Multifractal Characteristics Research Articles

Universal Markers Unveil Metastatic Cancerous Cross-Sections at Nanoscale.

Simple SummaryWe propose the use of two universal morphometric indices whose synergetic potency leads to the classification of a cancerous tissue of a few nanometers in size as metastatic or non-metastatic. The method is label-free, operates on conventional histological cross-sections, recording surface height–height roughness by AFM, and detects nanoscale changes associated with the progress of carcinogenesis which are the output of combined statistical approaches, namely multifractal analysis and the generalized moments method. The benefit of this approach is at least two-fold. On the one hand, its application in the context of early diagnosis can increase the life expectancy of patients, and on the other hand, differentiation between metastatic and non-metastatic tissues at the singular cell level can lead to new methodologies to treat cancer biology and therapies.The characterization of cancer histological sections as metastatic, M, or not-metastatic, NM, at the cellular size level is important for early diagnosis and treatment. We present timely warning markers of metastasis, not identified by existing protocols and used methods. Digitized atomic force microscopy images of human histological cross-sections of M and NM colorectal cancer cells were analyzed by multifractal detrended fluctuation analysis and the generalized moments method analysis. Findings emphasize the multifractal character of all samples and accentuate room for the differentiation of M from NM cross-sections. Two universal markers emphatically achieve this goal performing very well: (a) the ratio of the singularity parameters (left/right), which are defined relative to weak/strong fluctuations in the multifractal spectrum, is always greater than 0.8 for NM tissues; and (b) the index of multifractality, used to classify universal multifractals, points to log-normal distribution for NM and to log-Cauchy for M tissues. An immediate large-scale screening of cancerous sections is doable based on these findings.

Multifractal Characterization and Modeling of Blood Pressure Signals

In this paper, a multi-fractal analysis on a diastolic blood pressure signal is conducted. The signal is measured in a time span of circa one day through the multifractal detrended fluctuation analysis framework. The analysis is performed on asymptotic timescales where complex regulating mechanisms play a fundamental role in the blood pressure stability. Given a suitable frequency range and after removing non-stationarities, the blood pressure signal shows interesting scaling properties and a pronounced multifractality imputed to long-range correlations. Finally, a binomial multiplicative model is investigated showing how the analyzed signal can be described by a concise multifractal model with only two parameters.

Insights into Pore Structures and Multifractal Characteristics of Shale Oil Reservoirs: A Case Study from Dongying Sag, Bohai Bay Basin, China

Insights into Pore Structures and Multifractal Characteristics of Shale Oil Reservoirs: A Case Study from Dongying Sag, Bohai Bay Basin, China

Multifractal Characteristics and Genetic Mechanisms of Pore Throat Structures in Coal Measure Tight Sandstone

Multifractal Characteristics and Genetic Mechanisms of Pore Throat Structures in Coal Measure Tight Sandstone

The correlation between external magnetic field and multifractal characteristics of PLD deposited DLC films

The present study explores the application of the multifractal method in examining the surface characteristics of the diamond-like carbon (DLC) thin films deposited onto substrates of silicon through a magnetically-assisted pulsed laser deposition (MAPLD) method at room temperature (RT). Multifractal spectra f(α), obtained from atomic force microscopy (AFM) analysis, is adopted to investigate the surface morphology of the produced samples. The relationship between the applied magnetic field and multifractal characteristics of the obtained samples is examined as well. The findings attest to the apparent effect of the magnetic field on the quality of surface morphology and the multifractal spectrum width. Our results reveal that the root-mean-square (RMS) and average surface roughness are enhanced by applying and intensifying the magnetic field. Furthermore, the findings suggest that both the non-uniformity of the height distributions and the singularity spectrum width of the samples fabricated in this study increases with applying and intensifying the magnetic field. Further, Multifractal spectra f(α) demonstrate the multifractality nature of all the obtained samples, including conventionally and magnetically processed DLC thin films. Besides, the multifractality strength of thin films rises with increasing the magnetic field.

