Multifractal Detrended Fluctuation Analysis Research Articles

Multifractal Properties of Human Chromosome Sequences

The intricacy and fractal properties of human DNA sequences are examined in this work. The core of this study is to discern whether complete DNA sequences present distinct complexity and fractal attributes compared with sequences containing exclusively exon regions. In this regard, the entire base pair sequences of DNA are extracted from the NCBI (National Center for Biotechnology Information) database. In order to create a time series representation for the base pair sequence {G,C,T,A}, we use the Chaos Game Representation (CGR) approach and a mapping rule f, which enables us to apply the metric known as the Complexity–Entropy Plane (CEP) and multifractal detrended fluctuation analysis (MF-DFA). To carry out our investigation, we divided human DNA into two groups: the first is composed of the 24 chromosomes, which comprises all the base pairs that form the DNA sequence, and another group that also includes the 24 chromosomes, but the DNA sequences rely only on the exons’ presence. The results show that both sets provide fractal patterns in their structure, as obtained by the CGR approach. Complete DNA sequences show a sharper visual fractal pattern than sequences composed only of exons. Moreover, the sequences occupy distinct areas of the complexity–entropy plane, and the complete DNA sequences lead to greater statistical complexity and lower entropy than the exon sequences. Also, we observed that different fractal parameters between chromosomes indicate diversity in genomic sequences. All these results occur in different scales for all chromosomes.

The Multifractal Phenomenon of Stock Price Caused by “Tesla Rights Defense Event”

In this paper, we explore the periodicity of the multifractal phenomenon of stock price caused by public relations events using the multifractal detrended fluctuation analysis (MF-DFA) method. The Tesla stock closing price in the context of the Tesla rights defense event is used to obtain the generalized Hurst exponent and multifractal spectrum. We find that the stock price exhibits multifractal characteristics. Afterwards, we conduct a multifractal time-varying analysis using high-frequency data for 12 time periods before and after the Tesla rights defense event, which happened on 19 April 2021. We calculate the [Formula: see text] and [Formula: see text] before and after the rights defense event to measure the degree of multifractal of Tesla stock price. In addition, we also compute the difference between the two [Formula: see text] and two [Formula: see text], which are regarded as [Formula: see text] and [Formula: see text]. The results show that the Tesla stock market efficiency degree raised as the period time increases until the eighth period. And after the eighth period, both [Formula: see text] and [Formula: see text] tend to be stable, and the degree of market efficiency caused by the Tesla rights defense event remains almost unchanged. In addition, we use three broad market indices in the context of the Russia–Ukraine conflict to test the universality. The three broad market indices are Dow Jones Industrial Average (DJIA), Shanghai Stock Exchange Composite Index (SSEC) and Nikkei 225 ETF (N225). The results demonstrate that with the extending of time period, [Formula: see text] and [Formula: see text] gradually stabilize, indicating that public memorability will diminish and the market efficiency almost remains unchanged.

Multifractal analysis of maize and soybean DNA

This paper investigates the complexity of DNA sequences in maize and soybean using the multifractal detrended fluctuation analysis (MF-DFA) method, chaos game representation (CGR), and the complexity-entropy plane approach. The study aims to understand the patterns and structures of these DNA sequences, which can provide insights into their genetic makeup and improve crop yield and quality. The results show that maize and soybean DNA sequences exhibit fractal properties, indicating a complex and self-organizing structure. We observe the persistence trend between sequences of base pairs, which indicates long-range correlations between base pairs. We also identified the stochastic nature of the DNA sequences of both species.

