Search Results (65)

The paper examines the multifractal and asymmetric behavior of oil, freight and exchange rate markets in the global trade system with the help of the Asymmetric Multifractal Detrended Fluctuation Analysis (AMF-DFA) technique. Based on daily data of West Texas Intermediate (WTI) crude oil, the Baltic Dry Index (BDI), and the exchange rate between the RMB/USD over the period of post-COVID-19 (2021–2024), the analysis focuses on whether efficiency in the markets varies across time scales and directional regimes. The findings show that there is strong evidence of multifractality in all markets, which implies that the scaling behavior is heterogeneous, and that it is long-range-dependent. Notable directional persistence is found between up and down movements with oil and exchange rate markets showing stronger directional persistence, especially at longer horizons with the freight markets displaying relatively weaker directional persistence. Additional results imply that temporal dependence and nonlinearity are the main drivers of multifractality in oil and exchange rate markets, and short-term fluctuations are prevalent factors in the dynamics of the freight market. These findings not only refute the classical Efficient Market Hypothesis but also provide empirical evidence in support of the Adaptive Market Hypothesis, and how efficiency is dynamic, dependent on scale, and directionally asymmetric. The study contributes by examining asymmetric multifractal efficiency across three trading markets during the post-COVID period, while recognizing that formal cross-market spillover analysis remains a direction for future research. Full article

The pore-throat structure is a key factor in the exploration and development of tight sandstone reservoirs. In the present study, 14 tight sandstone samples from the Chang 8 member of the Ordos Basin were analyzed using high-pressure mercury intrusion, cast thin section analysis, scanning electron microscopy and cathodoluminescence imaging techniques. Fractal dimensions, obtained from the slopes of log(S_W) versus log(P_c) double-logarithmic plots, were applied to quantitatively characterize pore-throat structures and classify reservoirs through multifractal analysis, and discuss the diagenetic controlling factors affecting the pore-throat structure of different reservoir types. The results showed that the Chang 14 tight sandstones are characterized as two segments fractal features, which indicated that these samples have complex pore-throat structure and consist of two types of spaces: mesopore-throat spaces and micropore-throat spaces. The mesopore-throat system shows a higher fractal dimension (D1: 2.74–2.99), indicating greater heterogeneity and irregularity, while the micropore-throat system exhibits a lower dimension (D2: 2.28–2.61). D1 exhibits a negative correlation with the porosity and permeability of mesopores, while D2 shows a weak positive correlation with the properties of micropores. The total fractal dimension (D) is weakly correlated with overall reservoir properties, confirming that reservoir storage and flow capacity are primarily governed by the mesopore system rather than the micropore system. By analyzing the contribution of pore throats to sample physical properties, the results indicate that the 14 samples can be classified into two types based on 35% porosity contribution and 60% permeability contribution thresholds. Type 1, reservoirs dominated by microporous throat space (D values ranging from 2.603 to 2.644); Type 2, reservoirs dominated by mesoporous throat space (D values ranging from 2.544 to 2.598). Type 1 is characterized by primary intergranular pores, residual intergranular pores and intergranular dissolution pores, which enhance connectivity and reduce network complexity, thereby improving fluid permeability. In contrast, Type 2 consists mainly of intragranular dissolution pores, intergranular gap pores and micro-dissolution pores in clay minerals, which significantly inhibit fluid mobility. Diagenesis, including compaction, dissolution and cementation, exerts a significant control on the fractal characteristics and pore-throat structure evolution. The fractal characteristics exhibited in the pore-throat structure could provide a desirable analytical method, distinguishing from classification based on scale or size, for the evaluation and classification of tight sandstone reservoirs. Full article

Complex biological and medical systems often exhibit irregular and self-similar structures that can be effectively analyzed using fractal and multifractal frameworks. This study aims to provide a comprehensive overview of multifractal analysis as a mathematical tool for characterizing complex biomedical patterns and improving disease diagnosis. The methods discussed include the Wavelet Transform Modulus Maxima (WTMM) and box-counting techniques, which quantify local scaling behaviors and heterogeneity within medical images. A review of recent studies demonstrates that multifractal parameters have successfully differentiated between normal and pathological tissues in diseases such as cancer, cardiac disorders, and Alzheimer’s disease. This paper also examines the integration of artificial intelligence, particularly machine learning algorithms, with multifractal features to enhance diagnostic accuracy and automate image interpretation. The results indicate that this hybrid approach improves the reliability and sensitivity of early disease detection. In conclusion, multifractal analysis, when systematically applied and combined with AI, offers a promising complementary framework for advancing precision medicine and supporting clinical decision-making. 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

