Impact of atmospheric O3 and NO2 on the secondary sulfates in real atmosphere.

As an important component of secondary aerosols, sulfate plays a crucial role in regulating atmospheric radiative balance and influencing the secondary formation of ozone (O3). In real atmosphere, atmospheric oxidants NO2 and O3 can promote the oxidation of SO2 to form sulfate (SO42-) through multiphase chemistry that occur at different time scales. Due to the combined impact of meteorology, pollution sources, atmospheric chemistry, etc., time-scale dependence of SO2-SO42- conversion makes the impact of NO2/O3 on it more complex. In this study, based on long-term time series (2013-2020) of air pollution variables from seven stations in Hong Kong, the Multifractal Detrended Cross-Correlation Analysis (MFDCCA) method has been employed to quantify the cross-correlations between SO2 and SO42- in real atmosphere at different time scales, for examining the time-scale dependence of SO2-SO42- conversion efficiency. Furthermore, the Pearson correlation analysis has been used to study the influence of NO2/O3 on SO2-SO42- conversion, and the regional and seasonal differences have been analyzed by considering factors such as meteorology, pollution sources, and regional transport. Changes in the main components of secondary aerosols are closely linked with the co-control of regional PM2.5 and O3. Therefore, the exploration of the impact of co-existing NO2/O3 gases on the secondary formation of sulfates in real atmosphere is significant.

Cross-correlation and multifractality analysis of the Chinese and American stock markets based on the MF-DCCA model.

Objective: To compare the multifractal features and factors of the Chinese and American stock markets and their correlation, complexity and uncertainty. Methods: The paper analyzes the CSI 300 and S&P 500 indices from March 2018 to March 2023 using the MF-DCCA model and removes the long-term memory and nonlinear effects by random reshuffling and phase processing methods. Results: The paper shows that (1) CSI 300 and S&P 500 have multifractal features, with different long-term memory, complexity and irregularity at different scales; (2) The markets are fractal movements influenced by investors' irrationality and expectations, not efficient markets; (3) Long-term memory and nonlinear effects cause the multifractal features. The paper offers a new perspective and method for the market investors and regulators.

The environmental capacity of rare heavy metal calculation in the Qinghai‒Tibet Plateau region via multifractal analysis.

Accurate assessments of the soil environmental capacity are important for evaluating heavy metal pollution levels, facilitating effective prevention and control measures against such pollution. However, due to the lack of risk screening values for certain key elements, such as Rb, Sn, and Th, the assessment of the soil environmental capacity is not comprehensive. Therefore, in this study, the Menyuan-Huangzhong area of Qinghai Province was selected as the research area, and local background and risk values were established via multifractal analysis, thereby systematically examining the environmental capacity. The findings indicated that within the study area, the static environmental capacity values of 15 elements could be ranked as follows: Ba, Cu, Zn, Cr, Rb, Ni, La, Pb, Th, As, U, Sn, Tl, Cd, and Hg. In general, the residual capacity distribution of the various elements varied across the study area, with lower values primarily found in the northern and central regions and higher values obtained in the northwestern and southwestern regions. Between 2018 and 2068, there was a notable and rapid decline in the dynamic environmental capacity of Hg, Cu, and Cd in the study area. In the Menyuan-Huangzhong area of Qinghai, the average comprehensive soil environmental capacity index reached 0.91, indicating a moderate environmental capacity and slight associated health risks. The findings of this study could serve as a valuable reference for soil heavy metal pollution assessment, early warning, and management in this area; enhance the study of soil environmental capacity methods; and provide a theoretical foundation for subsequent research.

Temporal assessment of Gross alpha emissions from the petroleum industry in Tenerife, Canary Islands (2001-2022).

