Search Results (242)

Cryptocurrencies such as Bitcoin can be classified as commodities under the Commodity Exchange Act (CEA), giving the Commodity Futures Trading Commission (CFTC) jurisdiction over those cryptocurrencies deemed commodities, particularly in the context of futures trading. This paper presents a method for predicting both long- and short-term trends in selected cryptocurrencies based on the Fractal Market Hypothesis (FMH). The FMH applies the self-affine properties of fractal stochastic fields to model financial time series. After introducing the underlying theory and mathematical framework, a fundamental analysis of Bitcoin and Ethereum exchange rates against the U.S. dollar is conducted. The analysis focuses on changes in the polarity of the ‘Beta-to-Volatility’ and ‘Lyapunov-to-Volatility’ ratios as indicators of impending shifts in Bitcoin/Ethereum price trends. These signals are used to recommend long, short, or hold trading positions, with corresponding algorithms (implemented in Matlab R2023b) developed and back-tested. An optimisation of these algorithms identifies ideal parameter ranges that maximise both accuracy and profitability, thereby ensuring high confidence in the predictions. The resulting trading strategy provides actionable guidance for cryptocurrency investment and quantifies the likelihood of bull or bear market dominance. Under stable market conditions, machine learning (using the ‘TuringBot’ platform) is shown to produce reliable short-horizon estimates of future price movements and fluctuations. This reduces trading delays caused by data filtering and increases returns by identifying optimal positions within rapid ‘micro-trends’ that would otherwise remain undetected—yielding gains of up to approximately 10%. Empirical results confirm that Bitcoin and Ethereum exchanges behave as self-affine (fractal) stochastic fields with Lévy distributions, exhibiting a Hurst exponent of roughly 0.32, a fractal dimension of about 1.68, and a Lévy index near 1.22. These findings demonstrate that the Fractal Market Hypothesis and its associated indices provide a robust market model capable of generating investment returns that consistently outperform standard Buy-and-Hold strategies. Full article

Background and Objectives: This study retrospectively investigated the impact of regenerative endodontic treatments (RET) on the healing of periapical lesions in young permanent molars with open apices. Our objective was to evaluate the relationship between treatment outcomes and changes in the fractal dimension (FD) of the periapical bone before and after RET. The study was conducted at the Department of Pediatric Dentistry, Necmettin Erbakan University between January 2020 and December 2024. Materials and Methods: We examined panoramic radiographs from systematically healthy patients aged 6–16 years who underwent RET in the posterior mandible between January 2020 and December 2024. Changes in periapical bone were assessed using fractal analysis before treatment and after a 6-month follow-up. Additionally, mental index (MI), mandibular cortical width (MCW), mental length (ML), and periapical index (PAI) values were evaluated. Radiographs were taken with a Planmeca ProOne^® device and analyzed using ImageJ v1.54 software. Results: Comparison of FD values between treated and contralateral tooth areas, as well as before and after RET, revealed an average FD value of 1.27 ± 0.05 after regeneration, increasing to 1.29 ± 0.27 at the 6-month follow-up. Significant increases were observed in MCW (p = 0.005/p = 0.049) and ML (p = 0.022/p = 0.001) in the 35–36 and 45–46 regions post-RET, though MI values showed no significant change. Importantly, PAI scores demonstrated significant improvement after RET. Conclusions: The findings suggest that RET is effective in promoting the healing of periapical lesions in young permanent molars. The observed increases in cortical width and improvements in PAI scores support the positive impact of this treatment on bone healing. Furthermore, FD analysis, when combined with radiomorphometric indices, could provide a valuable and objective tool for evaluating RET outcomes. Full article

