≥ 2, and the most important features were used to construct a decision tree model. Results: RP of grade ≥ 2 occurred in 19 patients (22.3%) in the RT alone group and 44 patients (54.3%) in the CCRT group. Lacunarity increased significantly post-RT in both groups, while BoxFD and MSTFD showed no significant changes. In the RFM, pre-RT MSTFD and lung dose parameters (V10 in RT alone; V5–V20 in CCRT) were identified as key predictors. Decision tree models based on these features achieved high predictive performance, with AUROC of 0.83 and 0.85, and F1 scores of 0.92 and 0.76 for RT alone and CCRT groups, respectively. Conclusions: Fractal imaging biomarkers demonstrated promising prognostic value for predicting grade ≥ 2 RP in NSCLC patients. The proposed decision tree model may serve as a practical tool for early identification of high-risk patients, facilitating personalized treatment strategies and informing future research. Full article

The anti-slip performance of road surfaces directly affects traffic safety, yet existing evaluation methods based on texture features often suffer from limited interpretability and low accuracy. To overcome these limitations, a portable 3D laser surface analyzer was used to acquire road texture data, while a dynamic friction coefficient tester provided friction measurements. A multi-view fractal dimension index was developed to comprehensively describe the complexity of texture across spatial, cross-sectional, and depth dimensions. Combined with road surface temperature, this index was integrated into an XGBoost-based prediction model to evaluate friction at driving speeds of 10 km/h and 70 km/h. Comparative analysis with linear regression, decision tree, support vector machine, random forest, and backpropagation (BP) neural network models confirmed the superior predictive performance of the proposed approach. The model achieved backpropagation (R²) values of 0.80 and 0.82, with root mean square errors (RMSEs) of 0.05 and 0.04, respectively. Feature importance analysis indicated that fractal characteristics from multiple texture perspectives, together with temperature, significantly influence anti-slip performance. The results demonstrate the feasibility of using non-contact texture-based methods to replace traditional contact-based friction testing. Compared with traditional statistical indices and alternative machine learning algorithms, the proposed model achieved improvements in R² (up to 0.82) and reduced RMSE (as low as 0.04). This study provides a robust indicator system and predictive model to advance road surface safety assessment technologies. Full article

Understanding how people perceive urban streetscapes is essential for enhancing the visual quality of the urban environment and optimizing street space design. While perceptions are shaped by the interplay of multiple visual elements, existing studies often isolate single semantic features, overlooking their combinations. This study proposes a Landscape Element Combination Extraction Method (SLECEM), which integrates the UniSal saliency detection model and semantic segmentation to identify landscape combinations that play a dominant role in human perceptions of streetscapes. Using street view images (SVIs) from the central area of Futian District, Shenzhen, China, we further construct a multi-dimensional feature–perception coupling analysis framework. The key findings are as follows: 1. Both low-level visual features (e.g., color, contrast, fractal dimension) and high-level semantic features (e.g., tree, sky, and building proportions) significantly influence streetscape perceptions, with strong nonlinear effects from the latter. 2. K-Means clustering of salient landscape element combinations reveals six distinct streetscape types and perception patterns. 3. Combinations of landscape features better reflect holistic human perception than single variables. 4. Tailored urban design strategies are proposed for different streetscape perception goals (e.g., beauty, safety, and liveliness). Overall, this study deepens the understanding of streetscape perception mechanisms and proposes a highly operational quantitative framework, offering systematic theoretical guidance and methodological tools to enhance the responsiveness and sustainability of urban streetscapes. Full article