A ca. 76% decrease in gross alpha activity levels, measured in surface aerosols collected in the city of Santa Cruz de Tenerife (Spain), has been explained in the present study in connection with the reduction of activities, and eventual closure, of an oil refinery in the city. Gross Alpha in surface aerosols, collected at weekly intervals over a period of 22 years (2001-2022), was used for the analysis. The dynamic behaviour of the gross alpha time series was studied using statistical wavelet, multifractal analysis, empirical decomposition method, multivariate analysis, principal component, and cluster analyses approaches. This was performed to separate the impact of other sources of alpha emitting radionuclides influencing the gross alpha levels at this site. These in-depth analyses revealed a noteworthy shift in the dynamic behaviour of the gross alpha levels following the refinery's closure in 2013. This analysis also attributed fluctuations and trends in the gross alpha levels to factors such as the 2008 global economic crisis and the refinery's gradual reduction of activity leading up to its closure. The mixed-model approach, incorporating multivariate regression and autoregressive integrated moving average methods, explained approximately 84% of the variance of the gross alpha levels. Finally, this work underscored the marked reduction in alpha activity levels following the refinery's closure, alongside the decline of other pollutants (CO, SO2, NO, NO2, Benzene, Toluene and Xylene) linked to the primary industrial activity in the municipality of Santa Cruz de Tenerife.

Damage regularity and multifractal analysis of sol-gel reflection coating of KDP crystal under low UV irradiation flux.

This study employed multifractal analysis to investigate the changes in surface morphology of SiO2 anti-reflective coatings prepared on KDP substrates using the sol-gel method, under various conditions of ultraviolet (UV) irradiance. The coatings were successfully fabricated, and the chemical structure of the SiO2 sol was comprehensively characterized using Solid-State Nuclear Magnetic Resonance (SSNMR) technology. Under low UV irradiance (4 J/cm2), repeated experiments revealed a crack-induced mechanism of surface fatigue damage. Utilizing Scanning Electron Microscopy (SEM), the study discovered the induction effect of initial crack defects in UV-damaged coatings and established a damage model. Furthermore, Atomic Force Microscopy (AFM) was used to acquire images of the coatings' surface morphology at different damage levels, which were analyzed using the multifractal spectrum f(α). This analysis confirmed the multifractal nature of the coatings both before and after damage. This study identified significant effects of UV irradiation on the width of the multifractal spectrum and Δf, indicating that the SiO2 anti-reflective coatings exhibit multifractal characteristics under various damage states. The coatings displayed a pattern of decreasing and then increasing singularity spectrum width, height distribution unevenness, and surface roughness with increasing damage. This study demonstrates that multifractal analysis is an effective tool for describing the complexity of the surface morphology of sol-gel-derived anti-reflective coatings for the first time and for validating their multifractal properties across different stages of UV damage. HIGHLIGHTS: Damage dynamic process of KDP crystal sol-gel coating was described by SEM&AFM; The crack propagation mechanism of sol-gel coating under UV radiation is proposed; The damage evolution of sol-gel coating was described by multifractal analysis.

Complexity synchronization in living matter: a mini review.

Fractal time series have been argued to be ubiquitous in human physiology and some of the implications of that ubiquity are quite remarkable. One consequence of the omnipresent fractality is complexity synchronization (CS) observed in the interactions among simultaneously recorded physiologic time series discussed herein. This new kind of synchronization has been revealed in the interaction triad of organ-networks (ONs) consisting of the mutually interacting time series generated by the brain (electroencephalograms, EEGs), heart (electrocardiograms, ECGs), and lungs (Respiration). The scaled time series from each member of the triad look nothing like one another and yet they bear a deeply recorded synchronization invisible to the naked eye. The theory of scaling statistics is used to explain the source of the CS observed in the information exchange among these multifractal time series. The multifractal dimension (MFD) of each time series is a measure of the time-dependent complexity of that time series, and it is the matching of the MFD time series that provides the synchronization referred to as CS. The CS is one manifestation of the hypothesis given by a "Law of Multifractal Dimension Synchronization" (LMFDS) which is supported by data. Therefore, the review aspects of this paper are chosen to make the extended range of the LMFDS hypothesis sufficiently reasonable to warrant further empirical testing.

Exploring the physicochemical traits, antifungal capabilities, and 3D spatial complexity of hydroxyapatite with Ag+Mg2+ substitution in the biocomposite thin films.

