Reservoir nearshore areas are influenced by both terrestrial and aquatic ecosystems, making them sensitive regions to water quality changes. The analysis of basin landscape hydrological features provides limited insight into the spatial heterogeneity of eutrophication in these areas. The complex characteristics of shoreline morphology and their impact on eutrophication are often overlooked. To comprehensively analyze the complex relationships between shoreline morphology and landscape hydrological features, with eutrophication, this study uses Danjiangkou Reservoir as a case study. Utilizing Landsat 8 OLI remote sensing data from 2013 to 2022, combined with a semi-analytical approach, the spatial distribution of the Trophic State Index (TSI) during flood discharge periods (FDPs) and water storage periods (WSPs) was obtained. Using Extreme Gradient Boosting (XGBoost) and SHapley Additive exPlanations (SHAP), explained the relationships between landscape composition, landscape configuration, hydrological topography, shoreline morphology, and TSI, identified key factors at different spatial scales and validated their reliability. The results showed that: (1) There is significant spatial heterogeneity in the TSI distribution of Danjiangkou Reservoir. The eutrophication levels are significant in the shoreline and bay areas, with a tendency to extend inward only during the WSPs. (2) The importance of landscape composition, landscape configuration, hydrological topography, and shoreline morphology to TSI variations during the FDPs are 25.12 %, 29.6 %, 23.09 %, and 22.19 % respectively. Besides shoreline distance, the Landscape Shape Index (LSI) and Hypsometric Integral (HI) are the two most significant environmental variables overall during the FDPs. Forest and grassland areas become the most influential factors during the WSPs. The influence of landscape patterns and hydrological topography on TSI varies at different spatial scales. At the 200 m riparian buffer zone, the increase in cropland and impervious areas significantly elevates eutrophication levels. (3) Morphology complexity, shows a noticeable threshold effect on TSI, with complex shoreline morphology increasing the risk of eutrophication.

Particle geometric is a key parameter that defines the eometric attributes of calcareous sand particles and is intricately related to their mechanical traits, such as compression and shear. The scanning electron microscopy and digital imaging were applied to capture the microscopic properties and geometric projections of calcareous sand. The qualitative analysis, conventional statistical methods and fractal theory were employed to describe the geometric morphology of sand particles. Additionally, we analyzed the structural and physical traits of calcareous sand based on its unique biological genesis. We developed a hypothetical structural-physical model for calcareous sand. Our findings revealed the interwoven reticulation on the surface of calcareous gravel particles, along with an uneven distribution of pores on the external surface. As the particle size increased, the global profile factor decreased and the angularity increased. The critical threshold for the variations in flatness, surface roughness, and circularity was observed at a particle size of 5 mm, with the particle size having a relatively minor effect on these characteristics for particles smaller than 5 mm. The shape of the calcareous sand particles exhibited fractal characteristics, with fractal dimension serving as a measure of surface smoothness, particle breakage, and strength. These experimental results could significantly enhance our understanding of the mechanical behavior of calcareous sand.

To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25-0.5 (spilt and fracture), 0.5-0.9 (synergy between fracture and damage), 0.9-1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments.

With regard to deep mining in metal mines, an investigation into the failure mode of deep fractured rock masses and their corresponding acoustic emission signal characteristics is conducted via uniaxial compression tests. Subsequently, a fractal damage renormalization group mechanical model is developed to explain the behavior of those fractured rock masses. Employing the bonded block model (BBM) numerical simulation method, fracture process in synthetic rock samples is analyzed, thereby validating the efficacy of the mechanical model. The numerical simulations highlight the critical role of fractures expansion in underlying the deterioration of rock mass strength. As the peak load decreases, the fracture fractal dimension increases, leading to a significant 14.2% reduction in compressive strength accompanied by an approximate 8.7% rise in average fracture fractal dimension. A comparative analysis of tetrahedral and voronoi block synthetic rock samples reveals the tetrahedral block samples exhibit a superior ability to depict the fracture behavior of fractured rock masses. Specifically, they offer a more accurate simulation of acoustic emission characteristics and failure modes. Furthermore, variations in the fracture fractal dimension with respect to the hole defect\'s position are observed, with the maximum value occurring along the vertical axis of the hole defect. This observation underscores the potential utility of visually monitoring deep rock fracture dynamics as an effective mean for quantitatively evaluating fracture damage and strength degradation in deep rock formations.

