Search Results (497)

How to identify the key nodes in a complex network is a major challenge. In this paper, we propose a Second-Order Neighborhood Entropy Fuzzy Local Dimension Spring Model (SNEFLD-SM). SNEFLD-SM model combines a variety of centrality methods based on spring model, such as second-order neighborhood centrality, betweenness centrality, and fractal dimension, to evaluate the importance of nodes. Fractal technology can effectively boost the framework’s proficiency in understanding network self-similarity and hierarchical structure in multi-scale complex networks. It overcomes the limitation of the traditional centrality method which only focuses on local or global information. The method introduces information entropy and node influence range; information entropy can effectively capture the local and global features of the network. The node influence rangecan increase the node importance distinction and reduce the calculation cost. Meanwhile, an attenuation factor is introduced to suppress the “rich-club” phenomenon. Tests on six networks show that SNEFLD-SM has higher accuracy in critical node detection than traditional methods. Furthermore, the application of information entropy further strengthens the model’s capability to recognize key nodes. Full article

Early detection of physiological dysregulation is critical for timely intervention and effective health management. Traditional monitoring systems often rely on labeled data and predefined thresholds, limiting their adaptability and generalization to unseen conditions. To address this, we propose a framework for label-free classification of physiological states using Heart Rate Variability (HRV), combined with unsupervised machine learning techniques. This approach is particularly valuable when annotated datasets are scarce or unavailable—as is often the case in real-world wearable and IoT-based health monitoring. In this study, data were collected from participants under controlled conditions representing rest, stress, and physical exertion. Core HRV parameters such as the SDNN (Standard Deviation of all Normal-to-Normal intervals), RMSSD (Root Mean Square of the Successive Differences), DFA (Detrended Fluctuation Analysis) were extracted. Principal Component Analysis was applied for dimensionality reduction. K-Means, hierarchical clustering, and Density-based spatial clustering of applications with noise (DBSCAN) were used to uncover natural groupings within the data. DBSCAN identified outliers associated with atypical responses, suggesting potential for early anomaly detection. The combination of HRV descriptors enabled unsupervised classification with over 90% consistency between clusters and physiological conditions. The proposed approach successfully differentiated the three physiological conditions based on HRV and fractal features, with a clear separation between clusters in terms of DFA α1, α2, LF/HF, and RMSSD (with high agreement to physiological labels (Purity ≈ 0.93; ARI = 0.89; NMI = 0.92)). Furthermore, DBSCAN identified three outliers with atypical autonomic profiles, highlighting the potential of the method for early warning detection in real-time monitoring systems. Full article

This study presents a comprehensive grayscale texture analysis framework for investigating the microstructural evolution of cement-based materials during hydration. High-resolution X-ray computed tomography (X-CT) slice images were analyzed across five hydration ages (12 h, 1 d, 3 d, 7 d, and 31 d) using three complementary methods: grayscale histogram statistics, fractal dimension calculation via differential box-counting, and texture feature extraction based on the gray-level co-occurrence matrix (GLCM). The average value of the mean grayscale value of slice (Mean_{G_AVE}) shows a trend of increasing and then decreasing. Average fractal dimension values (D_{B_AVE}) decreased logarithmically from 2.48 (12 h) to 2.41 (31 d), quantifying progressive microstructural homogenization. The trend reflects pore refinement and gel network consolidation. GLCM texture parameters—including energy, entropy, contrast, and correlation—captured the directional statistical patterns and phase transitions during hydration. Energy increased with hydration time, reflecting greater spatial homogeneity and phase continuity, while entropy and contrast declined, signaling reduced structural complexity and interfacial sharpness. A quantitative evaluation of parameter performance based on intra-sample stability, inter-sample discrimination, and signal-to-noise ratio (SNR) revealed energy, entropy, and contrast as the most effective descriptors for tracking hydration-induced microstructural evolution. This work demonstrates a novel, integrative, and segmentation-free methodology for texture quantification, offering robust insights into the microstructural mechanisms of cement hydration. The findings provide a scalable basis for performance prediction, material optimization, and intelligent cementitious design. Full article