(1) Background: The impact of different drying methods on the functional properties and microstructure of milk powders was analyzed in this study. (2) Methods: Whole milk, skim milk, and buttermilk powders were obtained by freeze drying, spray drying, and roller drying. (3) Results: The examined powders differed in chemical composition, and these differences were attributed mainly to their fat content. The functional properties of the studied powders were determined mainly by the drying method and were less influenced by their composition. Loose and tapped bulk density was highest in roller-dried powders and lowest in freeze-dried powders. The flowability of milk powders was determined by calculating the Carr index and the Hausner ratio, and the results were used to classify the analyzed powders into the following groups: poorly flowing and cohesive (spray-dried samples), passable (roller-dried samples), and fair (freeze-dried samples). The volume of insoluble particles was highest in roller-dried powders and much lower in spray-dried powders, whereas freeze-dried powders were 99.8–99.9% soluble in water. Whole milk powder was characterized by low wettability (>180 s) regardless of the drying method. Powder morphology was influenced mainly by the drying method. (4) Conclusions: The fractal analysis demonstrated that spray-dried powders had the smallest fractal dimensions, which implies that their surface was least complex (most uniform). Regardless of the drying method, fractal dimensions were highest in whole milk powder, which could suggest that fat affects the microstructure of powders. The color parameters of milk powders were determined mainly by the drying method and were less influenced by the type of raw material used in powder production. Full article

Rice cultivation has the ability to ameliorate saline soils, but this monoculture pattern can lead to negative plant–soil feedback. In a previous study, we investigated the effects of long-term rice cultivation on saline soil chemistry, salt ions, root characteristics, and agglomerate formation, and concluded that the optimal rice planting period is 5 years. However, we do not know which crop rotation is most effective in improving this negative soil feedback and enhancing soil quality. In this study, we carried out an experiment on saline land planted with rice over 5 years and set up four different rotations, including rice–Hunan Jizi, rice–maize, rice–sweet sorghum, and rice–soybean, with perennial rice planting as CK, to analyze soil texture under different treatments. Physicochemical properties and enzyme activities were also analyzed under different treatments, and the soil quality index (SQI) was constructed using principal component analysis and correlation analysis for comprehensive evaluation of each treatment. The results showed that (1) the saline-alkali soil texture of perennial rice planting in the Yinbei Plain was silty soil, and different rice drought rotation methods changed the soil texture from silty to silty loam, which improved the fractal dimension of the soil. The fractal dimension of saline-alkali soil was significantly positively correlated with the clay volume content, negatively correlated with silt volume content, and negatively correlated with sand volume content. (2) There was no risk of structural degradation (SI > 9%) in saline-alkali soil planted in perennial rice, and it appeared that RS (rice–soybean) could improve the stability coefficient of soil structure in the 0~40 cm soil layer. (3) Different rice and drought rotation methods could significantly affect the physical and chemical properties and enzyme activities of soil, and the quality of soil in the 0~40 cm soil layer was evaluated; RS (rice–soybean) and RC (rice–maize) were suitable for rice drought rotation in the Yinbei area. The structural equation model showed that salinity and soil nutrients were the key factors restricting the improvement of saline-alkali soil quality in Yinbei. These results will deepen the current understanding of bio-modified saline soils. 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

This study examines the particle size distribution (PSD) of calcareous soils under cultivated and natural conditions in Chenggong District of Kunming, Yunnan Province, China, using single-fractal and multifractal analyses. Soil samples were collected from the profiles of both land use types, and the PSD parameters, organic matter, and total nitrogen were determined. Single-fractal analysis showed that the single-fractal dimension (D) was mainly influenced by the clay content, with higher clay fractions corresponding to larger D values. The generalized dimension spectrum revealed clear differences between natural and cultivated soils: natural soils exhibited greater sensitivity to probability density weight index(q) changes and a more compact particle distribution, whereas cultivation led to broader PSD ranges and higher heterogeneity. The ratio D₁/D₀ was negatively correlated with the clay content, and multifractal spectrum asymmetry (Δf) indicated that fine particles dominate the variability in deeper layers. Compared with natural soils, cultivated soils had higher organic matter and total nitrogen, reflecting the influence of fertilization and tillage on the soil aggregation and PSD. These findings demonstrate that fractal theory provides a sensitive tool for characterizing soil structural complexity and land use impacts, offering a theoretical basis for soil quality assessment and the sustainable management of calcareous soils. Full article