Classification of Mammographic ROI for Microcalcification Detection Using Multifractal Approach

Microcalcifications (MCs) are the main signs of precancerous cells. The development of aided-system for their detection has become a challenge for researchers in this field. In this paper, we propose a system for MCs detection based on the multifractal approach that classifies mammographic ROIs into normal (healthy) or abnormal ROIs containing MCs. The proposed method is divided into four main steps: a mammogram pre-processing step based on breast selection, breast density reduction using haze removal algorithm and contrast enhancement using multifractal measures. The second step consists of extracting the normal and abnormal ROIs and calculating the multifractal spectrum of each ROI. The next step represents the extraction of the multifractal features from the multifractal spectrum and the GLCM characteristics of each ROI. The last step is the classification of ROIs where three classifiers are tested (KNN, DT, and SVM). The system is evaluated on images from the INbreast database (308 images) with a total of 2688 extracted ROIs (1344 normal, 1344 with MC) from different BI-RADS classes. In this study, the SVM classifier gave the best classification results with a sensitivity, specificity, and precision of 98.66%, 97.77%, and 98.20% respectively. These results are very satisfactory and remarkable compared to the literature.

Asymmetric Fractal Characteristics and Market Efficiency Analysis of Style Stock Indices.

As a typical complex system, the stock market has attracted the attention of scholars and investors to comprehensively understand its fractal characteristics and analyze its market efficiency. Firstly, this paper proposes an asymmetric, detrended fluctuation analysis based on overlapping sliding windows (OSW-A-MFDFA). It reduces the generation of fluctuation errors, and the calculation results are more robust and reliable. The advantage of the OSW-A-MFDFA is that it not only can reveal the multifractal characteristics of time series clearly, but also can further accurately analyze the asymmetry of fractal characteristics under different trends. Secondly, this paper focuses on the variation in the width difference and height difference of the multifractal spectrum under different trends. Finally, based on multifractality, this paper proposes a comprehensive indicator MED that can be used to measure market efficiency, which is characterized by traversing all fluctuation orders. The application revealed many interesting findings in style stock indices. Style stock indices have asymmetric multifractal characteristics, and there are significant differences in the fractal spectrum of different style assets. Moreover, the market efficiency of style stock indices is time-varying, which can be reasonably explained from the perspective of the adaptive market hypothesis.

The multifractal nature of dew point

Dew point temperature is a critical air moisture parameter, used widely in the study of climate. In this work, the main multifractal characteristics of dew point temperature are studied using the MF-DFA (Multifractal Detrended Fluctuation Analysis) method. The time series used are extracted from observational records (22 stations located in Greece) and from ECMWF reanalysis dataset. The multifractal spectrum is the basic tool of the study, since significant information about the multifractality can be derived. The results revealed the multifractal nature of all time series and that they exhibit long-range positive correlations. The multifractality of the time series stems mainly from long-range correlations of different fluctuation magnitudes. The spatial distributions of the main multifractal parameters showed their dependency on local topography, weather conditions and the land/sea distribution. Finally, the results from observational and reanalysis data are compared. The basic conclusions about the multifractal characteristics are virtually the same, regardless of whether the time series comes from observations or reanalysis data.

Research on Risk Features and Prediction of China’s Crude Oil Futures Market Based on Machine Learning

Facing the rapidly changing domestic and foreign futures markets, how to accurately and immediately predict the price trend of crude oil futures in order to avoid the risks caused by price fluctuations is very important for all participants in the crude oil futures market. Based on the 5-min high-frequency trading data of China’s crude oil futures market in recent 3 years, this paper uses the EMD-MFDFA model combined with multifractal detrended fluctuation analysis (MF-DFA) and empirical mode decomposition unsupervised K-means clustering and Gaussian mixture model (GMM) to identify the risk status of each trading day. Further, Support vector machine (SVM), extreme gradient lifting (XGBoost) and their improved algorithms are used to predict the risk state of China’s crude oil futures market. The empirical results are as follows: first, There are obvious multifractal features in the return rate series of China’s crude oil futures market and its single trading day; Second, compared with the traditional SVM model, the improved Twin Support Vector Machine (TWSVM) based on solving the sample imbalance issue has better prediction ability for China’s crude oil futures risk.; Third, The XGBoost has a great impact on the prediction of China’s crude oil risk, and the Focal-XGBoost with focal loss function performs the best in predicting the risk of China’s crude oil futures market.

Spatial Characteristics Analysis for Coupling Strength among Air Pollutants during a Severe Haze Period in Zhengzhou, China.

This paper investigates the multifractal characteristics of six air pollutants using the coupling detrended fluctuation analysis method. The results show that coupling correlations exist among the air pollutants and have multifractal characteristics. The sources of multifractality are identified using the chi square test. The coupling strengths between different pollutants are quantified. In addition, the coupling contribution of a series in the haze system is calculated, and SO2, as the main pollutant, plays a key role in the pollution system. Moreover, the Kriging interpolation method is used to analyze the spatial characteristic on coupling contribution of SO2. The spatial analysis of coupling strength for air pollutants will provide an effective approach for pollution control.