This study investigates the influence of carbonation duration and sand-to-powder ratio on the compressive strength and pore structure of recycled cement paste–sand (RCP-S) mortar. Specimens incorporating four different sand contents were subjected to carbonation for 1 and 24 h. Fractal dimensions, ranging from 2.60159 to 3.86742, indicated increased pore complexity with extended carbonation exposure. Mercury intrusion porosimetry (MIP) and scanning electron microscopy (SEM) were employed to characterize pore features, including volume, surface area, and diameter. A Menger sponge-based fractal model was applied to compute the fractal dimensions and investigate their relationships with microstructural parameters and mechanical performance. Results showed that prolonged carbonation markedly reduced macropores and large capillary pores, enhanced fine pore content, and improved overall pore connectivity. Fractal analysis revealed that Segments I and IV exhibited the most significant fractal characteristics. The fractal dimension demonstrated exponential correlations with pore diameter; quadratic relationships—with superior statistical performance—with porosity, surface area, and pore volume; and a power–law relationship with compressive strength. These findings highlight the potential of fractal parameters as effective indicators of pore structure complexity and mechanical performance. This study offers a quantitative basis for optimizing pore structure in recycled cementitious materials, promoting their sustainable application in construction. Full article

Objectives: Non-small cell lung cancer (NSCLC), the most prevalent type of lung cancer, includes subtypes such as adenocarcinoma (ADC) and squamous cell carcinoma (SCC), which require distinct management approaches. Accurately differentiating NSCLC subtypes based on diagnostic imaging remains challenging. However, the extraction of radiomic features—such as first-order statistics (FOS), second-order statistics (SOS), and fractal dimension texture analysis (FDTA) features—from magnetic resonance (MR) images supports the development of quantitative NSCLC assessments. Methods: This study aims to evaluate whether the integration of FDTA features with FOS and SOS texture features in MR image analysis improves machine learning classification of NSCLC into ADC and SCC subtypes. The study was conducted on 274 MR images, comprising ADC (n = 122) and SCC (n = 152) cases. From the segmented MR images, 93 texture features were extracted. The random forest algorithm was used to identify informative features from both FOS/SOS and combined FOS/SOS/FDTA datasets. Subsequently, the k-nearest neighbors (kNN) algorithm was applied to classify MR images as ADC or SCC. Results: The highest performance (accuracy = 0.78, precision = 0.81, AUC = 0.89) was achieved using 37 texture features selected from the combined FOS/SOS/FDTA dataset. Conclusions: Incorporating fractal descriptors into the texture-based classification of lung MR images enhances the differentiation of NSCLC subtypes. Full article

In the field of deep learning, the traditional Vision Transformer (ViT) model has some limitations when dealing with local details and long-range dependencies; especially in the absence of sufficient training data, it is prone to overfitting. Structures such as retinal blood vessels and lesion boundaries have distinct fractal properties in medical images. The Fractional Convolution Vision Transformer (FCViT) model is proposed in this paper, which effectively compensates for the deficiency of ViT in local feature capture by fusing convolutional information. The ability to classify medical images is enhanced by analyzing frequency domain features using fractional-order Fourier transform and capturing global information through a self-attention mechanism. The three-branch architecture enables the model to fully understand the data from multiple perspectives, capturing both local details and global context, which in turn improves classification performance and generalization. The experimental results showed that the FCViT model achieved 93.52% accuracy, 93.32% precision, 92.79% recall, and a 93.04% F1-score on the standardized fundus glaucoma dataset. The accuracy on the Harvard Dataverse-V1 dataset reached 94.21%, with a precision of 93.73%, recall of 93.67%, and F1-score of 93.68%. The FCViT model achieves significant performance gains on a variety of neural network architectures and tasks with different source datasets, demonstrating its effectiveness and utility in the field of deep learning. Full article

