Lin, Aijing; Shang, Pengjian
2016-04-01
Considering the diverse application of multifractal techniques in natural scientific disciplines, this work underscores the versatility of multiscale multifractal detrended fluctuation analysis (MMA) method to investigate artificial and real-world data sets. The modified MMA method based on cumulative distribution function is proposed with the objective of quantifying the scaling exponent and multifractality of nonstationary time series. It is demonstrated that our approach can provide a more stable and faithful description of multifractal properties in comprehensive range rather than fixing the window length and slide length. Our analyzes based on CDF-MMA method reveal significant differences in the multifractal characteristics in the temporal dynamics between US and Chinese stock markets, suggesting that these two stock markets might be regulated by very different mechanism. The CDF-MMA method is important for evidencing the stable and fine structure of multiscale and multifractal scaling behaviors and can be useful to deepen and broaden our understanding of scaling exponents and multifractal characteristics.
Image edge detection based on multi-fractal spectrum analysis
Institute of Scientific and Technical Information of China (English)
WANG Shao-yuan; WANG Yao-nan
2006-01-01
In this paper,an image edge detection method based on multi-fractal spectrum analysis is presented.The coarse grain H(o)lder exponent of the image pixels is first computed,then,its multi-fractal spectrum is estimated by the kernel estimation method.Finally,the image edge detection is done by means of different multi-fractal spectrum values.Simulation results show that this method is efficient and has better locality compared with the traditional edge detection methods such as the Sobel method.
Soni, Jalpa; Ghosh, Sayantan; Pradhan, Asima; Sengupta, Tapas K; Panigrahi, Prasanta K; Ghosh, Nirmalya
2011-01-01
The refractive index fluctuations in the connective tissue layer (stroma) of human cervical tissues having different grades of precancers (dysplasia) was quantified using a wavelet-based multifractal detrended fluctuation analysis model. The results show clear signature of multi-scale self-similarity in the index fluctuations of the tissues. Importantly, the refractive index fluctuations were found to be more anti-correlated at higher grades of precancers. Moreover, the strength of multifractality was also observed to be considerably weaker in higher grades of precancers. These results were further complemented by Fourier domain analysis of the spectral fluctuations.
INDIVIDUAL COMMUNICATION TRANSMITTER IDENTIFICATION BASED ON MULTIFRACTAL ANALYSIS
Institute of Scientific and Technical Information of China (English)
Ren Chunhui; Wei Ping; Lou Zhiyou; Xiao Xianci
2005-01-01
In this letter, the communication transmitter transient signals are analyzed based on the time-variant hierarchy exponents of multifractal analysis. The species of optimized sample set is selected as the template of transmitter identification, so that the individual communication transmitter identification can be realized. The turn-on signals of four transmitters are used in the simulation. The experimental results show that the multifractal character of transmitter transient signals is an effective character of individual transmitter identification.
Wavelet-based multifractal analysis of laser biopsy imagery
Jagtap, Jaidip; Panigrahi, Prasanta K; Pradhan, Asima
2011-01-01
In this work, we report a wavelet based multi-fractal study of images of dysplastic and neoplastic HE- stained human cervical tissues captured in the transmission mode when illuminated by a laser light (He-Ne 632.8nm laser). It is well known that the morphological changes occurring during the progression of diseases like cancer manifest in their optical properties which can be probed for differentiating the various stages of cancer. Here, we use the multi-resolution properties of the wavelet transform to analyze the optical changes. For this, we have used a novel laser imagery technique which provides us with a composite image of the absorption by the different cellular organelles. As the disease progresses, due to the growth of new cells, the ratio of the organelle to cellular volume changes manifesting in the laser imagery of such tissues. In order to develop a metric that can quantify the changes in such systems, we make use of the wavelet-based fluctuation analysis. The changing self- similarity during di...