Multifractal Features of Particle-Size Distribution and Their Relationships With Soil Erosion Resistance Under Different Vegetation Types in Debris Flow Basin

Understanding the influence of vegetation types on soil particle-size distribution (PSD) is essential to evaluate the effects of sediment control by vegetation restoration. In this work, we studied the effects of different vegetation types, including bare land, meadow, shrub and forest on soil PSD in Jiangjiagou gully, Yunnan province, China. A total of 60 soil samples were collected and analyzed for soil particle size distribution using the laser diffraction method. Fractal theory was used to calculate multifractal parameters. The volume fraction of silt particles in shrub and forest is significantly higher than that in bare land, meadow, whereas the total volume fraction of sand particles in bare land and meadow exceed that in shrub and forest. The soil particle size distribution along soil layers has no significant difference in each vegetation type. The volumetric fractal dimension is significantly higher in forest and shrub than in bare land and grassland, but there is no significant difference between forest and shrub. In addition, soil erosion resistance exhibits significant differences of forest > shrub > grassland > bare land. Multifractal parameters are highest in bare land except for multifractal spectrum values (f (αmax) and f (αmin)) and the maximum value of singularity index (αmin). All generalized dimensions spectra curves of the PSD are sigmoidal, whereas the singular spectrum function shows an asymmetric upward convex curve. Furthermore, soil erosion resistance has significant relationships with multifractal parameters. Our results suggest that multifractal parameters of the soil PSD can predict its anti-ability to erosion. This study also provides an important insight for the evaluation of soil structure improvement and the effects of erosion control by vegetation restoration in dry-hot valley areas.

Crystallization of Ni50Ti50 metallic glass ribbon in the concept of multifractal formalism

ABSTRACT The NiTi metallic glass ribbon was subjected to 10-minute annealing at 400°C, 500°C and 600°C to detect changes in the surface relief and its statistical characteristics upon heating. Each annealing mode led to the ribbon crystallization with the formation of the Ni50Ti50 crystalline phases along with the transformation of the surface topography. Multifractal characteristics, such as the width of the singularity spectrum and fractal dimension, were calculated for the surface relief as a function of an annealing temperature. After the annealing at 500°C, along with the stepwise surface structure rearrangements, these parameters had extrema, including a local minimum of the width of the singularity spectrum, indicating a tendency towards monofractalization of the system. Abrupt changes in the parameters calculated by applying the multifractal formalism made it possible to detect the phase transition of the system in the form of its crystallization.

Multifractal properties of oil and gas indices in the Songnan Low Uplift of the Qiongdongnan Basin deepwater area

Recently, a high-quality reservoir was discovered in the Songnan Low Uplift in the eastern deepwater area of the Qiongdongnan Basin, northern South China Sea. To establish whether this area has good exploration prospects, this paper uses the multifractal moment method to analyse 2689 data points acquired from the basin in the SE of the southern low bulge. It is pointed out that the fractal behaviours of different types of geochemical indices are often distinguished by multifractal spectra of different shapes, therefore multifractal spectrum function analysis is used in this paper. These data were considered within the context of 13 oil and gas indices describing the multifractal spectrum function morphological characteristics. The results show that these indices can be divided into three types according to the multifractal spectrum. Indices with a strong multifractal spectrum function in the Songnan Low Uplift have the characteristics of a wide and continuous multifractal spectrum function, forming a right-skewed arc shape, while the other indices show weak or single-fractal characteristics. The results are in good agreement with principal component analysis results, where the spectral function of each principal component shows that the gas source of the C1, C2, C3, nC4, nC5, and heavy hydrocarbon indices in the Songnan Low Bulge has multifractal characteristics. The weight of these indices with strong multifractal characteristics shows that the principal components C1, C2 and C3, and heavy hydrocarbons, are important indices for delineating hydrocarbon prospects in the Songnan Low Uplift. Multifractal and spatial analysis techniques provide new ideas for index selection and comprehensive information extraction for oil and gas exploration. Thematic collection: This article is part of the Applications of Innovations in Geochemical Data Analysis collection available at: https://www.lyellcollection.org/cc/applications-of-innovations-in-geochemical-data-analysis

Does the “Delta Variant” affect the nonlinear dynamic characteristics of SARS-CoV-2 transmission?