The silver/magnesium doped hydroxyapatite (AgMgHAp, Ca10-x-yAgxMgy(PO4)6(OH)2, xAg=0.05 and yMg=0.02) nanocomposites coatings were deposited on Si substrate using the dip coating technique. The resulting coatings were characterized by scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), Fourier transform infrared (FTIR-ATR) spectroscopy, atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS). The EDS analysis highlighted the presence of the constitutive elements of the silver/magnesium doped hydroxyapatite (AgMgHAp) nanocomposites coatings. The surface microtexture of the AgMgHAp was assessed by atomic force microscopy (AFM) technique. The AFM data suggested the obtaining of a uniform deposited layer comprised of equally distributed nanoconglomerates. FT-IR studies highlighted the presence of vibrational modes associated with the phosphate and hydroxyl groups. No bands associated with silver or magnesium were observed. The XPS analysis highlighted the presence of the constituent elements of hydroxyapatite (Ca 2p, P 2 s, O 1 s), as well as dopants (Ag 3d, Mg 1 s and Mg 2p). The antifungal evaluation of AgMgHAp coatings was carried out using the Candida albicans ATCC 10231 fungal strain. The results of the antifungal assay revealed that the AgMgHAp coatings exhibited a strong inhibitory antifungal activity. Furthermore, the data highlighted that the AgMgHAp inhibited the development of biofilm on their surface. The results revealed that the antifungal activity of the coating varied based on the duration of incubation. On the other hand, the data also showed that AgMgHAp nanocomposites coatings inhibited the fungal cell adhesion and development from the early stages of the incubation. In addition to morphological analysis, we additionally take advantage of AFM images to investigate and explore the domain of fractal and multifractal analysis applied to the films under evaluation. Our studies indicates that nanocomposite coatings made from AgMgHAp demonstrate strong antifungal properties. Our studies indicates that nanocomposite coatings made from AgMgHAp demonstrate strong antifungal properties. These results suggest the potential of AgMgHAp nanocomposite coatings as a promising solution for developing innovative antifungal devices in biomedical applications.

Time series analysis of a 22-year record of 7Be, 210Pb and gross alpha activities in the Canary Islands (Spain) using Principal Component and Multifractal Detrended Fluctuation Analyses.

The long-term variability of a 22-year dataset of 7Be, 210Pb and gross alpha concentrations in surface aerosols collected in the Canary Islands has been analysed in this study. These "time series" were collected on a weekly basis. Various analytical techniques, including Principal Component Analysis (PCA), K-means clustering, correlation analyses, and back-trajectory were used to determine the variability of the data and assess the statistical importance of the source of the air masses reaching the study area. Monthly and annual variations for the time series were also studied. As expected, 7Be, 210Pb time series showed common variability, while gross alpha concentrations were strongly correlated with average PM10 concentration in air. The fractal properties of the time series were studied to gain a deeper understanding of the underlying structure and dynamics of the data. Multifractal Detrended Fluctuation Analysis (MF-DFA) and Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) techniques were also used to detect and analyse the multifractal characteristics of the 7Be, 210Pb, and gross alpha time series. Multifractality was observed, with values of 0.28, 0.67, and 0.61 for 7Be, 210Pb, and gross alpha, respectively. Long-range correlation was found to be the source of the observed multifractality in the three parameters. Multifractal detrended cross-correlation analysis supports the correlation between 7Be - Alpha, 210Pb - Alpha, and 7Be - 210Pb pairs. The results from this study will help model the transport and destiny of natural radionuclides in the atmosphere at this site. The evolution and interactions between 7Be, 210Pb, and gross alpha, reported herein occurred not just locally but also across extensive temporal domains, leading to the emergence of multifractal behaviour in their concentrations. These long-range behaviours/correlations might result from various factors such as atmospheric circulation patterns, global transport mechanisms, or large-scale environmental processes.

Prioritizing cervical cancer candidate genes using chaos game and fractal-based time series approach.