Detection of Gate Valve Leaks through the Analysis Fractal Characteristics of Acoustic Signal

This paper considers the possibility of using monofractal and multifractal analysis of acoustic signals to detect water leaks through gate valves. Detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MF-DFA) were used. Experimental studies were conducted on a ½-inch nominal diameter wedge valve, which was fitted to a ¾-inch nominal diameter steel pipeline. The water leak was simulated by opening the valve. The resulting leakage rates for different valve opening conditions were 5.3, 10.5, 14, 16.8, and 20 L per minute (L/min). The Hurst exponent for acoustic signals in a hermetically sealed valve is at the same level as a deterministic signal, while the width of the multifractal spectrum closely matches that of a monofractal process. When a leak occurs, turbulent flow pulsations appear, and with small leak sizes, the acoustic signals become anticorrelated with a high degree of multifractality. As the leakage increases, the Hurst exponent also increases and the width of the multifractal spectrum decreases. The main contributor to the multifractal structure of leak signals is small, noise-like fluctuations. The analysis of acoustic signals using the DFA and MF-DFA methods enables determining the extent of water leakage through a non-sealed gate valve. The results of the experimental studies are in agreement with the numerical simulations. Using the Ansys Fluent software (v. 19.2), the frequencies of flow vortices at different positions of gate valve were calculated. The k-ω SST turbulence model was employed for calculations. The calculations were conducted in a transient formulation of the problem. It was found that as the leakage decreases, the areas with a higher turbulence eddy frequency increase. An increase in the frequency of turbulent fluctuations leads to enhanced energy dissipation. Some of the energy from ordered processes is converted into the energy of disordered processes.

Stock Market Efficiency of the BRICS Countries Pre-, During, and Post Covid-19 Pandemic: A Multifractal Detrended Fluctuation Analysis

Stock Market Efficiency of the BRICS Countries Pre-, During, and Post Covid-19 Pandemic: A Multifractal Detrended Fluctuation Analysis

Multifractal Detrended Fluctuation Analysis on the Fracture Surface of Polycarbonate and Acrylonitrile-butadiene-styrene Alloy

Multifractal detrended fluctuation analysis (MF-DFA) has been carried out to evaluate the multifractal properties of the fracture morphology for Polycarbonate (PC) and Acrylonitrile-butadiene-styrene (ABS) alloy, and the relationship between the long-range correlation parameter of the samples fracture - Hurst exponent and fractal dimension was explored and analyzed. The results suggest that the existence of multifractal properties within the micrometer scale domain we investigated for the fracture surface of PC/ABS alloy samples. The Hurst exponent and fractal dimension can both be used to measure and characterize the fracture surface morphology of the PC/ABS alloys. As the content of compatibilizer PP-g-MAH increased, the tensile strength of PC/ABS alloy decreased, the fracture surface peaks tend to dominate, the Hurst exponent increased, the fractal dimension decreased, and its strength retention rate increases, displaying persistence.

Multifractal fluctuations in zebrafish (Danio rerio) polarization time series.

In this work, we study the polarization time series obtained from experimental observation of a group of zebrafish (Danio rerio) confined in a circular tank. The complex dynamics of the individual trajectory evolution lead to the appearance of multiple characteristic scales. Employing the Multifractal Detrended Fluctuation Analysis (MF-DFA), we found distinct behaviors according to the parameters used. The polarization time series are multifractal at low fish densities and their average scales with . On the other hand, they tend to be monofractal, and their average scales with for high fish densities. These two regimes overlap at critical density , suggesting the existence of a phase transition separating them. We also observed that for low densities, the polarization velocity shows a non-Gaussian behavior with heavy tails associated with long-range correlation and becomes Gaussian for high densities, presenting an uncorrelated regime.