In this paper, we analyzed the difference of nonlinear dynamic characteristics of SARS-CoV-2 transmission caused by ‘Delta Variant’. We selected the daily new diagnostic data of SARS-CoV-2 from 15 countries. Four different kinds of complexity metrics such as Kolmogorov complexity, Higuchi's Hurst exponent, Shannon entropy, and multifractal degrees were selected to explore the features of information content, persistence, randomness, multifractal complexity. Afterwards, Student's t-tests were performed to assess the presence of differences of these nonlinear dynamic characteristics for periods before and after “Delta Variant” appearance. The results of two-tailed Student's t-test showed that for all the nonlinear dynamic characteristics, the null hypothesis of equality of mean values were strongly rejected for the two periods. In addition, by one-tailed Student's t-test, we concluded that time series in “Delta period” exhibit higher value of Kolmogorov complexity and Shannon entropy, indicating a higher level of information content and randomness. On the other hand, the Higuchi's Hurst exponent in “Delta period” was lower, which showed the weaker persistent in this period. Moreover, the multifractal specturm width after “Delta” emergence were reduced, representing a more stable multifractality. The sources for the formation of multifractal features are also investigated.

Modification of multifractal analysis based on multiplicative cascade image

In this paper, we propose a two-dimensional multifractal detrended fluctuation norm (2D MF-DFN) method which is based on multifractal detrended fluctuation analysis (MF-DFA) with the norm constraints. The proposed 2D MF-DFN method is defined to adjust the internal structure of 2D MF-DFA by Lp-norm constraint on the basis of 2D MF-DFA, thus improving the performance. In addition, the multiplicative cascade method is used to construct the image, the 2D MF-DFN algorithm is used to analyze and test the constructed image, and the calculated multifractal features are compared with the results of 2D MF-DFA. The superiority of the proposed model is measured by the multifractal properties such as the generalized Hurst exponents H and mass exponent spectrums τ. We calculate the numerical solutions of the 2D MF-DFA and 2D MF-DFN of the image and compare them with the multifractal analytical solutions of the image. The results show that the numerical results of 2D MF-DFA can be optimized by controlling the norm constraint value so that the calculation results are more consistent with the real multifractal feature solution of the image. In addition, in the optimal norm selection test, we found that, when the numerical curve of 2D MF-DFA is below the analytical solution, the norm value needs to be increased so that the numerical curve can move up close to the analytical solution and vice versa. Through the test, we can obtain the appropriate norm value and construct the corresponding 2D MF-DFN model. The test results show that the performance of the proposed model is significantly better than that of 2D MF-DFA. Furthermore, we compare the performance of the two approaches when transforming the construction parameters of multiplicative cascade images. The numerical results show that 2D MF-DFN is more accurate. In addition, we apply the proposed method to the classification of medical images and the high classification accuracy demonstrates the robustness of the proposed method.

Correlation Analysis of Network Big Data and Film Time-Series Data Based on Machine Learning Algorithm

To expand the application of machine learning in movie data, in order to explore the correlation between network big data and film time-series data, based on the machine learning algorithm, the correlation and multifractal characteristics of happiness index (HI) and film box office (BO) were studied and described by introducing multifractal crossover method. On this basis, some indicators are introduced to optimize the neural network model so that the optimization model can describe and predict the box office and other related information well. The results show that the critical values of the happiness index and box office show a linear change trend with the increase of freedom, and the corresponding change curves of the happiness index and box office show obvious nonlinear characteristics, which can be divided into slow increase stage, steady increase stage, and approximately gentle stage. With the increase of iteration parameter q value, the change trend of the long-term and short-term curves of the generalized Hurst function is basically the same, and the difference between the two is getting smaller and smaller, while the difference between the two curves is getting bigger and bigger with the increase of q value of Renyi function. The changing trend of the dynamic Hurst index in the sliding window period all shows that it first rises rapidly to a certain value, then fluctuates rapidly with the increase of time, then drops rapidly to a constant value, and finally continues to show repeated small range fluctuation. Under the influence of time-series parameter α, the original sequence changes the most, the replacement sequence changes the medium, and the corresponding rearrangement sequence changes the least. The overall distribution of box office prediction data conforms to the characteristics of linear variation. The prediction index of the optimized HI-LSTM (Happiness Index-Long term short term memory neural network) model is higher in the box office, indicating that the model has better performance in describing and predicting the box office. This study can provide a theoretical basis for the correlation study of network big data and film data.