Cervical cancer is one of the most severe threats to women worldwide and holds fourth rank in lethality. It is estimated that 604, 127 cervical cancer cases have been reported in 2020 globally. With advancements in high throughput technologies and bioinformatics, several cervical candidate genes have been proposed for better therapeutic strategies. In this paper, we intend to prioritize the candidate genes that are involved in cervical cancer progression through a fractal time series-based cross-correlations approach. we apply the chaos game representation theory combining a two-dimensional multifractal detrended cross-correlations approach among the known and candidate genes involved in cervical cancer progression to prioritize the candidate genes. We obtained 16 candidate genes that showed cross-correlation with known cancer genes. Functional enrichment analysis of the candidate genes shows that they involve GO terms: biological processes, cell-cell junction assembly, cell-cell junction organization, regulation of cell shape, cortical actin cytoskeleton organization, and actomyosin structure organization. KEGG pathway analysis revealed genes' role in Rap1 signaling pathway, ErbB signaling pathway, MAPK signaling pathway, PI3K-Akt signaling pathway, mTOR signaling pathway, Acute myeloid leukemia, chronic myeloid leukemia, Breast cancer, Thyroid cancer, Bladder cancer, and Gastric cancer. Further, we performed survival analysis and prioritized six genes CDH2, PAIP1, BRAF, EPB41L3, OSMR, and RUNX1 as potential candidate genes for cervical cancer that has a crucial role in tumor progression. We found that our study through this integrative approach an efficient tool and paved a new way to prioritize the candidate genes and these genes could be evaluated experimentally for potential validation. We suggest this may be useful in analyzing the nucleotide sequences and protein sequences for clustering, classification, class affiliation, etc.

Scaling of damage mechanism for additively manufactured alloys at very high cycle fatigue.

A comparative analysis of fracture mechanisms in high- and very high- cycle fatigue (HCF, VHCF) regimes was carried out based on the results of multifractal analysis of the fracture surfaces of additively manufactured 316L stainless steel samples. In terms of scale invariants, the morphology of fracture surfaces in HCF and VHCF regimes inside and outside the fine granular area is shown. The analysis demonstrated that chaotic patterns of relief formation prevail in the crack initiation zone of VHCF samples. However, there is a self-similar relief with a pronounced correlation in the crack propagation area. The relief of the crack growth areas for HCF and VHCF samples are similar to each other.

Multifractal characteristics of soil particle size distribution of abandoned homestead reclamation under different forest management modes.

In this study, fast-growing poplar reclaimed from abandoned homestead in Xixian New District, Xi'an City, Shaanxi Province, was used as the research object to explore the multi-fractal characteristics of soil particle size distribution under different management modes of abandoned land (control), irrigation, fertilizer irrigation and mixed fertilizer irrigation. The results showed that the mean values of soil clay, silt and sand in abandoned land were 14.58%, 81.21% and 4.22% respectively, 14.08%, 79.92% and 5.99% under irrigation, 15.17%, 81.19% and 3.64% under fertilizer irrigation, and 16.75%, 80.20% and 3.05% in mixed fertilizer treatment. From 40 cm, with increasing soil depth, soil clay particles increase under irrigation, fertilizer irrigation, and mixed fertilizer irrigation modes. The single fractal dimension of soil particle size distribution (D) in each treatment ranges from 2.721 to 2.808. At 60-100 cm, D shows fertilizer irrigation > mixed fertilizer irrigation > irrigation > abandoned land, indicating that fertilization and irrigation can increase the fine-grained matter of deep soil particles and reduce soil roughness. Compared with abandoned land, under irrigation, fertilizer irrigation and mixed fertilizer modes the capacity dimension (D0), entropy dimension (D1), correlation dimension(D2), shape characteristics of the multifractal spectrum (Δf) and overall inhomogeneity of the soil particle size distribution (D0-D10) indicate an uneven distribution of soil particle size; fractal structure characteristics of soil (D-10-D0) indicate a simplified soil structure, and degree of dispersion of soil particle size distribution (D1/D0) indicates that soil particle size is distributed in dense areas. Pearson correlation analysis showed that D was significantly correlated with clay, sand, D0-D10, soil organic matter (SOM) and soil available phosphorus (SAP) (P < 0.05). Stepwise regression analysis showed that clay was the main controlling factor of D and D0-D10 changes. The research results can provide some potential indicators for the quality evaluation of abandoned homestead reclamation.

Differing patterns of cortical grey matter pathology identified by multifractal analysis in UMN-predominant ALS patients with and without corticospinal tract hyperintensity.

