Search Results (633)

Background: Gamma Knife radiosurgery (GKS) delivers highly conformal intracranial irradiation, yet clinical decision-making still relies predominantly on physical dose metrics that do not account for fractionation, dose rate, treatment time, or DNA repair. Classical radiobiological models—including the linear–quadratic (LQ) formula and the Jones–Hopewell single-session repair model—do not extend naturally to 3- and 5-fraction GKS. Meanwhile, growing evidence suggests that biologically effective dose (BED) may better capture radiosurgical response in selected pathologies. A unified, biologically grounded, multi-fraction GKS framework has been lacking. Methods: We developed AI-BED-Fx, the first multi-fraction extension of the Jones–Hopewell radiobiological model capable of computing fraction-resolved BED for 1-, 3-, and 5-fraction GKS. The framework incorporates α/β ratio, dual-component repair kinetics, isocentre geometry, beam-on–time structure, and lesion-specific biological parameters. Four synthetic pathology-specific cohorts—arteriovenous malformation (AVM), meningioma (MEN), vestibular schwannoma (VS), and brain metastasis (BM)—were generated using distinct radiobiological signatures. Machine-learning models were trained to quantify the predictive value of physical dose versus BED for local control or obliteration. Additional experiments included Bayesian estimation of α/β and a neural-network surrogate for fast BED prediction. An exploratory comparison with a 60-lesion clinical brain–metastasis dataset was performed to assess whether key trends observed in the synthetic BM cohort were consistent with real radiosurgical outcomes. Results: AI-BED-Fx produced realistic pathology-specific BED distributions (AVM 60–210 Gy_2.47; MEN 41–85 Gy_3.5; VS 46–68 Gy₃; BM 37–75 Gy₁₀) and biologically coherent dose–response relationships. Predictive modeling demonstrated strong pathology dependence. In AVM, the three models achieved AUCs of 0.921 (Model A), 0.922 (Model B), and 0.924 (Model C), with corresponding Brier scores of 0.054, 0.051, and 0.051, with BED-based models performing best. In meningioma, BED was the dominant predictor, with AUCs of 0.642 (Model A), 0.660 (Model B), and 0.661 (Model C) and Brier scores of 0.181, 0.177, and 0.179, respectively. In vestibular schwannoma, the narrow BED range resulted in minimal BED contribution, with AUCs of 0.812, 0.827, and 0.830 and Brier scores of 0.165, 0.160, and 0.162, with physical dose and tumor volume determining performance. In brain metastases, outcomes were driven primarily by volume and physical dose, with AUCs of 0.614, 0.630, and 0.629 and Brier scores of 0.254, 0.250, and 0.253, showing negligible improvement from BED. AI-BED-Fx also accurately recovered the true α/β from synthetic outcomes (posterior mean 2.54 vs. true 2.47), and a neural-network surrogate reproduced full radiobiological BED calculations with near-perfect fidelity (R² = 0.9991). Conclusions: AI-BED-Fx provides the first unified, biologically explicit framework for modeling single- and multi-fraction Gamma Knife radiosurgery. The findings show that the predictive usefulness of BED is pathology-specific rather than universal, and that radiobiological dose provides additional predictive value only when repair kinetics and dose–response biology support it. By integrating mechanistic radiobiology with machine learning, AI-BED-Fx establishes the conceptual and computational foundations for biologically adaptive, AI-guided radiosurgery, and cross-pathology comparison of treatment response. This work uses large radiobiologically grounded synthetic cohorts for methodological validation; limited real-patient data are included only for exploratory consistency checks, and full clinical validation is planned. Full article

Sleep disorders are prevalent in the world, and they lead to severe health issues such as cardiovascular disease and cognitive disabilities. Conventional polysomnography-based diagnosis is based on manual EEG analysis under the supervision of trained specialists, which is time-consuming and may have inter-rater variability. Although the predictions of deep learning (DL) models on the task of sleep classification of EEG have been promising, they, in many cases, do not explain the multiscale, temporal dynamics that physiological signals are characterized by. In this work, a hybrid model that is a combination of CNN and multifractal detrended fluctuation analysis (MF-DFA) was proposed to detect localized temporal features and long-term fractal-based dynamics of single-channel EEG recordings. The performance of the suggested model was tested using two separate polysomnographic datasets: the CAP Sleep Dataset of five-class sleep disorder classification (Healthy, Insomnia, Narcolepsy, PLM, and RBD) and the ISRUC Sleep Dataset on the three-class subject-independent validation. In the CAP dataset, the framework had an accuracy of 86.38%. Cross-dataset transfer to the ISRUC Sleep Dataset, where only the classification head was fine-tuned on a small labeled subset while all feature-extraction layers remained frozen from CAP training, achieved 87.50% accuracy, demonstrating that the learned representations generalize across differing recording protocols, sampling rates, and diagnostic label spaces. The experiments of ablation proved the paramount importance of the MF-DFA features, and the lack of them led to low classification rates. The findings demonstrate the clinical feasibility of applying fractal analysis in conjunction with DL to detect sleep disorders in an automated, generalizable manner, suitable for use in large-scale monitoring and resource-starved clinical environments. 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