Rolling bearing fault diagnosis based on LCD-TEO and multifractal detrended fluctuation analysis
Liu, Hongmei; Wang, Xuan; Lu, Chen
2015-08-01
A rolling bearing vibration signal is nonlinear and non-stationary and has multiple components and multifractal properties. A rolling-bearing fault-diagnosis method based on Local Characteristic-scale Decomposition-Teager Energy Operator (LCD-TEO) and multifractal detrended fluctuation analysis (MF-DFA) is first proposed in this paper. First, the vibration signal was decomposed into several intrinsic scale components (ISCs) by using LCD, which is a newly developed signal decomposition method. Second, the instantaneous amplitude was obtained by applying the TEO to each major ISC for demodulation. Third, the intrinsic multifractality features hidden in each major ISC were extracted by using MF-DFA, among which the generalized Hurst exponents are selected as the multifractal feature in this paper. Finally, the feature vectors were obtained by applying principal components analysis (PCA) to the extracted multifractality features, thus reducing the dimension of the multifractal features and obtaining the fault feature insensitive to variation in working conditions, further enhancing the accuracy of diagnosis. According to the extracted feature vector, rolling bearing faults can be diagnosed under variable working conditions. The experimental results demonstrate its desirable diagnostic performance under both different working conditions and different fault severities. Simultaneously, the results of comparison show that the performance of the proposed diagnostic method outperforms that of Hilbert-Huang transform (HHT) combined with MF-DFA or LCD-TEO combined with mono-fractal analysis.
Multiscale multifractal multiproperty analysis of financial time series based on Rényi entropy
Yujun, Yang; Jianping, Li; Yimei, Yang
This paper introduces a multiscale multifractal multiproperty analysis based on Rényi entropy (3MPAR) method to analyze short-range and long-range characteristics of financial time series, and then applies this method to the five time series of five properties in four stock indices. Combining the two analysis techniques of Rényi entropy and multifractal detrended fluctuation analysis (MFDFA), the 3MPAR method focuses on the curves of Rényi entropy and generalized Hurst exponent of five properties of four stock time series, which allows us to study more universal and subtle fluctuation characteristics of financial time series. By analyzing the curves of the Rényi entropy and the profiles of the logarithm distribution of MFDFA of five properties of four stock indices, the 3MPAR method shows some fluctuation characteristics of the financial time series and the stock markets. Then, it also shows a richer information of the financial time series by comparing the profile of five properties of four stock indices. In this paper, we not only focus on the multifractality of time series but also the fluctuation characteristics of the financial time series and subtle differences in the time series of different properties. We find that financial time series is far more complex than reported in some research works using one property of time series.
Multifractal characterization of gold market: A multifractal detrended fluctuation analysis
Mali, Provash; Mukhopadhyay, Amitabha
2014-11-01
The multifractal detrended fluctuation analysis technique is employed to analyze the time series of gold consumer price index (CPI) and the market trend of three world’s highest gold consuming countries, namely China, India and Turkey for the period: 1993-July 2013. Various multifractal variables, such as the generalized Hurst exponent, the multifractal exponent and the singularity spectrum, are calculated and the results are fitted to the generalized binomial multifractal (GBM) series that consists of only two parameters. Special emphasis is given to identify the possible source(s) of multifractality in these series. Our analysis shows that the CPI series and all three market series are of multifractal nature. The origin of multifractality for the CPI time series and Indian market series is found due to a long-range time correlation, whereas it is mostly due to the fat-tailed probability distributions of the values for the Chinese and Turkey markets. The GBM model series more or less describes all the time series analyzed here.
Directory of Open Access Journals (Sweden)
Souad Oudjemia
2013-01-01
Full Text Available This paper proposes a combined coarse-grained multifractal method to discriminate between distressed and normal foetuses. The coarse-graining operation was performed by means of a coarse-grained procedure and the multifractal operation was based on a structure function. The proposed method was evaluated by one hundred recordings including eighty normal foetuses and twenty distressed foetuses. We found that it was possible to discriminate between distressed and normal foetuses using the Hurst exponent, singularity, and Holder spectra.
Energy Technology Data Exchange (ETDEWEB)
Munoz-Diosdado, A [Department of Mathematics, Unidad Profesional Interdisciplinaria de Biotecnologia, Instituto Politecnico Nacional, Av. Acueducto s/n, 07340, Mexico City (Mexico)
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.