Geographic atrophy (GA) is an advanced form of dry age-related macular degeneration (AMD) that leads to progressive and irreversible vision loss. Identifying patients with greatest risk of GA progression is important for targeted utilization of emerging therapies. This study aimed to comprehensively evaluate the role of shape-based fractal dimension features ( F fd ) of sub-retinal pigment epithelium (sub-RPE) compartment and texture-based radiomics features ( F t ) of Ellipsoid Zone (EZ)-RPE and sub-RPE compartments for risk stratification for subfoveal GA (sfGA) progression. This was a retrospective study of 137 dry AMD subjects with a 5-year follow-up. Based on sfGA status at year 5, eyes were categorized as Progressors and Non-progressors. A total of 15 shape-based F fd of sub-RPE surface and 494 F t from each of sub-RPE and EZ-RPE compartments were extracted from baseline spectral domain-optical coherence tomography scans. The top nine features were identified from F fd and F t feature pool separately using minimum Redundancy maximum Relevance feature selection and used to train a Random Forest (RF) classifier independently using three-fold cross validation on the training set ( S t , N = 90) to distinguish between sfGA Progressors and Non-progressors. Combined F fd and F t was also evaluated in predicting risk of sfGA progression. The RF classifier yielded AUC of 0.85, 0.79 and 0.89 on independent test set ( S v , N = 47) using F fd , F t , and their combination, respectively. Using combined F fd and F t , the improvement in AUC was statistically significant on S v with p-values of 0.032 and 0.04 compared to using only F fd and only F t , respectively. Combined F fd and F t appears to identify high-risk patients. Our results show that FD and texture features could be potentially used for predicting risk of sfGA progression and future therapeutic response.

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The Mu Us Sandy Land is a region characterized by wind-blown sand and soil erosion in northern China. To enhance the soil quality of this area, various organic materials were incorporated into the mixed soil at a volume ratio of 1:2 for feldspathic sandstone to sand. Culture was conducted in the field and under constant temperature conditions in laboratory culture chambers. Four treatments were established in the experiment, each calculated based on weight ratio and controlled (with no organic material added, CK); single application of straw (5% straw, P1); single application of biochar (5% biochar, P2); combined application of biochar and straw (5% biochar + 5% straw, P3). After 90 days of culture, soil samples were collected for analysis of various indicators such as soil aggregate particle size distribution, water stability of soil aggregates, mean weight diameter, mean geometric diameter, and fractal dimension using dry sieving and wet sieving methods. The objective is to establish a scientific basis and provide technical support for addressing the challenges associated with compound soil and implementing rational fertilization measures. The research results indicate that: (1) The quantity of aggregates > 0.25 mm under different treatments follows the order CK < P1 < P2 < P3, and the differences between treatments are significant (P < 0.05); (2) Soil water stability, mean weight diameter (MWD), mean geometric diameter (GMD), and fractal dimension of soil aggregates in compound soil with different organic material additions are superior to the control, and the effect of biochar on improving soil aggregates is better than that of corn straw. The combined application of both significantly improves the effect compared to single applications. In both culture modes, under wet sieving, the P3 treatment shows the highest MWD and GMD of soil aggregates, with an increase ranging from 3.45% to 85% and 4.55% to 38.46%, respectively, compared to other treatments. (3) The trend of fractal dimension among treatments is consistent: P3 < P2 < P1 < CK, and the differences between treatments are significant (P < 0.05). Moreover, there is a good negative correlation linear equation relationship between the fractal dimension (y) and WR > 0.25 (x) of compound soil, with a correlation coefficient of up to 0.9851. In conclusion, the incorporation of organic materials can effectively enhance the proportion of macroaggregates in compound soil consisting of Feldspathic sandstone and sand, thereby improving soil stability and erosion resistance. The optimal outcome is achieved through the combined application of biochar and straw. Indoor culture proves to be more effective than field culture, while wet sieving accurately reflects the structural characteristics of compound soil under both dry and wet sieving treatments.