Tight sandstone reservoirs are characterized by highly heterogeneous pore structures, in which multiscale pore–throat systems jointly control the shapes of capillary pressure curves and relative permeability, thereby exerting a fundamental influence on water production behavior and the overall development performance of gas reservoirs. The Ordos Basin is generally characterized by the development of tight sandstone. The tight sandstones exhibit porosities of 2–13% and permeabilities of 0.01–10 × 10⁻³ μm². To quantitatively elucidate the controlling mechanisms of multiscale pore structure on capillary pressure curve morphology and relative permeability, this study systematically investigates the fractal and multifractal characteristics of pore structures in tight sandstones based on high-pressure mercury intrusion (MICP) and nuclear magnetic resonance (NMR) experimental data, and establishes a quantitative relationship between fractal parameters and the capillary pressure curve shape parameter λ. First, capillary pressure curves were fitted using the Brooks–Corey model within the effective saturation interval to extract the shape parameter λ, which characterizes the concentration degree of pore-size distribution and the drainage behavior. Subsequently, based on NMR T₂ spectra, the small-pore fractal dimension D₁, large-pore fractal dimension D₂, and the multifractal singularity spectrum width Δα were extracted to quantitatively describe the geometric complexity of pore structures at different scales. On this basis, the correlations between λ and D₁, D₂, and Δα were systematically analyzed, and the predictive performance of λ under different parameter combinations was compared. The results indicate that: (1) the pore structures of tight sandstones exhibit pronounced fractal and multifractal characteristics at the NMR T₂ scale, with significant differences among samples; (2) λ shows an overall negative correlation with fractal parameters, among which the correlations with the large-pore fractal dimension D₂ and the multifractal spectrum width Δα are the most significant; (3) compared with models using a single fractal dimension, the multiparameter model incorporating Δα provides a more comprehensive characterization of multiscale pore heterogeneity, leading to a substantial improvement in the accuracy and stability of λ prediction; and (4) λ exerts a clear control on the shape of relative permeability curves, where a larger λ corresponds to earlier initiation and forward-shifted rising segments of water-phase flow, while a smaller λ results in overall flatter relative permeability curves. From the perspectives of fractal and multifractal theory, this study establishes an intrinsic linkage among pore structure, capillary pressure curve shape parameters, and relative permeability, providing a novel quantitative framework for constraining relative permeability curve morphology in tight sandstones under conditions where systematic relative permeability experiments are unavailable. Full article

This study investigates the ongoing electrical activity of local neural networks—referred to as neurodynamics—across 37 anatomically defined brain regions. We analyzed stereotactic intracranial EEG (sEEG) recordings from 106 subjects during wakeful rest, focusing on scale-free (power-law) properties to determine whether distinct brain regions exhibit unique neurodynamic signatures. Results revealed a power-law regime in two frequency ranges (approximately 0.5–4 Hz and 33–80 Hz). Notably, the power-law exponent (slope) in the high-frequency band differed significantly between cortical and subcortical areas (p < 0.01). These findings suggest that local neurodynamics, as reflected in scale-free characteristics, may serve as a functional “fingerprint” for brain region classification. This approach may contribute to functional brain parcellation efforts and offer new insights into the intrinsic organization of neuronal networks as revealed by resting-state activity analysis. Full article