Directory of Open Access Journals (Sweden)
Evgeniya eGerasimova
2014-05-01
Full Text Available 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.
Multifractal analysis and simulation of multifractal random walks
Schmitt, Francois G.; Huang, Yongxiang
2016-04-01
Multifractal time series, characterized by a scale invariance and large fluctuations at all scales, are found in many fields of natural and applied sciences. They are found i.e. in many geophysical fields, such as atmospheric and oceanic turbulence, hydrology, earth sciences. Here we consider a quite general type of multifractal time series, called multifractal random walk, as non stationary stochastic processes with intermittent stationary increments. We first quickly recall how such time series can be analyzed and characterized, using structure functions and arbitrary order Hilbert spectral analysis. We then discuss the simulation approach. The main object is to provide a stochastic process generating time series having the same multiscale properties We review recent works on this topic, and provide stochastic simulations in order to verify the theoretical predictions. In the lognormal framework we provide a h - μ plane expressing the scale invariant properties of these simulations. The theoretical plane is compared to simulation results.
Wavelet-based multifractal analysis on a time series of solar activity and PDO climate index
Maruyama, Fumio; Kai, Kenji; Morimoto, Hiroshi
2017-09-01
There is increasing interest in finding the relation between solar activity and climate change. In general, fractal properties may be observed in the time series of the dynamics of complex systems, such as solar activity and climate. This study investigates the relations among solar activity, geomagnetic activity, and climatic regime shift by performing a multifractal analysis. To investigate the change in multifractality, we apply a wavelet transform to time series. The change in fractality of the sunspot number (SSN) correlates closely with that of the solar polar field strength. For the SSN and solar polar field strength, a weak multifractality or monofractality is present at the maximum SSN, minimum SSN, and maximum solar polar field strength. A strong multifractality is present two years before the maximum SSN. The climatic regime shift occurs when the SSN increases and the disturbance of the geomagnetic activity is large. At the climatic regime shift, the changes in the fractality of the Pacific Decadal Oscillation (PDO) index and changes in that of the solar activity indices corresponded with each other. From the fractals point of view, we clarify the relations among solar activity, geomagnetic activity, and climatic regime shift. The formation of the magnetic field of the sunspots is correlated with the solar polar field strength. The solar activity seems to influence the climatic regime shift. These findings will contribute to investigating the relation between solar activity and climate change.
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 analysis of complex networks
Institute of Scientific and Technical Information of China (English)
Wang Dan-Ling; Yu Zu-Guo; Anh V
2012-01-01
Complex networks have recently attracted much attention in diverse areas of science and technology.Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions.Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns.In this paper,we introduce a new box-covering algorithm for muttifractal analysis of complex networks.This algorithm is used to calculate the generalized fractal dimensions Dq of some theoretical networks,namely scale-free networks,small world networks,and random networks,and one kind of real network,namely protein-protein interaction networks of different species.Our numerical results indicate the existence of multifractality in scale-free networks and protein-protein interaction networks,while the multifractal behavior is not clear-cut for small world networks and random networks.The possible variation of Dq due to changes in the parameters of the theoretical network models is also discussed.
Multifractal Analysis for the Teichmueller Flow
Energy Technology Data Exchange (ETDEWEB)
Meson, Alejandro M., E-mail: meson@iflysib.unlp.edu.ar; Vericat, Fernando, E-mail: vericat@iflysib.unlp.edu.ar [Instituto de Fisica de Liquidos y Sistemas Biologicos (IFLYSIB) CCT-CONICET, La Plata-UNLP and Grupo de Aplicaciones Matematicas y Estadisticas de la Facultad de Ingenieria (GAMEFI) UNLP (Argentina)
2012-03-15
We present a multifractal description for Teichmueller flows. A key ingredient to do this is the Rauzy-Veech-Zorich reduction theory, which allows to treat the problem in the setting of suspension flows over subshifts. To perform the multifractal analysis we implement a thermodynamic formalism for suspension flows over countable alphabet subshifts a bit different from that developed by Barreira and Iommi.