This study investigates the influence of particle morphology on two-dimensional (2D) single rock particle breakage using the combined finite-discrete element method (FDEM) coupled with fractal dimension analysis. Three key shape descriptors (elongation index EI, roundness index Rd, and roughness index Rg) were systematically varied to generate realistic particle geometries using the Fourier transform and inverse Monte Carlo. Numerical uniaxial compression tests revealed distinct morphological influences: EI showed negligible impact on crushing strength or fragmentation, and Rd significantly increased crushing strength and fragmentation due to improved energy absorption and stress distribution. While Rg reduced strength through stress concentration at asperities, suppressing fragmentation and elastic energy storage. Fractal dimension analysis demonstrated an inverse linear correlation with crushing strength, confirming its predictive value for mechanical performance. The validated FDEM framework provides critical insights for optimizing granular materials in engineering applications requiring morphology-controlled fracture behavior. Full article

In this study, a new nonlinear dynamic model was established for functionally graded material (FGM) beams with layered/porous fractal microstructures, aiming to reveal the cross-scale propagation mechanism of flexural waves under large deflection conditions. The characteristics of layered/porous microstructures were equivalently mapped to the fractal dimension index. In the framework of the fractal derivative, a fractal nonlinear wave governing equation integrating geometric nonlinear effects and microstructure characteristics was derived, and the coupling effect of finite deformation and fractal characteristics was clarified. Four groups of deflection gradient traveling wave analytical solutions were obtained by solving the equation through the extended minimal (G′/G) expansion method. Compared with the traditional (G′/G) expansion method, the new method, which is concise and expands the solution space, generates additional csch² soliton solutions and csc² singular-wave solutions. Numerical simulations showed that the spatiotemporal fractal dimension can dynamically modulate the amplitude attenuation, waveform steepness, and phase rotation characteristics of kink solitary waves in beams. At the same time, it was found that the decrease in the spatial fractal dimension will make the deflection curve of the beam more gentle, revealing that the fractal characteristics of the microstructure have an active control effect on the geometric nonlinearity. This model provides theoretical support for the prediction and regulation of the wave behavior of fractal microstructure FGM components, and has application potential in acoustic metamaterial design and engineering vibration control. Full article

The geological structural complexity and microscale heterogeneity of shale reservoirs, characterized by the brittleness index and natural fracture density, exert a decisive effect on hydraulic fracturing’s effectiveness. However, the mechanisms underlying the true microscale heterogeneity of shale structures, which is neglected in conventional models and influences fracture evolution, remain unclear. Here, high-resolution scanning electron microscopy (SEM) was employed to obtain realistic distributions of mineral components and natural fractures, and hydraulic–mechanical coupled simulation models were developed within the Realistic Failure Process Analysis (RFPA) simulator using digital rock techniques. The analysis examined how the brittleness index and natural fracture density affect the fracture morphology’s complexity, mineral failure behavior, and flow conductivity. Numerical simulations show that the main fractures preferentially propagate toward areas with high local brittleness and dense natural fractures. Both the fracture’s fractal dimension and the stimulated reservoir volume increased with the brittleness index. A moderate natural fracture density promotes the fracture network’s complexity, whereas excessive densities may suppress the main fracture’s propagation. Microscopically, organic matter and silicate minerals are more prone to damage, predominantly tensile failures under external loading. These findings highlight the dominant role of microscale heterogeneity in shale fracturing and provide theoretical support for fracture control and stimulation optimization in complex reservoirs. Full article

