Search Results (367)

This study characterizes the multifractal structure of monthly precipitation in the semi-arid state of Guanajuato, Mexico, using Multifractal Detrended Fluctuation Analysis with quadratic detrending (MFDFA-2). We analyze 65 quality-controlled meteorological stations covering the period 1981–2016. All series exhibit multifractality, with generalized Hurst exponents $h\left(2\right)=0.568\pm 0.065$ indicating predominantly persistent dynamics and long-term positive autocorrelation (64.6% of stations). The multifractal spectrum width ($\Delta \alpha$) ranges from 0.15 to 0.72 (mean = 0.2423), revealing substantial spatial variability in scaling complexity. K-means clustering based on multifractal features identifies the following four hydroclimatic groups: one random cluster (29.2% of stations) and three persistence-dominated clusters (70.8%), with coherent spatial organization. These findings provide new insights into the temporal scaling properties of precipitation in semi-arid regions and have important implications for water resource management and regionalized drought-risk assessment. Full article

Dew constitutes a component of the near-surface water balance, but its large-scale fractal dynamical properties remain poorly documented across Africa. This study estimates dew amounts and investigates their fractal and multifractal behavior under African climatic conditions using gridded ERA5 datasets from 1993 to 2022. The Rescaled-Range (R/S) method, Multifractal Detrended Fluctuation Analysis (MFDFA), and the Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) algorithm are used. Hurst exponent (Hu) and the multifractal spectrum width (ω) are evaluated at daily and monthly scales over the full period and two sub-periods (1993–2007 and 2008–2022). The results reveal pronounced spatial heterogeneity in dew distribution. Daily mean amounts range between 0 and 0.18 mm, corresponding to annual accumulations reaching up to ~85 mm·yr⁻¹ in humid coastal, equatorial, and sub-equatorial regions, while remaining below 0.5 mm·yr⁻¹ in hyper-arid deserts. The continental mean annual amount is ~35.5 mm·yr⁻¹. The Hurst exponent exhibits values between zero and one, indicating region-dependent persistent and anti-persistent behaviors. This suggests that prediction schemes based on preceding values may be suitable for dew time series prediction in African regions exhibiting persistent characteristics. The multifractal spectrum width (ω), reaching values of up to 10, highlights strong scaling heterogeneity, particularly at the monthly timescale. These findings indicate that African dew dynamics exhibit significant long-range dependence and multifractal variability, providing new insights into the intrinsic temporal structure of dew and into appropriate approaches for its forecasting. Full article

Port activities significantly alter local atmospheric chemistry, yet the nonlinear coupling mechanisms between nitrogen oxides (NO_x) and ozone (O₃) in these complex environments remain underexplored. In this study, MF-DFA and MF-DCCA were applied to explore the coupling dynamics between NO_x and O₃ in Hong Kong’s Kwai Chung port and Tap Mun non-port areas. Results indicate that while both pollutants exhibit multifractality, O₃ shows stronger persistence and scale-invariant complexity than NO_x (e.g., in the port area, spectral width Δα = 0.61 for O₃ vs. 0.40 for NO_x). Crucially, the non-port area demonstrates significantly stronger and more stable cross-correlations (with the cross-correlation Hurst exponent h_xy(2) = 0.85 and h_xy(q) ranging from 0.80 to 0.99) compared to the port area (h_xy(2) = 0.60, h_xy (q) ranging from 0.54 to 0.74). The weaker coupling in the port zone is attributed to the fact that intermittent factors such as ship emissions have disrupted the long-term memory of the system. The connections in non-port areas are stronger and more stable because they are less affected by local emissions and chemical processes. The cross-correlation exhibited obvious seasonal dependence, with the strongest multifractal intensity in summer (cross-multifractal Δα reaching up to 0.81) and the weakest in winter under the modulation of photochemical and meteorological conditions. These findings reveal that port-side pollution coupling is structurally more fragile and heterogeneous than the stable regional background, suggesting that effective air quality management requires strategies accounting for these cross-scale nonlinear dynamics. Full article