Pore Size Distributions and Multi-Fractal Characteristics of the Intact and Pulverized Coal in High Gas Mine

Pore Size Distributions and Multi-Fractal Characteristics of the Intact and Pulverized Coal in High Gas Mine

CONVERGENCE INVESTIGATION OF MULTIFRACTAL ANALYSIS BASED ON Lp-NORM CONSTRAINT

In this paper, we propose the multifractal detrending fluctuation analysis based on [Formula: see text]-norm constrain (MF-DFN). We assess the performance of the proposed algorithm by constructing a [Formula: see text]-model based multiplicative cascades time series. We calculate the generalized [Formula: see text] exponent [Formula: see text], [Formula: see text] exponent [Formula: see text], singularity exponent [Formula: see text] and multifractal spectrum [Formula: see text] for multifractal detrended fluctuation analysis (MF-DFA) and MF-DFN, respectively. We notice that under different norm constraints, the distribution of multifractal characteristics is quite different. Appropriate norm constraints can make the multifractal characteristics of time series described more accurately. Based on the analytical solution curve, the distribution of different multifractal numerical curves determines the correct selection of norm constraint value. In this study, using a combination of norms [Formula: see text] and [Formula: see text], the depicted numerical curves almost overlap the theoretical curve, which shows that the proposed MF-DFN is superior to MF-DFA. To eliminate the influence of specific time series, we reset parameters [Formula: see text] and [Formula: see text] in [Formula: see text]-model. Various experimental results also show the effectiveness of the proposed MF-DFN. In addition, we also verify the efficiency of the proposed MF-DFN by using the practical application. The experimental results show that our proposed method plays a significant role in ECG classification.

Exploring the dynamic nonlinear relationship between crude oil price and implied volatility indices: A new perspective from MMV-MFDFA

This paper investigates the cross-correlations between the crude oil market and three implied volatility indices for the crude oil market, the stock markets in emerging and developed economies. We employed a newly developed method—the multiscale multivariate multifractal detrended fluctuation analysis (MMV-MFDFA) within the framework of the fractal market hypothesis (FMH). The research target here is to detect the fractal autocorrelation characteristics for the time series covered in this study. The empirical results demonstrate that cross-correlated behaviors have multifractal features. The cross-correlated behaviors of smaller fluctuations are persistent while large fluctuations are anti-persistent between crude oil and OVX. The cross-correlated behaviors between crude oil and implied indices of the developed and emerging markets are anti-persistent both small and large fluctuations. Crude oil price fluctuations and the implied volatility indices change in a positive direction in the short term, but in the reverse direction in the long term. In addition, the multifractal strength between crude oil and implied volatility index for crude oil market is larger than that between crude oil and emerging and developed stock markets. Political, economic, and military shocks, with relatively large influence have a major impact on the internal volatility of the system. The findings of nonlinear and multifractal correlations between crude oil and implied volatility indices suggest that, due to existing of market inefficiency and multifractality,​ investors can, to some extent, predict the future trends of crude oil price movements based on changes in the volatility indices, thereby adjusting their investment strategies to avoid risks.

NONLINEAR ANALYSIS AND PREDICTION OF BITCOIN RETURN’S VOLATILITY

This paper mainly studies the market nonlinearity and the prediction model based on the intrinsic generation mechanism (chaos) of Bitcoin’s daily return’s volatility from June 27, 2013 to November 7, 2019 with an econophysics perspective, so as to avoid the forecasting model misspecification. Firstly, this paper studies the multifractal and chaotic nonlinear characteristics of Bitcoin volatility by using multifractal detrended fluctuation analysis (MFDFA) and largest Lyapunov exponent (LLE) methods. Then, from the perspective of nonlinearity, the measured values of multifractal and chaos show that the volatility of Bitcoin has short-term predictability. The study of chaos and multifractal dynamics in nonlinear systems is very important in terms of their predictability. The chaos signals may have short-term predictability, while multifractals and self-similarity can increase the likelihood of accurately predicting future sequences of these signals. Finally, we constructed a number of chaotic artificial neural network models to forecast the Bitcoin return’s volatility avoiding the model misspecification. The results show that chaotic artificial neural network models have good prediction effect by comparing these models with the existing Artificial Neural Network (ANN) models. This is because the chaotic artificial neural network models can extract hidden patterns and accurately model time series from potential signals, while the benchmark ANN models are based on Gaussian kernel local approximation of non-stationary signals, so they cannot approach the global model with chaotic characteristics. At the same time, the multifractal parameters are further mined to obtain more market information to guide financial practice. These above findings matter for investors (especially for investors in quantitative trading) as well as effective supervision of financial institutions by government.