Multifractal detrended fluctuation analysis approach to the monthly total ozone concentration over New Delhi, India

Multifractal detrended fluctuation analysis approach to the monthly total ozone concentration over New Delhi, India

Unravelling the Fractal Complexity of Temperature Datasets across Indian Mainland

Studying atmospheric temperature characteristics is crucial under climate change, as it helps us to understand the changing patterns in temperature that have significant implications for the environment, ecosystems, and human well-being. This study presents the comprehensive analysis of the spatiotemporal variability of scaling behavior of daily temperature series across the whole Indian mainland, using a Multifractal Detrended Fluctuation Analysis (MFDFA). The analysis considered 1° × 1° datasets of maximum temperature (Tmax), minimum temperature (Tmin), mean temperature (Tmean), and diurnal temperature range (DTR) (TDTR = Tmax − Tmin) from 1951 to 2016 to compare their scaling behavior for the first time. Our results indicate that the Tmin series exhibits the highest persistence (with the Hurst exponent ranging from 0.849 to unity, and a mean of 0.971), and all four-temperature series display long-term persistence and multifractal characteristics. The variability of the multifractal characteristics is less significant in North–Central India, while it is highest along the western coast of India. Moreover, the assessment of multifractal characteristics of different temperature series during the pre- and post-1976–1977 period of the Pacific climate shift reveals a notable decrease in multifractal strength and persistence in the post-1976–1977 series across all regions. Moreover, for the detection of climate change and its dominant driver, we propose a new rolling window multifractal (RWM) framework by evaluating the temporal evolution of the spectral exponents and the Hurst exponent. This study successfully captured the regime shifts during the periods of 1976–1977 and 1997–1998. Interestingly, the earlier climatic shift primarily mitigated the persistence of the Tmax series, whereas the latter shift significantly influenced the persistence of the Tmean series in the majority of temperature-homogeneous regions in India.

A novel approach for cardiac pathology detection using phonocardiogram signal multifractal detrended fluctuation analysis and support vector machine classification

A novel approach for cardiac pathology detection using phonocardiogram signal multifractal detrended fluctuation analysis and support vector machine classification

Multifractal analysis of Chinese literary and web novels

Multifractal analysis of literary works, utilizing measures such as sentence length and word length as time series, have revealed the prevalence of multifractal structures within these works. After constructing a corpus of 712 Chinese novels, we performed multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrending moving average analysis (MF-DMA) on them. Both method revealed that non-monotonic generalized Hurst exponential curves and distorted spectral functions appeared in about half of the web novels, but were rarely found in literary novels. By conducting a meticulous examination of sentence length sequences and adjustment of the time series range covered by the computation, it becomes apparent that this irregular Hurst exponent curve stems from the uneven distribution of long sentences within the work. This uneven distribution mirrors the instability present in the author’s creative style, which is intimately linked to the characteristics of the publishing mechanisms for web novels.

Characterizing the Solar Cycle Variability Using Nonlinear Time Series Analysis at Different Amounts of Dynamo Supercriticality: Solar Dynamo is Not Highly Supercritical

The solar dynamo is essentially a cyclic process in which the toroidal component of the magnetic field is converted into the poloidal one and vice versa. This cyclic loop is disturbed by some nonlinear and stochastic processes mainly operating in the toroidal to poloidal part. Hence, the memory of the polar field decreases in every cycle. On the other hand, the dynamo efficiency and, thus, the supercriticality of the dynamo decreases with the Sun’s age. Previous studies have shown that the memory of the polar magnetic field decreases with the increase of supercriticality of the dynamo. In this study, we employ popular techniques of time series analysis, namely, compute Higuchi’s fractal dimension, Hurst exponent, and Multi-Fractal Detrended Fluctuation Analysis to the amplitude of the solar magnetic cycle obtained from dynamo models operating at near-critical and supercritical regimes. We show that the magnetic field in the near-critical regime is governed by strong memory, less stochasticity, intermittency, and breakdown of self-similarity. On the contrary, the magnetic field in the supercritical region has less memory, strong stochasticity, and shows a good amount of self-similarity. Finally, applying the same time series analysis techniques in the reconstructed sunspot data of 85 cycles and comparing their results with that from models, we conclude that the solar dynamo is possibly operating near the critical regime and not too much supercritical regime. Thus the Sun may not be too far from the critical dynamo transition.