This study focuses on the complex pore structure and pronounced heterogeneity of tight sandstone reservoirs in the Linxing area of the Ordos Basin and develops a multi-scale quantitative characterization approach to investigate the coupling mechanism between pore structure and reservoir properties. Six core samples were selected from the Shiqianfeng Formation (depth interval: 1326–1421 m) for detailed analysis. Cast thin sections and scanning electron microscopy (SEM) experiments were employed to characterize pore types and structural features. Nuclear magnetic resonance (NMR) experiments were conducted to obtain T₂ spectra, which were used to classify bound and movable pores, and their corresponding fractal dimensions were calculated separately. In addition, NMR logging data from the corresponding well intervals were integrated to assess the applicability and consistency of the fractal characteristics at the logging scale. The results reveal that the fractal dimension of bound pores shows a positive correlation with porosity, whereas that of movable pores is negatively correlated with permeability, indicating that different scales of pore structural complexity exert distinct influences on reservoir performance. Mineral composition affects the evolution of pore structures through mechanisms such as framework support, dissolution, and pore-filling, thereby further enhancing reservoir heterogeneity. The consistency between logging responses and experimental observations verifies the regional applicability of fractal analysis. Bound pores dominate within the studied interval, and the vertical variation of the PMF/BVI ratio aligns closely with both the NMR T₂ spectra and fractal results. This study demonstrates that fractal dimension is an effective descriptor of structural characteristics across different pore types and provides a theoretical foundation and methodological support for the evaluation of pore complexity and heterogeneity in tight sandstone reservoirs. Full article

Shale pore architecture governs gas storage capacity, permeability, and production potential in reservoirs. Therefore, this study systematically investigates the pore structure features and influencing factors of the Niutitang Formation shale from the QX1 well in northern Guizhou using field emission scanning electron microscopy (FE-SEM), high-pressure mercury intrusion (HPMI), low-temperature nitrogen adsorption (LTNA), and nuclear magnetic resonance (NMR) experiments. The results show that ① The pore size of the QX1 well’s Niutitang Formation shale is primarily in the nanometer range, with pore types including intragranular pores, intergranular pores, organic matter pores, and microfractures, with the former two types constituting the primary pore network. ② Pore shapes are plate-shaped intersecting conical microfractures or plate-shaped intersecting ink bottles, ellipsoidal, and beaded pores. ③ The pore size distribution showed a multi-peak distribution, predominantly mesopores, followed by micropores, with the fewest macropores. ④ The fractal dimension D₁ > D₂ indicates that the shale pore system is characterized by a rough surface and some connectivity of the pore network. ⑤ Carbonate mineral abundances are the main controlling factors affecting the pore structure of shales in the study area, and total organic carbon (TOC) content also has some influence, while clay mineral content shows negligible statistical correlation. Full article

Organic matter plays a vital role in shale reservoirs as both a hydrocarbon storage medium and migration pathway. However, the quantitative relationship between the microstructural features of organic matter and the macroscopic mechanical and failure behaviors of shale remains unclear due to rock heterogeneity and opacity. In this study, high-resolution three-dimensional digital core models of shale were reconstructed using Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) imaging. The digital models captured the spatial distribution of silicate minerals, clay minerals, and organic matter. Numerical simulations of uniaxial tensile failure were performed on these models, considering variations in the organic matter volume fraction and fractal dimension. The results indicate that an increased organic matter volume fraction and fractal dimension are associated with lower tensile strength, simpler fracture geometry, and reduced acoustic emission activity. Tensile cracks preferentially initiate at interfaces between minerals with contrasting elastic moduli, especially between organic matter and clay, and then propagate and coalesce under loading. These findings reveal that both the volume fraction and fractal structure of organic matter are reliable predictors of tensile strength and damage evolution in shale. This study provides new microscale insights into shale failure mechanisms and offers guidance for optimizing hydraulic fracturing in organic-rich formations. Full article