The pathological hallmarks of amyotrophic lateral sclerosis (ALS) are degeneration of the primary motor cortex grey matter (GM) and corticospinal tract (CST) resulting in upper motor neuron (UMN) dysfunction. Conventional brain magnetic resonance imaging (MRI) shows abnormal CST hyperintensity in some UMN-predominant ALS patients (ALS-CST+) but not in others (ALS-CST-). In addition to the CST differences, we aimed to determine whether GM degeneration differs between ALS-CST+ and ALS-CST- patients by cortical thickness (CT), voxel-based morphometry (VBM) and fractal dimension analyses. We hypothesized that MRI multifractal (MF) measures could differentiate between neurologic controls (n = 14) and UMN-predominant ALS patients as well as between patient subgroups (ALS-CST+, n = 21 vs ALS-CST-, n = 27). No significant differences were observed in CT or GM VBM in any brain regions between patients and controls or between ALS subgroups. MF analyses were performed separately on GM of the whole brain, of frontal, parietal, occipital, and temporal lobes as well as of cerebellum. Estimating MF measures D (Q = 0), D (Q = 1), D (Q = 2), Δf, Δα of frontal lobe GM classified neurologic controls, ALS-CST+ and ALS-CST- groups with 98% accuracy and > 95% in F1, recall, precision and specificity scores. Classification accuracy was only 74% when using whole brain MF measures and < 70% for other brain lobes. We demonstrate that MF analysis can distinguish UMN-predominant ALS subgroups based on GM changes, which the more commonly used quantitative approaches of CT and VBM cannot.

Investigation of microstructural, micromorphology, and surface plasmon resonance characteristics in Ni/Al, Ni/Cu, and Ni/SS thin films.

As the first boundary between the environment and the material, the surface plays an important role in their interaction with each other, therefore, the use of appropriate tools and analysis to examine the mechanical properties and morphology of surfaces has particular importance in industry and research. In this research, a thin film of nickel was deposited on metal substrates made of aluminum, copper, and steel by using the RF magnetic cathode. Then, using a non-contact atomic force microscope, the morphological properties of the nickel film with static parameters, Minkowski functionals (MF's), fractal, and multifractal were extracted to be analyzed and studied. After that, using parameters such as root mean square (RMS) roughness, skewness, and kurtosis, it was determined how the surface roughness, distribution, and probability density of particles on the film surface alters with the change of the substrate. Next, by examining and analyzing the Δα and Δf parameters obtained from the multifractal section, the morphology of the produced film on the metal substrates was investigated. Then, the change in the surface plasmon resonance (SPR) peak position is changed for the prepared film in the range of the absorption spectrum due to the substrate effect and the microstructural properties of the formed film. HIGHLIGHTS: Ni film has been deposited by Rf magnetron sputtering. The effect of metal substrates on the topography, fractality, and optical properties was studied. Minkowski functionals were used to investigate the surface morphology of the samples. Substrate's material and the topography of the formed film can changed the surface plasmon resonance position.

Multifractal Analysis of Choroidal SDOCT Images in the Detection of Retinitis Pigmentosa.

The aim of this paper is to investigate whether a multifractal analysis can be applied to study choroidal blood vessels and help ophthalmologists in the early diagnosis of retinitis pigmentosa (RP). In a case study, we used spectral domain optical coherence tomography (SDOCT), which is a noninvasive and highly sensitive imaging technique of the retina and choroid. The image of a choroidal branching pattern can be regarded as a multifractal. Therefore, we calculated the generalized Renyi point-centered dimensions, which are considered a measure of the inhomogeneity of data, to prove that it increases in patients with RP as compared to those in the control group.

A Holographic-Type Model in the Description of Polymer-Drug Delivery Processes.

A unitary model of drug release dynamics is proposed, assuming that the polymer-drug system can be assimilated into a multifractal mathematical object. Then, we made a description of drug release dynamics that implies, via Scale Relativity Theory, the functionality of continuous and undifferentiable curves (fractal or multifractal curves), possibly leading to holographic-like behaviors. At such a conjuncture, the Schrödinger and Madelung multifractal scenarios become compatible: in the Schrödinger multifractal scenario, various modes of drug release can be "mimicked" (via period doubling, damped oscillations, modulated and "chaotic" regimes), while the Madelung multifractal scenario involves multifractal diffusion laws (Fickian and non-Fickian diffusions). In conclusion, we propose a unitary model for describing release dynamics in polymer-drug systems. In the model proposed, the polymer-drug dynamics can be described by employing the Scale Relativity Theory in the monofractal case or also in the multifractal one.