The effect analysis of shape design of different charging piles based on Human physiological characteristics using the MF-DFA

With the rapid development of new energy vehicles, the users have an increasing demand for charging piles. It is generally believed that the charging pile is a kind of practical product, and it only needs to realize the charging function. However, as a product, the shape design of the charging pile will directly affect the user experience, thus affecting product sales. Therefore, in the face of increasingly fierce market competition, when designing the shape of charging piles, it is necessary to adopt the traditional evaluation method and human physiological cognitive characteristics to evaluate the shape of charging piles more objectively. From the user’s point of view, using the electroencephalogram (EEG) of the user, with the help of the multifractal detrended fluctuation analysis (MF-DFA) method, this paper comprehensively analyzes the differences in emotional cognitive characteristics between two kinds of charging piles, namely, the charging pile with a curved appearance design and the charging pile with square appearance design. The results show that there are significant differences in human physiological cognitive characteristics between two kinds of charging piles with different shapes. And different shapes of charging piles have different physiological cognitive differences for users. When designing charging pile product shapes, human beings can objectively evaluate the product shape design according to the physiological cognition differences of users, so as to optimize the charging pile product shape design.

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

In this paper, the possibility of using monofractal and multifractal analysis of acoustic signals of pipelines to detect leaks is considered. An experimental stand has been created to study the fractal characteristics of acoustic signals of pipelines with “slit” type defects. During the experiments, defects of the “slit” type pipeline with dimensions of 2 mm, 8 mm, and 20 mm were modeled. Detrended fluctuation analysis (DFA) and the multifractal detrended fluctuation analysis (MF-DFA) were used. As a result of the experimental studies, it was found that the occurrence of leakage leads to the occurrence of anticorrelated vibrations in a pipeline with multifractal properties. The analyses of acoustic signals by DFA and MF-DFA methods make it possible to reliably determine the leakage. The Hurst exponent and the width of the multifractal spectrum can serve as indicators of the occurrence of leaks in pipelines.

Insights into the dynamics of market efficiency spillover of financial assets in different equity markets

This paper provides multidisciplinary insights into the dynamics of market efficiency spillover of financial assets, considering Bitcoin, DXY (U.S. Dollar Index), S&P 500, and crude oil in different equity markets. Given this, we employ the multifractal detrended fluctuation analysis (MF-DFA) and the time-varying parameter vector autoregressive models (TVP-VAR) to illuminate these complex interplays between these assets and other equity markets. Our findings display that Bitcoin acts as a net transmitter, whereas DXY functions as a net receiver. Additionally, Bitcoin, DXY, and S&P 500 clearly exhibit dynamics in information transmission, whereas crude oil does not. It means that the low connectedness of the oil market in terms of market efficiency spillover, suggesting that the oil market may play an effective role as a hedging instrument for other assets.

Segmented Multifractal Detrended Fluctuation Analysis in Key Economic Sectors

This paper introduces an innovative method for segmented multifractal analysis, aimed at investigating the (in-) efficiency of major global economic sectors. The proposed approach, a modified version of the Multifractal Detrended Fluctuation Analysis (MF-DFA) technique, integrates change-point detection, followed by a segmentation of time series data, just before conducting multifractal measurements at various intervals. This novel method is applied to five indices representing the global financial and economic landscape, including the Standard and Poor 500 index, the Euro/USD exchange rate, Bitcoin’s price, crude oil prices, and the price of gold. The empirical findings reveal substantial structured multifractality, with particular prominence observed in the two commodity price indicators. These results prompt inquiries into the influence of significant events on the efficiency of economic and financial markets. The segmented multifractal analysis opens up new avenues for exploring the dynamics and resilience of these sectors, thereby enhancing our comprehension of their intricate behaviors and responses to diverse stimuli.

