Long-range fluctuations and multifractality in connectivity density time series of a wind speed monitoring network

NASA Astrophysics Data System (ADS)

Laib, Mohamed; Telesca, Luciano; Kanevski, Mikhail

2018-03-01

This paper studies the daily connectivity time series of a wind speed-monitoring network using multifractal detrended fluctuation analysis. It investigates the long-range fluctuation and multifractality in the residuals of the connectivity time series. Our findings reveal that the daily connectivity of the correlation-based network is persistent for any correlation threshold. Further, the multifractality degree is higher for larger absolute values of the correlation threshold.

Using multifractal analysis of ultra-weak photon emission from germinating wheat seedlings to differentiate between two grades of intoxication with potassium dichromate

NASA Astrophysics Data System (ADS)

Scholkmann, Felix; Cifra, Michal; Alexandre Moraes, Thiago; de Mello Gallep, Cristiano

2011-12-01

The aim of the present study was to test whether the multifractal properties of ultra-weak photon emission (UPE) from germinating wheat seedlings (Triticum aestivum) change when the seedlings are treated with different concentrations of the toxin potassium dichromate (PD). To this end, UPE was measured (50 seedlings in one Petri dish, duration: approx. 16.6- 28 h) from samples of three groups: (i) control (group C, N = 9), (ii) treated with 25 ppm of PD (group G25, N = 32), and (iii) treated with 150 ppm of PD (group G150, N = 23). For the multifractal analysis, the following steps where performed: (i) each UPE time series was trimmed to a final length of 1000 min; (ii) each UPE time series was filtered, linear detrended and normalized; (iii) the multifractal spectrum (f(α)) was calculated for every UPE time series using the backward multifractal detrended moving average (MFDMA) method; (iv) each multifractal spectrum was characterized by calculating the mode (αmode) of the spectrum and the degree of multifractality (Δα) (v) for every UPE time series its mean, skewness and kurtosis were also calculated; finally (vi) all obtained parameters where analyzed to determine their ability to differentiate between the three groups. This was based on Fisher's discriminant ratio (FDR), which was calculated for each parameter combination. Additionally, a non-parametric test was used to test whether the parameter values are significantly different or not. The analysis showed that when comparing all the three groups, FDR had the highest values for the multifractal parameters (αmode, Δα). Furthermore, the differences in these parameters between the groups were statistically significant (p < 0.05). The classical parameters (mean, skewness and kurtosis) had lower FDR values than the multifractal parameters in all cases and showed no significant difference between the groups (except for the skewness between group C and G150). In conclusion, multifractal analysis enables changes in UPE time series to be detected even when they are hidden for normal linear signal analysis methods. The analysis of changes in the multifractal properties might be a basis to design a classification system enabling the intoxication of cell cultures to be quantified based on UPE measurements.

Multifractal analysis of mobile social networks

NASA Astrophysics Data System (ADS)

Zheng, Wei; Zhang, Zifeng; Deng, Yufan

2017-09-01

As Wireless Fidelity (Wi-Fi)-enabled handheld devices have been widely used, the mobile social networks (MSNs) has been attracting extensive attention. Fractal approaches have also been widely applied to characterierize natural networks as useful tools to depict their spatial distribution and scaling properties. Moreover, when the complexity of the spatial distribution of MSNs cannot be properly charaterized by single fractal dimension, multifractal analysis is required. For further research, we introduced a multifractal analysis method based on box-covering algorithm to describe the structure of MSNs. Using this method, we find that the networks are multifractal at different time interval. The simulation results demonstrate that the proposed method is efficient for analyzing the multifractal characteristic of MSNs, which provides a distribution of singularities adequately describing both the heterogeneity of fractal patterns and the statistics of measurements across spatial scales in MSNs.

Efficiency and multifractality analysis of CSI 300 based on multifractal detrending moving average algorithm

NASA Astrophysics Data System (ADS)

Zhou, Weijie; Dang, Yaoguo; Gu, Rongbao

2013-03-01

We apply the multifractal detrending moving average (MFDMA) to investigate and compare the efficiency and multifractality of 5-min high-frequency China Securities Index 300 (CSI 300). The results show that the CSI 300 market becomes closer to weak-form efficiency after the introduction of CSI 300 future. We find that the CSI 300 is featured by multifractality and there are less complexity and risk after the CSI 300 index future was introduced. With the shuffling, surrogating and removing extreme values procedures, we unveil that extreme events and fat-distribution are the main origin of multifractality. Besides, we discuss the knotting phenomena in multifractality, and find that the scaling range and the irregular fluctuations for large scales in the Fq(s) vs s plot can cause a knot.

Probing multi-scale self-similarity of tissue structures using light scattering spectroscopy: prospects in pre-cancer detection

NASA Astrophysics Data System (ADS)

Chatterjee, Subhasri; Das, Nandan K.; Kumar, Satish; Mohapatra, Sonali; Pradhan, Asima; Panigrahi, Prasanta K.; Ghosh, Nirmalya

2013-02-01

Multi-resolution analysis on the spatial refractive index inhomogeneities in the connective tissue regions of human cervix reveals clear signature of multifractality. We have thus developed an inverse analysis strategy for extraction and quantification of the multifractality of spatial refractive index fluctuations from the recorded light scattering signal. The method is based on Fourier domain pre-processing of light scattering data using Born approximation, and its subsequent analysis through Multifractal Detrended Fluctuation Analysis model. The method has been validated on several mono- and multi-fractal scattering objects whose self-similar properties are user controlled and known a-priori. Following successful validation, this approach has initially been explored for differentiating between different grades of precancerous human cervical tissues.

Multifractal property of Chinese stock market in the CSI 800 index based on MF-DFA approach

NASA Astrophysics Data System (ADS)

Zhu, Huijian; Zhang, Weiguo

2018-01-01

CSI 800 index consists of CSI 500 index and CSI 300 index, aiming to reflect the performance of stocks with large, mid and small size of China A share market. In this paper we analyze the multifractal structure of Chinese stock market in the CSI 800 index based on the multifractal detrended fluctuation analysis (MF-DFA) method. We find that the fluctuation of the closing logarithmic returns have multifractal properties, the shape and width of multifractal spectrum are depended on the weighing order q. More interestingly, we observe a bigger market crash in June-August 2015 than the one in 2008 based on the local Hurst exponents. The result provides important information for further study on dynamic mechanism of return fluctuation and whether it would trigger a new financial crisis.

Super-Resolution Reconstruction of Remote Sensing Images Using Multifractal Analysis

PubMed Central

Hu, Mao-Gui; Wang, Jin-Feng; Ge, Yong

2009-01-01

Satellite remote sensing (RS) is an important contributor to Earth observation, providing various kinds of imagery every day, but low spatial resolution remains a critical bottleneck in a lot of applications, restricting higher spatial resolution analysis (e.g., intra-urban). In this study, a multifractal-based super-resolution reconstruction method is proposed to alleviate this problem. The multifractal characteristic is common in Nature. The self-similarity or self-affinity presented in the image is useful to estimate details at larger and smaller scales than the original. We first look for the presence of multifractal characteristics in the images. Then we estimate parameters of the information transfer function and noise of the low resolution image. Finally, a noise-free, spatial resolution-enhanced image is generated by a fractal coding-based denoising and downscaling method. The empirical case shows that the reconstructed super-resolution image performs well in detail enhancement. This method is not only useful for remote sensing in investigating Earth, but also for other images with multifractal characteristics. PMID:22291530

Multifractal detrended cross-correlation between the Chinese domestic and international gold markets based on DCCA and DMCA methods

NASA Astrophysics Data System (ADS)

Cao, Guangxi; Han, Yan; Chen, Yuemeng; Yang, Chunxia

2014-05-01

Based on the daily price data of Shanghai and London gold spot markets, we applied detrended cross-correlation analysis (DCCA) and detrended moving average cross-correlation analysis (DMCA) methods to quantify power-law cross-correlation between domestic and international gold markets. Results show that the cross-correlations between the Chinese domestic and international gold spot markets are multifractal. Furthermore, forward DMCA and backward DMCA seems to outperform DCCA and centered DMCA for short-range gold series, which confirms the comparison results of short-range artificial data in L. Y. He and S. P. Chen [Physica A 390 (2011) 3806-3814]. Finally, we analyzed the local multifractal characteristics of the cross-correlation between Chinese domestic and international gold markets. We show that multifractal characteristics of the cross-correlation between the Chinese domestic and international gold markets are time-varying and that multifractal characteristics were strengthened by the financial crisis in 2007-2008.

Continuous wavelet transform based time-scale and multifractal analysis of the nonlinear oscillations in a hollow cathode glow discharge plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nurujjaman, Md.; Narayanan, Ramesh; Iyengar, A. N. Sekar

2009-10-15

Continuous wavelet transform (CWT) based time-scale and multifractal analyses have been carried out on the anode glow related nonlinear floating potential fluctuations in a hollow cathode glow discharge plasma. CWT has been used to obtain the contour and ridge plots. Scale shift (or inversely frequency shift), which is a typical nonlinear behavior, has been detected from the undulating contours. From the ridge plots, we have identified the presence of nonlinearity and degree of chaoticity. Using the wavelet transform modulus maxima technique we have obtained the multifractal spectrum for the fluctuations at different discharge voltages and the spectrum was observed tomore » become a monofractal for periodic signals. These multifractal spectra were also used to estimate different quantities such as the correlation and fractal dimension, degree of multifractality, and complexity parameters. These estimations have been found to be consistent with the nonlinear time series analysis.« less

Investigation of multifractality in the Brazilian stock market

NASA Astrophysics Data System (ADS)

Maganini, Natália Diniz; Da Silva Filho, Antônio Carlos; Lima, Fabiano Guasti

2018-05-01

Many studies point to a possible new stylized fact for financial time series: the multifractality. Several authors have already detected this characteristic in multiple time series in several countries. With that in mind and based on Multifractal Detrended Fluctuation Analysis (MFDFA) method, this paper analyzes the multifractality in the Brazilian market. This analysis is performed with daily data from IBOVESPA index (Brazilian stock exchange's main index) and other four highly marketable stocks in the Brazilian market (VALE5, ITUB4, BBDC4 and CIEL3), which represent more than 25% of the index composition, making up 1961 observations for each asset in the period from June 26 2009 to May 31 2017. We found that the studied stock prices and Brazilian index are multifractal, but that the multifractality degree is not the same for all the assets. The use of shuffled and surrogated series indicates that for the period and the actions considered the long-range correlations do not strongly influence the multifractality, but the distribution (fat tails) exerts a possible influence on IBOVESPA and CIEL3.

Detrended cross-correlation analysis on RMB exchange rate and Hang Seng China Enterprises Index

NASA Astrophysics Data System (ADS)

Ruan, Qingsong; Yang, Bingchan; Ma, Guofeng

2017-02-01

In this paper, we investigate the cross-correlations between the Hang Seng China Enterprises Index and RMB exchange markets on the basis of a cross-correlation statistic test and multifractal detrended cross-correlation analysis (MF-DCCA). MF-DCCA has, at best, serious limitations for most of the signals describing complex natural processes and often indicates multifractal cross-correlations when there are none. In order to prevent these false multifractal cross-correlations, we apply MFCCA to verify the cross-correlations. Qualitatively, we find that the return series of the Hang Seng China Enterprises Index and RMB exchange markets were, overall, significantly cross-correlated based on the statistical analysis. Quantitatively, we find that the cross-correlations between the stock index and RMB exchange markets were strongly multifractal, and the multifractal degree of the onshore RMB exchange markets was somewhat larger than the offshore RMB exchange markets. Moreover, we use the absolute return series to investigate and confirm the fact of multifractality. The results from the rolling windows show that the short-term cross-correlations between volatility series remain high.

p-exponent and p-leaders, Part II: Multifractal analysis. Relations to detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Leonarduzzi, R.; Wendt, H.; Abry, P.; Jaffard, S.; Melot, C.; Roux, S. G.; Torres, M. E.

2016-04-01

Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and image processing tool and is commonly used in numerous applications of different natures. In its common formulation, it relies on the Hölder exponent as a measure of local regularity, which is by nature restricted to positive values and can hence be used for locally bounded functions only. In this contribution, it is proposed to replace the Hölder exponent with a collection of novel exponents for measuring local regularity, the p-exponents. One of the major virtues of p-exponents is that they can potentially take negative values. The corresponding wavelet-based multiscale quantities, the p-leaders, are constructed and shown to permit the definition of a new multifractal formalism, yielding an accurate practical estimation of the multifractal properties of real-world data. Moreover, theoretical and practical connections to and comparisons against another multifractal formalism, referred to as multifractal detrended fluctuation analysis, are achieved. The performance of the proposed p-leader multifractal formalism is studied and compared to previous formalisms using synthetic multifractal signals and images, illustrating its theoretical and practical benefits. The present contribution is complemented by a companion article studying in depth the theoretical properties of p-exponents and the rich classification of local singularities it permits.

Multifractality in plasma edge electrostatic turbulence

NASA Astrophysics Data System (ADS)

Neto, C. Rodrigues; Guimarães-Filho, Z. O.; Caldas, I. L.; Nascimento, I. C.; Kuznetsov, Yu. K.

2008-08-01

Plasma edge turbulence in Tokamak Chauffage Alfvén Brésilien (TCABR) [R. M. O. Galvão et al., Plasma Phys. Contr. Fusion 43, 1181 (2001)] is investigated for multifractal properties of the fluctuating floating electrostatic potential measured by Langmuir probes. The multifractality in this signal is characterized by the full multifractal spectra determined by applying the wavelet transform modulus maxima. In this work, the dependence of the multifractal spectrum with the radial position is presented. The multifractality degree inside the plasma increases with the radial position reaching a maximum near the plasma edge and becoming almost constant in the scrape-off layer. Comparisons between these results with those obtained for random test time series with the same Hurst exponents and data length statistically confirm the reported multifractal behavior. Moreover, the persistence of these signals, characterized by their Hurst exponent, present radial profile similar to the deterministic component estimated from analysis based on dynamical recurrences.

Multifractal characterization of energy stocks in China: A multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Yang, Liansheng; Zhu, Yingming; Wang, Yudong

2016-06-01

In this paper, we investigate the impacts of oil price changes on energy stocks in Chinese stock market from the multifractal perspective. The well-known multifractal detrended fluctuation analysis (MF-DFA) is applied to detect the multifractality. We find that both returns and volatilities of energy industry index display apparent multifractal behavior. Oil market activity is an important source of multifractality in energy stocks index in addition to long-range correlations and fat-tail distributions.

Multifractal detrended cross-correlations between crude oil market and Chinese ten sector stock markets

NASA Astrophysics Data System (ADS)

Yang, Liansheng; Zhu, Yingming; Wang, Yudong; Wang, Yiqi

2016-11-01

Based on the daily price data of spot prices of West Texas Intermediate (WTI) crude oil and ten CSI300 sector indices in China, we apply multifractal detrended cross-correlation analysis (MF-DCCA) method to investigate the cross-correlations between crude oil and Chinese sector stock markets. We find that the strength of multifractality between WTI crude oil and energy sector stock market is the highest, followed by the strength of multifractality between WTI crude oil and financial sector market, which reflects a close connection between energy and financial market. Then we do vector autoregression (VAR) analysis to capture the interdependencies among the multiple time series. By comparing the strength of multifractality for original data and residual errors of VAR model, we get a conclusion that vector auto-regression (VAR) model could not be used to describe the dynamics of the cross-correlations between WTI crude oil and the ten sector stock markets.

Analysis of concentric and eccentric contractions in biceps brachii muscles using surface electromyography signals and multifractal analysis.

PubMed

Marri, Kiran; Swaminathan, Ramakrishnan

2016-06-23

Muscle contractions can be categorized into isometric, isotonic (concentric and eccentric) and isokinetic contractions. The eccentric contractions are very effective for promoting muscle hypertrophy and produce larger forces when compared to the concentric or isometric contractions. Surface electromyography signals are widely used for analyzing muscle activities. These signals are nonstationary, nonlinear and exhibit self-similar multifractal behavior. The research on surface electromyography signals using multifractal analysis is not well established for concentric and eccentric contractions. In this study, an attempt has been made to analyze the concentric and eccentric contractions associated with biceps brachii muscles using surface electromyography signals and multifractal detrended moving average algorithm. Surface electromyography signals were recorded from 20 healthy individuals while performing a single curl exercise. The preprocessed signals were divided into concentric and eccentric cycles and in turn divided into phases based on range of motion: lower (0°-90°) and upper (>90°). The segments of surface electromyography signal were subjected to multifractal detrended moving average algorithm, and multifractal features such as strength of multifractality, peak exponent value, maximum exponent and exponent index were extracted in addition to conventional linear features such as root mean square and median frequency. The results show that surface electromyography signals exhibit multifractal behavior in both concentric and eccentric cycles. The mean strength of multifractality increased by 15% in eccentric contraction compared to concentric contraction. The lowest and highest exponent index values are observed in the upper concentric and lower eccentric contractions, respectively. The multifractal features are observed to be helpful in differentiating surface electromyography signals along the range of motion as compared to root mean square and median frequency. It appears that these multifractal features extracted from the concentric and eccentric contractions can be useful in the assessment of surface electromyography signals in sports medicine and training and also in rehabilitation programs. © IMechE 2016.

Quantitative assessment of submicron scale anisotropy in tissue multifractality by scattering Mueller matrix in the framework of Born approximation

NASA Astrophysics Data System (ADS)

Das, Nandan Kumar; Dey, Rajib; Chakraborty, Semanti; Panigrahi, Prasanta K.; Meglinski, Igor; Ghosh, Nirmalya

2018-04-01

A number of tissue-like disordered media exhibit local anisotropy of scattering in the scaling behavior. Scaling behavior contains wealth of fractal or multifractal properties. We demonstrate that the spatial dielectric fluctuations in a sample of biological tissue exhibit multifractal anisotropy. Multifractal anisotropy encoded in the wavelength variation of the light scattering Mueller matrix and manifesting as an intriguing spectral diattenuation effect. We developed an inverse method for the quantitative assessment of the multifractal anisotropy. The method is based on the processing of relevant Mueller matrix elements in Fourier domain by using Born approximation, followed by the multifractal analysis. The approach promises for probing subtle micro-structural changes in biological tissues associated with the cancer and precancer, as well as for non-destructive characterization of a wide range of scattering materials.

Multifractal analysis on international crude oil markets based on the multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Gu, Rongbao; Chen, Hongtao; Wang, Yudong

2010-07-01

The multifractal nature of WTI and Brent crude oil markets is studied employing the multifractal detrended fluctuation analysis. We find that two crude oil markets become more and more efficient for long-term and two Gulf Wars cannot change time scale behavior of crude oil return series. Considering long-term influence caused by Gulf Wars, we find such “turning windows” in generalized Hurst exponents obtained from three periods divided by two Gulf Wars so that WTI and Brent crude oil returns possess different properties above and below the windows respectively. Comparing with the results obtained from three periods we conclude that, before the First Gulf War, international crude oil markets possessed the highest multifractality degree, small-scope fluctuations presented the strongest persistence and large-scope fluctuations presented the strongest anti-persistence. We find that, for two Gulf Wars, the first one made a greater impact on international oil markets; for two markets, Brent was more influenced by Gulf Wars. In addition, we also verified that the multifractal structures of two markets’ indices are not only mainly attributed to the broad fat-tail distributions and persistence, but also affected by some other factors.

Dynamic Singularity Spectrum Distribution of Sea Clutter

NASA Astrophysics Data System (ADS)

Xiong, Gang; Yu, Wenxian; Zhang, Shuning

2015-12-01

The fractal and multifractal theory have provided new approaches for radar signal processing and target-detecting under the background of ocean. However, the related research mainly focuses on fractal dimension or multifractal spectrum (MFS) of sea clutter. In this paper, a new dynamic singularity analysis method of sea clutter using MFS distribution is developed, based on moving detrending analysis (DMA-MFSD). Theoretically, we introduce the time information by using cyclic auto-correlation of sea clutter. For transient correlation series, the instantaneous singularity spectrum based on multifractal detrending moving analysis (MF-DMA) algorithm is calculated, and the dynamic singularity spectrum distribution of sea clutter is acquired. In addition, we analyze the time-varying singularity exponent ranges and maximum position function in DMA-MFSD of sea clutter. For the real sea clutter data, we analyze the dynamic singularity spectrum distribution of real sea clutter in level III sea state, and conclude that the radar sea clutter has the non-stationary and time-varying scale characteristic and represents the time-varying singularity spectrum distribution based on the proposed DMA-MFSD method. The DMA-MFSD will also provide reference for nonlinear dynamics and multifractal signal processing.

Measuring daily Value-at-Risk of SSEC index: A new approach based on multifractal analysis and extreme value theory

NASA Astrophysics Data System (ADS)

Wei, Yu; Chen, Wang; Lin, Yu

2013-05-01

Recent studies in the econophysics literature reveal that price variability has fractal and multifractal characteristics not only in developed financial markets, but also in emerging markets. Taking high-frequency intraday quotes of the Shanghai Stock Exchange Component (SSEC) Index as example, this paper proposes a new method to measure daily Value-at-Risk (VaR) by combining the newly introduced multifractal volatility (MFV) model and the extreme value theory (EVT) method. Two VaR backtesting techniques are then employed to compare the performance of the model with that of a group of linear and nonlinear generalized autoregressive conditional heteroskedasticity (GARCH) models. The empirical results show the multifractal nature of price volatility in Chinese stock market. VaR measures based on the multifractal volatility model and EVT method outperform many GARCH-type models at high-risk levels.

Cross-correlations between West Texas Intermediate crude oil and the stock markets of the BRIC

NASA Astrophysics Data System (ADS)

Ma, Feng; Wei, Yu; Huang, Dengshi; Zhao, Lin

2013-11-01

In this paper, we investigate the cross-correlation properties between West Texas Intermediate crude oil and the stock markets of the BRIC. We use not only the qualitative analysis of the cross-correlation test, but also take the quantitative analysis of the MF-DXA, confirming the cross-correlation relationship between West Texas Intermediate crude oil and the stock markets of the BRIC (Brazil, Russia, India and China) respectively, which have strongly multifractal features, and the cross-correlations are more strongly multifractal in the short term than in the long term. Furthermore, based on the multifractal spectrum, we also find the multifractality strength between the crude oil WTI and Chinese stock market is stronger than the multifractality strength of other pairs. Based on the Iraq war (Mar 20, 2003) and the Financial crisis in 2008, we divide sample period into four segments to research the degree of the multifractal (ΔH) and the market efficiency (and the risk). Finally, we employ the technique of the rolling window to calculate the time-varying EI (efficiency index) and dependent on the EI, we can easily observe the change of stock markets. Furthermore, we explore the relationship between bivariate cross-correlation exponents (Hxy(q)) and the generalized Hurst exponents.

Fault diagnosis of rolling bearings based on multifractal detrended fluctuation analysis and Mahalanobis distance criterion

NASA Astrophysics Data System (ADS)

Lin, Jinshan; Chen, Qian

2013-07-01

Vibration data of faulty rolling bearings are usually nonstationary and nonlinear, and contain fairly weak fault features. As a result, feature extraction of rolling bearing fault data is always an intractable problem and has attracted considerable attention for a long time. This paper introduces multifractal detrended fluctuation analysis (MF-DFA) to analyze bearing vibration data and proposes a novel method for fault diagnosis of rolling bearings based on MF-DFA and Mahalanobis distance criterion (MDC). MF-DFA, an extension of monofractal DFA, is a powerful tool for uncovering the nonlinear dynamical characteristics buried in nonstationary time series and can capture minor changes of complex system conditions. To begin with, by MF-DFA, multifractality of bearing fault data was quantified with the generalized Hurst exponent, the scaling exponent and the multifractal spectrum. Consequently, controlled by essentially different dynamical mechanisms, the multifractality of four heterogeneous bearing fault data is significantly different; by contrast, controlled by slightly different dynamical mechanisms, the multifractality of homogeneous bearing fault data with different fault diameters is significantly or slightly different depending on different types of bearing faults. Therefore, the multifractal spectrum, as a set of parameters describing multifractality of time series, can be employed to characterize different types and severity of bearing faults. Subsequently, five characteristic parameters sensitive to changes of bearing fault conditions were extracted from the multifractal spectrum and utilized to construct fault features of bearing fault data. Moreover, Hilbert transform based envelope analysis, empirical mode decomposition (EMD) and wavelet transform (WT) were utilized to study the same bearing fault data. Also, the kurtosis and the peak levels of the EMD or the WT component corresponding to the bearing tones in the frequency domain were carefully checked and used as the bearing fault features. Next, MDC was used to classify the bearing fault features extracted by EMD, WT and MF-DFA in the time domain and assess the abilities of the three methods to extract fault features from bearing fault data. The results show that MF-DFA seems to outperform each of envelope analysis, statistical parameters, EMD and WT in feature extraction of bearing fault data and then the proposed method in this paper delivers satisfactory performances in distinguishing different types and severity of bearing faults. Furthermore, to further ascertain the nature causing the multifractality of bearing vibration data, the generalized Hurst exponents of the original bearing vibration data were compared with those of the shuffled and the surrogated data. Consequently, the long-range correlations for small and large fluctuations of data seem to be chiefly responsible for the multifractality of bearing vibration data.

Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates

NASA Astrophysics Data System (ADS)

Muniandy, S. V.; Lim, S. C.; Murugan, R.

2001-12-01

In this paper, we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to Malaysian currency, Ringgit Malaysia. These time series are examined piecewise before and after the currency control imposed in 1st September 1998 using the monofractal model based on fractional Brownian motion. The global Hurst exponents are determined using the R/ S analysis, the detrended fluctuation analysis and the method of second moment using the correlation coefficients. The limitation of these monofractal analyses is discussed. The usual multifractal analysis reveals that there exists a wide range of Hurst exponents in each of the time series. A new method of modelling the multifractal time series based on multifractional Brownian motion with time-varying Hurst exponents is studied.

Multifractal detrended cross-correlation analysis on NO, NO2 and O3 concentrations at traffic sites

NASA Astrophysics Data System (ADS)

Xu, Weijia; Liu, Chunqiong; Shi, Kai; Liu, Yonghong

2018-07-01

NOX plays the important role for O3 production in atmospheric photochemical processes. In this paper, the cross-correlations between NO (NO2) and O3 at three traffic sites in Hong Kong are investigated, using the multifractal detrended cross-correlation analysis (MFDCCA). The results show that the cross-correlations between NO (NO2) and O3 have multifractal nature and long term persistent power-law decaying behavior. The sources of multifractality are discussed based on the shuffling and phase randomization procedure. The chi square test is applied to identify the contributions degree of NO and NO2 to multifractality due to its own long term correlations respectively. And the temporal evolutions of the local contributions degree of NO and NO2 to multifractality are investigated by the sliding windows method. The differences between them are explained by the self-organized criticality mechanism of air pollution, combined with global solar radiation. MFDCCA provides a helpful approach for understanding the quantitative relationship between the O3 and its precursors.

Multifractal Cross Wavelet Analysis

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Gao, Xing-Lu; Zhou, Wei-Xing; Stanley, H. Eugene

Complex systems are composed of mutually interacting components and the output values of these components usually exhibit long-range cross-correlations. Using wavelet analysis, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call multifractal cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. For binomial multifractal measures, we find the empirical joint multifractality of MFXWT to be in approximate agreement with the theoretical formula. For bFBMs, MFXWT may provide spurious multifractality because of the wide spanning range of the multifractal spectrum. We also apply the MFXWT method to stock market indices, and in pairs of index returns and volatilities we find an intriguing joint multifractal behavior. The tests on surrogate series also reveal that the cross correlation behavior, particularly the cross correlation with zero lag, is the main origin of cross multifractality.

Tissue multifractality and hidden Markov model based integrated framework for optimum precancer detection

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Sabyasachi; Das, Nandan K.; Kurmi, Indrajit; Pradhan, Asima; Ghosh, Nirmalya; Panigrahi, Prasanta K.

2017-10-01

We report the application of a hidden Markov model (HMM) on multifractal tissue optical properties derived via the Born approximation-based inverse light scattering method for effective discrimination of precancerous human cervical tissue sites from the normal ones. Two global fractal parameters, generalized Hurst exponent and the corresponding singularity spectrum width, computed by multifractal detrended fluctuation analysis (MFDFA), are used here as potential biomarkers. We develop a methodology that makes use of these multifractal parameters by integrating with different statistical classifiers like the HMM and support vector machine (SVM). It is shown that the MFDFA-HMM integrated model achieves significantly better discrimination between normal and different grades of cancer as compared to the MFDFA-SVM integrated model.

Multifractal analysis with the probability density function at the three-dimensional anderson transition.

PubMed

Rodriguez, Alberto; Vasquez, Louella J; Römer, Rudolf A

2009-03-13

The probability density function (PDF) for critical wave function amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size corrections is properly analyzed. We show the non-Gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and the possible existence of termination points. A PDF-based multifractal analysis is shown to be a valid alternative to the standard approach based on the scaling of inverse participation ratios.

Multifractal cross-correlations between crude oil and tanker freight rate

NASA Astrophysics Data System (ADS)

Chen, Feier; Miao, Yuqi; Tian, Kang; Ding, Xiaoxu; Li, Tingyi

2017-05-01

Analysis of crude oil price and tanker freight rate volatility attract more attention as the mechanism is not only the basis of industrialization but also a vital role in economics, especially after the year 2008 when financial crisis notably blew the maritime transportation. In this paper, we studied the cross-correlations between the West Texas International crude oil (WTI) and Baltic Exchange Dirty Tanker Index (BDTI) employing the Multifractal Detrended Cross-Correlation Analysis (MF-DCCA). Empirical results show that the degree of short-term cross-correlation is higher than that in the long term and that the strength of multifractality after financial crisis is larger than that before. Moreover, the components of multifractal spectrum are quantified with the finite-size effect taken into consideration and an improved method in terms of constructing the surrogated time series provided. Numerical results show that the multifractality is generated mostly from the nonlinear and the fat-tailed probability distribution (PDF) part. Also, it is apparent that the PDF part changes a lot after the financial crisis. The research is contributory to risk management by providing various instructions for participants in shipping markets. Our main contribution is that we investigated both the multifractal features and the origin of multifractality and provided confirming evidence of multifractality through numerical results while applying quantitative analysis based on MF-DCCA; furthermore, the research is contributory to risk management since it provides instructions in both economic market and stock market simultaneously. However, constructing the surrogated series in order to obtain consistence seems less convincing which requires further discussion and attempts.

Multifractal spectrum analysis of nonlinear dynamical mechanisms in China’s agricultural futures markets

NASA Astrophysics Data System (ADS)

Chen, Shu-Peng; He, Ling-Yun

2010-04-01

Based on Partition Function and Multifractal Spectrum Analysis, we investigated the nonlinear dynamical mechanisms in China’s agricultural futures markets, namely, Dalian Commodity Exchange (DCE for short) and Zhengzhou Commodity Exchange (ZCE for short), where nearly all agricultural futures contracts are traded in the two markets. Firstly, we found nontrivial multifractal spectra, which are the empirical evidence of the existence of multifractal features, in 4 representative futures markets in China, that is, Hard Winter wheat (HW for short) and Strong Gluten wheat (SG for short) futures markets from ZCE and Soy Meal (SM for short) futures and Soy Bean No.1 (SB for short) futures markets from DCE. Secondly, by shuffling the original time series, we destroyed the underlying nonlinear temporal correlation; thus, we identified that long-range correlation mechanism constitutes major contributions in the formation in the multifractals of the markets. Thirdly, by tracking the evolution of left- and right-half spectra, we found that there exist critical points, between which there are different behaviors, in the left-half spectra for large price fluctuations; but for the right-hand spectra for small price fluctuations, the width of those increases slowly as the delay t increases in the long run. Finally, the dynamics of large fluctuations is significantly different from that of the small ones, which implies that there exist different underlying mechanisms in the formation of multifractality in the markets. Our main contributions focus on that we not only provided empirical evidence of the existence of multifractal features in China agricultural commodity futures markets; but also we pioneered in investigating the sources of the multifractality in China’s agricultural futures markets in current literature; furthermore, we investigated the nonlinear dynamical mechanisms based on spectrum analysis, which offers us insights into the underlying dynamical mechanisms in China’s agricultural futures markets.

Analyzing the Cross-Correlation Between Onshore and Offshore RMB Exchange Rates Based on Multifractal Detrended Cross-Correlation Analysis (MF-DCCA)

NASA Astrophysics Data System (ADS)

Xie, Chi; Zhou, Yingying; Wang, Gangjin; Yan, Xinguo

We use the multifractal detrended cross-correlation analysis (MF-DCCA) method to explore the multifractal behavior of the cross-correlation between exchange rates of onshore RMB (CNY) and offshore RMB (CNH) against US dollar (USD). The empirical data are daily prices of CNY/USD and CNH/USD from May 1, 2012 to February 29, 2016. The results demonstrate that: (i) the cross-correlation between CNY/USD and CNH/USD is persistent and its fluctuation is smaller when the order of fluctuation function is negative than that when the order is positive; (ii) the multifractal behavior of the cross-correlation between CNY/USD and CNH/USD is significant during the sample period; (iii) the dynamic Hurst exponents obtained by the rolling windows analysis show that the cross-correlation is stable when the global economic situation is good and volatile in bad situation; and (iv) the non-normal distribution of original data has a greater effect on the multifractality of the cross-correlation between CNY/USD and CNH/USD than the temporary correlation.

Clustering Multiple Sclerosis Subgroups with Multifractal Methods and Self-Organizing Map Algorithm

NASA Astrophysics Data System (ADS)

Karaca, Yeliz; Cattani, Carlo

Magnetic resonance imaging (MRI) is the most sensitive method to detect chronic nervous system diseases such as multiple sclerosis (MS). In this paper, Brownian motion Hölder regularity functions (polynomial, periodic (sine), exponential) for 2D image, such as multifractal methods were applied to MR brain images, aiming to easily identify distressed regions, in MS patients. With these regions, we have proposed an MS classification based on the multifractal method by using the Self-Organizing Map (SOM) algorithm. Thus, we obtained a cluster analysis by identifying pixels from distressed regions in MR images through multifractal methods and by diagnosing subgroups of MS patients through artificial neural networks.

Anti-correlation and multifractal features of Spain electricity spot market

NASA Astrophysics Data System (ADS)

Norouzzadeh, P.; Dullaert, W.; Rahmani, B.

2007-07-01

We use multifractal detrended fluctuation analysis (MF-DFA) to numerically investigate correlation, persistence, multifractal properties and scaling behavior of the hourly spot prices for the Spain electricity exchange-Compania O Peradora del Mercado de Electricidad (OMEL). Through multifractal analysis, fluctuations behavior, the scaling exponents and generalized Hurst exponents are studied. Moreover, contribution of fat-tailed probability distributions and nonlinear temporal correlations to multifractality is studied.

Multifractal detrended cross-correlations between the CSI 300 index futures and the spot markets based on high-frequency data

NASA Astrophysics Data System (ADS)

Cao, Guangxi; Han, Yan; Cui, Weijun; Guo, Yu

2014-11-01

The cross-correlation between the China Securities Index 300 (CSI 300) index futures and the spot markets based on high-frequency data is discussed in this paper. We empirically analyze the cross-correlation by using the multifractal detrended cross-correlation analysis (MF-DCCA), and investigate further the characteristics of asymmetry, frequency difference, and transmission direction of the cross-correlation. The results indicate that the cross-correlation between the two markets is significant and multifractal. Meanwhile, weak asymmetries exist in the cross-correlation, and higher data frequency results in a lower multifractality degree of the cross-correlation. The causal relationship between the two markets is bidirectional, but the CSI 300 index futures market has greater impact on the spot market.

Multifractal spectrum of physiological signals: a mechanism-related approach

NASA Astrophysics Data System (ADS)

Pavlov, Alexey N.; Pavlova, Olga N.; Abdurashitov, Arkady S.; Arinushkin, Pavel A.; Runnova, Anastasiya E.; Semyachkina-Glushkovskaya, Oxana V.

2017-04-01

In this paper we discuss an approach for mechanism-related analysis of physiological signals performed with the wavelet-based multifractal formalism. This approach assumes estimation of the singularity spectrum for the band-pass filtered processes at different physiological conditions in order to provide explanation of the occurred changes in the Hölder exponents and the multi-fractality degree. We illustrate the considered approach using two examples, namely, the dynamics of the cerebral blood flow (CBF) and the electrical activity of the brain.

Multifractal analysis of real and imaginary movements: EEG study

NASA Astrophysics Data System (ADS)

Pavlov, Alexey N.; Maksimenko, Vladimir A.; Runnova, Anastasiya E.; Khramova, Marina V.; Pisarchik, Alexander N.

2018-04-01

We study abilities of the wavelet-based multifractal analysis in recognition specific dynamics of electrical brain activity associated with real and imaginary movements. Based on the singularity spectra we analyze electroencephalograms (EEGs) acquired in untrained humans (operators) during imagination of hands movements, and show a possibility to distinguish between the related EEG patterns and the recordings performed during real movements or the background electrical brain activity. We discuss how such recognition depends on the selected brain region.

Price-volume multifractal analysis and its application in Chinese stock markets

NASA Astrophysics Data System (ADS)

Yuan, Ying; Zhuang, Xin-tian; Liu, Zhi-ying

2012-06-01

An empirical research on Chinese stock markets is conducted using statistical tools. First, the multifractality of stock price return series, ri(ri=ln(Pt+1)-ln(Pt)) and trading volume variation series, vi(vi=ln(Vt+1)-ln(Vt)) is confirmed using multifractal detrended fluctuation analysis. Furthermore, a multifractal detrended cross-correlation analysis between stock price return and trading volume variation in Chinese stock markets is also conducted. It is shown that the cross relationship between them is also found to be multifractal. Second, the cross-correlation between stock price Pi and trading volume Vi is empirically studied using cross-correlation function and detrended cross-correlation analysis. It is found that both Shanghai stock market and Shenzhen stock market show pronounced long-range cross-correlations between stock price and trading volume. Third, a composite index R based on price and trading volume is introduced. Compared with stock price return series ri and trading volume variation series vi, R variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume. Finally, we analyze the multifractal characteristics of R variation series before and after three financial events in China (namely, Price Limits, Reform of Non-tradable Shares and financial crisis in 2008) in the whole period of sample to study the changes of stock market fluctuation and financial risk. It is found that the empirical results verified the validity of R.

A new image segmentation method based on multifractal detrended moving average analysis

NASA Astrophysics Data System (ADS)

Shi, Wen; Zou, Rui-biao; Wang, Fang; Su, Le

2015-08-01

In order to segment and delineate some regions of interest in an image, we propose a novel algorithm based on the multifractal detrended moving average analysis (MF-DMA). In this method, the generalized Hurst exponent h(q) is calculated for every pixel firstly and considered as the local feature of a surface. And then a multifractal detrended moving average spectrum (MF-DMS) D(h(q)) is defined by the idea of box-counting dimension method. Therefore, we call the new image segmentation method MF-DMS-based algorithm. The performance of the MF-DMS-based method is tested by two image segmentation experiments of rapeseed leaf image of potassium deficiency and magnesium deficiency under three cases, namely, backward (θ = 0), centered (θ = 0.5) and forward (θ = 1) with different q values. The comparison experiments are conducted between the MF-DMS method and other two multifractal segmentation methods, namely, the popular MFS-based and latest MF-DFS-based methods. The results show that our MF-DMS-based method is superior to the latter two methods. The best segmentation result for the rapeseed leaf image of potassium deficiency and magnesium deficiency is from the same parameter combination of θ = 0.5 and D(h(- 10)) when using the MF-DMS-based method. An interesting finding is that the D(h(- 10)) outperforms other parameters for both the MF-DMS-based method with centered case and MF-DFS-based algorithms. By comparing the multifractal nature between nutrient deficiency and non-nutrient deficiency areas determined by the segmentation results, an important finding is that the gray value's fluctuation in nutrient deficiency area is much severer than that in non-nutrient deficiency area.

Multifractal Approach to the Analysis of Crime Dynamics: Results for Burglary in San Francisco

NASA Astrophysics Data System (ADS)

Melgarejo, Miguel; Obregon, Nelson

This paper provides evidence of fractal, multifractal and chaotic behaviors in urban crime by computing key statistical attributes over a long data register of criminal activity. Fractal and multifractal analyses based on power spectrum, Hurst exponent computation, hierarchical power law detection and multifractal spectrum are considered ways to characterize and quantify the footprint of complexity of criminal activity. Moreover, observed chaos analysis is considered a second step to pinpoint the nature of the underlying crime dynamics. This approach is carried out on a long database of burglary activity reported by 10 police districts of San Francisco city. In general, interarrival time processes of criminal activity in San Francisco exhibit fractal and multifractal patterns. The behavior of some of these processes is close to 1/f noise. Therefore, a characterization as deterministic, high-dimensional, chaotic phenomena is viable. Thus, the nature of crime dynamics can be studied from geometric and chaotic perspectives. Our findings support that crime dynamics may be understood from complex systems theories like self-organized criticality or highly optimized tolerance.

Multifractality, efficiency analysis of Chinese stock market and its cross-correlation with WTI crude oil price

NASA Astrophysics Data System (ADS)

Zhuang, Xiaoyang; Wei, Yu; Ma, Feng

2015-07-01

In this paper, the multifractality and efficiency degrees of ten important Chinese sectoral indices are evaluated using the methods of MF-DFA and generalized Hurst exponents. The study also scrutinizes the dynamics of the efficiency of Chinese sectoral stock market by the rolling window approach. The overall empirical findings revealed that all the sectoral indices of Chinese stock market exist different degrees of multifractality. The results of different efficiency measures have agreed on that the 300 Materials index is the least efficient index. However, they have a slight diffidence on the most efficient one. The 300 Information Technology, 300 Telecommunication Services and 300 Health Care indices are comparatively efficient. We also investigate the cross-correlations between the ten sectoral indices and WTI crude oil price based on Multifractal Detrended Cross-correlation Analysis. At last, some relevant discussions and implications of the empirical results are presented.

Multiscale multifractal properties between ground-level ozone and its precursors in rural area in Hong Kong.

PubMed

He, Hong-di; Qiao, Zhong-Xia; Pan, Wei; Lu, Wei-Zhen

2017-07-01

In rural area, due to the reduction of NOx and CO emitted from vehicle exhausts, the ozone photochemical reaction exhibits relatively weak effect and ozone formation presents different pattern with its precursors in contrast to urban situation. Hence, in this study, we apply detrended cross-correlation analysis to investigate the multifractal properties between ozone and its precursors in a rural area in Hong Kong. The observed databases of ozone, NO 2 , NOx and CO levels during 2005-2014 are obtained from a rural monitoring station in Hong Kong. Based on the collected database, the cross-correlation analysis is carried out firstly to examine the cross-correlation patterns and the results indicate that close interactive relations exist between them. Then the detrended cross-correlation analysis is performed for further analysis. The multifractal characters occur between ozone and its precursors. The long-term cross-correlations behaviors in winter are verified to be stronger than that in other seasons. Additionally, the method is extended on daily averaged data to explore the multifractal property on various time scales. The long-term cross-correlation behavior of ozone vs NO 2 and NOx on daily basis becomes weaker while that of ozone vs CO becomes stronger. The multifractal properties for all pairs in summer are found to be the strongest among the whole year. These findings successfully illustrate that the multifractal analysis is a useful tool for describing the temporal scaling behaviors of ozone trends in different time series in rural areas. Copyright © 2017 Elsevier Ltd. All rights reserved.

Multifractal analysis of managed and independent float exchange rates

NASA Astrophysics Data System (ADS)

Stošić, Darko; Stošić, Dusan; Stošić, Tatijana; Stanley, H. Eugene

2015-06-01

We investigate multifractal properties of daily price changes in currency rates using the multifractal detrended fluctuation analysis (MF-DFA). We analyze managed and independent floating currency rates in eight countries, and determine the changes in multifractal spectrum when transitioning between the two regimes. We find that after the transition from managed to independent float regime the changes in multifractal spectrum (position of maximum and width) indicate an increase in market efficiency. The observed changes are more pronounced for developed countries that have a well established trading market. After shuffling the series, we find that the multifractality is due to both probability density function and long term correlations for managed float regime, while for independent float regime multifractality is in most cases caused by broad probability density function.

Multifractal analysis and the NYHA index

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, A.; Ramírez-Hernández, L.; Aguilar-Molina, A. M.; Zamora-Justo, J. A.; Gutiérrez-Calleja, R. A.; Virgilio-González, C. D.

2014-11-01

We did multifractal analysis of heartbeat interval time series of healthy persons and patients with congestive heart failure (CHF). To analyze circadian rhythm variations we analyzed time series of 24 hours records and segments of six hours when the subject is asleep and segments of six hours when is awake. A decrease in the multifractality degree occurs in the heartbeat interval time series of CHF patients. This multifractality loss is associated with the width reduction of the spectrum and the complexity loss of the signal. Multifractal spectra of healthy persons are right skewed, but the spectra of CHF patients tend to be symmetrical and in some cases are left skewed. To determine the therapy for CHF patients, cardiologists use an index proposed by the NYHA (New York Heart Association). There is a correlation between this index and the multifractal analysis parameters, i.e. while higher is the NYHA index the width of the multifractal spectrum is lower and it is also more symmetrical. In contrast, patients with NYHA index equal to 1 have multifractal parameters similar to those of healthy subjects.

Comparing Monofractal and Multifractal Analysis of Corrosion Damage Evolution in Reinforcing Bars

PubMed Central

Xu, Yidong; Qian, Chunxiang; Pan, Lei; Wang, Bingbing; Lou, Chi

2012-01-01

Based on fractal theory and damage mechanics, the aim of this paper is to describe the monofractal and multifractal characteristics of corrosion morphology and develop a new approach to characterize the nonuniform corrosion degree of reinforcing bars. The relationship between fractal parameters and tensile strength of reinforcing bars are discussed. The results showed that corrosion mass loss ratio of a bar cannot accurately reflect the damage degree of the bar. The corrosion morphology of reinforcing bars exhibits both monofractal and multifractal features. The fractal dimension and the tensile strength of corroded steel bars exhibit a power function relationship, while the width of multifractal spectrum and tensile strength of corroded steel bars exhibit a linear relationship. By comparison, using width of multifractal spectrum as multifractal damage variable not only reflects the distribution of corrosion damage in reinforcing bars, but also reveals the influence of nonuniform corrosion on the mechanical properties of reinforcing bars. The present research provides a new approach for the establishment of corrosion damage constitutive models of reinforcing bars. PMID:22238682

The human genome: a multifractal analysis

PubMed Central

2011-01-01

Background Several studies have shown that genomes can be studied via a multifractal formalism. Recently, we used a multifractal approach to study the genetic information content of the Caenorhabditis elegans genome. Here we investigate the possibility that the human genome shows a similar behavior to that observed in the nematode. Results We report here multifractality in the human genome sequence. This behavior correlates strongly on the presence of Alu elements and to a lesser extent on CpG islands and (G+C) content. In contrast, no or low relationship was found for LINE, MIR, MER, LTRs elements and DNA regions poor in genetic information. Gene function, cluster of orthologous genes, metabolic pathways, and exons tended to increase their frequencies with ranges of multifractality and large gene families were located in genomic regions with varied multifractality. Additionally, a multifractal map and classification for human chromosomes are proposed. Conclusions Based on these findings, we propose a descriptive non-linear model for the structure of the human genome, with some biological implications. This model reveals 1) a multifractal regionalization where many regions coexist that are far from equilibrium and 2) this non-linear organization has significant molecular and medical genetic implications for understanding the role of Alu elements in genome stability and structure of the human genome. Given the role of Alu sequences in gene regulation, genetic diseases, human genetic diversity, adaptation and phylogenetic analyses, these quantifications are especially useful. PMID:21999602

Common multifractality in the heart rate variability and brain activity of healthy humans

NASA Astrophysics Data System (ADS)

Lin, D. C.; Sharif, A.

2010-06-01

The influence from the central nervous system on the human multifractal heart rate variability (HRV) is examined under the autonomic nervous system perturbation induced by the head-up-tilt body maneuver. We conducted the multifractal factorization analysis to factor out the common multifractal factor in the joint fluctuation of the beat-to-beat heart rate and electroencephalography data. Evidence of a central link in the multifractal HRV was found, where the transition towards increased (decreased) HRV multifractal complexity is associated with a stronger (weaker) multifractal correlation between the central and autonomic nervous systems.

NEW SUNS IN THE COSMOS. III. MULTIFRACTAL SIGNATURE ANALYSIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freitas, D. B. de; Nepomuceno, M. M. F.; Junior, P. R. V. de Moraes

2016-11-01

In the present paper, we investigate the multifractality signatures in hourly time series extracted from the CoRoT spacecraft database. Our analysis is intended to highlight the possibility that astrophysical time series can be members of a particular class of complex and dynamic processes, which require several photometric variability diagnostics to characterize their structural and topological properties. To achieve this goal, we search for contributions due to a nonlinear temporal correlation and effects caused by heavier tails than the Gaussian distribution, using a detrending moving average algorithm for one-dimensional multifractal signals (MFDMA). We observe that the correlation structure is the mainmore » source of multifractality, while heavy-tailed distribution plays a minor role in generating the multifractal effects. Our work also reveals that the rotation period of stars is inherently scaled by the degree of multifractality. As a result, analyzing the multifractal degree of the referred series, we uncover an evolution of multifractality from shorter to larger periods.« less

Price-volume multifractal analysis of the Moroccan stock market

NASA Astrophysics Data System (ADS)

El Alaoui, Marwane

2017-11-01

In this paper, we analyzed price-volume multifractal cross-correlations of Moroccan Stock Exchange. We chose the period from January 1st 2000 to January 20th 2017 to investigate the multifractal behavior of price change and volume change series. Then, we used multifractal detrended cross-correlations analysis method (MF-DCCA) and multifractal detrended fluctuation analysis (MF-DFA) to analyze the series. We computed bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross-correlations. Furthermore, we used detrended cross-correlations coefficient (DCCA) and cross-correlation test (Q(m)) to analyze cross-correlation quantitatively and qualitatively. By analyzing results, we found existence of price-volume multifractal cross-correlations. The spectrum width has a strong multifractal cross-correlation. We remarked that volume change series is anti-persistent when we analyzed the generalized Hurst exponent for all moments q. The cross-correlation test showed the presence of a significant cross-correlation. However, DCCA coefficient had a small positive value, which means that the level of correlation is not very significant. Finally, we analyzed sources of multifractality and their degree of contribution in the series.

Multifractal diffusion entropy analysis: Optimal bin width of probability histograms

NASA Astrophysics Data System (ADS)

Jizba, Petr; Korbel, Jan

2014-11-01

In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of Rényi’s entropy and the mean squared error analysis to discuss the conditions under which the error in the multifractal spectrum estimation is minimal. We illustrate the utility of our approach by focusing on a scaling behavior of financial time series. In particular, we analyze the S&P500 stock index as sampled at a daily rate in the time period 1950-2013. In order to demonstrate a strength of the method proposed we compare the multifractal δ-spectrum for various bin-widths and show the robustness of the method, especially for large values of q. For such values, other methods in use, e.g., those based on moment estimation, tend to fail for heavy-tailed data or data with long correlations. Connection between the δ-spectrum and Rényi’s q parameter is also discussed and elucidated on a simple example of multiscale time series.

Multifractal vector fields and stochastic Clifford algebra.

PubMed

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2015-12-01

In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

The effects of common risk factors on stock returns: A detrended cross-correlation analysis

NASA Astrophysics Data System (ADS)

Ruan, Qingsong; Yang, Bingchan

2017-10-01

In this paper, we investigate the cross-correlations between Fama and French three factors and the return of American industries on the basis of cross-correlation statistic test and multifractal detrended cross-correlation analysis (MF-DCCA). Qualitatively, we find that the return series of Fama and French three factors and American industries were overall significantly cross-correlated based on the analysis of a statistic. Quantitatively, we find that the cross-correlations between three factors and the return of American industries were strongly multifractal, and applying MF-DCCA we also investigate the cross-correlation of industry returns and residuals. We find that there exists multifractality of industry returns and residuals. The result of correlation coefficients we can verify that there exist other factors which influence the industry returns except Fama three factors.

Asymmetric multiscale multifractal analysis of wind speed signals

NASA Astrophysics Data System (ADS)

Zhang, Xiaonei; Zeng, Ming; Meng, Qinghao

We develop a new method called asymmetric multiscale multifractal analysis (A-MMA) to explore the multifractality and asymmetric autocorrelations of the signals with a variable scale range. Three numerical experiments are provided to demonstrate the effectiveness of our approach. Then, the proposed method is applied to investigate multifractality and asymmetric autocorrelations of difference sequences between wind speed fluctuations with uptrends or downtrends. The results show that these sequences appear to be far more complex and contain abundant fractal dynamics information. Through analyzing the Hurst surfaces of nine difference sequences, we found that all series exhibit multifractal properties and multiscale structures. Meanwhile, the asymmetric autocorrelations are observed in all variable scale ranges and the asymmetry results are of good consistency within a certain spatial range. The sources of multifractality and asymmetry in nine difference series are further discussed using the corresponding shuffled series and surrogate series. We conclude that the multifractality of these series is due to both long-range autocorrelation and broad probability density function, but the major source of multifractality is long-range autocorrelation, and the source of asymmetry is affected by the spatial distance.

Multifractal behavior of an air pollutant time series and the relevance to the predictability.

PubMed

Dong, Qingli; Wang, Yong; Li, Peizhi

2017-03-01

Compared with the traditional method of detrended fluctuation analysis, which is used to characterize fractal scaling properties and long-range correlations, this research provides new insight into the multifractality and predictability of a nonstationary air pollutant time series using the methods of spectral analysis and multifractal detrended fluctuation analysis. First, the existence of a significant power-law behavior and long-range correlations for such series are verified. Then, by employing shuffling and surrogating procedures and estimating the scaling exponents, the major source of multifractality in these pollutant series is found to be the fat-tailed probability density function. Long-range correlations also partly contribute to the multifractal features. The relationship between the predictability of the pollutant time series and their multifractal nature is then investigated with extended analyses from the quantitative perspective, and it is found that the contribution of the multifractal strength of long-range correlations to the overall multifractal strength can affect the predictability of a pollutant series in a specific region to some extent. The findings of this comprehensive study can help to better understand the mechanisms governing the dynamics of air pollutant series and aid in performing better meteorological assessment and management. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Smoothing Technique for the Multifractal Analysis of a Medium Voltage Feeders Electric Current

NASA Astrophysics Data System (ADS)

de Santis, Enrico; Sadeghian, Alireza; Rizzi, Antonello

2017-12-01

The current paper presents a data-driven detrending technique allowing to smooth complex sinusoidal trends from a real-world electric load time series before applying the Detrended Multifractal Fluctuation Analysis (MFDFA). The algorithm we call Smoothed Sort and Cut Fourier Detrending (SSC-FD) is based on a suitable smoothing of high power periodicities operating directly in the Fourier spectrum through a polynomial fitting technique of the DFT. The main aim consists of disambiguating the characteristic slow varying periodicities, that can impair the MFDFA analysis, from the residual signal in order to study its correlation properties. The algorithm performances are evaluated on a simple benchmark test consisting of a persistent series where the Hurst exponent is known, with superimposed ten sinusoidal harmonics. Moreover, the behavior of the algorithm parameters is assessed computing the MFDFA on the well-known sunspot data, whose correlation characteristics are reported in literature. In both cases, the SSC-FD method eliminates the apparent crossover induced by the synthetic and natural periodicities. Results are compared with some existing detrending methods within the MFDFA paradigm. Finally, a study of the multifractal characteristics of the electric load time series detrendended by the SSC-FD algorithm is provided, showing a strong persistent behavior and an appreciable amplitude of the multifractal spectrum that allows to conclude that the series at hand has multifractal characteristics.

A non linear analysis of human gait time series based on multifractal analysis and cross correlations

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, A.

2005-01-01

We analyzed databases with gait time series of adults and persons with Parkinson, Huntington and amyotrophic lateral sclerosis (ALS) diseases. We obtained the staircase graphs of accumulated events that can be bounded by a straight line whose slope can be used to distinguish between gait time series from healthy and ill persons. The global Hurst exponent of these series do not show tendencies, we intend that this is because some gait time series have monofractal behavior and others have multifractal behavior so they cannot be characterized with a single Hurst exponent. We calculated the multifractal spectra, obtained the spectra width and found that the spectra of the healthy young persons are almost monofractal. The spectra of ill persons are wider than the spectra of healthy persons. In opposition to the interbeat time series where the pathology implies loss of multifractality, in the gait time series the multifractal behavior emerges with the pathology. Data were collected from healthy and ill subjects as they walked in a roughly circular path and they have sensors in both feet, so we have one time series for the left foot and other for the right foot. First, we analyzed these time series separately, and then we compared both results, with direct comparison and with a cross correlation analysis. We tried to find differences in both time series that can be used as indicators of equilibrium problems.

Multifractal detrended cross-correlation analysis for two nonstationary signals.

PubMed

Zhou, Wei-Xing

2008-06-01

We propose a method called multifractal detrended cross-correlation analysis to investigate the multifractal behaviors in the power-law cross-correlations between two time series or higher-dimensional quantities recorded simultaneously, which can be applied to diverse complex systems such as turbulence, finance, ecology, physiology, geophysics, and so on. The method is validated with cross-correlated one- and two-dimensional binomial measures and multifractal random walks. As an example, we illustrate the method by analyzing two financial time series.

Nonlinear multi-analysis of agent-based financial market dynamics by epidemic system

NASA Astrophysics Data System (ADS)

Lu, Yunfan; Wang, Jun; Niu, Hongli

2015-10-01

Based on the epidemic dynamical system, we construct a new agent-based financial time series model. In order to check and testify its rationality, we compare the statistical properties of the time series model with the real stock market indices, Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index. For analyzing the statistical properties, we combine the multi-parameter analysis with the tail distribution analysis, the modified rescaled range analysis, and the multifractal detrended fluctuation analysis. For a better perspective, the three-dimensional diagrams are used to present the analysis results. The empirical research in this paper indicates that the long-range dependence property and the multifractal phenomenon exist in the real returns and the proposed model. Therefore, the new agent-based financial model can recurrence some important features of real stock markets.

Multifractal to monofractal evolution of the London street network.

PubMed

Murcio, Roberto; Masucci, A Paolo; Arcaute, Elsa; Batty, Michael

2015-12-01

We perform a multifractal analysis of the evolution of London's street network from 1786 to 2010. First, we show that a single fractal dimension, commonly associated with the morphological description of cities, does not suffice to capture the dynamics of the system. Instead, for a proper characterization of such a dynamics, the multifractal spectrum needs to be considered. Our analysis reveals that London evolves from an inhomogeneous fractal structure, which can be described in terms of a multifractal, to a homogeneous one, which converges to monofractality. We argue that London's multifractal to monofractal evolution might be a special outcome of the constraint imposed on its growth by a green belt. Through a series of simulations, we show that multifractal objects, constructed through diffusion limited aggregation, evolve toward monofractality if their growth is constrained by a nonpermeable boundary.

Wavelet versus detrended fluctuation analysis of multifractal structures

NASA Astrophysics Data System (ADS)

Oświȩcimka, Paweł; Kwapień, Jarosław; Drożdż, Stanisław

2006-07-01

We perform a comparative study of applicability of the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus maxima (WTMM) method in proper detecting of monofractal and multifractal character of data. We quantify the performance of both methods by using different sorts of artificial signals generated according to a few well-known exactly soluble mathematical models: monofractal fractional Brownian motion, bifractal Lévy flights, and different sorts of multifractal binomial cascades. Our results show that in the majority of situations in which one does not know a priori the fractal properties of a process, choosing MFDFA should be recommended. In particular, WTMM gives biased outcomes for the fractional Brownian motion with different values of Hurst exponent, indicating spurious multifractality. In some cases WTMM can also give different results if one applies different wavelets. We do not exclude using WTMM in real data analysis, but it occurs that while one may apply MFDFA in a more automatic fashion, WTMM must be applied with care. In the second part of our work, we perform an analogous analysis on empirical data coming from the American and from the German stock market. For this data both methods detect rich multifractality in terms of broad f(α) , but MFDFA suggests that this multifractality is poorer than in the case of WTMM.

Multifractal Analysis for Nutritional Assessment

PubMed Central

Park, Youngja; Lee, Kichun; Ziegler, Thomas R.; Martin, Greg S.; Hebbar, Gautam; Vidakovic, Brani; Jones, Dean P.

2013-01-01

The concept of multifractality is currently used to describe self-similar and complex scaling properties observed in numerous biological signals. Fractals are geometric objects or dynamic variations which exhibit some degree of similarity (irregularity) to the original object in a wide range of scales. This approach determines irregularity of biologic signal as an indicator of adaptability, the capability to respond to unpredictable stress, and health. In the present work, we propose the application of multifractal analysis of wavelet-transformed proton nuclear magnetic resonance (1H NMR) spectra of plasma to determine nutritional insufficiency. For validation of this method on 1H NMR signal of human plasma, standard deviation from classical statistical approach and Hurst exponent (H), left slope and partition function from multifractal analysis were extracted from 1H NMR spectra to test whether multifractal indices could discriminate healthy subjects from unhealthy, intensive care unit patients. After validation, the multifractal approach was applied to spectra of plasma from a modified crossover study of sulfur amino acid insufficiency and tested for associations with blood lipids. The results showed that standard deviation and H, but not left slope, were significantly different for sulfur amino acid sufficiency and insufficiency. Quadratic discriminant analysis of H, left slope and the partition function showed 78% overall classification accuracy according to sulfur amino acid status. Triglycerides and apolipoprotein C3 were significantly correlated with a multifractal model containing H, left slope, and standard deviation, and cholesterol and high-sensitivity C-reactive protein were significantly correlated to H. In conclusion, multifractal analysis of 1H NMR spectra provides a new approach to characterize nutritional status. PMID:23990878

Multifractal Desynchronization of the Cardiac Excitable Cell Network During Atrial Fibrillation. I. Multifractal Analysis of Clinical Data.

PubMed

Attuel, Guillaume; Gerasimova-Chechkina, Evgeniya; Argoul, Francoise; Yahia, Hussein; Arneodo, Alain

2017-01-01

Atrial fibrillation (AF) is a cardiac arrhythmia characterized by rapid and irregular atrial electrical activity with a high clinical impact on stroke incidence. Best available therapeutic strategies combine pharmacological and surgical means. But when successful, they do not always prevent long-term relapses. Initial success becomes all the more tricky to achieve as the arrhythmia maintains itself and the pathology evolves into sustained or chronic AF. This raises the open crucial issue of deciphering the mechanisms that govern the onset of AF as well as its perpetuation. In this study, we develop a wavelet-based multi-scale strategy to analyze the electrical activity of human hearts recorded by catheter electrodes, positioned in the coronary sinus (CS), during episodes of AF. We compute the so-called multifractal spectra using two variants of the wavelet transform modulus maxima method, the moment (partition function) method and the magnitude cumulant method. Application of these methods to long time series recorded in a patient with chronic AF provides quantitative evidence of the multifractal intermittent nature of the electric energy of passing cardiac impulses at low frequencies, i.e., for times (≳0.5 s) longer than the mean interbeat (≃ 10 -1 s). We also report the results of a two-point magnitude correlation analysis which infers the absence of a multiplicative time-scale structure underlying multifractal scaling. The electric energy dynamics looks like a "multifractal white noise" with quadratic (log-normal) multifractal spectra. These observations challenge concepts of functional reentrant circuits in mechanistic theories of AF, still leaving open the role of the autonomic nervous system (ANS). A transition is indeed observed in the computed multifractal spectra which group according to two distinct areas, consistently with the anatomical substrate binding to the CS, namely the left atrial posterior wall, and the ligament of Marshall which is innervated by the ANS. In a companion paper (II. Modeling), we propose a mathematical model of a denervated heart where the kinetics of gap junction conductance alone induces a desynchronization of the myocardial excitable cells, accounting for the multifractal spectra found experimentally in the left atrial posterior wall area.

Multifractal Desynchronization of the Cardiac Excitable Cell Network During Atrial Fibrillation. I. Multifractal Analysis of Clinical Data

PubMed Central

Attuel, Guillaume; Gerasimova-Chechkina, Evgeniya; Argoul, Francoise; Yahia, Hussein; Arneodo, Alain

2018-01-01

Atrial fibrillation (AF) is a cardiac arrhythmia characterized by rapid and irregular atrial electrical activity with a high clinical impact on stroke incidence. Best available therapeutic strategies combine pharmacological and surgical means. But when successful, they do not always prevent long-term relapses. Initial success becomes all the more tricky to achieve as the arrhythmia maintains itself and the pathology evolves into sustained or chronic AF. This raises the open crucial issue of deciphering the mechanisms that govern the onset of AF as well as its perpetuation. In this study, we develop a wavelet-based multi-scale strategy to analyze the electrical activity of human hearts recorded by catheter electrodes, positioned in the coronary sinus (CS), during episodes of AF. We compute the so-called multifractal spectra using two variants of the wavelet transform modulus maxima method, the moment (partition function) method and the magnitude cumulant method. Application of these methods to long time series recorded in a patient with chronic AF provides quantitative evidence of the multifractal intermittent nature of the electric energy of passing cardiac impulses at low frequencies, i.e., for times (≳0.5 s) longer than the mean interbeat (≃ 10−1 s). We also report the results of a two-point magnitude correlation analysis which infers the absence of a multiplicative time-scale structure underlying multifractal scaling. The electric energy dynamics looks like a “multifractal white noise” with quadratic (log-normal) multifractal spectra. These observations challenge concepts of functional reentrant circuits in mechanistic theories of AF, still leaving open the role of the autonomic nervous system (ANS). A transition is indeed observed in the computed multifractal spectra which group according to two distinct areas, consistently with the anatomical substrate binding to the CS, namely the left atrial posterior wall, and the ligament of Marshall which is innervated by the ANS. In a companion paper (II. Modeling), we propose a mathematical model of a denervated heart where the kinetics of gap junction conductance alone induces a desynchronization of the myocardial excitable cells, accounting for the multifractal spectra found experimentally in the left atrial posterior wall area. PMID:29632492

Multifractal analysis of heartbeat dynamics during meditation training

NASA Astrophysics Data System (ADS)

Song, Renliang; Bian, Chunhua; Ma, Qianli D. Y.

2013-04-01

We investigate the multifractality of heartbeat dynamics during Chinese CHI meditation in healthy young adults. The results show that the range of multifractal singularity spectrum of heartbeat interval time series during meditation is significantly narrower than those in the pre-meditation state of the same subject, which indicates that during meditation the heartbeat becomes regular and the degree of multifractality decreases.

Detrending moving average algorithm for multifractals

NASA Astrophysics Data System (ADS)

Gu, Gao-Feng; Zhou, Wei-Xing

2010-07-01

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter θ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward (θ=0) , centered (θ=0.5) , and forward (θ=1) detrending windows. We find that the estimated multifractal scaling exponent τ(q) and the singularity spectrum f(α) are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.

Multifractal detrended fluctuation analysis of sheep livestock prices in origin

NASA Astrophysics Data System (ADS)

Pavón-Domínguez, P.; Serrano, S.; Jiménez-Hornero, F. J.; Jiménez-Hornero, J. E.; Gutiérrez de Ravé, E.; Ariza-Villaverde, A. B.

2013-10-01

The multifractal detrended fluctuation analysis (MF-DFA) is used to verify whether or not the returns of time series of prices paid to farmers in original markets can be described by the multifractal approach. By way of example, 5 weekly time series of prices of different breeds, slaughter weight and market differentiation from 2000 to 2012 are analyzed. Results obtained from the multifractal parameters and multifractal spectra show that the price series of livestock products are of a multifractal nature. The Hurst exponent shows that these time series are stationary signals, some of which exhibit long memory (Merino milk-fed in Seville and Segureña paschal in Jaen), short memory (Merino paschal in Cordoba and Segureña milk-fed in Jaen) or even are close to an uncorrelated signals (Merino paschal in Seville). MF-DFA is able to discern the different underlying dynamics that play an important role in different types of sheep livestock markets, such as degree and source of multifractality. In addition, the main source of multifractality of these time series is due to the broadness of the probability function, instead of the long-range correlation properties between small and large fluctuations, which play a clearly secondary role.

Multifractal analysis of charged particle distributions using horizontal visibility graph and sandbox algorithm

NASA Astrophysics Data System (ADS)

Mali, P.; Mukhopadhyay, A.; Manna, S. K.; Haldar, P. K.; Singh, G.

2017-03-01

Horizontal visibility graphs (HVGs) and the sandbox (SB) algorithm usually applied for multifractal characterization of complex network systems that are converted from time series measurements, are used to characterize the fluctuations in pseudorapidity densities of singly charged particles produced in high-energy nucleus-nucleus collisions. Besides obtaining the degree distribution associated with event-wise pseudorapidity distributions, the common set of observables, typical of any multifractality measurement, are studied in 16O-Ag/Br and 32S-Ag/Br interactions, each at an incident laboratory energy of 200 GeV/nucleon. For a better understanding, we systematically compare the experiment with a Monte Carlo model simulation based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD). Our results suggest that the HVG-SB technique is an efficient tool that can characterize multifractality in multiparticle emission data, and in some cases, it is even superior to other methods more commonly used in this regard.

Multifractal analysis of visibility graph-based Ito-related connectivity time series.

PubMed

Czechowski, Zbigniew; Lovallo, Michele; Telesca, Luciano

2016-02-01

In this study, we investigate multifractal properties of connectivity time series resulting from the visibility graph applied to normally distributed time series generated by the Ito equations with multiplicative power-law noise. We show that multifractality of the connectivity time series (i.e., the series of numbers of links outgoing any node) increases with the exponent of the power-law noise. The multifractality of the connectivity time series could be due to the width of connectivity degree distribution that can be related to the exit time of the associated Ito time series. Furthermore, the connectivity time series are characterized by persistence, although the original Ito time series are random; this is due to the procedure of visibility graph that, connecting the values of the time series, generates persistence but destroys most of the nonlinear correlations. Moreover, the visibility graph is sensitive for detecting wide "depressions" in input time series.

Multifractal detrended cross-correlation analysis on air pollutants of University of Hyderabad Campus, India

NASA Astrophysics Data System (ADS)

Manimaran, P.; Narayana, A. C.