Financial markets often display nonlinear and turbulent dynamics during periods of stress, and crude-oil and global equity systems frequently demonstrate closely connected forms of instability. Earlier studies report multifractality, chaotic features and regime-dependent spillovers across commodities and equities, yet existing approaches rarely succeed in capturing both the intrinsic complexity of oil-market behavior and the changing structure of cross-asset dependence. This limitation reduces the ability to distinguish calm from turbulent regimes and weakens short-horizon risk assessment. The present study introduces a unified framework that quantifies and predicts systemic instability within the coupled oil–equity system. The analysis constructs a crude-oil complexity index based on multifractal fluctuation analysis, permutation and approximate entropy, and Lyapunov-based indicators of chaotic dynamics. At the same time, it develops an information-theoretic network of global equity and energy-sector returns and summarizes its instability through measures of edge turnover, spectral radius, degree entropy and strength dispersion. These components are combined to form the Coupled Multiscale Chaos Index (CMCI), a scalar state variable that distinguishes calm, transitional and chaotic market regimes. Empirical results indicate that Brent and WTI exhibit pronounced multifractality, elevated entropy and positive Lyapunov exponents, while the dependence network becomes more centralized, more clustered and more capable of shock amplification during high-CMCI states. The CMCI moves closely with realized volatility and provides significant predictive content for five-day variance across major global equity benchmarks, with performance superior to models that rely only on macro-financial controls. Out-of-sample evaluation shows that forecasts incorporating measures of complexity record substantially lower MSE and QLIKE losses. The findings indicate that systemic instability reflects the interaction between local chaotic dynamics in crude-oil markets and turbulence in the global dependence network. The CMCI offers a practical early-warning indicator that supports risk management, forecasting and macroprudential supervision. Full article

Quantifying the heterogeneity of pore-throat structure and evaluating reservoir quality are of great significance in the exploration and development of tight sandstone oil and gas reservoirs. This study focused on 10 samples of tight sandstone from the Benxi Formation in the Ordos Basin of China. Based on nuclear magnetic resonance (NMR) and combined with the theory of multifractal analysis to calculate multifractal parameters, the pore structure and fractal characteristics of tight sandstone reservoirs were characterized. The results showed that the dominant minerals are quartz, clay minerals, rock fragments and calcite, while feldspar content is relatively minor. The NMR T₂ spectra all exhibited bimodal characteristics. The pore size distribution of the reservoir has multifractal characteristics. The multifractal parameters D_min-D_max range from 2.02 to 2.88, D_min/D_max ranges from 3.69 to 5.11, and △α ranges from 2.441 to 3.316. Different mineral components had different effects on the fractal characteristics. The increase in quartz content retained more primary intergranular pores, affecting the fractal dimension of large pores, and weakening the heterogeneity of the pores. The increase in calcite and clay minerals corresponded to the enhancement of micropores and mesopores, increasing the heterogeneity of the pore structure. Based on the reservoir classification using multifractal parameters, the evolution of pore heterogeneity in tight sandstone rocks can be quantified, thereby effectively evaluating reservoir quality. Overall, reservoirs with larger D_min-D_max and D_min/D_max values, smaller △α, weaker porosity heterogeneity, and better connectivity are favorable areas for hydrocarbon exploration and development. The comprehensive fractal characterization of tight sandstone reservoirs demonstrates the applicability of multifractal dimensions in characterizing the heterogeneity of pore structures in tight sandstones, and is a key factor in improving the exploration effectiveness and development benefits of tight sandstone oil and gas reservoirs. Full article

The sustainable use of freshwater resources includes balancing between human demand for water and the long-term health of river systems. Although dams and reservoirs are essential for water supply, flood control and energy generation, they can induce significant hydrological alterations, affecting water quality, sediment transport, downstream water availability, and aquatic and riparian ecosystems. In this study, we employed multifractal analysis to investigate hydrological changes in the São Francisco River basin, Brazil, resulting from the construction of a cascade of dams and reservoirs. We applied multifractal detrended fluctuation analysis (MFDFA) to daily streamflow time-series spanning the period from 1929 to 2016, at locations both upstream and downstream of cascade dams, and for periods before and after dam construction. We calculated multifractal spectra f(α) and analyzed key complexity parameters: the position of the spectrum maximum α_0, representing the overall Hurst exponent H; the spectrum width W indicating the degree of multifractality; and the asymmetry parameter r, which reflects the dominance of small (r > 1) and large (r < 1) fluctuations. We found that after the construction of Sobradinho dam, located in the Sub-Middle São Francisco region, streamflow dynamics shifted towards a regime characterized by uncorrelated increments (H~0.5) and stronger multifractality (larger W), with the dominance of small fluctuations (r > 1). In contrast, the cumulative effect of all cascade dams downstream, in the Lower São Francisco region, led to streamflow regime with similarly uncorrelated increments (H~0.5), but with weaker multifractality (smaller W) and a dominance of large fluctuations (r < 1). The novelty of this work is the use of a sliding-window MFDFA approach to explore the temporal evolution of streamflow multifractality. This method uncovered otherwise hidden aspects of hydrological alterations, such as increasing tendency in spectrum width, indicating stronger multifractality and higher complexity of streamflow dynamics after the dam construction. These results demonstrate that multifractal analysis is a powerful tool for assessing the complexity of hydrological changes induced by human activities. Full article