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

Fine-grained sedimentary rocks exhibit significant textural heterogeneity, often obscured by conventional grain size analysis techniques that require sample disaggregation. We propose a non-destructive, image-based grain size characterization workflow, utilizing stitched polarized thin-section photomicrographs, k-means clustering, and watershed segmentation algorithms. Validation against laser granulometry data indicates strong methodological reliability (absolute errors ranging from −5% to 3%), especially for particle sizes greater than 0.039 mm. The methodology reveals substantial internal heterogeneity within Es3 laminated shale samples from the Shahejie Formation (Bohai Bay Basin), distinctly identifying coarser siliceous laminae (grain size >0.039 mm, Φ < 8 based on Udden-Wentworth classification) indicative of high-energy depositional environments, and finer-grained clay-rich laminae (grain size <0.039 mm, Φ > 8) representing low-energy conditions. Conversely, massive mudstones exhibit comparatively homogeneous grain size distributions. Additionally, a multifractal analysis (Multifractal method) based on the S_50bi/S_50si ratio further quantifies spatial heterogeneity and pore-structure complexity, significantly enhancing facies differentiation and reservoir characterization capabilities. This method significantly improves facies differentiation ability, provides reliable constraints for shale oil reservoir characterization, and has important reference value for the exploration and development of the Bohai Bay Basin and similar petroliferous basins. Full article

The root causes forcing the differential pore-throat performances and crude oil recoverability in heterogeneous shale lithofacies of saline-lacustrine fine-grained mixed sedimentary sequences are still debated. Especially application cases of fractal theory in characterizing pore-throat heterogeneity are still lacking and the significance of differential multifractal distribution patterns on reservoir assessment remains controversial. This present study focuses on the shale-oil reservoirs in saline-lacustrine fine-grained mixed depositional sequences of the Middle Permian Lucaogou Formation (southern Junggar Basin, NW China), and presents a set of new results from petrographical investigation, field-emission scanning electron microscopy (FE-SEM) imaging, fluid injection experiments (low-pressure N₂ adsorption and high-pressure mercury intrusion porosimetry (HMIP)), nuclear magnetic resonance (NMR) spectroscopy and T₁-T₂ mapping, directional spontaneous imbibition, as well as contact angle measurements. Our results demonstrated that the investigated lithofacies are mainly divided into a total of five lithofacies categories: felsic siltstones, sandy dolomitic sandstones, dolarenites, micritic dolomites, and dolomitic mudstones, respectively. More importantly, the felsic siltstone and sandy dolomitic siltstones can be identified as the most advantageous lithofacies categories exhibiting the strongest movable oil-bearing capacity owing to an acceptable complexity and heterogeneity of mesopore-throat structures, as evidenced by the corresponding moderate fractal dimension of mesopores (D₂) from HMIP and apparently lower fractal dimension of movable fluids’ pores (D₂) from NMR results. Particularly noteworthy is the relatively poor shale-oil movability recognized in the dolarenites, micritic dolomites, and dolomitic mudstones due to heterogeneous and unfavorable pore-throat systems, even though an acceptable micro-connectivity and a more oleophilic interfacial wettability prevails in crucial dolomitic components. Finally, a comprehensive and conceptual model is established for an effective and characteristic parameter system for assessing differential reservoir petrophysical properties, interfacial wettability, and shale-oil movability concerning heterogeneous lithofacies categories. Our achievements can serve as an analog for investigating saline-lacustrine mixed shale-oil reservoirs to gain a more comprehensive understanding of differential recoverability of dessert reservoir intervals, and to guide the assessment of “sweet spots” distribution and optimization of engineering technique schemes for commercial exploitation. Full article