2018-07-01

In this paper, we study the multifractal characteristics and cross-correlation behaviour of Air Pollution Index (API) time series data through multifractal detrended cross-correlation analysis method. We analyse the daily API records of nine air pollutants of the university of Hyderabad campus for a period of three years (2013-2016). The cross-correlation behaviour has been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the results, it is found that the cross-correlation analysis shows anti-correlation behaviour for all possible 36 bivariate time series. We also observe the existence of multifractal nature in all the bivariate time series in which many of them show strong multifractal behaviour. In particular, the hazardous particulate matter PM2.5 and inhalable particulate matter PM10 shows anti-correlated behaviour with all air pollutants.

Multifractal detrended cross-correlation analysis in the MENA area

NASA Astrophysics Data System (ADS)

El Alaoui, Marwane; Benbachir, Saâd

2013-12-01

In this paper, we investigated multifractal cross-correlations qualitatively and quantitatively using a cross-correlation test and the Multifractal detrended cross-correlation analysis method (MF-DCCA) for markets in the MENA area. We used cross-correlation coefficients to measure the level of this correlation. The analysis concerns four stock market indices of Morocco, Tunisia, Egypt and Jordan. The countries chosen are signatory of the Agadir agreement concerning the establishment of a free trade area comprising Arab Mediterranean countries. We computed the bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively the cross-correlations. By analyzing the results, we found the existence of multifractal cross-correlations between all of these markets. We compared the spectrum width of these indices; we also found which pair of indices has a strong multifractal cross-correlation.

Long-range memory and multifractality in gold markets

NASA Astrophysics Data System (ADS)

Mali, Provash; Mukhopadhyay, Amitabha

2015-03-01

Long-range correlation and fluctuation in the gold market time series of the world's two leading gold consuming countries, namely China and India, are studied. For both the market series during the period 1985-2013 we observe a long-range persistence of memory in the sequences of maxima (minima) of returns in successive time windows of fixed length, but the series, as a whole, are found to be uncorrelated. Multifractal analysis for these series as well as for the sequences of maxima (minima) is carried out in terms of the multifractal detrended fluctuation analysis (MF-DFA) method. We observe a weak multifractal structure for the original series that mainly originates from the fat-tailed probability distribution function of the values, and the multifractal nature of the original time series is enriched into their sequences of maximal (minimal) returns. A quantitative measure of multifractality is provided by using a set of ‘complexity parameters’.

Focused-based multifractal analysis of the wake in a wind turbine array utilizing proper orthogonal decomposition

NASA Astrophysics Data System (ADS)

Kadum, Hawwa; Ali, Naseem; Cal, Raúl

2016-11-01

Hot-wire anemometry measurements have been performed on a 3 x 3 wind turbine array to study the multifractality of the turbulent kinetic energy dissipations. A multifractal spectrum and Hurst exponents are determined at nine locations downstream of the hub height, and bottom and top tips. Higher multifractality is found at 0.5D and 1D downstream of the bottom tip and hub height. The second order of the Hurst exponent and combination factor show an ability to predict the flow state in terms of its development. Snapshot proper orthogonal decomposition is used to identify the coherent and incoherent structures and to reconstruct the stochastic velocity using a specific number of the POD eigenfunctions. The accumulation of the turbulent kinetic energy in top tip location exhibits fast convergence compared to the bottom tip and hub height locations. The dissipation of the large and small scales are determined using the reconstructed stochastic velocities. The higher multifractality is shown in the dissipation of the large scale compared to small-scale dissipation showing consistency with the behavior of the original signals.

Long-range correlation in cosmic microwave background radiation.

PubMed

Movahed, M Sadegh; Ghasemi, F; Rahvar, Sohrab; Tabar, M Reza Rahimi

2011-08-01

We investigate the statistical anisotropy and gaussianity of temperature fluctuations of Cosmic Microwave Background (CMB) radiation data from the Wilkinson Microwave Anisotropy Probe survey, using the Multifractal Detrended Fluctuation Analysis, Rescaled Range, and Scaled Windowed Variance methods. Multifractal Detrended Fluctuation Analysis shows that CMB fluctuations has a long-range correlation function with a multifractal behavior. By comparing the shuffled and surrogate series of CMB data, we conclude that the multifractality nature of the temperature fluctuation of CMB radiation is mainly due to the long-range correlations, and the map is consistent with a gaussian distribution.

Multifractal Analysis of Asian Foreign Exchange Markets and Financial Crisis

NASA Astrophysics Data System (ADS)

Oh, Gabjin; Kwon, Okyu; Jung, Woo-Sung

2012-02-01

We analyze the multifractal spectra of daily foreign exchange rates for Japan, Hong-Kong, Korea, and Thailand with respect to the United States Dollar from 1991 to 2005. We find that the return time series show multifractal spectrum features for all four cases. To observe the effect of the Asian currency crisis, we also estimate the multifractal spectra of limited series before and after the crisis. We find that the Korean and Thai foreign exchange markets experienced a significant increase in multifractality compared to Hong-Kong and Japan. We also show that the multifractality is stronge related to the presence of high values of returns in the series.

A multifractal analysis of Asian foreign exchange markets

NASA Astrophysics Data System (ADS)

Oh, G.; Eom, C.; Havlin, S.; Jung, W.-S.; Wang, F.; Stanley, H. E.; Kim, S.

2012-06-01

We analyze the multifractal spectra of daily foreign exchange rates for Japan, Hong-Kong, Korea, and Thailand with respect to the United States in the period from 1991 until 2005. We find that the return time series show multifractal spectrum features for all four cases. To observe the effect of the Asian currency crisis, we also estimate the multifractal spectra of limited series before and after the crisis. We find that the Korean and Thai foreign exchange markets experienced a significant increase in multifractality compared to Hong-Kong and Japan. We also show that the multifractality is stronger related to the presence of high values of returns in the series.

On the multifractal effects generated by monofractal signals

NASA Astrophysics Data System (ADS)

Grech, Dariusz; Pamuła, Grzegorz

2013-12-01

We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result of finite length of used data series and is additionally amplified by the long-term memory the data eventually may contain. We provide the detailed quantitative description of such apparent multifractal background signal as a threshold in spread of generalized Hurst exponent values Δh or a threshold in the width of multifractal spectrum Δα below which multifractal properties of the system are only apparent, i.e. do not exist, despite Δα≠0 or Δh≠0. We find this effect quite important for shorter or persistent series and we argue it is linear with respect to autocorrelation exponent γ. Its strength decays according to power law with respect to the length of time series. The influence of basic linear and nonlinear transformations applied to initial data in finite time series with various levels of long memory is also investigated. This provides additional set of semi-analytical results. The obtained formulas are significant in any interdisciplinary application of multifractality, including physics, financial data analysis or physiology, because they allow to separate the ‘true’ multifractal phenomena from the apparent (artificial) multifractal effects. They should be a helpful tool of the first choice to decide whether we do in particular case with the signal with real multiscaling properties or not.

Quantitative Assessment of Heart Rate Dynamics during Meditation: An ECG Based Study with Multi-Fractality and Visibility Graph

PubMed Central

Bhaduri, Anirban; Ghosh, Dipak

2016-01-01

The cardiac dynamics during meditation is explored quantitatively with two chaos-based non-linear techniques viz. multi-fractal detrended fluctuation analysis and visibility network analysis techniques. The data used are the instantaneous heart rate (in beats/minute) of subjects performing Kundalini Yoga and Chi meditation from PhysioNet. The results show consistent differences between the quantitative parameters obtained by both the analysis techniques. This indicates an interesting phenomenon of change in the complexity of the cardiac dynamics during meditation supported with quantitative parameters. The results also produce a preliminary evidence that these techniques can be used as a measure of physiological impact on subjects performing meditation. PMID:26909045

Quantitative Assessment of Heart Rate Dynamics during Meditation: An ECG Based Study with Multi-Fractality and Visibility Graph.

PubMed

Bhaduri, Anirban; Ghosh, Dipak

2016-01-01

The cardiac dynamics during meditation is explored quantitatively with two chaos-based non-linear techniques viz. multi-fractal detrended fluctuation analysis and visibility network analysis techniques. The data used are the instantaneous heart rate (in beats/minute) of subjects performing Kundalini Yoga and Chi meditation from PhysioNet. The results show consistent differences between the quantitative parameters obtained by both the analysis techniques. This indicates an interesting phenomenon of change in the complexity of the cardiac dynamics during meditation supported with quantitative parameters. The results also produce a preliminary evidence that these techniques can be used as a measure of physiological impact on subjects performing meditation.

Wavelet-based multifractal analysis of dynamic infrared thermograms to assist in early breast cancer diagnosis

PubMed Central

Gerasimova, Evgeniya; Audit, Benjamin; Roux, Stephane G.; Khalil, André; Gileva, Olga; Argoul, Françoise; Naimark, Oleg; Arneodo, Alain

2014-01-01

Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of screening X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. Here we propose a computer-aided multifractal analysis of dynamic infrared (IR) imaging as an efficient method for identifying women with risk of breast cancer. Using a wavelet-based multi-scale method to analyze the temporal fluctuations of breast skin temperature collected from a panel of patients with diagnosed breast cancer and some female volunteers with healthy breasts, we show that the multifractal complexity of temperature fluctuations observed in healthy breasts is lost in mammary glands with malignant tumor. Besides potential clinical impact, these results open new perspectives in the investigation of physiological changes that may precede anatomical alterations in breast cancer development. PMID:24860510

Graphic analysis and multifractal on percolation-based return interval series

NASA Astrophysics Data System (ADS)

Pei, A. Q.; Wang, J.

2015-05-01

A financial time series model is developed and investigated by the oriented percolation system (one of the statistical physics systems). The nonlinear and statistical behaviors of the return interval time series are studied for the proposed model and the real stock market by applying visibility graph (VG) and multifractal detrended fluctuation analysis (MF-DFA). We investigate the fluctuation behaviors of return intervals of the model for different parameter settings, and also comparatively study these fluctuation patterns with those of the real financial data for different threshold values. The empirical research of this work exhibits the multifractal features for the corresponding financial time series. Further, the VGs deviated from both of the simulated data and the real data show the behaviors of small-world, hierarchy, high clustering and power-law tail for the degree distributions.

Complexity measures of music

NASA Astrophysics Data System (ADS)

Pease, April; Mahmoodi, Korosh; West, Bruce J.

2018-03-01

We present a technique to search for the presence of crucial events in music, based on the analysis of the music volume. Earlier work on this issue was based on the assumption that crucial events correspond to the change of music notes, with the interesting result that the complexity index of the crucial events is mu ~ 2, which is the same inverse power-law index of the dynamics of the brain. The search technique analyzes music volume and confirms the results of the earlier work, thereby contributing to the explanation as to why the brain is sensitive to music, through the phenomenon of complexity matching. Complexity matching has recently been interpreted as the transfer of multifractality from one complex network to another. For this reason we also examine the mulifractality of music, with the observation that the multifractal spectrum of a computer performance is significantly narrower than the multifractal spectrum of a human performance of the same musical score. We conjecture that although crucial events are demonstrably important for information transmission, they alone are not suficient to define musicality, which is more adequately measured by the multifractality spectrum.

Forecasting volatility of SSEC in Chinese stock market using multifractal analysis

NASA Astrophysics Data System (ADS)

Wei, Yu; Wang, Peng

2008-03-01

In this paper, taking about 7 years’ high-frequency data of the Shanghai Stock Exchange Composite Index (SSEC) as an example, we propose a daily volatility measure based on the multifractal spectrum of the high-frequency price variability within a trading day. An ARFIMA model is used to depict the dynamics of this multifractal volatility (MFV) measures. The one-day ahead volatility forecasting performances of the MFV model and some other existing volatility models, such as the realized volatility model, stochastic volatility model and GARCH, are evaluated by the superior prediction ability (SPA) test. The empirical results show that under several loss functions, the MFV model obtains the best forecasting accuracy.

Multi-fractality in aeroelastic response as a precursor to flutter

NASA Astrophysics Data System (ADS)

Venkatramani, J.; Nair, Vineeth; Sujith, R. I.; Gupta, Sayan; Sarkar, Sunetra

2017-01-01

Wind tunnel tests on a NACA 0012 airfoil have been carried out to study the transition in aeroelastic response from an initial state characterised by low-amplitude aperiodic fluctuations to aeroelastic flutter when the system exhibits limit cycle oscillations. An analysis of the aeroelastic measurements reveals multi-fractal characteristics in the pre-flutter regime. This has not been studied in the literature. As the flow velocity approaches the flutter velocity from below, a gradual loss in multi-fractality is observed. Measures based on the generalised Hurst exponents are developed and are shown to have the potential to warn against impending aeroelastic flutter. The results of this study could be useful for health monitoring of aeroelastic structures.

Multifractality and Network Analysis of Phase Transition

PubMed Central

Li, Wei; Yang, Chunbin; Han, Jihui; Su, Zhu; Zou, Yijiang

2017-01-01

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems. PMID:28107414

Investigation of alterations in multifractality in optical coherence tomographic images of in vivo human retina

NASA Astrophysics Data System (ADS)

Das, Nandan Kumar; Mukhopadhyay, Sabyasachi; Ghosh, Nirmalya; Chhablani, Jay; Richhariya, Ashutosh; Divakar Rao, Kompalli; Sahoo, Naba Kishore

2016-09-01

Optical coherence tomography (OCT) enables us to monitor alterations in the thickness of the retinal layer as disease progresses in the human retina. However, subtle morphological changes in the retinal layers due to early disease progression often may not lead to detectable alterations in the thickness. OCT images encode depth-dependent backscattered intensity distribution arising due to the depth distributions of the refractive index from tissue microstructures. Here, such depth-resolved refractive index variations of different retinal layers were analyzed using multifractal detrended fluctuation analysis, a special class of multiresolution analysis tools. The analysis extracted and quantified microstructural multifractal information encoded in normal as well as diseased human retinal OCT images acquired in vivo. Interestingly, different layers of the retina exhibited different degrees of multifractality in a particular retina, and the individual layers displayed consistent multifractal trends in healthy retinas of different human subjects. In the retinal layers of diabetic macular edema (DME) subjects, the change in multifractality manifested prominently near the boundary of the DME as compared to the normal retinal layers. The demonstrated ability to quantify depth-resolved information on multifractality encoded in OCT images appears promising for the early diagnosis of diseases of the human eye, which may also prove useful for detecting other types of tissue abnormalities from OCT images.

Multifractal detrended Cross Correlation Analysis of Foreign Exchange and SENSEX fluctuation in Indian perspective

NASA Astrophysics Data System (ADS)

Dutta, Srimonti; Ghosh, Dipak; Chatterjee, Sucharita

2016-12-01

The manuscript studies autocorrelation and cross correlation of SENSEX fluctuations and Forex Exchange Rate in respect to Indian scenario. Multifractal detrended fluctuation analysis (MFDFA) and multifractal detrended cross correlation analysis (MFDXA) were employed to study the correlation between the two series. It was observed that the two series are strongly cross correlated. The change of degree of cross correlation with time was studied and the results are interpreted qualitatively.

Submicron scale tissue multifractal anisotropy in polarized laser light scattering

NASA Astrophysics Data System (ADS)

Das, Nandan Kumar; Dey, Rajib; Chakraborty, Semanti; Panigrahi, Prasanta K.; Meglinski, Igor; Ghosh, Nirmalya

2018-03-01

The spatial fluctuations of the refractive index within biological tissues exhibit multifractal anisotropy, leaving its signature as a spectral linear diattenuation of scattered polarized light. The multifractal anisotropy has been quantitatively assessed by the processing of relevant Mueller matrix elements in the Fourier domain, utilizing the Born approximation and subsequent multifractal analysis. The differential scaling exponent and width of the singularity spectrum appear to be highly sensitive to the structural multifractal anisotropy at the micron/sub-micron length scales. An immediate practical use of these multifractal anisotropy parameters was explored for non-invasive screening of cervical precancerous alterations ex vivo, with the indication of a strong potential for clinical diagnostic purposes.

Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Yuan, Ying; Zhuang, Xin-tian; Jin, Xiu

2009-06-01

Analyzing the Shanghai stock price index daily returns using MF-DFA method, it is found that there are two different types of sources for multifractality in time series, namely, fat-tailed probability distributions and non-linear temporal correlations. Based on that, a sliding window of 240 frequency data in 5 trading days was used to study stock price index fluctuation. It is found that when the stock price index fluctuates sharply, a strong variability is clearly characterized by the generalized Hurst exponents h(q). Therefore, two measures, Δh and σ, based on generalized Hurst exponents were proposed to compare financial risks before and after Price Limits and Reform of Non-tradable Shares. The empirical results verify the validity of the measures, and this has led to a better understanding of complex stock markets.

A copula-multifractal volatility hedging model for CSI 300 index futures

NASA Astrophysics Data System (ADS)

Wei, Yu; Wang, Yudong; Huang, Dengshi

2011-11-01

In this paper, we propose a new hedging model combining the newly introduced multifractal volatility (MFV) model and the dynamic copula functions. Using high-frequency intraday quotes of the spot Shanghai Stock Exchange Composite Index (SSEC), spot China Securities Index 300 (CSI 300), and CSI 300 index futures, we compare the direct and cross hedging effectiveness of the copula-MFV model with several popular copula-GARCH models. The main empirical results show that the proposed copula-MFV model obtains better hedging effectiveness than the copula-GARCH-type models in general. Furthermore, the hedge operating strategy based MFV hedging model involves fewer transaction costs than those based on the GARCH-type models. The finding of this paper indicates that multifractal analysis may offer a new way of quantitative hedging model design using financial futures.

Scaling and stochastic cascade properties of NEMO oceanic simulations and their potential value for GCM evaluation and downscaling

NASA Astrophysics Data System (ADS)

Verrier, Sébastien; Crépon, Michel; Thiria, Sylvie

2014-09-01

Spectral scaling properties have already been evidenced on oceanic numerical simulations and have been subject to several interpretations. They can be used to evaluate classical turbulence theories that predict scaling with specific exponents and to evaluate the quality of GCM outputs from a statistical and multiscale point of view. However, a more complete framework based on multifractal cascades is able to generalize the classical but restrictive second-order spectral framework to other moment orders, providing an accurate description of probability distributions of the fields at multiple scales. The predictions of this formalism still needed systematic verification in oceanic GCM while they have been confirmed recently for their atmospheric counterparts by several papers. The present paper is devoted to a systematic analysis of several oceanic fields produced by the NEMO oceanic GCM. Attention is focused to regional, idealized configurations that permit to evaluate the NEMO engine core from a scaling point of view regardless of limitations involved by land masks. Based on classical multifractal analysis tools, multifractal properties were evidenced for several oceanic state variables (sea surface temperature and salinity, velocity components, etc.). While first-order structure functions estimated a different nonconservativity parameter H in two scaling ranges, the multiorder statistics of turbulent fluxes were scaling over almost the whole available scaling range. This multifractal scaling was then parameterized with the help of the universal multifractal framework, providing parameters that are coherent with existing empirical literature. Finally, we argue that the knowledge of these properties may be useful for oceanographers. The framework seems very well suited for the statistical evaluation of OGCM outputs. Moreover, it also provides practical solutions to simulate subpixel variability stochastically for GCM downscaling purposes. As an independent perspective, the existence of multifractal properties in oceanic flows seems also interesting for investigating scale dependencies in remote sensing inversion algorithms.

Statistical characterisation of COSMO Sky-Med X-SAR retrieved precipitation fields by scale-invariance analysis

NASA Astrophysics Data System (ADS)

Deidda, Roberto; Mascaro, Giuseppe; Hellies, Matteo; Baldini, Luca; Roberto, Nicoletta

2013-04-01

COSMO Sky-Med (CSK) is an important programme of the Italian Space Agency aiming at supporting environmental monitoring and management of exogenous, endogenous and anthropogenic risks through X-band Synthetic Aperture Radar (X-SAR) on board of 4 satellites forming a constellation. Most of typical SAR applications are focused on land or ocean observation. However, X-band SAR can be detect precipitation that results in a specific signature caused by the combination of attenuation of surface returns induced by precipitation and enhancement of backscattering determined by the hydrometeors in the SAR resolution volume. Within CSK programme, we conducted an intercomparison between the statistical properties of precipitation fields derived by CSK SARs and those derived by the CNR Polar 55C (C-band) ground based weather radar located in Rome (Italy). This contribution presents main results of this research which was aimed at the robust characterisation of rainfall statistical properties across different scales by means of scale-invariance analysis and multifractal theory. The analysis was performed on a dataset of more two years of precipitation observations collected by the CNR Polar 55C radar and rainfall fields derived from available images collected by the CSK satellites during intense rainfall events. Scale-invariance laws and multifractal properties were detected on the most intense rainfall events derived from the CNR Polar 55C radar for spatial scales from 4 km to 64 km. The analysis on X-SAR retrieved rainfall fields, although based on few images, leaded to similar results and confirmed the existence of scale-invariance and multifractal properties for scales larger than 4 km. These outcomes encourage investigating SAR methodologies for future development of meteo-hydrological forecasting models based on multifractal theory.

Multifractal analysis of macro- and microcerebral circulation in rats

NASA Astrophysics Data System (ADS)

Pavlov, Alexey N.; Sindeeva, Olga S.; Sindeev, Sergey S.; Pavlova, Olga N.; Abdurashitov, Arkady S.; Rybalova, Elena V.; Semyachkina-Glushkovskaya, Oxana V.

2016-04-01

Application of noninvasive optical coherent-domain methods and advanced data processing tools such as the wavelet-based multifractal formalism allows revealing effective markers of early stages of functional distortions in the dynamics of cerebral vessels. Based on experiments performed in rats we discuss a possibility to diagnose a hidden stage of the development of intracranial hemorrhage (ICH). We also consider responses of the cerebrovascular dynamics to a pharmacologically induced increase in the peripheral blood pressure. We report distinctions occurring at the levels of macro- and microcerebral circulation.

Multifractal analysis of electronic cardiogram taken from healthy and unhealthy adult subjects

NASA Astrophysics Data System (ADS)

Wang, Jun; Ning, Xinbao; Chen, Ying

2003-05-01

Electronic Cardiogram (ECG) data taken from healthy adult subjects are found to characterize multifractality. In order to quantitatively analyze multifractal spectrum, the area of the spectrum is computed. We have a comparison between the spectrum of the young subjects and that of the old ones. We find that the area of young adult subject's multifractal spectrum is far larger than the older one's and the logarithm of the area of the spectrum is inversely proportion to age. It shows that when time is running on human heartbeat energy is exponentially decreasing until heart failure. And distinct difference between the area of the multifractal spectrum of healthy subjects and that of having coronary disease is not found. We analyze the ECG data taken from patients with brain injury. The area of their ECG multifractal spectrum is distinctly descending. It shows that a person's multifractal spectrum is controlled mainly by his neurosystem. With advancing age, the neuroautonomic control of people's body on the ECG decreases and tends from multifractality to monofractality.

Multifractal structures for the Russian stock market

NASA Astrophysics Data System (ADS)

Ikeda, Taro

2018-02-01

In this paper, we apply the multifractal detrended fluctuation analysis (MFDFA) to the Russian stock price returns. To the best of our knowledge, this paper is the first to reveal the multifractal structures for the Russian stock market by financial crises. The contributions of the paper are twofold. (i) Finding the multifractal structures for the Russian stock market. The generalized Hurst exponents estimated become highly-nonlinear to the order of the fluctuation functions. (ii) Computing the multifractality degree according to Zunino et al. (2008). We find that the multifractality degree of the Russian stock market can be categorized within emerging markets, however, the Russian 1998 crisis and the global financial crisis dampen the degree when we consider the order of the polynomial trends in the MFDFA.

MULTIFRACTAL STRUCTURES DETECTED BY VOYAGER 1 AT THE HELIOSPHERIC BOUNDARIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Macek, W. M.; Wawrzaszek, A.; Burlaga, L. F., E-mail: macek@cbk.waw.pl, E-mail: anna.wawrzaszek@cbk.waw.pl, E-mail: lburlagahsp@verizon.net

To better understand the dynamics of turbulent systems, we have proposed a phenomenological model based on a generalized Cantor set with two rescaling and one weight parameters. In this Letter, using recent Voyager 1 magnetic field data, we extend our two-scale multifractal analysis further in the heliosheath beyond the heliospheric termination shock, and even now near the heliopause, when entering the interstellar medium for the first time in human history. We have identified the scaling inertial region for magnetized heliospheric plasma between the termination shock and the heliopause. We also show that the degree of multifractality decreases with the heliocentricmore » distance and is still modulated by the phases of the solar cycle in the entire heliosphere including the heliosheath. Moreover, we observe the change of scaling toward a nonintermittent (nonmultifractal) behavior in the nearby interstellar medium, just beyond the heliopause. We argue that this loss of multifractal behavior could be a signature of the expected crossing of the heliopause by Voyager 2 in the near future. The results obtained demonstrate that our phenomenological multifractal model exhibits some properties of intermittent turbulence in the solar system plasmas, and we hope that it could shed light on universal characteristics of turbulence.« less

Magnetic resonance image segmentation using multifractal techniques

NASA Astrophysics Data System (ADS)

Yu, Yue-e.; Wang, Fang; Liu, Li-lin

2015-11-01

In order to delineate target region for magnetic resonance image (MRI) with diseases, the classical multifractal spectrum (MFS)-segmentation method and latest multifractal detrended fluctuation spectrum (MF-DFS)-based segmentation method are employed in our study. One of our main conclusions from experiments is that both of the two multifractal-based methods are workable for handling MRIs. The best result is obtained by MF-DFS-based method using Lh10 as local characteristic. The anti-noises experiments also suppot the conclusion. This interest finding shows that the features can be better represented by the strong fluctuations instead of the weak fluctuations for the MRIs. By comparing the multifractal nature between lesion and non-lesion area on the basis of the segmentation results, an interest finding is that the gray value's fluctuation in lesion area is much severer than that in non-lesion area.

Multi-fractal detrended texture feature for brain tumor classification

NASA Astrophysics Data System (ADS)

Reza, Syed M. S.; Mays, Randall; Iftekharuddin, Khan M.

2015-03-01

We propose a novel non-invasive brain tumor type classification using Multi-fractal Detrended Fluctuation Analysis (MFDFA) [1] in structural magnetic resonance (MR) images. This preliminary work investigates the efficacy of the MFDFA features along with our novel texture feature known as multifractional Brownian motion (mBm) [2] in classifying (grading) brain tumors as High Grade (HG) and Low Grade (LG). Based on prior performance, Random Forest (RF) [3] is employed for tumor grading using two different datasets such as BRATS-2013 [4] and BRATS-2014 [5]. Quantitative scores such as precision, recall, accuracy are obtained using the confusion matrix. On an average 90% precision and 85% recall from the inter-dataset cross-validation confirm the efficacy of the proposed method.

Multifractality of laser beam spatial intensity in a turbulent medium

NASA Astrophysics Data System (ADS)

Barille, Régis; Lapenna, Paolo

2006-05-01

We present the results of a laser beam passing through a turbulent medium. First we measure the geometric parameters and the spatial coherence of the beam as a function of wind velocities. A multifractal detrended fluctuation analysis algorithm is applied to determine the multifractal scaling behavior of the intensity patterns. The measurements are fitted with models used in the analysis of river runoff records. We show the surprising result that the multifractality decreases when the spatial coherence of the laser is decreased. Universal scaling properties could be applied to the spatial characterization of a laser propagating in a turbulent medium or random medium.

Multifractal Turbulence in the Heliosphere

NASA Astrophysics Data System (ADS)

Macek, Wieslaw M.; Wawrzaszek, Anna

2010-05-01

We consider a solar wind plasma with frozen-in interplanetary magnetic fields, which is a complex nonlinear system that may exhibit chaos and intermittency, resulting in a multifractal scaling of plasma characteristics. We analyze time series of plasma velocity and interplanetary magnetic field strengths measured during space missions onboard various spacecraft, such as Helios, Advanced Composition Explorer, Ulysses, and Voyager, exploring different regions of the heliosphere during solar minimum and maximum. To quantify the multifractality of solar wind turbulence, we use a generalized two-scale weighted Cantor set with two different rescaling parameters [1]. We investigate the resulting spectrum of generalized dimensions and the corresponding multifractal singularity spectrum depending on the parameters of this new cascade model [2]. We show that using the model with two different scaling parameters one can explain the multifractal singularity spectrum, which is often asymmetric. In particular, the multifractal scaling of magnetic fields is asymmetric in the outer heliosphere, in contrast to the symmetric spectrum observed in the heliosheath as described by the standard one-scale model [3]. We hope that the generalized multifractal model will be a useful tool for analysis of intermittent turbulence in the heliospheric plasma. We thus believe that multifractal analysis of various complex environments can shed light on the nature of turbulence. [1] W. M. Macek and A. Szczepaniak, Generalized two-scale weighted Cantor set model for solar wind turbulence, Geophys. Res. Lett., 35, L02108 (2008), doi:10.1029/2007GL032263. [2] W. M. Macek and A. Wawrzaszek, Evolution of asymmetric multifractal scaling of solar wind turbulence in the outer heliosphere, J. Geophys. Res., A013795 (2009), doi:10.1029/2008JA013795. [3] W. M. Macek and A. Wawrzaszek, Multifractal turbulence at the termination shock, in Solar Wind Twelve, edited by M. Maximovic et al., American Institute of Physics, 2010.

Complex multifractal nature in Mycobacterium tuberculosis genome

PubMed Central

Mandal, Saurav; Roychowdhury, Tanmoy; Chirom, Keilash; Bhattacharya, Alok; Brojen Singh, R. K.

2017-01-01

The mutifractal and long range correlation (C(r)) properties of strings, such as nucleotide sequence can be a useful parameter for identification of underlying patterns and variations. In this study C(r) and multifractal singularity function f(α) have been used to study variations in the genomes of a pathogenic bacteria Mycobacterium tuberculosis. Genomic sequences of M. tuberculosis isolates displayed significant variations in C(r) and f(α) reflecting inherent differences in sequences among isolates. M. tuberculosis isolates can be categorised into different subgroups based on sensitivity to drugs, these are DS (drug sensitive isolates), MDR (multi-drug resistant isolates) and XDR (extremely drug resistant isolates). C(r) follows significantly different scaling rules in different subgroups of isolates, but all the isolates follow one parameter scaling law. The richness in complexity of each subgroup can be quantified by the measures of multifractal parameters displaying a pattern in which XDR isolates have highest value and lowest for drug sensitive isolates. Therefore C(r) and multifractal functions can be useful parameters for analysis of genomic sequences. PMID:28440326

Complex multifractal nature in Mycobacterium tuberculosis genome

NASA Astrophysics Data System (ADS)

Mandal, Saurav; Roychowdhury, Tanmoy; Chirom, Keilash; Bhattacharya, Alok; Brojen Singh, R. K.

2017-04-01

The mutifractal and long range correlation (C(r)) properties of strings, such as nucleotide sequence can be a useful parameter for identification of underlying patterns and variations. In this study C(r) and multifractal singularity function f(α) have been used to study variations in the genomes of a pathogenic bacteria Mycobacterium tuberculosis. Genomic sequences of M. tuberculosis isolates displayed significant variations in C(r) and f(α) reflecting inherent differences in sequences among isolates. M. tuberculosis isolates can be categorised into different subgroups based on sensitivity to drugs, these are DS (drug sensitive isolates), MDR (multi-drug resistant isolates) and XDR (extremely drug resistant isolates). C(r) follows significantly different scaling rules in different subgroups of isolates, but all the isolates follow one parameter scaling law. The richness in complexity of each subgroup can be quantified by the measures of multifractal parameters displaying a pattern in which XDR isolates have highest value and lowest for drug sensitive isolates. Therefore C(r) and multifractal functions can be useful parameters for analysis of genomic sequences.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr

In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge upmore » the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.« less

Multiscale multifractal time irreversibility analysis of stock markets

NASA Astrophysics Data System (ADS)

Jiang, Chenguang; Shang, Pengjian; Shi, Wenbin

2016-11-01

Time irreversibility is one of the most important properties of nonstationary time series. Complex time series often demonstrate even multiscale time irreversibility, such that not only the original but also coarse-grained time series are asymmetric over a wide range of scales. We study the multiscale time irreversibility of time series. In this paper, we develop a method called multiscale multifractal time irreversibility analysis (MMRA), which allows us to extend the description of time irreversibility to include the dependence on the segment size and statistical moments. We test the effectiveness of MMRA in detecting multifractality and time irreversibility of time series generated from delayed Henon map and binomial multifractal model. Then we employ our method to the time irreversibility analysis of stock markets in different regions. We find that the emerging market has higher multifractality degree and time irreversibility compared with developed markets. In this sense, the MMRA method may provide new angles in assessing the evolution stage of stock markets.

Coupling detrended fluctuation analysis of Asian stock markets

NASA Astrophysics Data System (ADS)

Wang, Qizhen; Zhu, Yingming; Yang, Liansheng; Mul, Remco A. H.

2017-04-01

This paper uses the coupling detrended fluctuation analysis (CDFA) method to investigate the multifractal characteristics of four Asian stock markets using three stock indices: stock price returns, trading volumes and the composite index. The results show that coupled correlations exist among the four stock markets and the coupled correlations have multifractal characteristics. We then use the chi square (χ2) test to identify the sources of multifractality. For the different stock indices, the contributions of a single series to multifractality are different. In other words, the contributions of each country to coupled correlations are different. The comparative analysis shows that the research on the combine effect of stock price returns and trading volumes may be more comprehensive than on an individual index. By comparing the strength of multifractality for original data with the residual errors of the vector autoregression (VAR) model, we find that the VAR model could not be used to describe the dynamics of the coupled correlations among four financial time series.

Multifractal characteristics of multiparticle production in heavy-ion collisions at SPS energies

NASA Astrophysics Data System (ADS)

Khan, Shaista; Ahmad, Shakeel

Entropy, dimensions and other multifractal characteristics of multiplicity distributions of relativistic charged hadrons produced in ion-ion collisions at SPS energies are investigated. The analysis of the experimental data is carried out in terms of phase space bin-size dependence of multiplicity distributions following the Takagi’s approach. Yet another method is also followed to study the multifractality which, is not related to the bin-width and (or) the detector resolution, rather involves multiplicity distribution of charged particles in full phase space in terms of information entropy and its generalization, Rényi’s order-q information entropy. The findings reveal the presence of multifractal structure — a remarkable property of the fluctuations. Nearly constant values of multifractal specific heat “c” estimated by the two different methods of analysis followed indicate that the parameter “c” may be used as a universal characteristic of the particle production in high energy collisions. The results obtained from the analysis of the experimental data agree well with the predictions of Monte Carlo model AMPT.

Nonuniversality of the Archie exponent due to multifractality of resistivity well logs

NASA Astrophysics Data System (ADS)

Dashtian, Hassan; Yang, Yafan; Sahimi, Muhammad

2015-12-01

Archie's law expresses a relation between the formation factor F of porous media and their porosity ϕ, F∝ϕ-m, where m is the Archie or the cementation exponent. Despite widespread use of Archie's law, the value of m and whether it is universal and independent of the type of reservoir have remained controversial. We analyze various porosity and resistivity logs along 36 wells in six Iranian oil and gas reservoirs using wavelet transform coherence and multifractal detrended fluctuation analysis. m is estimated for two sets of data: one set contains the resistivity data that include those segments of the well that contain significant clay content and one without. The analysis indicates that the well logs are multifractal and that due to the multifractality the exponent m is nonuniversal. Thus, analysis of the resistivity of laboratory or outcrop samples that are not multifractal yields estimates of m that are not applicable to well logs in oil or gas reservoirs.

Analysis of normal human retinal vascular network architecture using multifractal geometry

PubMed Central

Ţălu, Ştefan; Stach, Sebastian; Călugăru, Dan Mihai; Lupaşcu, Carmen Alina; Nicoară, Simona Delia

2017-01-01

AIM To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina. METHODS Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images, corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms, applying the standard box-counting method. Statistical analyses were performed using the GraphPad InStat software. RESULTS The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions (Dq) for q=0, 1, 2, the width of the multifractal spectrum (Δα=αmax − αmin) and the spectrum arms' heights difference (|Δf|) of the normal images were expressed as mean±standard deviation (SD): for segmented versions, D0=1.7014±0.0057; D1=1.6507±0.0058; D2=1.5772±0.0059; Δα=0.92441±0.0085; |Δf|= 0.1453±0.0051; for skeletonised versions, D0=1.6303±0.0051; D1=1.6012±0.0059; D2=1.5531±0.0058; Δα=0.65032±0.0162; |Δf|= 0.0238±0.0161. The average of generalized dimensions (Dq) for q=0, 1, 2, the width of the multifractal spectrum (Δα) and the spectrum arms' heights difference (|Δf|) of the segmented versions was slightly greater than the skeletonised versions. CONCLUSION The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases. PMID:28393036

Introduction to multifractal detrended fluctuation analysis in matlab.

PubMed

Ihlen, Espen A F

2012-01-01

Fractal structures are found in biomedical time series from a wide range of physiological phenomena. The multifractal spectrum identifies the deviations in fractal structure within time periods with large and small fluctuations. The present tutorial is an introduction to multifractal detrended fluctuation analysis (MFDFA) that estimates the multifractal spectrum of biomedical time series. The tutorial presents MFDFA step-by-step in an interactive Matlab session. All Matlab tools needed are available in Introduction to MFDFA folder at the website www.ntnu.edu/inm/geri/software. MFDFA are introduced in Matlab code boxes where the reader can employ pieces of, or the entire MFDFA to example time series. After introducing MFDFA, the tutorial discusses the best practice of MFDFA in biomedical signal processing. The main aim of the tutorial is to give the reader a simple self-sustained guide to the implementation of MFDFA and interpretation of the resulting multifractal spectra.

Introduction to Multifractal Detrended Fluctuation Analysis in Matlab

PubMed Central

Ihlen, Espen A. F.

2012-01-01

Fractal structures are found in biomedical time series from a wide range of physiological phenomena. The multifractal spectrum identifies the deviations in fractal structure within time periods with large and small fluctuations. The present tutorial is an introduction to multifractal detrended fluctuation analysis (MFDFA) that estimates the multifractal spectrum of biomedical time series. The tutorial presents MFDFA step-by-step in an interactive Matlab session. All Matlab tools needed are available in Introduction to MFDFA folder at the website www.ntnu.edu/inm/geri/software. MFDFA are introduced in Matlab code boxes where the reader can employ pieces of, or the entire MFDFA to example time series. After introducing MFDFA, the tutorial discusses the best practice of MFDFA in biomedical signal processing. The main aim of the tutorial is to give the reader a simple self-sustained guide to the implementation of MFDFA and interpretation of the resulting multifractal spectra. PMID:22675302

Multifractal analysis of Moroccan family business stock returns

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2017-11-01

In this paper, long-range temporal correlations at different scales in Moroccan family business stock returns are investigated. For comparison purpose, presence of multifractality is also investigated in Casablanca Stock Exchange (CSE) major indices: MASI which is the all shares index and MADEX which is the index of most liquid shares. It is found that return series of both family business companies and major stock market indices show strong evidence of multifractality. In particular, empirical results reveal that short (long) fluctuations in family business stock returns are less (more) persistent (anti-persistent) than short fluctuations in market indices. In addition, both serial correlation and distribution characteristics significantly influence the strength of the multifractal spectrums of CSE and family business stocks returns. Furthermore, results from multifractal spectrum analysis suggest that family business stocks are less risky. Thus, such differences in price dynamics could be exploited by investors and forecasters in active portfolio management.

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel

PubMed Central

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel. PMID:26121468

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.

PubMed

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.

Multifractal Analysis of Human Heartbeat in Sleep

NASA Astrophysics Data System (ADS)

Ding, Liang-Jing; Peng, Hu; Cai, Shi-Min; Zhou, Pei-Ling

2007-07-01

We study the dynamical properties of heart rate variability (HRV) in sleep by analysing the scaling behaviour with the multifractal detrended fluctuation analysis method. It is well known that heart rate is regulated by the interaction of two branches of the autonomic nervous system: the parasympathetic and sympathetic nervous systems. By investigating the multifractal properties of light, deep, rapid-eye-movement (REM) sleep and wake stages, we firstly find an increasing multifractal behaviour during REM sleep which may be caused by augmented sympathetic activities relative to non-REM sleep. In addition, the investigation of long-range correlations of HRV in sleep with second order detrended fluctuation analysis presents irregular phenomena. These findings may be helpful to understand the underlying regulating mechanism of heart rate by autonomic nervous system during wake-sleep transitions.

Multifractal detrended fluctuation analysis to characterize phase couplings in seahorse (Hippocampus kuda) feeding clicks.

PubMed

Haris, K; Chakraborty, Bishwajit; Menezes, A; Sreepada, R A; Fernandes, W A

2014-10-01

Nonlinear phenomena in animal vocalizations fundamentally includes known features, namely, frequency jump, subharmonics, biphonation, and deterministic chaos. In the present study, the multifractal detrended fluctuation analysis (MFDFA) has been employed to characterize the phase couplings revealed in the feeding clicks of Hippocampus kuda yellow seahorse. The fluctuation function Fq(s), generalized Hurst exponent h(q), multifractal scaling exponent τ(q), and the multifractal spectrum f(α) calculated in the procedure followed were analyzed to comprehend the underlying nonlinearities in the seahorse clicks. The analyses carried out reveal long-range power-law correlation properties in the data, substantiating the multifractal behavior. The resulting h(q) spectrum exhibits a distinct characteristic pattern in relation to the seahorse sex and size, and reveals a spectral blind spot in the data that was not possible to detect by conventional spectral analyses. The corresponding multifractal spectrum related width parameter Δh(q) is well clustered, defining the individual seahorse clicks. The highest degree of multifractality is evident in the 18 cm male seahorse, signifying greater heterogeneity. A further comparison between the seahorse body size and weight (wet) with respect to the width parameter Δh(q) and the second-order Hurst exponent h(q=2) underscores the versatility of MFDFA as a robust statistical tool to analyze bioacoustic observations.

The origins of multifractality in financial time series and the effect of extreme events

NASA Astrophysics Data System (ADS)

Green, Elena; Hanan, William; Heffernan, Daniel

2014-06-01

This paper presents the results of multifractal testing of two sets of financial data: daily data of the Dow Jones Industrial Average (DJIA) index and minutely data of the Euro Stoxx 50 index. Where multifractal scaling is found, the spectrum of scaling exponents is calculated via Multifractal Detrended Fluctuation Analysis. In both cases, further investigations reveal that the temporal correlations in the data are a more significant source of the multifractal scaling than are the distributions of the returns. It is also shown that the extreme events which make up the heavy tails of the distribution of the Euro Stoxx 50 log returns distort the scaling in the data set. The most extreme events are inimical to the scaling regime. This result is in contrast to previous findings that extreme events contribute to multifractality.

Determination of key parameters of vector multifractal vector fields

NASA Astrophysics Data System (ADS)

Schertzer, D. J. M.; Tchiguirinskaia, I.

2017-12-01

For too long time, multifractal analyses and simulations have been restricted to scalar-valued fields (Schertzer and Tchiguirinskaia, 2017a,b). For instance, the wind velocity multifractality has been mostly analysed in terms of scalar structure functions and with the scalar energy flux. This restriction has had the unfortunate consequences that multifractals were applicable to their full extent in geophysics, whereas it has inspired them. Indeed a key question in geophysics is the complexity of the interactions between various fields or they components. Nevertheless, sophisticated methods have been developed to determine the key parameters of scalar valued fields. In this communication, we first present the vector extensions of the universal multifractal analysis techniques to multifractals whose generator belong to a Levy-Clifford algebra (Schertzer and Tchiguirinskaia, 2015). We point out further extensions noting the increased complexity. For instance, the (scalar) index of multifractality becomes a matrice. Schertzer, D. and Tchiguirinskaia, I. (2015) `Multifractal vector fields and stochastic Clifford algebra', Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p. 123127. doi: 10.1063/1.4937364. Schertzer, D. and Tchiguirinskaia, I. (2017) `An Introduction to Multifractals and Scale Symmetry Groups', in Ghanbarian, B. and Hunt, A. (eds) Fractals: Concepts and Applications in Geosciences. CRC Press, p. (in press). Schertzer, D. and Tchiguirinskaia, I. (2017b) `Pandora Box of Multifractals: Barely Open ?', in Tsonis, A. A. (ed.) 30 Years of Nonlinear Dynamics in Geophysics. Berlin: Springer, p. (in press).

Fractal analysis of the dark matter and gas distributions in the Mare-Nostrum universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaite, José, E-mail: jose.gaite@upm.es

2010-03-01

We develop a method of multifractal analysis of N-body cosmological simulations that improves on the customary counts-in-cells method by taking special care of the effects of discreteness and large scale homogeneity. The analysis of the Mare-Nostrum simulation with our method provides strong evidence of self-similar multifractal distributions of dark matter and gas, with a halo mass function that is of Press-Schechter type but has a power-law exponent -2, as corresponds to a multifractal. Furthermore, our analysis shows that the dark matter and gas distributions are indistinguishable as multifractals. To determine if there is any gas biasing, we calculate the cross-correlationmore » coefficient, with negative but inconclusive results. Hence, we develop an effective Bayesian analysis connected with information theory, which clearly demonstrates that the gas is biased in a long range of scales, up to the scale of homogeneity. However, entropic measures related to the Bayesian analysis show that this gas bias is small (in a precise sense) and is such that the fractal singularities of both distributions coincide and are identical. We conclude that this common multifractal cosmic web structure is determined by the dynamics and is independent of the initial conditions.« less

Statistical properties of the yuan exchange rate index

NASA Astrophysics Data System (ADS)

Wang, Dong-Hua; Yu, Xiao-Wen; Suo, Yuan-Yuan

2012-06-01

We choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after China's exchange rate system reform on the 21st July 2005. After dividing the time series into two parts according to the change in the yuan exchange rate regime in July 2008, we compare the statistical properties of the yuan exchange rate index during these two periods. We find that the distribution of the two return series has the exponential form. We also perform the detrending moving average analysis (DMA) and the multifractal detrending moving average analysis (MFDMA). The two periods possess different degrees of long-range correlations, and the multifractal nature is also unveiled in these two time series. Significant difference is found in the scaling exponents τ(q) and singularity spectra f(α) of the two periods obtained from the MFDMA analysis. Besides, in order to detect the sources of multifractality, shuffling and phase randomization procedures are applied to destroy the long-range temporal correlation and fat-tailed distribution of the yuan exchange rate index respectively. We find that the fat-tailedness plays a critical role in the sources of multifractality in the first period, while the long memory is the major cause in the second period. The results suggest that the change in China's exchange rate regime in July 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods, and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st July 2005.

Concept of Fractal Dimension use of Multifractal Cloud Liquid Models Based on Real Data as Input to Monte Carlo Radiation Models

NASA Technical Reports Server (NTRS)

Wiscombe, W.

1999-01-01

The purpose of this paper is discuss the concept of fractal dimension; multifractal statistics as an extension of this; the use of simple multifractal statistics (power spectrum, structure function) to characterize cloud liquid water data; and to understand the use of multifractal cloud liquid water models based on real data as input to Monte Carlo radiation models of shortwave radiation transfer in 3D clouds, and the consequences of this in two areas: the design of aircraft field programs to measure cloud absorptance; and the explanation of the famous "Landsat scale break" in measured radiance.

Distinguishing cognitive state with multifractal complexity of hippocampal interspike interval sequences

PubMed Central

Fetterhoff, Dustin; Kraft, Robert A.; Sandler, Roman A.; Opris, Ioan; Sexton, Cheryl A.; Marmarelis, Vasilis Z.; Hampson, Robert E.; Deadwyler, Sam A.

2015-01-01

Fractality, represented as self-similar repeating patterns, is ubiquitous in nature and the brain. Dynamic patterns of hippocampal spike trains are known to exhibit multifractal properties during working memory processing; however, it is unclear whether the multifractal properties inherent to hippocampal spike trains reflect active cognitive processing. To examine this possibility, hippocampal neuronal ensembles were recorded from rats before, during and after a spatial working memory task following administration of tetrahydrocannabinol (THC), a memory-impairing component of cannabis. Multifractal detrended fluctuation analysis was performed on hippocampal interspike interval sequences to determine characteristics of monofractal long-range temporal correlations (LRTCs), quantified by the Hurst exponent, and the degree/magnitude of multifractal complexity, quantified by the width of the singularity spectrum. Our results demonstrate that multifractal firing patterns of hippocampal spike trains are a marker of functional memory processing, as they are more complex during the working memory task and significantly reduced following administration of memory impairing THC doses. Conversely, LRTCs are largest during resting state recordings, therefore reflecting different information compared to multifractality. In order to deepen conceptual understanding of multifractal complexity and LRTCs, these measures were compared to classical methods using hippocampal frequency content and firing variability measures. These results showed that LRTCs, multifractality, and theta rhythm represent independent processes, while delta rhythm correlated with multifractality. Taken together, these results provide a novel perspective on memory function by demonstrating that the multifractal nature of spike trains reflects hippocampal microcircuit activity that can be used to detect and quantify cognitive, physiological, and pathological states. PMID:26441562

Multifractal Value at Risk model

NASA Astrophysics Data System (ADS)

Lee, Hojin; Song, Jae Wook; Chang, Woojin

2016-06-01

In this paper new Value at Risk (VaR) model is proposed and investigated. We consider the multifractal property of financial time series and develop a multifractal Value at Risk (MFVaR). MFVaR introduced in this paper is analytically tractable and not based on simulation. Empirical study showed that MFVaR can provide the more stable and accurate forecasting performance in volatile financial markets where large loss can be incurred. This implies that our multifractal VaR works well for the risk measurement of extreme credit events.

Multifractals embedded in short time series: An unbiased estimation of probability moment

NASA Astrophysics Data System (ADS)

Qiu, Lu; Yang, Tianguang; Yin, Yanhua; Gu, Changgui; Yang, Huijie

2016-12-01

An exact estimation of probability moments is the base for several essential concepts, such as the multifractals, the Tsallis entropy, and the transfer entropy. By means of approximation theory we propose a new method called factorial-moment-based estimation of probability moments. Theoretical prediction and computational results show that it can provide us an unbiased estimation of the probability moments of continuous order. Calculations on probability redistribution model verify that it can extract exactly multifractal behaviors from several hundred recordings. Its powerfulness in monitoring evolution of scaling behaviors is exemplified by two empirical cases, i.e., the gait time series for fast, normal, and slow trials of a healthy volunteer, and the closing price series for Shanghai stock market. By using short time series with several hundred lengths, a comparison with the well-established tools displays significant advantages of its performance over the other methods. The factorial-moment-based estimation can evaluate correctly the scaling behaviors in a scale range about three generations wider than the multifractal detrended fluctuation analysis and the basic estimation. The estimation of partition function given by the wavelet transform modulus maxima has unacceptable fluctuations. Besides the scaling invariance focused in the present paper, the proposed factorial moment of continuous order can find its various uses, such as finding nonextensive behaviors of a complex system and reconstructing the causality relationship network between elements of a complex system.

Comparison of Two Multifractal Analysis Methods: Generalized Structure Function and Multifractal Spectrum

NASA Astrophysics Data System (ADS)

Morato, M. Carmen; Castellanos, M. Teresa; Bird, Nigel; Tarquis, Ana M.

2016-04-01

Soil variability has often been a constant expected factor to take in account in soil studies. This variability could be considered to be composed of "functional" variations plus random fluctuations or noise. Multifractal formalism, first proposed by Mandelbrot (1982), is suitable for variables with self-similar distribution on a spatial domain. Multifractal analysis can provide insight into spatial variability of crop or soil parameters. In soil science, it has been quite popular to characterize the scaling property of a variable measured along a transect as a mass distribution of a statistical measure on a length domain of the studied transect. To do this, it divides it into a number of self similar segments and estimate the partition function and mass function. Based on this, the multifractal spectra (MFS) is calculated. However, another technique can be applied focus its attention in the variations of a measure analyzing the moments of the absolute differences at different scales, the Generalized Structure Function (GSF), and extracting the Generalized Hurst exponents. The aim of this study is to compare both techniques in a transect data. A common 1024 m transect across arable fields at Silsoe in Bedfordshire, east-central England were analyzed with these two multifractal methods. Properties studied were total porosity (Porosity), gravimetric water content (GWC) and nitrogen oxide flux (NO2 flux). The results showed in both methods that NO2 flux presents a clear multifractal character and a weak one in the GWC and Porosity cases. Several parameters were calculated from both methods and are discussed. On the other hand, using the partition function all the scale ranges were used, meanwhile in the GSF a shorter range of scales showed linear behavior in the bilog plots used to estimate the parameters. GWC exhibits a linear pattern from increments of 4 till 256 meters, Porosity showed this behavior from 4 till 64 meters. In case of NO2 flux only from 32 to 256 meters showed it. However, the relation between the mass exponent function and the GSF, found in the literature, was positively verified in the three variables.

MFDFA and Lacunarity Analysis of Synthetic Multifractals and Pre-Cancerous Tissues

NASA Astrophysics Data System (ADS)

Roy, A.; Das, N.; Ghosh, N.

2017-12-01

Multifractal Detrended Fluctuation Analysis (MFDFA) has been employed for evaluating complex variations in the refractive index (RI) of human pre-cancerous tissues. While this was primarily aimed towards the early diagnosis of cancer in the human cervix, question remains whether multifractal analysis alone can be conclusively used for distinguishing between various grades of pre-cancerous tissues. Lacunarity is a parameter that was developed for multiscale analysis of data and has been shown to be theoretically related to the correlation dimension, D2, by dlog(L)/dlog(x) = D2 - 2. Further, research has proven that not only can Lacunarity be used as a preliminary indicator of multifractal behavior but it also distinguishes between images with similar correlation dimension values. In order to compare the efficacy of the two approaches namely, MFDFA and Lacunarity, in distinguishing between pre-cancerous tissues of various grades, we test these techniques on a set of 2-dimensional theoretical random multifractal fields. MFDFA is employed for computing the width of the singularity spectrum f(α), which is a measure of multifractal behavior. A weighted mean of the log-transformed lacunarity values at different scales is employed for differentiating between patterns with the same correlation dimension but differences in texture. The two different techniques are then applied to images containing RI values of biopsy samples from human cervical tissues that were histo-pathologically characterized as grade-I and grade-II pre-cancerous cells. The results show that the two approaches are complementary to one another when it comes to multi-scale analysis of complex natural patterns manifested in the images of such pre-cancerous cells.

An analysis of stock market efficiency: Developed vs Islamic stock markets using MF-DFA

NASA Astrophysics Data System (ADS)

Rizvi, Syed Aun R.; Dewandaru, Ginanjar; Bacha, Obiyathulla I.; Masih, Mansur

An efficient market has been theoretically proven to be a key component for effective and efficient resource allocation in an economy. This paper incorporates econophysics with Efficient Market Hypothesis to undertake a comparative analysis of Islamic and developed countries’ markets by extending the understanding of their multifractal nature. By applying the Multifractal Detrended Fluctuation Analysis (MFDFA) we calculated the generalized Hurst exponents, multifractal scaling exponents and generalized multifractal dimensions for 22 broad market indices. The findings provide a deeper understanding of the markets in Islamic countries, where they have traces of highly efficient performance particularly in crisis periods. A key finding is the empirical evidence of the impact of the ‘stage of market development’ on the efficiency of the market. If Islamic countries aim to improve the efficiency of resource allocation, an important area to address is to focus, among others, on enhancing the stage of market development.

Multifractal Behaviors in Foreign Exchange Markets

NASA Astrophysics Data System (ADS)

Kim, Kyungsik; Kim, Soo Yong; Lim, Gyuchang; Scalas, Enrico; Lee, Dong-In

2008-03-01

The market information and its intensity for the context of two-phase phenomenon is introduced in financial exchange markets. To find the underlying process of the formation of market information, we investigate the multifractal properties of the market information in terms of the multifractal and the detrended fluctuation analysis and also examine the higher order correlations between successive pieces of market information. Although the multifractal properties of the market information process is clearly confirmed, the simple binomial multiplicative process is not appropriate to catch its dynamics. It means that the market information process can be essentially different from the fully developed turbulence.

Wavelets and Multifractal Analysis

DTIC Science & Technology

2004-07-01

distribution unlimited 13. SUPPLEMENTARY NOTES See also ADM001750, Wavelets and Multifractal Analysis (WAMA) Workshop held on 19-31 July 2004., The original...f)] . . . 16 2.5.4 Detrended Fluctuation Analysis [DFA(m)] . . . . . . . . . . . . . . . 17 2.6 Scale-Independent Measures...18 2.6.1 Detrended -Fluctuation- Analysis Power-Law Exponent (αD) . . . . . . 18 2.6.2 Wavelet-Transform Power-Law Exponent

Spatial analysis of cities using Renyi entropy and fractal parameters

NASA Astrophysics Data System (ADS)

Chen, Yanguang; Feng, Jian

2017-12-01

The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law distribution). The latter belongs to scale-free distributions, which can be modeled with fractal geometry. However, fractal dimension is not suitable for the former distribution. In contrast, spatial entropy can be used to measure any types of urban distributions. This paper is devoted to generalizing multifractal parameters by means of dual relation between Euclidean and fractal geometries. The main method is mathematical derivation and empirical analysis, and the theoretical foundation is the discovery that the normalized fractal dimension is equal to the normalized entropy. Based on this finding, a set of useful spatial indexes termed dummy multifractal parameters are defined for geographical analysis. These indexes can be employed to describe both the simple distributions and complex distributions. The dummy multifractal indexes are applied to the population density distribution of Hangzhou city, China. The calculation results reveal the feature of spatio-temporal evolution of Hangzhou's urban morphology. This study indicates that fractal dimension and spatial entropy can be combined to produce a new methodology for spatial analysis of city development.

Cross-correlations between RMB exchange rate and international commodity markets

NASA Astrophysics Data System (ADS)

Lu, Xinsheng; Li, Jianfeng; Zhou, Ying; Qian, Yubo

2017-11-01

This paper employs multifractal detrended analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DCCA) to study cross-correlation behaviors between China's RMB exchange rate market and four international commodity markets, using a comprehensive set of data covering the period from 22 July 2005 to 15 March 2016. Our empirical results from MF-DFA indicate that the RMB exchange rate is the most inefficient among the 4 selected markets. The results from quantitative analysis have testified the existence of cross-correlations and the result from MF-DCCA have further confirmed a strong multifractal behavior between RMB exchange rate and international commodity markets. We also demonstrate that the recent financial crisis has significant impact on the cross-correlated behavior. Through the rolling window analysis, we find that the RMB exchange rates and international commodity prices are anti-persistent cross-correlated. The main sources of multifractality in the cross-correlations are long-range correlations between RMB exchange rate and the aggregate commodity, energy and metals index.

Multifractal Analysis of Seismically Induced Soft-Sediment Deformation Structures Imaged by X-Ray Computed Tomography

NASA Astrophysics Data System (ADS)

Nakashima, Yoshito; Komatsubara, Junko

Unconsolidated soft sediments deform and mix complexly by seismically induced fluidization. Such geological soft-sediment deformation structures (SSDSs) recorded in boring cores were imaged by X-ray computed tomography (CT), which enables visualization of the inhomogeneous spatial distribution of iron-bearing mineral grains as strong X-ray absorbers in the deformed strata. Multifractal analysis was applied to the two-dimensional (2D) CT images with various degrees of deformation and mixing. The results show that the distribution of the iron-bearing mineral grains is multifractal for less deformed/mixed strata and almost monofractal for fully mixed (i.e. almost homogenized) strata. Computer simulations of deformation of real and synthetic digital images were performed using the egg-beater flow model. The simulations successfully reproduced the transformation from the multifractal spectra into almost monofractal spectra (i.e. almost convergence on a single point) with an increase in deformation/mixing intensity. The present study demonstrates that multifractal analysis coupled with X-ray CT and the mixing flow model is useful to quantify the complexity of seismically induced SSDSs, standing as a novel method for the evaluation of cores for seismic risk assessment.

Multifractal Fluctuations of Jiuzhaigou Tourists Before and after Wenchuan Earthquake

NASA Astrophysics Data System (ADS)

Shi, Kai; Li, Wen-Yong; Liu, Chun-Qiong; Huang, Zheng-Wen

2013-03-01

In this work, multifractal methods have been successfully used to characterize the temporal fluctuations of daily Jiuzhai Valley domestic and foreign tourists before and after Wenchuan earthquake in China. We used multifractal detrending moving average method (MF-DMA). It showed that Jiuzhai Valley tourism markets are characterized by long-term memory and multifractal nature in. Moreover, the major sources of multifractality are studied. Based on the concept of sliding window, the time evolutions of the multifractal behavior of domestic and foreign tourists were analyzed and the influence of Wenchuan earthquake on Jiuzhai Valley tourism system dynamics were evaluated quantitatively. The study indicates that the inherent dynamical mechanism of Jiuzhai Valley tourism system has not been fundamentally changed from long views, although Jiuzhai Valley tourism system was seriously affected by the Wenchuan earthquake. Jiuzhai Valley tourism system has the ability to restore to its previous state in the short term.

Multifractality Signatures in Quasars Time Series. I. 3C 273

NASA Astrophysics Data System (ADS)

Belete, A. Bewketu; Bravo, J. P.; Canto Martins, B. L.; Leão, I. C.; De Araujo, J. M.; De Medeiros, J. R.

2018-05-01

The presence of multifractality in a time series shows different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. The identification of a multifractal nature allows for a characterization of the dynamics and of the intermittency of the fluctuations in non-linear and complex systems. In this study, we search for a possible multifractal structure (multifractality signature) of the flux variability in the quasar 3C 273 time series for all electromagnetic wavebands at different observation points, and the origins for the observed multifractality. This study is intended to highlight how the scaling behaves across the different bands of the selected candidate which can be used as an additional new technique to group quasars based on the fractal signature observed in their time series and determine whether quasars are non-linear physical systems or not. The Multifractal Detrended Moving Average algorithm (MFDMA) has been used to study the scaling in non-linear, complex and dynamic systems. To achieve this goal, we applied the backward (θ = 0) MFDMA method for one-dimensional signals. We observe weak multifractal (close to monofractal) behaviour in some of the time series of our candidate except in the mm, UV and X-ray bands. The non-linear temporal correlation is the main source of the observed multifractality in the time series whereas the heaviness of the distribution contributes less.

Dynamics of bid-ask spread return and volatility of the Chinese stock market

NASA Astrophysics Data System (ADS)

Qiu, Tian; Chen, Guang; Zhong, Li-Xin; Wu, Xiao-Run

2012-04-01

The bid-ask spread is taken as an important measure of the financial market liquidity. In this article, we study the dynamics of the spread return and the spread volatility of four liquid stocks in the Chinese stock market, including the memory effect and the multifractal nature. By investigating the autocorrelation function and the Detrended Fluctuation Analysis (DFA), we find that the spread return is the lack of long-range memory, while the spread volatility is long-range time correlated. Besides, the spread volatilities of different stocks present long-range cross-correlations. Moreover, by applying the Multifractal Detrended Fluctuation Analysis (MF-DFA), the spread return is observed to possess a strong multifractality, which is similar to the dynamics of a variety of financial quantities. Different from the spread return, the spread volatility exhibits a weak multifractal nature.

Detecting Multifractal Properties in Asset Returns:

NASA Astrophysics Data System (ADS)

Lux, Thomas

It has become popular recently to apply the multifractal formalism of statistical physics (scaling analysis of structure functions and f(α) singularity spectrum analysis) to financial data. The outcome of such studies is a nonlinear shape of the structure function and a nontrivial behavior of the spectrum. Eventually, this literature has moved from basic data analysis to estimation of particular variants of multifractal models for asset returns via fitting of the empirical τ(q) and f(α) functions. Here, we reinvestigate earlier claims of multifractality using four long time series of important financial markets. Taking the recently proposed multifractal models of asset returns as our starting point, we show that the typical "scaling estimators" used in the physics literature are unable to distinguish between spurious and "true" multiscaling of financial data. Designing explicit tests for multiscaling, we can in no case reject the null hypothesis that the apparent curvature of both the scaling function and the Hölder spectrum are spuriously generated by the particular fat-tailed distribution of financial data. Given the well-known overwhelming evidence in favor of different degrees of long-term dependence in the powers of returns, we interpret this inability to reject the null hypothesis of multiscaling as a lack of discriminatory power of the standard approach rather than as a true rejection of multiscaling. However, the complete "failure" of the multifractal apparatus in this setting also raises the question whether results in other areas (like geophysics) suffer from similar shortcomings of the traditional methodology.

Multi- and monofractal indices of short-term heart rate variability.

PubMed

Fischer, R; Akay, M; Castiglioni, P; Di Rienzo, M

2003-09-01

Indices of heart rate variability (HRV) based on fractal signal models have recently been shown to possess value as predictors of mortality in specific patient populations. To develop more powerful clinical indices of HRV based on a fractal signal model, the study investigated two HRV indices based on a monofractal signal model called fractional Brownian motion and an index based on a multifractal signal model called multifractional Brownian motion. The performance of the indices was compared with an HRV index in common clinical use. To compare the indices, 18 normal subjects were subjected to postural changes, and the indices were compared on their ability to respond to the resulting autonomic events in HRV recordings. The magnitude of the response to postural change (normalised by the measurement variability) was assessed by analysis of variance and multiple comparison testing. Four HRV indices were investigated for this study: the standard deviation of all normal R-R intervals; an HRV index commonly used in the clinic; detrended fluctuation analysis, an HRV index found to be the most powerful predictor of mortality in a study of patients with depressed left ventricular function; an HRV index developed using the maximum likelihood estimation (MLE) technique for a monofractal signal model; and an HRV index developed for the analysis of multifractional Brownian motion signals. The HRV index based on the MLE technique was found to respond most strongly to the induced postural changes (95% CI). The magnitude of its response (normalised by the measurement variability) was at least 25% greater than any of the other indices tested.

Development of multiscale complexity and multifractality of fetal heart rate variability.

PubMed

Gierałtowski, Jan; Hoyer, Dirk; Tetschke, Florian; Nowack, Samuel; Schneider, Uwe; Zebrowski, Jan

2013-11-01

During fetal development a complex system grows and coordination over multiple time scales is formed towards an integrated behavior of the organism. Since essential cardiovascular and associated coordination is mediated by the autonomic nervous system (ANS) and the ANS activity is reflected in recordable heart rate patterns, multiscale heart rate analysis is a tool predestined for the diagnosis of prenatal maturation. The analyses over multiple time scales requires sufficiently long data sets while the recordings of fetal heart rate as well as the behavioral states studied are themselves short. Care must be taken that the analysis methods used are appropriate for short data lengths. We investigated multiscale entropy and multifractal scaling exponents from 30 minute recordings of 27 normal fetuses, aged between 23 and 38 weeks of gestational age (WGA) during the quiet state. In multiscale entropy, we found complexity lower than that of non-correlated white noise over all 20 coarse graining time scales investigated. Significant maturation age related complexity increase was strongest expressed at scale 2, both using sample entropy and generalized mutual information as complexity estimates. Multiscale multifractal analysis (MMA) in which the Hurst surface h(q,s) is calculated, where q is the multifractal parameter and s is the scale, was applied to the fetal heart rate data. MMA is a method derived from detrended fluctuation analysis (DFA). We modified the base algorithm of MMA to be applicable for short time series analysis using overlapping data windows and a reduction of the scale range. We looked for such q and s for which the Hurst exponent h(q,s) is most correlated with gestational age. We used this value of the Hurst exponent to predict the gestational age based only on fetal heart rate variability properties. Comparison with the true age of the fetus gave satisfying results (error 2.17±3.29 weeks; p<0.001; R(2)=0.52). In addition, we found that the normally used DFA scale range is non-optimal for fetal age evaluation. We conclude that 30 min recordings are appropriate and sufficient for assessing fetal age by multiscale entropy and multiscale multifractal analysis. The predominant prognostic role of scale 2 heart beats for MSE and scale 39 heart beats (at q=-0.7) for MMA cannot be explored neither by single scale complexity measures nor by standard detrended fluctuation analysis. Copyright © 2013 Elsevier B.V. All rights reserved.

Dynamic relationship between Japanese Yen exchange rates and market anxiety: A new perspective based on MF-DCCA

NASA Astrophysics Data System (ADS)

Lu, Xinsheng; Sun, Xinxin; Ge, Jintian

2017-05-01

This paper investigates the dynamic relationship between Japanese Yen exchange rates and market anxiety during the period from January 5, 1998 to April 18, 2016. A quantitative technique of multifractal detrended cross-correlation analysis (MF-DCCA) is used to explore the multifractal features of the cross-correlations between USD/JPY, AUD/JPY exchange rates and the market anxiety gauge VIX. The investigation shows that the causal relationship between Japanese Yen exchange rates and VIX are bidirectional in general, and the cross-correlations between the two sets of time series are multifractal. Strong evidence suggests that the cross-correlation exponents tend to exhibit different volatility patterns in response to diverse external shocks such as financial distress and widening in interest rate spread, suggesting that the cross-correlated behavior between Japanese Yen exchange rates and VIX are susceptible to economic uncertainties and risks. In addition, the performances of two market anxiety gauges, the VIX and the TED spread, are compared and the sources of multifractality are also traced. Thus, this paper contributes to the literature by shedding light on the unique driving forces of the Yen exchange rate fluctuations in the international foreign exchange market.

Extreme values in the Chinese and American stock markets based on detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Cao, Guangxi; Zhang, Minjia

2015-10-01

This paper focuses on the comparative analysis of extreme values in the Chinese and American stock markets based on the detrended fluctuation analysis (DFA) algorithm using the daily data of Shanghai composite index and Dow Jones Industrial Average. The empirical results indicate that the multifractal detrended fluctuation analysis (MF-DFA) method is more objective than the traditional percentile method. The range of extreme value of Dow Jones Industrial Average is smaller than that of Shanghai composite index, and the extreme value of Dow Jones Industrial Average is more time clustering. The extreme value of the Chinese or American stock markets is concentrated in 2008, which is consistent with the financial crisis in 2008. Moreover, we investigate whether extreme events affect the cross-correlation between the Chinese and American stock markets using multifractal detrended cross-correlation analysis algorithm. The results show that extreme events have nothing to do with the cross-correlation between the Chinese and American stock markets.