Multifractal detrended fluctuation analysis of boiling water reactors

The aim of this work is to determine a relationship between multifractal parameters and Boiling Water Reactor (BWR) stability; therefore, a Multifractal Detrended Fluctuation Analysis (MF-DFA) of the data series obtained from the Average Power Range Monitor (APRM) and the Local Power Range Monitors (LPRM) during stable operation and during an instability event of a BWR-5, which concludes with the SCRAM, was performed. First, a much larger number of data than recommended was considered to calculate the multifractality for the instability event (4,200 data points) and for stable operation (5,700 data points) and determine if there was any difference among these analyses. Subsequently, the data were divided into periods of 50 s (500 data points) to detect the moment when the reactor begins to operate in an unstable manner, here it was not necessary to have enough information to calculate the multifractal parameters because it was only of interest to detect any trend or difference between the multifractal parameters that indicated instability in the operation. The results show that the data from the stable operation present a behavior with higher multifractality compared to the data from the unstable operation. In fact, the results indicate that the data from the unstable operation of the reactor tend to monofractality. This can be seen more clearly through the width of the multifractal spectrum, it is larger for the data corresponding to the stable operation. The proposed methodology was successfully applied to a challenging case study (Forsmark stability benchmark) as it is difficult to detect unstable reactor operation.

Multifractal characterization and recognition of animal behavior based on deep wavelet transform

The study conduct an in-depth exploration of the multifractal characteristics of dairy cows behavioral data, aiming to reveal their complexity and representation in behavioral patterns. By means of Multifractal Detrended Fluctuation Analysis (MFDFA) in conjunction with deep wavelet transform, we extract multifractal indices that precisely depict the differences and dynamic changes of cows behavior. Further, we delves into the potential correlations between these multifractal features and the physiological states of dairy cattle, particularly focusing on their potential applications in predicting different physiological conditions. And an assessment model is developed based on these fractal indices and utilize advanced machine learning techniques to evaluate their effectiveness and accuracy in predicting the physiological states of dairy cattle. This study not only unveils the multifractal properties of cattle behavior but also demonstrates how these features can be utilized to predict significant physiological states, providing new scientific bases and methods for dairy cattle health management.

Multifractal and chaotic characteristics of geomagnetic inter-storm interval over eight solar cycles

The structure and characteristics of geomagnetic inter-storm intervals, the sequence of time differences between two successive storm events, can provide information about the origin and drivers of the storms compared to analyzing the entire data set. In this study, the inter-storm event was investigated using the Kp index over 8 solar cycles (17–24). Three nonlinear approaches were considered: burstiness, multifractal detrended fluctuation analysis, and chaos analysis. The burstiness analysis reveals that the inter-storm intervals are heterogeneous events with irregular time intervals. The multifractal strength of inter-storm intervals ranges from 0.23 to 0.65 for each of the solar cycles, compared to 0.38 for the entire period. Long-range correlations largely drove the multifractality across most solar cycles. Chaos analysis confirmed the low predictability of inter-storm intervals across each solar cycle. The results will be relevant to the prediction and understanding of drivers of storm events across different solar cycles.

Segmented multifractal detrended fluctuation analysis for assessing inefficiency in North African stock markets

This study employs segmented multifractal analysis to evaluate the efficiency of key financial markets in North Africa. The proposed method, an adapted version of Multifractal Detrended Fluctuation Analysis (MF-DFA), integrates a wavelet-based change-point detection to identify and separate the two most dynamically changing phases. Subsequent multifractal measurements are then conducted for each of these identified intervals. Focusing on three equity indices—the Egyptian Exchange Index (EGX30), Moroccan All Shares Index (MASI), and Tunisian Stock Index (Tunindex)–that collectively represent the North African financial and economic landscape, empirical results reveal significant asymmetric multifractality, especially notable in the two Maghreban indices. These findings prompt inquiries into the influence of major events on financial market efficiency. Segmented multifractal analysis introduces a novel approach to explore the dynamics and resilience of these sectors, contributing to a more profound understanding of their complex behaviors and responses to various stimuli.