Multifractal Analysis of Inhomogeneous Bernoulli Products
Batakis, Athanasios; Testud, Benoît
2011-03-01
We are interested to the multifractal analysis of inhomogeneous Bernoulli products which are also known as coin tossing measures. We give conditions ensuring the validity of the multifractal formalism for such measures. On another hand, we show that these measures can have a dense set of phase transitions.
Multifractal cross-correlation analysis in electricity spot market
Fan, Qingju; Li, Dan
2015-07-01
In this paper, we investigate the multiscale cross-correlations between electricity price and trading volume in Czech market based on a newly developed algorithm, called Multifractal Cross-Correlation Analysis (MFCCA). The new algorithm is a natural multifractal generalization of the Detrended Cross-Correlation Analysis (DCCA), and is sensitive to cross-correlation structure and free from limitations of other algorithms. By considering the original sign of the cross-covariance, it allows us to properly quantify and detect the subtle characteristics of two simultaneous recorded time series. First, the multifractality and the long range anti-persistent auto-correlations of price return and trading volume variation are confirmed using Multifractal Detrended Fluctuation Analysis (MF-DFA). Furthermore, we show that there exist long-range anti-persistent cross-correlations between price return and trading volume variation by MFCCA. And we also identify that the cross-correlations disappear on the level of relative small fluctuations. In order to obtain deeper insight into the dynamics of the electricity market, we analyze the relation between generalized Hurst exponent and the multifractal cross-correlation scaling exponent λq. We find that the difference between the generalized Hurst exponent and the multifractal cross-correlation scaling exponent is significantly different for smaller fluctuation, which indicates that the multifractal character of cross-correlations resembles more each other for electricity price and trading volume on the level of large fluctuations and weakens for the smaller ones.
Multifractal Analysis of Polyalanines Time Series
Figueirêdo, P H; Moret, M A; Coutinho, Sérgio; 10.1016/j.physa.2009.11.045
2010-01-01
Multifractal properties of the energy time series of short $\\alpha$-helix structures, specifically from a polyalanine family, are investigated through the MF-DFA technique ({\\it{multifractal detrended fluctuation analysis}}). Estimates for the generalized Hurst exponent $h(q)$ and its associated multifractal exponents $\\tau(q)$ are obtained for several series generated by numerical simulations of molecular dynamics in different systems from distinct initial conformations. All simulations were performed using the GROMOS force field, implemented in the program THOR. The main results have shown that all series exhibit multifractal behavior depending on the number of residues and temperature. Moreover, the multifractal spectra reveal important aspects on the time evolution of the system and suggest that the nucleation process of the secondary structures during the visits on the energy hyper-surface is an essential feature of the folding process.
Asymmetric joint multifractal analysis in Chinese stock markets
Chen, Yuwen; Zheng, Tingting
2017-04-01
In this paper, the asymmetric joint multifractal analysis method based on statistical physics is proposed to explore the asymmetric correlation between daily returns and trading volumes in Chinese stock markets. The result shows asymmetric multifractal correlations exist between return and trading volume in Chinese stock markets. Moreover, when the stock indexes are upward, the fluctuations of returns are always weaker than when they are downward, whether the trading volumes are more or less.
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.
Single and Joint Multifractal Analysis of Soil Particle Size Distributions
Institute of Scientific and Technical Information of China (English)
LI Yi; LI Min; R.HORTON
2011-01-01
It is noted that there has been little research to compare volume-based and number-based soil particle size distributions (PSDs).Our objectives were to characterize the scaling properties and the possible connections between volume-based and number-based PSDs by applying single and joint multifractal analysis.Twelve soil samples were taken from selected sites in Northwest China and their PSDs were analyzed using laser diffractometry.The results indicated that the volume-based PSDs of all 12 samples and thc number-based PSDs of 4 samples had multifractal scalings for moment order -6 ＜ q ＜ 6.Some empirical relationships were identified between the extreme probability values, maximum probability (Pmax), minimum probability (Pmin), and Pmax/Pmin, and the multifractal indices,the difference and the ratio of generalized dimensions at q=0 and 1(D0-D1 and D1/D0), maximum and minimum singularity strength (αmax and αmin) and their difference (αmax - αmin, spectrum width), and asymmetric index (RD).An increase in Pmax generally resulted in corresponding increases of D0 - D1, αmax, αmax - αmin, and RD, which indicated that a large Pmax increased the multifractality of a distribution.Joint multifractal analysis showed that there was significant correlation between the scaling indices of volume-based and number-based PSDs.The multifractality indices indicated that for a given soil, the volume-based PSD was more homogeneous than the number-based PSD, and more likely to display monofractal rather than multifractal scaling.