Supercritical CO₂ (ScCO₂) injection has emerged as a promising method to enhance shale gas recovery while simultaneously achieving CO₂ sequestration. This research investigates how ScCO₂ interacts with water and shale rock, altering the pore structure characteristics of shale reservoirs. The study examines shale samples from three marine shale formations in southern China under varying thermal and pressure regimes simulating burial conditions at 1000 m (45 °C and 10 MPa) and 2000 m (80 °C and 20 MPa). The research employs multiple analytical techniques including XRD for mineral composition analysis, MICP, N₂GA, and CO₂GA for comprehensive pore characterization, FE–SEM for visual observation of mineral and pore changes, and multifractal theory to analyze pore structure heterogeneity and connectivity. Key findings indicate that ScCO₂–water–shale interactions lead to dissolution of minerals such as kaolinite, calcite, dolomite, and chlorite, and as the reaction proceeds, substantial secondary mineral precipitation occurs, with these changes being more pronounced under 2000 m simulation conditions. Mineral dissolution and precipitation cause changes in pore structure parameters of different pore sizes, with macropores showing increased PV and decreased SSA, mesopores showing decreased PV and SSA, and micropores showing insignificant changes. Moreover, mineral precipitation effects are stronger than dissolution effects. These changes in pore structure parameters lead to alterations in multifractal parameters, with mineral precipitation reducing pore connectivity and consequently enhancing pore heterogeneity. Correlation analysis further revealed that H and D₋₁₀–D₁₀ exhibit a significant negative correlation, confirming that reduced connectivity corresponds to stronger heterogeneity, while mineral composition strongly controls the multifractal responses of macropores and mesopores, with micropores mainly undergoing morphological changes. However, these changes in micropores are mainly manifested as modifications of internal space. Siliceous shale samples exhibit stronger structural stability compared to argillaceous shale, which is attributed to the mechanical strength of the quartz framework. By integrating multifractal theory with multi–scale pore characterization, this study achieves a unified quantification of shale pore heterogeneity and connectivity under ScCO₂–water interactions at reservoir–representative pressure–temperature conditions. This novelty not only advances the methodological framework but also provides critical support for understanding CO₂–enhanced shale gas recovery mechanisms and CO₂ geological sequestration in depleted shale gas reservoirs, highlighting the complex coupling between geochemical reactions and pore structure evolution. Full article

This study focuses on a hydrocarbon reservoir located in southeastern Mexico. The analysis uses well log data derived from petrophysical evaluations of storage capacity. The structural complexity of the reservoir and observed heterogeneity in Cretaceous units motivate a fractal-based characterization of spatial fluctuations. The objective is to assess the fractal scaling of storage capacity fluctuations using the dynamic Family–Vicsek framework. Critical exponents $\alpha$ (roughness), $\beta$ (growth), and z (dynamic) are obtained through structure function metrics. Data collapse techniques and local Hurst exponent distributions are used to explore long-range memory and spatial heterogeneity across wells. This study aims to classify storage capacity fluctuation records based on Euclidean or fractal geometries. This analysis allows a novel characterization of storage trends in the reservoir. The analysis reveals persistent scaling behavior, indicating long-range correlations in the storage capacity fluctuations. Multiscale patterns and variations in local Hurst exponents highlight the presence of multifractality and regional heterogeneity. Specifically, the spatial distribution of local Hurst exponents obtained in this study enables the inference of statistical properties in synthetic wells, providing key input for the structural and functional characterization of the reservoir’s geological model. This approach aims to identify preferential subsurface flow pathways for hydrocarbons and gas. Full article

To alleviate environmental pressures, manufactured sand (MS) are increasingly being used in the production of ultra-high-performance concrete (UHPC) due to their consistent supply and environmental benefits. However, manufactured sand properties are critically influenced by processing and production techniques, resulting in substantial variations in fundamental characteristics that directly impact UHPC matrix pore structure and ultimately compromise performance. Traditional testing methods inadequately characterize UHPC’s pore structure, necessitating multifractal theory implementation to enhance pore structural interpretation capabilities. In this study, UHPC specimens were fabricated with five types of MS exhibiting distinct properties and at varying water to binder (w/b) ratios. The flowability, mechanical strength, and pore structure of the specimens were systematically evaluated. Additionally, multifractal analysis was conducted on each specimen group using mercury intrusion porosimetry (MIP) data to characterize pore complexity. SM-type sands have a more uniform distribution of pores of different scales, better pore structure and matrix homogeneity due to their finer particles, moderate stone powder content, and better cleanliness. Both excessively high and low stone powder content, as well as low cleanliness, will lead to pore aggregation and poor closure, degrading the pore structure. Full article