Modeling cross-correlations and efficiency of Islamic and conventional banks from Saudi Arabia: Evidence from MF-DFA and MF-DXA approaches

NASA Astrophysics Data System (ADS)

Mensi, Walid; Hamdi, Atef; Shahzad, Syed Jawad Hussain; Shafiullah, Muhammad; Al-Yahyaee, Khamis Hamed

2018-07-01

This paper analyzes the dynamic efficiency and interdependence of Islamic and conventional banks of Saudi Arabia. This analysis applies the Multifractal Detrended Fluctuation Analysis (MF-DFA) and Multifractal Detrended Cross-Correlation Analysis (MF-DXA) approaches. The MF-DFA results show strong multifractality in the daily returns of Saudi banks. Moreover, all eight banks studied exhibit persistence correlation, which demonstrates inefficiency. The rolling window results show significant change in the inefficiency levels over the time. The cross-correlation analysis between bank-pairs exhibits long term interdependence between most of them. These findings indicate that the banking sector in Saudi Arabia suffers from inefficiency and exhibits long term memory.

Multiscale multifractal detrended cross-correlation analysis of financial time series

NASA Astrophysics Data System (ADS)

Shi, Wenbin; Shang, Pengjian; Wang, Jing; Lin, Aijing

2014-06-01

In this paper, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA). The method allows us to extend the description of the cross-correlation properties between two time series. MM-DCCA may provide new ways of measuring the nonlinearity of two signals, and it helps to present much richer information than multifractal detrended cross-correlation analysis (MF-DCCA) by sweeping all the range of scale at which the multifractal structures of complex system are discussed. Moreover, to illustrate the advantages of this approach we make use of the MM-DCCA to analyze the cross-correlation properties between financial time series. We show that this new method can be adapted to investigate stock markets under investigation. It can provide a more faithful and more interpretable description of the dynamic mechanism between financial time series than traditional MF-DCCA. We also propose to reduce the scale ranges to analyze short time series, and some inherent properties which remain hidden when a wide range is used may exhibit perfectly in this way.

Wavelet analysis and scaling properties of time series

NASA Astrophysics Data System (ADS)

Manimaran, P.; Panigrahi, Prasanta K.; Parikh, Jitendra C.

2005-10-01

We propose a wavelet based method for the characterization of the scaling behavior of nonstationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes. Discrete wavelets from the Daubechies family are used to illustrate the efficacy of this procedure. After studying binomial multifractal time series with the present and earlier approaches of detrending for comparison, we analyze the time series of averaged spin density in the 2D Ising model at the critical temperature, along with several experimental data sets possessing multifractal behavior.

Multifractal detrending moving-average cross-correlation analysis

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Zhou, Wei-Xing

2011-07-01

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross correlations. The multifractal detrended cross-correlation analysis (MFDCCA) approaches can be used to quantify such cross correlations, such as the MFDCCA based on the detrended fluctuation analysis (MFXDFA) method. We develop in this work a class of MFDCCA algorithms based on the detrending moving-average analysis, called MFXDMA. The performances of the proposed MFXDMA algorithms are compared with the MFXDFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving-average processes, and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents hxy extracted from the MFXDMA and MFXDFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross correlation is independent of the cross-correlation coefficient between two time series, and the MFXDFA and centered MFXDMA algorithms have comparative performances, which outperform the forward and backward MFXDMA algorithms. For two-component autoregressive fractionally integrated moving-average processes, we also find that the MFXDFA and centered MFXDMA algorithms have comparative performances, while the forward and backward MFXDMA algorithms perform slightly worse. For binomial measures, the forward MFXDMA algorithm exhibits the best performance, the centered MFXDMA algorithms performs worst, and the backward MFXDMA algorithm outperforms the MFXDFA algorithm when the moment order q<0 and underperforms when q>0. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MFXDMA algorithm gives the best estimates of hxy(q) since its hxy(2) is closest to 0.5, as expected, and the MFXDFA algorithm has the second best performance. For the volatilities, the forward and backward MFXDMA algorithms give similar results, while the centered MFXDMA and the MFXDFA algorithms fail to extract rational multifractal nature.

Multifractal Properties of Process Control Variables

NASA Astrophysics Data System (ADS)

Domański, Paweł D.

2017-06-01

Control system is an inevitable element of any industrial installation. Its quality affects overall process performance significantly. The assessment, whether control system needs any improvement or not, requires relevant and constructive measures. There are various methods, like time domain based, Minimum Variance, Gaussian and non-Gaussian statistical factors, fractal and entropy indexes. Majority of approaches use time series of control variables. They are able to cover many phenomena. But process complexities and human interventions cause effects that are hardly visible for standard measures. It is shown that the signals originating from industrial installations have multifractal properties and such an analysis may extend standard approach to further observations. The work is based on industrial and simulation data. The analysis delivers additional insight into the properties of control system and the process. It helps to discover internal dependencies and human factors, which are hardly detectable.

Detailed Analysis of the Interoccurrence Time Statistics in Seismic Activity

NASA Astrophysics Data System (ADS)

Tanaka, Hiroki; Aizawa, Yoji

2017-02-01

The interoccurrence time statistics of seismiciry is studied theoretically as well as numerically by taking into account the conditional probability and the correlations among many earthquakes in different magnitude levels. It is known so far that the interoccurrence time statistics is well approximated by the Weibull distribution, but the more detailed information about the interoccurrence times can be obtained from the analysis of the conditional probability. Firstly, we propose the Embedding Equation Theory (EET), where the conditional probability is described by two kinds of correlation coefficients; one is the magnitude correlation and the other is the inter-event time correlation. Furthermore, the scaling law of each correlation coefficient is clearly determined from the numerical data-analysis carrying out with the Preliminary Determination of Epicenter (PDE) Catalog and the Japan Meteorological Agency (JMA) Catalog. Secondly, the EET is examined to derive the magnitude dependence of the interoccurrence time statistics and the multi-fractal relation is successfully formulated. Theoretically we cannot prove the universality of the multi-fractal relation in seismic activity; nevertheless, the theoretical results well reproduce all numerical data in our analysis, where several common features or the invariant aspects are clearly observed. Especially in the case of stationary ensembles the multi-fractal relation seems to obey an invariant curve, furthermore in the case of non-stationary (moving time) ensembles for the aftershock regime the multi-fractal relation seems to satisfy a certain invariant curve at any moving times. It is emphasized that the multi-fractal relation plays an important role to unify the statistical laws of seismicity: actually the Gutenberg-Richter law and the Weibull distribution are unified in the multi-fractal relation, and some universality conjectures regarding the seismicity are briefly discussed.

Multifractal analysis of time series generated by discrete Ito equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Telesca, Luciano; Czechowski, Zbigniew; Lovallo, Michele

2015-06-15

In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.

Testing for multifractality of Islamic stock markets

NASA Astrophysics Data System (ADS)

Saâdaoui, Foued

2018-04-01

Studying the power-law scaling of financial time series is a promising area of econophysics, which has often contributed to the understanding of the intricate features of the global markets. In this article, we examine the multifractality of some financial processes and the underlying formation mechanisms in the context of Islamic equity markets. The well-known Multifractal Detrended Fluctuation Analysis (MF-DFA) is used to investigate the self-similar properties of two Dow Jones Islamic Market Indexes (DJIM). The results prove that both indexes exhibit multifractal properties. By discussing the sources of multifractality, we find that they are related to the occurrence of extreme events, long-range dependency of autocorrelations and fat-tailed distribution of returns. These results have several important implications for analysts and decision makers in modeling the dynamics of Islamic markets, thus recommending efficient asset allocation plans to investors dealing with Islamic equity markets.

Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces

NASA Astrophysics Data System (ADS)

Qian, Xi-Yuan; Liu, Ya-Min; Jiang, Zhi-Qiang; Podobnik, Boris; Zhou, Wei-Xing; Stanley, H. Eugene

2015-06-01

When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation analysis (DPXA) to uncover the intrinsic power-law cross correlations between two simultaneously recorded time series in the presence of nonstationarity after removing the effects of other time series acting as common forces. The DPXA method is a generalization of the detrended cross-correlation analysis that takes into account partial correlation analysis. We demonstrate the method by using bivariate fractional Brownian motions contaminated with a fractional Brownian motion. We find that the DPXA is able to recover the analytical cross Hurst indices, and thus the multiscale DPXA coefficients are a viable alternative to the conventional cross-correlation coefficient. We demonstrate the advantage of the DPXA coefficients over the DCCA coefficients by analyzing contaminated bivariate fractional Brownian motions. We calculate the DPXA coefficients and use them to extract the intrinsic cross correlation between crude oil and gold futures by taking into consideration the impact of the U.S. dollar index. We develop the multifractal DPXA (MF-DPXA) method in order to generalize the DPXA method and investigate multifractal time series. We analyze multifractal binomial measures masked with strong white noises and find that the MF-DPXA method quantifies the hidden multifractal nature while the multifractal DCCA method fails.

Stochastic multifractal forecasts: from theory to applications in radar meteorology

NASA Astrophysics Data System (ADS)

da Silva Rocha Paz, Igor; Tchiguirinskaia, Ioulia; Schertzer, Daniel

2017-04-01

Radar meteorology has been very inspiring for the development of multifractals. It has enabled to work on a 3D+1 field with many challenging applications, including predictability and stochastic forecasts, especially nowcasts that are particularly demanding in computation speed. Multifractals are indeed parsimonious stochastic models that require only a few physically meaningful parameters, e.g. Universal Multifractal (UM) parameters, because they are based on non-trivial symmetries of nonlinear equations. We first recall the physical principles of multifractal predictability and predictions, which are so closely related that the latter correspond to the most optimal predictions in the multifractal framework. Indeed, these predictions are based on the fundamental duality of a relatively slow decay of large scale structures and an injection of new born small scale structures. Overall, this triggers a mulfitractal inverse cascade of unpredictability. With the help of high resolution rainfall radar data (≈ 100 m), we detail and illustrate the corresponding stochastic algorithm in the framework of (causal) UM Fractionally Integrated Flux models (UM-FIF), where the rainfall field is obtained with the help of a fractional integration of a conservative multifractal flux, whose average is strictly scale invariant (like the energy flux in a dynamic cascade). Whereas, the introduction of small structures is rather straightforward, the deconvolution of the past of the field is more subtle, but nevertheless achievable, to obtain the past of the flux. Then, one needs to only fractionally integrate a multiplicative combination of past and future fluxes to obtain a nowcast realisation.

Multifractals of investor behavior in stock market

NASA Astrophysics Data System (ADS)

Oh, Gabjin

2017-07-01

In this paper, we analyze the nonlinear properties of investor activity using the multifractal detrended fluctuation analysis (MF-DFA) method. Using the aggregated trading volumes of buying, selling, and normalized net investor trading (NIT) to quantify the characteristics of trader behavior in the KOSPI market, we find that the cumulative distribution functions of all NIT time series, except for individual traders, follow a power-law distribution with an exponent in the range of 2.92 ≤ γ ≤ 3.87. To observe the nonlinear features of investor activity, we also calculate the multifractal spectra for the buyer, seller, and NIT data sets and find that a multifractal structure exists in all of the data, regardless of the investor type studied.

Multifractal Analysis in Mining Microseismicity and its Application to Seismic Hazard Analysis in Mines

NASA Astrophysics Data System (ADS)

Pasten, D.; Comte, D.; Vallejos, J.

2013-05-01

During the last decades several authors showing that the spatial distribution of earthquakes follows multifractal laws and the most interesting behavior is the decreasing of the fratal dimensions before the ocurrence of a large earthquake, and also before its main aftershocks. A multifractal analysis to over 55920 microseismicity events recorded from January 2006 to January 2009 at Creighton mine, Canada was applied. In order to work with a complete catalogue in magnitude, it was taken the data associated with the linear part of the Gutenber-Richter law, with magnitudes greater than -1.5. A multifractal analysis was performed using microseismic data, considering that significant earthquakes are those with magnitude MW ≥ 1.0. A moving window was used, containing a constant number of events in order to guarantee the precise estimations of the fractal dimensions. After different trials, we choose 200 events for the number of the data points in each windows. Two consecutive windows were shifted by 20 events. The complete data set was separated in six sections and this multifractal analysis was applied for each section of 9320 data. The multifractal analysis of each section shows that there is a systematic decreasing of the fractal dimension (Dq) with time before the occurrence of rockburst or natural event with magnitude greater than MW ≥ 1.0, as it is observed in the seismic sequence of large earthquakes. This metodology was repeated for minimum magnitudes MW ≥ 1.5 and MW ≥ 2.0, obtaining same results. The best result was obtained using MW >= 2.0, a right answer rate vary between fifty and eighty percent. The result shows the possibility to use systematically the determination of the Dq parameter in order to detect the next rockburst or natural event in the studied mine. This project has been financially suppoerted by FONDECyT No 3120237 Grant (D.P).

Discrete wavelet approach to multifractality

NASA Astrophysics Data System (ADS)

Isaacson, Susana I.; Gabbanelli, Susana C.; Busch, Jorge R.

2000-12-01

The use of wavelet techniques for the multifractal analysis generalizes the box counting approach, and in addition provides information on eventual deviations of multifractal behavior. By the introduction of a wavelet partition function Wq and its corresponding free energy (beta) (q), the discrepancies between (beta) (q) and the multifractal free energy r(q) are shown to be indicative of these deviations. We study with Daubechies wavelets (D4) some 1D examples previously treated with Haar wavelets, and we apply the same ideas to some 2D Monte Carlo configurations, that simulate a solution under the action of an attractive potential. In this last case, we study the influence in the multifractal spectra and partition functions of four physical parameters: the intensity of the pairwise potential, the temperature, the range of the model potential, and the concentration of the solution. The wavelet partition function Wq carries more information about the cluster statistics than the multifractal partition function Zq, and the location of its peaks contributes to the determination of characteristic sales of the measure. In our experiences, the information provided by Daubechies wavelet sis slightly more accurate than the one obtained by Haar wavelets.

Decomposing Multifractal Crossovers

PubMed Central

Nagy, Zoltan; Mukli, Peter; Herman, Peter; Eke, Andras

2017-01-01

Physiological processes—such as, the brain's resting-state electrical activity or hemodynamic fluctuations—exhibit scale-free temporal structuring. However, impacts common in biological systems such as, noise, multiple signal generators, or filtering by transport function, result in multimodal scaling that cannot be reliably assessed by standard analytical tools that assume unimodal scaling. Here, we present two methods to identify breakpoints or crossovers in multimodal multifractal scaling functions. These methods incorporate the robust iterative fitting approach of the focus-based multifractal formalism (FMF). The first approach (moment-wise scaling range adaptivity) allows for a breakpoint-based adaptive treatment that analyzes segregated scale-invariant ranges. The second method (scaling function decomposition method, SFD) is a crossover-based design aimed at decomposing signal constituents from multimodal scaling functions resulting from signal addition or co-sampling, such as, contamination by uncorrelated fractals. We demonstrated that these methods could handle multimodal, mono- or multifractal, and exact or empirical signals alike. Their precision was numerically characterized on ideal signals, and a robust performance was demonstrated on exemplary empirical signals capturing resting-state brain dynamics by near infrared spectroscopy (NIRS), electroencephalography (EEG), and blood oxygen level-dependent functional magnetic resonance imaging (fMRI-BOLD). The NIRS and fMRI-BOLD low-frequency fluctuations were dominated by a multifractal component over an underlying biologically relevant random noise, thus forming a bimodal signal. The crossover between the EEG signal components was found at the boundary between the δ and θ bands, suggesting an independent generator for the multifractal δ rhythm. The robust implementation of the SFD method should be regarded as essential in the seamless processing of large volumes of bimodal fMRI-BOLD imaging data for the topology of multifractal metrics free of the masking effect of the underlying random noise. PMID:28798694

Multifractality and heteroscedastic dynamics: An application to time series analysis

NASA Astrophysics Data System (ADS)

Nascimento, C. M.; Júnior, H. B. N.; Jennings, H. D.; Serva, M.; Gleria, Iram; Viswanathan, G. M.

2008-01-01

An increasingly important problem in physics concerns scale invariance symmetry in diverse complex systems, often characterized by heteroscedastic dynamics. We investigate the nature of the relationship between the heteroscedastic and fractal aspects of the dynamics of complex systems, by analyzing the sensitivity to heteroscedasticity of the scaling properties of weakly nonstationary time series. By using multifractal detrended fluctuation analysis, we study the singularity spectra of currency exchange rate fluctuations, after partially or completely eliminating n-point correlations via data shuffling techniques. We conclude that heteroscedasticity can significantly increase multifractality and interpret these findings in the context of self-organizing and adaptive complex systems.

Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

NASA Astrophysics Data System (ADS)

Walker, David Lee

1999-12-01

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the ``Chaos Game Representation'' (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, a recently developed technique from the field of signal processing. A multi-fractal model is built by using wavelet transforms to estimate the Hurst exponent, H. The Hurst exponent is a non-parametric measurement of the dynamism of a system. This procedure is used to evaluate gene- coding events in the DNA sequence of cystic fibrosis mutations. The H exponent is calculated for various mutation sites in this gene. The results of this study indicate the presence of anti-persistent, random walks and persistent ``sub-periods'' in the sequence. This indicates the hypothesis of a multi-fractal model of DNA information encoding warrants further consideration. This work examines the model's behavior in both pathological (mutations) and non-pathological (healthy) base pair sequences of the cystic fibrosis gene. These mutations both natural and synthetic were introduced by computer manipulation of the original base pair text files. The results show that disease severity and system ``information dynamics'' correlate. These results have implications for genetic engineering as well as in mathematical biology. They suggest that there is scope for more multi-fractal models to be developed.

Measuring efficiency of international crude oil markets: A multifractality approach

NASA Astrophysics Data System (ADS)

Niere, H. M.

2015-01-01

The three major international crude oil markets are treated as complex systems and their multifractal properties are explored. The study covers daily prices of Brent crude, OPEC reference basket and West Texas Intermediate (WTI) crude from January 2, 2003 to January 2, 2014. A multifractal detrended fluctuation analysis (MFDFA) is employed to extract the generalized Hurst exponents in each of the time series. The generalized Hurst exponent is used to measure the degree of multifractality which in turn is used to quantify the efficiency of the three international crude oil markets. To identify whether the source of multifractality is long-range correlations or broad fat-tail distributions, shuffled data and surrogated data corresponding to each of the time series are generated. Shuffled data are obtained by randomizing the order of the price returns data. This will destroy any long-range correlation of the time series. Surrogated data is produced using the Fourier-Detrended Fluctuation Analysis (F-DFA). This is done by randomizing the phases of the price returns data in Fourier space. This will normalize the distribution of the time series. The study found that for the three crude oil markets, there is a strong dependence of the generalized Hurst exponents with respect to the order of fluctuations. This shows that the daily price time series of the markets under study have signs of multifractality. Using the degree of multifractality as a measure of efficiency, the results show that WTI is the most efficient while OPEC is the least efficient market. This implies that OPEC has the highest likelihood to be manipulated among the three markets. This reflects the fact that Brent and WTI is a very competitive market hence, it has a higher level of complexity compared against OPEC, which has a large monopoly power. Comparing with shuffled data and surrogated data, the findings suggest that for all the three crude oil markets, the multifractality is mainly due to long-range correlations.

Multifractal modeling, segmentation, prediction, and statistical validation of posterior fossa tumors

NASA Astrophysics Data System (ADS)

Islam, Atiq; Iftekharuddin, Khan M.; Ogg, Robert J.; Laningham, Fred H.; Sivakumar, Bhuvaneswari

2008-03-01

In this paper, we characterize the tumor texture in pediatric brain magnetic resonance images (MRIs) and exploit these features for automatic segmentation of posterior fossa (PF) tumors. We focus on PF tumor because of the prevalence of such tumor in pediatric patients. Due to varying appearance in MRI, we propose to model the tumor texture with a multi-fractal process, such as a multi-fractional Brownian motion (mBm). In mBm, the time-varying Holder exponent provides flexibility in modeling irregular tumor texture. We develop a detailed mathematical framework for mBm in two-dimension and propose a novel algorithm to estimate the multi-fractal structure of tissue texture in brain MRI based on wavelet coefficients. This wavelet based multi-fractal feature along with MR image intensity and a regular fractal feature obtained using our existing piecewise-triangular-prism-surface-area (PTPSA) method, are fused in segmenting PF tumor and non-tumor regions in brain T1, T2, and FLAIR MR images respectively. We also demonstrate a non-patient-specific automated tumor prediction scheme based on these image features. We experimentally show the tumor discriminating power of our novel multi-fractal texture along with intensity and fractal features in automated tumor segmentation and statistical prediction. To evaluate the performance of our tumor prediction scheme, we obtain ROCs and demonstrate how sharply the curves reach the specificity of 1.0 sacrificing minimal sensitivity. Experimental results show the effectiveness of our proposed techniques in automatic detection of PF tumors in pediatric MRIs.

Financial Markets during Highly Anxious Time: Multifractal Fluctuations in Asset Returns

NASA Astrophysics Data System (ADS)

Siokis, Fotios M.

Building on the notion that systems and in particular complex systems such as stock exchange markets reveal their structure better when they are under stress, we analyze the multifractal character and nonlinear properties of four major stock market indices during financial meltdowns by means of the multifractal detrended fluctuation analysis (MF-DFA). The three distinct financial crises under investigation are the Black Monday, the Dot-Com and the Great Recession. Scaling and Hurst exponents are derived as well as the singularity spectra. The results show that all indices exhibit strong multifractal properties. The complexity of the markets is higher under the Black Monday event revealed by the width of the singularity spectrum and the higher α0 parameter.

Modified cross sample entropy and surrogate data analysis method for financial time series

NASA Astrophysics Data System (ADS)

Yin, Yi; Shang, Pengjian

2015-09-01

For researching multiscale behaviors from the angle of entropy, we propose a modified cross sample entropy (MCSE) and combine surrogate data analysis with it in order to compute entropy differences between original dynamics and surrogate series (MCSDiff). MCSDiff is applied to simulated signals to show accuracy and then employed to US and Chinese stock markets. We illustrate the presence of multiscale behavior in the MCSDiff results and reveal that there are synchrony containing in the original financial time series and they have some intrinsic relations, which are destroyed by surrogate data analysis. Furthermore, the multifractal behaviors of cross-correlations between these financial time series are investigated by multifractal detrended cross-correlation analysis (MF-DCCA) method, since multifractal analysis is a multiscale analysis. We explore the multifractal properties of cross-correlation between these US and Chinese markets and show the distinctiveness of NQCI and HSI among the markets in their own region. It can be concluded that the weaker cross-correlation between US markets gives the evidence for the better inner mechanism in the US stock markets than that of Chinese stock markets. To study the multiscale features and properties of financial time series can provide valuable information for understanding the inner mechanism of financial markets.

Multifractal analysis of geophysical time series in the urban lake of Créteil (France).

NASA Astrophysics Data System (ADS)

Mezemate, Yacine; Tchiguirinskaia, Ioulia; Bonhomme, Celine; Schertzer, Daniel; Lemaire, Bruno Jacques; Vinçon leite, Brigitte; Lovejoy, Shaun

2013-04-01

Urban water bodies take part in the environmental quality of the cities. They regulate heat, contribute to the beauty of landscape and give some space for leisure activities (aquatic sports, swimming). As they are often artificial they are only a few meters deep. It confers them some specific properties. Indeed, they are particularly sensitive to global environmental changes, including climate change, eutrophication and contamination by micro-pollutants due to the urbanization of the watershed. Monitoring their quality has become a major challenge for urban areas. The need for a tool for predicting short-term proliferation of potentially toxic phytoplankton therefore arises. In lakes, the behavior of biological and physical (temperature) fields is mainly driven by the turbulence regime in the water. Turbulence is highly non linear, nonstationary and intermittent. This is why statistical tools are needed to characterize the evolution of the fields. The knowledge of the probability distribution of all the statistical moments of a given field is necessary to fully characterize it. This possibility is offered by the multifractal analysis based on the assumption of scale invariance. To investigate the effect of space-time variability of temperature, chlorophyll and dissolved oxygen on the cyanobacteria proliferation in the urban lake of Creteil (France), a spectral analysis is first performed on each time series (or on subsamples) to have an overall estimate of their scaling behaviors. Then a multifractal analysis (Trace Moment, Double Trace Moment) estimates the statistical moments of different orders. This analysis is adapted to the specific properties of the studied time series, i. e. the presence of large scale gradients. The nonlinear behavior of the scaling functions K(q) confirms that the investigated aquatic time series are indeed multifractal and highly intermittent .The knowledge of the universal multifractal parameters is the key to calculate the different statistical moments and thus make some predictions on the fields. As a conclusion, the relationships between the fields will be highlighted with a discussion on the cross predictability of the different fields. This draws a prospective for the use of this kind of time series analysis in the field of limnology. The authors acknowledge the financial support from the R2DS-PLUMMME and Climate-KIC BlueGreenDream projects.

Beyond Fractals and 1/f Noise: Multifractal Analysis of Complex Physiological Time Series

NASA Astrophysics Data System (ADS)

Ivanov, Plamen Ch.; Amaral, Luis A. N.; Ashkenazy, Yosef; Stanley, H. Eugene; Goldberger, Ary L.; Hausdorff, Jeffrey M.; Yoneyama, Mitsuru; Arai, Kuniharu

2001-03-01

We investigate time series with 1/f-like spectra generated by two physiologic control systems --- the human heartbeat and human gait. We show that physiological fluctuations exhibit unexpected ``hidden'' structures often described by scaling laws. In particular, our studies indicate that when analyzed on different time scales the heartbeat fluctuations exhibit cascades of branching patterns with self-similar (fractal) properties, characterized by long-range power-law anticorrelations. We find that these scaling features change during sleep and wake phases, and with pathological perturbations. Further, by means of a new wavelet-based technique, we find evidence of multifractality in the healthy human heartbeat even under resting conditions, and show that the multifractal character and nonlinear properties of the healthy heart are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure. In contrast to the heartbeat, we find that the interstride interval time series of healthy human gait, a voluntary process under neural regulation, is described by a single fractal dimension (such as classical 1/f noise) indicating monofractal behavior. Thus our approach can help distinguish physiological and physical signals with comparable frequency spectra and two-point correlations, and guide modeling of their control mechanisms.

Comparison of various multifractal approaches to analyze the intermittent magnetic fluctuations observed in the Earth's magnetospheric cusp

NASA Astrophysics Data System (ADS)

Lamy, Hervé; Echim, Marius; Chang, Tom

2014-05-01

Several approaches exist to compute the multifractal characteristics of an intermittent set of fluctuations. First, the classical method based on the computation of the partition function uses the full set of fluctuations . Since it is dominated by the more numerous fluctuations of small amplitudes, this method can mask the fractal characteristics of minor fluctuations of much larger amplitude. To solve this issue, a new method was developed by Chang & Wu (2008) : the Rank-Ordered Multifractal Analysis (ROMA) The ROMA method offers a natural connection between the one-parameter monofractal scaling idea and the multifractal phenomenon of intermittency. The key-element in ROMA is to find s(Y), the spectrum of the scaling exponents, and Ps(Y), the scaled Probability Distribution Function (PDFs), from the raw PDFs of the variable X at various scales tau , P(X,tau), with the following scaling: P(X,tau) tau ^s(Y)=Ps(Y) with Y= X/tau ^s(Y) The first (direct) method is to use range-limited structure functions in a sufficiently small range of the scaled variable Y and search for the value of monofroctal exponent s(Y). A drawback of this approach is that the range of Y must be large enough to ensure that the statistics is meaningful. As a consequence, some cross-over behavior between fluctuations with different monofractal exponents can lead to an ambiguity with several solutions s(Y) for some ranges of Y. Also the multifractal spectrum produced is step-wise discontinuous. To overcome these difficulties, Wu & Chang (2011) have suggested a refined method where a value of the parameter s is assumed and the corresponding value of Y ensuring a collapse of the raw PDFs is searched for. The advantage of this latter approach is that s(Y) and Ps(Y) can be obtained for single values of Y. The two ROMA methods and the partition function method are used on a set of intermittent magnetic field fluctuations observed by the Cluster spacecraft in the Earth's magnetospheric cusp. Results are presented and discussed. Research supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 313038/STORM. TC was also partially supported by the US National Science Foundation. T. Chang and C.C. Wu, Rank-Ordered Multifractal Spectrum for Intermittent Fluctuations, Phys. Rev. E77,045401(R), 2008 CC. Wu and T. Chang, Application of rank-ordered multifractal analysis (ROMA) to intermittent fluctuations in 3D turbulent flows, 2D MHD simulation and solar wind data, to be submitted to the special issue "Multifractals and Intermittent Turbulence in the Solar-Terrestrial System", Nonlinear Processes in Geophysics, 2011.

An examination of coherent structures in a lobed mixer using multifractal measures in conjunction with the proper orthogonal decomposition

NASA Technical Reports Server (NTRS)

Ukeiley, L.; Varghese, M.; Glauser, M.; Valentine, D.

1991-01-01

A 'lobed mixer' device that enhances mixing through secondary flows and streamwise vorticity is presently studied within the framework of multifractal-measures theory, in order to deepen understanding of velocity time trace data gathered on its operation. Proper orthogonal decomposition-based knowledge of coherent structures has been applied to obtain the generalized fractal dimensions and multifractal spectrum of several proper eigenmodes for data samples of the velocity time traces; this constitutes a marked departure from previous multifractal theory applications to self-similar cascades. In certain cases, a single dimension may suffice to capture the entire spectrum of scaling exponents for the velocity time trace.

(Multi)fractality of Earthquakes by use of Wavelet Analysis

NASA Astrophysics Data System (ADS)

Enescu, B.; Ito, K.; Struzik, Z. R.

2002-12-01

The fractal character of earthquakes' occurrence, in time, space or energy, has by now been established beyond doubt and is in agreement with modern models of seismicity. Moreover, the cascade-like generation process of earthquakes -with one "main" shock followed by many aftershocks, having their own aftershocks- may well be described through multifractal analysis, well suited for dealing with such multiplicative processes. The (multi)fractal character of seismicity has been analysed so far by using traditional techniques, like the box-counting and correlation function algorithms. This work introduces a new approach for characterising the multifractal patterns of seismicity. The use of wavelet analysis, in particular of the wavelet transform modulus maxima, to multifractal analysis was pioneered by Arneodo et al. (1991, 1995) and applied successfully in diverse fields, such as the study of turbulence, the DNA sequences or the heart rate dynamics. The wavelets act like a microscope, revealing details about the analysed data at different times and scales. We introduce and perform such an analysis on the occurrence time of earthquakes and show its advantages. In particular, we analyse shallow seismicity, characterised by a high aftershock "productivity", as well as intermediate and deep seismic activity, known for its scarcity of aftershocks. We examine as well declustered (aftershocks removed) versions of seismic catalogues. Our preliminary results show some degree of multifractality for the undeclustered, shallow seismicity. On the other hand, at large scales, we detect a monofractal scaling behaviour, clearly put in evidence for the declustered, shallow seismic activity. Moreover, some of the declustered sequences show a long-range dependent (LRD) behaviour, characterised by a Hurst exponent, H > 0.5, in contrast with the memory-less, Poissonian model. We demonstrate that the LRD is a genuine characteristic and is not an effect of the time series probability distribution function. One of the most attractive features of wavelet analysis is its ability to determine a local Hurst exponent. We show that this feature together with the possibility of extending the analysis to spatial patterns may constitute a valuable approach to search for anomalous (precursory?) patterns of seismic activity.

The cross-correlation analysis of multi property of stock markets based on MM-DFA

NASA Astrophysics Data System (ADS)

Yang, Yujun; Li, Jianping; Yang, Yimei

2017-09-01

In this paper, we propose a new method called DH-MXA based on distribution histograms of Hurst surface and multiscale multifractal detrended fluctuation analysis. The method allows us to investigate the cross-correlation characteristics among multiple properties of different stock time series. It may provide a new way of measuring the nonlinearity of several signals. It also can provide a more stable and faithful description of cross-correlation of multiple properties of stocks. The DH-MXA helps us to present much richer information than multifractal detrented cross-correlation analysis and allows us to assess many universal and subtle cross-correlation characteristics of stock markets. We show DH-MXA by selecting four artificial data sets and five properties of four stock time series from different countries. The results show that our proposed method can be adapted to investigate the cross-correlation of stock markets. In general, the American stock markets are more mature and less volatile than the Chinese stock markets.

A Rolling Element Bearing Fault Diagnosis Approach Based on Multifractal Theory and Gray Relation Theory

PubMed Central

Li, Jingchao; Cao, Yunpeng; Ying, Yulong; Li, Shuying

2016-01-01

Bearing failure is one of the dominant causes of failure and breakdowns in rotating machinery, leading to huge economic loss. Aiming at the nonstationary and nonlinear characteristics of bearing vibration signals as well as the complexity of condition-indicating information distribution in the signals, a novel rolling element bearing fault diagnosis method based on multifractal theory and gray relation theory was proposed in the paper. Firstly, a generalized multifractal dimension algorithm was developed to extract the characteristic vectors of fault features from the bearing vibration signals, which can offer more meaningful and distinguishing information reflecting different bearing health status in comparison with conventional single fractal dimension. After feature extraction by multifractal dimensions, an adaptive gray relation algorithm was applied to implement an automated bearing fault pattern recognition. The experimental results show that the proposed method can identify various bearing fault types as well as severities effectively and accurately. PMID:28036329

A Rolling Element Bearing Fault Diagnosis Approach Based on Multifractal Theory and Gray Relation Theory.

PubMed

Li, Jingchao; Cao, Yunpeng; Ying, Yulong; Li, Shuying

2016-01-01

Bearing failure is one of the dominant causes of failure and breakdowns in rotating machinery, leading to huge economic loss. Aiming at the nonstationary and nonlinear characteristics of bearing vibration signals as well as the complexity of condition-indicating information distribution in the signals, a novel rolling element bearing fault diagnosis method based on multifractal theory and gray relation theory was proposed in the paper. Firstly, a generalized multifractal dimension algorithm was developed to extract the characteristic vectors of fault features from the bearing vibration signals, which can offer more meaningful and distinguishing information reflecting different bearing health status in comparison with conventional single fractal dimension. After feature extraction by multifractal dimensions, an adaptive gray relation algorithm was applied to implement an automated bearing fault pattern recognition. The experimental results show that the proposed method can identify various bearing fault types as well as severities effectively and accurately.

A multifractal detrended fluctuation analysis of financial market efficiency: Comparison using Dow Jones sector ETF indices

NASA Astrophysics Data System (ADS)

Tiwari, Aviral Kumar; Albulescu, Claudiu Tiberiu; Yoon, Seong-Min

2017-10-01

This study challenges the efficient market hypothesis, relying on the Dow Jones sector Exchange-Traded Fund (ETF) indices. For this purpose, we use the generalized Hurst exponent and multifractal detrended fluctuation analysis (MF-DFA) methods, using daily data over the timespan from 2000 to 2015. We compare the sector ETF indices in terms of market efficiency between short- and long-run horizons, small and large fluctuations, and before and after the global financial crisis (GFC). Our findings can be summarized as follows. First, there is clear evidence that the sector ETF markets are multifractal in nature. We also find a crossover in the multifractality of sector ETF market dynamics. Second, the utilities and consumer goods sector ETF markets are more efficient compared with the financial and telecommunications sector ETF markets, in terms of price prediction. Third, there are noteworthy discrepancies in terms of market efficiency, between the short- and long-term horizons. Fourth, the ETF market efficiency is considerably diminished after the global financial crisis.

Multifractal Detrended Fluctuation Analysis of Self-Potential Field Prior to the M 6.5, October 24, 1993 Earthquake in MÉXICO

NASA Astrophysics Data System (ADS)

Cervantes, F.; González-Trejo, J. I.; Real-Ramírez, C. A.; Hoyos-Reyes, L. F.; Area de Sistemas Computacionales

2013-05-01

In the current literature on seismo electromagnetic, it has been reported many earthquakes which present electromagnetic anomalies as probable precursors of their occurrences. Although this methodology remains yet under discussion, is relevant to study many particular cases. In this work, we report a multifractal detrended fluctuation analysis (MFDFA) of electroseismic signals recorded in the Acapulco station during 1993. In October 24, 1993, occurred and earthquake (EQ) with M 6.5, with epicenter at (16.54 N, 98.98 W), 100Km away from the mentioned station. The multifractal spectrum identifies the deviations in fractal structure within time periods with large and small fluctuations. We discuss the dynamical meaning of this analysis and its possible relation with the mentioned EQ.

On uses, misuses and potential abuses of fractal analysis in zooplankton behavioral studies: A review, a critique and a few recommendations

NASA Astrophysics Data System (ADS)

Seuront, Laurent

2015-08-01

Fractal analysis is increasingly used to describe, and provide further understanding to, zooplankton swimming behavior. This may be related to the fact that fractal analysis and the related fractal dimension D have the desirable properties to be independent of measurement scale and to be very sensitive to even subtle behavioral changes that may be undetectable to other behavioral variables. As early claimed by Coughlin et al. (1992), this creates "the need for fractal analysis" in behavioral studies, which has hence the potential to become a valuable tool in zooplankton behavioral ecology. However, this paper stresses that fractal analysis, as well as the more elaborated multifractal analysis, is also a risky business that may lead to irrelevant results, without paying extreme attention to a series of both conceptual and practical steps that are all likely to bias the results of any analysis. These biases are reviewed and exemplified on the basis of the published literature, and remedial procedures are provided not only for geometric and stochastic fractal analyses, but also for the more complicated multifractal analysis. The concept of multifractals is finally introduced as a direct, objective and quantitative tool to identify models of motion behavior, such as Brownian motion, fractional Brownian motion, ballistic motion, Lévy flight/walk and multifractal random walk. I finally briefly review the state of this emerging field in zooplankton behavioral research.

A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pesin, Y.; Weiss, H.

1997-01-01

In this paper we establish the complete multifractal formalism for equilibrium measures for Holder continuous conformal expanding maps and expanding Markov Moran-like geometric constructions. Examples include Markov maps of an interval, beta transformations of an interval, rational maps with hyperbolic Julia sets, and conformal total endomorphisms. We also construct a Holder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex, and hence the multifractal formalism fails.

Joint Multifractal Analysis of penetration resistance variability in an olive orchard.

NASA Astrophysics Data System (ADS)

Lopez-Herrera, Juan; Herrero-Tejedor, Tomas; Saa-Requejo, Antonio; Villeta, Maria; Tarquis, Ana M.

2016-04-01

Spatial variability of soil properties is relevant for identifying those zones with physical degradation. We used descriptive statistics and multifractal analysis for characterizing the spatial patterns of soil penetrometer resistance (PR) distributions and compare them at different soil depths and soil water content to investigate the tillage effect in soil compactation. The study was conducted on an Inceptisol dedicated to olive orchard for the last 70 years. Two parallel transects of 64 m were selected as different soil management plots, conventional tillage (CT) and no tillage (NT). Penetrometer resistance readings were carried out at 50 cm intervals within the first 20 cm of soil depth (López de Herrera et al., 2015a). Two way ANOVA highlighted that tillage system, soil depth and their interaction are statistically significant to explain the variance of PR data. The comparison of CT and NT results at different depths showed that there are significant differences deeper than 10 cm but not in the first two soil layers. The scaling properties of each PR profile was characterized by τ(q) function, calculated in the range of moment orders (q) between -5 and +5 taken at 0.5 lag increments. Several parameters were calculated from this to establish different comparisons (López de Herrera et al., 2015b). While the multifractal analysis characterizes the distribution of a single variable along its spatial support, the joint multifractal analysis can be used to characterize the joint distribution of two or more variables along a common spatial support (Kravchenko et al., 2000; Zeleke and Si, 2004). This type of analysis was performed to study the scaling properties of the joint distribution of PR at different depths. The results showed that this type of analysis added valuable information to describe the spatial arrangement of depth-dependent penetrometer data sets in all the soil layers. References Kravchenko AN, Bullock DG, Boast CW (2000) Joint multifractal analysis of crop yield and terrain slope. Agro. j. 92: 1279-1290. López de Herrera, J., Tomas Herrero Tejedor, Antonio Saa-Requejo and Ana M. Tarquis (2015a) Influence of tillage in soil penetration resistance variability in an olive orchard. Geophysical Research Abstracts, 17, EGU2015-15425. López de Herrera, J., Tomás Herrero Tejedor, Antonio Saa-Requejo, A.M. Tarquis. Influence of tillage in soil penetration resistance variability in an olive orchard. Soil Research, accepted, 2015b. doi: SR15046 Zeleke TB, Si BC (2004) Scaling properties of topographic indices and crop yield: Multifractal and joint multifractal approaches. Agro. j. 96: 1082-1090.

Statistical analysis on multifractal detrended cross-correlation coefficient for return interval by oriented percolation

NASA Astrophysics Data System (ADS)

Deng, Wei; Wang, Jun

2015-06-01

We investigate and quantify the multifractal detrended cross-correlation of return interval series for Chinese stock markets and a proposed price model, the price model is established by oriented percolation. The return interval describes the waiting time between two successive price volatilities which are above some threshold, the present work is an attempt to quantify the level of multifractal detrended cross-correlation for the return intervals. Further, the concept of MF-DCCA coefficient of return intervals is introduced, and the corresponding empirical research is performed. The empirical results show that the return intervals of SSE and SZSE are weakly positive multifractal power-law cross-correlated, and exhibit the fluctuation patterns of MF-DCCA coefficients. The similar behaviors of return intervals for the price model is also demonstrated.

Effect of spatial averaging on multifractal properties of meteorological time series

NASA Astrophysics Data System (ADS)

Hoffmann, Holger; Baranowski, Piotr; Krzyszczak, Jaromir; Zubik, Monika

2016-04-01

Introduction The process-based models for large-scale simulations require input of agro-meteorological quantities that are often in the form of time series of coarse spatial resolution. Therefore, the knowledge about their scaling properties is fundamental for transferring locally measured fluctuations to larger scales and vice-versa. However, the scaling analysis of these quantities is complicated due to the presence of localized trends and non-stationarities. Here we assess how spatially aggregating meteorological data to coarser resolutions affects the data's temporal scaling properties. While it is known that spatial aggregation may affect spatial data properties (Hoffmann et al., 2015), it is unknown how it affects temporal data properties. Therefore, the objective of this study was to characterize the aggregation effect (AE) with regard to both temporal and spatial input data properties considering scaling properties (i.e. statistical self-similarity) of the chosen agro-meteorological time series through multifractal detrended fluctuation analysis (MFDFA). Materials and Methods Time series coming from years 1982-2011 were spatially averaged from 1 to 10, 25, 50 and 100 km resolution to assess the impact of spatial aggregation. Daily minimum, mean and maximum air temperature (2 m), precipitation, global radiation, wind speed and relative humidity (Zhao et al., 2015) were used. To reveal the multifractal structure of the time series, we used the procedure described in Baranowski et al. (2015). The diversity of the studied multifractals was evaluated by the parameters of time series spectra. In order to analyse differences in multifractal properties to 1 km resolution grids, data of coarser resolutions was disaggregated to 1 km. Results and Conclusions Analysing the spatial averaging on multifractal properties we observed that spatial patterns of the multifractal spectrum (MS) of all meteorological variables differed from 1 km grids and MS-parameters were biased by -29.1 % (precipitation; width of MS) up to >4 % (min. Temperature, Radiation; asymmetry of MS). Also, the spatial variability of MS parameters was strongly affected at the highest aggregation (100 km). Obtained results confirm that spatial data aggregation may strongly affect temporal scaling properties. This should be taken into account when upscaling for large-scale studies. Acknowledgements The study was conducted within FACCE MACSUR. Please see Baranowski et al. (2015) for details on funding. References Baranowski, P., Krzyszczak, J., Sławiński, C. et al. (2015). Climate Research 65, 39-52. Hoffman, H., G. Zhao, L.G.J. Van Bussel et al. (2015). Climate Research 65, 53-69. Zhao, G., Siebert, S., Rezaei E. et al. (2015). Agricultural and Forest Meteorology 200, 156-171.

Symmetries and stochastic symmetry breaking in multifractal geophysics: analysis and simulation with the help of the Lévy-Clifford algebra of cascade generators..

NASA Astrophysics Data System (ADS)

Schertzer, D. J. M.; Tchiguirinskaia, I.

2016-12-01

Multifractal fields, whose definition is rather independent of their domain dimension, have opened a new approach of geophysics enabling to explore its spatial extension that is of prime importance as underlined by the expression "spatial chaos". However multifractals have been until recently restricted to be scalar valued, i.e. to one-dimensional codomains. This has prevented to deal with the key question of complex component interactions and their non trivial symmetries. We first emphasize that the Lie algebra of stochastic generators of cascade processes enables us to generalize multifractals to arbitrarily large codomains, e.g. flows of vector fields on large dimensional manifolds. In particular, we have recently investigated the neat example of stable Levy generators on Clifford algebra that have a number of seductive properties, e.g. universal statistical and robust algebra properties, both defining the basic symmetries of the corresponding fields (Schertzer and Tchiguirinskaia, 2015). These properties provide a convenient multifractal framework to study both the symmetries of the fields and how they stochastically break the symmetries of the underlying equations due to boundary conditions, large scale rotations and forcings. These developments should help us to answer to challenging questions such as the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013), to fully address the question of the limitations of quasi- geostrophic turbulence (Schertzer et al., 2012) and to explore the peculiar phenomenology of turbulent dynamics of the atmosphere or oceans that is neither two- or three-dimensional. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.8183. Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327336. Schertzer, D. & Tchiguirinskaia, I., 2015. Multifractal vector fields and stochastic Clifford algebra. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p.123127

Scaling and Multifractality in Road Accidental Distances

NASA Astrophysics Data System (ADS)

Qiu, Tian; Wan, Chi; Zou, Xiang-Xiang; Wang, Xiao-Fan

Accidental distance dynamics is investigated, based on the road accidental data of the Great Britain. The distance distribution of all the districts as an ensemble presents a power law tail, which is different from that of the individual district. A universal distribution is found for different districts, by rescaling the distribution functions of individual districts, which can be well fitted by the Weibull distribution. The male and female drivers behave similarly in the distance distribution. The multifractal characteristic is further studied for the individual district and all the districts as an ensemble, and different behaviors are also revealed between them. The accidental distances of the individual district show a weak multifractality, whereas of all the districts present a strong multifractality when taking them as an ensemble.

Coupling detrended fluctuation analysis for analyzing coupled nonstationary signals.

PubMed

Hedayatifar, L; Vahabi, M; Jafari, G R

2011-08-01

When many variables are coupled to each other, a single case study could not give us thorough and precise information. When these time series are stationary, different methods of random matrix analysis and complex networks can be used. But, in nonstationary cases, the multifractal-detrended-cross-correlation-analysis (MF-DXA) method was introduced for just two coupled time series. In this article, we have extended the MF-DXA to the method of coupling detrended fluctuation analysis (CDFA) for the case when more than two series are correlated to each other. Here, we have calculated the multifractal properties of the coupled time series, and by comparing CDFA results of the original series with those of the shuffled and surrogate series, we can estimate the source of multifractality and the extent to which our series are coupled to each other. We illustrate the method by selected examples from air pollution and foreign exchange rates.

Coupling detrended fluctuation analysis for analyzing coupled nonstationary signals

NASA Astrophysics Data System (ADS)

Hedayatifar, L.; Vahabi, M.; Jafari, G. R.

2011-08-01

When many variables are coupled to each other, a single case study could not give us thorough and precise information. When these time series are stationary, different methods of random matrix analysis and complex networks can be used. But, in nonstationary cases, the multifractal-detrended-cross-correlation-analysis (MF-DXA) method was introduced for just two coupled time series. In this article, we have extended the MF-DXA to the method of coupling detrended fluctuation analysis (CDFA) for the case when more than two series are correlated to each other. Here, we have calculated the multifractal properties of the coupled time series, and by comparing CDFA results of the original series with those of the shuffled and surrogate series, we can estimate the source of multifractality and the extent to which our series are coupled to each other. We illustrate the method by selected examples from air pollution and foreign exchange rates.

Asymmetric statistical features of the Chinese domestic and international gold price fluctuation

NASA Astrophysics Data System (ADS)

Cao, Guangxi; Zhao, Yingchao; Han, Yan

2015-05-01

Analyzing the statistical features of fluctuation is remarkably significant for financial risk identification and measurement. In this study, the asymmetric detrended fluctuation analysis (A-DFA) method was applied to evaluate asymmetric multifractal scaling behaviors in the Shanghai and New York gold markets. Our findings showed that the multifractal features of the Chinese and international gold spot markets were asymmetric. The gold return series persisted longer in an increasing trend than in a decreasing trend. Moreover, the asymmetric degree of multifractals in the Chinese and international gold markets decreased with the increase in fluctuation range. In addition, the empirical analysis using sliding window technology indicated that multifractal asymmetry in the Chinese and international gold markets was characterized by its time-varying feature. However, the Shanghai and international gold markets basically shared a similar asymmetric degree evolution pattern. The American subprime mortgage crisis (2008) and the European debt crisis (2010) enhanced the asymmetric degree of the multifractal features of the Chinese and international gold markets. Furthermore, we also make statistical tests for the results of multifractatity and asymmetry, and discuss the origin of them. Finally, results of the empirical analysis using the threshold autoregressive conditional heteroskedasticity (TARCH) and exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models exhibited that good news had a more significant effect on the cyclical fluctuation of the gold market than bad news. Moreover, good news exerted a more significant effect on the Chinese gold market than on the international gold market.

Fractal density modeling of crustal heterogeneity from the KTB deep hole

NASA Astrophysics Data System (ADS)

Chen, Guoxiong; Cheng, Qiuming

2017-03-01

Fractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α-dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low-porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high-pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.

Nonlinear Analysis on Cross-Correlation of Financial Time Series by Continuum Percolation System

NASA Astrophysics Data System (ADS)

Niu, Hongli; Wang, Jun

We establish a financial price process by continuum percolation system, in which we attribute price fluctuations to the investors’ attitudes towards the financial market, and consider the clusters in continuum percolation as the investors share the same investment opinion. We investigate the cross-correlations in two return time series, and analyze the multifractal behaviors in this relationship. Further, we study the corresponding behaviors for the real stock indexes of SSE and HSI as well as the liquid stocks pair of SPD and PAB by comparison. To quantify the multifractality in cross-correlation relationship, we employ multifractal detrended cross-correlation analysis method to perform an empirical research for the simulation data and the real markets data.

Characterizing scaling properties of complex signals with missed data segments using the multifractal analysis.

PubMed

Pavlov, A N; Pavlova, O N; Abdurashitov, A S; Sindeeva, O A; Semyachkina-Glushkovskaya, O V; Kurths, J

2018-01-01

The scaling properties of complex processes may be highly influenced by the presence of various artifacts in experimental recordings. Their removal produces changes in the singularity spectra and the Hölder exponents as compared with the original artifacts-free data, and these changes are significantly different for positively correlated and anti-correlated signals. While signals with power-law correlations are nearly insensitive to the loss of significant parts of data, the removal of fragments of anti-correlated signals is more crucial for further data analysis. In this work, we study the ability of characterizing scaling features of chaotic and stochastic processes with distinct correlation properties using a wavelet-based multifractal analysis, and discuss differences between the effect of missed data for synchronous and asynchronous oscillatory regimes. We show that even an extreme data loss allows characterizing physiological processes such as the cerebral blood flow dynamics.

Characterizing scaling properties of complex signals with missed data segments using the multifractal analysis

NASA Astrophysics Data System (ADS)

Pavlov, A. N.; Pavlova, O. N.; Abdurashitov, A. S.; Sindeeva, O. A.; Semyachkina-Glushkovskaya, O. V.; Kurths, J.

2018-01-01

The scaling properties of complex processes may be highly influenced by the presence of various artifacts in experimental recordings. Their removal produces changes in the singularity spectra and the Hölder exponents as compared with the original artifacts-free data, and these changes are significantly different for positively correlated and anti-correlated signals. While signals with power-law correlations are nearly insensitive to the loss of significant parts of data, the removal of fragments of anti-correlated signals is more crucial for further data analysis. In this work, we study the ability of characterizing scaling features of chaotic and stochastic processes with distinct correlation properties using a wavelet-based multifractal analysis, and discuss differences between the effect of missed data for synchronous and asynchronous oscillatory regimes. We show that even an extreme data loss allows characterizing physiological processes such as the cerebral blood flow dynamics.

Multifractal analysis of the time series of daily means of wind speed in complex regions

NASA Astrophysics Data System (ADS)

Laib, Mohamed; Golay, Jean; Telesca, Luciano; Kanevski, Mikhail

2018-04-01

In this paper, we applied the multifractal detrended fluctuation analysis to the daily means of wind speed measured by 119 weather stations distributed over the territory of Switzerland. The analysis was focused on the inner time fluctuations of wind speed, which could be more linked with the local conditions of the highly varying topography of Switzerland. Our findings point out to a persistent behaviour of all the measured wind speed series (indicated by a Hurst exponent significantly larger than 0.5), and to a high multifractality degree indicating a relative dominance of the large fluctuations in the dynamics of wind speed, especially in the Swiss plateau, which is comprised between the Jura and Alp mountain ranges. The study represents a contribution to the understanding of the dynamical mechanisms of wind speed variability in mountainous regions.

Multifractal investigation of continuous seismic signal recorded at El Hierro volcano (Canary Islands) during the 2011-2012 pre- and eruptive phases

NASA Astrophysics Data System (ADS)

Telesca, Luciano; Lovallo, Michele; Martì Molist, Joan; López Moreno, Carmen; Abella Meléndez, Rafael

2015-02-01

The Multifractal Detrended Fluctuation Analysis (MF-DFA) is an effective method that allows detecting multifractality in non-stationary signals. We applied the MF-DFA to the continuous seismic signal recorded at El Hierro volcano (Canary Islands), which was affected by a submarine monogenetic eruption in October 2011. We investigated the multifractal properties of the continuous seismic signal before the onset of the eruption and after. We analysed three frames of the signal, one measured before the onset of eruption that occurred on October 10, 2011; and two after, but corresponding to two distinct eruptive episodes, the second one started on November 22, 2011 and lasting until late February 2012. The results obtained show a striking difference in the width of the multifractal spectrum, which is generally used to quantify the multifractal degree of a signal: the multifractal spectra of the signal frames recorded during the eruptive episodes are almost identical and much narrower than that of the signal frame measured before the onset of the eruption. Such difference indicates that the seismic signal recorded during the unrest reflects mostly the fracturing of the host rock under the overpressure exerted by the intruding magma, while that corresponding to the eruptive phases was mostly influenced by the flow of magma through the plumbing system, even some fracturing remains, not being possible to distinguish among the two eruptive episodes in terms of rock fracture mechanics.

Nonlinear stratospheric variability: multifractal de-trended fluctuation analysis and singularity spectra

PubMed Central

Domeisen, Daniela I. V.

2016-01-01

Characterizing the stratosphere as a turbulent system, temporal fluctuations often show different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. In this study, the different scaling laws in the long-term stratospheric variability are studied using multifractal de-trended fluctuation analysis (MF-DFA). The analysis is performed comparing four re-analysis products and different realizations of an idealized numerical model, isolating the role of topographic forcing and seasonal variability, as well as the absence of climate teleconnections and small-scale forcing. The Northern Hemisphere (NH) shows a transition of scaling exponents for time scales shorter than about 1 year, for which the variability is multifractal and scales in time with a power law corresponding to a red spectrum, to longer time scales, for which the variability is monofractal and scales in time with a power law corresponding to white noise. Southern Hemisphere (SH) variability also shows a transition at annual scales. The SH also shows a narrower dynamical range in multifractality than the NH, as seen in the generalized Hurst exponent and in the singularity spectra. The numerical integrations show that the models are able to reproduce the low-frequency variability but are not able to fully capture the shorter term variability of the stratosphere. PMID:27493560

Influence of urban morphology on total noise pollution: multifractal description.

PubMed

Ariza-Villaverde, Ana B; Jiménez-Hornero, Francisco J; Gutiérrez De Ravé, Eduardo

2014-02-15

Exposure to ambient noise levels above 65 dB can cause public health problems. The spatial distribution of this kind of pollution is linked to various elements which make up the urban form, such as construction density, the existence of open spaces and the shape and physical position of buildings. Since urban morphology displays multifractal behaviour, the present research studies for the first time the relationship between total noise pollution and urban features, such as street width and building height by means of a joint multifractal spectrum in two neighbourhoods of the city of Cordoba (Andalusia, Spain). According to the results, the joint multifractal spectrum reveals a positive correlation between the total noise pollution and the street width to building height ratio, this being more evident when urban morphology is regular. The information provided by the multifractal analysis completes the description obtained by using urban indexes and landscape metrics and might be useful for urban planning once the linkage between both frameworks has been done. Copyright © 2013 Elsevier B.V. All rights reserved.

Climate and weather across scales: singularities and stochastic Levy-Clifford algebra

NASA Astrophysics Data System (ADS)

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2016-04-01

There have been several attempts to understand and simulate the fluctuations of weather and climate across scales. Beyond mono/uni-scaling approaches (e.g. using spectral analysis), this was done with the help of multifractal techniques that aim to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations of these equations (Royer et al., 2008, Lovejoy and Schertzer, 2013). However, these techniques were limited to deal with scalar fields, instead of dealing directly with a system of complex interactions and non trivial symmetries. The latter is unfortunately indispensable to answer to the challenging question of being able to assess the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013) or to fully address the question of the relevance of quasi-geostrophic turbulence and to define an effective, fractal dimension of the atmospheric motions (Schertzer et al., 2012). In this talk, we present a plausible candidate based on the combination of Lévy stable processes and Clifford algebra. Together they combine stochastic and structural properties that are strongly universal. They therefore define with the help of a few physically meaningful parameters a wide class of stochastic symmetries, as well as high dimensional vector- or manifold-valued fields respecting these symmetries (Schertzer and Tchiguirinskaia, 2015). Lovejoy, S. & Schertzer, D., 2013. The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge U.K. Cambridge Univeristy Press. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.81-83. Royer, J.F. et al., 2008. Multifractal analysis of the evolution of simulated precipitation over France in a climate scenario. C.R. Geoscience, 340(431-440). Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327-336. Schertzer, D. & Tchiguirinskaia, I., 2015. Multifractal vector fields and stochastic Clifford algebra. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p.123127.

Fractal and Multifractal Analysis of Human Gait

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, A.; del Río Correa, J. L.; Angulo-Brown, F.

2003-09-01

We carried out a fractal and multifractal analysis of human gait time series of young and old individuals, and adults with three illnesses that affect the march: The Parkinson's and Huntington's diseases and the amyotrophic lateral sclerosis (ALS). We obtained cumulative plots of events, the correlation function, the Hurst exponent and the Higuchi's fractal dimension of these time series and found that these fractal markers could be a factor to characterize the march, since we obtained different values of these quantities for youths and adults and they are different also for healthy and ill persons and the most anomalous values belong to ill persons. In other physiological signals there is complexity lost related with the age and the illness, in the case of the march the opposite occurs. The multifractal analysis could be also a useful tool to understand the dynamics of these and other complex systems.

The complexity of the HANG SENG Index and its constituencies during the 2007-2008 Great Recession

NASA Astrophysics Data System (ADS)

Argyroudis, G.; Siokis, F.

2018-04-01

We apply the multifractal detrended moving average (MF-DMA) procedure to the daily data from HANG SENG Index (HSI) and two sub-indices, the Properties Index which consists of 10 Real Estate Companies and the Finance Index with 12 companies respectively. Two major events are considered: the 2007 and the 1997 crises. Based on scaling exponents and the singularity spectrum analysis, we show that both events reveal multiscaling and the results are robust across different indices. Furthermore, by dividing the data into two equal sub-samples for prior and after the crisis periods, we reveal that for the 2007-2008 crisis, the complexity of the HSI and Properties index remain the same between periods, while for the Finance Index, the after crisis period exhibits richer multifractality and higher complexity. Especially for the Properties Index, the results indicate that the Real Estate sector was not affected as much, by the transitory shocks of the Great Recession. As for the 1997 event, the HS Index is impacted greatly in the after period crisis exhibiting higher degree of multifractality and heterogeneity.

Examining the efficiency and interdependence of US credit and stock markets through MF-DFA and MF-DXA approaches

NASA Astrophysics Data System (ADS)

Shahzad, Syed Jawad Hussain; Nor, Safwan Mohd; Mensi, Walid; Kumar, Ronald Ravinesh

2017-04-01

This study examines the power law properties of 11 US credit and stock markets at the industry level. We use multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DXA) to first investigate the relative efficiency of credit and stock markets and then evaluate the mutual interdependence between CDS-equity market pairs. The scaling exponents of the MF-DFA approach suggest that CDS markets are relatively more inefficient than their equity counterparts. However, Banks and Financial credit markets are relatively more efficient. Basic Materials (both CDS and equity indices) is the most inefficient sector of the US economy. The cross-correlation exponents obtained through MF-DXA also suggest that the relationship of the CDS and equity sectors within and across markets is multifractal for all pairs. Within the CDS market, Basic Materials is the most dependent sector, whereas equity market sectors can be divided into two distinct groups based on interdependence. The pair-wise dependence between Basic Materials sector CDSs and the equity index is also the highest. The degree of cross-correlation shows that the sectoral pairs of CDS and equity markets belong to a persistent cross-correlated series within selected time intervals.

European economies in crisis: A multifractal analysis of disruptive economic events and the effects of financial assistance

NASA Astrophysics Data System (ADS)

Siokis, Fotios M.

2014-02-01

We analyze the complexity of rare economic events in troubled European economies. The economic crisis initiated at the end of 2009, forced a number of European economies to request financial assistance from world organizations. By employing the stock market index as a leading indicator of the economic activity, we test whether the financial assistance programs altered the statistical properties of the index. The effects of major financial program agreements on the economies can be best illustrated by the comparison of the multifractal spectra of the time series before and after the agreement. We reveal that the returns of the time series exhibit strong multifractal properties for all periods under investigation. In two of the three investigated economies, financial assistance along with governments’ initiatives appear to have altered the statistical properties of the stock market indexes increasing the width of the multifractal spectra and thus the complexity of the market.

Statistical analysis of Geopotential Height (GH) timeseries based on Tsallis non-extensive statistical mechanics

NASA Astrophysics Data System (ADS)

Karakatsanis, L. P.; Iliopoulos, A. C.; Pavlos, E. G.; Pavlos, G. P.

2018-02-01

In this paper, we perform statistical analysis of time series deriving from Earth's climate. The time series are concerned with Geopotential Height (GH) and correspond to temporal and spatial components of the global distribution of month average values, during the period (1948-2012). The analysis is based on Tsallis non-extensive statistical mechanics and in particular on the estimation of Tsallis' q-triplet, namely {qstat, qsens, qrel}, the reconstructed phase space and the estimation of correlation dimension and the Hurst exponent of rescaled range analysis (R/S). The deviation of Tsallis q-triplet from unity indicates non-Gaussian (Tsallis q-Gaussian) non-extensive character with heavy tails probability density functions (PDFs), multifractal behavior and long range dependences for all timeseries considered. Also noticeable differences of the q-triplet estimation found in the timeseries at distinct local or temporal regions. Moreover, in the reconstructive phase space revealed a lower-dimensional fractal set in the GH dynamical phase space (strong self-organization) and the estimation of Hurst exponent indicated multifractality, non-Gaussianity and persistence. The analysis is giving significant information identifying and characterizing the dynamical characteristics of the earth's climate.

Temporal scaling and spatial statistical analyses of groundwater level fluctuations

NASA Astrophysics Data System (ADS)

Sun, H.; Yuan, L., Sr.; Zhang, Y.

2017-12-01

Natural dynamics such as groundwater level fluctuations can exhibit multifractionality and/or multifractality due likely to multi-scale aquifer heterogeneity and controlling factors, whose statistics requires efficient quantification methods. This study explores multifractionality and non-Gaussian properties in groundwater dynamics expressed by time series of daily level fluctuation at three wells located in the lower Mississippi valley, after removing the seasonal cycle in the temporal scaling and spatial statistical analysis. First, using the time-scale multifractional analysis, a systematic statistical method is developed to analyze groundwater level fluctuations quantified by the time-scale local Hurst exponent (TS-LHE). Results show that the TS-LHE does not remain constant, implying the fractal-scaling behavior changing with time and location. Hence, we can distinguish the potentially location-dependent scaling feature, which may characterize the hydrology dynamic system. Second, spatial statistical analysis shows that the increment of groundwater level fluctuations exhibits a heavy tailed, non-Gaussian distribution, which can be better quantified by a Lévy stable distribution. Monte Carlo simulations of the fluctuation process also show that the linear fractional stable motion model can well depict the transient dynamics (i.e., fractal non-Gaussian property) of groundwater level, while fractional Brownian motion is inadequate to describe natural processes with anomalous dynamics. Analysis of temporal scaling and spatial statistics therefore may provide useful information and quantification to understand further the nature of complex dynamics in hydrology.

Changes in multifractal properties for stable angina pectoris

NASA Astrophysics Data System (ADS)

Knežević, Andrea; Martinis, Mladen; Krstačić, Goran; Vargović, Emil

2005-12-01

The multifractal approach has been applied to temporal fluctuations of heartbeat (RR) intervals, measured in various regimes of physical activity (ergometric data), taken from healthy subjects and those having stable angina pectoris (SAP). The problem we address here is whether SAP changes multifractality observed in healthy subjects. The G-moment method is used to analyse the multifractal spectrum. It is observed that both sets of data characterize multifractality, but a different trend in multifractal behaviour is found for SAP disease, under pronounced physical activity.

Multifractal analysis of 2001 Mw 7 . 7 Bhuj earthquake sequence in Gujarat, Western India

NASA Astrophysics Data System (ADS)

Aggarwal, Sandeep Kumar; Pastén, Denisse; Khan, Prosanta Kumar

2017-12-01

The 2001 Mw 7 . 7 Bhuj mainshock seismic sequence in the Kachchh area, occurring during 2001 to 2012, has been analyzed using mono-fractal and multi-fractal dimension spectrum analysis technique. This region was characterized by frequent moderate shocks of Mw ≥ 5 . 0 for more than a decade since the occurrence of 2001 Bhuj earthquake. The present study is therefore important for precursory analysis using this sequence. The selected long-sequence has been investigated first time for completeness magnitude Mc 3.0 using the maximum curvature method. Multi-fractal Dq spectrum (Dq ∼ q) analysis was carried out using effective window-length of 200 earthquakes with a moving window of 20 events overlapped by 180 events. The robustness of the analysis has been tested by considering the magnitude completeness correction term of 0.2 to Mc 3.0 as Mc 3.2 and we have tested the error in the calculus of Dq for each magnitude threshold. On the other hand, the stability of the analysis has been investigated down to the minimum magnitude of Mw ≥ 2 . 6 in the sequence. The analysis shows the multi-fractal dimension spectrum Dq decreases with increasing of clustering of events with time before a moderate magnitude earthquake in the sequence, which alternatively accounts for non-randomness in the spatial distribution of epicenters and its self-organized criticality. Similar behavior is ubiquitous elsewhere around the globe, and warns for proximity of a damaging seismic event in an area. OS: Please confirm math roman or italics in abs.

Interaction-Dominant Dynamics in Human Cognition: Beyond 1/f[superscript [alpha

ERIC Educational Resources Information Center

Ihlen, Espen A. F.; Vereijken, Beatrix

2010-01-01

It has been suggested that human behavior in general and cognitive performance in particular emerge from coordination between multiple temporal scales. In this article, we provide quantitative support for such a theory of interaction-dominant dynamics in human cognition by using wavelet-based multifractal analysis and accompanying multiplicative…

Multifractal texture estimation for detection and segmentation of brain tumors.

PubMed

Islam, Atiq; Reza, Syed M S; Iftekharuddin, Khan M

2013-11-01

A stochastic model for characterizing tumor texture in brain magnetic resonance (MR) images is proposed. The efficacy of the model is demonstrated in patient-independent brain tumor texture feature extraction and tumor segmentation in magnetic resonance images (MRIs). Due to complex appearance in MRI, brain tumor texture is formulated using a multiresolution-fractal model known as multifractional Brownian motion (mBm). Detailed mathematical derivation for mBm model and corresponding novel algorithm to extract spatially varying multifractal features are proposed. A multifractal feature-based brain tumor segmentation method is developed next. To evaluate efficacy, tumor segmentation performance using proposed multifractal feature is compared with that using Gabor-like multiscale texton feature. Furthermore, novel patient-independent tumor segmentation scheme is proposed by extending the well-known AdaBoost algorithm. The modification of AdaBoost algorithm involves assigning weights to component classifiers based on their ability to classify difficult samples and confidence in such classification. Experimental results for 14 patients with over 300 MRIs show the efficacy of the proposed technique in automatic segmentation of tumors in brain MRIs. Finally, comparison with other state-of-the art brain tumor segmentation works with publicly available low-grade glioma BRATS2012 dataset show that our segmentation results are more consistent and on the average outperforms these methods for the patients where ground truth is made available.

Multifractal Texture Estimation for Detection and Segmentation of Brain Tumors

PubMed Central

Islam, Atiq; Reza, Syed M. S.

2016-01-01

A stochastic model for characterizing tumor texture in brain magnetic resonance (MR) images is proposed. The efficacy of the model is demonstrated in patient-independent brain tumor texture feature extraction and tumor segmentation in magnetic resonance images (MRIs). Due to complex appearance in MRI, brain tumor texture is formulated using a multiresolution-fractal model known as multifractional Brownian motion (mBm). Detailed mathematical derivation for mBm model and corresponding novel algorithm to extract spatially varying multifractal features are proposed. A multifractal feature-based brain tumor segmentation method is developed next. To evaluate efficacy, tumor segmentation performance using proposed multifractal feature is compared with that using Gabor-like multiscale texton feature. Furthermore, novel patient-independent tumor segmentation scheme is proposed by extending the well-known AdaBoost algorithm. The modification of AdaBoost algorithm involves assigning weights to component classifiers based on their ability to classify difficult samples and confidence in such classification. Experimental results for 14 patients with over 300 MRIs show the efficacy of the proposed technique in automatic segmentation of tumors in brain MRIs. Finally, comparison with other state-of-the art brain tumor segmentation works with publicly available low-grade glioma BRATS2012 dataset show that our segmentation results are more consistent and on the average outperforms these methods for the patients where ground truth is made available. PMID:23807424

Dual-induced multifractality in online viewing activity.