Accurate detection of surface defects such as wear, cracks, and flaws in metallic components is critical for equipment reliability and longevity, representing a core challenge in surface integrity engineering. To solve the information loss, low estimation accuracy and poor noise immunity associated with Multiscale Dispersion Entropy (MDE) are utilized to address the sensitivity to parameter selection and overfitting susceptibility of the Least Squares Twin Support Vector Machines (LSTSVM). A brand new fault diagnosis method which combined Time Shift Multiscale Ensemble Fuzzy Dispersion Entropy (TSMEFuDE) with binary tree LSTSVM (BT LSTSVM) was proposed. Firstly, a time shift method based on Higuchi Fractal Dimension was introduced to TSMEFuDE, resolving the continuity loss between coarse-grained levels. Second, four mapping techniques, linear, NCDF, tansig and logsig, are introduced. This synergetic combination of each advantage results in the improvement of entropy output stability. Furthermore, triangular and trapezoidal membership functions are incorporated into dispersion patterns and abolished in the round function, therefore enhancing the boundaries between the classes after signal mapping to discrete classes. Lastly, the proposed BT LSTSVM algorithm decomposes the multi-classification problem to a binary classification problem, which promotes the robustness of the algorithm. Simulation experiments maintain that TSMEFuDE has stronger adaptability, higher stability, and better noise resistance. In the fault diagnosis experiment, when compared to the Multiscale Fuzzy Dispersion Entropy (MFuDE) combined with the BT TSVM method, the TSMEFuDE combined with BT LSTSVM method improved the accuracy of bearing fault diagnosis by 5.65% and 2.82%. Full article

Globally, there are now more than 19 billion connected Internet of Things (IoT) devices, which are fostering innovation across various sectors, including industry, healthcare, education, energy, and agriculture. With the rapid expansion of IoT devices, there is an increasing demand for sustainable, self-powered, eco-friendly solutions for next-generation IoT devices. Harvesting and converting radio frequency (RF) energy through rectennas is being explored as a potential solution for next-generation self-powered wireless devices. This paper presents a methodology for designing, optimizing, and fabricating a flexible rectenna for RF energy harvesting in the 5G lower mid-band and ISM 2.45 GHz band. The antenna element has a tree form based on a fractal structure, which provides a small size for the rectenna. Furthermore, to reduce the rectenna’s environmental impact, we fabricated the rectenna on a substrate from biodegradable materials—natural rubber filled with rice husk ash. The rectifier circuit was also designed and fabricated on the flexible substrate, facilitating the seamless integration of the rectenna in next-generation low-power IoT devices. The numerical analysis of the parameters and characteristics of rectenna elements, based on the finite-difference time-domain method, demonstrates a high degree of agreement with the experimental results. Full article

Deciphering the structural hierarchy of musical compositions is indispensable for a range of music analysis applications, encompassing feature extraction, data compression, interpretation, and visualization. In this paper, we introduce a quantitative model grounded in fractal theory to evaluate the significance of individual notes within a musical piece. To analyze the quantized note importance, we adopt a rhythm-based approach and propose a series of detection operators informed by fundamental rhythmic combinations. Employing the Mamba model, we carry out recursive detection operations that offer a hierarchic understanding of musical structures. By organizing the composition into a tree data structure, we achieve an ordered layer traversal that highlights the music piece’s multi-dimensional features. Musical compositions often exhibit intrinsic symmetry in their temporal organization, manifested through repetition, variation, and self-similar patterns across scales. Among these symmetry properties, fractality stands out as a prominent characteristic, reflecting recursive structures both rhythmically and melodically. Our model effectively captures this property, providing insights into the fractal-like regularities within music. It also proves effective in musical phrase boundary detection tasks, enhancing the clarity and visualization of musical information. The findings illustrate the model’s potential to advance the quantitative analysis of music hierarchy, promoting novel methodologies in musicological research. Full article

This paper presents and examines a discrete-time predator–prey model of the Leslie type, integrating a Holling type IV functional response for analysis. The mathematical analysis succinctly identifies fixed points and evaluates their local stability within the model. The study employs the normal form approach and bifurcation theory to explore codimension-one and two bifurcation behaviors for this model. The primary conclusions are substantiated by a combination of rigorous theoretical analysis and meticulous computational simulations. Additionally, utilizing fractal basin boundaries, periodicity variations, and Lyapunov exponent distributions within two-parameter spaces, we observe a mode-locking structure akin to Arnold tongues. These periods are arranged in a Farey tree sequence and embedded within quasi-periodic/chaotic regions. These findings enhance comprehension of bifurcation cascade emergence and structural patterns in diverse biological systems with discrete dynamics. Full article