Retina images classification based on 2D empirical mode decomposition and multifractal analysis.

Diabetic retinopathy is an ocular disease caused by long-term damage to the retina due to high blood sugar levels. Elevated blood sugar can impair the microvasculature in the retina, leading to vascular abnormalities and the formation of abnormal new blood vessels. These changes can manifest in the retina as hemorrhages, leaks, vessel dilation, retinal edema, and retinal detachment. The retinas of individuals with diabetes exhibit different morphologies compared to those without the condition. Most histological images cannot be accurately described using traditional geometric shapes or methods. Therefore, this study aims to evaluate and classify the morphology of retinas with varying degrees of severity using multifractal geometry. In the initial experiments, two-dimensional empirical mode decomposition was employed to extract high-frequency detailed features, and the classification process was based on the most relevant features in the multifractal spectrum associated with disease factors. To eliminate less significant features, the random forest algorithm was utilized. The proposed method achieved an accuracy of 96%, sensitivity of 96%, and specificity of 95%.

Dynamic multifractal characteristics of acoustic emission about composite samples with different stress loading and unloading conditions.

Studying the failure characteristics of the common composite strata structure in western China is essential for evaluating stope stability and predicting coal mine dynamic disasters. To investigate the influence of different stress loading and unloading conditions on the instability characteristics of composite samples, three triaxial loading and unloading test schemes simulating different in-situ mining depths were designed. Complex triaxial tests were conducted on 12 sets of composite samples, and the bearing capacity, acoustic emission (AE) parameters and dynamic multifractal characteristics of the samples under different stress loading or unloading conditions were analyzed. The results indicate that samples tested by stress schemes simulating greater mining depths exhibit less damage, and the failure mode is a tensile-shear mixed failure, but the tensile failure is the main failure mode. The multifractal spectral parameters Δ α of AE time series during the failure of composite samples tested with triaxial loading and unloading schemes simulating different mining depths show a decreasing trend in Δ α values with increasing mining depth, while the change rules of Δ f α values are the opposite. The multifractal parameter changes degree in four-layer rock structure composite samples under different stress conditions are lower than those in three-layer rock structure composite samples, indicating that the microcrack propagation process in the three-layer composite sample is more complex, resulting in higher levels of damage. The dynamic change of multifractal parameters Δ α and Δ f α during different stress loading and unloading stages reflects the influence of axial pressure or confining pressure changes on crack propagation in composite samples. Compared to the initial stress stage, the non-uniformity of AE signals increases in the residual stress stage, and the proportion of large signals becomes more prominent, signifying a complex micro-fracture process in the composite samples.

Multifractal Analysis in Neuroimaging.

The characteristics of biomedical signals are not captured by conventional measures like the average amplitude of the signal. The methodologies derived from fractal geometry have been a very useful approach to study the degree of irregularity of a signal. The monofractal analysis of a signal is defined by a single power-law exponent in assuming a scale invariance in time and space. However, temporal and spatial variation in the scale-invariant structure of the biomedical signal often appears. In this case, multifractal analysis is well-suited because it is defined by a multifractal spectrum of power-law exponents. There are several approaches to the implementation of this analysis, and there are numerous ways to present these.In this chapter, we review the use of multifractal analysis for the purpose of characterizing signals in neuroimaging. After describing the tenets of multifractal analysis, we present several approaches to estimating the multifractal spectrum. Finally, we describe the applications of this spectrum on biomedical signals in the characterization of several diseases in neurosciences.

Box-Counting Fractal Analysis: A Primer for the Clinician.

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Multifractal Analysis of Brain Tumor Interface in Glioblastoma.

The dynamics of tumor growth is a very complex process, generally accompanied by numerous chromosomal aberrations that determine its genetic and dynamical heterogeneity. Consequently, the tumor interface exhibits a non-regular and heterogeneous behavior often described by a single fractal dimension. A more suitable approach is to consider the tumor interface as a multifractal object that can be described by a set of generalized fractal dimensions. In the present work, detrended fluctuation and multifractal analysis are used to characterize the complexity of glioblastoma.