Soil phosphorus (P) availability is a critical factor affecting the productivity of Phyllostachys edulis (moso bamboo) forests. However, the mechanisms underlying the physiological and growth responses of moso bamboo to varying soil P conditions remain poorly understood. The aim of this study was to elucidate the adaptive mechanisms of moso bamboo to different soil P levels from the perspectives of root morphological and architectural plasticity, as well as the allocation strategies of nutrient elements and photosynthates. One-year-old potted seedlings of moso bamboo were subjected to four P addition treatments (P1: 0, P2: 25 mg·kg⁻¹, P3: 50 mg·kg⁻¹, P4: 100 mg·kg⁻¹) for one year. The biomass of different seedling organs, root morphological and architectural indices, and the contents of nitrogen (N), P, and non-structural carbohydrates in the roots, stems, and leaves were measured in July and December. P addition increased the root length (by 113.8%), root surface area (by 146.5%), root average diameter (by 14.8%), root length ratio of thicker roots (diameter > 0.9 mm), number of root tips (by 31.9%), fractal dimension (by 5.6%), P accumulation (by 235.8%), and contents of starch (ST) and soluble sugars (SS), while it decreased the specific root length (by 31.7%), root branching angle (by 1.9%), root topological index (by 4.8%), root length ratio of finer roots (diameter ≤ 0.3 mm), SS/ST, and N/P. The root–shoot ratio showed a downward trend in July and an upward trend in December. Our results indicated that moso bamboo seedlings tended to form roots with a small diameter, high absorption efficiency, and minimal internal competition to adapt to soil P deficiency and carbon limitation caused by low P. Under low-P conditions, moso bamboo prioritized allocating photosynthates and P to roots, promoting the conversion of starch to soluble sugars to support root morphological and architectural plasticity and maintain root growth and physiological functions. Sole P addition eliminated the constraints of low P on moso bamboo growth and nutrient accumulation but caused imbalances in the N/P. 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

Soil phosphorus (P) availability is an important determinant of productivity in Pinus massoniana (Masson pine) forests. The mechanistic bases governing the physiological and growth responses of Masson pine to varying soil P conditions remain insufficiently characterized. This study aims to decipher the adaptive strategies of Masson pine to different soil P levels, focusing on root morphological–architectural plasticity and the allocation dynamics of nutrient elements and photosynthetic assimilates. One-year-old potted Masson pine seedlings were exposed to four P addition treatments for one year: P0 (0 mg kg⁻¹), P1 (25 mg kg⁻¹), P2 (50 mg·kg⁻¹), and P3 (100 mg kg⁻¹). In July and December, measurements were conducted on seedling organ biomass, root morphological indices [root length (RL), root surface area (RSA), root diameter (RD), specific root length (SRL), and root length ratio (RLR) for each diameter grade], root architectural indices [number of root tips (RTs), fractal dimension (FD), root branching angle (RBA), and root topological index (TI)], as well as the content of nitrogen (N), phosphorus (P), carbon (C), and non-structural carbohydrates (NSCs) in roots, stems, and leaves. Compared with the P0 treatment, P2 and P3 significantly increased root biomass, root–shoot ratio, RL, RSA, RTs, RLR of finer roots (diameter ≤ 0.4 mm), nutrient accumulation ratio in roots, and starch (ST) content in roots, stems and leaves. Meanwhile, they decreased soluble sugar (SS) content, SS/ST ratio, C and N content, and N/P and C/P ratios in stems and leaves, as well as nutrient accumulation ratio in leaves. The P3 treatment significantly reduced RBA and increased FD and SRL. Our results indicated that Masson pine adapts to low P by developing shallower roots with a reduced branching intensity and promoting the conversion of ST to SS. P’s addition effectively alleviates growth limitations imposed by low P, stimulating root growth, branching, and gravitropism. Although a sole P addition promotes short-term growth and P uptake, it triggers a substantial consumption of N, C, and SS, leading to significant decreases in N/P and C/P ratios and exacerbating N’s limitation, which is detrimental to long-term growth. Under high-P conditions, Masson pine strategically prioritizes allocating limited N and SS to roots, facilitating the formation of thinner roots with low C costs. Full article