Marathons are one of the ultimate challenges of human endeavor. As a consequence of the growing passion of amateur runners for this discipline, a strong need has been shown for counselling during the preparation and for advice on how to manage their efforts during the race. This monitoring should be based on parameters collected during the race and correctly interpreted. Multifractality parameters, which have proved their relevance in many other areas of signal processing, are natural candidates for this purpose. This paper shows that, due to the extreme irregularity of the data, the previously used multifractal techniques cannot be applied in this context, in contrast with the recently introduced parameters based on the weak scaling exponent, which require no a priori assumptions for their use; these parameters yield new classification parameters in the processing of physiological data captured on marathon runners. The comparison of their values reveals how marathon runners handle variations in the irregularity of their races and therefore gives a new insight on the way that runners of different levels conduct their run; therefore, this study shows that the use of these parameters offers a promising tool in order to give advice on how to improve performances. Full article

This study investigates the scaling properties of rainfall in Tunis over temporal scales ranging from 5 min to 2.5 years using high-resolution rain gauge data from three recording stations. We employ the Universal Multifractal (UM) framework to characterize scaling properties across multiple temporal regimes. The UM model was selected over alternative multifractal approaches because of its parsimonious three-parameter formulation (C₁, α, H). It explicitly accounts for non-conservative processes through the Fractionally Integrated Flux (FIF) extension and includes established bias correction methods for highly intermittent signals. This framework has demonstrated universality across diverse climatic conditions and enables direct comparison with existing rainfall studies in Mediterranean environments. Spectral analysis reveals three distinct scaling regimes: micro-scale (5 min–2 h 40 min), meso-scale (2 h 40 min–7 days), and synoptic scale (>7 days). The non-conservative nature of the micro-scale regime is addressed through a multifractal fractionally integrated flux model. A key challenge in applying UM analysis to rainfall data is the prevalence of low and zero rain rates (>98% zeros in our dataset). This extreme intermittency introduces significant bias in parameter estimation. Existing correction methods require either continuous rain sequences—scarce in semi-arid climates—or are limited to moderate intermittency levels. We propose an empirical correction method that extends the existing semi-empirical approach by explicitly linking the percentage of zero values to biased UM parameters through empirical relationships applicable to sequences with as few as 50% rainy observations. This advancement enables reliable parameter estimation from highly intermittent datasets. In such conditions, traditional event-by-event analysis yields insufficient samples (only five continuous events longer than 2 h 40 min over 2.5 years in Tunis). The corrected estimates (α = 1.63, C₁ = 0.16 for micro-scales) demonstrate strong consistency with continuous rainfall events and align well with high-resolution studies, validating our approach for extreme intermittency conditions characteristic of Mediterranean semi-arid climates. Full article

Accurately determining the T₂ cutoff value is critical for evaluating fluid mobility in deep tight reservoirs, yet strong pore structure heterogeneity challenges traditional methods. This study proposes a non-destructive prediction method based on multifractal singularity spectrum analysis of nuclear magnetic resonance T₂ spectra. Using 10 tight sandstone cores from the Denglouku Formation (Songliao Basin), we quantify the intrinsic relationship between multifractal parameters and T₂ cutoff values. Results indicate that the minimum generalized dimension (D_min) and singularity spectrum width (Δα) are not merely mathematical fits but reveal the physical mechanisms controlling fluid binding in micro-throats. A multivariate regression model based on these parameters significantly outperforms traditional methods in accuracy (R² > 0.85). This approach provides a robust, non-destructive tool for identifying reservoir ‘sweet spots’ without compromising core integrity. Full article