Power system blackouts represent typical manifestations of instability in complex systems, whose evolution often exhibits non-stationarity, long-range correlations, and nonlinear scaling behavior. Most reliability assessment methods widely used in engineering practice are built on the core assumptions of event independence and light-tailed distribution, which will inevitably lead to systematic underestimation of extreme tail risks when blackouts actually present long-range memory and power-law heavy-tailed characteristics. Based on long-cycle historical blackout records of China’s power grid spanning 1981–2025, this paper develops an integrated framework combining Self-Organized Criticality (SOC) theory, Hurst exponent analysis, symbolic time-series methods, and Multifractal Detrended Fluctuation Analysis (MFDFA). This study systematically characterizes the evolution law and inherent dependence structure of blackout events from four dimensions: statistical scaling, temporal correlation, nonlinear structure, and multi-scale fractal spectrum. The results show that both the load-loss magnitudes and inter-event intervals of blackouts follow strict power-law distributions, with the system exhibiting scaling behavior consistent with SOC theory. The blackout event sequence presents significant long-range positive correlation and self-similarity, confirming a persistent long-term memory effect in the system evolution. Symbolic analysis further reveals the nonlinear fluctuation patterns and burst clustering behavior of the blackout process, reflecting the intermittency and complexity of blackout risks. MFDFA results verify that the blackout sequence has a broad-spectrum multifractal structure across different temporal scales, and Monte Carlo shuffle tests demonstrate that this multifractality mainly arises from intrinsic long-range temporal correlations, rather than being driven solely by heavy-tailed distribution. This study confirms that blackouts in China’s power grid are not random independent events, but present fractal statistical characteristics consistent with the self-organized critical mechanism. The findings provide a novel fractal perspective and quantitative framework for the statistical characterization, operational security assessment, and multi-scale early-warning modeling of blackout risks in China’s large-scale power systems. Full article

The dominant pores governing methane adsorption in coal are micropores (pore size < 2 nm). Their spatial heterogeneity can be quantitatively characterized using multifractal theory; however, the evolution patterns and mechanisms of microporous structures across different coalification degrees remain unclear. This research selected a series of coal samples from different ranks and identified the coalification degree using the maximum vitrinite reflectance (Rₒ_,max). By comprehensively employing low-temperature CO₂ adsorption experiments and multifractal analysis, the evolution patterns of the microporous structures and their multifractal spectral parameters were systematically revealed, and the underlying control mechanisms were explored. Results indicate that micropore volume (PV) and specific surface area (SSA) first exhibit a decrease and then increase as Rₒ_,max increases, with the trough occurring during the second coalification jump at Rₒ_,max = 1.2–1.4%. The pore sizes exhibit bimodal distributions, with the primary peak occurring in the range of 0.45–0.65 nm and the secondary peak occurring in the range of 0.8–0.9 nm. All microporous structures possess pronounced multifractal characteristics. The generalized dimension spectrum width (ΔD) and singularity spectrum width (Δα) exhibit an increasing–decreasing–increasing trend with Rₒ_,max, whereas the Hurst exponent (H) follows an inverted parabolic curve, first increases then decreases. This contrasts with the trends in PV and SSA, indicating that the evolution of pore-space heterogeneity and connectivity is independent of and lags the changes in micropore quantity. These patterns are governed by a structural phase transition within the coal macromolecular network. Marked by the second coalification jump, the microporous system shifts from a flexible degradation–polycondensation paradigm to a rigid ordering–construction paradigm. This transition drives the asynchronous, synergistic evolutions of pore quantity, spatial heterogeneity (ΔD and Δα), and topological connectivity (H). This research provides a theoretical basis for quantitatively evaluating pore heterogeneity in coal reservoirs. Full article

This study investigates the structural, chemical, and morphological characteristics of electron-beam–deposited GO/Ag nanocomposite thin films and establishes a compact continuum–spectral framework for quantifying their post-deposition roughness. Since atomic force microscope (AFM) measurements provide only the final, frozen morphology and no direct temporal information, distinguishing between transient and stationary spectra is not experimentally feasible within the limited AFM wavenumber band. In practice, the accessible power spectral densities (PSDs) show no resolvable deviation from the stationary form, and transient contributions cannot be uniquely identified. The stationary PSD is fitted directly to azimuthally averaged AFM spectra, allowing the smoothing coefficients, noise intensity, correlation length, and crossover scale to be extracted in a fully data-driven manner. The fitted model accurately reproduces the characteristic dual (k⁻²)/(k⁻⁴) spectral scaling and predicts the scan-size dependence of root-mean-square roughness, typically achieving logarithmic determination coefficients above 0.98. The close agreement among parameters obtained from spatially separated sampling points confirms the lateral uniformity of the deposited films and highlights the robustness of the continuum–spectral approach for data-guided roughness control in electron-beam-grown nanocomposite coatings. Full article