PubMed

Qin, Yu-Hao; Zhao, Zhi-Dan; Cai, Shi-Min; Gao, Liang; Stanley, H Eugene

2018-01-01

Although recent studies have found that the long-term correlations relating to the fat-tailed distribution of inter-event times exist in human activity and that these correlations indicate the presence of fractality, the property of fractality and its origin have not been analyzed. We use both detrended fluctuation analysis and multifractal detrended fluctuation analysis to analyze the time series in online viewing activity separating from Movielens and Netflix. We find long-term correlations at both the individual and communal levels and that the extent of correlation at the individual level is determined by the activity level. These long-term correlations also indicate that there is fractality in the pattern of online viewing. We first find a multifractality that results from the combined effect of the fat-tailed distribution of inter-event times (i.e., the times between successive viewing actions of individuals) and the long-term correlations in online viewing activity and verify this finding using three synthesized series. Therefore, it can be concluded that the multifractality in online viewing activity is caused by both the fat-tailed distribution of inter-event times and the long-term correlations and that this enlarges the generic property of human activity to include not just physical space but also cyberspace.

Dual-induced multifractality in online viewing activity

NASA Astrophysics Data System (ADS)

Qin, Yu-Hao; Zhao, Zhi-Dan; Cai, Shi-Min; Gao, Liang; Stanley, H. Eugene

2018-01-01

Although recent studies have found that the long-term correlations relating to the fat-tailed distribution of inter-event times exist in human activity and that these correlations indicate the presence of fractality, the property of fractality and its origin have not been analyzed. We use both detrended fluctuation analysis and multifractal detrended fluctuation analysis to analyze the time series in online viewing activity separating from Movielens and Netflix. We find long-term correlations at both the individual and communal levels and that the extent of correlation at the individual level is determined by the activity level. These long-term correlations also indicate that there is fractality in the pattern of online viewing. We first find a multifractality that results from the combined effect of the fat-tailed distribution of inter-event times (i.e., the times between successive viewing actions of individuals) and the long-term correlations in online viewing activity and verify this finding using three synthesized series. Therefore, it can be concluded that the multifractality in online viewing activity is caused by both the fat-tailed distribution of inter-event times and the long-term correlations and that this enlarges the generic property of human activity to include not just physical space but also cyberspace.

Effect of tillage system and cumulative rainfall on multifractal parameters of soil surface microrelief

NASA Astrophysics Data System (ADS)

Vidal Vázquez, E.; Miranda, J. G. V.; Mirás-Avalos, J. M.; Díaz, M. C.; Paz-Ferreiro, J.

2009-04-01

Mathematical description of the spatial characteristics of soil surface microrelief still remains a challenge. Soil surface roughness parameters are required for modelling overland flow and erosion. The objective of this work was to evaluate the potential of multifractal for analyzing the decay of initial surface roughness induced by natural rainfall under different soil tillage systems. Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil). Six tillage treatments, namely, disc harrow, disc plow, chisel plow, disc harrow + disc level, disc plow + disc level and chisel plow + disc level were tested. In each plot soil surface microrelief was measured for times, with increasing amounts of natural rainfall using a pinmeter. The sampling scheme was a square grid with 25 x 25 mm point spacing and the plot size was 1350 x 1350 mm, so that each data set consisted of 3025 individual elevation points. Duplicated measurements were taken per treatment and date, yielding a total of 48 experimental data sets. All the investigated microrelief data sets exhibited, in general, scale properties, and the degree of multifractality showed wide differences between them. Multifractal analysis distinguishes two different patterns of soil surface microrelief, the first one has features close to monofractal spectra and the second clearly indicates multifractal behavior. Both, singularity spectra and generalized dimension spectra allow differentiating between soil tillage systems. In general, changes in values of multifractal parameters under simulated rainfall showed no or little correspondence with the evolution of the vertical microrelief component described by indices such as the standard deviation of the point height measurements. Multifractal parameters provided valuable information for chararacterizing the spatial features of soil surface microrelief as they were able to discriminate data sets with similar values for the vertical component of roughness.

Multifractal-based nuclei segmentation in fish images.

PubMed

Reljin, Nikola; Slavkovic-Ilic, Marijeta; Tapia, Coya; Cihoric, Nikola; Stankovic, Srdjan

2017-09-01

The method for nuclei segmentation in fluorescence in-situ hybridization (FISH) images, based on the inverse multifractal analysis (IMFA) is proposed. From the blue channel of the FISH image in RGB format, the matrix of Holder exponents, with one-by-one correspondence with the image pixels, is determined first. The following semi-automatic procedure is proposed: initial nuclei segmentation is performed automatically from the matrix of Holder exponents by applying predefined hard thresholding; then the user evaluates the result and is able to refine the segmentation by changing the threshold, if necessary. After successful nuclei segmentation, the HER2 (human epidermal growth factor receptor 2) scoring can be determined in usual way: by counting red and green dots within segmented nuclei, and finding their ratio. The IMFA segmentation method is tested over 100 clinical cases, evaluated by skilled pathologist. Testing results show that the new method has advantages compared to already reported methods.

Multifractal Detrended Cross-correlation Analysis of Market Clearing Price of electricity and SENSEX in India

NASA Astrophysics Data System (ADS)

Ghosh, Dipak; Dutta, Srimonti; Chakraborty, Sayantan

2015-09-01

This paper reports a study on the cross-correlation between the electric bid price and SENSEX using Multifractal Detrended Cross-correlation Analysis (MF-DXA). MF-DXA is a very rigorous and robust technique for assessment of cross-correction between two non-linear time series. The study reveals power law cross-correlation between Market Clearing Price (MCP) and SENSEX which suggests that a change in the value of one can create a subjective change in the value of the other.

Scaling properties of Polish rain series

NASA Astrophysics Data System (ADS)

Licznar, P.

2009-04-01

Scaling properties as well as multifractal nature of precipitation time series have not been studied for local Polish conditions until recently due to lack of long series of high-resolution data. The first Polish study of precipitation time series scaling phenomena was made on the base of pluviograph data from the Wroclaw University of Environmental and Life Sciences meteorological station located at the south-western part of the country. The 38 annual rainfall records from years 1962-2004 were converted into digital format and transformed into a standard format of 5-minute time series. The scaling properties and multifractal character of this material were studied by means of several different techniques: power spectral density analysis, functional box-counting, probability distribution/multiple scaling and trace moment methods. The result proved the general scaling character of time series at the range of time scales ranging form 5 minutes up to at least 24 hours. At the same time some characteristic breaks at scaling behavior were recognized. It is believed that the breaks were artificial and arising from the pluviograph rain gauge measuring precision limitations. Especially strong limitations at the precision of low-intensity precipitations recording by pluviograph rain gauge were found to be the main reason for artificial break at energy spectra, as was reported by other authors before. The analysis of co-dimension and moments scaling functions showed the signs of the first-order multifractal phase transition. Such behavior is typical for dressed multifractal processes that are observed by spatial or temporal averaging on scales larger than the inner-scale of those processes. The fractal dimension of rainfall process support derived from codimension and moments scaling functions geometry analysis was found to be 0.45. The same fractal dimension estimated by means of the functional box-counting method was equal to 0.58. At the final part of the study implementation of double trace moment method allowed for estimation of local universal multifractal rainfall parameters (α=0.69; C1=0.34; H=-0.01). The research proved the fractal character of rainfall process support and multifractal character of the rainfall intensity values variability among analyzed time series. It is believed that scaling of local Wroclaw's rainfalls for timescales at the range from 24 hours up to 5 minutes opens the door for future research concerning for example random cascades implementation for daily precipitation totals disaggregation for smaller time intervals. The results of such a random cascades functioning in a form of 5 minute artificial rainfall scenarios could be of great practical usability for needs of urban hydrology, and design and hydrodynamic modeling of storm water and combined sewage conveyance systems.

Multifractal Approach to Time Clustering of Earthquakes. Application to Mt. Vesuvio Seismicity

NASA Astrophysics Data System (ADS)

Codano, C.; Alonzo, M. L.; Vilardo, G.

The clustering structure of the Vesuvian earthquakes occurring is investigated by means of statistical tools: the inter-event time distribution, the running mean and the multifractal analysis. The first cannot clearly distinguish between a Poissonian process and a clustered one due to the difficulties of clearly distinguishing between an exponential distribution and a power law one. The running mean test reveals the clustering of the earthquakes, but looses information about the structure of the distribution at global scales. The multifractal approach can enlighten the clustering at small scales, while the global behaviour remains Poissonian. Subsequently the clustering of the events is interpreted in terms of diffusive processes of the stress in the earth crust.

Long-Range Temporal Correlations, Multifractality, and the Causal Relation between Neural Inputs and Movements

PubMed Central

Hu, Jing; Zheng, Yi; Gao, Jianbo

2013-01-01

Understanding the causal relation between neural inputs and movements is very important for the success of brain-machine interfaces (BMIs). In this study, we analyze 104 neurons’ firings using statistical, information theoretic, and fractal analysis. The latter include Fano factor analysis, multifractal adaptive fractal analysis (MF-AFA), and wavelet multifractal analysis. We find neuronal firings are highly non-stationary, and Fano factor analysis always indicates long-range correlations in neuronal firings, irrespective of whether those firings are correlated with movement trajectory or not, and thus does not reveal any actual correlations between neural inputs and movements. On the other hand, MF-AFA and wavelet multifractal analysis clearly indicate that when neuronal firings are not well correlated with movement trajectory, they do not have or only have weak temporal correlations. When neuronal firings are well correlated with movements, they are characterized by very strong temporal correlations, up to a time scale comparable to the average time between two successive reaching tasks. This suggests that neurons well correlated with hand trajectory experienced a “re-setting” effect at the start of each reaching task, in the sense that within the movement correlated neurons the spike trains’ long-range dependences persisted about the length of time the monkey used to switch between task executions. A new task execution re-sets their activity, making them only weakly correlated with their prior activities on longer time scales. We further discuss the significance of the coalition of those important neurons in executing cortical control of prostheses. PMID:24130549

Comparative analysis of time-scaling properties about water pH in Poyang Lake Inlet and Outlet on the basis of fractal methods.

PubMed

Shi, K; Liu, C Q; Huang, Z W; Zhang, B; Su, Y

2010-01-01

Detrended fluctuation analysis (DFA) and multifractal methods are applied to the time-scaling properties analysis of water pH series in Poyang Lake Inlet and Outlet in China. The results show that these pH series are characterised by long-term memory and multifractal scaling, and these characteristics have obvious differences between the Lake Inlet and Outlet. The comparison results suggest that monofractal and multifractal parameters can be quantitative dynamical indexes reflecting the capability of anti-acidification of Poyang Lake. Furthermore, we investigated the frequency-size distribution of pH series in Poyang Lake Inlet and Outlet. Our findings suggest that water pH is an example of a self-organised criticality (SOC) process. The results show that it is different SOC behaviours that result in the differences of power-law relations between pH series in Poyang Lake Inlet and Outlet. This work can be helpful to improvement of modelling of lake water quality.

Volatility-constrained multifractal detrended cross-correlation analysis: Cross-correlation among Mainland China, US, and Hong Kong stock markets

NASA Astrophysics Data System (ADS)

Cao, Guangxi; Zhang, Minjia; Li, Qingchen

2017-04-01

This study focuses on multifractal detrended cross-correlation analysis of the different volatility intervals of Mainland China, US, and Hong Kong stock markets. A volatility-constrained multifractal detrended cross-correlation analysis (VC-MF-DCCA) method is proposed to study the volatility conductivity of Mainland China, US, and Hong Kong stock markets. Empirical results indicate that fluctuation may be related to important activities in real markets. The Hang Seng Index (HSI) stock market is more influential than the Shanghai Composite Index (SCI) stock market. Furthermore, the SCI stock market is more influential than the Dow Jones Industrial Average stock market. The conductivity between the HSI and SCI stock markets is the strongest. HSI was the most influential market in the large fluctuation interval of 1991 to 2014. The autoregressive fractionally integrated moving average method is used to verify the validity of VC-MF-DCCA. Results show that VC-MF-DCCA is effective.

Multifractal cross-correlation effects in two-variable time series of complex network vertex observables

NASA Astrophysics Data System (ADS)

OświÈ©cimka, Paweł; Livi, Lorenzo; DroŻdŻ, Stanisław

2016-10-01

We investigate the scaling of the cross-correlations calculated for two-variable time series containing vertex properties in the context of complex networks. Time series of such observables are obtained by means of stationary, unbiased random walks. We consider three vertex properties that provide, respectively, short-, medium-, and long-range information regarding the topological role of vertices in a given network. In order to reveal the relation between these quantities, we applied the multifractal cross-correlation analysis technique, which provides information about the nonlinear effects in coupling of time series. We show that the considered network models are characterized by unique multifractal properties of the cross-correlation. In particular, it is possible to distinguish between Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks on the basis of fractal cross-correlation. Moreover, the analysis of protein contact networks reveals characteristics shared with both scale-free and small-world models.

Multiscaling of vegetative indexes from remote sensing images obtained at different spatial resolutions

NASA Astrophysics Data System (ADS)

Alonso, Carmelo; Tarquis, Ana M.; Zuñiga, Ignacio; Benito, Rosa M.

2017-04-01

Vegetation indexes, such as Normalized Difference Vegetation Index (NDVI) and enhanced Vegetation index (EVI), can been used to estimate root zone soil moisture through high resolution remote sensing images. These indexes are based in red (R), near infrared (NIR) and blue (B) wavelengths data. In this work we have studied the scaling properties of both vegetation indexes analyzing the information contained in two satellite data: Landsat-7 and Ikonos. Because of the potential capacity for systematic observations at various scales, remote sensing technology extends possible data archives from present time to over several decades back. For this advantage, enormous efforts have been made by researchers and application specialists to delineate vegetation indexes from local scale to global scale by applying remote sensing imagery. To study the influence of the spatial resolution the vegetation indexes map estimated with Ikonos-2 coded in 8 bits, with a resolution of 4m, have been compared through a multifractal analysis with the ones obtained with Lansat-7 8 bits, of 30 m. resolution, on the same area of study. The scaling behaviour of NDVI and EVI presents several differences that will be discussed based on the multifractal parameters extracted from the analysis. REFERENCES Alonso, C., Tarquis, A. M., Benito, R. M. and Zuñiga, I. Correlation scaling properties between soil moisture and vegetation indices. Geophysical Research Abstracts, 11, EGU2009-13932, 2009. Alonso, C., Tarquis, A. M. and Benito, R. M. Comparison of fractal dimensions based on segmented NDVI fields obtained from different remote sensors. Geophysical Research Abstracts, 14, EGU2012-14342, 2012. Escribano Rodriguez, J., Alonso, C., Tarquis, A.M., Benito, R.M. and Hernandez Diaz-Ambrona, C. Comparison of NDVI fields obtained from different remote sensors. Geophysical Research Abstracts,15, EGU2013-14153, 2013. Lovejoy, S., Tarquis, A., Gaonac'h, H. and Schertzer, D. Single and multiscale remote sensing techniques, multifractals and MODIS derived vegetation and soil moisture, Vadose Zone J., 7, 533-546, 2008. Renosh, P. R., Schmitt, F. G., and Loisel, H.: Scaling analysis of ocean surface turbulent heterogeneities from satellite remote sensing: use of 2D structure functions. PLoS ONE, 10, e0126975, 2015. Tarquis, A.M., Platonov, A., Matulka, A., Grau, J., Sekula, E., Diez, M. and Redondo J. M. Application of multifractal analysis to the study of SAR features and oil spills on the ocean surface. Nonlin. Processes Geophys., 21, 439-450, 2014.

Nonlinear analysis of saccade speed fluctuations during combined action and perception tasks

PubMed Central

Stan, C.; Astefanoaei, C.; Pretegiani, E.; Optican, L.; Creanga, D.; Rufa, A.; Cristescu, C.P.

2014-01-01

Background: Saccades are rapid eye movements used to gather information about a scene which requires both action and perception. These are usually studied separately, so that how perception influences action is not well understood. In a dual task, where the subject looks at a target and reports a decision, subtle changes in the saccades might be caused by action-perception interactions. Studying saccades might provide insight into how brain pathways for action and for perception interact. New method: We applied two complementary methods, multifractal detrended fluctuation analysis and Lempel-Ziv complexity index to eye peak speed recorded in two experiments, a pure action task and a combined action-perception task. Results: Multifractality strength is significantly different in the two experiments, showing smaller values for dual decision task saccades compared to simple-task saccades. The normalized Lempel-Ziv complexity index behaves similarly i.e. is significantly smaller in the decision saccade task than in the simple task. Comparison with existing methods: Compared to the usual statistical and linear approaches, these analyses emphasize the character of the dynamics involved in the fluctuations and offer a sensitive tool for quantitative evaluation of the multifractal features and of the complexity measure in the saccades peak speeds when different brain circuits are involved. Conclusion: Our results prove that the peak speed fluctuations have multifractal characteristics with lower magnitude for the multifractality strength and for the complexity index when two neural pathways are simultaneously activated, demonstrating the nonlinear interaction in the brain pathways for action and perception. PMID:24854830

The high order dispersion analysis based on first-passage-time probability in financial markets

NASA Astrophysics Data System (ADS)

Liu, Chenggong; Shang, Pengjian; Feng, Guochen

2017-04-01

The study of first-passage-time (FPT) event about financial time series has gained broad research recently, which can provide reference for risk management and investment. In this paper, a new measurement-high order dispersion (HOD)-is developed based on FPT probability to explore financial time series. The tick-by-tick data of three Chinese stock markets and three American stock markets are investigated. We classify the financial markets successfully through analyzing the scaling properties of FPT probabilities of six stock markets and employing HOD method to compare the differences of FPT decay curves. It can be concluded that long-range correlation, fat-tailed broad probability density function and its coupling with nonlinearity mainly lead to the multifractality of financial time series by applying HOD method. Furthermore, we take the fluctuation function of multifractal detrended fluctuation analysis (MF-DFA) to distinguish markets and get consistent results with HOD method, whereas the HOD method is capable of fractionizing the stock markets effectively in the same region. We convince that such explorations are relevant for a better understanding of the financial market mechanisms.

Multifractality and freezing phenomena in random energy landscapes: An introduction

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.

2010-10-01

We start our lectures with introducing and discussing the general notion of multifractality spectrum for random measures on lattices, and how it can be probed using moments of that measure. Then we show that the Boltzmann-Gibbs probability distributions generated by logarithmically correlated random potentials provide a simple yet non-trivial example of disorder-induced multifractal measures. The typical values of the multifractality exponents can be extracted from calculating the free energy of the associated Statistical Mechanics problem. To succeed in such a calculation we introduce and discuss in some detail two analytically tractable models for logarithmically correlated potentials. The first model uses a special definition of distances between points in space and is based on the idea of multiplicative cascades which originated in theory of turbulent motion. It is essentially equivalent to statistical mechanics of directed polymers on disordered trees studied long ago by Derrida and Spohn (1988) in Ref. [12]. In this way we introduce the notion of the freezing transition which is identified with an abrupt change in the multifractality spectrum. Second model which allows for explicit analytical evaluation of the free energy is the infinite-dimensional version of the problem which can be solved by employing the replica trick. In particular, the latter version allows one to identify the freezing phenomenon with a mechanism of the replica symmetry breaking (RSB) and to elucidate its physical meaning. The corresponding one-step RSB solution turns out to be marginally stable everywhere in the low-temperature phase. We finish with a short discussion of recent developments and extensions of models with logarithmic correlations, in particular in the context of extreme value statistics. The first appendix summarizes the standard elementary information about Gaussian integrals and related subjects, and introduces the notion of the Gaussian free field characterized by logarithmic correlations. Three other appendices provide the detailed exposition of a few technical details underlying the replica analysis of the model discussed in the lectures.

Multifractal analysis and topological properties of a new family of weighted Koch networks

NASA Astrophysics Data System (ADS)

Huang, Da-Wen; Yu, Zu-Guo; Anh, Vo

2017-03-01

Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality of weighted complex networks are still to be undertaken. In this paper, inspired by the concepts of Koch networks and Koch island, we propose a new family of weighted Koch networks, and investigate their multifractal behavior and topological properties. We find some key topological properties of the new networks: their vertex cumulative strength has a power-law distribution; there is a power-law relationship between their topological degree and weight strength; the networks have a high weighted clustering coefficient of 0.41004 (which is independent of the scaling factor c) in the limit of large generation t; the second smallest eigenvalue μ2 and the maximum eigenvalue μn are approximated by quartic polynomials of the scaling factor c for the general Laplacian operator, while μ2 is approximately a quartic polynomial of c and μn= 1.5 for the normalized Laplacian operator. Then, we find that weighted koch networks are both fractal and multifractal, their fractal dimension is influenced by the scaling factor c. We also apply these analyses to six real-world networks, and find that the multifractality in three of them are strong.

Fractal scaling analysis of groundwater dynamics in confined aquifers

NASA Astrophysics Data System (ADS)

Tu, Tongbi; Ercan, Ali; Kavvas, M. Levent

2017-10-01

Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

Feature selection method based on multi-fractal dimension and harmony search algorithm and its application

NASA Astrophysics Data System (ADS)

Zhang, Chen; Ni, Zhiwei; Ni, Liping; Tang, Na

2016-10-01

Feature selection is an important method of data preprocessing in data mining. In this paper, a novel feature selection method based on multi-fractal dimension and harmony search algorithm is proposed. Multi-fractal dimension is adopted as the evaluation criterion of feature subset, which can determine the number of selected features. An improved harmony search algorithm is used as the search strategy to improve the efficiency of feature selection. The performance of the proposed method is compared with that of other feature selection algorithms on UCI data-sets. Besides, the proposed method is also used to predict the daily average concentration of PM2.5 in China. Experimental results show that the proposed method can obtain competitive results in terms of both prediction accuracy and the number of selected features.

Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations

NASA Astrophysics Data System (ADS)

Kwapień, Jarosław; Oświecimka, Paweł; DroŻdŻ, Stanisław

2015-11-01

The detrended cross-correlation coefficient ρDCCA has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, nonstationary time series. It is based on the detrended cross-correlation and detrended fluctuation analyses (DCCA and DFA, respectively) and can be viewed as an analog of the Pearson coefficient in the case of the fluctuation analysis. The coefficient ρDCCA works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross-correlated, without the possibility to obtain information on the amplitude of fluctuations that are responsible for those cross-correlations. In order to introduce some related flexibility, here we propose an extension of ρDCCA that exploits the multifractal versions of DFA and DCCA: multifractal detrended fluctuation analysis and multifractal detrended cross-correlation analysis, respectively. The resulting new coefficient ρq not only is able to quantify the strength of correlations but also allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study. We show how the coefficient ρq works in practical situations by applying it to stochastic time series representing processes with long memory: autoregressive and multiplicative ones. Such processes are often used to model signals recorded from complex systems and complex physical phenomena like turbulence, so we are convinced that this new measure can successfully be applied in time-series analysis. In particular, we present an example of such application to highly complex empirical data from financial markets. The present formulation can straightforwardly be extended to multivariate data in terms of the q -dependent counterpart of the correlation matrices and then to the network representation.

Multifractal geometry in analysis and processing of digital retinal photographs for early diagnosis of human diabetic macular edema.

PubMed

Tălu, Stefan

2013-07-01

The purpose of this paper is to determine a quantitative assessment of the human retinal vascular network architecture for patients with diabetic macular edema (DME). Multifractal geometry and lacunarity parameters are used in this study. A set of 10 segmented and skeletonized human retinal images, corresponding to both normal (five images) and DME states of the retina (five images), from the DRIVE database was analyzed using the Image J software. Statistical analyses were performed using Microsoft Office Excel 2003 and GraphPad InStat software. The human retinal vascular network architecture has a multifractal geometry. The average of generalized dimensions (Dq) for q = 0, 1, 2 of the normal images (segmented versions), is similar to the DME cases (segmented versions). The average of generalized dimensions (Dq) for q = 0, 1 of the normal images (skeletonized versions), is slightly greater than the DME cases (skeletonized versions). However, the average of D2 for the normal images (skeletonized versions) is similar to the DME images. The average of lacunarity parameter, Λ, for the normal images (segmented and skeletonized versions) is slightly lower than the corresponding values for DME images (segmented and skeletonized versions). The multifractal and lacunarity analysis provides a non-invasive predictive complementary tool for an early diagnosis of patients with DME.

Hartree-Fock study of the Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents

NASA Astrophysics Data System (ADS)

Lee, Hyun-Jung; Kim, Ki-Seok

2018-04-01

We investigate the role of Coulomb interaction in the multifractality of Anderson metal-insulator transition, where the Coulomb interaction is treated within the Hartree-Fock approximation, but disorder effects are taken into account exactly. An innovative technical aspect in our simulation is to utilize the Ewald-sum technique, which allows us to introduce the long-range nature of the Coulomb interaction into Hartree-Fock self-consistent equations of order parameters more accurately. This numerical simulation reproduces the Altshuler-Aronov correction in a metallic state and the Efros-Shklovskii pseudogap in an insulating phase, where the density of states ρ (ω ) is evaluated in three dimensions. Approaching the quantum critical point of a metal-insulator transition from either the metallic or insulting phase, we find that the density of states is given by ρ (ω ) ˜|ω| 1 /2 , which determines one critical exponent of the McMillan-Shklovskii scaling theory. Our main result is to evaluate the eigenfunction multifractal scaling exponent αq, given by the Legendre transformation of the fractal dimension τq, which characterizes the scaling behavior of the inverse participation ratio with respect to the system size L . Our multifractal analysis leads us to identify two kinds of mobility edges, one of which occurs near the Fermi energy and the other of which appears at a high energy, where the density of states at the Fermi energy shows the Coulomb-gap feature. We observe that the multifractal exponent at the high-energy mobility edge remains to be almost identical to that of the Anderson localization transition in the absence of Coulomb interactions. On the other hand, we find that the multifractal exponent near the Fermi energy is more enhanced than that at the high-energy mobility edge, suspected to result from interaction effects. However, both the multifractal exponents do not change even if the strength of the Coulomb interaction varies. We also show that the multifractality singular spectrum can be classified into two categories, confirming the appearance of two types of mobility edges.

Multifractal two-scale Cantor set model for slow solar wind turbulence in the outer heliosphere during solar maximum

NASA Astrophysics Data System (ADS)

Macek, W. M.; Wawrzaszek, A.

2011-05-01

To quantify solar wind turbulence, we consider a generalized two-scale weighted Cantor set with two different scales describing nonuniform distribution of the kinetic energy flux between cascading eddies of various sizes. We examine generalized dimensions and the corresponding multifractal singularity spectrum depending on one probability measure parameter and two rescaling parameters. In particular, we analyse time series of velocities of the slow speed streams of the solar wind measured in situ by Voyager 2 spacecraft in the outer heliosphere during solar maximum at various distances from the Sun: 10, 30, and 65 AU. This allows us to look at the evolution of multifractal intermittent scaling of the solar wind in the distant heliosphere. Namely, it appears that while the degree of multifractality for the solar wind during solar maximum is only weakly correlated with the heliospheric distance, but the multifractal spectrum could substantially be asymmetric in a very distant heliosphere beyond the planetary orbits. Therefore, one could expect that this scaling near the frontiers of the heliosphere should rather be asymmetric. It is worth noting that for the model with two different scaling parameters a better agreement with the solar wind data is obtained, especially for the negative index of the generalized dimensions. Therefore we argue that there is a need to use a two-scale cascade model. Hence we propose this model as a useful tool for analysis of intermittent turbulence in various environments and we hope that our general asymmetric multifractal model could shed more light on the nature of turbulence.

Scale-Free and Multifractal Time Dynamics of fMRI Signals during Rest and Task

PubMed Central

Ciuciu, P.; Varoquaux, G.; Abry, P.; Sadaghiani, S.; Kleinschmidt, A.

2012-01-01

Scaling temporal dynamics in functional MRI (fMRI) signals have been evidenced for a decade as intrinsic characteristics of ongoing brain activity (Zarahn et al., 1997). Recently, scaling properties were shown to fluctuate across brain networks and to be modulated between rest and task (He, 2011): notably, Hurst exponent, quantifying long memory, decreases under task in activating and deactivating brain regions. In most cases, such results were obtained: First, from univariate (voxelwise or regionwise) analysis, hence focusing on specific cognitive systems such as Resting-State Networks (RSNs) and raising the issue of the specificity of this scale-free dynamics modulation in RSNs. Second, using analysis tools designed to measure a single scaling exponent related to the second order statistics of the data, thus relying on models that either implicitly or explicitly assume Gaussianity and (asymptotic) self-similarity, while fMRI signals may significantly depart from those either of those two assumptions (Ciuciu et al., 2008; Wink et al., 2008). To address these issues, the present contribution elaborates on the analysis of the scaling properties of fMRI temporal dynamics by proposing two significant variations. First, scaling properties are technically investigated using the recently introduced Wavelet Leader-based Multifractal formalism (WLMF; Wendt et al., 2007). This measures a collection of scaling exponents, thus enables a richer and more versatile description of scale invariance (beyond correlation and Gaussianity), referred to as multifractality. Also, it benefits from improved estimation performance compared to tools previously used in the literature. Second, scaling properties are investigated in both RSN and non-RSN structures (e.g., artifacts), at a broader spatial scale than the voxel one, using a multivariate approach, namely the Multi-Subject Dictionary Learning (MSDL) algorithm (Varoquaux et al., 2011) that produces a set of spatial components that appear more sparse than their Independent Component Analysis (ICA) counterpart. These tools are combined and applied to a fMRI dataset comprising 12 subjects with resting-state and activation runs (Sadaghiani et al., 2009). Results stemming from those analysis confirm the already reported task-related decrease of long memory in functional networks, but also show that it occurs in artifacts, thus making this feature not specific to functional networks. Further, results indicate that most fMRI signals appear multifractal at rest except in non-cortical regions. Task-related modulation of multifractality appears only significant in functional networks and thus can be considered as the key property disentangling functional networks from artifacts. These finding are discussed in the light of the recent literature reporting scaling dynamics of EEG microstate sequences at rest and addressing non-stationarity issues in temporally independent fMRI modes. PMID:22715328

Complexity of Continuous Glucose Monitoring Data in Critically Ill Patients: Continuous Glucose Monitoring Devices, Sensor Locations, and Detrended Fluctuation Analysis Methods

PubMed Central

Signal, Matthew; Thomas, Felicity; Shaw, Geoffrey M.; Chase, J. Geoffrey

2013-01-01

Background Critically ill patients often experience high levels of insulin resistance and stress-induced hyperglycemia, which may negatively impact outcomes. However, evidence surrounding the causes of negative outcomes remains inconclusive. Continuous glucose monitoring (CGM) devices allow researchers to investigate glucose complexity, using detrended fluctuation analysis (DFA), to determine whether it is associated with negative outcomes. The aim of this study was to investigate the effects of CGM device type/calibration and CGM sensor location on results from DFA. Methods This study uses CGM data from critically ill patients who were each monitored concurrently using Medtronic iPro2s on the thigh and abdomen and a Medtronic Guardian REAL-Time on the abdomen. This allowed interdevice/calibration type and intersensor site variation to be assessed. Detrended fluctuation analysis is a technique that has previously been used to determine the complexity of CGM data in critically ill patients. Two variants of DFA, monofractal and multifractal, were used to assess the complexity of sensor glucose data as well as the precalibration raw sensor current. Monofractal DFA produces a scaling exponent (H), where H is inversely related to complexity. The results of multifractal DFA are presented graphically by the multifractal spectrum. Results From the 10 patients recruited, 26 CGM devices produced data suitable for analysis. The values of H from abdominal iPro2 data were 0.10 (0.03–0.20) higher than those from Guardian REAL-Time data, indicating consistently lower complexities in iPro2 data. However, repeating the analysis on the raw sensor current showed little or no difference in complexity. Sensor site had little effect on the scaling exponents in this data set. Finally, multifractal DFA revealed no significant associations between the multifractal spectrums and CGM device type/calibration or sensor location. Conclusions Monofractal DFA results are dependent on the device/calibration used to obtain CGM data, but sensor location has little impact. Future studies of glucose complexity should consider the findings presented here when designing their investigations. PMID:24351175

Morphological Properties of Siloxane-Hydrogel Contact Lens Surfaces.

PubMed

Stach, Sebastian; Ţălu, Ştefan; Trabattoni, Silvia; Tavazzi, Silvia; Głuchaczka, Alicja; Siek, Patrycja; Zając, Joanna; Giovanzana, Stefano

2017-04-01

The aim of this study was to quantitatively characterize the micromorphology of contact lens (CL) surfaces using atomic force microscopy (AFM) and multifractal analysis. AFM and multifractal analysis were used to characterize the topography of new and worn siloxane-hydrogel CLs made of Filcon V (I FDA group). CL surface roughness was studied by AFM in intermittent-contact mode, in air, on square areas of 25 and 100 μm 2 , by using a Nanoscope V MultiMode (Bruker). Detailed surface characterization of the surface topography was obtained using statistical parameters of 3-D (three-dimensional) surface roughness, in accordance with ISO 25178-2: 2012. Before wear, the surface was found to be characterized by out-of-plane and sharp structures, whilst after a wear of 8 h, two typical morphologies were observed. One morphology (sharp type) has a similar aspect as the unworn CLs and the other morphology (smooth type) is characterized by troughs and bumpy structures. The analysis of the AFM images revealed a multifractal geometry. The generalized dimension D q and the singularity spectrum f(α) provided quantitative values that characterize the local scale properties of CL surface geometry at nanometer scale. Surface statistical parameters deduced by multifractal analysis can be used to assess the CL micromorphology and can be used by manufacturers in developing CLs with improved surface characteristics. These parameters can also be used in understanding the tribological interactions of the back surface of the CL with the corneal surface and the front surface of the CL with the under-surface of the eyelid (friction, wear, and micro-elastohydrodynamic lubrication at a nanometer scale).

Multifractal analysis of a GCM climate

NASA Astrophysics Data System (ADS)

Carl, P.

2003-04-01

Multifractal analysis using the Wavelet Transform Modulus Maxima (WTMM) approach is being applied to the climate of a Mintz--Arakawa type, coarse resolution, two--layer AGCM. The model shows a backwards running period multiplication scenario throughout the northern summer, subsequent to a 'hard', subcritical Hopf bifurcation late in spring. This 'route out of chaos' (seen in cross sections of a toroidal phase space structure) is born in the planetary monsoon system which inflates the seasonal 'cycle' into these higher order structures and is blamed for the pronounced intraseasonal--to--centennial model climate variability. Previous analyses of the latter using advanced modal decompositions showed regularity based patterns in the time--frequency plane which are qualitatively similar to those obtained from the real world. The closer look here at the singularity structures, as a fundamental diagnostic supplement, aims at both more complete understanding (and quantification) of the model's qualitative dynamics and search for further tools of model intercomparison and verification in this respect. Analysing wavelet is the 10th derivative of the Gaussian which might suffice to suppress regular patterns in the data. Intraseasonal attractors, studied in time series of model precipitation over Central India, show shifting and braodening singularity spectra towards both more violent extreme events (premonsoon--monsoon transition) and weaker events (late summer to postmonsoon transition). Hints at a fractal basin boundary are found close to transition from period--2 to period--1 in the monsoon activity cycle. Interannual analyses are provided for runs with varied solar constants. To address the (in--)stationarity issue, first results are presented with a windowed multifractal analysis of longer--term runs ("singularity spectrogram").

Complexity and multifractality of neuronal noise in mouse and human hippocampal epileptiform dynamics

NASA Astrophysics Data System (ADS)

Serletis, Demitre; Bardakjian, Berj L.; Valiante, Taufik A.; Carlen, Peter L.

2012-10-01

Fractal methods offer an invaluable means of investigating turbulent nonlinearity in non-stationary biomedical recordings from the brain. Here, we investigate properties of complexity (i.e. the correlation dimension, maximum Lyapunov exponent, 1/fγ noise and approximate entropy) and multifractality in background neuronal noise-like activity underlying epileptiform transitions recorded at the intracellular and local network scales from two in vitro models: the whole-intact mouse hippocampus and lesional human hippocampal slices. Our results show evidence for reduced dynamical complexity and multifractal signal features following transition to the ictal epileptiform state. These findings suggest that pathological breakdown in multifractal complexity coincides with loss of signal variability or heterogeneity, consistent with an unhealthy ictal state that is far from the equilibrium of turbulent yet healthy fractal dynamics in the brain. Thus, it appears that background noise-like activity successfully captures complex and multifractal signal features that may, at least in part, be used to classify and identify brain state transitions in the healthy and epileptic brain, offering potential promise for therapeutic neuromodulatory strategies for afflicted patients suffering from epilepsy and other related neurological disorders. This paper is based on chapter 5 of Serletis (2010 PhD Dissertation Department of Physiology, Institute of Biomaterials and Biomedical Engineering, University of Toronto).

Assessment of 48 Stock markets using adaptive multifractal approach

NASA Astrophysics Data System (ADS)

Ferreira, Paulo; Dionísio, Andreia; Movahed, S. M. S.

2017-11-01

In this paper, Stock market comovements are examined using cointegration, Granger causality tests and nonlinear approaches in context of mutual information and correlations. Since underlying data sets are affected by non-stationarities and trends, we also apply Adaptive Multifractal Detrended Fluctuation Analysis (AMF-DFA) and Adaptive Multifractal Detrended Cross-Correlation Analysis (AMF-DXA). We find only 170 pair of Stock markets cointegrated, and according to the Granger causality and mutual information, we realize that the strongest relations lies between emerging markets, and between emerging and frontier markets. According to scaling exponent given by AMF-DFA, h(q = 2) > 1, we find that all underlying data sets belong to non-stationary process. According to Efficient Market Hypothesis (EMH), only 8 markets are classified in uncorrelated processes at 2 σ confidence interval. 6 Stock markets belong to anti-correlated class and dominant part of markets has memory in corresponding daily index prices during January 1995 to February 2014. New-Zealand with H = 0 . 457 ± 0 . 004 and Jordan with H = 0 . 602 ± 0 . 006 are far from EMH. The nature of cross-correlation exponents based on AMF-DXA is almost multifractal for all pair of Stock markets. The empirical relation, Hxy ≤ [Hxx +Hyy ] / 2, is confirmed. Mentioned relation for q > 0 is also satisfied while for q < 0 there is a deviation from this relation confirming behavior of markets for small fluctuations is affected by contribution of major pair. For larger fluctuations, the cross-correlation contains information from both local (internal) and global (external) conditions. Width of singularity spectrum for auto-correlation and cross-correlation are Δαxx ∈ [ 0 . 304 , 0 . 905 ] and Δαxy ∈ [ 0 . 246 , 1 . 178 ] , respectively. The wide range of singularity spectrum for cross-correlation confirms that the bilateral relation between Stock markets is more complex. The value of σDCCA indicates that all pairs of stock market studied in this time interval belong to cross-correlated processes.

Multiscale multifractal DCCA and complexity behaviors of return intervals for Potts price model

NASA Astrophysics Data System (ADS)

Wang, Jie; Wang, Jun; Stanley, H. Eugene

2018-02-01

To investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events, we use a Potts dynamic system to construct a random financial time series model of the attitudes of market traders. We use multiscale multifractal detrended cross-correlation analysis (MM-DCCA) and Lempel-Ziv complexity (LZC) perform numerical research of the return intervals for two significant China's stock market indices and for the proposed model. The new MM-DCCA method is based on the Hurst surface and provides more interpretable cross-correlations of the dynamic mechanism between different return interval series. We scale the LZC method with different exponents to illustrate the complexity of return intervals in different scales. Empirical studies indicate that the proposed return intervals from the Potts system and the real stock market indices hold similar statistical properties.

Linear and Nonlinear Statistical Characterization of DNA

NASA Astrophysics Data System (ADS)

Norio Oiwa, Nestor; Goldman, Carla; Glazier, James

2002-03-01

We find spatial order in the distribution of protein-coding (including RNAs) and control segments of GenBank genomic sequences, irrespective of ATCG content. This is achieved by correlations, histograms, fractal dimensions and singularity spectra. Estimates of these quantities in complete nuclear genome indicate that coding sequences are long-range correlated and their disposition are self-similar (multifractal) for eukaryotes. These characteristics are absent in prokaryotes, where there are few noncoding sequences, suggesting the `junk' DNA play a relevant role to the genome structure and function. Concerning the genetic message of ATCG sequences, we build a random walk (Levy flight), using DNA symmetry arguments, where we associate A, T, C and G as left, right, down and up steps, respectively. Nonlinear analysis of mitochondrial DNA walks reveal multifractal pattern based on palindromic sequences, which fold in hairpins and loops.

A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs

NASA Astrophysics Data System (ADS)

Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin

2018-05-01

It is generally argued that the solution to a stochastic PDE with multiplicative noise—such as \\dot{u}= 1/2 u''+uξ, where {ξ} denotes space-time white noise—routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (Arch Ration Mech Anal 177:115-150, 2005), Gibbon and Titi (Proc R Soc A 461:3089-3097, 2005), and Zimmermann et al. (Phys Rev Lett 85(17):3612-3615, 2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (J Phys A 22(13):2621-2626, 1989; Proc Lond Math Soc (3) 64:125-152, 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.

A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs

NASA Astrophysics Data System (ADS)

Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin

2018-04-01

It is generally argued that the solution to a stochastic PDE with multiplicative noise—such as \\dot{u}= 1/2 u''+uξ, where {ξ} denotes space-time white noise—routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (Arch Ration Mech Anal 177:115-150, 2005), Gibbon and Titi (Proc R Soc A 461:3089-3097, 2005), and Zimmermann et al. (Phys Rev Lett 85(17):3612-3615, 2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (J Phys A 22(13):2621-2626, 1989; Proc Lond Math Soc (3) 64:125-152, 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.

Expectations on Hierarchical Scales of Discourse: Multifractality Predicts Both Short- and Long-Range Effects of Violating Gender Expectations in Text Reading

ERIC Educational Resources Information Center

Booth, Chase R.; Brown, Hannah L.; Eason, Elizabeth G.; Wallot, Sebastian; Kelty-Stephen, Damian G.

2018-01-01

Reader expectations form across hierarchical scales of discourse (e.g., from coarse to fine: genre, narrative, syntax). Cross-scale interactivity produces word reading times (RTs) with multifractal structure. After introducing multifractals, we test two hypotheses regarding their relevance to reader expectations: (1) multifractal evidence of…

Spatial and radiometric characterization of multi-spectrum satellite images through multi-fractal analysis

NASA Astrophysics Data System (ADS)

Alonso, Carmelo; Tarquis, Ana M.; Zúñiga, Ignacio; Benito, Rosa M.

2017-03-01

Several studies have shown that vegetation indexes can be used to estimate root zone soil moisture. Earth surface images, obtained by high-resolution satellites, presently give a lot of information on these indexes, based on the data of several wavelengths. Because of the potential capacity for systematic observations at various scales, remote sensing technology extends the possible data archives from the present time to several decades back. Because of this advantage, enormous efforts have been made by researchers and application specialists to delineate vegetation indexes from local scale to global scale by applying remote sensing imagery. In this work, four band images have been considered, which are involved in these vegetation indexes, and were taken by satellites Ikonos-2 and Landsat-7 of the same geographic location, to study the effect of both spatial (pixel size) and radiometric (number of bits coding the image) resolution on these wavelength bands as well as two vegetation indexes: the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI). In order to do so, a multi-fractal analysis of these multi-spectral images was applied in each of these bands and the two indexes derived. The results showed that spatial resolution has a similar scaling effect in the four bands, but radiometric resolution has a larger influence in blue and green bands than in red and near-infrared bands. The NDVI showed a higher sensitivity to the radiometric resolution than EVI. Both were equally affected by the spatial resolution. From both factors, the spatial resolution has a major impact in the multi-fractal spectrum for all the bands and the vegetation indexes. This information should be taken in to account when vegetation indexes based on different satellite sensors are obtained.

Multifractal analysis of multiparticle emission data in the framework of visibility graph and sandbox algorithm

NASA Astrophysics Data System (ADS)

Mali, P.; Manna, S. K.; Mukhopadhyay, A.; Haldar, P. K.; Singh, G.

2018-03-01

Multiparticle emission data in nucleus-nucleus collisions are studied in a graph theoretical approach. The sandbox algorithm used to analyze complex networks is employed to characterize the multifractal properties of the visibility graphs associated with the pseudorapidity distribution of charged particles produced in high-energy heavy-ion collisions. Experimental data on 28Si+Ag/Br interaction at laboratory energy Elab = 14 . 5 A GeV, and 16O+Ag/Br and 32S+Ag/Br interactions both at Elab = 200 A GeV, are used in this analysis. We observe a scale free nature of the degree distributions of the visibility and horizontal visibility graphs associated with the event-wise pseudorapidity distributions. Equivalent event samples simulated by ultra-relativistic quantum molecular dynamics, produce degree distributions that are almost identical to the respective experiment. However, the multifractal variables obtained by using sandbox algorithm for the experiment to some extent differ from the respective simulated results.

Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series

NASA Astrophysics Data System (ADS)

Pal, Mayukha; Madhusudana Rao, P.; Manimaran, P.

2014-12-01

We apply the recently developed multifractal detrended cross-correlation analysis method to investigate the cross-correlation behavior and fractal nature between two non-stationary time series. We analyze the daily return price of gold, West Texas Intermediate and Brent crude oil, foreign exchange rate data, over a period of 18 years. The cross correlation has been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the results, the existence of multifractal cross-correlation between all of these time series is found. We also found that the cross correlation between gold and oil prices possess uncorrelated behavior and the remaining bivariate time series possess persistent behavior. It was observed for five bivariate series that the cross-correlation exponents are less than the calculated average generalized Hurst exponents (GHE) for q<0 and greater than GHE when q>0 and for one bivariate series the cross-correlation exponent is greater than GHE for all q values.

Characterizing spatial heterogeneity based on the b-value and fractal analyses of the 2015 Nepal earthquake sequence

NASA Astrophysics Data System (ADS)

Nampally, Subhadra; Padhy, Simanchal; Dimri, Vijay P.

2018-01-01

The nature of spatial distribution of heterogeneities in the source area of the 2015 Nepal earthquake is characterized based on the seismic b-value and fractal analysis of its aftershocks. The earthquake size distribution of aftershocks gives a b-value of 1.11 ± 0.08, possibly representing the highly heterogeneous and low stress state of the region. The aftershocks exhibit a fractal structure characterized by a spectrum of generalized dimensions, Dq varying from D2 = 1.66 to D22 = 0.11. The existence of a fractal structure suggests that the spatial distribution of aftershocks is not a random phenomenon, but it self-organizes into a critical state, exhibiting a scale-independent structure governed by a power-law scaling, where a small perturbation in stress is sufficient enough to trigger aftershocks. In order to obtain the bias in fractal dimensions resulting from finite data size, we compared the multifractal spectrum for the real data and random simulations. On comparison, we found that the lower limit of bias in D2 is 0.44. The similarity in their multifractal spectra suggests the lack of long-range correlation in the data, with an only weakly multifractal or a monofractal with a single correlation dimension D2 characterizing the data. The minimum number of events required for a multifractal process with an acceptable error is discussed. We also tested for a possible correlation between changes in D2 and energy released during the earthquakes. The values of D2 rise during the two largest earthquakes (M > 7.0) in the sequence. The b- and D2 values are related by D2 = 1.45 b that corresponds to the intermediate to large earthquakes. Our results provide useful constraints on the spatial distribution of b- and D2-values, which are useful for seismic hazard assessment in the aftershock area of a large earthquake.

Multifractal analysis of the Korean agricultural market

NASA Astrophysics Data System (ADS)

Kim, Hongseok; Oh, Gabjin; Kim, Seunghwan

2011-11-01

We have studied the long-term memory effects of the Korean agricultural market using the detrended fluctuation analysis (DFA) method. In general, the return time series of various financial data, including stock indices, foreign exchange rates, and commodity prices, are uncorrelated in time, while the volatility time series are strongly correlated. However, we found that the return time series of Korean agricultural commodity prices are anti-correlated in time, while the volatility time series are correlated. The n-point correlations of time series were also examined, and it was found that a multifractal structure exists in Korean agricultural market prices.

Statistical and Multifractal Evaluation of Soil Compaction in a Vineyard

NASA Astrophysics Data System (ADS)

Marinho, M.; Raposo, J. R.; Mirás Avalos, J. M.; Paz González, A.

2012-04-01

One of the detrimental effects caused by agricultural machines is soil compaction, which can be defined by an increase in soil bulk density. Soil compaction often has a negative impact on plant growth, since it reduces the macroporosity and soil permeability and increases resistance to penetration. Our research explored the effect of the agricultural machinery on soil when trafficking through a vineyard at a small spatial scale, based on the evaluation of the soil compaction status. The objectives of this study were: i) to quantify soil bulk density along transects following wine row, wheel track and outside track, and, ii) to characterize the variability of the bulk density along these transects using multifractal analysis. The field work was conducted at the experimental farm of EVEGA (Viticulture and Enology Centre of Galicia) located in Ponte San Clodio, Leiro, Orense, Spain. Three parallel transects were marked on positions with contrasting machine traffic effects, i.e. vine row, wheel-track and outside-track. Undisturbed samples were collected in 16 points of each transect, spaced 0.50 m apart, for bulk density determination using the cylinder method. Samples were taken in autumn 2011, after grape harvest. Since soil between vine rows was tilled and homogenized beginning spring 2011, cumulative effects of traffic during the vine growth period could be evaluated. The distribution patterns of soil bulk density were characterized by multifractal analysis carried out by the method of moments. Multifractality was assessed by several indexes derived from the mass exponent, τq, the generalized dimension, Dq, and the singularity spectrum, f(α), curves. Mean soil bulk density values determined for vine row, outside-track and wheel-track transects were 1.212 kg dm-3, 1.259 kg dm-3and 1.582 kg dm-3, respectively. The respective coefficients of variation (CV) for these three transects were 7.76%, 4.82% and 2.03%. Therefore mean bulk density under wheel-track was 30.5% higher than along the vine row. Vine row and outside-track positions showed not significant differences between means. The bulk density of the wheel-track transect also showed the lowest CV. The multifractal spectra of the three transects were asymmetric curves, rather short toward the left and much longer toward the right. The width of the right deviating shaped multifractal spectra was ranked as: wine row > outside-track ≈ wheel-track. Entropy dimension, D1, was 0.998, 0.992 and 0.992 for vine row, outside-track and track transects, respectively. These results show different patterns of variability of bulk density for parallel transects. They also suggest that multifractal parameters may be useful in assessing the variability of other soil properties such as soil particle density, soil porosity or soil water content, at different spatial scales as well. Acknowledgments. This work was funded in part by Spanish Ministry of Science and Innovation (MICINN) in the frame of project CGL2009-13700-C02. Financial support from CAPES/GOV., Brazil, is also acknowledged by Prof. M. Marinho.

Multifractal characteristics of NDVI maps in space and time in the Community of Madrid (Spain)

NASA Astrophysics Data System (ADS)

Sotoca, Juan J. Martin; Saa-Requejo, Antonio; Grau, Juan B.; Tarquis, Ana M.

2015-04-01

Satellite information has contributed to improve our understanding of the spatial variability of hydro-climatic and ecological processes. Vegetation activity is tightly coupled with climate, hydro-ecological fluxes, and terrain dynamics in river basins at a wide range of space-time scales (Scheuring and Riedi, 1994). Indices of vegetation activity are constructed using satellite information of reflectance of the relevant spectral bands which enhance the contribution of vegetation being Normalized Difference Vegetation Index (NDVI) widely used. How can we study such a complex system? Multifractals and fractals are related techniques mainly used in physics to characterize the scaling behaviour of a system; they differ in that fractals look at the geometry of presence/absence patterns, while multifractals look at the arrangement of quantities such as population or biomass densities (Saravia et al., 2012). Scaling laws are an emergent general feature of ecological systems; they reflect constraints in their organization that can provide tracks about the underlying mechanisms (Solé and Bascompte, 2006). In this work, we have applied these techniques to study the spatial pattern through one year of NDVI maps. A rectangular area that includes the Community of Madrid and part of the surroundings, consisting of 300 x 280 pixels with a resolution of 500 x 500 m2 has been selected and monthly NDVI maps analyzed using the multifractal spectrum and the map of singularities (Cheng and Agterberg, 1996). The results show a cyclical pattern in the multifractal behaviour and singularity points related to river basin networks (Martín-Sotoca, 2014). References Cheng, Q. and Agterberg, F.P. (1996). Multifractal modeling and spatial statistics. Math. Geol. Vol 28, 1-16. Martín-Sotoca, J.J. (2014) Estructura Espacial de la Sequía en Pastos y sus Aplicaciones en el Seguro Agrario. Master Thesis, UPM (In Spanish). Saravia LA, Giorgi A, Momo F.: Multifractal growth in periphyton communities. Oikos. 2012;121(11):1810-1820 10.1111/j.1600-0706.2011.20423.x Scheuring, I., Riedi, R.H., 1994. Application of multifractals to the analysis of vegetation pattern. J. Veg. Sci. 5, 489-496. Solé RV, Bascompte J.: Self-organization in complex ecosystems. Princeton University Press,2006. Acknowledgements First author acknowledges the Research Grant obtained from CEIGRAM in 2014

Multifractal surrogate-data generation algorithm that preserves pointwise Hölder regularity structure, with initial applications to turbulence

NASA Astrophysics Data System (ADS)

Keylock, C. J.

2017-03-01

An algorithm is described that can generate random variants of a time series while preserving the probability distribution of original values and the pointwise Hölder regularity. Thus, it preserves the multifractal properties of the data. Our algorithm is similar in principle to well-known algorithms based on the preservation of the Fourier amplitude spectrum and original values of a time series. However, it is underpinned by a dual-tree complex wavelet transform rather than a Fourier transform. Our method, which we term the iterated amplitude adjusted wavelet transform can be used to generate bootstrapped versions of multifractal data, and because it preserves the pointwise Hölder regularity but not the local Hölder regularity, it can be used to test hypotheses concerning the presence of oscillating singularities in a time series, an important feature of turbulence and econophysics data. Because the locations of the data values are randomized with respect to the multifractal structure, hypotheses about their mutual coupling can be tested, which is important for the velocity-intermittency structure of turbulence and self-regulating processes.

From standard alpha-stable Lévy motions to horizontal visibility networks: dependence of multifractal and Laplacian spectrum

NASA Astrophysics Data System (ADS)

Zou, Hai-Long; Yu, Zu-Guo; Anh, Vo; Ma, Yuan-Lin

2018-05-01

In recent years, researchers have proposed several methods to transform time series (such as those of fractional Brownian motion) into complex networks. In this paper, we construct horizontal visibility networks (HVNs) based on the -stable Lévy motion. We aim to study the relations of multifractal and Laplacian spectrum of transformed networks on the parameters and of the -stable Lévy motion. First, we employ the sandbox algorithm to compute the mass exponents and multifractal spectrum to investigate the multifractality of these HVNs. Then we perform least squares fits to find possible relations of the average fractal dimension , the average information dimension and the average correlation dimension against using several methods of model selection. We also investigate possible dependence relations of eigenvalues and energy on , calculated from the Laplacian and normalized Laplacian operators of the constructed HVNs. All of these constructions and estimates will help us to evaluate the validity and usefulness of the mappings between time series and networks, especially between time series of -stable Lévy motions and HVNs.

Multifractal Characteristics of Axisymmetric Jet Turbulence Intensity from Rans Numerical Simulation

NASA Astrophysics Data System (ADS)

Seo, Yongwon; Ko, Haeng Sik; Son, Sangyoung

A turbulent jet bears diverse physical characteristics that have been unveiled yet. Of particular interest is to analyze the turbulent intensity, which has been a key factor to assess and determine turbulent jet performance since diffusive and mixing conditions are largely dependent on it. Multifractal measures are useful in terms of identifying characteristics of a physical quantity distributed over a spatial domain. This study examines the multifractal exponents of jet turbulence intensities obtained through numerical simulation. We acquired the turbulence intensities from numerical jet discharge experiments, where two types of nozzle geometry were tested based on a Reynolds-Averaged Navier-Stokes (RANS) equations. The k-𝜀 model and k-ω model were used for turbulence closure models. The results showed that the RANS model successfully regenerates transversal velocity profile, which is almost identical to an analytical solution. The RANS model also shows the decay of turbulence intensity in the longitudinal direction but it depends on the outfall nozzle lengths. The result indicates the existence of a common multifractal spectrum for turbulence intensity obtained from numerical simulation. Although the transverse velocity profiles are similar for two different turbulence models, the minimum Lipschitz-Hölder exponent (αmin) and entropy dimension (α1) are different. These results suggest that the multifractal exponents capture the difference in turbulence structures of hierarchical turbulence intensities produced by different turbulence models.

Extended self-similarity in the two-dimensional metal-insulator transition

NASA Astrophysics Data System (ADS)

Moriconi, L.

2003-09-01

We show that extended self-similarity, a scaling phenomenon first observed in classical turbulent flows, holds for a two-dimensional metal-insulator transition that belongs to the universality class of random Dirac fermions. Deviations from multifractality, which in turbulence are due to the dominance of diffusive processes at small scales, appear in the condensed-matter context as a large-scale, finite-size effect related to the imposition of an infrared cutoff in the field theory formulation. We propose a phenomenological interpretation of extended self-similarity in the metal-insulator transition within the framework of the random β-model description of multifractal sets. As a natural step, our discussion is bridged to the analysis of strange attractors, where crossovers between multifractal and nonmultifractal regimes are found and extended self-similarity turns out to be verified as well.

Multifractal features in stock and foreign exchange markets

NASA Astrophysics Data System (ADS)

Kim, Kyungsik; Yoon, Seong-Min

2004-03-01

We investigate the tick dynamical behavior of three assets(the yen-dollar exchange rate, the won-dollar exchange rate, and the KOSPI) using the rescaled range analysis in stock and foreign exchange markets. The multifractal Hurst exponents with long-run memory effects can be obtained from assets, and we discuss whether it exists the crossover or not for the Hurst exponents at charateristic time scales. Particularly, we find that the probability distribution of prices is approached to a Lorentz distribution, different from fat-tailed properties.

Integrated Central-Autonomic Multifractal Complexity in the Heart Rate Variability of Healthy Humans

PubMed Central

Lin, D. C.; Sharif, A.

2012-01-01

Purpose of Study: The aim of this study was to characterize the central-autonomic interaction underlying the multifractality in heart rate variability (HRV) of healthy humans. Materials and Methods: Eleven young healthy subjects participated in two separate ~40 min experimental sessions, one in supine (SUP) and one in, head-up-tilt (HUT), upright (UPR) body positions. Surface scalp electroencephalography (EEG) and electrocardiogram (ECG) were collected and fractal correlation of brain and heart rate data was analyzed based on the idea of relative multifractality. The fractal correlation was further examined with the EEG, HRV spectral measures using linear regression of two variables and principal component analysis (PCA) to find clues for the physiological processing underlying the central influence in fractal HRV. Results: We report evidence of a central-autonomic fractal correlation (CAFC) where the HRV multifractal complexity varies significantly with the fractal correlation between the heart rate and brain data (P = 0.003). The linear regression shows significant correlation between CAFC measure and EEG Beta band spectral component (P = 0.01 for SUP and P = 0.002 for UPR positions). There is significant correlation between CAFC measure and HRV LF component in the SUP position (P = 0.04), whereas the correlation with the HRV HF component approaches significance (P = 0.07). The correlation between CAFC measure and HRV spectral measures in the UPR position is weak. The PCA results confirm these findings and further imply multiple physiological processes underlying CAFC, highlighting the importance of the EEG Alpha, Beta band, and the HRV LF, HF spectral measures in the supine position. Discussion and Conclusion: The findings of this work can be summarized into three points: (i) Similar fractal characteristics exist in the brain and heart rate fluctuation and the change toward stronger fractal correlation implies the change toward more complex HRV multifractality. (ii) CAFC is likely contributed by multiple physiological mechanisms, with its central elements mainly derived from the EEG Alpha, Beta band dynamics. (iii) The CAFC in SUP and UPR positions is qualitatively different, with a more predominant central influence in the fractal HRV of the UPR position. PMID:22403548

Multifractality in individual honeybee behavior hints at colony-specific social cascades: Reanalysis of radio-frequency identification data from five different colonies

NASA Astrophysics Data System (ADS)

Carver, Nicole S.; Kelty-Stephen, Damian G.

2017-02-01

Honeybees (Apis mellifera) exhibit complex coordination and interaction across multiple behaviors such as swarming. This coordination among honeybees in the same colony is remarkably similar to the concept of informational cascades. The multifractal geometry of cascades suggests that multifractal measures of individual honeybee activity might carry signatures of these colony-wide coordinations. The present work reanalyzes time stamps of entrances to and exits from the hive captured by radio-frequency identification (RFID) sensors reading RFID tags on individual bees. Indeed, both multifractal spectrum width for individual bees' inter-reading interval series and differences of those widths from surrogates significantly predicted not just whether the individual bee's hive had a mesh enclosure but also predicted the specific membership of individual bees in one of five colonies. The significant effects of multifractality in matching honeybee activity to type of colony and, further, matching individual honeybees to their exact home colony suggests that multifractality quantifies key features of the colony-wide interactions across many scales. This relevance of multifractality to predicting colony type or colony membership adds additional credence to the cascade metaphor for colony organization. Perhaps, multifractality provides a new tool for exploring the relationship between individual organisms and larger, more complex social behaviors.

Nonlinear dynamics of the atmospheric pollutants in Mexico City

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, Alejandro; Barrera-Ferrer, Amilcar; Angulo-Brown, Fernando

2014-05-01

The atmospheric pollution in the Metropolitan Zone of Mexico City (MZMC) is a serious problem with social, economical and political consequences, in virtue that it is the region which concentrates both the greatest country population and a great part of commercial and industrial activities. According to the World Health Organization, maximum permissible concentrations of atmospheric pollutants are exceeded frequently. In the MZMC, the environmental monitoring has been limited to criteria pollutants, named in this way due to when their levels are measured in the atmosphere, they indicate in a precise way the air quality. The Automatic Atmospheric Monitoring Network monitors and registers the values of pollutants concentration in air in the MZMC. Actually, it is integrated by approximately 35 automatic-equipped remote stations, which report an every-hour register. Local and global invariant quantities have been widely used to describe the fractal properties of diverse time series. In the study of certain time series, many times it is assumed that they are monofractal, which means that they can be described only with one fractal dimension. But this hypothesis is unrealistic because a lot of time series are heterogeneous and non stationary, so their scaling properties are not the same throughout time and therefore they may require more fractal dimensions for their description. Complexity of the atmospheric pollutants dynamics suggests us to analyze its time series of hourly concentration registers with the multifractal formalism. So, in this work, air concentration time series of MZMC criteria pollutants were studied with the proposed method. The chosen pollutants to perform this analysis are ozone, sulfur dioxide, carbon monoxide, nitrogen dioxide and PM10 (particles less than 10 micrometers). We found that pollutants air concentration time series are multifractal. When we calculate the degree of multifractality for each time series we know that while more multifractal are the time series, there is more complexity both in the time series and in the system from which the measurements were obtained. We studied the variation of the degree of multifractality over time, by calculating the multifractal spectra of the time series for each year; we see the variation in each monitoring station from 1990 until 2013. Multifractal analysis can tell us what kinds of correlations are present in the time series, and it is interesting to consider how these correlations vary over time. Our results show that for all the pollutants and all the monitoring stations the time series have long range correlations and they are highly persistent.

Diagnostics of multi-fractality of magnetized plasma inside coronal holes and quiet sun areas

NASA Astrophysics Data System (ADS)

Abramenko, Valentyna

Turbulent and multi-fractal properties of magnetized plasma in solar Coronal Holes (CHs) and Quiet Sun (QS) photosphere were explored using high-resolution magnetograms measured with the New Solar Telescope (NST) at the Big Bear Solar Observatory (BBSO, USA), Hinode/SOT and SDO/HMI instruments. Distribution functions of size and magnetic flux measured for small-scale magnetic elements follow the log-normal law, which implies multi-fractal organization of the magnetic field and the absence of a unique power law for all scales. The magnetograms show multi-fractality in CHs on scales 400 - 10000 km, which becomes better pronounced as the spatial resolution of data improves. Photospheric granulation measured with NST exhibits multi-fractal properties on very small scales of 50 - 600 km. While multi-fractal nature of solar active regions is well known, newly established multi-fractality of weakest magnetic fields on the solar surface, i.e., in CHs and QS, leads us to a conclusion that the entire variety of solar magnetic fields is generated by a unique nonlinear dynamical process.

Downscaling Soil Moisture in the Southern Great Plains Through a Calibrated Multifractal Model for Land Surface Modeling Applications

NASA Technical Reports Server (NTRS)

Mascaro, Giuseppe; Vivoni, Enrique R.; Deidda, Roberto

2010-01-01

Accounting for small-scale spatial heterogeneity of soil moisture (theta) is required to enhance the predictive skill of land surface models. In this paper, we present the results of the development, calibration, and performance evaluation of a downscaling model based on multifractal theory using aircraft!based (800 m) theta estimates collected during the southern Great Plains experiment in 1997 (SGP97).We first demonstrate the presence of scale invariance and multifractality in theta fields of nine square domains of size 25.6 x 25.6 sq km, approximately a satellite footprint. Then, we estimate the downscaling model parameters and evaluate the model performance using a set of different calibration approaches. Results reveal that small-scale theta distributions are adequately reproduced across the entire region when coarse predictors include a dynamic component (i.e., the spatial mean soil moisture ) and a stationary contribution accounting for static features (i.e., topography, soil texture, vegetation). For wet conditions, we found similar multifractal properties of soil moisture across all domains, which we ascribe to the signature of rainfall spatial variability. For drier states, the theta fields in the northern domains are more intermittent than in southern domains, likely because of differences in the distribution of vegetation coverage. Through our analyses, we propose a regional downscaling relation for coarse, satellite-based soil moisture estimates, based on ancillary information (static and dynamic landscape features), which can be used in the study area to characterize statistical properties of small-scale theta distribution required by land surface models and data assimilation systems.

Evolution of Multiscale Multifractal Turbulence in the Heliosphere

NASA Astrophysics Data System (ADS)

Macek, W. M.; Wawrzaszek, A.

2009-04-01

The aim of this study is to examine the question of scaling properties of intermittent turbulence in the space environment. We analyze time series of velocities of the slow and fast speed streams of the solar wind measured in situ by Helios 2, Advanced Composition Explorer and Voyager 2 spacecraft in the inner and outer heliosphere during solar minimum and maximum at various distances from the Sun. To quantify asymmetric scaling of solar wind turbulence, we consider a generalized two-scale weighted Cantor set with two different scales describing nonuniform distribution of the kinetic energy flux between cascading eddies of various sizes. We investigate the resulting spectrum of generalized dimensions and the corresponding multifractal singularity spectrum depending on one probability measure parameter and two rescaling parameters, demonstrating that the multifractal scaling is often rather asymmetric. In particular, we show that the degree of multifractality for the solar wind during solar minimum is greater for fast streams velocity fluctuations than that for the slow streams; the fast wind during solar minimum may exhibit strong asymmetric scaling. Moreover, we observe the evolution of multifractal scaling of the solar wind in the outer heliosphere. It is worth noting that for the model with two different scaling parameters a much better agreement with the solar wind data is obtained, especially for the negative index of the generalized dimensions. Therefore we argue that there is a need to use a two-scale cascade model. Hence we propose this new more general model as a useful tool for analysis of intermittent turbulence in various environments. References [1] W. M. Macek and A. Szczepaniak, Generalized two-scale weighted Cantor set model for solar wind turbulence, Geophys. Res. Lett., 35, L02108, doi:10.1029/2007GL032263 (2008). [2] A. Szczepaniak and W. M. Macek, Asymmetric multifractal model for solar wind intermittent turbulence, Nonlin. Processes Geophys., 15, 615-620 (2008), http://www.nonlin-processes-geophys.net/15/615/2008/. [3] W. M. Macek and A. Wawrzaszek, Evolution of asymmetric multifractal scaling of solar wind turbulence in the outer heliosphere, J. Geophys. Res., A013795, doi:10.1029/2008JA013795, in press.

Model for interevent times with long tails and multifractality in human communications: An application to financial trading

NASA Astrophysics Data System (ADS)

Perelló, Josep; Masoliver, Jaume; Kasprzak, Andrzej; Kutner, Ryszard

2008-09-01

Social, technological, and economic time series are divided by events which are usually assumed to be random, albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics has therefore become a central issue. The approach we present is taken from the continuous-time random-walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the intertransaction time intervals of several financial markets. We observe that empirical data describe a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. A stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.

Cross-correlations between agricultural commodity futures markets in the US and China

NASA Astrophysics Data System (ADS)

Li, Zhihui; Lu, Xinsheng

2012-08-01

This paper examines the cross-correlation properties of agricultural futures markets between the US and China using a cross-correlation statistic test and multifractal detrended cross-correlation analysis (MF-DCCA). The results show that the cross-correlations between the two geographically distant markets for four pairs of important agricultural commodities futures are significantly multifractal. By introducing the concept of a “crossover”, we find that the multifractality of cross-correlations between the two markets is not long lasting. The cross-correlations in the short term are more strongly multifractal, but they are weakly so in the long term. Moreover, cross-correlations of small fluctuations are persistent and those of large fluctuations are anti-persistent in the short term while cross-correlations of all kinds of fluctuations for soy bean and soy meal futures are persistent and for corn and wheat futures are anti-persistent in the long term. We also find that cross-correlation exponents are less than the averaged generalized Hurst exponent when q<0 and more than the averaged generalized Hurst exponent when q>0 in the short term, while in the long term they are almost the same.

Multifractal spectra of laser Doppler flowmetry signals in healthy and sleep apnea syndrome subjects

NASA Astrophysics Data System (ADS)

Buard, Benjamin; Trzepizur, Wojciech; Mahe, Guillaume; Chapeau-Blondeau, François; Rousseau, David; Gagnadoux, Frédéric; Abraham, Pierre; Humeau, Anne

2009-07-01

Laser Doppler flowmetry (LDF) signals give a peripheral view of the cardiovascular system. To better understand the possible modifications brought by sleep apnea syndrome (SAS) in LDF signals, we herein propose to analyze the complexity of such signals in obstructive SAS subjects, and to compare the results with those obtained in healthy subjects. SAS is a pathology that leads to a drop in the parasympathetic tone associated with an increase in the sympathetic tone in awakens SAS patients. Nine men with obstructive SAS and nine healthy men participated awaken in our study and LDF signals were recorded in the forearm. In our work, complexity of LDF signals is analyzed through the computation and analysis of their multifractal spectra. The multifractal spectra are estimated by first estimating the discrete partition function of the signals, then by determining their Renyi exponents with a linear regression, and finally by computing their Legendre transform. The results show that, at rest, obstructive SAS has no or little impact on the multifractal spectra of LDF signals recorded in the forearm. This study shows that the physiological modifications brought by obstructive SAS do not modify the complexity of LDF signals when recorded in the forearm.