The spatial genes of rural settlements show a lot of different traditional settlement traits, which makes them a great starting point for studying rural spatial morphology. However, qualitative and macro-regional statistical indicators are usually used to find and extract rural settlement spatial genes. Taking Yubei Village in the Nanxi River Basin as an example, this study combined remote sensing images, real-time drone mapping, GIS (geographic information system), and space syntax, extracted 12 key indicators from five dimensions (landform and water features (environment), boundary morphology, spatial structure, street scale, and building scale), and quantitatively “decoded” the spatial genes of the settlement. The results showed that (1) the settlement is a “three mountains and one water” pattern, with cultivated land accounting for 37.4% and forest land accounting for 34.3% of the area within the 500 m buffer zone, while the landscape spatial diversity index (LSDI) is 0.708. (2) The boundary morphology is compact and agglomerated, and locally complex but overall orderly, with an aspect ratio of 1.04, a comprehensive morphological index of 1.53, and a comprehensive fractal dimension of 1.31. (3) The settlement is a “clan core–radial lane” network: the global integration degree of the axis to the holy hall is the highest (0.707), and the local integration degree R3 peak of the six-room ancestral hall reaches 2.255. Most lane widths are concentrated between 1.2 and 2.8 m, and the eaves are mostly higher than 4 m, forming a typical “narrow lanes and high houses” water town streetscape. (4) The architectural style is a combination of black bricks and gray tiles, gable roofs and horsehead walls, and “I”-shaped planes (63.95%). This study ultimately constructed a settlement space gene map and digital library, providing a replicable quantitative process for the diagnosis of Jiangnan water town settlements and heritage protection planning. Full article

The microfractured tight reservoirs in Yongjin Oilfield have low permeability and a complex pore structure. The development of microfractures in reservoirs is crucial for their impact on productivity. To understand the impact of pore structure and microfracture development on permeability and productivity, research on the fractal dimension and classification evaluation of microfractured tight reservoirs is proposed. Micropore and microfracture parameter characteristics are determined via CT scanning and mercury intrusion experiments. Based on the fractal theory and box counting dimension methods, the fractal dimension of pores and fractures in microfractured tight reservoirs are calculated, which can be used as an evaluation index. Then, a comprehensive quantitative evaluation method (REI) is conducted on the microfractured tight reservoir of Yongjin Oilfield to determine the classification boundary of evaluation indicators and reservoir classification results. The research results show that the microfractured tight reservoirs in Yongjin Oilfield can be classified into three types based on their development effect from good to poor. The comprehensive evaluation index (REI) of type I reservoirs is greater than 0.7, and the fractal dimension of pores and fractures is less than 2.4. The comprehensive evaluation index (REI) of type II reservoirs ranges from 0.4 to 0.7, and the fractal dimension of pores and fractures ranges from 2.4 to 2.6. The comprehensive evaluation index (REI) of type III reservoirs is less than 0.4, and the fractal dimension of pores and fractures is greater than 2.6. The classification results are consistent with the dynamic data, and this achievement can provide a scientific basis for rapid reservoir evaluation and development strategy formulation. Full article

The stochastic correlation for Brownian motions is the integrand in the formula of their quadratic covariation. The estimation of this stochastic process becomes available from the temporally localized correlation of latent price driving Brownian motions in stochastic volatility models for asset prices. By analyzing this process for Apple and Microsoft stock prices traded minute-wise, we give statistical evidence for the roughness of its paths. Moment scaling indicates fractal behavior, and both fractal dimensions (approx. 1.95) and Hurst exponent estimates (around 0.05) point to rough paths. We model this rough stochastic correlation by a suitably transformed fractional Ornstein–Uhlenbeck process and simulate artificial stock prices, which allows computing tail dependence and the Herding Behavior Index (HIX) as functions in time. The computed HIX is hardly variable in time (e.g., standard deviation of 0.003–0.006); on the contrary, tail dependence fluctuates more heavily (e.g., standard deviation approx. 0.04). This results in a higher correlation risk, i.e., more frequent sudden coincident appearance of extreme prices than a steady HIX value indicates. Full article