Multifractal analysis has been used in the exploration of soil grain size distributions (GSDs) in environmental and agricultural research. However, multifractal studies regarding the GSDs of sediments in braided delta-front are currently scarce. Open-source software designed for the realization of this technique has not yet been programmed. In this paper, the multifractal parameters of 61 GSDs from braided delta-front in the Paleogene Enping Formation in Huilu Low Uplift, Pearl River Mouth basin, are calculated and compared with traditional parameters. Multifractal generalized dimension spectrum curves are sigmoidal and decrease monotonically. Multifractal singularity spectrum curves are asymmetric, convex, and right-hook unimodal. The entropy dimension and singularity spectrum width ranges of silt-mudstones and gravelly sandstones are wider than those of fine and medium-coarse sandstones. The symmetry degree scopes from different lithologies are concentrated in distinguishing intervals. With the increase of grain sizes, the symmetry degree decreases overall. Both the symmetry degree and mean of GSDs are effective to distinguish the different lithologies from various depositional environments. A flexible and easy-to-use MATLAB (2021b)^® GUI (graphic user interface) package, MfGSD (Multifractal of GSD, V1.0), is provided to perform multifractal analysis on sediment GSDs. After raw GSDs imported into MfGSD, multifractal parameters are batch calculated and graphed in the interface. Then, all multifractal parameters can be exported to an Excel file, including entropy dimension, singularity spectrum, correlation dimension, symmetry degree of multifractal spectrum, etc. MfGSD is effective, and the multifractal parameters outputted from MfGSD are helpful to distinguish depositional environments of GSDs. MfGSD is open-source software that can be used to explore GSDs from various kinds of depositional environments, including water or wind deposits. Full article

A novel method of exploring linguistic networks is introduced by mapping word-adjacency networks to time series and applying multifractal analysis techniques. This approach captures the complex structural patterns of language by encoding network properties—such as clustering coefficients and node degrees—into temporal sequences. Using Alice’s Adventures in Wonderland by Lewis Carroll as a case study, both traditional word-adjacency networks and extended versions that incorporate punctuation are examined. The results indicate that the time series derived from clustering coefficients, when following the natural reading order, exhibits multifractal characteristics, revealing inherent complexity in textual organization. Statistical validation confirms that observed multifractal properties arise from genuine correlations rather than from spurious effects. Extending this analysis by taking into account punctuation equally with words, however, changes the nature of the global scaling to a more convolved form that is not describable by a uniform multifractal. An analogous analysis based on the node degrees does not show such rich behaviors, however. These findings reveal a new perspective for quantitative linguistics and network science, providing a deeper understanding of the interplay between text structure and complex systems. Full article

Complexity is one of those descriptive terms adopted in science that we think we understand until it comes time to form a coherent definition upon which everyone can agree. Suddenly, we are awash in conditions that qualify this or that situation, much like we were in the middle of the last century when it came time to determine the solutions to differential equations that were not linear. Consequently, this tutorial is not an essay on the mathematics of complexity nor is it a rigorous review of the recent growth spurt of complexity science, but is rather an exploration of how physiologic time series (PTS) in the life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions are discarded and so-called ordinary statistical events in PTS are replaced with crucial events (CEs) using mutifractal dimensionality as the working measure of complexity. The empirical datasets considered include respiration, electrocardiograms (ECGs), and electroencephalograms (EEGs), and as different as these time series appear from one another when recorded, they are in fact shown to be in synchrony when properly processed using the technique of modified diffusion entropy analysis (MDEA). This processing reveals a new synchronization mechanism among the time series which simultaneously measures their complexity by means of the multifractal dimension of each time series and are shown to track one another across time. These results reveal a set of priciples that capture the manner in which information is exchanged among physiologic organ networks. Full article

This study investigates the complexity, efficiency, and sectoral interdependencies of the S&P Global BMI indices during critical global events, including the COVID-19 pandemic and the Russia–Ukraine war. The analysis is conducted in three dimensions: (1) evaluating market efficiency using permutation entropy and the Fisher information measure, (2) exploring sectoral alignments through clustering techniques (hierarchical and k-means clustering), and (3) assessing the influence of geopolitical risk using Multifractal Detrended Cross-Correlation Analysis (MFDCCA). The results highlight significant variations in informational efficiency across sectors, with Utilities and Consumer Staples exhibiting high efficiency, while Emerging Markets and Financials reflect lower efficiency levels. Temporal analysis reveals widespread efficiency declines during the pandemic, followed by mixed recovery patterns during the Ukraine conflict. Clustering analysis uncovers dynamic shifts in sectoral relationships, emphasizing the resilience of defensive sectors and the unique behavior of Developed BMI throughout crises. MFDCCA further demonstrates the multifractality in cross-correlations with geopolitical risk, with Consumer Staples and Energy showing stable persistence and Information Technology exhibiting sensitive complexity. These findings emphasize the adaptive nature of global markets in response to systemic and geopolitical shocks, offering insights for risk management and investment strategies. Full article