Multiple sclerosis (MS), a chronic disease of the central nervous system, is known to cause structural and vascular changes in the retina. Although optical coherence tomography (OCT) and fundus photography can detect retinal thinning and circulatory abnormalities, these findings are not specific to MS. This study explores the potential of Infrared Scanning-Laser-Ophthalmoscopy (IR-SLO) imaging to uncover vascular morphological features that may serve as MS-specific biomarkers. Using an age-matched, subject-wise stratified k-fold cross-validation approach, a deep learning model originally designed for color fundus images was adapted to segment optic disc, optic cup, and retinal vessels in IR-SLO images, achieving Dice coefficients of 91%, 94.5%, and 97%, respectively. This process included tailored pre- and post-processing steps to optimize segmentation accuracy. Subsequently, clinically relevant features were extracted. Statistical analyses followed by SHapley Additive exPlanations (SHAP) identified vessel fractal dimension, vessel density in zones B and C (circular regions extending 0.5–1 and 0.5–2 optic disc diameters from the optic disc margin, respectively), along with vessel intensity and width, as key differentiators between MS patients and healthy controls. These findings suggest that IR-SLO can non-invasively detect retinal vascular biomarkers that may serve as additional or alternative diagnostic markers for MS diagnosis, complementing current invasive procedures. Full article

In the field of deep learning, the design of optimization algorithms and neural network structures is crucial for improving model performance. Recent advances in medical image analysis have revealed that many pathological features exhibit fractal-like characteristics in their spatial distribution and morphological patterns. This observation has opened new possibilities for developing fractal-inspired deep learning approaches. In this study, we propose the following: (1) a novel Region-Module Adam (RMA) optimizer that incorporates fractal-inspired region-weighting to prioritize areas with higher fractal dimensionality, and (2) an ECA-Enhanced Shuffle MobileNet (ESM) architecture designed to capture multi-scale fractal patterns through its enhanced feature extraction modules. Our experiments demonstrate that this fractal-informed approach significantly improves classification accuracy compared to conventional methods. On gastrointestinal image datasets, the RMA algorithm achieved accuracies of 83.60%, 81.60%, and 87.30% with MobileNetV2, ShuffleNetV2, and ESM networks, respectively. For glaucoma fundus images, the corresponding accuracies reached 84.90%, 83.60%, and 92.73%. These results suggest that explicitly considering fractal properties in medical image analysis can lead to more effective diagnostic tools. Full article

As a discontinuous deformation method, the block element method (BEM) characterizes a material’s elastoplastic behavior through the constitutive relation of thin-layer elements between adjacent blocks. To realistically simulate rock damage paths, this work improves the traditional BEM by using random Voronoi polygonal grids for discrete modeling. This approach mitigates the distortion of damage paths caused by regular grids through the randomness of the Voronoi grids. As the innovation of this work, the iterative algorithm is combined with polygonal geometric features so that the area–perimeter fractal dimension can be introduced to optimize random Voronoi grids. The iterative control index can effectively improve the geometric characteristics of the grid while maintaining the necessary randomness. On this basis, a constitutive relation model that considers both normal and tangential damage is proposed. The entire process from damage initiation to macroscopic fracture failure in rocks is described using two independent damage surfaces and a damage relationship based on geometric mapping relationships. The analysis results are in good agreement with existing experimental data. Furthermore, the sensitivity method is used to analyze the influence of key mechanical parameters in the constitutive model. Full article