Under dynamic loading conditions, the output voltage of proton exchange membrane fuel cells (PEMFCs) exhibits nonlinear degradation characterized by non-Gaussian fluctuations, abrupt changes, and long-range temporal dependence, which are difficult to model using conventional short-correlation or remaining useful life (RUL) prediction approaches. To capture both historical dependency and stochastic jump behavior, this study proposes a SHAP-driven mechanism–data fusion fractional stochastic degradation model based on fractional Brownian motion (fBm) and fractional Poisson process (fPp) for degradation trend forecasting. A terminal voltage mechanism model considering activation, ohmic, and concentration polarization losses is first established, and SHapley Additive exPlanations (SHAP) analysis is employed to quantify the contributions of multi-source operational variables and enhance interpretability. The Hurst exponent is then used to verify long-range dependence and jump characteristics in the voltage sequence. Subsequently, fBm is integrated with a fPp to construct a unified stochastic degradation framework capable of jointly describing continuous decay and discrete abrupt variations, enabling multi-step probabilistic prediction with confidence intervals. Validation on the publicly available FCLAB FC1 and FC2 datasets shows that the proposed model achieves superior overall performance under both steady and dynamic conditions, with MAPE/RMSE/R² of 0.027%/0.00178/0.9895 and 0.056%/0.00259/0.9896, respectively, outperforming fBm, Wiener, WTD-RS-LSTM, and CNN-LSTM methods. The proposed approach provides accurate and interpretable degradation forecasting for PEMFC health management and maintenance decision support. Full article

Drought is a complex natural hazard with severe impacts on ecosystems, agriculture, water resources, and socio-economic stability. Understanding its spatiotemporal evolution is critical for effective drought monitoring and prevention. This study analyzed drought characteristics in Henan province from 1961 to 2023 using the Standardized Precipitation Evapotranspiration Index (SPEI), calculated from daily meteorological data at 111 meteorological stations. Drought was examined at annual and seasonal scales across multiple time scales, including the 1-month time scale (SPEI1), 3-month time scale (SPEI3), and 12-month time scale (SPEI12), and future trends were assessed using Theil–Sen Median and Hurst exponent analyses. Key findings revealed the following: (1) Drought frequency showed a non-significant increasing trend overall, but drought intensity increased significantly, with severe and extreme droughts becoming more frequent. Most areas are projected to continue aridification. (2) Winter recorded the highest frequency and occurrence of droughts, followed by autumn and summer. Except for summer, moderate and severe droughts increased across all seasons. Extreme droughts increased significantly across all seasons, especially in spring and autumn. (3) High annual drought frequency was concentrated in the northwest, north, and east. Spatial patterns varied by drought severity: slight droughts were more common in the north, moderate droughts in the central–east, severe droughts in the west and south, and extreme droughts in the southwest and north. (4) Empirical Orthogonal Function (EOF) analysis revealed three main spatial modes: a uniform regional pattern, a southeast–northwest contrast, and a central–eastern opposition. Shorter time scales provided more detailed spatial patterns, while longer scales better reflected interannual characteristics of drought and flood variations. This study offers valuable insights for improving drought assessment and supporting risk management and policy decisions. Full article

Econophysics is an interdisciplinary field that applies physics concepts to economic and financial systems. By utilizing tools such as statistical physics, including fractal analysis and entropy measures, econophysics helps model the complex and non-linear dynamics of equity markets. This paper examines the intrinsic dynamics and regularity in information content in green finance markets (carbon, clean energy, and sustainability markets) by means of range scale analysis (R/S), detrended fluctuation analysis (DFA), fractionally integrated generalized auto-regressive conditionally heteroskedastic (FIGARCH) process, and Shannon entropy (SE). The empirical results can be summarized as follows. First, prices in all markets are persistent; however, returns are likely random as estimated Hurst exponents are close to 0.5. Second, the FIGARCH process shows that volatility series in carbon and sustainability markets are persistent, whilst volatility in clean energy is anti-persistent. Third, in carbon and sustainability markets, entropy is high in prices compared to returns and volatility series. On the contrary, the clean energy market shows lower entropy for prices than for returns and volatility. In sum, it is concluded that price and volatility series are predictable, whilst return series are not. Finally, based on a rolling window framework, it is concluded that the COVID-19 pandemic and the Russia–Ukraine war have altered long memory and randomness in all three green finance markets. Full article