The ongoing exploration of brain–computer interfaces (BCIs) provides deeper insights into the workings of the human brain. Motor imagery (MI) tasks, such as imagining movements of the tongue, left and right hands, or feet, can be identified through the analysis of electroencephalography (EEG) signals. The development of BCI systems opens up opportunities for their application in assistive devices, neurorehabilitation, and brain stimulation and brain feedback technologies, potentially helping patients to regain the ability to eat and drink without external help, move, or even speak. In this context, the accurate recognition and deciphering of a patient’s imagined intentions is critical for the development of effective BCI systems. Therefore, to distinguish motor tasks in a manner differing from the commonly used methods in this context, we propose a fractal dimension (FD)-based approach, which effectively captures the self-similarity and complexity of EEG signals. For this purpose, all four classes provided in the BCI Competition IV 2a dataset are utilized with nine different combinations of seven FD methods: Katz, Petrosian, Higuchi, box-counting, MFDFA, DFA, and correlation dimension. The resulting features are then used to train five machine learning models: linear, Gaussian, polynomial support vector machine, regression tree, and stochastic gradient descent. As a result, the proposed method obtained top-tier results, achieving 79.2% accuracy when using the Katz vs. box-counting vs. correlation dimension FD combination (KFD vs. BCFD vs. CDFD) classified by LinearSVM, thus outperforming the state-of-the-art TWSB method (achieving 79.1% accuracy). These results demonstrate that fractal dimension features can be applied to achieve higher classification accuracy for online/offline MI-BCIs, when compared to traditional methods. The application of these findings is expected to facilitate the enhancement of motor imagery brain–computer interface systems, which is a key issue faced by neuroscientists. Full article

Tree-like fractals as internal structures are a novel alternative to conventional lattice structures for mechanical components produced via Selective Laser Melting (SLM). This study explores the mechanical behavior of tree-like fractals, targeting flexure tests on SLM test samples manufactured using two distinct fractal configurations. The main objective is to develop numerical models that can predict the effect of the branching angle on the stress-strain curves, for both fractal configurations, from experimental flexure tests. A polynomial regression model is proposed to predict mechanical response variations based on fractal geometry, and the prediction model provides acceptable errors, less than the natural variance of multiple experiments. Furthermore, the tree-like fractal samples showed an interesting behavior on the flexure test, where the fractals deformed uniformly and in a predictable pattern, enabling mechanical advantages in impact absorption applications. Full article

This paper reports the improved thermal and drying performance of a solar air heater powered by real solar irradiance and equipped with a tree-like fractal-based cylindrical pin (SAH-TFCP) as a turbulator for drying applications. The main purpose of this work is to demonstrate the SAH-TFCP’s improvement potential based on its thermal and drying performance as compared with a conventional solar air heater based on a flat-plate absorber (SAH-FP). The test was implemented based on solar time from 8:30 to 17:30 under Thailand’s climatic conditions at a latitude angle of 14° and a longitude angle of 100°. Turmeric slices were used to evaluate the SAH’s drying performance. The thermal efficiency, moisture content wet basis (MC_wb), drying rate (DR), and drying efficiency were measured as parameters of interest to assess the improvement potential of the SAH-TFCP over the SAH-FP. The results indicate that the SAH-TFCP provides better thermal and drying performance than the SAH-FP. A higher flow rate yields a higher thermal efficiency and a greater improvement potential. The improvement potential is around 44–85%. The drying efficiency of the SAH-TFCP is always higher than that of the SAH-FP and has an improvement potential of 32–44%, depending on the airflow rate. Full article