Community detection in complex networks plays a pivotal role in modern scientific research, including in social network analysis and protein structure analysis. Traditional community detection methods face challenges in integrating heterogeneous multi-source information, capturing global semantic relationships, and adapting to dynamic network evolution. This paper proposes a novel unsupervised multimodal community detection algorithm (UMM) based on fractal iteration. The core idea is to design a dual-channel encoder that comprehensively considers node semantic features and network topological structures. Initially, node representation vectors are derived from structural information (using feature vectors when available, or singular value decomposition to obtain feature vectors for nodes without attributes). Subsequently, a parameter-free graph convolutional encoder (PFGC) is developed based on fractal iteration principles to extract high-order semantic representations from structural encodings without requiring any training process. Furthermore, a semantic–structural dual-channel encoder (DC-SSE) is designed, which integrates semantic encodings—reduced in dimensionality via UMAP—with structural features extracted by PFGC to obtain the final node embeddings. These embeddings are then clustered using the K-means algorithm to achieve community partitioning. Experimental results demonstrate that the UMM outperforms existing methods on multiple real-world network datasets. Full article

The palm-vein recognition system has garnered attention as a biometric technology due to its resilience to external environmental factors, protection of personal privacy, and low risk of external exposure. However, with recent advancements in deep learning-based generative models for image synthesis, the quality and sophistication of fake images have improved, leading to an increased security threat from counterfeit images. In particular, palm-vein images acquired through near-infrared illumination exhibit low resolution and blurred characteristics, making it even more challenging to detect fake images. Furthermore, spoof detection specifically targeting palm-vein images has not been studied in detail. To address these challenges, this study proposes the Fourier-gated feature-fusion network (FGFNet) as a novel spoof detector for palm-vein recognition systems. The proposed network integrates masked fast Fourier transform, a map-based gated feature fusion block, and a fast Fourier convolution (FFC) attention block with global contrastive loss to effectively detect distortion patterns caused by generative models. These components enable the efficient extraction of critical information required to determine the authenticity of palm-vein images. In addition, fractal dimension estimation (FDE) was employed for two purposes in this study. In the spoof attack procedure, FDE was used to evaluate how closely the generated fake images approximate the structural complexity of real palm-vein images, confirming that the generative model produced highly realistic spoof samples. In the spoof detection procedure, the FDE results further demonstrated that the proposed FGFNet effectively distinguishes between real and fake images, validating its capability to capture subtle structural differences induced by generative manipulation. To evaluate the spoof detection performance of FGFNet, experiments were conducted using real palm-vein images from two publicly available palm-vein datasets—VERA Spoofing PalmVein (VERA dataset) and PLUSVein-contactless (PLUS dataset)—as well as fake palm-vein images generated based on these datasets using a cycle-consistent generative adversarial network. The results showed that, based on the average classification error rate, FGFNet achieved 0.3% and 0.3% on the VERA and PLUS datasets, respectively, demonstrating superior performance compared to existing state-of-the-art spoof detection methods. Full article

Prefabricated Ultra-High-Performance Concrete (UHPC) and cast-in-place Normal Concrete (NC) composite members are increasingly used in bridge engineering because they combine high performance with cost-effectiveness. The bond at the UHPC-NC interface is critical as it directly impacts the composite structure’s safety. This study employed 3D laser scanning acquired the UHPC substrate geometry, utilized fractal dimension analysis to quantify the interface roughness, and adopted the slant shear test to evaluate the effects of retarder application mass and hydration delay duration on roughness and bond strength. The research results indicate that the failure modes of UHPC-NC specimens can be categorized into interface shear failure and NC splitting tensile failure. With the extension of hydration delay duration, both the interface roughness and bond strength show a decreasing trend. The influence of retarder dosage on interface roughness and bond strength exhibits a threshold effect. This study also confirms the effectiveness of fractal dimension as a quantitative tool for characterizing the macroscopic roughness features of the bonding interface. The findings of this paper provide a solid theoretical basis and quantitative support for optimizing key process parameters such as retarder dosage and precisely controlling hydration delay duration, offering significant engineering guidance for enhancing the interface bonding performance of UHPC-NC composite structures. Full article