This study examines the role of volatility mean reversion in option pricing and evaluates the performance of commonly used volatility estimators within a broad market context. Using a comprehensive dataset of end-of-day option chains for the 100 most actively traded U.S. equities from 2018 to 2023, we apply several established statistical techniques—including unit root tests, variance ratio analysis, Hurst exponent estimation, and GARCH modeling—to quantify the presence and strength of mean reversion in volatility. To assess the accuracy and practical usability of volatility metrics for option valuation, we compare realized volatility, GARCH-based forecasts, range-based estimators, and widely used implied volatility measures such as the VIX and daily implied volatility averages, benchmarking each against contract-specific implied volatility. The results indicate that more than 65% of the analyzed tickers exhibit statistically significant mean-reverting behavior, and that the 30-day average implied volatility consistently provides the most reliable predictive performance among the tested metrics, while range-based estimators perform poorly when applied to end-of-day data. Finally, backtests of six delta-neutral option strategies informed by these findings did not yield consistent profitability or statistically significant outperformance, suggesting that although volatility mean reversion is measurable, its direct application to systematic trading remains challenging. Full article

The nature of nonlinear dynamics of financial markets results in fractal geometry and chaotic behavior that can be viewed on a variety of scales in time. This paper conducts research on the fractal characteristics of the stock network and its contribution to the price of assets based on the Fractal Market Hypothesis (FMH). A multiscale network centrality measure is built based on high-frequency return dependencies to measure the self-similar, scale-invariant nature of inter-stock dependencies. The network factor and portfolio returns are then broken down with the wavelet packet decomposition (WPD) to obtain frequency-domain profiles, which characterize the variability of risk transmission in relation to investment horizons. The profiles are consistent with scaling properties of fractal, but the decomposition does not identify causal pathways on its own. Estimation of fractal dimension by use of the box-counting technique aided by the Hurst exponent analysis reveals that the A-share of China market exhibited long-range dependence and multifractal scaling. Network factor has the largest explanatory power in mid-frequency between the D5 and D6 bands of 32 to 128 days. This intermediary frequency concentration is consistent with the hypothesis of heterogeneous markets, in which the groups of investors with varying time horizons generate scale-related price dynamics. The addition of the network factor to a 6-factor specification lowers the GRS under the 5-factor specification by 31.45 to 17.82 on the same test-asset universe, indicating better cross-sectional coverage in the sample. The estimates of the Lyapunov exponents (0.039) as well as the correlation dimension ($D_2=4.7$) confirm the presence of low-dimensional chaotic processes of the network factor series, but these values are specific to the Chinese A-share market over the 2005–2023 sample period. These results provide a frequency-disaggregated use of network-based factor modeling and suggest that it can be applicable in multiscale portfolio risk management where the investor horizon is not uniform. Full article

Timber price dynamics are most often analysed using trends, seasonality, and classical measures of volatility, which describe the magnitude of fluctuations but only to a limited extent capture the temporal structure of the price-generating process. The aim of this study is to identify the structural complexity and long-term memory of quarterly prices of WC0 pine timber in the regional timber market in Poland. The analysis is based on nominal net prices (PLN/m³) from 16 forest districts of the Regional Directorate of State Forests in Kraków over the period 2005–2024, with reference to nationally averaged timber prices. Long-term dependence is assessed using the Hurst exponent estimated by detrended fluctuation analysis (DFA) applied to log returns, while the geometric complexity of price trajectories is characterised by the fractal dimension and additionally validated using the Higuchi estimator. Cross-sectional results reveal substantial spatial heterogeneity in scaling properties, indicating the coexistence of persistent (trend-following) and corrective (anti-persistent) dynamics across forest districts. Rolling-window analysis (40 quarters) demonstrates temporal variability in price dynamics, with particularly pronounced shifts observed in 2019–2021. Cluster analysis based on time-varying Hurst exponent values identifies two groups of forest districts with distinct persistence trajectories, corresponding to more trend-dominated and corrective price dynamics. In contrast, national-level prices generally exhibit higher persistence than local prices, reflecting the effects of price aggregation. Overall, the results show that fractal analysis uncovers persistent spatial and temporal differences in timber price structures that remain invisible when relying solely on variance-based measures, with direct implications for the choice of planning horizons and timber sale strategies in regional markets. Full article