Viscoelastic materials are commonly used in civil engineering, biomedical sciences, and polymers, where understanding their creep and relaxation behaviors is essential for predicting long-term performance. This paper introduces an operator-based method for modeling viscoelastic materials, providing a unified framework to describe both creep and relaxation functions. The method utilizes stiffness and compliance operators, offering a systematic approach for analyzing viscoelastic problems. The operator-based method enhances the mathematical duality between the creep and relaxation functions, providing greater physical intuition and understanding of time-dependent material behavior. It directly reflects the intrinsic properties of materials, independent of input and output conditions. The method is extended to dynamic problems, with complex modulus and compliance derived through operator representations. The fractal tree model, with its constant loss factor across the frequency spectrum, demonstrates potential engineering applications. By incorporating a damage-based variable coefficient, the model now also accounts for the accelerated creep phase of rocks, capturing damage evolution under prolonged loading. While promising, the current method is limited to one-dimensional problems, and future research will aim to extend it to three-dimensional cases, integrate experimental validation, and explore broader applications. Full article

The transformation of the Cerrado biome into areas with different levels of activity and anthropic pressure negatively impacts biodiversity. This study evaluated the response of the dung beetle community to changes in land use systems: forests, rubber trees, pastures, and soybeans. Five areas were sampled in each system with a minimum distance of 2 km between them. Dung beetles were collected using pitfall traps, and both local (vegetation density, basal area of wooded vegetation, fractal dimension, litter height, electrical conductance (mV), water content in the soil (%), and soil resistance (kPa)) and landscape-related environmental variables (land use and overall composition and configuration of the landscape surrounding the sampling areas) were measured. In total, 2294 specimens were collected and distributed among 34 species and 18 genera. There was no significant difference in abundance between the systems, but differences in the number of species and biomass were observed between forest and soybean systems, as well as a separation of communities between the tree-covered (forest and rubber tree) and open (pasture and soybean) systems. Density and arboreal basal area were the main predictive variables for the diversity of the dung beetle community, reinforcing the importance of vegetation cover for maintaining diversity, whereas local and landscape-related variables influenced community composition. Full article

Silicone gel and silicone rubber are widely used in packaging insulation because of their high comprehensive performance. Nevertheless, the special deterioration mechanism under pulsed electric fields is not yet clear and needs to be studied in depth. This study has successfully built an experimental platform of the electrical tree under a thermal coupled pulsed electric field. Moreover, the effects of the pulse edge time, repetition frequency, and temperature on the tree initiation voltage, intuitive development morphology, and fractal dimension of the electrical tree are also investigated, respectively. In conclusion, silicone rubber has a higher insulation strength, while silicone gel has a certain self-recovery performance. The aim of the study is to realize the electrical tree deterioration characteristics of silicone gel and silicone rubber. The increase in repetition frequency, the decrease in edge time, and the increase in temperature all contribute to the initiation and growth of the electrical tree from different degrees and angles, making the electrical tree transform between a fine, dendritic, clumped, and pine-like shape. Full article

The accurate description of fracture distributions is a crucial prerequisite for fracturing design and the evaluation of fracturing effects in tight reservoirs. We employed a fractal L-system to establish a tree branch model and derived a planar simulation method to characterize the distribution of natural weak discontinuities in rock. Weak discontinuities are classified using fractal similarity principles, enabling the determination of shear and opening criteria for weak discontinuities at various levels in water-based and CO₂ fracturing, as well as the pressure drop gradient within fractures after the initiation of weak discontinuities. Based on a weak discontinuity distribution model and fracture criteria, a simulation calculation method for the distribution of fracturing branch fractures was formulated. The results indicate that the number of branch fractures is closely related to the net pressure within the fractures at the wellbore and the difference between the maximum and minimum principal stresses in the reservoir. Compared with water-based fracturing fluids, CO₂ fracturing can facilitate the opening of branch fractures by reducing the opening conditions required for them to occur. The proposed calculation method can generate planar fracture morphologies and opening conditions with fractal characteristics, providing a basis for studying complex fracture formation mechanisms during CO₂ fracturing in tight reservoirs. Full article