Identification of Geochemical Anomaly by Multifractal Analysis
Institute of Scientific and Technical Information of China (English)
Xie Shuyun; Cheng Qiuming; Ke Xianzhong; Bao Zhengyu; Wang Changming; Quan Haoli
2008-01-01
The separation of anomalies from geochemical background is an important part of data analysis because lack of such identifications might have profound influence on or even distort the final analysis results. In this article, 1 672 geochemical analytical data of 11 elements, including Cu, Mo, Ag, Sn, and others, from a region within Tibet, South China, are used as one example. Together with the traditional anomaly recognition method of using the iterative mean ±2σ, local multifractality theory has been utilized to delineate the ranges of geochemical anomalies of the elements. To different degrees, on the basis of original data mapping, C-A fractal analysis and singularity exponents, Sn differs from the other 10 elements. Moreover, geochemical mapping results based on values of the multifractal asymmetry index for all elements delineate the highly anomalous area. Similar to other 10 elements, the anomalous areas of Sn delineated by the asymmetry index distribute along the main structure orientations. According to the asymmetry indexes, the 11 elements could be classified into 3 groups: (1) Ag and Au, (2) As-Sb-Cu-Pb-Zn-Mo, and (3) Sn-Bi-W.This paragenetic association of elements can be used to interpret possible origins of mineralization, which is in agreement with petrological analysis and field survey results.
Multifractality and Network Analysis of Phase Transition
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
Multifractal Analysis of Human Heartbeat in Sleep
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 Analysis of Human Heartbeat in Sleep
Institute of Scientific and Technical Information of China (English)
DING Liang-Jing; PENG Hu; CAI Shi-Min; ZHOU Pei-Ling
2007-01-01
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.
Refined Multifractal Cross-Correlation Analysis
Oświȩcimka, Paweł; Forczek, Marcin; Jadach, Stanisław; Kwapień, Jarosław
2013-01-01
We propose a modified algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that is able to consistently identify and quantify multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods like MF-DXA have serious limitations for most of the signals describing complex natural processes. The principal component of the related improvement is proper incorporation of the sign of fluctuations. We present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust tool and allows a reliable quantification of the cross-correlative structure of analyzed processes. We, in particular, analyze a relation between the generalized Hurst exponent and the MFCCA parameter $\\lambda_q$. This relation provides information about the character of potential multifractality in cross-correlations of the processes under study and thus enables selective insight into their dynamics. Us...
Exoplanetary Detection By Multifractal Spectral Analysis
Agarwal, Sahil; Wettlaufer, John S
2016-01-01
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 time scales that characterize planetary orbital motion around the host star. Without fitting spectral data to stellar models, we show how the planetary signal can be robustly detected from noisy data using noise amplitude as a source of information. For observation of transiting planets, combining this method with simple geometry allows us to relate the time scales obtained to primary transit and secondary exoplanet 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 dop...
Multifractal and mechanical analysis of amorphous solid dispersions.