Clarifying the complex interaction between climate risks and the new energy industry chain is of key significance to advancing the energy transition and strengthening industrial chain robustness. This research pairwise-matches the climate physical risk and the climate transition risk with the entire range of the new energy industry chain segments, comprehensively examining the pairwise interactive relationships. By applying the MF-ADCCA series of methods, it was revealed that there are prevalent asymmetric cross-correlated multifractal characteristics between climate risks and the new energy industry. The long-term memory under the upward trend of the market is distinctly stronger than that under the downward trend. Given that this correlation can indirectly reflect market efficiency differences, this paper constructs the Hurst Volatility Sensitivity Index (HVI) and the Hurst Asymmetry Index (HAI) and further proposes the Unified Market Efficiency Index (UMEI). Its innovative advantage resides in the balanced integration of volatility efficiency and structural symmetry, in turn enabling a comprehensive assessment of the new energy market efficiency under climate risk perturbations. Static analysis reveals that the overall market efficiency of the new energy industry under the climate transition risk is generally higher than that under the climate physical risk, and the market efficiency of mature upstream and midstream new energy segments is significantly superior to that of the downstream. Dynamic evolution characteristics indicate that market efficiency has typical time-varying traits, the evolution of which is often driven by significant policies or extreme events. The climate transition risk tends to trigger aperiodic structural adjustments, while the climate physical risk mostly induces periodic efficiency fluctuations. This study furnishes solid evidence for the new energy market in coping with climate risks. Full article

We detail a procedure to transform the current empirical stage in the study of complex systems into a predictive phenomenological one. Our approach starts with the statistical-mechanical Landau-Ginzburg equation for dissipative processes, such as kinetics of phase change. Then, it imposes discrete time evolution to explicit back feeding, and adopts a power-law driving force to incorporate the onset of chaos, or, alternatively, criticality, the guiding principles of complexity. One obtains, in closed analytical form, a nonlinear renormalization-group (RG) fixed-point map descriptive of any of the three known (one-dimensional) transitions to or out of chaos. Furthermore, its Lyapunov function is shown to be the thermodynamic potential in q-statistics, because the regular or multifractal attractors at the transitions to chaos impose a severe impediment to access the system’s built-in configurations, leaving only a subset of vanishing measure available. To test the pertinence of our approach, we refer to the following complex systems issues: (i) Basic questions, such as demonstration of paradigms equivalence, illustration of self-organization, thermodynamic viewpoint of diversity, biological or other. (ii) Derivation of empirical laws, e.g., ranked data distributions (Zipf law), biological regularities (Kleiber law), river and cosmological structures (Hack law). (iii) Complex systems methods, for example, evolutionary game theory, self-similar networks, central-limit theorem questions. (iv) Condensed-matter physics complex problems (and their analogs in other disciplines), like, critical fluctuations (catastrophes), glass formation (traffic jams), localization transition (foraging, collective motion). Full article

This article examines the behavior of seismic noise fields over the Japanese islands recorded by the F-net seismic network for 1997–2025. This paper uses nonlinear noise statistics: the entropy of the wavelet coefficient distribution, the Donoho–Johnston (DJ) wavelet index, and the multifractal singularity spectrum support width. These parameters were chosen because their changes reflect the complication or simplification of the noise structure. Changes in the structure of seismic noise properties are analyzed in comparison with a sequence of strong earthquakes. Using a model of the intensity of interacting point processes, the effect of the leading of local noise property extrema relative to the seismic event times is estimated. Using the Hilbert–Huang decomposition, the synchronization of the amplitudes of the envelopes of noise property time series for different IMF levels is estimated. A sequence of weighted probability density maps of extreme values of noise properties is analyzed in comparison with the mega-earthquake of 11 March 2011 and the preparation of another possible strong seismic event. Full article

Complex systems—ranging from biological organisms to turbulent fluids—exhibit multiscale heterogeneity and intermittency that traditional, differentiable calculus fails to adequately capture. Therefore, we propose a mathematical framework for analyzing complex system dynamics by assimilating the trajectories of structural units to continuous but non-differentiable multifractal curves. Utilizing the scale covariance principle, the authors recast the conservation of momentum as a geodesic equation within a multifractal space. This approach naturally separates the complex velocity field into differentiable and non-differentiable scale resolutions, where the balance of multifractal acceleration, convection, and dissipation is parametrized by a singularity spectrum f(α). We also discuss broad interdisciplinary implications, because, in our opinion, non-differentiability can enhance predictive capabilities in various fields such as oncology, pharmacology, and geophysics. Full article