Long memory and multifractality: A joint test

NASA Astrophysics Data System (ADS)

Goddard, John; Onali, Enrico

2016-06-01

The properties of statistical tests for hypotheses concerning the parameters of the multifractal model of asset returns (MMAR) are investigated, using Monte Carlo techniques. We show that, in the presence of multifractality, conventional tests of long memory tend to over-reject the null hypothesis of no long memory. Our test addresses this issue by jointly estimating long memory and multifractality. The estimation and test procedures are applied to exchange rate data for 12 currencies. Among the nested model specifications that are investigated, in 11 out of 12 cases, daily returns are most appropriately characterized by a variant of the MMAR that applies a multifractal time-deformation process to NIID returns. There is no evidence of long memory.

Extracting sensitive spectrum bands of rapeseed using multiscale multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Jiang, Shan; Wang, Fang; Shen, Luming; Liao, Guiping; Wang, Lin

2017-03-01

Spectrum technology has been widely used in crop non-destructive testing diagnosis for crop information acquisition. Since spectrum covers a wide range of bands, it is of critical importance to extract the sensitive bands. In this paper, we propose a methodology to extract the sensitive spectrum bands of rapeseed using multiscale multifractal detrended fluctuation analysis. Our obtained sensitive bands are relatively robust in the range of 534 nm-574 nm. Further, by using the multifractal parameter (Hurst exponent) of the extracted sensitive bands, we propose a prediction model to forecast the Soil and plant analyzer development values ((SPAD), often used as a parameter to indicate the chlorophyll content) and an identification model to distinguish the different planting patterns. Three vegetation indices (VIs) based on previous work are used for comparison. Three evaluation indicators, namely, the root mean square error, the correlation coefficient, and the relative error employed in the SPAD values prediction model all demonstrate that our Hurst exponent has the best performance. Four rapeseed compound planting factors, namely, seeding method, planting density, fertilizer type, and weed control method are considered in the identification model. The Youden indices calculated by the random decision forest method and the K-nearest neighbor method show that our Hurst exponent is superior to other three Vis, and their combination for the factor of seeding method. In addition, there is no significant difference among the five features for other three planting factors. This interesting finding suggests that the transplanting and the direct seeding would make a big difference in the growth of rapeseed.

Solar system plasma Turbulence: Observations, inteRmittency and Multifractals

NASA Astrophysics Data System (ADS)

Echim, Marius M.

2016-04-01

The FP7 project STORM is funded by the European Commission to "add value to existing data bases through a more comprehensive interpretation". STORM targets plasma and magnetic field databases collected in the solar wind (Ulysses and also some planetary missions), planetary magnetospheres (Venus Express, Cluster, a few orbits from Cassini), cometary magnetosheaths (e.g. Haley from Giotto observations). The project applies the same package of analysis methods on geomagnetic field observations from ground and on derived indices (e.g. AE, AL, AU, SYM-H). The analysis strategy adopted in STORM is built on the principle of increasing complexity, from lower (like, e.g., the Power Spectral Density - PSD) to higher order analyses (the Probability Distribution Functions - PDFs, Structure Functions - SFs, Fractals and Multifractals - MFs). Therefore STORM targets not only the spectral behavior of turbulent fluctuations but also their topology and scale behavior inferred from advanced mathematical algorithms and geometrical-like analogs. STORM started in January 2013 and ended in December 2015. We will report on a selection of scientific and technical achievements and will highlight: (1) the radial evolution of solar wind turbulence and intermittency based on Ulysses data with some contributions from Venus Express and Cluster; (2) comparative study of fast and slow wind turbulence and intermittency at solar minimum; (3) comparative study of the planetary response (Venus and Earth magnetosheaths) to turbulent solar wind; (4) the critical behavior of geomagnetic fluctuations and indices; (5) an integrated library for non-linear analysis of time series that includes all the approaches adopted in STORM to investigate solar system plasma turbulence. STORM delivers an unprecedented volume of analysed data for turbulence. The project made indeed a systematic survey, orbit by orbit, of data available from ESA repositories and Principal Investigators and provides results ordered as a function of the targeted system (solar wind/magnetospheres/geomagnetic indices), solar cycle phase (minimum versus maximum), type of result (PSDs, PDFs, Multifractals). The results catalogues, available online from http://www.storm-fp7.eu, include 4094 PSD spectra, 9566 PDFs and 15633 multifractal spectra (from partition function and respectively Rank Ordered (ROMA) formalisms). These results are obtained at solar maximum (2001-2002, both in the solar wind and the terrestrial magnetosheath) and solar minimum (1997-1998 in the solar wind, 2007-2008 in the solar wind, Venus and Earth magnetosheath and selected regions of the magnetosphere). Research supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 313038/STORM.

Multifractality analysis of crack images from indirect thermal drying of thin-film dewatered sludge

NASA Astrophysics Data System (ADS)

Wang, Weiyun; Li, Aimin; Zhang, Xiaomin; Yin, Yulei

2011-07-01

Crack formation is inevitable during sludge drying because of the existence of uneven thermal stress. Experiments have been conducted to study crack pattern formation in thin film sludge. Crack images show that the thinner the sewage sludge film, the more even the crack distribution. The crack changes from a flaky texture to a banded structure with increasing thickness. Multifractal methods are proposed to analyze the crack image of four different thicknesses of dried sludge. Several parameters are conducted for quantification of the crack image and the results indicate that the width of spectra increases with thicker sludge film, that is to say, nonunifromity of crack distribution increases with increasing thickness, which proves that the multifractal method is sensitive enough to quantify the crack distribution and can be seen as a new approach for the changing research of crack images of sewage sludge drying.

Complexity and multifractal behaviors of multiscale-continuum percolation financial system for Chinese stock markets

NASA Astrophysics Data System (ADS)

Zeng, Yayun; Wang, Jun; Xu, Kaixuan

2017-04-01

A new financial agent-based time series model is developed and investigated by multiscale-continuum percolation system, which can be viewed as an extended version of continuum percolation system. In this financial model, for different parameters of proportion and density, two Poisson point processes (where the radii of points represent the ability of receiving or transmitting information among investors) are applied to model a random stock price process, in an attempt to investigate the fluctuation dynamics of the financial market. To validate its effectiveness and rationality, we compare the statistical behaviors and the multifractal behaviors of the simulated data derived from the proposed model with those of the real stock markets. Further, the multiscale sample entropy analysis is employed to study the complexity of the returns, and the cross-sample entropy analysis is applied to measure the degree of asynchrony of return autocorrelation time series. The empirical results indicate that the proposed financial model can simulate and reproduce some significant characteristics of the real stock markets to a certain extent.

Intermittency measurement in two-dimensional bacterial turbulence

NASA Astrophysics Data System (ADS)

Qiu, Xiang; Ding, Long; Huang, Yongxiang; Chen, Ming; Lu, Zhiming; Liu, Yulu; Zhou, Quan

2016-06-01

In this paper, an experimental velocity database of a bacterial collective motion, e.g., Bacillus subtilis, in turbulent phase with volume filling fraction 84 % provided by Professor Goldstein at Cambridge University (UK), was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β -limitation. A dual-power-law behavior separated by the viscosity scale ℓν was observed for the q th -order Hilbert moment Lq(k ) . This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R , e.g., the bacterial body length. The measured scaling exponents ζ (q ) of both the small-scale (k >kν ) and large-scale (k

Single-Fraction Versus Multifraction (3 × 9 Gy) Stereotactic Radiosurgery for Large (>2 cm) Brain Metastases: A Comparative Analysis of Local Control and Risk of Radiation-Induced Brain Necrosis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Minniti, Giuseppe, E-mail: gminniti@ospedalesantandrea.it; IRCCS Neuromed, Pozzilli; Scaringi, Claudia

Purpose: To investigate the local control and radiation-induced brain necrosis in patients with brain metastases >2 cm in size who received single-fraction or multifraction stereotactic radiosurgery (SRS); factors associated with clinical outcomes and the development of brain radionecrosis were assessed. Methods and Materials: Two hundred eighty-nine consecutive patients with brain metastases >2.0 cm who received SRS as primary treatment at Sant'Andrea Hospital, University of Rome Sapienza, Rome, Italy, were analyzed. Cumulative incidence analysis was used to compare local control and radiation-induced brain necrosis between groups from the time of SRS. To achieve a balanced distribution of baseline covariates between treatment groups, amore » propensity score analysis was used. Results: The 1-year cumulative local control rates were 77% in the single-fraction SRS (SF-SRS) group and 91% in the multifraction SRS (MF-SRS) group (P=.01). Recurrences occurred in 25 and 11 patients who received SF-SRS or MF-SRS (P=.03), respectively. Thirty-one patients (20%) undergoing SF-SRS and 11 (8%) subjected to MF-SRS experienced brain radionecrosis (P=.004); the 1-year cumulative incidence rate of radionecrosis was 18% and 9% (P=.01), respectively. Significant differences between the 2 groups in terms of local control and risk of radionecrosis were maintained after propensity score adjustment. Conclusions: Multifraction SRS at a dose of 27 Gy in 3 daily fractions seems to be an effective treatment modality for large brain metastases, associated with better local control and a reduced risk of radiation-induced radionecrosis as compared with SF-SRS.« less

Multiscale multifractal detrended-fluctuation analysis of two-dimensional surfaces

NASA Astrophysics Data System (ADS)

Wang, Fang; Fan, Qingju; Stanley, H. Eugene

2016-04-01

Two-dimensional (2D) multifractal detrended fluctuation analysis (MF-DFA) has been used to study monofractality and multifractality on 2D surfaces, but when it is used to calculate the generalized Hurst exponent in a fixed time scale, the presence of crossovers can bias the outcome. To solve this problem, multiscale multifractal analysis (MMA) was recent employed in a one-dimensional case. MMA produces a Hurst surface h (q ,s ) that provides a spectrum of local scaling exponents at different scale ranges such that the positions of the crossovers can be located. We apply this MMA method to a 2D surface and identify factors that influence the results. We generate several synthesized surfaces and find that crossovers are consistently present, which means that their fractal properties differ at different scales. We apply MMA to the surfaces, and the results allow us to observe these differences and accurately estimate the generalized Hurst exponents. We then study eight natural texture images and two real-world images and find (i) that the moving window length (WL) and the slide length (SL) are the key parameters in the MMA method, that the WL more strongly influences the Hurst surface than the SL, and that the combination of WL =4 and SL =4 is optimal for a 2D image; (ii) that the robustness of h (2 ,s ) to four common noises is high at large scales but variable at small scales; and (iii) that the long-term correlations in the images weaken as the intensity of Gaussian noise and salt and pepper noise is increased. Our findings greatly improve the performance of the MMA method on 2D surfaces.

Nonlinear temperature effects on multifractal complexity of metabolic rate of mice

PubMed Central

Bogdanovich, Jose M.; Bozinovic, Francisco

2016-01-01

Complex physiological dynamics have been argued to be a signature of healthy physiological function. Here we test whether the complexity of metabolic rate fluctuations in small endotherms decreases with lower environmental temperatures. To do so, we examine the multifractal temporal scaling properties of the rate of change in oxygen consumption r(VO2), in the laboratory mouse Mus musculus, assessing their long range correlation properties across seven different environmental temperatures, ranging from 0 °C to 30 °C. To do so, we applied multifractal detrended fluctuation analysis (MF-DFA), finding that r(VO2) fluctuations show two scaling regimes. For small time scales below the crossover time (approximately 102 s), either monofractal or weak multifractal dynamics are observed depending on whether Ta < 15 °C or Ta > 15 °C respectively. For larger time scales, r(VO2) fluctuations are characterized by an asymptotic scaling exponent that indicates multifractal anti-persistent or uncorrelated dynamics. For both scaling regimes, a generalization of the multiplicative cascade model provides very good fits for the Renyi exponents τ(q), showing that the infinite number of exponents h(q) can be described by only two independent parameters, a and b. We also show that the long-range correlation structure of r(VO2) time series differs from randomly shuffled series, and may not be explained as an artifact of stochastic sampling of a linear frequency spectrum. These results show that metabolic rate dynamics in a well studied micro-endotherm are consistent with a highly non-linear feedback control system. PMID:27781179

Nonlinear temperature effects on multifractal complexity of metabolic rate of mice.

PubMed

Labra, Fabio A; Bogdanovich, Jose M; Bozinovic, Francisco

2016-01-01

Complex physiological dynamics have been argued to be a signature of healthy physiological function. Here we test whether the complexity of metabolic rate fluctuations in small endotherms decreases with lower environmental temperatures. To do so, we examine the multifractal temporal scaling properties of the rate of change in oxygen consumption r ( VO 2 ), in the laboratory mouse Mus musculus , assessing their long range correlation properties across seven different environmental temperatures, ranging from 0 °C to 30 °C. To do so, we applied multifractal detrended fluctuation analysis (MF-DFA), finding that r(VO 2 ) fluctuations show two scaling regimes. For small time scales below the crossover time (approximately 10 2 s), either monofractal or weak multifractal dynamics are observed depending on whether T a < 15 °C or T a > 15 °C respectively. For larger time scales, r(VO 2 ) fluctuations are characterized by an asymptotic scaling exponent that indicates multifractal anti-persistent or uncorrelated dynamics. For both scaling regimes, a generalization of the multiplicative cascade model provides very good fits for the Renyi exponents τ ( q ), showing that the infinite number of exponents h(q) can be described by only two independent parameters, a and b . We also show that the long-range correlation structure of r(VO 2 ) time series differs from randomly shuffled series, and may not be explained as an artifact of stochastic sampling of a linear frequency spectrum. These results show that metabolic rate dynamics in a well studied micro-endotherm are consistent with a highly non-linear feedback control system.

Cross-correlations between crude oil and agricultural commodity markets

NASA Astrophysics Data System (ADS)

Liu, Li

2014-02-01

In this paper, we investigate cross-correlations between crude oil and agricultural commodity markets. Based on a popular statistical test proposed by Podobnik et al. (2009), we find that the linear return cross-correlations are significant at larger lag lengths and the volatility cross-correlations are highly significant at all of the lag lengths under consideration. Using a detrended cross-correlation analysis (DCCA), we find that the return cross-correlations are persistent for corn and soybean and anti-persistent for oat and soybean. The volatility cross-correlations are strongly persistent. Using a nonlinear cross-correlation measure, our results show that cross-correlations are relatively weak but they are significant for smaller time scales. For larger time scales, the cross-correlations are not significant. The reason may be that information transmission from crude oil market to agriculture markets can complete within a certain period of time. Finally, based on multifractal extension of DCCA, we find that the cross-correlations are multifractal and high oil prices partly contribute to food crisis during the period of 2006-mid-2008.

Nonstationarity Versus Intermittency: A Wavelet/Multifractal Perspective with Operational Criteria

NASA Astrophysics Data System (ADS)

Davis, A. B.; Marshak, A.

2001-12-01

The signal from a seismograph is mostly low-level white background- and/or instrumental noise with the occasional burst of high-level transient activity that results from a (generally) remote earthquake. The former component can justifiably be deemed stationary on intuitive grounds; by contrast, the latter component has been called ``nonstationary'' by statisticians since it seriously perturbs their running means and variances over relatively short time-scales. Recall here that the eminently theoretical definition of stationarity as time-invariance of ensemble-averages is of little use when a single realization is available, the generic case in geophysics. A high-pass filtered trace of turbulent velocity looks much the same as the seismic signal but the bursts are seen by physicists as a manifestation of ``intermittency'' rather than nonstationarity. We side with the second characterization by allegiance, but fully appreciate the statistician's concern for robustness. In this context, the weaknesses of the nonstationarity model are: the over-reliance on low-order moments (Gaussian ideology), the restriction on scales, and the need for a threshold to define ``serious perturbation.'' At the same time, an added advantage of the intermittency model for bursts is that it frees up the notion of nonstationarity to describe the low-pass components of turbulent geophysical signals which are as important as their high-pass counterparts, if not more, in many applications. The stationarity versus nonstationarity question is best recast in terms of spatial correlations and scaling enables us to do this, even when dealing with a single realization: are they short-range (as in ``noises'') or long-range (as in ``motions'')? However, care must be taken about what spatial statistic to use here, and finite sample-size effects can add to the confusion. Every quantification of intermittency based on higher-order multifractal statistics should also be scrutinized for finite-sample effects. Using the unifying framework of wavelet transforms for multifractal analysis, we offer unambiguous criteria to decide whether a given dataset that is scaling (within limits) is stationary or not, and then intermittent or not. In the latter case, there is an arbitrary threshold that is easily set in any specific application. Having established the presence of significant intermittency, we can anticipate that the selection of one particular brand of multifractality versus another will be quite difficult based on data alone. This relates in particular to the proliferation of competing multifractal theories of turbulence in spite of on-going efforts to collect high-quality data.

Tsallis q-triplet, intermittent turbulence and Portevin-Le Chatelier effect

NASA Astrophysics Data System (ADS)

Iliopoulos, A. C.; Aifantis, E. C.

2018-05-01

In this paper, we extend a previous study concerning Portevin-LeChatelier (PLC) effect and Tsallis statistics (Iliopoulos et al., 2015). In particular, we estimate Tsallis' q-triplet, namely {qstat, qsens, qrel} for two sets of stress serration time series concerning the deformation of Cu-15%Al alloy corresponding to different deformation temperatures and thus types (A and B) of PLC bands. The results concerning the stress serrations analysis reveal that Tsallis q- triplet attains values different from unity ({qstat, qsens, qrel} ≠ {1,1,1}). In particular, PLC type A bands' serrations were found to follow Tsallis super-q-Gaussian, non-extensive, sub-additive, multifractal statistics indicating that the underlying dynamics are at the edge of chaos, characterized by global long range correlations and power law scaling. For PLC type B bands' serrations, the results revealed a Tsallis sub-q-Gaussian, non-extensive, super-additive, multifractal statistical profile. In addition, our results reveal also significant differences in statistical and dynamical features, indicating important variations of the stress field dynamics in terms of rate of entropy production, relaxation dynamics and non-equilibrium meta-stable stationary states. We also estimate parameters commonly used for characterizing fully developed turbulence, such as structure functions and flatness coefficient (F), in order to provide further information about jerky flow underlying dynamics. Finally, we use two multifractal models developed to describe turbulence, namely Arimitsu and Arimitsu (A&A) [2000, 2001] theoretical model which is based on Tsallis statistics and p-model to estimate theoretical multifractal spectrums f(a). Furthermore, we estimate flatness coefficient (F) using a theoretical formula based on Tsallis statistics. The theoretical results are compared with the experimental ones showing a remarkable agreement between modeling and experiment. Finally, the results of this study verify, as well as, extend previous studies which stated that type B and type A PLC bands underlying dynamics are connected with distinct dynamical behavior, namely chaotic behavior for the first and self-organized critical (SOC) behavior for the latter, while they shed new light concerning the turbulent character of the PLC jerky flow.

Statistical classifiers on multifractal parameters for optical diagnosis of cervical cancer

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Sabyasachi; Pratiher, Sawon; Kumar, Rajeev; Krishnamoorthy, Vigneshram; Pradhan, Asima; Ghosh, Nirmalya; Panigrahi, Prasanta K.

2017-06-01

An augmented set of multifractal parameters with physical interpretations have been proposed to quantify the varying distribution and shape of the multifractal spectrum. The statistical classifier with accuracy of 84.17% validates the adequacy of multi-feature MFDFA characterization of elastic scattering spectroscopy for optical diagnosis of cancer.

Multifractals in Western Major STOCK Markets Historical Volatilities in Times of Financial Crisis

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

In this paper, the generalized Hurst exponent is used to investigate multifractal properties of historical volatility (CHV) in stock market price and return series before, during and after 2008 financial crisis. Empirical results from NASDAQ, S&P500, TSE, CAC40, DAX, and FTSE stock market data show that there is strong evidence of multifractal patterns in HV of both price and return series. In addition, financial crisis deeply affected the behavior and degree of multifractality in volatility of Western financial markets at price and return levels.

Statistical physics and physiology: monofractal and multifractal approaches

NASA Technical Reports Server (NTRS)

Stanley, H. E.; Amaral, L. A.; Goldberger, A. L.; Havlin, S.; Peng, C. K.

1999-01-01

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.

Temporal multiscaling characteristics of particulate matter PM 10 and ground-level ozone O3 concentrations in Caribbean region

NASA Astrophysics Data System (ADS)

Plocoste, Thomas; Calif, Rudy; Jacoby-Koaly, Sandra

2017-11-01

A good knowledge of the intermittency of atmospheric pollutants is crucial for air pollution management. We consider here particulate matter PM 10 and ground-level ozone O3 time series in Guadeloupe archipelago which experiments a tropical and humid climate in the Caribbean zone. The aim of this paper is to study their scaling statistics in the framework of fully developed turbulence and Kolmogorov's theory. Firstly, we estimate their Fourier power spectra and consider their scaling properties in the physical space. The power spectra computed follows a power law behavior for both considered pollutants. Thereafter we study the scaling behavior of PM 10 and O3 time series. Contrary to numerous studies where the multifractal detrended fluctuation analysis is frequently applied, here, the classical structure function analysis is used to extract the scaling exponent or multifractal spectrum ζ(q) ; this function provides a full characterization of a process at all intensities and all scales. The obtained results show that PM 10 and O3 possess intermittent and multifractal properties. The singularity spectrum MS(α) also confirms both pollutants multifractal features. The originality of this work comes from a statistical modeling performed on ζ(q) and MS(α) by a lognormal model to compute the intermittency parameter μ. By contrast with PM 10 which mainly depends on puffs of Saharan dust (synoptic-scale), O3 is more intermittent due to variability of its local precursors. The results presented in this paper can help to better understand the mechanisms governing the dynamics of PM 10 and O3 in Caribbean islands context.

Comparison of the multifractal characteristics of heavy metals in soils within two areas of contrasting economic activities in China

NASA Astrophysics Data System (ADS)

Li, Xiaohui; Li, Xiangling; Yuan, Feng; Jowitt, Simon M.; Zhou, Taofa; Yang, Kui; Zhou, Jie; Hu, Xunyu; Li, Yang

2016-09-01

Industrial and agricultural activities can generate heavy metal pollution that can cause a number of negative environmental and health impacts. This means that evaluating heavy metal pollution and identifying the sources of these pollutants, especially in urban or developed areas, is an important first step in mitigating the effects of these contaminating but necessary economic activities. Here, we present the results of a heavy metal (Cu, Pb, Zn, Cd, As, and Hg) soil geochemical survey in Hefei city. We used a multifractal spectral technique to identify and compare the multifractality of heavy metal concentrations of soils within the industrial Daxing and agricultural Yicheng areas. This paper uses three multifractal parameters (Δα, Δf(α), and τ''(1)) to indicate the overall amount of multifractality within the soil geochemical data. The results show all of the elements barring Hg have larger Δα, Δf(α), and τ''(1) values in the Daxing area compared to the Yicheng area. The degree of multifractality suggests that the differing economic activities in Daxing and Yicheng generate very different heavy metal pollution loads. In addition, the industrial Daxing area contains significant Pb and Cd soil contamination, whereas Hg is the main heavy metal present in soils within the Yicheng area, indicating that differing clean-up procedures and approaches to remediating these polluted areas are needed. The results also indicate that multifractal modelling and the associated generation of multifractal parameters can be a useful approach in the evaluation of heavy metal pollution in soils.

Multifractal Characterization of Geologic Noise for Improved UXO Detection and Discrimination

DTIC Science & Technology

2008-03-01

12 Recovery of the Universal Multifractal Parameters ...dipole-model to each magnetic anomaly and compares the extracted model parameters with a library of UXO items. They found that remnant magnetization...the survey parameters , and the geologic environment. In this pilot study we have focused on the multifractal representation of natural variations

Breast cancer evaluation by fluorescent dot detection using combined mathematical morphology and multifractal techniques

PubMed Central

2011-01-01

Background Fluorescence in situ hybridization (FISH) is very accurate method for measuring HER2 gene copies, as a sign of potential breast cancer. This method requires small tissue samples, and has a high sensitivity to detect abnormalities from a histological section. By using multiple colors, this method allows the detection of multiple targets simultaneously. The target parts in the cells become visible as colored dots. The HER-2 probes are visible as orange stained spots under a fluorescent microscope while probes for centromere 17 (CEP-17), the chromosome on which the gene HER-2/neu is located, are visible as green spots. Methods The conventional analysis involves the scoring of the ratio of HER-2/neu over CEP 17 dots within each cell nucleus and then averaging the scores for a number of 60 cells. A ratio of 2.0 of HER-2/neu to CEP 17 copy number denotes amplification. Several methods have been proposed for the detection and automated evaluation (dot counting) of FISH signals. In this paper the combined method based on the mathematical morphology (MM) and inverse multifractal (IMF) analysis is suggested. Similar method was applied recently in detection of microcalcifications in digital mammograms, and was very successful. Results The combined MM using top-hat and bottom-hat filters, and the IMF method was applied to FISH images from Molecular Biology Lab, Department of Pathology, Wielkoposka Cancer Center, Poznan. Initial results indicate that this method can be applied to FISH images for the evaluation of HER2/neu status. Conclusions Mathematical morphology and multifractal approach are used for colored dot detection and counting in FISH images. Initial results derived on clinical cases are promising. Note that the overlapping of colored dots, particularly red/orange dots, needs additional improvements in post-processing. PMID:21489192

Nonlinear bivariate dependency of price-volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis

NASA Astrophysics Data System (ADS)

He, Ling-Yun; Chen, Shu-Peng

2011-01-01

Nonlinear dependency between characteristic financial and commodity market quantities (variables) is crucially important, especially between trading volume and market price. Studies on nonlinear dependency between price and volume can provide practical insights into market trading characteristics, as well as the theoretical understanding of market dynamics. Actually, nonlinear dependency and its underlying dynamical mechanisms between price and volume can help researchers and technical analysts in understanding the market dynamics by integrating the market variables, instead of investigating them in the current literature. Therefore, for investigating nonlinear dependency of price-volume relationships in agricultural commodity futures markets in China and the US, we perform a new statistical test to detect cross-correlations and apply a new methodology called Multifractal Detrended Cross-Correlation Analysis (MF-DCCA), which is an efficient algorithm to analyze two spatially or temporally correlated time series. We discuss theoretically the relationship between the bivariate cross-correlation exponent and the generalized Hurst exponents for time series of respective variables. We also perform an empirical study and find that there exists a power-law cross-correlation between them, and that multifractal features are significant in all the analyzed agricultural commodity futures markets.

Log-Normality and Multifractal Analysis of Flame Surface Statistics

NASA Astrophysics Data System (ADS)

Saha, Abhishek; Chaudhuri, Swetaprovo; Law, Chung K.

2013-11-01

The turbulent flame surface is typically highly wrinkled and folded at a multitude of scales controlled by various flame properties. It is useful if the information contained in this complex geometry can be projected onto a simpler regular geometry for the use of spectral, wavelet or multifractal analyses. Here we investigate local flame surface statistics of turbulent flame expanding under constant pressure. First the statistics of local length ratio is experimentally obtained from high-speed Mie scattering images. For spherically expanding flame, length ratio on the measurement plane, at predefined equiangular sectors is defined as the ratio of the actual flame length to the length of a circular-arc of radius equal to the average radius of the flame. Assuming isotropic distribution of such flame segments we convolute suitable forms of the length-ratio probability distribution functions (pdfs) to arrive at corresponding area-ratio pdfs. Both the pdfs are found to be near log-normally distributed and shows self-similar behavior with increasing radius. Near log-normality and rather intermittent behavior of the flame-length ratio suggests similarity with dissipation rate quantities which stimulates multifractal analysis. Currently at Indian Institute of Science, India.

Assessing spatial variability of soil properties and ions associated to salinity using the multifractal approach

NASA Astrophysics Data System (ADS)

Machado Siqueira, Glécio; Soares da Silva, Jucicleia; Farías França e Silva, Ênio; Lado, Marcos; Paz-González, Antonio; Vidal-Vázquez, Eva

2017-04-01

The lowlands coastal region of the state of Pernambuco, Northeast of Brazil, was formerly covered by humid Atlantic forest (Mata Atlântica) and then has been increasingly devoted to Sugar cane production. Because the water table is near to the soil surface salinity can occur in this area. The objective of this study was to assess the scale dependence of parameters associated to soil salinity and ions responsible for salination using multifractal analysis. The field work was conducted at an experimental field located in the Goiania municipality, Pernambuco, Brazil. This site is located 10 km east from the Atlantic coast. The field has been devoted to monoculture of sugarcane (Saccharum of?cinarum sp.) since 25 years. The climate of the region is tropical, with average annual temperature of 24°C and 1800 mm of precipitation per year. Soil was sampled every 3 m at 128 locations across a 384 m transect at a depth of 0-20 cm. The soil samples were analysed for pH, electrical conductivity (EC), Na+, K+, Ca2+, Mg2+, Cl- and SO4-2; also sodium adsorption ratio (SAR) was calculated. The spatial distributions of all the studied variables associated to soil salinity exhibited multifractal behaviour. Although all the variables studied exhibited a very strong power law scaling, different degrees of multifractality, assessed by differences in the amplitude and several selected parameters of the generalized dimension and singularity spectrum curves, have been appreciated. The multifractal approach gives a good description of the patterns of spatial variability of properties and ions describing soil salinity, and allows discriminating differences between them.

Fractal and multifractal analyses of bipartite networks

NASA Astrophysics Data System (ADS)

Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

2017-03-01

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

Fractal and multifractal analyses of bipartite networks.

PubMed

Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

2017-03-31

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

Fractal and multifractal analyses of bipartite networks

PubMed Central

Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

2017-01-01

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions. PMID:28361962

Experimental confirmation of long-memory correlations in star-wander data.

PubMed

Zunino, Luciano; Gulich, Damián; Funes, Gustavo; Ziad, Aziz

2014-07-01

In this Letter we have analyzed the temporal correlations of the angle-of-arrival fluctuations of stellar images. Experimentally measured data were carefully examined by implementing multifractal detrended fluctuation analysis. This algorithm is able to discriminate the presence of fractal and multifractal structures in recorded time sequences. We have confirmed that turbulence-degraded stellar wavefronts are compatible with a long-memory correlated monofractal process. This experimental result is quite significant for the accurate comprehension and modeling of the atmospheric turbulence effects on the stellar images. It can also be of great utility within the adaptive optics field.

Approximated maximum likelihood estimation in multifractal random walks

NASA Astrophysics Data System (ADS)

Løvsletten, O.; Rypdal, M.

2012-04-01

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.64.026103 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the r computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.

Dynamical mechanism in aero-engine gas path system using minimum spanning tree and detrended cross-correlation analysis

NASA Astrophysics Data System (ADS)

Dong, Keqiang; Zhang, Hong; Gao, You

2017-01-01

Identifying the mutual interaction in aero-engine gas path system is a crucial problem that facilitates the understanding of emerging structures in complex system. By employing the multiscale multifractal detrended cross-correlation analysis method to aero-engine gas path system, the cross-correlation characteristics between gas path system parameters are established. Further, we apply multiscale multifractal detrended cross-correlation distance matrix and minimum spanning tree to investigate the mutual interactions of gas path variables. The results can infer that the low-spool rotor speed (N1) and engine pressure ratio (EPR) are main gas path parameters. The application of proposed method contributes to promote our understanding of the internal mechanisms and structures of aero-engine dynamics.

Comparative Multifractal Analysis of Dynamic Infrared Thermograms and X-Ray Mammograms Enlightens Changes in the Environment of Malignant Tumors.

PubMed

Gerasimova-Chechkina, Evgeniya; Toner, Brian; Marin, Zach; Audit, Benjamin; Roux, Stephane G; Argoul, Francoise; Khalil, Andre; Gileva, Olga; Naimark, Oleg; Arneodo, Alain

2016-01-01

There is growing evidence that the microenvironment surrounding a tumor plays a special role in cancer development and cancer therapeutic resistance. Tumors arise from the dysregulation and alteration of both the malignant cells and their environment. By providing tumor-repressing signals, the microenvironment can impose and sustain normal tissue architecture. Once tissue homeostasis is lost, the altered microenvironment can create a niche favoring the tumorigenic transformation process. A major challenge in early breast cancer diagnosis is thus to show that these physiological and architectural alterations can be detected with currently used screening techniques. In a recent study, we used a 1D wavelet-based multi-scale method to analyze breast skin temperature temporal fluctuations collected with an IR thermography camera in patients with breast cancer. This study reveals that the multifractal complexity of temperature fluctuations superimposed on cardiogenic and vasomotor perfusion oscillations observed in healthy breasts is lost in malignant tumor foci in cancerous breasts. Here we use a 2D wavelet-based multifractal method to analyze the spatial fluctuations of breast density in the X-ray mammograms of the same panel of patients. As compared to the long-range correlations and anti-correlations in roughness fluctuations, respectively observed in dense and fatty breast areas, some significant change in the nature of breast density fluctuations with some clear loss of correlations is detected in the neighborhood of malignant tumors. This attests to some architectural disorganization that may deeply affect heat transfer and related thermomechanics in breast tissues, corroborating the change to homogeneous monofractal temperature fluctuations recorded in cancerous breasts with the IR camera. These results open new perspectives in computer-aided methods to assist in early breast cancer diagnosis.

Comparative Multifractal Analysis of Dynamic Infrared Thermograms and X-Ray Mammograms Enlightens Changes in the Environment of Malignant Tumors

PubMed Central

Gerasimova-Chechkina, Evgeniya; Toner, Brian; Marin, Zach; Audit, Benjamin; Roux, Stephane G.; Argoul, Francoise; Khalil, Andre; Gileva, Olga; Naimark, Oleg; Arneodo, Alain

2016-01-01

There is growing evidence that the microenvironment surrounding a tumor plays a special role in cancer development and cancer therapeutic resistance. Tumors arise from the dysregulation and alteration of both the malignant cells and their environment. By providing tumor-repressing signals, the microenvironment can impose and sustain normal tissue architecture. Once tissue homeostasis is lost, the altered microenvironment can create a niche favoring the tumorigenic transformation process. A major challenge in early breast cancer diagnosis is thus to show that these physiological and architectural alterations can be detected with currently used screening techniques. In a recent study, we used a 1D wavelet-based multi-scale method to analyze breast skin temperature temporal fluctuations collected with an IR thermography camera in patients with breast cancer. This study reveals that the multifractal complexity of temperature fluctuations superimposed on cardiogenic and vasomotor perfusion oscillations observed in healthy breasts is lost in malignant tumor foci in cancerous breasts. Here we use a 2D wavelet-based multifractal method to analyze the spatial fluctuations of breast density in the X-ray mammograms of the same panel of patients. As compared to the long-range correlations and anti-correlations in roughness fluctuations, respectively observed in dense and fatty breast areas, some significant change in the nature of breast density fluctuations with some clear loss of correlations is detected in the neighborhood of malignant tumors. This attests to some architectural disorganization that may deeply affect heat transfer and related thermomechanics in breast tissues, corroborating the change to homogeneous monofractal temperature fluctuations recorded in cancerous breasts with the IR camera. These results open new perspectives in computer-aided methods to assist in early breast cancer diagnosis. PMID:27555823

Strict parabolicity of the multifractal spectrum at the Anderson transition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suslov, I. M., E-mail: suslov@kapitza.ras.ru

Using the well-known “algebra of multifractality,” we derive the functional equation for anomalous dimensions Δ{sub q}, whose solution Δ = χq(q–1) corresponds to strict parabolicity of the multifractal spectrum. This result demonstrates clearly that a correspondence of the nonlinear σ-models with the initial disordered systems is not exact.

Investigation of the structure and lithology of bedrock concealed by basin fill, using ground-based magnetic-field-profile data acquired in the San Rafael Basin, southeastern Arizona

USGS Publications Warehouse

Bultman, Mark W.

2013-01-01

Data on the Earth’s total-intensity magnetic field acquired near ground level and at measurement intervals as small as 1 m include information on the spatial distribution of nearsurface magnetic dipoles that in many cases are unique to a specific lithology. Such spatial information is expressed in the texture (physical appearance or characteristics) of the data at scales of hundreds of meters to kilometers. These magnetic textures are characterized by several descriptive statistics, their power spectrum, and their multifractal spectrum. On the basis of a graphical comparison and textural characterization, ground-based magnetic-field profile data can be used to estimate bedrock lithology concealed by as much as 100 m of basin fill in some cases, information that is especially important in assessing and exploring for concealed mineral deposits. I demonstrate that multifractal spectra of ground-based magnetic-field-profile data can be used to differentiate exposed lithologies and that the shape and position of the multifractal spectrum of the ground-based magnetic-field-profile of concealed lithologies can be matched to the upward-continued multifractal spectrum of an exposed lithology to help distinguish the concealed lithology. In addition, ground-based magnetic-field-profile data also detect minute differences in the magnetic susceptibility of rocks over small horizontal and vertical distances and so can be used for precise modeling of bedrock geometry and structure, even when that bedrock is concealed by 100 m or more of nonmagnetic basin fill. Such data contain valuable geologic information on the bedrock concealed by basin fill that may not be so visible in aeromagnetic data, including areas of hydrothermal alteration, faults, and other bedrock structures. Interpretation of these data in the San Rafael Basin, southeastern Arizona, has yielded results for estimating concealed lithologies, concealed structural geology, and a concealed potential mineral-resource target.

Power law cross-correlations between price change and volume change of Indian stocks

NASA Astrophysics Data System (ADS)

Hasan, Rashid; Mohammed Salim, M.

2017-05-01

We study multifractal long-range correlations and cross-correlations of daily price change and volume change of 50 stocks that comprise Nifty index of National Stock Exchange, Mumbai, using MF-DFA and MF-DCCA methods. We find that the time series of price change are uncorrelated, whereas anti-persistent long-range multifractal correlations are found in volume change series. We also find antipersistent long-range multifractal cross-correlations between the time series of price change and volume change. As multifractality is a signature of complexity, we estimate complexity parameters of the time series of price change, volume change, and cross-correlated price-volume change by fitting the fourth-degree polynomials to their multifractal spectra. Our results indicate that the time series of price change display high complexity, whereas the time series of volume change and cross-correlated price-volume change display low complexity.

Multifractal Approaches of the Ring Tensile Rupture Patterns of Dried Laver (Porphyra) as Affected by the Relative Humidity.

PubMed

Jung, Hwabin; Yoon, Won Byong

2017-12-01

The effect of water activity (a w ) or the relative humidity (RH) on the tensile rupture properties of dried laver (DL) associated with structures formed with phycocolloids was investigated. The morphological characteristics of tensile ruptured DL samples at various relative humidities were evaluated by multifractal analysis. The RH of the microclimate was controlled from 10% to 90% at 25 °C using supersaturated salt solutions. The sorption isotherm of DL was experimentally obtained and quantitatively analyzed using mathematical models. The monolayer moisture contents from the Guggenheim-Anderson-de Boer (GAB) model was 5.92% (w.b.). An increase in the RH resulted in increasing ring tensile stress and maintaining constant ring tensile strain up to 58% to 75% RH, whereas the ring tensile stress and the ring tensile strain rapidly decreased and increased, respectively, when the RH was higher than 75%. The general fractal dimensions and the multifractal spectra f(α) manifested that the patterns of the lowest and the highest moisture content of dried laver showed high irregularity. The different multifractal parameters obtained from the DL at various RHs well-represented the transient moment of the structures from the monolayer moisture to texture changes associated with RH. Overall, the ring tensile test and the multifractal analysis were useful tools to analyze the change of crispness of DL from its structural characteristics. In addition, the results of this study revealed that the integration and disintegration properties of DL occurred through the networks of phycocolloids at various moisture contents. Texture properties are the most important quality attributes for commercial dried laver (DL) products. The relative humidity influences the texture properties of DL during production, storage, shipping, and consuming. This study well characterized the effect of the relative humidity on the texture properties of DL using the tensile tests under microclimate conditions. This information is very practical and can be immediately applied to control the relative humidity of the packaging and the storage room for DL. © 2017 Institute of Food Technologists®.

Multifractal evaluation of simulated precipitation intensities from the COSMO NWP model

NASA Astrophysics Data System (ADS)

Wolfensberger, Daniel; Gires, Auguste; Tchiguirinskaia, Ioulia; Schertzer, Daniel; Berne, Alexis

2017-12-01

The framework of universal multifractals (UM) characterizes the spatio-temporal variability in geophysical data over a wide range of scales with only a limited number of scale-invariant parameters. This work aims to clarify the link between multifractals (MFs) and more conventional weather descriptors and to show how they can be used to perform a multi-scale evaluation of model data. The first part of this work focuses on a MF analysis of the climatology of precipitation intensities simulated by the COSMO numerical weather prediction model. Analysis of the spatial structure of the MF parameters, and their correlations with external meteorological and topographical descriptors, reveals that simulated precipitation tends to be smoother at higher altitudes, and that the mean intermittency is mostly influenced by the latitude. A hierarchical clustering was performed on the external descriptors, yielding three different clusters, which correspond roughly to Alpine/continental, Mediterranean and temperate regions. Distributions of MF parameters within these three clusters are shown to be statistically significantly different, indicating that the MF signature of rain is indeed geographically dependent. The second part of this work is event-based and focuses on the smaller scales. The MF parameters of precipitation intensities at the ground are compared with those obtained from the Swiss radar composite during three events corresponding to typical synoptic conditions over Switzerland. The results of this analysis show that the COSMO simulations exhibit spatial scaling breaks that are not present in the radar data, indicating that the model is not able to simulate the observed variability at all scales. A comparison of the operational one-moment microphysical parameterization scheme of COSMO with a more advanced two-moment scheme reveals that, while no scheme systematically outperforms the other, the two-moment scheme tends to produce larger extreme values and more discontinuous precipitation fields, which agree better with the radar composite.

Investigation of the complexity of streamflow fluctuations in a large heterogeneous lake catchment in China

NASA Astrophysics Data System (ADS)

Ye, Xuchun; Xu, Chong-Yu; Li, Xianghu; Zhang, Qi

2018-05-01

The occurrence of flood and drought frequency is highly correlated with the temporal fluctuations of streamflow series; understanding of these fluctuations is essential for the improved modeling and statistical prediction of extreme changes in river basins. In this study, the complexity of daily streamflow fluctuations was investigated by using multifractal detrended fluctuation analysis (MF-DFA) in a large heterogeneous lake basin, the Poyang Lake basin in China, and the potential impacts of human activities were also explored. Major results indicate that the multifractality of streamflow fluctuations shows significant regional characteristics. In the study catchment, all the daily streamflow series present a strong long-range correlation with Hurst exponents bigger than 0.8. The q-order Hurst exponent h( q) of all the hydrostations can be characterized well by only two parameters: a (0.354 ≤ a ≤ 0.384) and b (0.627 ≤ b ≤ 0.677), with no pronounced differences. Singularity spectrum analysis pointed out that small fluctuations play a dominant role in all daily streamflow series. Our research also revealed that both the correlation properties and the broad probability density function (PDF) of hydrological series can be responsible for the multifractality of streamflow series that depends on watershed areas. In addition, we emphasized the relationship between watershed area and the estimated multifractal parameters, such as the Hurst exponent and fitted parameters a and b from the q-order Hurst exponent h( q). However, the relationship between the width of the singularity spectrum (Δ α) and watershed area is not clear. Further investigation revealed that increasing forest coverage and reservoir storage can effectively enhance the persistence of daily streamflow, decrease the hydrological complexity of large fluctuations, and increase the small fluctuations.

Multifractal spectrum and lacunarity as measures of complexity of osseointegration.

PubMed

de Souza Santos, Daniel; Dos Santos, Leonardo Cavalcanti Bezerra; de Albuquerque Tavares Carvalho, Alessandra; Leão, Jair Carneiro; Delrieux, Claudio; Stosic, Tatijana; Stosic, Borko

2016-07-01

The goal of this study is to contribute to a better quantitative description of the early stages of osseointegration, by application of fractal, multifractal, and lacunarity analysis. Fractal, multifractal, and lacunarity analysis are performed on scanning electron microscopy (SEM) images of titanium implants that were first subjected to different treatment combinations of i) sand blasting, ii) acid etching, and iii) exposition to calcium phosphate, and were then submersed in a simulated body fluid (SBF) for 30 days. All the three numerical techniques are applied to the implant SEM images before and after SBF immersion, in order to provide a comprehensive set of common quantitative descriptors. It is found that implants subjected to different physicochemical treatments before submersion in SBF exhibit a rather similar level of complexity, while the great variety of crystal forms after SBF submersion reveals rather different quantitative measures (reflecting complexity), for different treatments. In particular, it is found that acid treatment, in most combinations with the other considered treatments, leads to a higher fractal dimension (more uniform distribution of crystals), lower lacunarity (lesser variation in gap sizes), and narrowing of the multifractal spectrum (smaller fluctuations on different scales). The current quantitative description has shown the capacity to capture the main features of complex images of implant surfaces, for several different treatments. Such quantitative description should provide a fundamental tool for future large scale systematic studies, considering the large variety of possible implant treatments and their combinations. Quantitative description of early stages of osseointegration on titanium implants with different treatments should help develop a better understanding of this phenomenon, in general, and provide basis for further systematic experimental studies. Clinical practice should benefit from such studies in the long term, by more ready access to implants of higher quality.

Multifractal spectra in shear flows

NASA Technical Reports Server (NTRS)

Keefe, L. R.; Deane, Anil E.

1989-01-01

Numerical simulations of three-dimensional homogeneous shear flow and fully developed channel flow, are used to calculate the associated multifractal spectra of the energy dissipation field. Only weak parameterization of the results with the nondimensional shear is found, and this only if the flow has reached its asymptotic development state. Multifractal spectra of these flows coincide with those from experiments only at the range alpha less than 1.

Editorial

NASA Astrophysics Data System (ADS)

Liu, Shuai

Fractal represents a special feature of nature and functional objects. However, fractal based computing can be applied to many research domains because of its fixed property resisted deformation, variable parameters and many unpredictable changes. Theoretical research and practical application of fractal based computing have been hotspots for 30 years and will be continued. There are many pending issues awaiting solutions in this domain, thus this thematic issue containing 14 papers publishes the state-of-the-art developments in theorem and application of fractal based computing, including mathematical analysis and novel engineering applications. The topics contain fractal and multifractal features in application and solution of nonlinear odes and equation.

Identification of magnetic anomalies based on ground magnetic data analysis using multifractal modeling: a case study in Qoja-Kandi, East Azerbaijan Province, Iran

NASA Astrophysics Data System (ADS)

Mansouri, E.; Feizi, F.; Karbalaei Ramezanali, A. A.

2015-07-01

Ground magnetic anomaly separation using reduction-to-the-pole (RTP) technique and the fractal concentration-area (C-A) method has been applied to the Qoja-Kandi prosepecting area in NW Iran. The geophysical survey that resulted in the ground magnetic data was conducted for magnetic elements exploration. Firstly, RTP technique was applied for recognizing underground magnetic anomalies. RTP anomalies was classified to different populations based on this method. For this reason, drilling points determination with RTP technique was complicated. Next, C-A method was applied on the RTP-Magnetic-Anomalies (RTP-MA) for demonstrating magnetic susceptibility concentration. This identification was appropriate for increasing the resolution of the drilling points determination and decreasing the drilling risk, due to the economic costs of underground prospecting. In this study, the results of C-A Modeling on the RTP-MA are compared with 8 borehole data. The results show there is good correlation between anomalies derived via C-A method and log report of boreholes. Two boreholes were drilled in magnetic susceptibility concentration, based on multifractal modeling data analyses, between 63 533.1 and 66 296 nT. Drilling results show appropriate magnetite thickness with the grades greater than 20 % Fe total. Also, anomalies associated with andesite units host iron mineralization.

EXOPLANETARY DETECTION BY MULTIFRACTAL SPECTRAL ANALYSIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agarwal, Sahil; Wettlaufer, John S.; Sordo, Fabio Del

2017-01-01

Owing to technological advances, the number of exoplanets discovered has risen dramatically in the last few years. However, when trying to observe Earth analogs, it is often difficult to test the veracity of detection. We have developed a new approach to the analysis of exoplanetary spectral observations based on temporal multifractality, which identifies timescales that characterize planetary orbital motion around the host star and those that arise from stellar features such as spots. Without fitting stellar models to spectral data, we show how the planetary signal can be robustly detected from noisy data using noise amplitude as a source ofmore » information. For observation of transiting planets, combining this method with simple geometry allows us to relate the timescales obtained to primary and secondary eclipse of the exoplanets. Making use of data obtained with ground-based and space-based observations we have tested our approach on HD 189733b. Moreover, we have investigated the use of this technique in measuring planetary orbital motion via Doppler shift detection. Finally, we have analyzed synthetic spectra obtained using the SOAP 2.0 tool, which simulates a stellar spectrum and the influence of the presence of a planet or a spot on that spectrum over one orbital period. We have demonstrated that, so long as the signal-to-noise-ratio ≥ 75, our approach reconstructs the planetary orbital period, as well as the rotation period of a spot on the stellar surface.« less

Influence of tillage in soil penetration resistance variability in an olive orchard

NASA Astrophysics Data System (ADS)

López de Herrera, Juan; Herrero Tejedor, Tomas; Saa-Requejo, Antonio; Tarquis, Ana M.

2015-04-01

Soil attributes usually present a high degree of spatial variation due to a combination of physical, chemical, biological or climatic processes operating at different scales. The quantification and interpretation of such variability is a key issue for site-specific soil management (Brouder et al., 2001). The usual geostatistical approach studies soil variability by means of the semi-variograms. However, recently a multiscaling approach has been applied on the determination of the scaling data properties (Kravechenko et al., 1999; Caniego et al., 2005; Tarquis et al., 2008). This work focus in the multifractal analysis as a way to characterize the variability of field data in a case study of soil penetrometer resistance (SPR) in two olive orchards, one applying tillage for 20 years and the other one non. The field measurements and soil data were obtained at the village of Puebla de Almenara (Cuenca, Spain) (39o 47'42.37'N, 2o 49'29.23'W) with 869 m of elevation approximately. The characteristic of the soil at the surface is classified as clay loam texture according to Guidelines for soil description of FAO. The soil consists of clays and red silts with some clusters of limestone's and sands. Two transect data were collected from 128 points between the squared of the olive tree, tillage and no tillage area, for SPR readings with a sampling interval of 50 cm. In each sampling, readings were obtained from 0 cm till 20 cm of depth, with an interval of 5 cm. The multifractal spectrum for each area and depth was estimated showing a characteristic pattern and differentiating both treatments. References Brouder, S., Hofmann, B., Reetz, H.F., 2001. Evaluating spatial variability of soil parameters for input management. Better Crops 85, 8-11. Kravchenko, A.N., Boast, C.W., Bullock, D.G., 1999. Multifractal analysis of soil spatial variability. Agron. J. 91, 1033-1041. Caniego, F.J., R. Espejo, M.A. Martín, F. San José, 2005. Multifractal scaling of soil spatial variability. Ecological Modelling, 182, 291-303. Tarquis, A.M., N. Bird, M.C. Cartagena, A. Whitmore and Y. Pachepsky, 2008. Multiscale entropy-based analyses of soil transect data. Vadose Zone Journal, 7(2), 563-569.

Multifractality and value-at-risk forecasting of exchange rates

NASA Astrophysics Data System (ADS)

Batten, Jonathan A.; Kinateder, Harald; Wagner, Niklas

2014-05-01

This paper addresses market risk prediction for high frequency foreign exchange rates under nonlinear risk scaling behaviour. We use a modified version of the multifractal model of asset returns (MMAR) where trading time is represented by the series of volume ticks. Our dataset consists of 138,418 5-min round-the-clock observations of EUR/USD spot quotes and trading ticks during the period January 5, 2006 to December 31, 2007. Considering fat-tails, long-range dependence as well as scale inconsistency with the MMAR, we derive out-of-sample value-at-risk (VaR) forecasts and compare our approach to historical simulation as well as a benchmark GARCH(1,1) location-scale VaR model. Our findings underline that the multifractal properties in EUR/USD returns in fact have notable risk management implications. The MMAR approach is a parsimonious model which produces admissible VaR forecasts at the 12-h forecast horizon. For the daily horizon, the MMAR outperforms both alternatives based on conditional as well as unconditional coverage statistics.

Computer aided system for segmentation and visualization of microcalcifications in digital mammograms.

PubMed

Reljin, Branimir; Milosević, Zorica; Stojić, Tomislav; Reljin, Irini

2009-01-01

Two methods for segmentation and visualization of microcalcifications in digital or digitized mammograms are described. First method is based on modern mathematical morphology, while the second one uses the multifractal approach. In the first method, by using an appropriate combination of some morphological operations, high local contrast enhancement, followed by significant suppression of background tissue, irrespective of its radiology density, is obtained. By iterative procedure, this method highly emphasizes only small bright details, possible microcalcifications. In a multifractal approach, from initial mammogram image, a corresponding multifractal "images" are created, from which a radiologist has a freedom to change the level of segmentation. An appropriate user friendly computer aided visualization (CAV) system with embedded two methods is realized. The interactive approach enables the physician to control the level and the quality of segmentation. Suggested methods were tested through mammograms from MIAS database as a gold standard, and from clinical praxis, using digitized films and digital images from full field digital mammograph.

EGS Richardson AGU Chapman NVAG3 Conference: Nonlinear Variability in Geophysics: scaling and multifractal processes

NASA Astrophysics Data System (ADS)

Schertzer, D.; Lovejoy, S.

1. The conference The third conference on "Nonlinear VAriability in Geophysics: scaling and multifractal processes" (NVAG 3) was held in Cargese, Corsica, Sept. 10-17, 1993. NVAG3 was joint American Geophysical Union Chapman and European Geophysical Society Richardson Memorial conference, the first specialist conference jointly sponsored by the two organizations. It followed NVAG1 (Montreal, Aug. 1986), NVAG2 (Paris, June 1988; Schertzer and Lovejoy, 1991), five consecutive annual sessions at EGS general assemblies and two consecutive spring AGU meeting sessions. As with the other conferences and workshops mentioned above, the aim was to develop confrontation between theories and experiments on scaling/multifractal behaviour of geophysical fields. Subjects covered included climate, clouds, earthquakes, atmospheric and ocean dynamics, tectonics, precipitation, hydrology, the solar cycle and volcanoes. Areas of focus included new methods of data analysis (especially those used for the reliable estimation of multifractal and scaling exponents), as well as their application to rapidly growing data bases from in situ networks and remote sensing. The corresponding modelling, prediction and estimation techniques were also emphasized as were the current debates about stochastic and deterministic dynamics, fractal geometry and multifractals, self-organized criticality and multifractal fields, each of which was the subject of a specific general discussion. The conference started with a one day short course of multifractals featuring four lectures on a) Fundamentals of multifractals: dimension, codimensions, codimension formalism, b) Multifractal estimation techniques: (PDMS, DTM), c) Numerical simulations, Generalized Scale Invariance analysis, d) Advanced multifractals, singular statistics, phase transitions, self-organized criticality and Lie cascades (given by D. Schertzer and S. Lovejoy, detailed course notes were sent to participants shortly after the conference). This was followed by five days with 8 oral sessions and one poster session. Overall, there were 65 papers involving 74 authors. In general, the main topics covered are reflected in this special issue: geophysical turbulence, clouds and climate, hydrology and solid earth geophysics. In addition to AGU and EGS, the conference was supported by the International Science Foundation, the Centre Nationale de Recherche Scientifique, Meteo-France, the Department of Energy (US), the Commission of European Communities (DG XII), the Comite National Francais pour le Programme Hydrologique International, the Ministere de l'Enseignement Superieur et de la Recherche (France). We thank P. Hubert, Y. Kagan, Ph. Ladoy, A. Lazarev, S.S. Moiseev, R. Pierrehumbert, F. Schmitt and Y. Tessier, for help with the organization of the conference. However special thanks goes to A. Richter and the EGS office, B. Weaver and the AGU without whom this would have been impossible. We also thank the Institut d' Etudes Scientifiques de Cargese whose beautiful site was much appreciated, as well as the Bar des Amis whose ambiance stimulated so many discussions. 2. Tribute to L.F. Richardson With NVAG3, the European geophysical community paid tribute to Lewis Fry Richardson (1881-1953) on the 40th anniversary of his death. Richardson was one of the founding fathers of the idea of scaling and fractality, and his life reflects the European geophysical community and its history in many ways. Although many of Richardson's numerous, outstanding scientific contributions to geophysics have been recognized, perhaps his main contribution concerning the importance of scaling and cascades has still not received the attention it deserves. Richardson was the first not only to suggest numerical integration of the equations of motion of the atmosphere, but also to attempt to do so by hand, during the First World War. This work, as well as a presentation of a broad vision of future developments in the field, appeared in his famous, pioneering book "Weather prediction by numerical processes" (1922). As a consequence of his atmospheric studies, the nondimensional number associated with fluid convective stability has been called the "Richardson number". In addition, his book presents a study of the limitations of numerical integration of these equations, it was in this book that - through a celebrated poem - that the suggestion that turbulent cascades were the fundamental driving mechanism of the atmosphere was first made. In these cascades, large eddies break up into smaller eddies in a manner which involves no characteristic scales, all the way from the planetary scale down to the viscous scale. This led to the Richardson law of turbulent diffusion (1926) and tot he suggestion that particles trajectories might not be describable by smooth curves, but that such trajectories might instead require highly convoluted curves such as the Peano or Weierstrass (fractal) curves for their description. As a founder of the cascade and scaling theories of atmospheric dynamics, he more or less anticipated the Kolmogorov law (1941). He also used scaling ideas to invent the "Richardson dividers method" of successively increasing the resolution of fractal curves and tested out the method on geographical boundaries (as part of his wartime studies). In the latter work he anticipated recent efforts to study scale invariance in rivers and topography. His complex life typifies some of the hardships that the European scientific community has had to face. His educational career is unusual: he received a B.A. degree in physics, mathematics, chemistry, biology and zoology at Cambridge University, and he finally obtained his Ph.D. in mathematical psychology at the age of 47 from the University of London. As a conscientious objector he was compelled to quit the United Kingdom Meteorological Office in 1920 when the latter was militarized by integration into the Air Ministry. He subsequently became the head of a physics department and the principal of a college. In 1940, he retired to do research on war, which was published posthumously in book form (Richardson, 1963). This latter work is testimony to the trauma caused by the two World Wars and which led some scientists including Richardson to use their skills in rational attempts to eradicate the source of conflict. Unfortunately, this remains an open field of research. 3. The contributions in this special issue Perhaps the area of geophysics where scaling ideas have the longest history, and where they have made the largest impact in the last few years, is turbulence. The paper by Tsinober is an example where geometric fractal ideas are used to deduce corrections to standard dimensional analysis results for turbulence. Based on local spontaneous breaking of isotropy of turbulent flows, the fractal notion is used in order to deduce diffusion laws (anomalous with respect to the Richardson law). It is argued that his law is ubiquitous from the atmospheric boundary layer to the stratosphere. The asymptotic intermittency exponent i hypothesized to be not only finite but to be determined by the angular momentum flux. Schmitt et al., Chigirinskaya et al. and Lazarev et al. apply statistical multifractal notions to atmospheric turbulence. In the former, the formal analogy between multifractals and thermodynamics is exploited, in particular to confirm theoretical predictions that sample-size dependent multifractal phase transitions occur. While this quantitatively explains the behavior of the most extreme turbulent events, it suggests that - contrary to the type of multifractals most commonly discussed in the literature which are bounded - more violent (unbounded) multifractals are indeed present in the atmospheric wind field. Chigirinskaya et al. use a tropical rather than mid-latitude set to study the extreme fluctuations form yet another angle: That of coherent structures, which, in the multifractal framework, are identified with singularities of various orders. The existence of a critical order of singularity which distinguishes violent "self-organized critical structures" was theoretically predicted ten years ago; here it is directly estimated. The second of this two part series (Lazarev et al.) investigates yet another aspect of tropical atmospheric dynamics: the strong multiscaling anisotropy. Beyond the determination of universal multifractal indices and critical singularities in the vertical, this enables a comparison to be made with Chigirinskaya et al.'s horizontal results, requiring an extension of the unified scaling model of atmospheric dynamics. Other approaches to the problem of geophysical turbulence are followed in the papers by Pavlos et al., Vassiliadis et al., Voros et al. All of them share a common assumption that a very small number of degrees of freedom (deterministic chaos) might be sufficient for characterizing/modelling the systems under consideration. Pavlos et al. consider the magnetospheric response to solar wind, showing that scaling occurs both in real space (using spectra), and also in phase space; the latter being characterized by a correlation dimension. The paper by Vassiliadis et al. follows on directly by investigating the phase space properties of power-law filtered and rectified gaussian noise; the results further quantify how low phase space correlation dimensions can occur even with very large number of degrees of freedom (stochastic) processes. Voros et al. analyze time series of geomagnetic storms and magnetosphere pulsations, also estimating their correlation dimensions and Lyapounov exponents taking special care of the stability of the estimates. They discriminate low dimensional events from others, which are for instance attributed to incoherent waves. While clouds and climate were the subject of several talks at the conference (including several contributions on multifractal clouds), Cahalan's contribution is the only one in this special issue. Addressing the fundamental problem of the relationship of horizontal cloud heterogeneity and the related radiation fields, he first summarizes some recent numerical results showing that even for comparatively thin clouds that fractal heterogeneity will significantly reduce the albedo. The model used for the distribution of cloud liquid water is the monofractal "bounded cascade" model, whose properties are also outlined. The paper by Falkovich addresses another problem concerning the general circulation: the nonlinear interaction of waves. By assuming the existence of a peak (i.e. scale break) at the inertial oscillation frequency, it is argued that due to remarkable cancellations, the interactions between long inertio-gravity waves and Rossby waves are anomalously weak, producing a "wave condensate" of large amplitude so that wave breaking with front creation can occur. Kagan et al., Eneva and Hooge et al. consider fractal and multifractal behaviour in seismic events. Eneva estimates multifractal exponents of the density of micro-earthquakes induced by mining activity. The effects of sample limitations are discussed, especially in order to distinguish between genuine from spurious multifractal behaviour. With the help of an analysis of the CALNET catalogue, Hooge et al. points out, that the origin of the celebrated Gutenberg-Richter law could be related to a non-classical Self-Organized Criticality generated by a first order phase transition in a multifractal earthquake process. They also analyze multifractal seismic fields which are obtained by raising earthquake amplitudes to various powers and summing them on a grid. In contrast, Kagan, analyzing several earthquake catalogues discussed the various laws associated with earthquakes. Giving theoretical and empirical arguments, he proposes an additive (monofractal) model of earthquake stress, emphasizing the relevance of (asymmetric) stable Cauchy probability distributions to describe earthquake stress distributions. This would yield a linear model for self-organized critical earthquakes. References: Kolmogorov, A.N.: Local structure of turbulence in an incompressible liquid for very large Reynolds number, Proc. Acad. Sci. URSS Geochem. Sect., 30, 299-303, 1941. Perrin, J.: Les Atomes, NRF-Gallimard, Paris, 1913. Richardson, L.F.: Weather prediction by numerical process. Cambridge Univ. Press 1922 (republished by Dover, 1965). Richardson, L.F.: Atmospheric diffusion on a distance neighbour graph. Proc. Roy. of London A110, 709-737, 1923. Richardson, L.F.: The problem of contiguity: an appendix of deadly quarrels. General Systems Yearbook, 6, 139-187, 1963. Schertzer, D., Lovejoy, S.: Nonlinear Variability in Geophysics, Kluwer, 252 pp, 1991.

Multifractal characteristics of optical turbulence measured through a single beam holographic process.

PubMed

Pérez, Darío G; Barillé, Regis; Morille, Yohann; Zielińska, Sonia; Ortyl, Ewelina

2014-08-11

We have previously shown that azopolymer thin films exposed to coherent light that has travelled through a turbulent medium produces a surface relief grating containing information about the intensity of the turbulence; for instance, a relation between the refractive index structure constant C(n)2 as a function of the surface parameters was obtained. In this work, we show that these films capture much more information about the turbulence dynamics. Multifractal detrended fluctuation and fractal dimension analysis from images of the surface roughness produced by the light on the azopolymer reveals scaling properties related to those of the optical turbulence.

Multifractality as a Measure of Complexity in Solar Flare Activity

NASA Astrophysics Data System (ADS)

Sen, Asok K.

2007-03-01

In this paper we use the notion of multifractality to describe the complexity in H α flare activity during the solar cycles 21, 22, and 23. Both northern and southern hemisphere flare indices are analyzed. Multifractal behavior of the flare activity is characterized by calculating the singularity spectrum of the daily flare index time series in terms of the Hölder exponent. The broadness of the singularity spectrum gives a measure of the degree of multifractality or complexity in the flare index data. The broader the spectrum, the richer and more complex is the structure with a higher degree of multifractality. Using this broadness measure, complexity in the flare index data is compared between the northern and southern hemispheres in each of the three cycles, and among the three cycles in each of the two hemispheres. Other parameters of the singularity spectrum can also provide information about the fractal properties of the flare index data. For instance, an asymmetry to the left or right in the singularity spectrum indicates a dominance of high or low fractal exponents, respectively, reflecting a relative abundance of large or small fluctuations in the total energy emitted by the flares. Our results reveal that in the even (22nd) cycle the singularity spectra are very similar for the northern and southern hemispheres, whereas in the odd cycles (21st and 23rd) they differ significantly. In particular, we find that in cycle 21, the northern hemisphere flare index data have higher complexity than its southern counterpart, with an opposite pattern prevailing in cycle 23. Furthermore, small-scale fluctuations in the flare index time series are predominant in the northern hemisphere in the 21st cycle and are predominant in the southern hemisphere in the 23rd cycle. Based on these findings one might suggest that, from cycle to cycle, there exists a smooth switching between the northern and southern hemispheres in the multifractality of the flaring process. This new observational result may bring an insight into the mechanisms of the solar dynamo operation and may also be useful for forecasting solar cycles.

Breathing modes of Kolumbo submarine volcano (Santorini, Greece).

PubMed

Bakalis, Evangelos; Mertzimekis, Theo J; Nomikou, Paraskevi; Zerbetto, Francesco

2017-04-13

Submarine volcanoes, such as Kolumbo (Santorini, Greece) are natural laboratories for fostering multidisciplinary studies. Their investigation requires the most innovative marine technology together with advanced data analysis. Conductivity and temperature of seawater were recorded directly above Kolumbo's hydrothermal vent system. The respective time series have been analyzed in terms of non-equilibrium techniques. The energy dissipation of the volcanic activity is monitored by the temperature variations of seawater. The venting dynamics of chemical products is monitored by water conductivity. The analysis of the time series in terms of stochastic processes delivers scaling exponents with turning points between consecutive regimes for both conductivity and temperature. Changes of conductivity are shown to behave as a universal multifractal and their variance is subdiffusive as the scaling exponents indicate. Temperature is constant over volcanic rest periods and a universal multifractal behavior describes its changes in line with a subdiffusive character otherwise. The universal multifractal description illustrates the presence of non-conservative conductivity and temperature fields showing that the system never retains a real equilibrium state. The existence of a repeated pattern of the combined effect of both seawater and volcanic activity is predicted. The findings can shed light on the dynamics of chemical products emitted from the vents and point to the presence of underlying mechanisms that govern potentially hazardous, underwater volcanic environments.

Breathing modes of Kolumbo submarine volcano (Santorini, Greece)

NASA Astrophysics Data System (ADS)

Bakalis, Evangelos; Mertzimekis, Theo J.; Nomikou, Paraskevi; Zerbetto, Francesco

2017-04-01

Submarine volcanoes, such as Kolumbo (Santorini, Greece) are natural laboratories for fostering multidisciplinary studies. Their investigation requires the most innovative marine technology together with advanced data analysis. Conductivity and temperature of seawater were recorded directly above Kolumbo’s hydrothermal vent system. The respective time series have been analyzed in terms of non-equilibrium techniques. The energy dissipation of the volcanic activity is monitored by the temperature variations of seawater. The venting dynamics of chemical products is monitored by water conductivity. The analysis of the time series in terms of stochastic processes delivers scaling exponents with turning points between consecutive regimes for both conductivity and temperature. Changes of conductivity are shown to behave as a universal multifractal and their variance is subdiffusive as the scaling exponents indicate. Temperature is constant over volcanic rest periods and a universal multifractal behavior describes its changes in line with a subdiffusive character otherwise. The universal multifractal description illustrates the presence of non-conservative conductivity and temperature fields showing that the system never retains a real equilibrium state. The existence of a repeated pattern of the combined effect of both seawater and volcanic activity is predicted. The findings can shed light on the dynamics of chemical products emitted from the vents and point to the presence of underlying mechanisms that govern potentially hazardous, underwater volcanic environments.

Understanding the source of multifractality in financial markets

NASA Astrophysics Data System (ADS)

Barunik, Jozef; Aste, Tomaso; Di Matteo, T.; Liu, Ruipeng

2012-09-01

In this paper, we use the generalized Hurst exponent approach to study the multi-scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multi-scaling. We observe a puzzling phenomenon where an apparent increase in multifractality is measured in time series generated from shuffled returns, where all time-correlations are destroyed, while the return distributions are conserved. This effect is robust and it is reproduced in several real financial data including stock market indices, exchange rates and interest rates. In order to understand the origin of this effect we investigate different simulated time series by means of the Markov switching multifractal model, autoregressive fractionally integrated moving average processes with stable innovations, fractional Brownian motion and Levy flights. Overall we conclude that the multifractality observed in financial time series is mainly a consequence of the characteristic fat-tailed distribution of the returns and time-correlations have the effect to decrease the measured multifractality.

Dynamical Mechanism of Scaling Behaviors in Multifractal Structure

NASA Astrophysics Data System (ADS)

Kim, Kyungsik; Jung, Jae Won; Kim, Soo Yong

2010-03-01

The pattern of stone distribution in the game of Go (Baduk, Weiqi, or Igo) can be treated in the mathematical and physical languages of multifractals. The concepts of fractals and multifractals have relevance to many fields of science and even arts. A significant and fascinating feature of this approach is that it provides a proper interpretation for the pattern of the two-colored (black and white) stones in terms of the numerical values of the generalized dimension and the scaling exponent. For our case, these statistical quantities can be estimated numerically from the black, white, and mixed stones, assuming the excluded edge effect that the cell form of the Go game has the self-similar structure. The result from the multifractal structure allows us to find a definite and reliable fractal dimension, and it precisely verifies that the fractal dimension becomes larger, as the cell of grids increases. We also find the strength of multifractal structures from the difference in the scaling exponents in the black, white, and mixed stones.