BACKGROUND: The fractal dimension (FD) is a valuable tool for analysing the complexity of neural structures and functions in the human brain. To assess the spatiotemporal complexity of brain activations derived from electroencephalogram (EEG) signals, the fractal dimension index (FDI) was developed. This measure integrates two distinct complexity metrics: 1) integration FD, which calculates the FD of the spatiotemporal coordinates of all significantly active EEG sources (4DFD); and 2) differentiation FD, determined by the complexity of the temporal evolution of the spatial distribution of cortical activations (3DFD), estimated via the Higuchi FD [HFD(3DFD)]. The final FDI value is the product of these two measurements: 4DFD × HFD(3DFD). Although FDI has shown utility in various research on neurological and neurodegenerative disorders, existing literature lacks standardized implementation methods and accessible coding resources, limiting wider adoption within the field.
METHODS: We introduce an open-source MATLAB software named FDI for measuring FDI values in EEG datasets.
RESULTS: By using CUDA for leveraging the GPU massive parallelism to optimize performance, our software facilitates efficient processing of large-scale EEG data while ensuring compatibility with pre-processed data from widely used tools such as Brainstorm and EEGLab. Additionally, we illustrate the applicability of FDI by demonstrating its usage in two neuroimaging studies. Access to the MATLAB source code and a precompiled executable for Windows system is provided freely.
CONCLUSIONS: With these resources, neuroscientists can readily apply FDI to investigate cortical activity complexity within their own studies.

An important aspect of water treatment is removing fine-grain materials from water. Due to the properties of fine-grain materials, they are difficult to remove from water. During the sedimentation process, which takes place in settling tanks, such materials are removed. The sedimentation process is often accompanied by coagulation and flocculation processes, which form aggregates of particles (flocs) from the fine-grained material particles in a suspension (non-grainy suspension). This kind of suspension (consisting of aggregates of particles or flocs) shows a different behaviour when falling compared with classic grainy suspensions. The main goal and novelty of this article are to propose (and test) a modification of the often used Stokes\' formula with the addition of fractal geometry into the calculation of the terminal velocity of free-falling particles in order to overcome Stokes\' formula\'s limitation, thus obtaining the sedimentation process efficiency. Because of this fractal modification, it is possible to use the simple and elegant Stokes\' formula in order to calculate better the terminal velocity of non-grainy particles-aggregates or flocs-and thus obtain the sedimentation efficiency for the whole range of suspensions, both non-grainy and grainy. The results obtained in this article show that the sedimentation process efficiency calculated by using the modified formula based on the fractal geometry morphology of particles (the proposed fractal method) describes and agrees more with the data from the experiment than the sedimentation efficiency calculated only based on particle size (classic method).

Copper-zinc-tin Cu2ZnSn (CZT) thin films are promising materials for solar cell applications. This thin film was deposited on a fluorine-doped tin oxide (FTO) using an electrochemical deposition hierarchy. X-ray diffraction of thin-film studies confirms the variation in the structural orientation of CZT on the FTO surface. As the pH of the solution is increased, the nature of the CZT thin-film aggregate changes from a fern-like leaf CZT dendrite crystal to a disk pattern. The FE-SEM surface micrograph shows the dendrite fern leaf and sharp edge disks. The 2-D diffusion limitation aggregation under slippery conditions for ternary thin films was performed for the first time. The simulation showed that by changing the diffusing species, the sticking probability was responsible for the pH-dependent morphological change. Convincingly, diffusion-limited aggregation (DLA) simulations confirm that the initial structure of copper is responsible for the final structure of the CZT thin films. An experimental simulation with pH as a controlled parameter revealed phase transition in CZT thin films. The top and back contact of Ag-CZT thin films based on Schottky behavior give a better electronic mechanism in superstrate and substrate solar cells.