As the net gain of carbon by plants after accounting for respiration, vegetation net primary productivity (NPP) plays a central role in the terrestrial carbon cycle. However, a systematic and quantitative analysis of the spatiotemporal evolution and driving mechanisms of vegetation NPP on Hainan Island, a tropical region, is still lacking. Focusing on Hainan Island, this study employs an integrated approach—including the coefficient of variation, Mann–Kendall test, Hurst exponent, geographical detector, and PLS-SEM—to investigate the spatiotemporal dynamics of vegetation NPP and its underlying drivers from 2001 to 2022. The main conclusions as follows: (1) Vegetation NPP on Hainan Island showed a fluctuating upward trend from 2001 to 2022, with a mean annual increase of 3.6 g C·m⁻²·yr⁻¹, and displayed a spatial pattern of decrease from the central-southern mountainous areas toward the coastal regions. (2) NPP changes were generally stable; historically, areas showing an increasing trend exceeded those with a decreasing trend by 30.55%. In the future, the predominant projected trends are “persistent decrease” and “increase to decrease,” which together account for over 80% of the total area. (3) Topography and climate were the dominant drivers of NPP spatial heterogeneity. Elevation had the strongest explanatory power, followed by evapotranspiration and temperature. A significant, nonlinear enhancement effect was observed in the interaction between any two factors. (4) Topographic, climatic, anthropogenic, and vegetation factors all exerted direct positive effects on vegetation NPP. Anthropogenic activities also indirectly promoted NPP by influencing pathways such as vegetation growth. The conclusions of this research provide support for the implementation and evaluation of land-use planning, afforestation projects, and ecological protection and restoration measures on Hainan Island. Full article

As Guangdong is a pivotal province in China’s national forest city initiative, examining the spatiotemporal evolution and key drivers of eco-environmental quality (EEQ) in Guangdong is essential for advancing regional sustainable development. To address the complexity of EEQ assessments in areas that are characterized by dense hydrological networks, extensive vegetation cover, and rapid urban expansion, the Google Earth Engine platform was utilized in this study, and remote sensing indices with heightened sensitivity to vegetation and moisture dynamics—namely, the kernel normalized difference vegetation index and the kernel normalized difference moisture index—were introduced to develop an improved water benefit-based ecological index (ImWBEI). Through an integrated analytical framework incorporating Theil–Sen trend analysis, Mann–Kendall significance testing, Hurst exponent analysis, an optimal parameter-based geographical detector, and a coupled coordination degree model, this research systematically evaluated the spatiotemporal patterns, future trends, driving mechanisms, and coordination with urbanization of the EEQ in Guangdong from 2000 to 2021. The results demonstrated that the ImWBEI enhanced the detailed characterization of complex underlying surfaces, such as urban built-up areas and land–water transition zones. Throughout the study period, the EEQ in Guangdong displayed a stable spatial distribution characterized by higher values in the north and lower values in the south. Concurrently, the EEQ significantly improved at a rate of 0.0092 per year. Hurst index analysis indicated that this trajectory would likely persist, with the future trend dominated by a pattern of weak persistent improvement. The comprehensive urbanization index was identified as the most critical factor influencing the spatial differentiation of the EEQ in Guangdong. Although notable north–south disparities were observed in the coordination between the EEQ and comprehensive urbanization, the provincial-level coupled coordination consistently improved. Consequently, this work yielded actionable insights and a replicable framework for ecological monitoring and coordinated development in similar water–forest integrated urban regions. It was particularly relevant for informing ecological restoration prioritization and development restriction decisions in critical land–water transition zones—areas where the ImWBEI demonstrated enhanced sensitivity. Full article

The development of portable electrocardiographic analysis systems necessitates identifying an optimal balance between diagnostic precision and computational efficiency. This research addresses the challenge of optimal feature selection for automated cardiac arrhythmia classification in resource-constrained portable applications. We present a comparative investigation of three distinct feature selection strategies for ECG classification: the MRMR (Minimum Redundancy Maximum Relevance) method, which maximizes relevance while minimizing feature interdependencies; the ReliefF technique, which evaluates discriminative power through proximity analysis in the feature space; and permutation-based importance analysis implemented with neural networks. Utilizing the Large-Scale 12-Lead Electrocardiogram Database for Arrhythmia Study, we construct a hybrid feature space integrating 12 conventional time- and frequency-domain parameters (previously validated and included in the database’s official documentation) with 26 advanced nonlinear descriptors, including the Hurst exponent, DFA scaling parameter, log-absolute correlation measures, mean standard increment from the Poincaré plot, and wavelet entropy. The experimental results demonstrate remarkable convergence among the three paradigms in selecting optimal feature subsets, achieving classification accuracies of 87–89% for four arrhythmia classes using compact configurations of 7–10 features, and 93.57% with an extended 12-parameter set. The 7-feature configuration achieves an 82% complexity reduction compared to the full 38-feature set. Multi-algorithmic analysis confirms the consistent discriminative contribution of the proposed nonlinear descriptors, demonstrating that MRMR, ReliefF, and permutation analyses yield convergent rankings of critical parameters for automated cardiac pathology diagnosis. Full article