Relationship research between meteorological disasters and stock markets based on a multifractal detrending moving average algorithm

NASA Astrophysics Data System (ADS)

Li, Qingchen; Cao, Guangxi; Xu, Wei

2018-01-01

Based on a multifractal detrending moving average algorithm (MFDMA), this study uses the fractionally autoregressive integrated moving average process (ARFIMA) to demonstrate the effectiveness of MFDMA in the detection of auto-correlation at different sample lengths and to simulate some artificial time series with the same length as the actual sample interval. We analyze the effect of predictable and unpredictable meteorological disasters on the US and Chinese stock markets and the degree of long memory in different sectors. Furthermore, we conduct a preliminary investigation to determine whether the fluctuations of financial markets caused by meteorological disasters are derived from the normal evolution of the financial system itself or not. We also propose several reasonable recommendations.

Integration of Scale Invariant Generator Technique and S-A Technique for Characterizing 2-D Patterns for Information Retrieve

NASA Astrophysics Data System (ADS)

Cao, L.; Cheng, Q.

2004-12-01

The scale invariant generator technique (SIG) and spectrum-area analysis technique (S-A) were developed independently relevant to the concept of the generalized scale invariance (GSI). The former was developed for characterizing the parameters involved in the GSI for characterizing and simulating multifractal measures whereas the latter was for identifying scaling breaks for decomposition of superimposed multifractal measures caused by multiple geophysical processes. A natural integration of these two techniques may yield a new technique to serve two purposes, on the one hand, that can enrich the power of S-A by increasing the interpretability of decomposed patterns in some applications of S-A and, on the other hand, that can provide a mean to test the uniqueness of multifractality of measures which is essential for application of SIG technique in more complicated environment. The implementation of the proposed technique has been done as a Dynamic Link Library (DLL) in Visual C++. The program can be friendly used for method validation and application in different fields.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cadavid, A. C.; Lawrence, J. K.; Christian, D. J.

We investigate the scaling properties of the long-range temporal evolution and intermittency of Atmospheric Imaging Assembly/ Solar Dynamics Observatory intensity observations in four solar environments: an active region core, a weak emission region, and two core loops. We use two approaches: the probability distribution function (PDF) of time series increments and multifractal detrended fluctuation analysis (MF-DFA). Noise taints the results, so we focus on the 171 Å waveband, which has the highest signal-to-noise ratio. The lags between pairs of wavebands distinguish between coronal versus transition region (TR) emission. In all physical regions studied, scaling in the range of 15–45 minutesmore » is multifractal, and the time series are anti-persistent on average. The degree of anti-correlation in the TR time series is greater than that for coronal emission. The multifractality stems from long-term correlations in the data rather than the wide distribution of intensities. Observations in the 335 Å waveband can be described in terms of a multifractal with added noise. The multiscaling of the extreme-ultraviolet data agrees qualitatively with the radiance from a phenomenological model of impulsive bursts plus noise, and also from ohmic dissipation in a reduced magnetohydrodynamic model for coronal loop heating. The parameter space must be further explored to seek quantitative agreement. Thus, the observational “signatures” obtained by the combined tests of the PDF of increments and the MF-DFA offer strong constraints that can systematically discriminate among models for coronal heating.« less

Complexity and multifractality of neuronal noise in mouse and human hippocampal epileptiform dynamics.

PubMed

Serletis, Demitre; Bardakjian, Berj L; Valiante, Taufik A; Carlen, Peter L

2012-10-01

Fractal methods offer an invaluable means of investigating turbulent nonlinearity in non-stationary biomedical recordings from the brain. Here, we investigate properties of complexity (i.e. the correlation dimension, maximum Lyapunov exponent, 1/f(γ) noise and approximate entropy) and multifractality in background neuronal noise-like activity underlying epileptiform transitions recorded at the intracellular and local network scales from two in vitro models: the whole-intact mouse hippocampus and lesional human hippocampal slices. Our results show evidence for reduced dynamical complexity and multifractal signal features following transition to the ictal epileptiform state. These findings suggest that pathological breakdown in multifractal complexity coincides with loss of signal variability or heterogeneity, consistent with an unhealthy ictal state that is far from the equilibrium of turbulent yet healthy fractal dynamics in the brain. Thus, it appears that background noise-like activity successfully captures complex and multifractal signal features that may, at least in part, be used to classify and identify brain state transitions in the healthy and epileptic brain, offering potential promise for therapeutic neuromodulatory strategies for afflicted patients suffering from epilepsy and other related neurological disorders.

Geometry and scaling laws of excursion and iso-sets of enstrophy and dissipation in isotropic turbulence

NASA Astrophysics Data System (ADS)

Elsas, José Hugo; Szalay, Alexander S.; Meneveau, Charles

2018-04-01

Motivated by interest in the geometry of high intensity events of turbulent flows, we examine the spatial correlation functions of sets where turbulent events are particularly intense. These sets are defined using indicator functions on excursion and iso-value sets. Their geometric scaling properties are analysed by examining possible power-law decay of their radial correlation function. We apply the analysis to enstrophy, dissipation and velocity gradient invariants Q and R and their joint spatial distributions, using data from a direct numerical simulation of isotropic turbulence at Reλ ≈ 430. While no fractal scaling is found in the inertial range using box-counting in the finite Reynolds number flow considered here, power-law scaling in the inertial range is found in the radial correlation functions. Thus, a geometric characterisation in terms of these sets' correlation dimension is possible. Strong dependence on the enstrophy and dissipation threshold is found, consistent with multifractal behaviour. Nevertheless, the lack of scaling of the box-counting analysis precludes direct quantitative comparisons with earlier work based on multifractal formalism. Surprising trends, such as a lower correlation dimension for strong dissipation events compared to strong enstrophy events, are observed and interpreted in terms of spatial coherence of vortices in the flow.

A space-time multifractal analysis on radar rainfall sequences from central Poland

NASA Astrophysics Data System (ADS)

Licznar, Paweł; Deidda, Roberto

2014-05-01

Rainfall downscaling belongs to most important tasks of modern hydrology. Especially from the perspective of urban hydrology there is real need for development of practical tools for possible rainfall scenarios generation. Rainfall scenarios of fine temporal scale reaching single minutes are indispensable as inputs for hydrological models. Assumption of probabilistic philosophy of drainage systems design and functioning leads to widespread application of hydrodynamic models in engineering practice. However models like these covering large areas could not be supplied with only uncorrelated point-rainfall time series. They should be rather supplied with space time rainfall scenarios displaying statistical properties of local natural rainfall fields. Implementation of a Space-Time Rainfall (STRAIN) model for hydrometeorological applications in Polish conditions, such as rainfall downscaling from the large scales of meteorological models to the scale of interest for rainfall-runoff processes is the long-distance aim of our research. As an introduction part of our study we verify the veracity of the following STRAIN model assumptions: rainfall fields are isotropic and statistically homogeneous in space; self-similarity holds (so that, after having rescaled the time by the advection velocity, rainfall is a fully homogeneous and isotropic process in the space-time domain); statistical properties of rainfall are characterized by an "a priori" known multifractal behavior. We conduct a space-time multifractal analysis on radar rainfall sequences selected from the Polish national radar system POLRAD. Radar rainfall sequences covering the area of 256 km x 256 km of original 2 km x 2 km spatial resolution and 15 minutes temporal resolution are used as study material. Attention is mainly focused on most severe summer convective rainfalls. It is shown that space-time rainfall can be considered with a good approximation to be a self-similar multifractal process. Multifractal analysis is carried out assuming Taylor's hypothesis to hold and the advection velocity needed to rescale the time dimension is assumed to be equal about 16 km/h. This assumption is verified by the analysis of autocorrelation functions along the x and y directions of "rainfall cubes" and along the time axis rescaled with assumed advection velocity. In general for analyzed rainfall sequences scaling is observed for spatial scales ranging from 4 to 256 km and for timescales from 15 min to 16 hours. However in most cases scaling break is identified for spatial scales between 4 and 8, corresponding to spatial dimensions of 16 km to 32 km. It is assumed that the scaling break occurrence at these particular scales in central Poland conditions could be at least partly explained by the rainfall mesoscale gap (on the edge of meso-gamma, storm-scale and meso-beta scale).

Markov-switching multifractal models as another class of random-energy-like models in one-dimensional space

NASA Astrophysics Data System (ADS)

Saakian, David B.

2012-03-01

We map the Markov-switching multifractal model (MSM) onto the random energy model (REM). The MSM is, like the REM, an exactly solvable model in one-dimensional space with nontrivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multifractal behavior. We also introduce the continuous branching version of the model, calculate the moments, and prove multiscaling behavior. Different phases have different multiscaling properties.

Single- versus Multifraction Stereotactic Body Radiation Therapy for Pancreatic Adenocarcinoma: Outcomes and Toxicity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pollom, Erqi L.; Alagappan, Muthuraman; Eyben, Rie von

2014-11-15

Purpose: We report updated outcomes of single- versus multifraction stereotactic body radiation therapy (SBRT) for unresectable pancreatic adenocarcinoma. Methods and Materials: We included 167 patients with unresectable pancreatic adenocarcinoma treated at our institution from 2002 to 2013, with 1-fraction (45.5% of patient) or 5-fraction (54.5% of patients) SBRT. The majority of patients (87.5%) received chemotherapy. Results: Median follow-up was 7.9 months (range: 0.1-63.6). The 6- and 12-month cumulative incidence rates (CIR) of local recurrence for patients treated with single-fraction SBRT were 5.3% (95% confidence interval [CI], 0.2%-10.4%) and 9.5% (95% CI, 2.7%-16.2%), respectively. The 6- and 12-month CIR with multifraction SBRTmore » were 3.4% (95% CI, 0.0-7.2%) and 11.7% (95% CI, 4.8%-18.6%), respectively. Median survival from diagnosis for all patients was 13.6 months (95% CI, 12.2-15.0 months). The 6- and 12- month survival rates from SBRT for the single-fraction group were 67.0% (95% CI, 57.2%-78.5%) and 30.8% (95% CI, 21.9%-43.6%), respectively. The 6- and 12- month survival rates for the multifraction group were 75.7% (95% CI, 67.2%-85.3%) and 34.9% (95% CI, 26.1%-46.8%), respectively. There were no differences in CIR or survival rates between the single- and multifraction groups. The 6- and 12-month cumulative incidence rates of gastrointestinal toxicity grade ≥3 were 8.1% (95% CI, 1.8%-14.4%) and 12.3% (95% CI, 4.7%-20.0%), respectively, in the single-fraction group, and both were 5.6% (95% CI, 0.8%-10.5%) in the multifraction group. There were significantly fewer instances of toxicity grade ≥2 with multifraction SBRT (P=.005). Local recurrence and toxicity grade ≥2 were independent predictors of worse survival. Conclusions: Multifraction SBRT for pancreatic cancer significantly reduces gastrointestinal toxicity without compromising local control.« less

The foreign exchange market: return distributions, multifractality, anomalous multifractality and the Epps effect

NASA Astrophysics Data System (ADS)

Drożdż, Stanisław; Kwapień, Jarosław; Oświȩcimka, Paweł; Rak, Rafał

2010-10-01

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all of the pairs considered are well described by the non-extensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the non-extensivity q-parameter values for different exchange rates (which depend also on the time scales studied), and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all of the exchange rates, with a varying degree of symmetry of the singularity spectrum f(α), however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations, which excludes description in terms of q-Gaussians. The multifractal characteristics of these residual returns reveal such anomalous properties as negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with diffusion-limited aggregation and with turbulence. Studying the cross-correlations among different exchange rates, we found that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales, but comparable to the ones for the stock market. Although the currency market is much more liquid than the stock markets and has a much greater transaction frequency, the building up of correlations takes up to several hours—a duration that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect.

Multifractal dissipation of intermittent turbulence generated by the magnetic reconnection in the solar wind

NASA Astrophysics Data System (ADS)

Wang, Y.; Wei, F.; Feng, X.

2013-12-01

Recent observations revealed a scale-invariant dissipation process in the fast ambient solar wind, while numerical simulations indicated that the dissipation process in collisionless reconnection was multifractal. Here, we investigate the properties of turbulent fluctuations in the magnetic reconnection prevailed region. It is found that there are large magnetic field shear angle and obvious intermittent structures in these regions. The deduced scaling exponents in the dissipation subrange show a multifractal scaling. In comparison, in the nearby region where magnetic reconnection is less prevailed, we find smaller magnetic field shear angle, less intermittent structures, and most importantly, a monofractal dissipation process. These results provide additionally observational evidence for previous observation and simulation work, and they also imply that magnetic dissipation in the solar wind magnetic reconnection might be caused by the intermittent cascade as multifractal processes.

Cross-correlations between crude oil and exchange markets for selected oil rich economies

NASA Astrophysics Data System (ADS)

Li, Jianfeng; Lu, Xinsheng; Zhou, Ying

2016-07-01

Using multifractal detrended cross-correlation analysis (MF-DCCA), this paper studies the cross-correlation behavior between crude oil market and five selected exchange rate markets. The dataset covers the period of January 1,1996-December 31,2014, and contains 4,633 observations for each of the series, including daily closing prices of crude oil, Australian Dollars, Canadian Dollars, Mexican Pesos, Russian Rubles, and South African Rand. Our empirical results obtained from cross-correlation statistic and cross-correlation coefficient have confirmed the existence of cross-correlations, and the MF-DCCA results have demonstrated a strong multifractality between cross-correlated crude oil market and exchange rate markets in both short term and long term. Using rolling window analysis, we have also found the persistent cross-correlations between the exchange rates and crude oil returns, and the cross-correlation scaling exponents exhibit volatility during some time periods due to its sensitivity to sudden events.

Mustiscaling Analysis applied to field Water Content through Distributed Fiber Optic Temperature sensing measurements

NASA Astrophysics Data System (ADS)

Benitez Buelga, Javier; Rodriguez-Sinobas, Leonor; Sanchez, Raul; Gil, Maria; Tarquis, Ana M.

2014-05-01

Soils can be seen as the result of spatial variation operating over several scales. This observation points to 'variability' as a key soil attribute that should be studied. Soil variability has often been considered to be composed of 'functional' (explained) variations plus random fluctuations or noise. However, the distinction between these two components is scale dependent because increasing the scale of observation almost always reveals structure in the noise. Geostatistical methods and, more recently, multifractal/wavelet techniques have been used to characterize scaling and heterogeneity of soil properties among others coming from complexity science. Multifractal formalism, first proposed by Mandelbrot (1982), is suitable for variables with self-similar distribution on a spatial domain (Kravchenko et al., 2002). Multifractal analysis can provide insight into spatial variability of crop or soil parameters (Vereecken et al., 2007). This technique has been used to characterize the scaling property of a variable measured along a transect as a mass distribution of a statistical measure on a spatial domain of the studied field (Zeleke and Si, 2004). To do this, it divides the transect into a number of self-similar segments. It identifies the differences among the subsets by using a wide range of statistical moments. Wavelets were developed in the 1980s for signal processing, and later introduced to soil science by Lark and Webster (1999). The wavelet transform decomposes a series; whether this be a time series (Whitcher, 1998; Percival and Walden, 2000), or as in our case a series of measurements made along a transect; into components (wavelet coefficients) which describe local variation in the series at different scale (or frequency) intervals, giving up only some resolution in space (Lark et al., 2003, 2004). Wavelet coefficients can be used to estimate scale specific components of variation and correlation. This allows us to see which scales contribute most to signal variation, or to see at which scales signals are most correlated. This can give us an insight into the dominant processes An alternative to both of the above methods has been described recently. Relative entropy and increments in relative entropy has been applied in soil images (Bird et al., 2006) and in soil transect data (Tarquis et al., 2008) to study scale effects localized in scale and provide the information that is complementary to the information about scale dependencies found across a range of scales. We will use them in this work to describe the spatial scaling properties of a set of field water content data measured in an extension of a corn field, in a plot of 500 m2 and an spatial resolution of 25 cm. These measurements are based on an optics cable (BruggSteal) buried on a ziz-zag deployment at 30cm depth. References Bird, N., M.C. Díaz, A. Saa, and A.M. Tarquis. 2006. A review of fractal and multifractal analysis of soil pore-scale images. J. Hydrol. 322:211-219. Kravchenko, A.N., R. Omonode, G.A. Bollero, and D.G. Bullock. 2002. Quantitative mapping of soil drainage classes using topographical data and soil electrical conductivity. Soil Sci. Soc. Am. J. 66:235-243. Lark, R.M., A.E. Milne, T.M. Addiscott, K.W.T. Goulding, C.P. Webster, and S. O'Flaherty. 2004. Scale- and location-dependent correlation of nitrous oxide emissions with soil properties: An analysis using wavelets. Eur. J. Soil Sci. 55:611-627. Lark, R.M., S.R. Kaffka, and D.L. Corwin. 2003. Multiresolution analysis of data on electrical conductivity of soil using wavelets. J. Hydrol. 272:276-290. Lark, R. M. and Webster, R. 1999. Analysis and elucidation of soil variation using wavelets. European J. of Soil Science, 50(2): 185-206. Mandelbrot, B.B. 1982. The fractal geometry of nature. W.H. Freeman, New York. Percival, D.B., and A.T. Walden. 2000. Wavelet methods for time series analysis. Cambridge Univ. Press, Cambridge, UK. Tarquis, A.M., N.R. Bird, A.P. Whitmore, M.C. Cartagena, and Y. Pachepsky. 2008. Multiscale analysis of soil transect data. Vadose Zone J. 7: 563-569. Vereecken, H., R. Kasteel, J. Vanderborght, and T. Harter. 2007. Upscaling hydraulic properties and soil water flow processes in heterogeneous soils: A review. Vadose Zone J. 6:1-28. Whitcher, B.J. 1998. Assessing nonstationary time series using wavelets. Ph.D. diss. Univ. of Washington, Seattle (Diss. Abstr. 9907961). Zeleke, T.B., and B.C. Si. 2004. Scaling properties of topographic indices and crop yield: Multifractal and joint multifractal approaches. Agron J., 96:1082-1090.

Coherent changes of multifractal properties of continuous acoustic emission at failure of heterogeneous materials

NASA Astrophysics Data System (ADS)

Panteleev, Ivan; Bayandin, Yuriy; Naimark, Oleg

2017-12-01

This work performs a correlation analysis of the statistical properties of continuous acoustic emission recorded in different parts of marble and fiberglass laminate samples under quasi-static deformation. A spectral coherent measure of time series, which is a generalization of the squared coherence spectrum on a multidimensional series, was chosen. The spectral coherent measure was estimated in a sliding time window for two parameters of the acoustic emission multifractal singularity spectrum: the spectrum width and the generalized Hurst exponent realizing the maximum of the singularity spectrum. It is shown that the preparation of the macrofracture focus is accompanied by the synchronization (coherent behavior) of the statistical properties of acoustic emission in allocated frequency intervals.

Extreme values and fat tails of multifractal fluctuations

NASA Astrophysics Data System (ADS)

Muzy, J. F.; Bacry, E.; Kozhemyak, A.

2006-06-01

In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with such data. We show that because of strong correlations, the standard extreme value approach is not valid and classical tail exponent estimators should be interpreted cautiously. Extreme statistics associated with multifractal random processes turn out to be characterized by non-self-averaging properties. Our considerations rely upon some analogy between random multiplicative cascades and the physics of disordered systems and also on recent mathematical results about the so-called multifractal formalism. Applied to financial time series, our findings allow us to propose an unified framework that accounts for the observed multiscaling properties of return fluctuations, the volatility clustering phenomenon and the observed “inverse cubic law” of the return pdf tails.

Dependency structure and scaling properties of financial time series are related

PubMed Central

Morales, Raffaello; Di Matteo, T.; Aste, Tomaso

2014-01-01

We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations. We propose a dynamical model that reproduces this observation along with an array of other empirical properties. The structure of this model is such that the hierarchical structure of heterogeneous risks plays a crucial role in the time evolution of the correlation matrix, providing an interpretation to the mechanism behind the interplay between cross-correlation and multifractality in financial markets, where the degree of multifractality of stocks is associated to their hierarchical positioning in the cross-correlation structure. Empirical observations reported in this paper present a new perspective towards the merging of univariate multi scaling and multivariate cross-correlation properties of financial time series. PMID:24699417

Empirical method to measure stochasticity and multifractality in nonlinear time series

NASA Astrophysics Data System (ADS)

Lin, Chih-Hao; Chang, Chia-Seng; Li, Sai-Ping

2013-12-01

An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm, and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.

Dependency structure and scaling properties of financial time series are related

NASA Astrophysics Data System (ADS)

Morales, Raffaello; Di Matteo, T.; Aste, Tomaso

2014-04-01

We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations. We propose a dynamical model that reproduces this observation along with an array of other empirical properties. The structure of this model is such that the hierarchical structure of heterogeneous risks plays a crucial role in the time evolution of the correlation matrix, providing an interpretation to the mechanism behind the interplay between cross-correlation and multifractality in financial markets, where the degree of multifractality of stocks is associated to their hierarchical positioning in the cross-correlation structure. Empirical observations reported in this paper present a new perspective towards the merging of univariate multi scaling and multivariate cross-correlation properties of financial time series.

Framework based on stochastic L-Systems for modeling IP traffic with multifractal behavior

NASA Astrophysics Data System (ADS)

Salvador, Paulo S.; Nogueira, Antonio; Valadas, Rui

2003-08-01

In a previous work we have introduced a multifractal traffic model based on so-called stochastic L-Systems, which were introduced by biologist A. Lindenmayer as a method to model plant growth. L-Systems are string rewriting techniques, characterized by an alphabet, an axiom (initial string) and a set of production rules. In this paper, we propose a novel traffic model, and an associated parameter fitting procedure, which describes jointly the packet arrival and the packet size processes. The packet arrival process is modeled through a L-System, where the alphabet elements are packet arrival rates. The packet size process is modeled through a set of discrete distributions (of packet sizes), one for each arrival rate. In this way the model is able to capture correlations between arrivals and sizes. We applied the model to measured traffic data: the well-known pOct Bellcore, a trace of aggregate WAN traffic and two traces of specific applications (Kazaa and Operation Flashing Point). We assess the multifractality of these traces using Linear Multiscale Diagrams. The suitability of the traffic model is evaluated by comparing the empirical and fitted probability mass and autocovariance functions; we also compare the packet loss ratio and average packet delay obtained with the measured traces and with traces generated from the fitted model. Our results show that our L-System based traffic model can achieve very good fitting performance in terms of first and second order statistics and queuing behavior.

Multifractal scaling of the kinetic energy flux in solar wind turbulence

NASA Technical Reports Server (NTRS)

Marsch, E.; Rosenbauer, H.; Tu, C.-Y.

1995-01-01

The geometrical and scaling properties of the energy flux of the turbulent kinetic energy in the solar wind have been studied. By present experimental technology in solar wind measurements, we cannot directly measure the real volumetric dissipation rate, epsilon(t), but are constrained to represent it by surrogating the energy flux near the dissipation range at the proton gyro scales. There is evidence for the multifractal nature of the so defined dissipation field epsilon(t), a result derived from the scaling exponents of its statistical q-th order moments. The related generalized dimension D(q) has been determined and reveals that the dissipation field has a multifractal structure. which is not compatible with a scale-invariant cascade. The associated multifractal spectrum f(alpha) has been estimated for the first time for MHD turbulence in the solar wind. Its features resemble those obtained for turbulent fluids and other nonlinear multifractal systems. The generalized dimension D(q) can, for turbulence in high-speed streams, be fitted well by the functional dependence of the p-model with a comparatively large parameter, p = 0.87. indicating a strongly intermittent multifractal energy cascade. The experimental value for D(p)/3, if used in the scaling exponent s(p) of the velocity structure function, gives an exponent that can describe some of the observations. The scaling exponent mu of the auto correlation function of epsilon(t) has also been directly evaluated. It has the value of 0.37. Finally. the mean dissipation rate was determined, which could be used in solar wind heating models.

Disappearance of Anisotropic Intermittency in Large-amplitude MHD Turbulence and Its Comparison with Small-amplitude MHD Turbulence

NASA Astrophysics Data System (ADS)

Yang, Liping; Zhang, Lei; He, Jiansen; Tu, Chuanyi; Li, Shengtai; Wang, Xin; Wang, Linghua

2018-03-01

Multi-order structure functions in the solar wind are reported to display a monofractal scaling when sampled parallel to the local magnetic field and a multifractal scaling when measured perpendicularly. Whether and to what extent will the scaling anisotropy be weakened by the enhancement of turbulence amplitude relative to the background magnetic strength? In this study, based on two runs of the magnetohydrodynamic (MHD) turbulence simulation with different relative levels of turbulence amplitude, we investigate and compare the scaling of multi-order magnetic structure functions and magnetic probability distribution functions (PDFs) as well as their dependence on the direction of the local field. The numerical results show that for the case of large-amplitude MHD turbulence, the multi-order structure functions display a multifractal scaling at all angles to the local magnetic field, with PDFs deviating significantly from the Gaussian distribution and a flatness larger than 3 at all angles. In contrast, for the case of small-amplitude MHD turbulence, the multi-order structure functions and PDFs have different features in the quasi-parallel and quasi-perpendicular directions: a monofractal scaling and Gaussian-like distribution in the former, and a conversion of a monofractal scaling and Gaussian-like distribution into a multifractal scaling and non-Gaussian tail distribution in the latter. These results hint that when intermittencies are abundant and intense, the multifractal scaling in the structure functions can appear even if it is in the quasi-parallel direction; otherwise, the monofractal scaling in the structure functions remains even if it is in the quasi-perpendicular direction.

Risk management of a fund for natural disasters

NASA Astrophysics Data System (ADS)

Flores, C.

2003-04-01

Mexico is a country which has to deal with several natural disaster risks: earthquakes, droughts, volcanic eruptions, floods, slides, wild fires, extreme temperatures, etc. In order to reduce the country's vulnerability to the impact of these natural disasters and to support rapid recovery when they occur, the government established in 1996 Mexico's Fund for Natural Disasters (FONDEN). Since its creation, its resources have been insufficient to meet all government obligations. The aim of this project is the development of a dynamic strategy to optimise the management of a fund for natural disasters starting from the example of FONDEN. The problem of budgetary planning is being considered for the modelling. We control the level of the fund's cash (R_t)0<= t0 at t=0 and then we try to pull at every moment the process to this objective. Multifractal models in geophysics are physically based stochastic models. A multiplicative cascade model fitted to a data set can be used for generation of synthetic sequences that resemble the original data in terms of its scaling properties. Since recent years, uncertainty concepts based on multifractal fields are being applied to the development of techniques to calculate marginal and conditional probabilities of an extreme rainfall event in a determined zone. As initial point to the development of the model, a multifractal model for extreme rainfall events will be used as part of the input for the stochastic control model. A theme for further research is linking more warning systems to the model. Keywords: risk management, stochastic control, multifractal measures, multiplicative cascades, heavy rainfall events.

Multifractality and autoregressive processes of dry spell lengths in Europe: an approach to their complexity and predictability

NASA Astrophysics Data System (ADS)

Lana, X.; Burgueño, A.; Serra, C.; Martínez, M. D.

2017-01-01

Dry spell lengths, DSL, defined as the number of consecutive days with daily rain amounts below a given threshold, may provide relevant information about drought regimes. Taking advantage of a daily pluviometric database covering a great extension of Europe, a detailed analysis of the multifractality of the dry spell regimes is achieved. At the same time, an autoregressive process is applied with the aim of predicting DSL. A set of parameters, namely Hurst exponent, H, estimated from multifractal spectrum, f( α), critical Hölder exponent, α 0, for which f( α) reaches its maximum value, spectral width, W, and spectral asymmetry, B, permits a first clustering of European rain gauges in terms of the complexity of their DSL series. This set of parameters also allows distinguishing between time series describing fine- or smooth-structure of the DSL regime by using the complexity index, CI. Results of previous monofractal analyses also permits establishing comparisons between smooth-structures, relatively low correlation dimensions, notable predictive instability and anti-persistence of DSL for European areas, sometimes submitted to long droughts. Relationships are also found between the CI and the mean absolute deviation, MAD, and the optimum autoregressive order, OAO, of an ARIMA( p, d,0) autoregressive process applied to the DSL series. The detailed analysis of the discrepancies between empiric and predicted DSL underlines the uncertainty over predictability of long DSL, particularly for the Mediterranean region.

Coupled uncertainty provided by a multifractal random walker

NASA Astrophysics Data System (ADS)

Koohi Lai, Z.; Vasheghani Farahani, S.; Movahed, S. M. S.; Jafari, G. R.

2015-10-01

The aim here is to study the concept of pairing multifractality between time series possessing non-Gaussian distributions. The increasing number of rare events creates ;criticality;. We show how the pairing between two series is affected by rare events, which we call ;coupled criticality;. A method is proposed for studying the coupled criticality born out of the interaction between two series, using the bivariate multifractal random walk (BiMRW). This method allows studying dependence of the coupled criticality on the criticality of each individual system. This approach is applied to data sets of gold and oil markets, and inflation and unemployment.

Multifractal analyis of soil invertebrates along a transect under different land uses

NASA Astrophysics Data System (ADS)

Machado Siqueira, Glécio; Alves Silva, Raimunda; Vidal-Vázquez, Eva; Paz-González, Antonio

2017-04-01

Soil fauna play a central role in many essential ecosystem processes. Land use and management can have a dramatic effect upon soil invertebrate community. Indices based on soil invertebrates abundance and diversity are fundamental for soil quality assessment. Many soil properties and attributes have been shown to exhibit spatial variabilityThe aim of this study was to analyze the scaling heterogeneity of the soil invertebrate community sampled using pitfall traps across a transect. The field study was conducted at Mata Roma municipality, Maranhão State, Brazil. Transects were marked under seven different agricultural/forestry land uses (millet, soybean, maize, eucalyptus, pasture, secondary savannah and native savannah). Native vegetation was considered as a reference, whereas the agricultural fields showed a range of soil use intensities. Along these transects 130 pitfall per land use were installed. First, differences in community assemblages and composition under different land use systems were evaluated using classical indices. Then, the spatial distribution of soil fauna trapped by pitfall techniques, characterized through generalized dimension, Dq, and singularity spectra, f(α) - α, showed a well-defined multifractal structure. Differences in scaling heterogeneity and other multifractal characteristics were examined in relation to land use intensification.

Stacked sparse autoencoder in hyperspectral data classification using spectral-spatial, higher order statistics and multifractal spectrum features

NASA Astrophysics Data System (ADS)

Wan, Xiaoqing; Zhao, Chunhui; Wang, Yanchun; Liu, Wu

2017-11-01

This paper proposes a novel classification paradigm for hyperspectral image (HSI) using feature-level fusion and deep learning-based methodologies. Operation is carried out in three main steps. First, during a pre-processing stage, wave atoms are introduced into bilateral filter to smooth HSI, and this strategy can effectively attenuate noise and restore texture information. Meanwhile, high quality spectral-spatial features can be extracted from HSI by taking geometric closeness and photometric similarity among pixels into consideration simultaneously. Second, higher order statistics techniques are firstly introduced into hyperspectral data classification to characterize the phase correlations of spectral curves. Third, multifractal spectrum features are extracted to characterize the singularities and self-similarities of spectra shapes. To this end, a feature-level fusion is applied to the extracted spectral-spatial features along with higher order statistics and multifractal spectrum features. Finally, stacked sparse autoencoder is utilized to learn more abstract and invariant high-level features from the multiple feature sets, and then random forest classifier is employed to perform supervised fine-tuning and classification. Experimental results on two real hyperspectral data sets demonstrate that the proposed method outperforms some traditional alternatives.

Cross-correlations between the US monetary policy, US dollar index and crude oil market

NASA Astrophysics Data System (ADS)

Sun, Xinxin; Lu, Xinsheng; Yue, Gongzheng; Li, Jianfeng

2017-02-01

This paper investigates the cross-correlations between the US monetary policy, US dollar index and WTI crude oil market, using a dataset covering a period from February 4, 1994 to February 29, 2016. Our study contributes to the literature by examining the effect of the US monetary policy on US dollar index and WTI crude oil through the MF-DCCA approach. The empirical results show that the cross-correlations between the three sets of time series exhibit strong multifractal features with the strength of multifractality increasing over the sample period. Employing a rolling window analysis, our empirical results show that the US monetary policy operations have clear influences on the cross-correlated behavior of the three time series covered by this study.

Identification of magnetic anomalies based on ground magnetic data analysis using multifractal modelling: a case study in Qoja-Kandi, East Azerbaijan Province, Iran

NASA Astrophysics Data System (ADS)

Mansouri, E.; Feizi, F.; Karbalaei Ramezanali, A. A.

2015-10-01

Ground magnetic anomaly separation using the reduction-to-the-pole (RTP) technique and the fractal concentration-area (C-A) method has been applied to the Qoja-Kandi prospecting area in northwestern Iran. The geophysical survey resulting in the ground magnetic data was conducted for magnetic element exploration. Firstly, the RTP technique was applied to recognize underground magnetic anomalies. RTP anomalies were classified into different populations based on the current method. For this reason, drilling point area determination by the RTP technique was complicated for magnetic anomalies, which are in the center and north of the studied area. Next, the C-A method was applied to the RTP magnetic anomalies (RTP-MA) to demonstrate magnetic susceptibility concentrations. This identification was appropriate for increasing the resolution of the drilling point area determination and decreasing the drilling risk issue, due to the economic costs of underground prospecting. In this study, the results of C-A modelling on the RTP-MA are compared with 8 borehole data. The results show that there is a good correlation between anomalies derived via the C-A method and the log report of boreholes. Two boreholes were drilled in magnetic susceptibility concentrations, based on multifractal modelling data analyses, between 63 533.1 and 66 296 nT. Drilling results showed appropriate magnetite thickness with grades greater than 20 % Fe. The total associated with anomalies containing andesite units hosts iron mineralization.

Molecular thermal transistor: Dimension analysis and mechanism

NASA Astrophysics Data System (ADS)

Behnia, S.; Panahinia, R.

2018-04-01

Recently, large challenge has been spent to realize high efficient thermal transistors. Outstanding properties of DNA make it as an excellent nano material in future technologies. In this paper, we introduced a high efficient DNA based thermal transistor. The thermal transistor operates when the system shows an increase in the thermal flux despite of decreasing temperature gradient. This is what called as negative differential thermal resistance (NDTR). Based on multifractal analysis, we could distinguish regions with NDTR state from non-NDTR state. Moreover, Based on dimension spectrum of the system, it is detected that NDTR state is accompanied by ballistic transport regime. The generalized correlation sum (analogous to specific heat) shows that an irregular decrease in the specific heat induces an increase in the mean free path (mfp) of phonons. This leads to the occurrence of NDTR.

Quantifying the pattern of microbial cell dispersion, density and clustering on surfaces of differing chemistries and topographies using multifractal analysis.

PubMed

Wickens, David; Lynch, Stephen; West, Glen; Kelly, Peter; Verran, Joanna; Whitehead, Kathryn A

2014-09-01

The effects of surface topography on bacterial distribution across a surface are of extreme importance when designing novel, hygienic or antimicrobial surface coatings. The majority of methods that are deployed to describe the pattern of cell dispersion, density and clustering across surfaces are currently qualitative. This paper presents a novel application of multifractal analysis to quantitatively measure these factors using medically relevant microorganisms (Staphylococcus aureus or Staphylococcus epidermidis). Surfaces (medical grade 316 stainless steel) and coatings (Ti-ZrN, Ti-ZrN/6.0%Ag, Ti-ZrN/15.6%Ag, TiZrN/24.7%Ag) were used in microbiological retention assays. Results demonstrated that S. aureus displayed a more heterogeneous cell dispersion (∆αAS<1) whilst the dispersion of S. epidermidis was more symmetric and homogeneous (∆αAS≥1). Further, although the surface topography and chemistry had an effect on cell dispersion, density and clustering, the type of bonding that occurred at the surface interface was also important. Both types of cells were influenced by both surface topographical and chemical effects; however, S. aureus was influenced marginally more by surface chemistry whilst S. epidermidis cells was influenced marginally more by surface topography. Thus, this effect was bacterially species specific. The results demonstrate that multifractal analysis is a method that can be used to quantitatively analyse the cell dispersion, density and clustering of retained microorganisms on surfaces. Using quantitative descriptors has the potential to aid the understanding the effect of surface properties on the production of hygienic and antimicrobial coatings. Copyright © 2014 Elsevier B.V. All rights reserved.

Multifractality of cerebral blood flow

NASA Astrophysics Data System (ADS)

West, Bruce J.; Latka, Miroslaw; Glaubic-Latka, Marta; Latka, Dariusz

2003-02-01

Scale invariance, the property relating time series across multiple scales, has provided a new perspective of physiological phenomena and their underlying control systems. The traditional “signal plus noise” paradigm of the engineer was first replaced with a model in which biological time series have a fractal structure in time (Fractal Physiology, Oxford University Press, Oxford, 1994). This new paradigm was subsequently shown to be overly restrictive when certain physiological signals were found to be characterized by more than one scaling parameter and therefore to belong to a class of more complex processes known as multifractals (Fractals, Plenum Press, New York, 1988). Here we demonstrate that in addition to heart rate (Nature 399 (1999) 461) and human gait (Phys. Rev. E, submitted for publication), the nonlinear control system for cerebral blood flow (CBF) (Phys. Rev. Lett., submitted for publication; Phys. Rev. E 59 (1999) 3492) is multifractal. We also find that this multifractality is greatly reduced for subjects with “serious” migraine and we present a simple model for the underlying control process to describe this effect.

Right-side-stretched multifractal spectra indicate small-worldness in networks

NASA Astrophysics Data System (ADS)

Oświȩcimka, Paweł; Livi, Lorenzo; Drożdż, Stanisław

2018-04-01

Complex network formalism allows to explain the behavior of systems composed by interacting units. Several prototypical network models have been proposed thus far. The small-world model has been introduced to mimic two important features observed in real-world systems: i) local clustering and ii) the possibility to move across a network by means of long-range links that significantly reduce the characteristic path length. A natural question would be whether there exist several ;types; of small-world architectures, giving rise to a continuum of models with properties (partially) shared with other models belonging to different network families. Here, we take advantage of the interplay between network theory and time series analysis and propose to investigate small-world signatures in complex networks by analyzing multifractal characteristics of time series generated from such networks. In particular, we suggest that the degree of right-sided asymmetry of multifractal spectra is linked with the degree of small-worldness present in networks. This claim is supported by numerical simulations performed on several parametric models, including prototypical small-world networks, scale-free, fractal and also real-world networks describing protein molecules. Our results also indicate that right-sided asymmetry emerges with the presence of the following topological properties: low edge density, low average shortest path, and high clustering coefficient.

True and apparent scaling: The proximity of the Markov-switching multifractal model to long-range dependence

NASA Astrophysics Data System (ADS)

Liu, Ruipeng; Di Matteo, T.; Lux, Thomas

2007-09-01

In this paper, we consider daily financial data of a collection of different stock market indices, exchange rates, and interest rates, and we analyze their multi-scaling properties by estimating a simple specification of the Markov-switching multifractal (MSM) model. In order to see how well the estimated model captures the temporal dependence of the data, we estimate and compare the scaling exponents H(q) (for q=1,2) for both empirical data and simulated data of the MSM model. In most cases the multifractal model appears to generate ‘apparent’ long memory in agreement with the empirical scaling laws.

Long-range dependence and multifractality in the term structure of LIBOR interest rates

NASA Astrophysics Data System (ADS)

Cajueiro, Daniel O.; Tabak, Benjamin M.

2007-01-01

In this paper we present evidence of long-range dependence in LIBOR interest rates. We study a data set from 2000 to 2005, for six different currencies and various maturities. Empirical results suggest that the degree of long-range dependence decreases with maturity, with the exception of interest rates on Japanese Yen and on Indonesian Rupiah. Furthermore, interest rates have a multifractal nature and the degree of multifractality is much stronger for Indonesia (emerging market). These findings suggest that interest rates derivatives should take these features into account. Furthermore, fixed income risk and portfolio management should incorporate long-range dependence in the modeling of interest rates.

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulated Serratia marcescens

PubMed Central

Bogdan, Paul; Wei, Guopeng; Marculescu, Radu; Zhuang, Jiang; Carlsen, Rika Wright; Sitti, Metin

2017-01-01

To add to the current state of knowledge about bacterial swimming dynamics, in this paper, we study the fractal swimming dynamics of populations of Serratia marcescens bacteria both in vitro and in silico, while accounting for realistic conditions like volume exclusion, chemical interactions, obstacles and distribution of chemoattractant in the environment. While previous research has shown that bacterial motion is non-ergodic, we demonstrate that, besides the non-ergodicity, the bacterial swimming dynamics is multi-fractal in nature. Finally, we demonstrate that the multi-fractal characteristic of bacterial dynamics is strongly affected by bacterial density and chemoattractant concentration. PMID:28804259

The weather and climate: emergent laws and multifractal cascades

NASA Astrophysics Data System (ADS)

Lovejoy, Shaun; Schertzer, Daniel

2013-04-01

Science in general and physics and geophysics in particular are hierarchies of interlocking theories and models with low level, fundamental laws such as quantum mechanics and statistical mechanics providing the underpinnings for the emergence of the qualitatively new, higher level laws of thermodynamics and continuum mechanics that provide the current bases for modelling the weather and climate. Yest it was the belief of generations of turbulence pioneers (notably Richardson, Kolmogorov, Obhukhov, Corrsin, Bolgiano) that at sufficiently high levels of nonlinearity (quantified by the Reynold's number, of the order 10**12 in the atmosphere) that new even higher level laws would emerge describing "fully developed turbulence". However for atmospheric applications, the pioneers' eponymous laws suffered from two basic restrictions - isotropy and homogeneity - that prevented them from being valid over wide ranges of scale. Over the last thirty years both of these restrictions have been overcome - the former with the generalization from isotropic to strongly anisotropic notions of scale (to account notably for stratification), and from homogeneity to strong heterogeneity (intermittency) via multifractal cascades. In this presentation we give an overview of recent developments and analyses covering huge ranges of space-time scales (including weather, macroweather and climate time scales). We show how the combination of strong anisotropy and strong intermittency commonly leads to the "phenomenological fallacy" in which morphology is confounded with mechanism. With the help of stochastic models, we show how processes with vastly different large and small scale morphologies can arise from a unique multifractal dynamical mechanisms [Lovejoy and Schertzer, 2013]. References: Lovejoy, S., and D. Schertzer (2013), The Weather and Climate: Emergent Laws and Multifractal Cascades, 480 pp., Cambridge University Press, Cambridge.

From Mathematical Monsters to Generalized Scale Invariance in Geophysics: Highlights of the Multifractal Saga

NASA Astrophysics Data System (ADS)

Schertzer, D. J.; Tchiguirinskaia, I.; Lovejoy, S.

2013-12-01

Fractals and multifractals are very illustrative of the profound synergies between mathematics and geophysics. The book ';Fractal Geometry of Nature' (Mandelbrot, 1982) brilliantly demonstrated the genericity in geophysics of geometric forms like Cantor set, Peano curve and Koch snowflake, which were once considered as mathematical monsters. However, to tame the geophysical monsters (e.g. extreme weather, floods, earthquakes), it was required to go beyond geometry and a unique fractal dimension. The concept of multifractal was coined in the course of rather theoretical debates on intermittency in hydrodynamic turbulence, sometimes with direct links to atmospheric dynamics. The latter required a generalized notion of scale in order to deal both with scale symmetries and strong anisotropies (e.g. time vs. space, vertical vs. horizontal). It was thus possible to show that the consequences of intermittency are of first order, not just 'corrections' with respect to the classical non-intermittent modeling. This was in fact a radical paradigm shift for geophysics: the extreme variability of geophysical fields over wide ranges of scale, which had long been so often acknowledged and deplored, suddenly became handy. Recent illustrations are the possibility to track down in large date sets the Higgs boson of intermittence, i.e. a first order multifractal phase transition leading to self-organized criticality, and to simulate intermittent vector fields with the help of Lie cascades, based for instance on random Clifford algebra. It is rather significant that this revolution is no longer limited to fundamental and theoretical problems of geophysics, but now touches many applications including environmental management, in particular for urban management and resilience. These applications are particularly stimulating when taken in their full complexity.

Mesoscale Turbulence in the Ocean and Synergy of Variables: Merging of Smos and Aquarius SSS Maps Using New, Non-Parametric Methods

NASA Astrophysics Data System (ADS)

Turiel, A.; Umbert, M.; Hoareau, N.; Ballabrera-Poy, J.; Font, J.

2012-12-01

Remote sensing platforms onboard satellites provide synoptic maps of ocean surface and thus an accurate picture of many processes taking place in the ocean at mesoscale and sub-mesoscale levels mainly can be gained. Since the first ocean observation satellites these images has been exploited to assess ocean processes; however, extracting further dynamic information from remote sensing maps generally implies a higher degree of processing complexity, involving the use of numerical models and assimilation schemes. A critical variable for the understanding the climate system is Sea Surface Salinity (SSS). The arrival of SMOS and Aquarius missions has given us access to SSS in a regular basis. However, those images still suffer of many acquisition and processing issues, what precludes gaining a complete picture of ocean surface dynamics. In order to favor the oceanographic exploitation of SMOS and Aquarius maps new filtering schemes need to be devised. During the last years a new branch of image processing techniques applied to ocean observation has arisen with force, namely multiscale/multifractal analysis. Different scalars submitted to the action of the ocean flow develop an identical inner structure (multifractal structure) that can be revealed by means of the appropriate analysis tools (singularity analysis). These tools allow for instance to characterize surface currents from snapshots of different scalars (Turiel et al, Ocean Sciences, 2009). In this work we go further away, with the introduction of a new method to blend different types of scalar in a single map of improved quality. The method does not imply the introduction of any parameter, nor relies in any numerical model, but in the assumption that the action of the oceanic flow leads to the same multifractal structure in any ocean variable. The method allows, for instance, to use the multifractal structure coming from SST images to improve the quality of SSS maps (as illustrated in the figure). It can also be applied to merge SMOS and Aquarius maps to increase the quality and spatial coverage.; Top row: 10-day MW SST (left), SMOS SSS (middle), and SSS resulting from fusing SST singularities (right). Bottom row: Associated singularity exponents. Brighter colors are associated to most singular (i.e., negative) exponents.

Global financial crisis and weak-form efficiency of Islamic sectoral stock markets: An MF-DFA analysis

NASA Astrophysics Data System (ADS)

Mensi, Walid; Tiwari, Aviral Kumar; Yoon, Seong-Min

2017-04-01

This paper estimates the weak-form efficiency of Islamic stock markets using 10 sectoral stock indices (basic materials, consumer services, consumer goods, energy, financials, health care, industrials, technology, telecommunication, and utilities). The results based on the multifractal detrended fluctuation analysis (MF-DFA) approach show time-varying efficiency for the sectoral stock markets. Moreover, we find that they tend to show high efficiency in the long term but moderate efficiency in the short term, and that these markets become less efficient after the onset of the global financial crisis. These results have several significant implications in terms of asset allocation for investors dealing with Islamic markets.

Anderson localization on the Cayley tree: multifractal statistics of the transmission at criticality and off criticality

NASA Astrophysics Data System (ADS)

Monthus, Cécile; Garel, Thomas

2011-04-01

In contrast to finite dimensions where disordered systems display multifractal statistics only at criticality, the tree geometry induces multifractal statistics for disordered systems also off criticality. For the Anderson tight-binding localization model defined on a tree of branching ratio K = 2 with N generations, we consider the Miller-Derrida scattering geometry (1994 J. Stat. Phys. 75 357), where an incoming wire is attached to the root of the tree, and where KN outcoming wires are attached to the leaves of the tree. In terms of the KN transmission amplitudes tj, the total Landauer transmission is T ≡ ∑j|tj|2, so that each channel j is characterized by the weight wj = |tj|2/T. We numerically measure the typical multifractal singularity spectrum f(α) of these weights as a function of the disorder strength W and we obtain the following conclusions for its left termination point α+(W). In the delocalized phase W < Wc, α+(W) is strictly positive α+(W) > 0 and is associated with a moment index q+(W) > 1. At criticality, it vanishes α+(Wc) = 0 and is associated with the moment index q+(Wc) = 1. In the localized phase W > Wc, α+(W) = 0 is associated with some moment index q+(W) < 1. We discuss the similarities with the exact results concerning the multifractal properties of the directed polymer on the Cayley tree.

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.

2017-10-01

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

Cross-correlation analysis between Chinese TF contracts and treasury ETF based on high-frequency data

NASA Astrophysics Data System (ADS)

Zhou, Yu; Chen, Shi

2016-02-01

In this paper, we investigate the high-frequency cross-correlation relationship between Chinese treasury futures contracts and treasury ETF. We analyze the logarithmic return of these two price series, from which we can conclude that both return series are not normally distributed and the futures markets have greater volatility. We find significant cross-correlation between these two series. We further confirm the relationship using the DCCA coefficient and the DMCA coefficient. We quantify the long-range cross-correlation with DCCA method, and we further show that the relationship is multifractal. An arbitrage algorithm based on DFA regression with stable return is proposed in the last part.

Parametric scaling from species to growth-form diversity: an interesting analogy with multifractal functions.

PubMed

Ricotta, Carlo; Pacini, Alessandra; Avena, Giancarlo

2002-01-01

We propose a measure of divergence from species to life-form diversity aimed at summarizing the ecological similarity among different plant communities without losing information on traditional taxonomic diversity. First, species and life-form relative abundances within a given plant community are determined. Next, using Rényi's generalized entropy, the diversity profiles of the analyzed community are computed both from species and life-form relative abundances. Finally, the speed of decrease from species to life-form diversity is obtained by combining the outcome of both profiles. Interestingly, the proposed measure shows some formal analogies with multifractal functions developed in statistical physics for the analysis of spatial patterns. As an application for demonstration, a small data set from a plant community sampled in the archaeological site of Paestum (southern Italy) is used.

3D Structure of Tillage Soils

NASA Astrophysics Data System (ADS)

González-Torre, Iván; Losada, Juan Carlos; Falconer, Ruth; Hapca, Simona; Tarquis, Ana M.

2015-04-01

Soil structure may be defined as the spatial arrangement of soil particles, aggregates and pores. The geometry of each one of these elements, as well as their spatial arrangement, has a great influence on the transport of fluids and solutes through the soil. Fractal/Multifractal methods have been increasingly applied to quantify soil structure thanks to the advances in computer technology (Tarquis et al., 2003). There is no doubt that computed tomography (CT) has provided an alternative for observing intact soil structure. These CT techniques reduce the physical impact to sampling, providing three-dimensional (3D) information and allowing rapid scanning to study sample dynamics in near real-time (Houston et al., 2013a). However, several authors have dedicated attention to the appropriate pore-solid CT threshold (Elliot and Heck, 2007; Houston et al., 2013b) and the better method to estimate the multifractal parameters (Grau et al., 2006; Tarquis et al., 2009). The aim of the present study is to evaluate the effect of the algorithm applied in the multifractal method (box counting and box gliding) and the cube size on the calculation of generalized fractal dimensions (Dq) in grey images without applying any threshold. To this end, soil samples were extracted from different areas plowed with three tools (moldboard, chissel and plow). Soil samples for each of the tillage treatment were packed into polypropylene cylinders of 8 cm diameter and 10 cm high. These were imaged using an mSIMCT at 155keV and 25 mA. An aluminium filter (0.25 mm) was applied to reduce beam hardening and later several corrections where applied during reconstruction. References Elliot, T.R. and Heck, R.J. 2007. A comparison of 2D and 3D thresholding of CT imagery. Can. J. Soil Sci., 87(4), 405-412. Grau, J, Médez, V.; Tarquis, A.M., Saa, A. and Díaz, M.C.. 2006. Comparison of gliding box and box-counting methods in soil image analysis. Geoderma, 134, 349-359. González-Torres, Iván. Theory and application of multifractal analysis methods in images for the study of soil structure. Master thesis, UPM, 2014. Houston, A.N.; S. Schmidt, A.M. Tarquis, W. Otten, P.C. Baveye, S.M. Hapca. Effect of scanning and image reconstruction settings in X-ray computed tomography on soil image quality and segmentation performance. Geoderma, 207-208, 154-165, 2013a. Houston, A, Otten, W., Baveye, Ph., Hapca, S. Adaptive-Window Indicator Kriging: A Thresholding Method for Computed Tomography, Computers & Geosciences, 54, 239-248, 2013b. Tarquis, A.M., R.J. Heck, D. Andina, A. Alvarez and J.M. Antón. Multifractal analysis and thresholding of 3D soil images. Ecological Complexity, 6, 230-239, 2009. Tarquis, A.M.; D. Giménez, A. Saa, M.C. Díaz. and J.M. Gascó. Scaling and Multiscaling of Soil Pore Systems Determined by Image Analysis. Scaling Methods in Soil Systems. Pachepsky, Radcliffe and Selim Eds., 19-33, 2003. CRC Press, Boca Ratón, Florida. Acknowledgements First author acknowledges the financial support obtained from Soil Imaging Laboratory (University of Gueplh, Canada) in 2014.

Multifractality to Photonic Crystal & Self-Organization to Metamaterials through Anderson Localizations & Group/Gauge Theory

NASA Astrophysics Data System (ADS)

Hidajatullah-Maksoed, Widastra

2015-04-01

Arthur Cayley at least investigate by creating the theory of permutation group[F:∖∖Group_theory.htm] where in cell elements addressing of the lattice Qmf used a Cayley tree, the self-afine object Qmf is described by the combination of the finite groups of rotation & inversion and the infinite groups of translation & dilation[G Corso & LS Lacena: ``Multifractal lattice and group theory'', Physica A: Statistical Mechanics &Its Applications, 2005, v 357, issue I, h 64-70; http://www.sciencedirect.com/science/articel/pii/S0378437105005005 ] hence multifractal can be related to group theory. Many grateful Thanks to HE. Mr. Drs. P. SWANTORO & HE. Mr. Ir. SARWONO KUSUMAATMADJA.

Generalization of multifractal theory within quantum calculus

NASA Astrophysics Data System (ADS)

Olemskoi, A.; Shuda, I.; Borisyuk, V.

2010-03-01

On the basis of the deformed series in quantum calculus, we generalize the partition function and the mass exponent of a multifractal, as well as the average of a random variable distributed over a self-similar set. For the partition function, such expansion is shown to be determined by binomial-type combinations of the Tsallis entropies related to manifold deformations, while the mass exponent expansion generalizes the known relation τq=Dq(q-1). We find the equation for the set of averages related to ordinary, escort, and generalized probabilities in terms of the deformed expansion as well. Multifractals related to the Cantor binomial set, exchange currency series, and porous-surface condensates are considered as examples.

The relationship between nernst equilibrium variability and the multifractality of interspike intervals in the hippocampus.

PubMed

Meier, Stephen R; Lancaster, Jarrett L; Fetterhoff, Dustin; Kraft, Robert A; Hampson, Robert E; Starobin, Joseph M

2017-04-01

Spatiotemporal patterns of action potentials are considered to be closely related to information processing in the brain. Auto-generating neurons contributing to these processing tasks are known to cause multifractal behavior in the inter-spike intervals of the output action potentials. In this paper we define a novel relationship between this multifractality and the adaptive Nernst equilibrium in hippocampal neurons. Using this relationship we are able to differentiate between various drugs at varying dosages. Conventional methods limit their ability to account for cellular charge depletion by not including these adaptive Nernst equilibria. Our results provide a new theoretical approach for measuring the effects which drugs have on single-cell dynamics.

Volatility of linear and nonlinear time series

NASA Astrophysics Data System (ADS)

Kalisky, Tomer; Ashkenazy, Yosef; Havlin, Shlomo

2005-07-01

Previous studies indicated that nonlinear properties of Gaussian distributed time series with long-range correlations, ui , can be detected and quantified by studying the correlations in the magnitude series ∣ui∣ , the “volatility.” However, the origin for this empirical observation still remains unclear and the exact relation between the correlations in ui and the correlations in ∣ui∣ is still unknown. Here we develop analytical relations between the scaling exponent of linear series ui and its magnitude series ∣ui∣ . Moreover, we find that nonlinear time series exhibit stronger (or the same) correlations in the magnitude time series compared with linear time series with the same two-point correlations. Based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series; the nonlinear multifractal time series is generated by multiplying a long-range correlated time series (that represents the magnitude series) with uncorrelated time series [that represents the sign series sgn(ui) ]. We apply our techniques on daily deep ocean temperature records from the equatorial Pacific, the region of the El-Ninõ phenomenon, and find: (i) long-range correlations from several days to several years with 1/f power spectrum, (ii) significant nonlinear behavior as expressed by long-range correlations of the volatility series, and (iii) broad multifractal spectrum.

Fractal and Multifractal Models Applied to Porous Media - Editorial

USDA-ARS?s Scientific Manuscript database

Given the current high level of interest in the use of fractal geometry to characterize natural porous media, a special issue of the Vadose Zone Journal was organized in order to expose established fractal analysis techniques and cutting-edge new developments to a wider Earth science audience. The ...

Quantifying Spatial Variability of Selected Soil Trace Elements and Their Scaling Relationships Using Multifractal Techniques

PubMed Central

Zhang, Fasheng; Yin, Guanghua; Wang, Zhenying; McLaughlin, Neil; Geng, Xiaoyuan; Liu, Zuoxin

2013-01-01

Multifractal techniques were utilized to quantify the spatial variability of selected soil trace elements and their scaling relationships in a 10.24-ha agricultural field in northeast China. 1024 soil samples were collected from the field and available Fe, Mn, Cu and Zn were measured in each sample. Descriptive results showed that Mn deficiencies were widespread throughout the field while Fe and Zn deficiencies tended to occur in patches. By estimating single multifractal spectra, we found that available Fe, Cu and Zn in the study soils exhibited high spatial variability and the existence of anomalies ([α(q)max−α(q)min]≥0.54), whereas available Mn had a relatively uniform distribution ([α(q)max−α(q)min]≈0.10). The joint multifractal spectra revealed that the strong positive relationships (r≥0.86, P<0.001) among available Fe, Cu and Zn were all valid across a wider range of scales and over the full range of data values, whereas available Mn was weakly related to available Fe and Zn (r≥0.18, P<0.01) but not related to available Cu (r = −0.03, P = 0.40). These results show that the variability and singularities of selected soil trace elements as well as their scaling relationships can be characterized by single and joint multifractal parameters. The findings presented in this study could be extended to predict selected soil trace elements at larger regional scales with the aid of geographic information systems. PMID:23874944

Simulating and mapping spatial complexity using multi-scale techniques

USGS Publications Warehouse

De Cola, L.

1994-01-01

A central problem in spatial analysis is the mapping of data for complex spatial fields using relatively simple data structures, such as those of a conventional GIS. This complexity can be measured using such indices as multi-scale variance, which reflects spatial autocorrelation, and multi-fractal dimension, which characterizes the values of fields. These indices are computed for three spatial processes: Gaussian noise, a simple mathematical function, and data for a random walk. Fractal analysis is then used to produce a vegetation map of the central region of California based on a satellite image. This analysis suggests that real world data lie on a continuum between the simple and the random, and that a major GIS challenge is the scientific representation and understanding of rapidly changing multi-scale fields. -Author

EVOLUTION OF INTERMITTENCY IN THE SLOW AND FAST SOLAR WIND BEYOND THE ECLIPTIC PLANE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wawrzaszek, A.; Macek, W. M.; Echim, M.

2015-12-01

We study intermittency as a departure from self-similarity of the solar wind magnetic turbulence and investigate the evolution with the heliocentric distance and latitude. We use data from the Ulysses spacecraft measured during two solar minima (1997–1998 and 2007–2008) and one solar maximum (1999–2001). In particular, by modeling a multifractal spectrum, we revealed the intermittent character of turbulence in the small-scale fluctuations of the magnetic field embedded in the slow and fast solar wind. Generally, at small distances from the Sun, in both the slow and fast solar wind, we observe the high degree of multifractality (intermittency) that decreases somewhatmore » slowly with distance and slowly with latitude. The obtained results seem to suggest that generally intermittency in the solar wind has a solar origin. However, the fast and slow streams, shocks, and other nonlinear interactions can only be considered as the drivers of the intermittent turbulence. It seems that analysis shows that turbulence beyond the ecliptic plane evolves too slowly to maintain the intermittency with the distance and latitude. Moreover, we confirm that the multifractality and intermittency are at a lower level than in the ecliptic, as well as the existence of symmetry with respect to the ecliptic plane, suggesting that there are similar turbulent properties observed in the two hemispheres.« less

Multiscaling behavior of atomic-scale friction

NASA Astrophysics Data System (ADS)

Jannesar, M.; Jamali, T.; Sadeghi, A.; Movahed, S. M. S.; Fesler, G.; Meyer, E.; Khoshnevisan, B.; Jafari, G. R.

2017-06-01

The scaling behavior of friction between rough surfaces is a well-known phenomenon. It might be asked whether such a scaling feature also exists for friction at an atomic scale despite the absence of roughness on atomically flat surfaces. Indeed, other types of fluctuations, e.g., thermal and instrumental fluctuations, become appreciable at this length scale and can lead to scaling behavior of the measured atomic-scale friction. We investigate this using the lateral force exerted on the tip of an atomic force microscope (AFM) when the tip is dragged over the clean NaCl (001) surface in ultra-high vacuum at room temperature. Here the focus is on the fluctuations of the lateral force profile rather than its saw-tooth trend; we first eliminate the trend using the singular value decomposition technique and then explore the scaling behavior of the detrended data, which contains only fluctuations, using the multifractal detrended fluctuation analysis. The results demonstrate a scaling behavior for the friction data ranging from 0.2 to 2 nm with the Hurst exponent H =0.61 ±0.02 at a 1 σ confidence interval. Moreover, the dependence of the generalized Hurst exponent, h (q ) , on the index variable q confirms the multifractal or multiscaling behavior of the nanofriction data. These results prove that fluctuation of nanofriction empirical data has a multifractal behavior which deviates from white noise.

Multifractal analysis of 2D gray soil images

NASA Astrophysics Data System (ADS)

González-Torres, Ivan; Losada, Juan Carlos; Heck, Richard; Tarquis, Ana M.

2015-04-01

Soil structure, understood as the spatial arrangement of soil pores, is one of the key factors in soil modelling processes. Geometric properties of individual and interpretation of the morphological parameters of pores can be estimated from thin sections or 3D Computed Tomography images (Tarquis et al., 2003), but there is no satisfactory method to binarized these images and quantify the complexity of their spatial arrangement (Tarquis et al., 2008, Tarquis et al., 2009; Baveye et al., 2010). The objective of this work was to apply a multifractal technique, their singularities (α) and f(α) spectra, to quantify it without applying any threshold (Gónzalez-Torres, 2014). Intact soil samples were collected from four horizons of an Argisol, formed on the Tertiary Barreiras group of formations in Pernambuco state, Brazil (Itapirema Experimental Station). The natural vegetation of the region is tropical, coastal rainforest. From each horizon, showing different porosities and spatial arrangements, three adjacent samples were taken having a set of twelve samples. The intact soil samples were imaged using an EVS (now GE Medical. London, Canada) MS-8 MicroCT scanner with 45 μm pixel-1 resolution (256x256 pixels). Though some samples required paring to fit the 64 mm diameter imaging tubes, field orientation was maintained. References Baveye, P.C., M. Laba, W. Otten, L. Bouckaert, P. Dello, R.R. Goswami, D. Grinev, A. Houston, Yaoping Hu, Jianli Liu, S. Mooney, R. Pajor, S. Sleutel, A. Tarquis, Wei Wang, Qiao Wei, Mehmet Sezgin. Observer-dependent variability of the thresholding step in the quantitative analysis of soil images and X-ray microtomography data. Geoderma, 157, 51-63, 2010. González-Torres, Iván. Theory and application of multifractal analysis methods in images for the study of soil structure. Master thesis, UPM, 2014. Tarquis, A.M., R.J. Heck, J.B. Grau; J. Fabregat, M.E. Sanchez and J.M. Antón. Influence of Thresholding in Mass and Entropy Dimension of 3-D Soil Images. Nonlinear Process in Geophysics, 15, 881-891, 2008. Tarquis, A.M., R.J. Heck, D. Andina, A. Alvarez and J.M. Antón. Multifractal analysis and thresholding of 3D soil images. Ecological Complexity, 6, 230-239, 2009. Tarquis, A.M.; D. Giménez, A. Saa, M.C. Díaz. and J.M. Gascó. Scaling and Multiscaling of Soil Pore Systems Determined by Image Analysis. Scaling Methods in Soil Systems. Pachepsky, Radcliffe and Selim Eds., 19-33, 2003. CRC Press, Boca Ratón, Florida. Acknowledgements First author acknowledges the financial support obtained from Soil Imaging Laboratory (University of Gueplh, Canada) in 2014.

Scaling forecast models for wind turbulence and wind turbine power intermittency

NASA Astrophysics Data System (ADS)

Duran Medina, Olmo; Schmitt, Francois G.; Calif, Rudy

2017-04-01

The intermittency of the wind turbine power remains an important issue for the massive development of this renewable energy. The energy peaks injected in the electric grid produce difficulties in the energy distribution management. Hence, a correct forecast of the wind power in the short and middle term is needed due to the high unpredictability of the intermittency phenomenon. We consider a statistical approach through the analysis and characterization of stochastic fluctuations. The theoretical framework is the multifractal modelisation of wind velocity fluctuations. Here, we consider three wind turbine data where two possess a direct drive technology. Those turbines are producing energy in real exploitation conditions and allow to test our forecast models of power production at a different time horizons. Two forecast models were developed based on two physical principles observed in the wind and the power time series: the scaling properties on the one hand and the intermittency in the wind power increments on the other. The first tool is related to the intermittency through a multifractal lognormal fit of the power fluctuations. The second tool is based on an analogy of the power scaling properties with a fractional brownian motion. Indeed, an inner long-term memory is found in both time series. Both models show encouraging results since a correct tendency of the signal is respected over different time scales. Those tools are first steps to a search of efficient forecasting approaches for grid adaptation facing the wind energy fluctuations.

Stochastic downscaling of numerically simulated spatial rain and cloud fields using a transient multifractal approach

NASA Astrophysics Data System (ADS)

Nogueira, M.; Barros, A. P.; Miranda, P. M.

2012-04-01

Atmospheric fields can be extremely variable over wide ranges of spatial scales, with a scale ratio of 109-1010 between largest (planetary) and smallest (viscous dissipation) scale. Furthermore atmospheric fields with strong variability over wide ranges in scale most likely should not be artificially split apart into large and small scales, as in reality there is no scale separation between resolved and unresolved motions. Usually the effects of the unresolved scales are modeled by a deterministic bulk formula representing an ensemble of incoherent subgrid processes on the resolved flow. This is a pragmatic approach to the problem and not the complete solution to it. These models are expected to underrepresent the small-scale spatial variability of both dynamical and scalar fields due to implicit and explicit numerical diffusion as well as physically based subgrid scale turbulent mixing, resulting in smoother and less intermittent fields as compared to observations. Thus, a fundamental change in the way we formulate our models is required. Stochastic approaches equipped with a possible realization of subgrid processes and potentially coupled to the resolved scales over the range of significant scale interactions range provide one alternative to address the problem. Stochastic multifractal models based on the cascade phenomenology of the atmosphere and its governing equations in particular are the focus of this research. Previous results have shown that rain and cloud fields resulting from both idealized and realistic numerical simulations display multifractal behavior in the resolved scales. This result is observed even in the absence of scaling in the initial conditions or terrain forcing, suggesting that multiscaling is a general property of the nonlinear solutions of the Navier-Stokes equations governing atmospheric dynamics. Our results also show that the corresponding multiscaling parameters for rain and cloud fields exhibit complex nonlinear behavior depending on large scale parameters such as terrain forcing and mean atmospheric conditions at each location, particularly mean wind speed and moist stability. A particularly robust behavior found is the transition of the multiscaling parameters between stable and unstable cases, which has a clear physical correspondence to the transition from stratiform to organized (banded) convective regime. Thus multifractal diagnostics of moist processes are fundamentally transient and should provide a physically robust basis for the downscaling and sub-grid scale parameterizations of moist processes. Here, we investigate the possibility of using a simplified computationally efficient multifractal downscaling methodology based on turbulent cascades to produce statistically consistent fields at scales higher than the ones resolved by the model. Specifically, we are interested in producing rainfall and cloud fields at spatial resolutions necessary for effective flash flood and earth flows forecasting. The results are examined by comparing downscaled field against observations, and tendency error budgets are used to diagnose the evolution of transient errors in the numerical model prediction which can be attributed to aliasing.

Multiscaling properties of tropical rainfall: Analysis of rain gauge datasets in Lesser Antilles island environment

NASA Astrophysics Data System (ADS)

Bernard, Didier C.; Pasquier, Raphaël; Cécé, Raphaël; Dorville, Jean-François

2014-05-01

Changes in rainfall seem to be the main impact of climate change in the Caribbean area. The last conclusions of IPCC (2013), indicate that the end of this century will be marked by a rise of extreme rainfalls in tropical areas, linked with increase of the mean surface temperature. Moreover, most of the Lesser Antilles islands are characterized by a complex topography which tends to enhance the rainfall from synoptic disturbances by orographic effects. In the past five years, out of hurricanes passage, several extreme rainy events (approx. 16 mm in 6 minutes), including fatal cases, occurred in the Lesser Antilles Arc: in Guadeloupe (January 2011, May 2012 and 2013), in Martinique (May 2009, April 2011 and 2013), in Saint-Lucia (December 2013). These phenomena inducing floods, loss of life and material damages (agriculture sector and public infrastructures), inhibit the development of the islands. At this time, numerical weather prediction models as WRF, which are based on the equations of the atmospheric physics, do not show great results in the focused area (Bernard et al., 2013). Statistical methods may be used to examine explicitly local rainy updrafts, thermally and orographically induced at micro-scale. The main goal of the present insular tropical study is to characterize the multifractal symmetries occurring in the 6-min rainfall time series, registered since 2006 by the French Met. Office network weather stations. The universal multifractal model (Schertzer and Lovejoy, 1991) is used to define the statistical properties of measured rainfalls at meso-scale and micro-scale. This model is parametrized by a fundamental exponents set (H,a,C1,q) which are determined and compared with values found in the literature. The first three parameters characterize the mean pattern and the last parameter q, the extreme pattern. The occurrence ranges of multifractal regime are examined. The suggested links between the internal variability of the tropical rainy events and the multifractal properties found, are preliminary discussed. References Bernard, D., R. Cécé and J.-F. Dorville (2013). High resolution numerical simulation (WRF V3) of an extrem rainy event over the Guadeloupe archipelago: Case of 3-5 January 2011. EGU General Assembly 2013, Geophysical Research Abstracts, Vol. 15, EGU2013-9988, Vienna, April 2013. Schertzer, D., S. Lovejoy (1991). Nonlinear geodynamical variability: Multiple singularities, universality and observables. Scaling, fractals and non-linear variability in geophysics, D. Schertzer, S. Lovejoy eds.,41-82, Kluwer.

Man-made Earthquakes & Multifractals in Neutral Fluid Turbulence/Injection

NASA Astrophysics Data System (ADS)

Maksoed, Wh-

Man-made earthquakes coincides with induced seismicity:''typically minor earthquakes & tremors that are caused by human activity that alters the stresses & Strains on the earth crust''[Wikipedia:''induced seismicity'']. For these, RD Andrews wrote:''Based on observed seismicity rate &geographical trends following major oil & gas plays with large amounts of produced water, the rates &trends in seismicity are very unlikely to represent a naturally occurring process''. ``The Prague, Oklahoma, earthquake sequence of 2011, along the Wilzetta faults zone, included the significant foreshock, a main shock of magnetic 5.7, it has been suggested that this sequence represent earthquakes triggered by fluid injection/natural fluid turbulence shows multifractal characteristics , of [405 ]-325-7968 of Dr. G. Randy Keller to UI tuitions of @ Rp. 29, 405, 000.00. Acknowledgements to HE. Mr. H. TUK SETYOHADI, Jl. Sriwijaya Raya 3, South-Jakarta, INDONESIA.

Multiscale structure of Cs-137 soil contamination on the Bryansk Region (Russia) due to the accident at the Chernobyl NPP

NASA Astrophysics Data System (ADS)

Linnik, Vitaly; Sokolov, Alexander

2013-04-01

The Cs-137 contamination of the Bryansk Region occurred in the period from April 27 to May 10 into several stages. The complicated character of the soil radionuclide contamination on the Bryansk Region is caused by different nature of the radioactive fallout: dry and wet. Thus, in a number of cases Cs-137 soil pollution is directly connected with the rain intensity, which is well known, have multifractal nature. In some parts of contaminated territory the overlay of different types of fallout was observed. The radioactive contamination of the landscape is a result from nonlinear interplay of geophysical factors which intervene over a large range of scale. As a result of the fallout Cs-137 pattern can be described as a multifractal. Consequently, fields of contamination observed have an extreme spatial variability, frequently cited "hot spots" or "leopard's skin. As an estimate of background radiation levels, we relied on a dataset of air-gamma-survey of the Bryansk Region, carried out by SSC AEROGEOFIZIKA in the summer of 1993. This dataset includes geo-positioned data of Cs-137 deposition in a grid of 100x100 m with values range from 3 to 11*104 kBq/m2. Airborne gamma survey gave the smoothed values of the Cs-137 density of contamination in comparison with the data, obtained directly as a result of soil sampling. However, even in this case in the east part of the Bryansk test site we can observed the"hot spots" (by size several hundred meters) as natural phenomenon. The article presents the results of the geostatistical and multifractal analysis of the Cs-137 contamination. Scaling analysis was conducted to investigate the linkages between the spatial variability of soil Cs-137 contamination and some landscape characteristics.

Retinal vasculature classification using novel multifractal features

NASA Astrophysics Data System (ADS)

Ding, Y.; Ward, W. O. C.; Duan, Jinming; Auer, D. P.; Gowland, Penny; Bai, L.

2015-11-01

Retinal blood vessels have been implicated in a large number of diseases including diabetic retinopathy and cardiovascular diseases, which cause damages to retinal blood vessels. The availability of retinal vessel imaging provides an excellent opportunity for monitoring and diagnosis of retinal diseases, and automatic analysis of retinal vessels will help with the processes. However, state of the art vascular analysis methods such as counting the number of branches or measuring the curvature and diameter of individual vessels are unsuitable for the microvasculature. There has been published research using fractal analysis to calculate fractal dimensions of retinal blood vessels, but so far there has been no systematic research extracting discriminant features from retinal vessels for classifications. This paper introduces new methods for feature extraction from multifractal spectra of retinal vessels for classification. Two publicly available retinal vascular image databases are used for the experiments, and the proposed methods have produced accuracies of 85.5% and 77% for classification of healthy and diabetic retinal vasculatures. Experiments show that classification with multiple fractal features produces better rates compared with methods using a single fractal dimension value. In addition to this, experiments also show that classification accuracy can be affected by the accuracy of vessel segmentation algorithms.

A DETERMINISTIC GEOMETRIC REPRESENTATION OF TEMPORAL RAINFALL: SENSITIVITY ANALYSIS FOR A STORM IN BOSTON. (R824780)

EPA Science Inventory

In an earlier study, Puente and Obregón [Water Resour. Res. 32(1996)2825] reported on the usage of a deterministic fractal–multifractal (FM) methodology to faithfully describe an 8.3 h high-resolution rainfall time series in Boston, gathered every 15 s ...

Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion

NASA Astrophysics Data System (ADS)

Setty, V. A.; Sharma, A. S.

2015-02-01

The Hurst exponent (H) is widely used to quantify long range dependence in time series data and is estimated using several well known techniques. Recognizing its ability to remove trends the Detrended Fluctuation Analysis (DFA) is used extensively to estimate a Hurst exponent in non-stationary data. Multifractional Brownian motion (mBm) broadly encompasses a set of models of non-stationary data exhibiting time varying Hurst exponents, H(t) as against a constant H. Recently, there has been a growing interest in time dependence of H(t) and sliding window techniques have been used to estimate a local time average of the exponent. This brought to fore the ability of DFA to estimate scaling exponents in systems with time varying H(t) , such as mBm. This paper characterizes the performance of DFA on mBm data with linearly varying H(t) and further test the robustness of estimated time average with respect to data and technique related parameters. Our results serve as a bench-mark for using DFA as a sliding window estimator to obtain H(t) from time series data.

Lorentz violations in multifractal spacetimes

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca

2017-05-01

Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E_{*}>10^{14} {GeV} (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E_{*}> 10^{17} {GeV} or greater.

Analysis of the sensitivity to rainfall spatio-temporal variability of an operational urban rainfall-runoff model in a multifractal framework

NASA Astrophysics Data System (ADS)

Gires, A.; Tchiguirinskaia, I.; Schertzer, D. J.; Lovejoy, S.

2011-12-01

In large urban areas, storm water management is a challenge with enlarging impervious areas. Many cities have implemented real time control (RTC) of their urban drainage system to either reduce overflow or limit urban contamination. A basic component of RTC is hydraulic/hydrologic model. In this paper we use the multifractal framework to suggest an innovative way to test the sensitivity of such a model to the spatio-temporal variability of its rainfall input. Indeed the rainfall variability is often neglected in urban context, being considered as a non-relevant issue at the scales involve. Our results show that on the contrary the rainfall variability should be taken into account. Universal multifractals (UM) rely on the concept of multiplicative cascade and are a standard tool to analyze and simulate with a reduced number of parameters geophysical processes that are extremely variable over a wide range of scales. This study is conducted on a 3 400 ha urban area located in Seine-Saint-Denis, in the North of Paris (France). We use the operational semi-distributed model that was calibrated by the local authority (Direction Eau et Assainnissement du 93) that is in charge of urban drainage. The rainfall data comes from the C-Band radar of Trappes operated by Météo-France. The rainfall event of February 9th, 2009 was used. A stochastic ensemble approach was implemented to quantify the uncertainty on discharge associated to the rainfall variability occurring at scales smaller than 1 km x 1 km x 5 min that is usually available with C-band radar networks. An analysis of the quantiles of the simulated peak flow showed that the uncertainty exceeds 20 % for upstream links. To evaluate a potential gain from a direct use of the rainfall data available at the resolution of X-band radar, we performed similar analysis of the rainfall fields of the degraded resolution of 9 km x 9 km x 20 min. The results show a clear decrease in uncertainty when the original resolution of C-band radar data is used. This analysis highlights the interest of implementing X-band radars in urban areas. Indeed such radars provide the rainfall data at a hectometric resolution that would enable a better nowcasting and management of storm water. The multifractal properties of the simulated hydrographs were analysed with the help of simulated rainfall fields of resolution 111 m x 111 m x 1 min, lasting 4 hours, and corresponding to a 5 year return period event. On the whole, the discharge exhibits a good scaling behaviour over the range 4 h - 5 min. Both UM parameters tend to be greater for the discharge than for the rainfall. The notion of maximum probable singularity was used to clarify the consequences on the assessment of extremes. It appears that the urban drainage network basically reproduces the extremes, or only slightly damps them, at least in terms of multifractal statistics. The results were obtained with the financial support from the EU FP7 SMARTesT Project and the Chair "Hydrology for Resilient Cities" (sponsored by Veolia) of Ecole des Ponts ParisTech.

Pooled analysis of stereotactic ablative radiotherapy for primary renal cell carcinoma: A report from the International Radiosurgery Oncology Consortium for Kidney (IROCK).

PubMed

Siva, Shankar; Louie, Alexander V; Warner, Andrew; Muacevic, Alexander; Gandhidasan, Senthilkumar; Ponsky, Lee; Ellis, Rodney; Kaplan, Irving; Mahadevan, Anand; Chu, William; Swaminath, Anand; Onishi, Hiroshi; Teh, Bin; Correa, Rohann J; Lo, Simon S; Staehler, Michael

2018-03-01

Stereotactic ablative radiotherapy (SABR) is an emerging therapy for primary renal cell carcinoma. The authors assessed safety, efficacy, and survival in a multi-institutional setting. Outcomes between single-fraction and multifraction SABR were compared. Individual patient data sets from 9 International Radiosurgery Oncology Consortium for Kidney institutions across Germany, Australia, the United States, Canada, and Japan were pooled. Toxicities were recorded using Common Terminology Criteria for Adverse Events, version 4.0. Patient, tumor, and treatment characteristics were stratified according to the number of radiotherapy fractions (single vs multiple). Survival outcomes were examined using Kaplan-Meier estimates and Cox proportional-hazards regression. Of 223 patients, 118 received single-fraction SABR, and 105 received multifraction SABR. The mean patient age was 72 years, and 69.5% of patients were men. There were 83 patients with grade 1 and 2 toxicity (35.6%) and 3 with grade 3 and 4 toxicities (1.3%). The rates of local control, cancer-specific survival, and progression-free survival were 97.8%, 95.7%, and 77.4%, respectively, at 2 years; and they were 97.8%, 91.9%, and 65.4%, respectively, at 4 years. On multivariable analysis, tumors with a larger maximum dimension and the receipt of multifraction SABR were associated with poorer progression-free survival (hazard ratio, 1.16 [P < .01] and 1.13 [P = .02], respectively) and poorer cancer-specific survival (hazard ratio, 1.28 [P < .01] and 1.33 [P = .01], respectively). There were no differences in local failure between the single-fraction cohort (n = 1) and the multifraction cohort (n = 2; P = .60). The mean ( ± standard deviation) estimated glomerular filtration rate at baseline was 59.9 ± 21.9 mL per minute, and it decreased by 5.5 ± 13.3 mL per minute (P < .01). SABR is well tolerated and locally effective for treating patients who have primary renal cell carcinoma and has an acceptable impact on renal function. An interesting observation is that patients who receive single-fraction SABR appear to be less likely to progress distantly or to die of cancer. Cancer 2018;124:934-42. © 2017 American Cancer Society. © 2017 American Cancer Society.

Detection of crossover time scales in multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Ge, Erjia; Leung, Yee

2013-04-01

Fractal is employed in this paper as a scale-based method for the identification of the scaling behavior of time series. Many spatial and temporal processes exhibiting complex multi(mono)-scaling behaviors are fractals. One of the important concepts in fractals is crossover time scale(s) that separates distinct regimes having different fractal scaling behaviors. A common method is multifractal detrended fluctuation analysis (MF-DFA). The detection of crossover time scale(s) is, however, relatively subjective since it has been made without rigorous statistical procedures and has generally been determined by eye balling or subjective observation. Crossover time scales such determined may be spurious and problematic. It may not reflect the genuine underlying scaling behavior of a time series. The purpose of this paper is to propose a statistical procedure to model complex fractal scaling behaviors and reliably identify the crossover time scales under MF-DFA. The scaling-identification regression model, grounded on a solid statistical foundation, is first proposed to describe multi-scaling behaviors of fractals. Through the regression analysis and statistical inference, we can (1) identify the crossover time scales that cannot be detected by eye-balling observation, (2) determine the number and locations of the genuine crossover time scales, (3) give confidence intervals for the crossover time scales, and (4) establish the statistically significant regression model depicting the underlying scaling behavior of a time series. To substantive our argument, the regression model is applied to analyze the multi-scaling behaviors of avian-influenza outbreaks, water consumption, daily mean temperature, and rainfall of Hong Kong. Through the proposed model, we can have a deeper understanding of fractals in general and a statistical approach to identify multi-scaling behavior under MF-DFA in particular.

Roadmap for Scaling and Multifractals in Geosciences: still a long way to go ?

NASA Astrophysics Data System (ADS)

Schertzer, Daniel; Lovejoy, Shaun

2010-05-01

The interest in scale symmetries (scaling) in Geosciences has never lessened since the first pioneering EGS session on chaos and fractals 22 years ago. The corresponding NP activities have been steadily increasing, covering a wider and wider diversity of geophysical phenomena and range of space-time scales. Whereas interest was initially largely focused on atmospheric turbulence, rain and clouds at small scales, it has quickly broadened to much larger scales and to much wider scale ranges, to include ocean sciences, solid earth and space physics. Indeed, the scale problem being ubiquitous in Geosciences, it is indispensable to share the efforts and the resulting knowledge as much as possible. There have been numerous achievements which have followed from the exploration of larger and larger datasets with finer and finer resolutions, from both modelling and theoretical discussions, particularly on formalisms for intermittency, anisotropy and scale symmetry, multiple scaling (multifractals) vs. simple scaling,. We are now way beyond the early pioneering but tentative attempts using crude estimates of unique scaling exponents to bring some credence to the fact that scale symmetries are key to most nonlinear geoscience problems. Nowadays, we need to better demonstrate that scaling brings effective solutions to geosciences and therefore to society. A large part of the answer corresponds to our capacity to create much more universal and flexible tools to multifractally analyse in straightforward and reliable manners complex and complicated systems such as the climate. Preliminary steps in this direction are already quite encouraging: they show that such approaches explain both the difficulty of classical techniques to find trends in climate scenarios (particularly for extremes) and resolve them with the help of scaling estimators. The question of the reliability and accuracy of these methods is not trivial. After discussing these important, but rather short term issues, we will point out more general questions, which can be put together into the following provocative question: how to convert the classical time evolving deterministic PDE's into dynamical multifractal systems? We will argue that this corresponds to an already active field of research, which include: multifractals as generic solutions of nonlinear PDE (exact results for 1D Burgers equation and a few other caricatures of Navier-Stokes equations, prospects for 3D Burgers equations), cascade structures of numerical weather models, links between multifractal processes and random dynamical systems, and the challenging debate on the most relevant stochastic multifractal formalism, whereas there is already a rather general consent about the deterministic one.

Site effect classification based on microtremor data analysis using a concentration-area fractal model

NASA Astrophysics Data System (ADS)

Adib, A.; Afzal, P.; Heydarzadeh, K.

2015-01-01

The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modelling reveal that proper soil types are located around the central city. The results derived via the fractal modelling were utilized to improve the Nogoshi and Igarashi (1970, 1971) classification results in the Meybod city. The resulting categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Site effect classification based on microtremor data analysis using concentration-area fractal model

NASA Astrophysics Data System (ADS)

Adib, A.; Afzal, P.; Heydarzadeh, K.

2014-07-01

The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, Central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modeling reveal that proper soil types are located around the central city. The results derived via the fractal modeling were utilized to improve the Nogoshi's classification results in the Meybod city. The resulted categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Comparison of Machine Learning Methods for the Arterial Hypertension Diagnostics

PubMed Central

Belo, David; Gamboa, Hugo

2017-01-01

The paper presents results of machine learning approach accuracy applied analysis of cardiac activity. The study evaluates the diagnostics possibilities of the arterial hypertension by means of the short-term heart rate variability signals. Two groups were studied: 30 relatively healthy volunteers and 40 patients suffering from the arterial hypertension of II-III degree. The following machine learning approaches were studied: linear and quadratic discriminant analysis, k-nearest neighbors, support vector machine with radial basis, decision trees, and naive Bayes classifier. Moreover, in the study, different methods of feature extraction are analyzed: statistical, spectral, wavelet, and multifractal. All in all, 53 features were investigated. Investigation results show that discriminant analysis achieves the highest classification accuracy. The suggested approach of noncorrelated feature set search achieved higher results than data set based on the principal components. PMID:28831239

Multifractality in Cardiac Dynamics

NASA Astrophysics Data System (ADS)

Ivanov, Plamen Ch.; Rosenblum, Misha; Stanley, H. Eugene; Havlin, Shlomo; Goldberger, Ary

1997-03-01

Wavelet decomposition is used to analyze the fractal scaling properties of heart beat time series. The singularity spectrum D(h) of the variations in the beat-to-beat intervals is obtained from the wavelet transform modulus maxima which contain information on the hierarchical distribution of the singularities in the signal. Multifractal behavior is observed for healthy cardiac dynamics while pathologies are associated with loss of support in the singularity spectrum.

Multi-scaling modelling in financial markets

NASA Astrophysics Data System (ADS)

Liu, Ruipeng; Aste, Tomaso; Di Matteo, T.

2007-12-01

In the recent years, a new wave of interest spurred the involvement of complexity in finance which might provide a guideline to understand the mechanism of financial markets, and researchers with different backgrounds have made increasing contributions introducing new techniques and methodologies. In this paper, Markov-switching multifractal models (MSM) are briefly reviewed and the multi-scaling properties of different financial data are analyzed by computing the scaling exponents by means of the generalized Hurst exponent H(q). In particular we have considered H(q) for price data, absolute returns and squared returns of different empirical financial time series. We have computed H(q) for the simulated data based on the MSM models with Binomial and Lognormal distributions of the volatility components. The results demonstrate the capacity of the multifractal (MF) models to capture the stylized facts in finance, and the ability of the generalized Hurst exponents approach to detect the scaling feature of financial time series.

Kullback-Leibler divergence measure of intermittency: Application to turbulence

NASA Astrophysics Data System (ADS)

Granero-Belinchón, Carlos; Roux, Stéphane G.; Garnier, Nicolas B.

2018-01-01

For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a simple tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the deformation of a probability density function from Gaussian at large scales to non-Gaussian at smaller scales. Our framework is based on information theory and uses Shannon entropy and Kullback-Leibler divergence. We provide an extensive application to three-dimensional fully developed turbulence, seen here as a paradigmatic complex system where intermittency was historically defined and the concepts of scale invariance and multifractality were extensively studied and benchmarked. We compute our quantity on experimental Eulerian velocity measurements, as well as on synthetic processes and phenomenological models of fluid turbulence. Our approach is very general and does not require any underlying model of the system, although it can probe the relevance of such a model.

Multifractal properties of solar filaments and sunspots numbers

NASA Astrophysics Data System (ADS)

Wu, Nan; Li, Qi-Xiu; Zou, Peng

2015-07-01

We analyze multifractal properties of low (LLSFNs; < 50 °), high (HLSFNs; ⩾ 50 °), full-disk (FDSFNs; 0 ° ˜ 90 °) solar filament numbers (SFNs) and international sunspot numbers (ISNs) by estimating characteristic parameters (α0, Δα , spectrum skewness) of f (α) singularity spectrum. We find that the SFNs and ISNs have multifractal nature. The obtained α0 and Δα indicate that long-term behaviour of the solar filaments is more complex than that of the sunspots and the high-latitude filaments is the most complex in long-term behaviour. The spectrum skewnesses manifest that the ISNs display well symmetrical distribution in singularity strengths, whereas the SFNs are dominated by low singularity strengths, which means that the long-term behaviour of sunspots has homogenous structures and the filaments display averagely small fluctuations in amplitude. To detect the origin of their multifractality, we decompose the raw data of ISNs and SFNs: smoothed data represent ˜11-year cyclic activities and detrended data represent accidental activities. We also calculate their f (α) spectra, respectively. We find that the ˜11-year cyclic activities of filaments and sunspots tend to be a monofractal and display a bit predominance of low singularity strengths. Their accidental activities have the most complex behaviour than the raw and smoothed data. The accidental activities are dominated by high singularity strengths showing averagely large fluctuations in amplitude. Furthermore, multifractal properties from α0 and Δα of the accidental activities have the same features as that of raw data. We think that the ˜11-year periodic activity determines global fluctuations, while the accidental activities rule local complexity.

Multifractal model of magnetic susceptibility distributions in some igneous rocks

USGS Publications Warehouse

Gettings, Mark E.

2012-01-01

Measurements of in-situ magnetic susceptibility were compiled from mainly Precambrian crystalline basement rocks beneath the Colorado Plateau and ranges in Arizona, Colorado, and New Mexico. The susceptibility meter used measures about 30 cm3 of rock and measures variations in the modal distribution of magnetic minerals that form a minor component volumetrically in these coarsely crystalline granitic to granodioritic rocks. Recent measurements include 50–150 measurements on each outcrop, and show that the distribution of magnetic susceptibilities is highly variable, multimodal and strongly non-Gaussian. Although the distribution of magnetic susceptibility is well known to be multifractal, the small number of data points at an outcrop precludes calculation of the multifractal spectrum by conventional methods. Instead, a brute force approach was adopted using multiplicative cascade models to fit the outcrop scale variability of magnetic minerals. Model segment proportion and length parameters resulted in 26 676 models to span parameter space. Distributions at each outcrop were normalized to unity magnetic susceptibility and added to compare all data for a rock body accounting for variations in petrology and alteration. Once the best-fitting model was found, the equation relating the segment proportion and length parameters was solved numerically to yield the multifractal spectrum estimate. For the best fits, the relative density (the proportion divided by the segment length) of one segment tends to be dominant and the other two densities are smaller and nearly equal. No other consistent relationships between the best fit parameters were identified. The multifractal spectrum estimates appear to distinguish between metamorphic gneiss sites and sites on plutons, even if the plutons have been metamorphosed. In particular, rocks that have undergone multiple tectonic events tend to have a larger range of scaling exponents.

Developing trading strategies based on fractal finance: An application of MF-DFA in the context of Islamic equities

NASA Astrophysics Data System (ADS)

Dewandaru, Ginanjar; Masih, Rumi; Bacha, Obiyathulla Ismath; Masih, A. Mansur. M.

2015-11-01

We provide a new contribution to trading strategies by using multi-fractal de-trended fluctuation analysis (MF-DFA), imported from econophysics, to complement various momentum strategies. The method provides a single measure that can capture both persistency and anti-persistency in stock prices, accounting for multifractality. This study uses a sample of Islamic stocks listed in the U.S. Dow Jones Islamic market for a sample period covering 16 years starting in 1996. The findings show that the MF-DFA strategy produces monthly excess returns of 6.12%, outperforming other various momentum strategies. Even though the risk of the MF-DFA strategy may be relatively higher, it can still produce a Sharpe ratio of 0.164, which is substantially higher than that of the other strategies. When we control for the MF-DFA factor with the other factors, its pure factor return is still able to yield a monthly excess return of 1.35%. Finally, we combine the momentum and MF-DFA strategies, with the proportions of 90/10, 80/20, and 70/30 and by doing so we demonstrate that the MF-DFA measure can boost the total monthly excess returns as well as Sharpe ratio. The value added is non-linear which implies that the additional returns are associated with lower incremental risk.

Temporal variation of aftershocks by means of multifractal characterization of their inter-event time and cluster analysis

NASA Astrophysics Data System (ADS)

Figueroa-Soto, A.; Zuñiga, R.; Marquez-Ramirez, V.; Monterrubio-Velasco, M.

2017-12-01

. The inter-event time characteristics of seismic aftershock sequences can provide important information to discern stages in the aftershock generation process. In order to investigate whether separate dynamic stages can be identified, (1) aftershock series after selected earthquake mainshocks, which took place at similar tectonic regimes were analyzed. To this end we selected two well-defined aftershock sequences from New Zealand and one aftershock sequence for Mexico, we (2) analyzed the fractal behavior of the logarithm of inter-event times (also called waiting times) of aftershocks by means of Holdeŕs exponent, and (3) their magnitude and spatial location based on a methodology proposed by Zaliapin and Ben Zion [2011] which accounts for the clustering properties of the sequence. In general, more than two coherent process stages can be identified following the main rupture, evidencing a type of "cascade" process which precludes implying a single generalized power law even though the temporal rate and average fractal character appear to be unique (as in a single Omorís p value). We found that aftershock processes indeed show multi-fractal characteristics, which may be related to different stages in the process of diffusion, as seen in the temporary-spatial distribution of aftershocks. Our method provides a way of defining the onset of the return to seismic background activity and the end of the main aftershock sequence.

Apparent multifractality of self-similar Lévy processes

NASA Astrophysics Data System (ADS)

Zamparo, Marco

2017-07-01

Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments are generally regarded as a sign of multifractality in the data. We show that, except for the Brownian motion, this method fails to disclose the correct monofractal nature of self-similar Lévy processes. We prove that for this class of processes it produces apparent multifractality characterised by a piecewise-linear scaling function with two different regimes, which match at the stability index of the considered process. This result is motivated by previous numerical evidence. It is obtained by introducing an appropriate stochastic normalisation which is able to cure empirical moments, without hiding their dependence on time, when moments they aim at estimating do not exist.

Characterization of turbulence stability through the identification of multifractional Brownian motions

NASA Astrophysics Data System (ADS)

Lee, K. C.

2013-02-01

Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.

A Self-Affine Multi-Fractal Wave/Turbulence Discrimination Method Using Data from Single Point Fast Response Sensors in a Nocturnal Atmospheric Boundary Layer

DTIC Science & Technology

1992-04-10

and passive tracer concentrations, and their cross correlations have generally been used to estimate the magnitude of dispersive atmospheric transport...of gravity waves and turbulence. . 10 III. METHODS .......... ........................ 12 A. Data .......... ........................ 12 B. Analysis ...unstable, i.e., strange. For waves or even limit cycle motion about fixed attractors, self-similarity does not occur. Pertinent to time series analysis , this

Origin of generalized entropies and generalized statistical mechanics for superstatistical multifractal systems

NASA Astrophysics Data System (ADS)

Gadjiev, Bahruz; Progulova, Tatiana

2015-01-01

We consider a multifractal structure as a mixture of fractal substructures and introduce a distribution function f (α), where α is a fractal dimension. Then we can introduce g(p)˜ ∫- ln p μe-yf(y)dy and show that the distribution functions f (α) in the form of f(α) = δ(α-1), f(α) = δ(α-θ) , f(α) = 1/α-1 , f(y)= y α-1 lead to the Boltzmann - Gibbs, Shafee, Tsallis and Anteneodo - Plastino entropies conformably. Here δ(x) is the Dirac delta function. Therefore the Shafee entropy corresponds to a fractal structure, the Tsallis entropy describes a multifractal structure with a homogeneous distribution of fractal substructures and the Anteneodo - Plastino entropy appears in case of a power law distribution f (y). We consider the Fokker - Planck equation for a fractal substructure and determine its stationary solution. To determine the distribution function of a multifractal structure we solve the two-dimensional Fokker - Planck equation and obtain its stationary solution. Then applying the Bayes theorem we obtain a distribution function for the entire system in the form of q-exponential function. We compare the results of the distribution functions obtained due to the superstatistical approach with the ones obtained according to the maximum entropy principle.

A systematic review of palliative bone radiotherapy based on pain relief and retreatment rates.

PubMed

Pin, Yvan; Paix, Adrien; Le Fèvre, Clara; Antoni, Delphine; Blondet, Cyrille; Noël, Georges

2018-03-01

Palliative radiotherapy has been shown to have effects on Quality of Life during painful bone metastasis. This review aimed to determine equivalence in pain relief (PR) and retreatment rate (RR) using both single and multi-fraction irradiations, based on evaluation of the trial's quality. We performed a systematic review since ICRU 50 Report (1993) to June 2017, then evaluated trials for reproducibility and good methodology criteria. We found five studies that were reproducible in both dose and volume prescription. One study used three-dimensional (3D) treatment planning. Equivalence between single and multi-fraction schedules was demonstrated for PR after 3 months, but a 2-3 time RR appeared after single-fraction schedules, notably in the first year after treatment (primarily during the first four months). Reserving long course therapy for well-preserved patients would allow for better long-term efficacy with lower RR, while altered patients would suffer less from single-fraction treatments. It appears that life expectancy might not be used as a criterion for this choice. Copyright © 2018 Elsevier B.V. All rights reserved.

Modeling heart rate variability including the effect of sleep stages

NASA Astrophysics Data System (ADS)

Soliński, Mateusz; Gierałtowski, Jan; Żebrowski, Jan

2016-02-01

We propose a model for heart rate variability (HRV) of a healthy individual during sleep with the assumption that the heart rate variability is predominantly a random process. Autonomic nervous system activity has different properties during different sleep stages, and this affects many physiological systems including the cardiovascular system. Different properties of HRV can be observed during each particular sleep stage. We believe that taking into account the sleep architecture is crucial for modeling the human nighttime HRV. The stochastic model of HRV introduced by Kantelhardt et al. was used as the initial starting point. We studied the statistical properties of sleep in healthy adults, analyzing 30 polysomnographic recordings, which provided realistic information about sleep architecture. Next, we generated synthetic hypnograms and included them in the modeling of nighttime RR interval series. The results of standard HRV linear analysis and of nonlinear analysis (Shannon entropy, Poincaré plots, and multiscale multifractal analysis) show that—in comparison with real data—the HRV signals obtained from our model have very similar properties, in particular including the multifractal characteristics at different time scales. The model described in this paper is discussed in the context of normal sleep. However, its construction is such that it should allow to model heart rate variability in sleep disorders. This possibility is briefly discussed.

Irregular-regular mode oscillations inside plasma bubble and its fractal analysis in glow discharge magnetized plasma

NASA Astrophysics Data System (ADS)

Megalingam, Mariammal; Hari Prakash, N.; Solomon, Infant; Sarma, Arun; Sarma, Bornali

2017-04-01

Experimental evidence of different kinds of oscillations in floating potential fluctuations of glow discharge magnetized plasma is being reported. A spherical gridded cage is inserted into the ambient plasma volume for creating plasma bubbles. Plasma is produced between a spherical mesh grid and chamber. The spherical mesh grid of 80% optical transparency is connected to the positive terminal of power supply and considered as anode. Two Langmuir probes are kept in the ambient plasma to measure the floating potential fluctuations in different positions within the system, viz., inside and outside the spherical mesh grid. At certain conditions of discharge voltage (Vd) and magnetic field, irregular to regular mode appears, and it shows chronological changes with respect to magnetic field. Further various nonlinear analyses such as Recurrence Plot, Hurst exponent, and Lyapunov exponent have been carried out to investigate the dynamics of oscillation at a range of discharge voltages and external magnetic fields. Determinism, entropy, and Lmax are important measures of Recurrence Quantification Analysis which indicate an irregular to regular transition in the dynamics of the fluctuations. Furthermore, behavior of the plasma oscillation is characterized by the technique called multifractal detrended fluctuation analysis to explore the nature of the fluctuations. It reveals that it has a multifractal nature and behaves as a long range correlated process.

The fractal-multifractal method and temporal resolution: Application to precipitation and streamflow

NASA Astrophysics Data System (ADS)

Maskey, M.; Puente, C. E.; Sivakumar, B.

2017-12-01

In the past, we have established that the deterministic fractal-multifractal (FM) method is a promising geometric tool to analyze hydro-climatic variables, such as precipitation, river flow, and temperature. In this study, we address the issue of temporal resolution to advance the suitability and usefulness of the FM approach in hydro-climate. Specifically, we elucidate the evolution of FM geometric parameters as computed at different time scales ranging from a day to a month (30-day) in increments of a day. For this purpose, both rainfall and river discharge records at Sacramento, California gathered over a year are encoded at different time scales. The analysis reveals that: (a) the FM approach yields faithful encodings of both kinds of data sets at the resolutions considered with reasonably small errors; and (b) the "best" FM parameters ultimately converge when the resolution is increased, thus allowing visualizing both hydrologic attributes. By addressing the scalability of the geometric patterns, these results further advance the suitability of the FM approach.

Volatility Behaviors of Financial Time Series by Percolation System on Sierpinski Carpet Lattice

NASA Astrophysics Data System (ADS)

Pei, Anqi; Wang, Jun

2015-01-01

The financial time series is simulated and investigated by the percolation system on the Sierpinski carpet lattice, where percolation is usually employed to describe the behavior of connected clusters in a random graph, and the Sierpinski carpet lattice is a graph which corresponds the fractal — Sierpinski carpet. To study the fluctuation behavior of returns for the financial model and the Shanghai Composite Index, we establish a daily volatility measure — multifractal volatility (MFV) measure to obtain MFV series, which have long-range cross-correlations with squared daily return series. The autoregressive fractionally integrated moving average (ARFIMA) model is used to analyze the MFV series, which performs better when compared to other volatility series. By a comparative study of the multifractality and volatility analysis of the data, the simulation data of the proposed model exhibits very similar behaviors to those of the real stock index, which indicates somewhat rationality of the model to the market application.

Multifractal and wavelet analysis of epileptic seizures

NASA Astrophysics Data System (ADS)

Dick, Olga E.; Mochovikova, Irina A.

The aim of the study is to develop quantitative parameters of human electroencephalographic (EEG) recordings with epileptic seizures. We used long-lasting recordings from subjects with epilepsy obtained as part of their clinical investigation. The continuous wavelet transform of the EEG segments and the wavelet-transform modulus maxima method enable us to evaluate the energy spectra of the segments, to fin lines of local maximums, to gain the scaling exponents and to construct the singularity spectra. We have shown that the significant increase of the global energy with respect to background and the redistribution of the energy over the frequency range are observed in the patterns involving the epileptic activity. The singularity spectra expand so that the degree of inhomogenety and multifractality of the patterns enhances. Comparing the results gained for the patterns during different functional probes such as open and closed eyes or hyperventilation we demonstrate the high sensitivity of the analyzed parameters (the maximal global energy, the width and asymmetry of the singularity spectrum) for detecting the epileptic patterns.

Time irreversibility and multifractality of power along single particle trajectories in turbulence

NASA Astrophysics Data System (ADS)

Cencini, Massimo; Biferale, Luca; Boffetta, Guido; De Pietro, Massimo

2017-10-01

The irreversible turbulent energy cascade epitomizes strongly nonequilibrium systems. At the level of single fluid particles, time irreversibility is revealed by the asymmetry of the rate of kinetic energy change, the Lagrangian power, whose moments display a power-law dependence on the Reynolds number, as recently shown by Xu et al. [H. Xu et al., Proc. Natl. Acad. Sci. USA 111, 7558 (2014), 10.1073/pnas.1321682111]. Here Lagrangian power statistics are rationalized within the multifractal model of turbulence, whose predictions are shown to agree with numerical and empirical data. Multifractal predictions are also tested, for very large Reynolds numbers, in dynamical models of the turbulent cascade, obtaining remarkably good agreement for statistical quantities insensitive to the asymmetry and, remarkably, deviations for those probing the asymmetry. These findings raise fundamental questions concerning time irreversibility in the infinite-Reynolds-number limit of the Navier-Stokes equations.

An extended algebraic variational multiscale-multigrid-multifractal method (XAVM4) for large-eddy simulation of turbulent two-phase flow

NASA Astrophysics Data System (ADS)

Rasthofer, U.; Wall, W. A.; Gravemeier, V.

2018-04-01

A novel and comprehensive computational method, referred to as the eXtended Algebraic Variational Multiscale-Multigrid-Multifractal Method (XAVM4), is proposed for large-eddy simulation of the particularly challenging problem of turbulent two-phase flow. The XAVM4 involves multifractal subgrid-scale modeling as well as a Nitsche-type extended finite element method as an approach for two-phase flow. The application of an advanced structural subgrid-scale modeling approach in conjunction with a sharp representation of the discontinuities at the interface between two bulk fluids promise high-fidelity large-eddy simulation of turbulent two-phase flow. The high potential of the XAVM4 is demonstrated for large-eddy simulation of turbulent two-phase bubbly channel flow, that is, turbulent channel flow carrying a single large bubble of the size of the channel half-width in this particular application.

Influence of Sub-Daily Variation on Multi-Fractal Detrended Fluctuation Analysis of Wind Speed Time Series

PubMed Central

Li, Weinan; Kong, Yanjun; Cong, Xiangyu

2016-01-01

Using multi-fractal detrended fluctuation analysis (MF-DFA), the scaling features of wind speed time series (WSTS) could be explored. In this paper, we discuss the influence of sub-daily variation, which is a natural feature of wind, in MF-DFA of WSTS. First, the choice of the lower bound of the segment length, a significant parameter of MF-DFA, was studied. The results of expanding the lower bound into sub-daily scope shows that an abrupt declination and discrepancy of scaling exponents is caused by the inability to keep the whole diel process of wind in one single segment. Additionally, the specific value, which is effected by the sub-daily feature of local meteo-climatic, might be different. Second, the intra-day temporal order of wind was shuffled to determine the impact of diel variation on scaling exponents of MF-DFA. The results illustrate that disregarding diel variation leads to errors in scaling. We propose that during the MF-DFA of WSTS, the segment length should be longer than 1 day and the diel variation of wind should be maintained to avoid abnormal phenomena and discrepancy in scaling exponents. PMID:26741491

Investigating the complexity of precipitation sets within California via the fractal-multifractal method

NASA Astrophysics Data System (ADS)

Puente, Carlos E.; Maskey, Mahesh L.; Sivakumar, Bellie

2017-04-01

A deterministic geometric approach, the fractal-multifractal (FM) method, is adapted in order to encode highly intermittent daily rainfall records observed over a year. Using such a notion, this research investigates the complexity of rainfall in various stations within the State of California. Specifically, records gathered at (from South to North) Cherry Valley, Merced, Sacramento and Shasta Dam, containing 59, 116, 115 and 72 years, all ending at water year 2015, were encoded and analyzed in detail. The analysis reveals that: (a) the FM approach yields faithful encodings of all records, by years, with mean square and maximum errors in accumulated rain that are less than a mere 2% and 10%, respectively; (b) the evolution of the corresponding "best" FM parameters, allowing visualization of the inter-annual rainfall dynamics from a reduced vantage point, exhibit implicit variability that precludes discriminating between sites and extrapolating to the future; (c) the evolution of the FM parameters, restricted to specific regions within space, allows finding sensible future simulations; and (d) the rain signals at all sites may be termed "equally complex," as usage of k-means clustering and conventional phase space analysis of FM parameters yields comparable results for all sites.

SU-E-T-563: Multi-Fraction Stereotactic Radiosurgery with Extend System of Gamma Knife: Treatment Verification Using Indigenously Designed Patient Simulating Multipurpose Phantom

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bisht, R; Kale, S; Gopishankar, N

2015-06-15

Purpose: Aim of the study is to evaluate mechanical and radiological accuracy of multi-fraction regimen and validate Gamma knife based fractionation using newly developed patient simulating multipurpose phantom. Methods: A patient simulating phantom was designed to verify fractionated treatments with extend system (ES) of Gamma Knife however it could be used to validate other radiotherapy procedures as well. The phantom has options to insert various density material plugs and mini CT/MR distortion phantoms to analyze the quality of stereotactic imaging. An additional thorax part designed to predict surface doses at various organ sites. The phantom was positioned using vacuum headmore » cushion and patient control unit for imaging and treatment. The repositioning check tool (RCT) was used to predict phantom positioning under ES assembly. The phantom with special inserts for film in axial, coronal and sagittal plane were scanned with X-Ray CT and the acquired images were transferred to treatment planning system (LGP 10.1). The focal precession test was performed with 4mm collimator and an experimental plan of four 16mm collimator shots was prepared for treatment verification of multi-fraction regimen. The prescription dose of 5Gy per fraction was delivered in four fractions. Each fraction was analyzed using EBT3 films scanned with EPSON 10000XL Scanner. Results: The measurement of 38 RCT points showed an overall positional accuracy of 0.28mm. The mean deviation of 0.28% and 0.31 % were calculated as CT and MR image distortion respectively. The radiological focus accuracy test showed its deviation from mechanical center point of 0.22mm. The profile measurement showed close agreement between TPS planned and film measured dose. At tolerance criteria of 1%/1mm gamma index analysis showed a pass rate of > 95%. Conclusion: Our results show that the newly developed multipurpose patient simulating phantom is highly suitable for the verification of fractionated stereotactic radiosurgery using ES of Gamma knife. The study is a part of intramural research project of Research Section, All India Institute of Medical Sciences New Delhi India (A 247)« less

Analysis of HD 73045 light curve data

NASA Astrophysics Data System (ADS)

Das, Mrinal Kanti; Bhatraju, Naveen Kumar; Joshi, Santosh

2018-04-01

In this work we analyzed the Kepler light curve data of HD 73045. The raw data has been smoothened using standard filters. The power spectrum has been obtained by using a fast Fourier transform routine. It shows the presence of more than one period. In order to take care of any non-stationary behavior, we carried out a wavelet analysis to obtain the wavelet power spectrum. In addition, to identify the scale invariant structure, the data has been analyzed using a multifractal detrended fluctuation analysis. Further to characterize the diversity of embedded patterns in the HD 73045 flux time series, we computed various entropy-based complexity measures e.g. sample entropy, spectral entropy and permutation entropy. The presence of periodic structure in the time series was further analyzed using the visibility network and horizontal visibility network model of the time series. The degree distributions in the two network models confirm such structures.

DETECTION OF SMALL-SCALE GRANULAR STRUCTURES IN THE QUIET SUN WITH THE NEW SOLAR TELESCOPE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abramenko, V. I.; Yurchyshyn, V. B.; Goode, P. R.

2012-09-10

Results of a statistical analysis of solar granulation are presented. A data set of 36 images of a quiet-Sun area on the solar disk center was used. The data were obtained with the 1.6 m clear aperture New Solar Telescope at Big Bear Solar Observatory and with a broadband filter centered at the TiO (705.7 nm) spectral line. The very high spatial resolution of the data (diffraction limit of 77 km and pixel scale of 0.''0375) augmented by the very high image contrast (15.5% {+-} 0.6%) allowed us to detect for the first time a distinct subpopulation of mini-granular structures.more » These structures are dominant on spatial scales below 600 km. Their size is distributed as a power law with an index of -1.8 (which is close to the Kolmogorov's -5/3 law) and no predominant scale. The regular granules display a Gaussian (normal) size distribution with a mean diameter of 1050 km. Mini-granular structures contribute significantly to the total granular area. They are predominantly confined to the wide dark lanes between regular granules and often form chains and clusters, but different from magnetic bright points. A multi-fractality test reveals that the structures smaller than 600 km represent a multi-fractal, whereas on larger scales the granulation pattern shows no multi-fractality and can be considered as a Gaussian random field. The origin, properties, and role of the population of mini-granular structures in the solar magnetoconvection are yet to be explored.« less

Multiscaling statistics of high frequency global solar radiation data in the Guadeloupean Archipelago

NASA Astrophysics Data System (ADS)

Calif, R.; Schmitt, F. G.; Huang, Y.; Soubdhan, T.

2013-12-01

The part of the solar power production from photovoltaiccs systems is constantly increasing in the electric grids. Solar energy converter devices such as photovoltaic cells are very sensitive to instantaneous solar radiation fluctuations. Thus rapid variation of solar radiation due to changes in the local meteorological condition can induce large amplitude fluctuations of the produced electrical power and reduce the overall efficiency of the system. When large amount of photovoltaic electricity is send into a weak or small electricity network such as island network, the electric grid security can be in jeopardy due to these power fluctuations. The integration of this energy into the electrical network remains a major challenge, due to the high variability of solar radiation in time and space. To palliate these difficulties, it is essential to identify the characteristic of these fluctuations in order to anticipate the eventuality of power shortage or power surge. A good knowledge of the intermittency of global solar radiation is crucial for selecting the location of a solar power plant and predicting the generation of electricity. This work presents a multifractal analysis study of 367 daily global solar radiation sequences measured with a sampling rate of 1 Hz over one year at Guadeloupean Archipelago (French West Indies) located at 16o15'N latitude and 60o30'W longitude. The mean power spectrum computed follows a power law behaviour close to the Kolmogorov spectrum. The intermittent and multifractal properties of global solar radiation data are investigated using several methods. Under this basis, a characterization for each day using three multifractal parameters is proposed.

Classifying acoustic signals into phoneme categories: average and dyslexic readers make use of complex dynamical patterns and multifractal scaling properties of the speech signal

PubMed Central

2015-01-01

Several competing aetiologies of developmental dyslexia suggest that the problems with acquiring literacy skills are causally entailed by low-level auditory and/or speech perception processes. The purpose of this study is to evaluate the diverging claims about the specific deficient peceptual processes under conditions of strong inference. Theoretically relevant acoustic features were extracted from a set of artificial speech stimuli that lie on a /bAk/-/dAk/ continuum. The features were tested on their ability to enable a simple classifier (Quadratic Discriminant Analysis) to reproduce the observed classification performance of average and dyslexic readers in a speech perception experiment. The ‘classical’ features examined were based on component process accounts of developmental dyslexia such as the supposed deficit in Envelope Rise Time detection and the deficit in the detection of rapid changes in the distribution of energy in the frequency spectrum (formant transitions). Studies examining these temporal processing deficit hypotheses do not employ measures that quantify the temporal dynamics of stimuli. It is shown that measures based on quantification of the dynamics of complex, interaction-dominant systems (Recurrence Quantification Analysis and the multifractal spectrum) enable QDA to classify the stimuli almost identically as observed in dyslexic and average reading participants. It seems unlikely that participants used any of the features that are traditionally associated with accounts of (impaired) speech perception. The nature of the variables quantifying the temporal dynamics of the speech stimuli imply that the classification of speech stimuli cannot be regarded as a linear aggregate of component processes that each parse the acoustic signal independent of one another, as is assumed by the ‘classical’ aetiologies of developmental dyslexia. It is suggested that the results imply that the differences in speech perception performance between average and dyslexic readers represent a scaled continuum rather than being caused by a specific deficient component. PMID:25834769

Temporal and spatial characteristics of extreme precipitation events in the Midwest of Jilin Province based on multifractal detrended fluctuation analysis method and copula functions

NASA Astrophysics Data System (ADS)

Guo, Enliang; Zhang, Jiquan; Si, Ha; Dong, Zhenhua; Cao, Tiehua; Lan, Wu

2017-10-01

Environmental changes have brought about significant changes and challenges to water resources and management in the world; these include increasing climate variability, land use change, intensive agriculture, and rapid urbanization and industrial development, especially much more frequency extreme precipitation events. All of which greatly affect water resource and the development of social economy. In this study, we take extreme precipitation events in the Midwest of Jilin Province as an example; daily precipitation data during 1960-2014 are used. The threshold of extreme precipitation events is defined by multifractal detrended fluctuation analysis (MF-DFA) method. Extreme precipitation (EP), extreme precipitation ratio (EPR), and intensity of extreme precipitation (EPI) are selected as the extreme precipitation indicators, and then the Kolmogorov-Smirnov (K-S) test is employed to determine the optimal probability distribution function of extreme precipitation indicators. On this basis, copulas connect nonparametric estimation method and the Akaike Information Criterion (AIC) method is adopted to determine the bivariate copula function. Finally, we analyze the characteristics of single variable extremum and bivariate joint probability distribution of the extreme precipitation events. The results show that the threshold of extreme precipitation events in semi-arid areas is far less than that in subhumid areas. The extreme precipitation frequency shows a significant decline while the extreme precipitation intensity shows a trend of growth; there are significant differences in spatiotemporal of extreme precipitation events. The spatial variation trend of the joint return period gets shorter from the west to the east. The spatial distribution of co-occurrence return period takes on contrary changes and it is longer than the joint return period.

Multifractal Omori law for earthquake triggering: new tests on the California, Japan and worldwide catalogues

NASA Astrophysics Data System (ADS)

Ouillon, G.; Sornette, D.; Ribeiro, E.

2009-07-01

The Multifractal Stress-Activated model is a statistical model of triggered seismicity based on mechanical and thermodynamic principles. It predicts that, above a triggering magnitude cut-off M0, the exponent p of the Omori law for the time decay of the rate of aftershocks is a linear increasing function p(M) = a0M + b0 of the main shock magnitude M. We previously reported empirical support for this prediction, using the Southern California Earthquake Center (SCEC) catalogue. Here, we confirm this observation using an updated, longer version of the same catalogue, as well as new methods to estimate p. One of this methods is the newly defined Scaling Function Analysis (SFA), adapted from the wavelet transform. This method is able to measure a mathematical singularity (hence a p-value), erasing the possible regular part of a time-series. The SFA also proves particularly efficient to reveal the coexistence and superposition of several types of relaxation laws (typical Omori sequences and short-lived swarms sequences) which can be mixed within the same catalogue. Another new method consists in monitoring the largest aftershock magnitude observed in successive time intervals, and thus shortcuts the problem of missing events with small magnitudes in aftershock catalogues. The same methods are used on data from the worldwide Harvard Centroid Moment Tensor (CMT) catalogue and show results compatible with those of Southern California. For the Japan Meteorological Agency (JMA) catalogue, we still observe a linear dependence of p on M, but with a smaller slope. The SFA shows however that results for this catalogue may be biased by numerous swarm sequences, despite our efforts to remove them before the analysis.

Multifractal spectra in homogeneous shear flow

NASA Technical Reports Server (NTRS)

Deane, A. E.; Keefe, L. R.

1988-01-01

Employing numerical simulations of 3-D homogeneous shear flow, the associated multifractal spectra of the energy dissipation, scalar dissipation and vorticity fields were calculated. The results for (128) cubed simulations of this flow, and those obtained in recent experiments that analyzed 1- and 2-D intersections of atmospheric and laboratory flows, are in some agreement. A two-scale Cantor set model of the energy cascade process which describes the experimental results from 1-D intersections quite well, describes the 3-D results only marginally.

Space-filling, multifractal, localized thermal spikes in Si, Ge and ZnO

NASA Astrophysics Data System (ADS)

Ahmad, Shoaib; Abbas, Muhammad Sabtain; Yousuf, Muhammad; Javeed, Sumera; Zeeshan, Sumaira; Yaqub, Kashif

2018-04-01

The mechanism responsible for the emission of clusters from heavy ion irradiated solids is proposed to be thermal spikes. Collision cascade-based theories describe atomic sputtering but cannot explain the consistently observed experimental evidence for significant cluster emission. Statistical thermodynamic arguments for thermal spikes are employed here for qualitative and quantitative estimation of the thermal spike-induced cluster emission from Si, Ge and ZnO. The evolving cascades and spikes in elemental and molecular semiconducting solids are shown to have fractal characteristics. Power law potential is used to calculate the fractal dimension. With the loss of recoiling particles' energy the successive branching ratios get smaller. The fractal dimension is shown to be dependent upon the exponent of the power law interatomic potential D = 1/2m. Each irradiating ion has the probability of initiating a space-filling, multifractal thermal spike that may sublime a localized region near the surface by emitting clusters in relative ratios that depend upon the energies of formation of respective surface vacancies.

Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates

NASA Astrophysics Data System (ADS)

Garcin, Matthieu

2017-10-01

Hurst exponents depict the long memory of a time series. For human-dependent phenomena, as in finance, this feature may vary in the time. It justifies modelling dynamics by multifractional Brownian motions, which are consistent with time-dependent Hurst exponents. We improve the existing literature on estimating time-dependent Hurst exponents by proposing a smooth estimate obtained by variational calculus. This method is very general and not restricted to the sole Hurst framework. It is globally more accurate and easier than other existing non-parametric estimation techniques. Besides, in the field of Hurst exponents, it makes it possible to make forecasts based on the estimated multifractional Brownian motion. The application to high-frequency foreign exchange markets (GBP, CHF, SEK, USD, CAD, AUD, JPY, CNY and SGD, all against EUR) shows significantly good forecasts. When the Hurst exponent is higher than 0.5, what depicts a long-memory feature, the accuracy is higher.

Modeling Fractal Structure of City-Size Distributions Using Correlation Functions

PubMed Central

Chen, Yanguang

2011-01-01

Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences. PMID:21949753

Non-stationary dynamics in the bouncing ball: A wavelet perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Behera, Abhinna K., E-mail: abhinna@iiserkol.ac.in; Panigrahi, Prasanta K., E-mail: pprasanta@iiserkol.ac.in; Sekar Iyengar, A. N., E-mail: ansekar.iyengar@saha.ac.in

2014-12-01

The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures of self-similarity, complex scaling behavior, and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding tomore » neutral turbulence, viscous dissipation regions, and different time varying periodic modulations.« less

Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Ronco, Michele

2017-10-01

We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

A study on Improvisation in a Musical performance using Multifractal Detrended Cross Correlation Analysis

NASA Astrophysics Data System (ADS)

Sanyal, Shankha; Banerjee, Archi; Patranabis, Anirban; Banerjee, Kaushik; Sengupta, Ranjan; Ghosh, Dipak

2016-11-01

MFDFA (the most rigorous technique to assess multifractality) was performed on four Hindustani music samples played on same 'raga' sung by the same performer. Each music sample was divided into six parts and 'multifractal spectral width' was determined for each part corresponding to the four samples. The results obtained reveal that different parts of all the four sound signals possess spectral width of widely varying values. This gives a cue of the so called 'musical improvisation' in all music samples, keeping in mind they belong to the bandish part of the same raga. Formal compositions in Hindustani raga are juxtaposed with the improvised portions, where an artist manoeuvers his/her own creativity to bring out a mood that is specific for that particular performance, which is known as 'improvisation'. Further, this observation hints at the association of different emotions even in the same bandish of the same raga performed by the same artist, this interesting observation cannot be revealed unless rigorous non-linear technique explores the nature of musical structure. In the second part, we applied MFDXA technique to explore more in-depth about 'improvisation' and association with emotion. This technique is applied to find the degree of cross-correlation (γx) between the different parts of the samples. Pronounced correlation has been observed in the middle parts of the all the four samples evident from higher values of γx ​whereas the other parts show weak correlation. This gets further support from the values of spectral width from different parts of the sample - width of those parts is significantly different from other parts. This observation is extremely new both in respect of musical structure of so called improvisation and associated emotion. The importance of this study in application area of cognitive music therapy is immense.

Empirical meaning of DTM multifractal parameters in the precipitation context

NASA Astrophysics Data System (ADS)

Portilla Farfan, Freddy; Valencia, Jose Luis; Villeta, Maria; Tarquis, Ana M.; Saa-Requejo, Antonio

2015-04-01

The main objective of this research is to interpret the multifractal parameters in the case of precipitation series from an empirical approach. In order to do so nineteen precipitation series were generated with a daily precipitation simulator derived from year and month estimations and considering the classical statistics, used commonly in hydrology studies, from actual data of four Spanish rain gauges located in a gradient from NW to SE. For all generated series the multifractal parameters were estimated following the technique DTM (Double Trace Moments) developed by Lavalle et al. (1993) and the variations produced considered. The results show the following conclusions: 1. The intermittency, C1, increases when precipitation is concentrating for fewer days, making it more variable, or when increasing its concentration on maximum monthly precipitation days, while it is not affected due to the modification in the variability in the number of days rained. 2. Multifractility, α, increases with the number of rainy days and the variability of the precipitation, yearly as well as monthly, as well as with the concentration of precipitation on the maximum monthly precipitation day. 3. The maximum probable singularity, γs, increases with the concentration of rain on the day of the maximum monthly precipitation and the variability in yearly and monthly level. 4. The non-conservative degree, H, depends on the number of rainy days that appear on the series and secondly on the general variability of the rain. References Lavallée D., S. Lovejoy, D. Schertzer and P. Ladoy, 1993. Nonlinear variability and landscape topography: analysis and simulation. In: Fractals in Geography (N. Lam and L. De Cola, Eds.) Prentice Hall, Englewood Cliffs, 158-192.

The Application of Fractal and Multifractal Theory in Hydraulic-Flow-Unit Characterization and Permeability Estimation

NASA Astrophysics Data System (ADS)

Chen, X.; Yao, G.; Cai, J.

2017-12-01

Pore structure characteristics are important factors in influencing the fluid transport behavior of porous media, such as pore-throat ratio, pore connectivity and size distribution, moreover, wettability. To accurately characterize the diversity of pore structure among HFUs, five samples selected from different HFUs (porosities are approximately equal, however permeability varies widely) were chosen to conduct micro-computerized tomography test to acquire direct 3D images of pore geometries and to perform mercury injection experiments to obtain the pore volume-radii distribution. To characterize complex and high nonlinear pore structure of all samples, three classic fractal geometry models were applied. Results showed that each HFU has similar box-counting fractal dimension and generalized fractal dimension in the number-area model, but there are significant differences in multifractal spectrums. In the radius-volume model, there are three obvious linear segments, corresponding to three fractal dimension values, and the middle one is proved as the actual fractal dimension according to the maximum radius. In the number-radius model, the spherical-pore size distribution extracted by maximum ball algorithm exist a decrease in the number of small pores compared with the fractal power rate rather than the traditional linear law. Among the three models, only multifractal analysis can classify the HFUs accurately. Additionally, due to the tightness and low-permeability in reservoir rocks, connate water film existing in the inner surface of pore channels commonly forms bound water. The conventional model which is known as Yu-Cheng's model has been proved to be typically not applicable. Considering the effect of irreducible water saturation, an improved fractal permeability model was also deduced theoretically. The comparison results showed that the improved model can be applied to calculate permeability directly and accurately in such unconventional rocks.

A Renormalization-Group Interpretation of the Connection between Criticality and Multifractals

NASA Astrophysics Data System (ADS)

Chang, Tom

2014-05-01

Turbulent fluctuations in space plasmas beget phenomena of dynamic complexity. It is known that dynamic renormalization group (DRG) may be employed to understand the concept of forced and/or self-organized criticality (FSOC), which seems to describe certain scaling features of space plasma turbulence. But, it may be argued that dynamic complexity is not just a phenomenon of criticality. It is therefore of interest to inquire if DRG may be employed to study complexity phenomena that are distinctly more complicated than dynamic criticality. Power law scaling generally comes about when the DRG trajectory is attracted to the vicinity of a fixed point in the phase space of the relevant dynamic plasma parameters. What happens if the trajectory lies within a domain influenced by more than one single fixed point or more generally if the transformation underlying the DRG is fully nonlinear? The global invariants of the group under such situations (if they exist) are generally not power laws. Nevertheless, as we shall argue, it may still be possible to talk about local invariants that are power laws with the nonlinearity of transformation prescribing a specific phenomenon as crossovers. It is with such concept in mind that we may provide a connection between the properties of dynamic criticality and multifractals from the point of view of DRG (T. Chang, Chapter VII, "An Introduction to Space Plasma Complexity", Cambridge University Press, 2014). An example in terms of the concepts of finite-size scaling (FSS) and rank-ordered multifractal analysis (ROMA) of a toy model shall be provided. Research partially supported by the US National Science Foundation and the European Community's Seventh Framework Programme (FP7/ 2007-2013) under Grant agreement no. 313038/STORM.

Turbulence Characteristics in an Elevated Shear Layer over Owens Valley

DTIC Science & Technology

2010-02-14

Arnéodo, G. Grasseau, Y. Gagne, E. J. Hopfinger, and U. Frisch, 1989: Wavelet analysis of turbulence reveals the multifractal nature of the Richardson...Helmholtz (KH) instability, the tur- bulence inertial subrange, turbulence intermittency, and cross -scale energy transfer over complex terrain. The...or cross -valley) and the normal (also referred to as along- valley) wind components, respectively. Figure 2 shows profiles derived from the 1800 UTC

Runoff generation in karst catchments: multifractal analysis

NASA Astrophysics Data System (ADS)

Majone, Bruno; Bellin, Alberto; Borsato, Andrea

2004-07-01

Time series of hydrological and geochemical signals at two karst springs, located in the Dolomiti del Brenta region, near Trento, Italy, are used to infer how karst catchments work internally to generate runoff. The data analyzed include precipitation, spring flow and electric conductivity of the spring water. All the signals show the signature of multifractality but with different intermittency and non-stationarity. In particular, precipitation and spring flow are shown to have nearly the same degree of non-stationarity and intermittency, while electric conductivity, which mimics the travel time distribution of water in the karst system, is less intermittent and smoother than both spring flow and precipitations. We found that spring flow can be obtained from precipitation through fractional convolution with a power law transfer function. An important result of our study is that the probability distribution of travel times is inconsistent with the advection dispersion equation, while it supports the anomalous transport model. This result is in line with what was observed by Painter et al. [Geophys. Res. Lett. 29 (2002) 21.1] for transport in fractured rocks.

Multifractal analysis of implied volatility in index options

NASA Astrophysics Data System (ADS)

Oh, GabJin

2014-06-01

In this paper, we analyze the statistical and the non-linear properties of the log-variations in implied volatility for the CAC40, DAX and S& P500 daily index options. The price of an index option is generally represented by its implied volatility surface, including its smile and skew properties. We utilize a Lévy process model as the underlying asset to deepen our understanding of the intrinsic property of the implied volatility in the index options and estimate the implied volatility surface. We find that the options pricing models with the exponential Lévy model can reproduce the smile or sneer features of the implied volatility that are observed in real options markets. We study the variation in the implied volatility for at-the-money index call and put options, and we find that the distribution function follows a power-law distribution with an exponent of 3.5 ≤ γ ≤ 4.5. Especially, the variation in the implied volatility exhibits multifractal spectral characteristics, and the global financial crisis has influenced the complexity of the option markets.

Scale-free avalanches in the multifractal random walk

NASA Astrophysics Data System (ADS)

Bartolozzi, M.

2007-06-01

Avalanches, or Avalanche-like, events are often observed in the dynamical behaviour of many complex systems which span from solar flaring to the Earth's crust dynamics and from traffic flows to financial markets. Self-organized criticality (SOC) is one of the most popular theories able to explain this intermittent charge/discharge behaviour. Despite a large amount of theoretical work, empirical tests for SOC are still in their infancy. In the present paper we address the common problem of revealing SOC from a simple time series without having much information about the underlying system. As a working example we use a modified version of the multifractal random walk originally proposed as a model for the stock market dynamics. The study reveals, despite the lack of the typical ingredients of SOC, an avalanche-like dynamics similar to that of many physical systems. While, on one hand, the results confirm the relevance of cascade models in representing turbulent-like phenomena, on the other, they also raise the question about the current state of reliability of SOC inference from time series analysis.

Multiscale volatility duration characteristics on financial multi-continuum percolation dynamics

NASA Astrophysics Data System (ADS)

Wang, Min; Wang, Jun

A random stock price model based on the multi-continuum percolation system is developed to investigate the nonlinear dynamics of stock price volatility duration, in an attempt to explain various statistical facts found in financial data, and have a deeper understanding of mechanisms in the financial market. The continuum percolation system is usually referred to be a random coverage process or a Boolean model, it is a member of a class of statistical physics systems. In this paper, the multi-continuum percolation (with different values of radius) is employed to model and reproduce the dispersal of information among the investors. To testify the rationality of the proposed model, the nonlinear analyses of return volatility duration series are preformed by multifractal detrending moving average analysis and Zipf analysis. The comparison empirical results indicate the similar nonlinear behaviors for the proposed model and the actual Chinese stock market.

Self-similar seismogenic structure of the crust: A review of the problem and a mathematical model

NASA Astrophysics Data System (ADS)

Stakhovsky, I. R.

2007-12-01

The paper presents a brief review of studies of the structural organization of a seismogenic medium showing that the crust of seismically active regions possesses a fractal structure. A new mathematical model of the self-similar seismogenic structure (SSS) of the crust generalizing the reviewed publications is proposed on the basis of the scaling correspondence between the fault, seismic, and seismic energy multifractal fields of the crust. Multifractal fields of other physical origin can also be incorporated in the SSS model.

A deterministic width function model

NASA Astrophysics Data System (ADS)

Puente, C. E.; Sivakumar, B.

Use of a deterministic fractal-multifractal (FM) geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States), that the FM approach may also be used to closely approximate existing width functions.

To what extent can global warming events influence scaling properties of climatic fluctuations in glacial periods?

NASA Astrophysics Data System (ADS)

Alberti, Tommaso; Lepreti, Fabio; Vecchio, Antonio; Carbone, Vincenzo

2017-04-01

The Earth's climate is an extremely unstable complex system consisting of nonlinear and still rather unknown interactions among atmosphere, land surface, ice and oceans. The system is mainly driven by solar irradiance, even if internal components as volcanic eruptions and human activities affect the atmospheric composition thus acting as a driver for climate changes. Since the extreme climate variability is the result of a set of phenomena operating from daily to multi-millennial timescales, with different correlation times, a study of the scaling properties of the system can evidence non-trivial persistent structures, internal or external physical processes. Recently, the scaling properties of the paleoclimate changes have been analyzed by distinguish between interglacial and glacial climates [Shao and Ditlevsen, 2016]. The results show that the last glacial record (20-120 kyr BP) presents some elements of multifractality, while the last interglacial period (0-10 kyr BP), say the Holocene period, seems to be characterized by a mono-fractal structure. This is associated to the absence of Dansgaard-Oeschger (DO) events in the interglacial climate that could be the cause for the absence of multifractality. This hypothesis is supported by the analysis of the period between 18 and 27 kyr BP, i.e. during the Last Glacial Period, in which a single DO event have been registred. Through the Empirical Mode Decomposition (EMD) we were able to detect a timescale separation within the Last Glacial Period (20-120 kyr BP) in two main components: a high-frequency component, related to the occurrence of DO events, and a low-frequency one, associated to the cooling/warming phase switch [Alberti et al., 2014]. Here, we investigate the scaling properties of the climate fluctuations within the Last Glacial Period, where abrupt climate changes, characterized by fast increase of temperature usually called Dansgaard-Oeschger (DO) events, have been particularly pronounced. By using the MultiFractal Detrended Fluctuation Analysis (MF-DFA), we show that a multifractal structure exists for both high- and low-frequency fluctuations in Northern and Southern hemispheres, with different scaling exponents, thus indicating a long-range persistence of the climatic variability within the whole Last Glacial Period. Our results evidence that both DO events and cooling/warming cycles must be considered as processes of the internal component of the Earth's climate, rather than processes related to external forcings. This study should be helpful for investigation of the internal origin of climate changes. References Shao, Z.G. and Ditlevsen, P.D., Nature Commun., 7, 10951, (2016). Alberti, T., Lepreti, F., Vecchio, A., Bevacqua, E., Capparelli, V. and Carbone, V., Clim. Past, 10, 1751 (2014).

Frozen Fractals all Around: Solar flares, Ampere’s Law, and the Search for Units in Scale-Free Processes.

NASA Astrophysics Data System (ADS)

McAteer, R. T. James

2015-08-01

My soul is spiraling in frozen fractals all around, And one thought crystallizes like an icy blast, I'm never going back, the past is in the past.Elsa, from Disney’s Frozen, characterizes two fundamental aspects of scale-free processes in Nature: fractals are everywhere in space; fractals can be used to probe changes in time. Self-Organized Criticality provides a powerful set of tools to study scale-free processes. It connects spatial fractals (more generically, multifractals) to temporal evolution. The drawback is that this usually results in scale-free, unit-less, indices, which can be difficult to connect to everyday physics. Here, I show a novel method that connects one of the most powerful SOC tools - the wavelet transform modulus maxima approach to calculating multifractality - to one of the most powerful equations in all of physics - Ampere’s law. In doing so I show how the multifractal spectra can be expressed in terms of current density, and how current density can then be used for the prediction of future energy release from such a system.Our physical understanding of the solar magnetic field structure, and hence our ability to predict solar activity, is limited by the type of data currently available. I show that the multifractal spectrum provides a powerful physical connection between the details of photospheric magnetic gradients of current data and the coronal magnetic structure. By decomposing Ampere’s law and comparing it to the wavelet transform modulus maximum method, I show how the scale-free Holder exponent provides a direct measure of current density across all relevant sizes. The prevalence of this current density across various scales is connected to its stability in time, and hence to the ability of the magnetic structure to store and then release energy. Hence (spatial) multifractals inform us of (future) solar activity.Finally I discuss how such an approach can be used in any study of scale-free processes, and highlight the necessary key steps in identifying the nature of the mother wavelet to ensuring the viability of this powerful connection.

INTERMITTENCY AND MULTIFRACTALITY SPECTRA OF THE MAGNETIC FIELD IN SOLAR ACTIVE REGIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abramenko, Valentyna; Yurchyshyn, Vasyl

We present the results of a study of intermittency and multifractality of magnetic structures in solar active regions (ARs). Line-of-sight magnetograms for 214 ARs of different flare productivity observed at the center of the solar disk from 1997 January until 2006 December are utilized. Data from the Michelson Doppler Imager (MDI) instrument on board the Solar and Heliospheric Observatory operating in the high resolution mode, the Big Bear Solar Observatory digital magnetograph, and the Hinode SOT/SP instrument were used. Intermittency spectra were derived from high-order structure functions and flatness functions. The flatness function exponent is a measure of the degreemore » of intermittency. We found that the flatness function exponent at scales below approximately 10 Mm is correlated with flare productivity (the correlation coefficient is -0.63). The Hinode data show that the intermittency regime is extended toward small scales (below 2 Mm) as compared to the MDI data. The spectra of multifractality, derived from the structure functions and flatness functions, are found to be broader for ARs of higher flare productivity as compared to those of low flare productivity. The magnetic structure of high-flaring ARs consists of a voluminous set of monofractals, and this set is much richer than that for low-flaring ARs. The results indicate the relevance of the multifractal organization of the photospheric magnetic fields to the flaring activity. The strong intermittency observed in complex and high-flaring ARs is a hint that we observe a photospheric imprint of enhanced sub-photospheric dynamics.« less

Life in Meridiani Planum. Mars. (Italian Title: Vita in Meridiani Planum, Marte)

NASA Astrophysics Data System (ADS)

Bianciardi, G.; Rizzo, V.; Cantasano, V.

2015-05-01

We performed a quantitative image analysis to compare microstructures of microbialites with the images photographed by the Rover Opportunity. Terrestrial and Martian textures present a multifractal aspect. Mean values and confidence intervals from the Martian images overlapped perfectly with those from the terrestrial samples (p<0.004). Our work shows the presumptive evidence of microbialites in the Martian outcroppings: the presence of unicellular life widespread on the ancient Mars.

Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise, and multifractality.

PubMed

Kendal, Wayne S; Jørgensen, Bent

2011-12-01

Plants and animals of a given species tend to cluster within their habitats in accordance with a power function between their mean density and the variance. This relationship, Taylor's power law, has been variously explained by ecologists in terms of animal behavior, interspecies interactions, demographic effects, etc., all without consensus. Taylor's law also manifests within a wide range of other biological and physical processes, sometimes being referred to as fluctuation scaling and attributed to effects of the second law of thermodynamics. 1/f noise refers to power spectra that have an approximately inverse dependence on frequency. Like Taylor's law these spectra manifest from a wide range of biological and physical processes, without general agreement as to cause. One contemporary paradigm for 1/f noise has been based on the physics of self-organized criticality. We show here that Taylor's law (when derived from sequential data using the method of expanding bins) implies 1/f noise, and that both phenomena can be explained by a central limit-like effect that establishes the class of Tweedie exponential dispersion models as foci for this convergence. These Tweedie models are probabilistic models characterized by closure under additive and reproductive convolution as well as under scale transformation, and consequently manifest a variance to mean power function. We provide examples of Taylor's law, 1/f noise, and multifractality within the eigenvalue deviations of the Gaussian unitary and orthogonal ensembles, and show that these deviations conform to the Tweedie compound Poisson distribution. The Tweedie convergence theorem provides a unified mathematical explanation for the origin of Taylor's law and 1/f noise applicable to a wide range of biological, physical, and mathematical processes, as well as to multifractality.

Price Formation Based on Particle-Cluster Aggregation

NASA Astrophysics Data System (ADS)

Wang, Shijun; Zhang, Changshui

In the present work, we propose a microscopic model of financial markets based on particle-cluster aggregation on a two-dimensional small-world information network in order to simulate the dynamics of the stock markets. "Stylized facts" of the financial market time series, such as fat-tail distribution of returns, volatility clustering and multifractality, are observed in the model. The results of the model agree with empirical data taken from historical records of the daily closures of the NYSE composite index.

Chaotic Dynamics of Linguistic-Like Processes at the Syntactical and Semantic Levels: in the Pursuit of a Multifractal Attractor

NASA Astrophysics Data System (ADS)

Nicolis, John S.; Katsikas, Anastassis A.

Collective parameters such as the Zipf's law-like statistics, the Transinformation, the Block Entropy and the Markovian character are compared for natural, genetic, musical and artificially generated long texts from generating partitions (alphabets) on homogeneous as well as on multifractal chaotic maps. It appears that minimal requirements for a language at the syntactical level such as memory, selectivity of few keywords and broken symmetry in one dimension (polarity) are more or less met by dynamically iterating simple maps or flows e.g. very simple chaotic hardware. The same selectivity is observed at the semantic level where the aim refers to partitioning a set of enviromental impinging stimuli onto coexisting attractors-categories. Under the regime of pattern recognition and classification, few key features of a pattern or few categories claim the lion's share of the information stored in this pattern and practically, only these key features are persistently scanned by the cognitive processor. A multifractal attractor model can in principle explain this high selectivity, both at the syntactical and the semantic levels.

Black holes in multi-fractional and Lorentz-violating models

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele

2017-05-01

We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length ℓ _*. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to ℓ _*. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.

Generalized Hurst exponent estimates differentiate EEG signals of healthy and epileptic patients

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2018-01-01

The aim of our current study is to check whether multifractal patterns of the electroencephalographic (EEG) signals of normal and epileptic patients are statistically similar or different. In this regard, the generalized Hurst exponent (GHE) method is used for robust estimation of the multifractals in each type of EEG signals, and three powerful statistical tests are performed to check existence of differences between estimated GHEs from healthy control subjects and epileptic patients. The obtained results show that multifractals exist in both types of EEG signals. Particularly, it was found that the degree of fractal is more pronounced in short variations of normal EEG signals than in short variations of EEG signals with seizure free intervals. In contrary, it is more pronounced in long variations of EEG signals with seizure free intervals than in normal EEG signals. Importantly, both parametric and nonparametric statistical tests show strong evidence that estimated GHEs of normal EEG signals are statistically and significantly different from those with seizure free intervals. Therefore, GHEs can be efficiently used to distinguish between healthy and patients suffering from epilepsy.

Brain Neurons as Quantum Computers:

NASA Astrophysics Data System (ADS)

Bershadskii, A.; Dremencov, E.; Bershadskii, J.; Yadid, G.

The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of brain neurons, has been actively discussed in the last years. A positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In the present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied in vivo on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in the generation of pleasure and in the development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a quantum system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental (in vivo) indication in the favor of the quantum (at least partially) nature of brain neurons activity.

Simulation of sovereign CDS market based on interaction between market participant

NASA Astrophysics Data System (ADS)

Ko, Bonggyun; Kim, Kyungwon

2017-08-01

A research for distributional property of financial asset is the subject of intense interest not only for financial theory but also for practitioner. Such respect is no exception to CDS market. The CDS market, which began to receive attention since the global financial debacle, is not well researched despite of the importance of research necessity. This research introduces creation of CDS market and use Ising system utilizing occurrence characteristics (to shift risk) as an important factor. Therefore the results of this paper would be of great assistance to both financial theory and practice. From this study, not only distributional property of the CDS market but also various statistics like multifractal characteristics could promote understanding about the market. A salient point in this study is that countries are mainly clustering into 2 groups and it might be because of market situation and geographical characteristics of each country. This paper suggested 2 simulation parameters representing this market based on understanding such CDS market situation. The estimated parameters are suitable for high and low risk event of CDS market respectively and these two parameters are complementary and can cover not only basic statistics but also multifractal properties of most countries. Therefore these estimated parameters can be used in researches preparing for a certain event (high or low risk). Finally this research will serve as a momentum double-checking indirectly the performance of Ising system based on these results.

Long and Short Range Correlations in Healthy and Pathologic Human Cardiac Prosses

NASA Astrophysics Data System (ADS)

Bunde, Armin

2001-03-01

Healthy sleep consists of several stages: deep sleep, light sleep and REM sleep. In this talk, recent work on the characterization of heart-rates in the three stages by long-range correlations is presented. Only in REM sleep, long-range correlations reminiscent to the wake phase occur, and the heart-rates show multifractal behaviour. In contrast, in non-REM phases, the heart-rates are uncorrelated above the typical breathing cycle time, pointing to a random regulation of the heartbeat during non-REM sleep. In deep sleep, the heart-rates show simple multifractal behaviour.

A better understanding of long-range temporal dependence of traffic flow time series

NASA Astrophysics Data System (ADS)

Feng, Shuo; Wang, Xingmin; Sun, Haowei; Zhang, Yi; Li, Li

2018-02-01

Long-range temporal dependence is an important research perspective for modelling of traffic flow time series. Various methods have been proposed to depict the long-range temporal dependence, including autocorrelation function analysis, spectral analysis and fractal analysis. However, few researches have studied the daily temporal dependence (i.e. the similarity between different daily traffic flow time series), which can help us better understand the long-range temporal dependence, such as the origin of crossover phenomenon. Moreover, considering both types of dependence contributes to establishing more accurate model and depicting the properties of traffic flow time series. In this paper, we study the properties of daily temporal dependence by simple average method and Principal Component Analysis (PCA) based method. Meanwhile, we also study the long-range temporal dependence by Detrended Fluctuation Analysis (DFA) and Multifractal Detrended Fluctuation Analysis (MFDFA). The results show that both the daily and long-range temporal dependence exert considerable influence on the traffic flow series. The DFA results reveal that the daily temporal dependence creates crossover phenomenon when estimating the Hurst exponent which depicts the long-range temporal dependence. Furthermore, through the comparison of the DFA test, PCA-based method turns out to be a better method to extract the daily temporal dependence especially when the difference between days is significant.

Detection of meso-micro scale surface features based on microcanonical multifractal formalism

NASA Astrophysics Data System (ADS)

Yang, Yuanyuan; Chen, Wei; Xie, Tao; Perrie, William

2018-01-01

Not Available Project supported by the National Key R&D Program of China (Grant No. 2016YFC1401007), the Global Change Research Program of China (Grant No. 2015CB953901), the National Natural Science Foundation of China (Grant No. 41776181), the Canadian Program on Energy Research and Development (OERD), Canadian Space Agency’s SWOT Program, and the Canadian Marine Environmental Observation Prediction and Response Network (MEOPAR).

Fractal analysis of multiscale spatial autocorrelation among point data

USGS Publications Warehouse

De Cola, L.

1991-01-01

The analysis of spatial autocorrelation among point-data quadrats is a well-developed technique that has made limited but intriguing use of the multiscale aspects of pattern. In this paper are presented theoretical and algorithmic approaches to the analysis of aggregations of quadrats at or above a given density, in which these sets are treated as multifractal regions whose fractal dimension, D, may vary with phenomenon intensity, scale, and location. The technique is illustrated with Matui's quadrat house-count data, which yield measurements consistent with a nonautocorrelated simulated Poisson process but not with an orthogonal unit-step random walk. The paper concludes with a discussion of the implications of such analysis for multiscale geographic analysis systems. -Author

Relationship of The Tropical Cyclogenesis With Solar and Magnetospheric Activities

NASA Astrophysics Data System (ADS)

Vishnevsky, O. V.; Pankov, V. M.; Erokhine, N. S.

Formation of tropical cyclones is a badly studied period in their life cycle even though there are many papers dedicated to analysis of influence of different parameters upon cyclones occurrence frequency (see e.g., Gray W.M.). Present paper is dedicated to study of correlation of solar and magnetospheric activity with the appearance of tropical cyclones in north-west region of Pacific ocean. Study of correlation was performed by using both classical statistical methods (including maximum entropy method) and quite modern ones, for example multifractal analysis. Information about Wolf's numbers and cyclogenesis intensity in period of 1944-2000 was received from different Internet databases. It was shown that power spectra maximums of Wolf's numbers and appeared tropical cyclones ones corresponds to 11-year period; solar activity and cyclogenesis processes intensity are in antiphase; maximum of mutual correlation coefficient (~ 0.8) between Wolf's numbers and cyclogenesis intensity is in South-China sea. There is a relation of multifractal characteristics calculated for both time series with the mutual correlation function that is another indicator of correlation between tropical cyclogenesis and solar-magnetospheric activity. So, there is the correlation between solar-magnetospheric activity and tropical cyclone intensity in this region. Possible physical mechanisms of such correlation including anomalous precipitations charged particles from the Earth radiation belts and wind intensity amplification in the troposphere are discussed.

Relationship of The Tropical Cyclogenesis With Solar and Magnetospheric Activities

NASA Astrophysics Data System (ADS)

Vishnevsky, O.; Pankov, V.; Erokhine, N.

Formation of tropical cyclones is a badly studied period in their life cycle even though there are many papers dedicated to analysis of influence of different parameters upon cyclones occurrence frequency (see e.g., Gray W.M.). Present paper is dedicated to study of correlation of solar and magnetospheric activity with the appearance of tropi- cal cyclones in north-west region of Pacific ocean. Study of correlation was performed by using both classical statistical methods (including maximum entropy method) and quite modern ones, for example multifractal analysis. Information about Wolf's num- bers and cyclogenesis intensity in period of 1944-2000 was received from different Internet databases. It was shown that power spectra maximums of Wolf's numbers and appeared tropical cyclones ones corresponds to 11-year period; solar activity and cyclogenesis processes intensity are in antiphase; maximum of mutual correlation co- efficient ( 0.8) between Wolf's numbers and cyclogenesis intensity is in South-China sea. There is a relation of multifractal characteristics calculated for both time series with the mutual correlation function that is another indicator of correlation between tropical cyclogenesis and solar-magnetospheric activity. So, there is the correlation between solar-magnetospheric activity and tropical cyclone intensity in this region. Possible physical mechanisms of such correlation including anomalous precipitations charged particles from the Earth radiation belts and wind intensity amplification in the troposphere are discussed.

Fractal dynamics of heartbeat time series of young persons with metabolic syndrome

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, A.; Alonso-Martínez, A.; Ramírez-Hernández, L.; Martínez-Hernández, G.

2012-10-01

Many physiological systems have been in recent years quantitatively characterized using fractal analysis. We applied it to study heart variability of young subjects with metabolic syndrome (MS); we examined the RR time series (time between two R waves in ECG) with the detrended fluctuation analysis (DFA) method, the Higuchi's fractal dimension method and the multifractal analysis to detect the possible presence of heart problems. The results show that although the young persons have MS, the majority do not present alterations in the heart dynamics. However, there were cases where the fractal parameter values differed significantly from the healthy people values.

Persistence in eye movement during visual search

NASA Astrophysics Data System (ADS)

Amor, Tatiana A.; Reis, Saulo D. S.; Campos, Daniel; Herrmann, Hans J.; Andrade, José S.

2016-02-01

As any cognitive task, visual search involves a number of underlying processes that cannot be directly observed and measured. In this way, the movement of the eyes certainly represents the most explicit and closest connection we can get to the inner mechanisms governing this cognitive activity. Here we show that the process of eye movement during visual search, consisting of sequences of fixations intercalated by saccades, exhibits distinctive persistent behaviors. Initially, by focusing on saccadic directions and intersaccadic angles, we disclose that the probability distributions of these measures show a clear preference of participants towards a reading-like mechanism (geometrical persistence), whose features and potential advantages for searching/foraging are discussed. We then perform a Multifractal Detrended Fluctuation Analysis (MF-DFA) over the time series of jump magnitudes in the eye trajectory and find that it exhibits a typical multifractal behavior arising from the sequential combination of saccades and fixations. By inspecting the time series composed of only fixational movements, our results reveal instead a monofractal behavior with a Hurst exponent , which indicates the presence of long-range power-law positive correlations (statistical persistence). We expect that our methodological approach can be adopted as a way to understand persistence and strategy-planning during visual search.

Multifractal Modeling of Turbulent Mixing

NASA Astrophysics Data System (ADS)

Samiee, Mehdi; Zayernouri, Mohsen; Meerschaert, Mark M.

2017-11-01

Stochastic processes in random media are emerging as interesting tools for modeling anomalous transport phenomena. Applications include intermittent passive scalar transport with background noise in turbulent flows, which are observed in atmospheric boundary layers, turbulent mixing in reactive flows, and long-range dependent flow fields in disordered/fractal environments. In this work, we propose a nonlocal scalar transport equation involving the fractional Laplacian, where the corresponding fractional index is linked to the multifractal structure of the nonlinear passive scalar power spectrum. This work was supported by the AFOSR Young Investigator Program (YIP) award (FA9550-17-1-0150) and partially by MURI/ARO (W911NF-15-1-0562).

Polarization-correlation study of biotissue multifractal structure

NASA Astrophysics Data System (ADS)

Olar, O. I.; Ushenko, A. G.

2003-09-01

This paper presents the results of polarization-correlation study of multifractal collagen structure of physiologically normal and pathologically changed tissues of women"s reproductive sphere and skin. The technique of polarization selection of coherent images of biotissues with further determination of their autocorrelation functions and spectral densities is suggested. The correlation-optical criteria of early diagnostics of appearance of pathological changes in the cases of myometry (forming the germ of fibromyoma) and skin (psoriasis) are determined. This study is directed to investigate the possibilities of recognition of pathological changes of biotissue morphological structure by determining the polarization-dependent autocorrelation functions (ACF) and corresponding spectral densities of tissue coherent images.

Polarization-correlation investigation of biotissue multifractal structure and diagnostics of its pathological change

NASA Astrophysics Data System (ADS)

Angelsky, Oleg V.; Pishak, Vasyl P.; Ushenko, Alexander G.; Burkovets, Dimitry N.; Pishak, Olga V.

2001-05-01

The paper presents the results of polarization-correlation investigation of multifractal collagen structure of physiologically normal and pathologically changed tissues of women's reproductive sphere and of skin. The technique of polarization selection of coherent biotissues' images followed by determination of their autocorrelation functions and spectral densities is suggested. The correlation- optical criteria of early diagnostics of pathological changes' appearance of myometry (forming of the germ of fibromyoma) and of skin (psoriasis) are determined. The present paper examines the possibilities of diagnostics of pathological changes of biotissues' morphological structure by means of determining the polarizationally filtered autocorrelation functions (ACF) and corresponding spectral densities of their coherent images.

Multifractal Downscaling of Rainfall Using Normalized Difference Vegetation Index (NDVI) in the Andes Plateau.

PubMed

Duffaut Espinosa, L A; Posadas, A N; Carbajal, M; Quiroz, R

2017-01-01

In this paper, a multifractal downscaling technique is applied to adequately transformed and lag corrected normalized difference vegetation index (NDVI) in order to obtain daily estimates of rainfall in an area of the Peruvian Andean high plateau. This downscaling procedure is temporal in nature since the original NDVI information is provided at an irregular temporal sampling period between 8 and 11 days, and the desired final scale is 1 day. The spatial resolution of approximately 1 km remains the same throughout the downscaling process. The results were validated against on-site measurements of meteorological stations distributed in the area under study.

Multifractal Downscaling of Rainfall Using Normalized Difference Vegetation Index (NDVI) in the Andes Plateau

PubMed Central

Posadas, A. N.; Carbajal, M.; Quiroz, R.

2017-01-01

In this paper, a multifractal downscaling technique is applied to adequately transformed and lag corrected normalized difference vegetation index (NDVI) in order to obtain daily estimates of rainfall in an area of the Peruvian Andean high plateau. This downscaling procedure is temporal in nature since the original NDVI information is provided at an irregular temporal sampling period between 8 and 11 days, and the desired final scale is 1 day. The spatial resolution of approximately 1 km remains the same throughout the downscaling process. The results were validated against on-site measurements of meteorological stations distributed in the area under study. PMID:28125607

Multifractal resilience and viability

NASA Astrophysics Data System (ADS)

Tchiguirinskaia, I.; Schertzer, D. J. M.

2017-12-01

The term resilience has become extremely fashionable and there had been many attempts to provide operational definition and in fact metrics going beyond a set of more or less ad-hoc indicators. The viability theory (Aubin and Saint-Pierre, 2011) have been used to give a rather precise mathematical definition of resilience (Deffuant and Gilbert, 2011). However, it does not grasp the multiscale nature of resilience that is rather fundamental as particularly stressed by Folke et al (2010). In this communication, we first recall a preliminary attempt (Tchiguirinskaia et al., 2014) to define multifractal resilience with the help of the maximal probable singularity. Then we extend this multifractal approach to the capture basin of the viability, therefore the resilient basin. Aubin, J P, A. Bayen, and P Saint-Pierre (2011). Viability Theory. New Directions. Springer, Berlin,. Deffuant, G. and Gilbert, N. (eds) (2011) Viability and Resilience of Complex Systems. Springer Berlin.Folke, C., S R Carpenter, B Walker, M Sheffer, T Chapin, and J Rockstroem (2010). Resilience thinking: integrating re- silience, adaptability and transformability. Ecology and So- ciety, 14(4):20, Tchiguirinskaia,I., D. Schertzer, , A. Giangola-Murzyn and T. C. Hoang (2014). Multiscale resilience metrics to assess flood. Proceedings of ICCSA 2014, Normandie University, Le Havre, France -.

ABC of multi-fractal spacetimes and fractional sea turtles

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca

2016-04-01

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

Black holes in multi-fractional and Lorentz-violating models.

PubMed

Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele

2017-01-01

We study static and radially symmetric black holes in the multi-fractional theories of gravity with q -derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length [Formula: see text]. In the q -derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to [Formula: see text]. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q -derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.

Multifractal characterisation of a simulated surface flow: A case study with Multi-Hydro in Jouy-en-Josas, France

NASA Astrophysics Data System (ADS)

Gires, Auguste; Abbes, Jean-Baptiste; da Silva Rocha Paz, Igor; Tchiguirinskaia, Ioulia; Schertzer, Daniel

2018-03-01

In this paper we suggest to innovatively use scaling laws and more specifically Universal Multifractals (UM) to analyse simulated surface runoff and compare the retrieved scaling features with the rainfall ones. The methodology is tested on a 3 km2 semi-urbanised with a steep slope study area located in the Paris area along the Bièvre River. First Multi-Hydro, a fully distributed model is validated on this catchment for four rainfall events measured with the help of a C-band radar. The uncertainty associated with small scale unmeasured rainfall, i.e. occurring below the 1 km × 1 km × 5 min observation scale, is quantified with the help of stochastic downscaled rainfall fields. It is rather significant for simulated flow and more limited on overland water depth for these rainfall events. Overland depth is found to exhibit a scaling behaviour over small scales (10 m-80 m) which can be related to fractal features of the sewer network. No direct and obvious dependency between the overland depth multifractal features (quality of the scaling and UM parameters) and the rainfall ones was found.

Intrapartum fetal heart rate classification from trajectory in Sparse SVM feature space.

PubMed

Spilka, J; Frecon, J; Leonarduzzi, R; Pustelnik, N; Abry, P; Doret, M

2015-01-01

Intrapartum fetal heart rate (FHR) constitutes a prominent source of information for the assessment of fetal reactions to stress events during delivery. Yet, early detection of fetal acidosis remains a challenging signal processing task. The originality of the present contribution are three-fold: multiscale representations and wavelet leader based multifractal analysis are used to quantify FHR variability ; Supervised classification is achieved by means of Sparse-SVM that aim jointly to achieve optimal detection performance and to select relevant features in a multivariate setting ; Trajectories in the feature space accounting for the evolution along time of features while labor progresses are involved in the construction of indices quantifying fetal health. The classification performance permitted by this combination of tools are quantified on a intrapartum FHR large database (≃ 1250 subjects) collected at a French academic public hospital.

Pointwise regularity of parameterized affine zipper fractal curves

NASA Astrophysics Data System (ADS)

Bárány, Balázs; Kiss, Gergely; Kolossváry, István

2018-05-01

We study the pointwise regularity of zipper fractal curves generated by affine mappings. Under the assumption of dominated splitting of index-1, we calculate the Hausdorff dimension of the level sets of the pointwise Hölder exponent for a subinterval of the spectrum. We give an equivalent characterization for the existence of regular pointwise Hölder exponent for Lebesgue almost every point. In this case, we extend the multifractal analysis to the full spectrum. In particular, we apply our results for de Rham’s curve.

Dissipation, intermittency, and singularities in incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Debue, P.; Shukla, V.; Kuzzay, D.; Faranda, D.; Saw, E.-W.; Daviaud, F.; Dubrulle, B.

2018-05-01

We examine the connection between the singularities or quasisingularities in the solutions of the incompressible Navier-Stokes equation (INSE) and the local energy transfer and dissipation, in order to explore in detail how the former contributes to the phenomenon of intermittency. We do so by analyzing the velocity fields (a) measured in the experiments on the turbulent von Kármán swirling flow at high Reynolds numbers and (b) obtained from the direct numerical simulations of the INSE at a moderate resolution. To compute the local interscale energy transfer and viscous dissipation in experimental and supporting numerical data, we use the weak solution formulation generalization of the Kármán-Howarth-Monin equation. In the presence of a singularity in the velocity field, this formulation yields a nonzero dissipation (inertial dissipation) in the limit of an infinite resolution. Moreover, at finite resolutions, it provides an expression for local interscale energy transfers down to the scale where the energy is dissipated by viscosity. In the presence of a quasisingularity that is regularized by viscosity, the formulation provides the contribution to the viscous dissipation due to the presence of the quasisingularity. Therefore, our formulation provides a concrete support to the general multifractal description of the intermittency. We present the maps and statistics of the interscale energy transfer and show that the extreme events of this transfer govern the intermittency corrections and are compatible with a refined similarity hypothesis based on this transfer. We characterize the probability distribution functions of these extreme events via generalized Pareto distribution analysis and find that the widths of the tails are compatible with a similarity of the second kind. Finally, we make a connection between the topological and the statistical properties of the extreme events of the interscale energy transfer field and its multifractal properties.

Multiscale Resilience of Complex Systems

NASA Astrophysics Data System (ADS)

Tchiguirinskaia, I.; Schertzer, D. J. M.; Giangola-Murzyn, A.; Hoang Cong, T.

2014-12-01

We first argue the need for well defined resilience metrics to better evaluate the resilience of complex systems such as (peri-)urban flood management systems. We review both the successes and limitations of resilience metrics in the framework of dynamical systems and their generalization in the framework of the viability theory. We then point out that the most important step to achieve is to define resilience across scales instead of doing it at a given scale. Our preliminary, critical analysis of the series of attempts to define an operational resilience metrics led us to consider a scale invariant metrics based on the scale independent codimension of extreme singularities. Multifractal downscaling of climate scenarios can be considered as a first illustration. We focussed on a flood scenario evaluation method with the help of two singularities γ_s and γ_Max, corresponding respectively to an effective and a probable maximum singularity, that yield an innovative framework to address the issues of flood resilience systems in a scale independent manner. Indeed, the stationarity of the universal multifractal parameters would result into a rather stable value of probable maximum singularity γ_s. By fixing the limit of acceptability for a maximum flood water depth at a given scale, with a corresponding singularity, we effectively fix the threshold of the probable maximum singularity γ_s as a criterion of the flood resilience we accept. Then various scenarios of flood resilient measures could be simulated with the help of Multi-Hydro under upcoming climat scenarios. The scenarios that result in estimates of either γ_Max or γ_s below the pre-selected γ_s value will assure the effective flood resilience of the whole modeled system across scales. The research for this work was supported, in part, by the EU FP7 SMARTesT and INTERREG IVB RainGain projects.

An analysis of the financial crisis in the KOSPI market using Hurst exponents

NASA Astrophysics Data System (ADS)

Yim, Kyubin; Oh, Gabjin; Kim, Seunghwan

2014-09-01

Recently, the study of the financial crisis has progressed to include the concept of the complex system, thereby improving the understanding of this extreme event from a neoclassical economic perspective. To determine which variables are related to the financial event caused by the 2008 US subprime crisis using temporal correlations, we investigate the diverse variables that may explain the financial system. These variables include return, volatility, trading volume and inter-trade duration data sets within the TAQ data for 27 highly capitalized individual companies listed on the KOSPI stock market. During 2008 and 2009, the Hurst exponent for the return time series over the whole period was less than 0.5, and the Hurst exponents for other variables, such as the volatility, trading volume and inter-trade duration, were greater than 0.5. Additionally, we analyze the relationships between the variation of temporal correlation and market instability based on these Hurst exponents and the degree of multifractality. We find that for the data related to trading volume, the Hurst exponents do not allow us to detect changes in market status, such as changes from normal to abnormal status, whereas other variables, including the return, volatility and weekly inter-trade duration, indicate a significant change in market status after the Lehman Brothers' bankruptcy. In addition, the multifractality and the measurement defined by subtracting the Hurst exponent of the return time series from that of the volatility time series decrease sharply after the US subprime event and recover approximately 50 days after the Lehman Brothers' collapse. Our findings suggest that the temporal features of financial quantities in the TAQ data set and the market complexity perform very well at diagnosing financial market stability.

Annual Rainfall Maxima: Theoretical Estimation of the GEV Shape Parameter k Using Multifractal Models

NASA Astrophysics Data System (ADS)

Veneziano, D.; Langousis, A.; Lepore, C.

2009-12-01

The annual maximum of the average rainfall intensity in a period of duration d, Iyear(d), is typically assumed to have generalized extreme value (GEV) distribution. The shape parameter k of that distribution is especially difficult to estimate from either at-site or regional data, making it important to constraint k using theoretical arguments. In the context of multifractal representations of rainfall, we observe that standard theoretical estimates of k from extreme value (EV) and extreme excess (EE) theories do not apply, while estimates from large deviation (LD) theory hold only for very small d. We then propose a new theoretical estimator based on fitting GEV models to the numerically calculated distribution of Iyear(d). A standard result from EV and EE theories is that k depends on the tail behavior of the average rainfall in d, I(d). This result holds if Iyear(d) is the maximum of a sufficiently large number n of variables, all distributed like I(d); therefore its applicability hinges on whether n = 1yr/d is large enough and the tail of I(d) is sufficiently well known. One typically assumes that at least for small d the former condition is met, but poor knowledge of the upper tail of I(d) remains an obstacle for all d. In fact, in the case of multifractal rainfall, also the first condition is not met because, irrespective of d, 1yr/d is too small (Veneziano et al., 2009, WRR, in press). Applying large deviation (LD) theory to this multifractal case, we find that, as d → 0, Iyear(d) approaches a GEV distribution whose shape parameter kLD depends on a region of the distribution of I(d) well below the upper tail, is always positive (in the EV2 range), is much larger than the value predicted by EV and EE theories, and can be readily found from the scaling properties of I(d). The scaling properties of rainfall can be inferred also from short records, but the limitation remains that the result holds under d → 0 not for finite d. Therefore, for different reasons, none of the above asymptotic theories applies to Iyear(d). In practice, one is interested in the distribution of Iyear(d) over a finite range of averaging durations d and return periods T. Using multifractal representations of rainfall, we have numerically calculated the distribution of Iyear(d) and found that, although not GEV, the distribution can be accurately approximated by a GEV model. The best-fitting parameter k depends on d, but is insensitive to the scaling properties of rainfall and the range of return periods T used for fitting. We have obtained a default expression for k(d) and compared it with estimates from historical rainfall records. The theoretical function tracks well the empirical dependence on d, although it generally overestimates the empirical k values, possibly due to deviations of rainfall from perfect scaling. This issue is under investigation.

Comparison of detrending methods for fluctuation analysis in hydrology

NASA Astrophysics Data System (ADS)

Zhang, Qiang; Zhou, Yu; Singh, Vijay P.; Chen, Yongqin David

2011-03-01

SummaryTrends within a hydrologic time series can significantly influence the scaling results of fluctuation analysis, such as rescaled range (RS) analysis and (multifractal) detrended fluctuation analysis (MF-DFA). Therefore, removal of trends is important in the study of scaling properties of the time series. In this study, three detrending methods, including adaptive detrending algorithm (ADA), Fourier-based method, and average removing technique, were evaluated by analyzing numerically generated series and observed streamflow series with obvious relative regular periodic trend. Results indicated that: (1) the Fourier-based detrending method and ADA were similar in detrending practices, and given proper parameters, these two methods can produce similarly satisfactory results; (2) detrended series by Fourier-based detrending method and ADA lose the fluctuation information at larger time scales, and the location of crossover points is heavily impacted by the chosen parameters of these two methods; and (3) the average removing method has an advantage over the other two methods, i.e., the fluctuation information at larger time scales is kept well-an indication of relatively reliable performance in detrending. In addition, the average removing method performed reasonably well in detrending a time series with regular periods or trends. In this sense, the average removing method should be preferred in the study of scaling properties of the hydrometeorolgical series with relative regular periodic trend using MF-DFA.

Hierarchical coefficient of a multifractal based network

NASA Astrophysics Data System (ADS)

Moreira, Darlan A.; Lucena, Liacir dos Santos; Corso, Gilberto

2014-02-01

The hierarchical property for a general class of networks stands for a power-law relation between clustering coefficient, CC and connectivity k: CC∝kβ. This relation is empirically verified in several biologic and social networks, as well as in random and deterministic network models, in special for hierarchical networks. In this work we show that the hierarchical property is also present in a Lucena network. To create a Lucena network we use the dual of a multifractal lattice ML, the vertices are the sites of the ML and links are established between neighbouring lattices, therefore this network is space filling and planar. Besides a Lucena network shows a scale-free distribution of connectivity. We deduce a relation for the maximal local clustering coefficient CCimax of a vertex i in a planar graph. This condition expresses that the number of links among neighbour, N△, of a vertex i is equal to its connectivity ki, that means: N△=ki. The Lucena network fulfils the condition N△≃ki independent of ki and the anisotropy of ML. In addition, CCmax implies the threshold β=1 for the hierarchical property for any scale-free planar network.

Scaling in cognitive performance reflects multiplicative multifractal cascade dynamics

PubMed Central

Stephen, Damian G.; Anastas, Jason R.; Dixon, James A.

2012-01-01

Self-organized criticality purports to build multi-scaled structures out of local interactions. Evidence of scaling in various domains of biology may be more generally understood to reflect multiplicative interactions weaving together many disparate scales. The self-similarity of power-law scaling entails homogeneity: fluctuations distribute themselves similarly across many spatial and temporal scales. However, this apparent homogeneity can be misleading, especially as it spans more scales. Reducing biological processes to one power-law relationship neglects rich cascade dynamics. We review recent research into multifractality in executive-function cognitive tasks and propose that scaling reflects not criticality but instead interactions across multiple scales and among fluctuations of multiple sizes. PMID:22529819

[Fractal characteristics of the functional state of the brain in patients with anxious phobic disorders].

PubMed

Dik, O E; Sviatogor, I A; Ishinova, V A; Nozdrachev, A D

2012-01-01

The task of estimation of the functional state of the human brain during psychotherapeutic treatment of psychogenic pain in patients with anxious phobic disorders is examined. For solving the task the methods of spectral and multifractal analyses of EEG fragments are applied during the perception of psychogenic pain and its removal by the psychorelaxation technique. Contrary to power spectra singularity spectra allow to distinguish EEGs quanitatively in the examined functional states of the human brain. The pain suppression in patients with anxious phobic disorders during psychorelaxation is accompanied by changing the width of the singularity spectrum and approximation of this multifractal partameter to the value corresponding to a healthy subject.

Structural characterization of a magnetic granular system under a time-dependent magnetic field: Voronoi tessellation and multifractal analysis

NASA Astrophysics Data System (ADS)

Moctezuma, R. E.; Arauz-Lara, J. L.; Donado, F.

2018-04-01

The structure of a two-dimensional magnetic granular system was determined by multifractal and Voronoi polygon analysis for a wide range of particle concentrations. Randomizing of the particle motions are produced by applying to the system a time-dependent sinusoidal magnetic field directed along the vertical direction. Both repulsive and attractive short-range interactions between the particles are induced. A direct observation of such system shows qualitatively that, as particle concentration increases, the structure evolves from being liquid-like at low particle concentrations to solid-like at high concentrations. We observe the formation of clusters which are small and weakly bonded and short-lived at low concentrations. Above a threshold particle concentration, clusters grow larger and are more strongly attached. In the system, one can distinguish the mobile particles from the immobile particles belonging to clusters, they can be considered separately as two different phases, a fluid and a solid. We determined the information entropy of the system as a whole and separately from each phase as particle concentration increases. The distribution of the Voronoi polygon areas are well fitted by a two-parameter gamma distribution and we have found that the regularity factor shows a notable change when pieces of the solid phase start to form. The methods we use here show that they can use even when the system is heterogeneous and they provide information when changes start.

A picture for the coupling of unemployment and inflation

NASA Astrophysics Data System (ADS)

Safdari, H.; Hosseiny, A.; Vasheghani Farahani, S.; Jafari, G. R.

2016-02-01

The aim of this article is to illustrate the scaling features of two well heard characters in the media; unemployment and inflation. We carry out a scaling analysis on the coupling between unemployment and inflation. This work is based on the wavelet analysis as well as the detrended fluctuation analysis (DFA). Through our analysis we state that while unemployment is time scale invariant, inflation is bi-scale. We show that inflation possess a five year time scale where it experiences different behaviours before and after this scale period. This behaviour of inflation provides basis for the coupling to inherit the stated time interval. Although inflation is bi-scale, it is unemployment that shows a strong multifractality feature. Owing to the cross wavelet analysis we provide a picture that illustrates the dynamics of coupling between unemployment and inflation regarding intensity, direction, and scale. The fact of the matter is that the coupling between inflation and unemployment is not equal in one way compared to the opposite. Regarding the scaling; coupling exhibits different features in various scales. In a sense that although in one scale its correlation behaves in a positive/negative manner, at the same time it can be negative/positive for another scale.

Multifractal Model of Soil Water Erosion

NASA Astrophysics Data System (ADS)

Oleshko, Klaudia

2017-04-01

Breaking of solid surface symmetry during the interaction between the rainfall of high erosivity index and internally unstable volcanic soil/vegetation systems, results in roughness increasing as well as fertile horizon loosing. In these areas, the sustainability of management practices depends on the ability to select and implement the precise indicators of soil erodibility and vegetation capacity to protect the system against the extreme damaging precipitation events. Notwithstanding, the complex, non-linear and scaling nature of the phenomena involved in the interaction among the soil, vegetation and precipitation is still not taken into account by the numerous commonly used empirical, mathematical and computer simulation models: for instance, by the universal soil loss equation (USLE). The soil erodibility factor (K-factor) is still measuring by a set of empirical, dimensionless parameters and indexes, without taking into account the scaling (frequently multifractal) origin of a broad range of heterogeneous, anisotropic and dynamical phenomena involved in hydric erosion. Their mapping is not representative of this complex system spatial variability. In our research, we propose to use the toolbox of fractals and multifractals techniques in vista of its ability to measure the scale invariance and type/degree of soil, vegetation and precipitation symmetry breaking. The hydraulic units are chosen as the precise measure of soil/vegetation stability. These units are measured and modeled for soils with contrasting architecture, based on their porosity/permeability (Poroperm) as well as retention capacity relations. The simple Catalog of the most common Poroperm relations is proposed and the main power law relations among the elements of studied system are established and compared for some representative agricultural and natural Biogeosystems of Mexico. All resulted are related with the Mandelbrot' Baby Theorem in order to construct the universal Phase Diagram which graphically represents the critical points of the dynamics of soil erodibility as function of the vegetation cover and precipitation parameters.

Multiscale Analysis of the Water Content Output the NWP Model COSMO Over Switzerland and Comparison With Radar Data

NASA Astrophysics Data System (ADS)

Wolfensberger, D.; Gires, A.; Berne, A.; Tchiguirinskaia, I.; Schertzer, D. J. M.

2015-12-01

The resolution of operational numerical prediction models is typically of the order of a few kilometres meaning that small-scale features of precipitation can not be resolved explicitly. This creates the need for representative parametrizations of microphysical processes whose properties should be carefully analysed. In this study we will focus on the COSMO model which is a non-hydrostatic limited-area model, initially developed as the Lokal Model and used operationally in Switzerland and Germany. In its operational version, cloud microphysical processes are simulated with a one-moment bulk scheme where five hydrometeor classes are considered: cloud droplets, rain, ice crystals, snow, and graupel. A more sophisticated two-moment scheme is also available. The study will focus on two case studies: one in Payerne in western Switzerland in a relatively flat region and one in Davos in the eastern Swiss Alps in a more complex terrain.The objective of this work is to characterize the ability of the COSMO NWP model to reproduce the microphysics of precipitation across temporal and spatial scales as well as scaling variability. The characterization of COSMO outputs will rely on the Universal Multifractals framework, which allows to analyse and simulate geophysical fields extremely variabile over a wide range of scales with the help of a reduced number of parameters. First COSMO outputs are analysed; spatial multifractal analysis of 2D maps at various altitudes for each time steps are carried out for simulated solid, liquid, vapour and total water content. In general the fields exhibit a good quality of scaling on the whole range of available scales (2 km - 250 km), but some loss of scaling quality corresponding to the emergence of a scaling break are sometimes visible. This behaviour is not found at the same time or at the same altitude according to the water state and does not necessarily spread to the total water content. It is interpreted with the help of the underlying physical process at stake during the events.Second Multifractal comparisons of model outputs will also be made with radar data provided by the Meteo Swiss, both indirectly in terms of precipitation intensities and directly using a polarimetric forward radar operator which is able to simulate radar observations from model outputs.

Are galaxy distributions scale invariant? A perspective from dynamical systems theory

NASA Astrophysics Data System (ADS)

McCauley, J. L.

2002-06-01

Unless there is an evidence for fractal scaling with a single exponent over distances 0.1<=r<=100h-1Mpc, then the widely accepted notion of scale invariance of the correlation integral for 0.1<=r<=10h-1Mpc must be questioned. The attempt to extract a scaling exponent /ν from the correlation integral /n(r) by plotting /log(n(r)) vs. /log(r) is unreliable unless the underlying point set is approximately monofractal. The extraction of a spectrum of generalized dimensions νq from a plot of the correlation integral generating function Gn(q) by a similar procedure is probably an indication that Gn(q) does not scale at all. We explain these assertions after defining the term multifractal, mutually inconsistent definitions having been confused together in the cosmology literature. Part of this confusion is traced to the confusion in interpreting a measure-theoretic formula written down by Hentschel and Procaccia in the dynamical systems theory literature, while other errors follow from confusing together entirely different definitions of multifractal from two different schools of thought. Most important are serious errors in data analysis that follow from taking for granted a largest term approximation that is inevitably advertised in the literature on both fractals and dynamical systems theory.

Multifractal analysis of Asian markets during 2007-2008 financial crisis

NASA Astrophysics Data System (ADS)

Hasan, Rashid; Mohammad, Salim M.

2015-02-01

2007-2008 US financial crisis adversely affected the stock markets all over the world. Asian markets also came under pressure and were differently affected. As markets under stress could reveal features that remain hidden under normal conditions, we use MF-DFA technique to investigate the multifractal structure of the US and seven Asian stock markets during the crisis period. The overall period of study, from 01 July 2002 to 31 December 2013, is divided into three sub-periods: pre-crisis period, crisis period and post-crisis period. We find during the crisis period markets of the US, Japan, Hong Kong, S. Korea and Indonesia show very strong non-linearity for positive values of the moment q. We calculate the singularity spectra, f(α) for the three sub-periods for all markets. During the crisis period, we observe that the peaks of the f(α) spectra shift to lower values of α and markets of the US, Japan, Hong Kong, Korea and Indonesia exhibit increased long range correlations of large fluctuations in index returns. We also study the impact of the crisis on the power law exponent in the tail region of the cumulative return distribution and find that by excluding the crisis period from the overall data sets, the tail exponent increases across all markets.

Modeling the complexity of acoustic emission during intermittent plastic deformation: Power laws and multifractal spectra

NASA Astrophysics Data System (ADS)

Kumar, Jagadish; Ananthakrishna, G.

2018-01-01

Scale-invariant power-law distributions for acoustic emission signals are ubiquitous in several plastically deforming materials. However, power-law distributions for acoustic emission energies are reported in distinctly different plastically deforming situations such as hcp and fcc single and polycrystalline samples exhibiting smooth stress-strain curves and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there have been no models that predict the power-law statistics for discontinuous flow. Furthermore, the statistics of the acoustic emission signals in jerky flow is even more complex, requiring multifractal measures for a proper characterization. There has been no model that explains the complex statistics either. Here we address the problem of statistical characterization of the acoustic emission signals associated with the three types of the Portevin-Le Chatelier bands. Following our recently proposed general framework for calculating acoustic emission, we set up a wave equation for the elastic degrees of freedom with a plastic strain rate as a source term. The energy dissipated during acoustic emission is represented by the Rayleigh-dissipation function. Using the plastic strain rate obtained from the Ananthakrishna model for the Portevin-Le Chatelier effect, we compute the acoustic emission signals associated with the three Portevin-Le Chatelier bands and the Lüders-like band. The so-calculated acoustic emission signals are used for further statistical characterization. Our results show that the model predicts power-law statistics for all the acoustic emission signals associated with the three types of Portevin-Le Chatelier bands with the exponent values increasing with increasing strain rate. The calculated multifractal spectra corresponding to the acoustic emission signals associated with the three band types have a maximum spread for the type C bands and decreasing with types B and A. We further show that the acoustic emission signals associated with Lüders-like band also exhibit a power-law distribution and multifractality.

Modeling the complexity of acoustic emission during intermittent plastic deformation: Power laws and multifractal spectra.

PubMed

Kumar, Jagadish; Ananthakrishna, G

2018-01-01

Scale-invariant power-law distributions for acoustic emission signals are ubiquitous in several plastically deforming materials. However, power-law distributions for acoustic emission energies are reported in distinctly different plastically deforming situations such as hcp and fcc single and polycrystalline samples exhibiting smooth stress-strain curves and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there have been no models that predict the power-law statistics for discontinuous flow. Furthermore, the statistics of the acoustic emission signals in jerky flow is even more complex, requiring multifractal measures for a proper characterization. There has been no model that explains the complex statistics either. Here we address the problem of statistical characterization of the acoustic emission signals associated with the three types of the Portevin-Le Chatelier bands. Following our recently proposed general framework for calculating acoustic emission, we set up a wave equation for the elastic degrees of freedom with a plastic strain rate as a source term. The energy dissipated during acoustic emission is represented by the Rayleigh-dissipation function. Using the plastic strain rate obtained from the Ananthakrishna model for the Portevin-Le Chatelier effect, we compute the acoustic emission signals associated with the three Portevin-Le Chatelier bands and the Lüders-like band. The so-calculated acoustic emission signals are used for further statistical characterization. Our results show that the model predicts power-law statistics for all the acoustic emission signals associated with the three types of Portevin-Le Chatelier bands with the exponent values increasing with increasing strain rate. The calculated multifractal spectra corresponding to the acoustic emission signals associated with the three band types have a maximum spread for the type C bands and decreasing with types B and A. We further show that the acoustic emission signals associated with Lüders-like band also exhibit a power-law distribution and multifractality.

Improved brain tumor segmentation by utilizing tumor growth model in longitudinal brain MRI

NASA Astrophysics Data System (ADS)

Pei, Linmin; Reza, Syed M. S.; Li, Wei; Davatzikos, Christos; Iftekharuddin, Khan M.

2017-03-01

In this work, we propose a novel method to improve texture based tumor segmentation by fusing cell density patterns that are generated from tumor growth modeling. To model tumor growth, we solve the reaction-diffusion equation by using Lattice-Boltzmann method (LBM). Computational tumor growth modeling obtains the cell density distribution that potentially indicates the predicted tissue locations in the brain over time. The density patterns is then considered as novel features along with other texture (such as fractal, and multifractal Brownian motion (mBm)), and intensity features in MRI for improved brain tumor segmentation. We evaluate the proposed method with about one hundred longitudinal MRI scans from five patients obtained from public BRATS 2015 data set, validated by the ground truth. The result shows significant improvement of complete tumor segmentation using ANOVA analysis for five patients in longitudinal MR images.

Improved brain tumor segmentation by utilizing tumor growth model in longitudinal brain MRI.

PubMed

Pei, Linmin; Reza, Syed M S; Li, Wei; Davatzikos, Christos; Iftekharuddin, Khan M

2017-02-11

In this work, we propose a novel method to improve texture based tumor segmentation by fusing cell density patterns that are generated from tumor growth modeling. In order to model tumor growth, we solve the reaction-diffusion equation by using Lattice-Boltzmann method (LBM). Computational tumor growth modeling obtains the cell density distribution that potentially indicates the predicted tissue locations in the brain over time. The density patterns is then considered as novel features along with other texture (such as fractal, and multifractal Brownian motion (mBm)), and intensity features in MRI for improved brain tumor segmentation. We evaluate the proposed method with about one hundred longitudinal MRI scans from five patients obtained from public BRATS 2015 data set, validated by the ground truth. The result shows significant improvement of complete tumor segmentation using ANOVA analysis for five patients in longitudinal MR images.

The q-dependent detrended cross-correlation analysis of stock market

NASA Astrophysics Data System (ADS)

Zhao, Longfeng; Li, Wei; Fenu, Andrea; Podobnik, Boris; Wang, Yougui; Stanley, H. Eugene

2018-02-01

Properties of the q-dependent cross-correlation matrices of the stock market have been analyzed by using random matrix theory and complex networks. The correlation structures of the fluctuations at different magnitudes have unique properties. The cross-correlations among small fluctuations are much stronger than those among large fluctuations. The large and small fluctuations are dominated by different groups of stocks. We use complex network representation to study these q-dependent matrices and discover some new identities. By utilizing those q-dependent correlation-based networks, we are able to construct some portfolios of those more independent stocks which consistently perform better. The optimal multifractal order for portfolio optimization is around q  =  2 under the mean-variance portfolio framework, and q\\in[2, 6] under the expected shortfall criterion. These results have deepened our understanding regarding the collective behavior of the complex financial system.

The Analysis of Eigenstates of a Few Generalized Quantum Baker’s Maps Using Hadamard and Related Transforms

NASA Astrophysics Data System (ADS)

Meenakshisundaram, N.

Application of the Hadamard and related transforms on a few generalized quantum baker’s maps have been studied. Effectiveness of the Hadamard transform and a new transform which combines the Fourier and the Hadamard transforms, for simplifying the eigenstates or resonances of the quantization of a few generalized baker’s map namely tetradic baker and lazy baker’s map when the Hilbert space dimension is power of 2 has been done by comparing the participation ratios in the transformed basis with respect to the position basis. Several special family of states based on their maximal compression in either Hadamard transform or the new transform are identified and they are related to the ubiquitous Thue-Morse and allied sequences. Evidence is provided that these special family of states as well as average over all eigenstates exhibits multifractal nature.

The multifractal nature of plume structure in high-Rayleigh-number convection

NASA Astrophysics Data System (ADS)

Puthenveettil, Baburaj A.; Ananthakrishna, G.; Arakeri, Jaywant H.

2005-03-01

The geometrically different planforms of near-wall plume structure in turbulent natural convection, visualized by driving the convection using concentration differences across a membrane, are shown to have a common multifractal spectrum of singularities for Rayleigh numbers in the range 1010-1011 at Schmidt number of 602. The scaling is seen for a length scale range of 25 and is independent of the Rayleigh number, the flux, the strength and nature of the large-scale flow, and the aspect ratio. Similar scaling is observed for the plume structures obtained in the presence of a weak flow across the membrane. This common non-trivial spatial scaling is proposed to be due to the same underlying generating process for the near-wall plume structures.

Sign and magnitude scaling properties of heart rate variability in patients with end-stage renal failure: Are these properties useful to identify pathophysiological adaptations?

NASA Astrophysics Data System (ADS)

Lerma, Claudia; Echeverría, Juan C.; Infante, Oscar; Pérez-Grovas, Héctor; González-Gómez, Hortensia

2017-09-01

The scaling properties of heart rate variability data are reliable dynamical features to predict mortality and for the assessment of cardiovascular risk. The aim of this manuscript was to determine if the scaling properties, as provided by the sign and magnitude analysis, can be used to differentiate between pathological changes and those adaptations basically introduced by modifications of the mean heart rate in distinct manoeuvres (active standing or hemodialysis treatment, HD), as well as clinical conditions (end stage renal disease, ESRD). We found that in response to active standing, the short-term scaling index (α1) increased in healthy subjects and in ESRD patients only after HD. The sign short-term scaling exponent (α1sign) increased in healthy subjects and ESRD patients, showing a less anticorrelated behavior in active standing. Both α1 and α1sign did show covariance with the mean heart rate in healthy subjects, while in ESRD patients, this covariance was observed only after HD. A reliable estimation of the magnitude short-term scaling exponent (α1magn) required the analysis of time series with a large number of samples (>3000 data points). This exponent was similar for both groups and conditions and did not show covariance with the mean heart rate. A surrogate analysis confirmed the presence of multifractal properties (α1magn > 0.5) in the time series of healthy subjects and ESDR patients. In conclusion, α1 and α1sign provided insights into the physiological adaptations during active standing, which revealed a transitory impairment before HD in ESRD patients. The presence of multifractal properties indicated that a reduced short-term variability does not necessarily imply a declined regulatory complexity in these patients.

Sign and magnitude scaling properties of heart rate variability in patients with end-stage renal failure: Are these properties useful to identify pathophysiological adaptations?

PubMed

Lerma, Claudia; Echeverría, Juan C; Infante, Oscar; Pérez-Grovas, Héctor; González-Gómez, Hortensia

2017-09-01

The scaling properties of heart rate variability data are reliable dynamical features to predict mortality and for the assessment of cardiovascular risk. The aim of this manuscript was to determine if the scaling properties, as provided by the sign and magnitude analysis, can be used to differentiate between pathological changes and those adaptations basically introduced by modifications of the mean heart rate in distinct manoeuvres (active standing or hemodialysis treatment, HD), as well as clinical conditions (end stage renal disease, ESRD). We found that in response to active standing, the short-term scaling index (α 1 ) increased in healthy subjects and in ESRD patients only after HD. The sign short-term scaling exponent (α 1sign ) increased in healthy subjects and ESRD patients, showing a less anticorrelated behavior in active standing. Both α 1 and α 1sign did show covariance with the mean heart rate in healthy subjects, while in ESRD patients, this covariance was observed only after HD. A reliable estimation of the magnitude short-term scaling exponent (α 1magn ) required the analysis of time series with a large number of samples (>3000 data points). This exponent was similar for both groups and conditions and did not show covariance with the mean heart rate. A surrogate analysis confirmed the presence of multifractal properties (α 1magn  > 0.5) in the time series of healthy subjects and ESDR patients. In conclusion, α 1 and α 1sign provided insights into the physiological adaptations during active standing, which revealed a transitory impairment before HD in ESRD patients. The presence of multifractal properties indicated that a reduced short-term variability does not necessarily imply a declined regulatory complexity in these patients.

Investigation of market efficiency and Financial Stability between S&P 500 and London Stock Exchange: Monthly and yearly Forecasting of Time Series Stock Returns using ARMA model

NASA Astrophysics Data System (ADS)

Rounaghi, Mohammad Mahdi; Nassir Zadeh, Farzaneh

2016-08-01

We investigated the presence and changes in, long memory features in the returns and volatility dynamics of S&P 500 and London Stock Exchange using ARMA model. Recently, multifractal analysis has been evolved as an important way to explain the complexity of financial markets which can hardly be described by linear methods of efficient market theory. In financial markets, the weak form of the efficient market hypothesis implies that price returns are serially uncorrelated sequences. In other words, prices should follow a random walk behavior. The random walk hypothesis is evaluated against alternatives accommodating either unifractality or multifractality. Several studies find that the return volatility of stocks tends to exhibit long-range dependence, heavy tails, and clustering. Because stochastic processes with self-similarity possess long-range dependence and heavy tails, it has been suggested that self-similar processes be employed to capture these characteristics in return volatility modeling. The present study applies monthly and yearly forecasting of Time Series Stock Returns in S&P 500 and London Stock Exchange using ARMA model. The statistical analysis of S&P 500 shows that the ARMA model for S&P 500 outperforms the London stock exchange and it is capable for predicting medium or long horizons using real known values. The statistical analysis in London Stock Exchange shows that the ARMA model for monthly stock returns outperforms the yearly. ​A comparison between S&P 500 and London Stock Exchange shows that both markets are efficient and have Financial Stability during periods of boom and bust.

Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations

NASA Astrophysics Data System (ADS)

Kwapień, Jarosław; Oświecimka, Paweł; Forczek, Marcin; DroŻdŻ, Stanisław

2017-05-01

Based on a recently proposed q -dependent detrended cross-correlation coefficient, ρq [J. Kwapień, P. Oświęcimka, and S. Drożdż, Phys. Rev. E 92, 052815 (2015), 10.1103/PhysRevE.92.052815], we generalize the concept of the minimum spanning tree (MST) by introducing a family of q -dependent minimum spanning trees (q MST s ) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data. They inherit this ability directly from the coefficients ρq, which are processed here to construct a distance matrix being the input to the MST-constructing Kruskal's algorithm. The conventional MST with detrending corresponds in this context to q =2 . In order to illustrate their performance, we apply the q MSTs to sample empirical data from the American stock market and discuss the results. We show that the q MST graphs can complement ρq in disentangling "hidden" correlations that cannot be observed in the MST graphs based on ρDCCA, and therefore, they can be useful in many areas where the multivariate cross-correlations are of interest. As an example, we apply this method to empirical data from the stock market and show that by constructing the q MSTs for a spectrum of q values we obtain more information about the correlation structure of the data than by using q =2 only. More specifically, we show that two sets of signals that differ from each other statistically can give comparable trees for q =2 , while only by using the trees for q ≠2 do we become able to distinguish between these sets. We also show that a family of q MSTs for a range of q expresses the diversity of correlations in a manner resembling the multifractal analysis, where one computes a spectrum of the generalized fractal dimensions, the generalized Hurst exponents, or the multifractal singularity spectra: the more diverse the correlations are, the more variable the tree topology is for different q 's. As regards the correlation structure of the stock market, our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes, while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry.

Correlations in magnitude series to assess nonlinearities: Application to multifractal models and heartbeat fluctuations.

PubMed

Bernaola-Galván, Pedro A; Gómez-Extremera, Manuel; Romance, A Ramón; Carpena, Pedro

2017-09-01

The correlation properties of the magnitude of a time series are associated with nonlinear and multifractal properties and have been applied in a great variety of fields. Here we have obtained the analytical expression of the autocorrelation of the magnitude series (C_{|x|}) of a linear Gaussian noise as a function of its autocorrelation (C_{x}). For both, models and natural signals, the deviation of C_{|x|} from its expectation in linear Gaussian noises can be used as an index of nonlinearity that can be applied to relatively short records and does not require the presence of scaling in the time series under study. In a model of artificial Gaussian multifractal signal we use this approach to analyze the relation between nonlinearity and multifractallity and show that the former implies the latter but the reverse is not true. We also apply this approach to analyze experimental data: heart-beat records during rest and moderate exercise. For each individual subject, we observe higher nonlinearities during rest. This behavior is also achieved on average for the analyzed set of 10 semiprofessional soccer players. This result agrees with the fact that other measures of complexity are dramatically reduced during exercise and can shed light on its relationship with the withdrawal of parasympathetic tone and/or the activation of sympathetic activity during physical activity.

Correlations in magnitude series to assess nonlinearities: Application to multifractal models and heartbeat fluctuations

NASA Astrophysics Data System (ADS)

Bernaola-Galván, Pedro A.; Gómez-Extremera, Manuel; Romance, A. Ramón; Carpena, Pedro

2017-09-01

The correlation properties of the magnitude of a time series are associated with nonlinear and multifractal properties and have been applied in a great variety of fields. Here we have obtained the analytical expression of the autocorrelation of the magnitude series (C|x |) of a linear Gaussian noise as a function of its autocorrelation (Cx). For both, models and natural signals, the deviation of C|x | from its expectation in linear Gaussian noises can be used as an index of nonlinearity that can be applied to relatively short records and does not require the presence of scaling in the time series under study. In a model of artificial Gaussian multifractal signal we use this approach to analyze the relation between nonlinearity and multifractallity and show that the former implies the latter but the reverse is not true. We also apply this approach to analyze experimental data: heart-beat records during rest and moderate exercise. For each individual subject, we observe higher nonlinearities during rest. This behavior is also achieved on average for the analyzed set of 10 semiprofessional soccer players. This result agrees with the fact that other measures of complexity are dramatically reduced during exercise and can shed light on its relationship with the withdrawal of parasympathetic tone and/or the activation of sympathetic activity during physical activity.

Propagation of registration uncertainty during multi-fraction cervical cancer brachytherapy

NASA Astrophysics Data System (ADS)

Amir-Khalili, A.; Hamarneh, G.; Zakariaee, R.; Spadinger, I.; Abugharbieh, R.

2017-10-01

Multi-fraction cervical cancer brachytherapy is a form of image-guided radiotherapy that heavily relies on 3D imaging during treatment planning, delivery, and quality control. In this context, deformable image registration can increase the accuracy of dosimetric evaluations, provided that one can account for the uncertainties associated with the registration process. To enable such capability, we propose a mathematical framework that first estimates the registration uncertainty and subsequently propagates the effects of the computed uncertainties from the registration stage through to the visualizations, organ segmentations, and dosimetric evaluations. To ensure the practicality of our proposed framework in real world image-guided radiotherapy contexts, we implemented our technique via a computationally efficient and generalizable algorithm that is compatible with existing deformable image registration software. In our clinical context of fractionated cervical cancer brachytherapy, we perform a retrospective analysis on 37 patients and present evidence that our proposed methodology for computing and propagating registration uncertainties may be beneficial during therapy planning and quality control. Specifically, we quantify and visualize the influence of registration uncertainty on dosimetric analysis during the computation of the total accumulated radiation dose on the bladder wall. We further show how registration uncertainty may be leveraged into enhanced visualizations that depict the quality of the registration and highlight potential deviations from the treatment plan prior to the delivery of radiation treatment. Finally, we show that we can improve the transfer of delineated volumetric organ segmentation labels from one fraction to the next by encoding the computed registration uncertainties into the segmentation labels.

Time fluctuation analysis of forest fire sequences

NASA Astrophysics Data System (ADS)

Vega Orozco, Carmen D.; Kanevski, Mikhaïl; Tonini, Marj; Golay, Jean; Pereira, Mário J. G.

2013-04-01

Forest fires are complex events involving both space and time fluctuations. Understanding of their dynamics and pattern distribution is of great importance in order to improve the resource allocation and support fire management actions at local and global levels. This study aims at characterizing the temporal fluctuations of forest fire sequences observed in Portugal, which is the country that holds the largest wildfire land dataset in Europe. This research applies several exploratory data analysis measures to 302,000 forest fires occurred from 1980 to 2007. The applied clustering measures are: Morisita clustering index, fractal and multifractal dimensions (box-counting), Ripley's K-function, Allan Factor, and variography. These algorithms enable a global time structural analysis describing the degree of clustering of a point pattern and defining whether the observed events occur randomly, in clusters or in a regular pattern. The considered methods are of general importance and can be used for other spatio-temporal events (i.e. crime, epidemiology, biodiversity, geomarketing, etc.). An important contribution of this research deals with the analysis and estimation of local measures of clustering that helps understanding their temporal structure. Each measure is described and executed for the raw data (forest fires geo-database) and results are compared to reference patterns generated under the null hypothesis of randomness (Poisson processes) embedded in the same time period of the raw data. This comparison enables estimating the degree of the deviation of the real data from a Poisson process. Generalizations to functional measures of these clustering methods, taking into account the phenomena, were also applied and adapted to detect time dependences in a measured variable (i.e. burned area). The time clustering of the raw data is compared several times with the Poisson processes at different thresholds of the measured function. Then, the clustering measure value depends on the threshold which helps to understand the time pattern of the studied events. Our findings detected the presence of overdensity of events in particular time periods and showed that the forest fire sequences in Portugal can be considered as a multifractal process with a degree of time-clustering of the events. Key words: time sequences, Morisita index, fractals, multifractals, box-counting, Ripley's K-function, Allan Factor, variography, forest fires, point process. Acknowledgements This work was partly supported by the SNFS Project No. 200021-140658, "Analysis and Modelling of Space-Time Patterns in Complex Regions". References - Kanevski M. (Editor). 2008. Advanced Mapping of Environmental Data: Geostatistics, Machine Learning and Bayesian Maximum Entropy. London / Hoboken: iSTE / Wiley. - Telesca L. and Pereira M.G. 2010. Time-clustering investigation of fire temporal fluctuations in Portugal, Nat. Hazards Earth Syst. Sci., vol. 10(4): 661-666. - Vega Orozco C., Tonini M., Conedera M., Kanevski M. (2012) Cluster recognition in spatial-temporal sequences: the case of forest fires, Geoinformatica, vol. 16(4): 653-673.

Zipf's Law Application To Oil Spill Detection In The Ocean

NASA Astrophysics Data System (ADS)

Platonov, A.; Redondo, J. M.

One of the results of the CLEAN SEAS European Union project using SAR imaging of European Coastal Waters was the statistical analysis and detection of thousands of oil spills and slicks in the three compared sections, Baltic Sea, North Sea and N.W. Mediterranean. The results of another European Project, OIL WATCH together with the past 30 years of recorded mayor tanker accidental oil spills have been used in a predictive scheme that subject to spatial and temporal normalization of these two different scale processes clearly shows that the annual probability of the occurence of an oil spill follows Zipf's law. Local deviations from the law may be also explained in terms of multifractal analysis.

Multifractal Detrended Fluctuation Analysis of Regional Precipitation Sequences Based on the CEEMDAN-WPT

NASA Astrophysics Data System (ADS)

Liu, Dong; Cheng, Chen; Fu, Qiang; Liu, Chunlei; Li, Mo; Faiz, Muhammad Abrar; Li, Tianxiao; Khan, Muhammad Imran; Cui, Song

2018-03-01

In this paper, the complete ensemble empirical mode decomposition with the adaptive noise (CEEMDAN) algorithm is introduced into the complexity research of precipitation systems to improve the traditional complexity measure method specific to the mode mixing of the Empirical Mode Decomposition (EMD) and incomplete decomposition of the ensemble empirical mode decomposition (EEMD). We combined the CEEMDAN with the wavelet packet transform (WPT) and multifractal detrended fluctuation analysis (MF-DFA) to create the CEEMDAN-WPT-MFDFA, and used it to measure the complexity of the monthly precipitation sequence of 12 sub-regions in Harbin, Heilongjiang Province, China. The results show that there are significant differences in the monthly precipitation complexity of each sub-region in Harbin. The complexity of the northwest area of Harbin is the lowest and its predictability is the best. The complexity and predictability of the middle and Midwest areas of Harbin are about average. The complexity of the southeast area of Harbin is higher than that of the northwest, middle, and Midwest areas of Harbin and its predictability is worse. The complexity of Shuangcheng is the highest and its predictability is the worst of all the studied sub-regions. We used terrain and human activity as factors to analyze the causes of the complexity of the local precipitation. The results showed that the correlations between the precipitation complexity and terrain are obvious, and the correlations between the precipitation complexity and human influence factors vary. The distribution of the precipitation complexity in this area may be generated by the superposition effect of human activities and natural factors such as terrain, general atmospheric circulation, land and sea location, and ocean currents. To evaluate the stability of the algorithm, the CEEMDAN-WPT-MFDFA was compared with the equal probability coarse graining LZC algorithm, fuzzy entropy, and wavelet entropy. The results show that the CEEMDAN-WPT-MFDFA was more stable than 3 contrast methods under the influence of white noise and colored noise, which proves that the CEEMDAN-WPT-MFDFA has a strong robustness under the influence of noise.

Pitfalls in Fractal Time Series Analysis: fMRI BOLD as an Exemplary Case

PubMed Central

Eke, Andras; Herman, Peter; Sanganahalli, Basavaraju G.; Hyder, Fahmeed; Mukli, Peter; Nagy, Zoltan

2012-01-01

This article will be positioned on our previous work demonstrating the importance of adhering to a carefully selected set of criteria when choosing the suitable method from those available ensuring its adequate performance when applied to real temporal signals, such as fMRI BOLD, to evaluate one important facet of their behavior, fractality. Earlier, we have reviewed on a range of monofractal tools and evaluated their performance. Given the advance in the fractal field, in this article we will discuss the most widely used implementations of multifractal analyses, too. Our recommended flowchart for the fractal characterization of spontaneous, low frequency fluctuations in fMRI BOLD will be used as the framework for this article to make certain that it will provide a hands-on experience for the reader in handling the perplexed issues of fractal analysis. The reason why this particular signal modality and its fractal analysis has been chosen was due to its high impact on today’s neuroscience given it had powerfully emerged as a new way of interpreting the complex functioning of the brain (see “intrinsic activity”). The reader will first be presented with the basic concepts of mono and multifractal time series analyses, followed by some of the most relevant implementations, characterization by numerical approaches. The notion of the dichotomy of fractional Gaussian noise and fractional Brownian motion signal classes and their impact on fractal time series analyses will be thoroughly discussed as the central theme of our application strategy. Sources of pitfalls and way how to avoid them will be identified followed by a demonstration on fractal studies of fMRI BOLD taken from the literature and that of our own in an attempt to consolidate the best practice in fractal analysis of empirical fMRI BOLD signals mapped throughout the brain as an exemplary case of potentially wide interest. PMID:23227008

The use of multifractal modelling for targeting resources from soil and stream geochemistry data: the case of the Variscan basement of the Iberian Peninsula

NASA Astrophysics Data System (ADS)

Gonçalves, Mario; Mateus, Antonio

2016-04-01

The safeguarding of access/use of many critical raw materials for Society requires that much of previously dismissed areas for exploration must be re-evaluated with new criteria in which the significance of "anomaly" should not be treated independently of the geochemical signals of the ore-forming processes and how the different chemical elements are interrelated. For much of the previous decade, several multifractal methods were methodically being refined as automatic tools to analyze and detect geochemical anomalies. These included the early concentration-area method (Cheng et al., 1994), singularity mapping (Cheng, 2007), and spectrum-area (Cheng et al., 2000), which has been recently combined with the bi-dimensional empirical mode decomposition (Xu et al., 2016) as a tool to separate different contributing sources of an otherwise complex geochemical pattern. We propose yet another approach, the use of geochemical indexes, which links to the geological and ore-forming processes known to define a given region in order to assess much of these numerical approaches. Therefore, we picked several areas from the Variscan basement in Portugal, with different geologic and metallogentic contexts, some of them previously analyzed with multifractal methods (Gonçalves et al., 2001; Jesus et al., 2013) and a multi-element geochemical campaign on which to test the different multifractal methods combined with the geochemical indexes, as an advantageous alternative to principal component mapping, for example. Some preliminary essays with stochastic models similar to those reported in Gonçalves (2001) and Agterberg (2007), with different overprinted pulses are presented as well. Acknowledgments: This is a contribution from UID/GEO/50019/2013 - Instituto Dom Luiz, supported by FCT. Agterberg, 2007, Math. Geol., 39, 1. Cheng et al, 1994, J. Geochem. Explor., 51, 109. Cheng et al., 2000, Nat. Resour. Res, 9, 43. Cheng, 2007, Ore Geol. Rev., 32, 314. Gonçalves, 2001, Math. Geol., 33, 41. Gonçalves et al., 2001, J. Geochem. Explor., 72, 91. Jesus et al., 2013, J. Geochem. Explor., 126-127, 23. Xu et al., 2016, J. Geochem. Explor., in press

Fractal model of polarization switching kinetics in ferroelectrics under nonequilibrium conditions of electron irradiation

NASA Astrophysics Data System (ADS)

Maslovskaya, A. G.; Barabash, T. K.

2018-03-01

The paper presents the results of the fractal and multifractal analysis of polarization switching current in ferroelectrics under electron irradiation, which allows statistical memory effects to be estimated at dynamics of domain structure. The mathematical model of formation of electron beam-induced polarization current in ferroelectrics was suggested taking into account the fractal nature of domain structure dynamics. In order to realize the model the computational scheme was constructed using the numerical solution approximation of fractional differential equation. Evidences of electron beam-induced polarization switching process in ferroelectrics were specified at a variation of control model parameters.