Adler, Camille; Teleki, Alexandra; Kuentz, Martin
2017-03-09
The formulation of lipophilic and hydrophobic compounds is a challenge for the pharmaceutical industry and it requires the development of complex formulations. Our first aim was to investigate hot-melt extrudate microstructures by means of multifractal analysis using scanning electron microscopy imaging. Since the microstructure can affect solid dosage form performance such as mechanical properties, a second objective was to study the influence of the type of adsorbent and of the presence of an amorphous compound on extrudate hardness. β-Carotene (BC) was chosen as poorly water-soluble model compound. Formulations containing a polymer, a lipid and two different silica based inorganic carriers were produced by hot-melt extrusion. Based on scanning electron microscopy/energy dispersive X-ray spectroscopy, the obtained images were analyzed using multifractal formalism. The breaking force of the strands was assessed by a three point bending test. Multifractal analysis and three point bending results showed that the nature of interparticle interactions in the inorganic carrier as well as the presence of amorphous BC had an influence on the microstructure and thus on the mechanical performance. The use of multifractal analysis and the study of the mechanical properties were complementary to better characterize and understand complex formulations obtained by hot-melt extrusion.
Assessing microstructures of pyrrhotites in basalts by multifractal analysis
Directory of Open Access Journals (Sweden)
S. Xie
2010-07-01
Full Text Available Understanding and describing spatial arrangements of mineral particles and determining the mineral distribution structure are important to model the rock-forming process. Geometric properties of individual mineral particles can be estimated from thin sections, and different models have been proposed to quantify the spatial complexity of mineral arrangement. The Gejiu tin-polymetallic ore-forming district, located in Yunnan province, southwestern China, is chosen as the study area. The aim of this paper is to apply fractal and multifractal analysis to quantify distribution patterns of pyrrhotite particles from twenty-eight binary images obtained from seven basalt segments and then to discern the possible petrological formation environments of the basalts based on concentrations of trace elements. The areas and perimeters of pyrrhotite particles were measured for each image. Perimeter-area fractal analysis shows that the perimeter and area of pyrrhotite particles follow a power-law relationship, which implies the scale-invariance of the shapes of the pyrrhotites. Furthermore, the spatial variation of the pyrrhotite particles in space was characterized by multifractal analysis using the method of moments. The results show that the average values of the area-perimeter exponent (D_{AP}, the width of the multifractal spectra (Δ(D(0−D(2 and Δ(D(q_{min}−D(q_{max} and the multifractality index (τ"(1 for the pyrrhotite particles reach their minimum in the second basalt segment, which implies that the spatial arrangement of pyrrhotite particles in Segment 2 is less heterogeneous. Geochemical trace element analysis results distinguish the second basalt segment sample from other basalt samples. In this aspect, the fractal and multifractal analysis may provide new insights into the quantitative assessment of mineral microstructures which may be closely associated with the petrogenesis as shown by the
Institute of Scientific and Technical Information of China (English)
Zhou Yu; Leung Yee; Yu Zu-Guo
2011-01-01
Multifractal detrended fluctuation analysis (MF-DFA) is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis (DFA),which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method,some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper,we theoretically and experimentally demonstrate the invalidity of the expression τ(q)＝qh(q)-1 stipulating the relationship between the multifractal exponent τ(q) and the generalized Hurst exponent h(q). As a replacement,a general relationship is established on the basis of the universal multifractal formalism for the stationary series as τ(q)＝qh(q)-qH'-1,where H'is the nonconservation parameter in the universal multifractal formalism. The singular spectra,a and f (a),are also derived according to this new relationship.
A comparison between two OLS-based approaches to estimating urban multifractal parameters
Huang, Linshan
2016-01-01
Multifractal theory provides a powerful tool to describe urban form and growth, but many basic problems remain to be solved. Among various pending problems, the most significant one is how to obtain proper multifractal dimension spectrums. If an algorithm is improperly used, the parameter values will be abnormal. This paper is devoted to drawing a comparison between two OLS-based approaches for estimating urban multifractal parameters. Using observational data and empirical analysis, we will demonstrate how to utilize the double logarithmic linear regression to evaluate multifractal parameters. The OLS regression analysis has two different approaches. One is to fix the intercept to zero, and the other is not to fix it. The case studies show that the advisable method is to constrain the intercept to zero. The zero-intercept regression yields proper multifractal parameter spectrums within certain scale range of moment order, while the common regression results are not normal. In practice, the zero-intercept reg...
Toledo, B A; Chian, A C-L; Rempel, E L; Miranda, R A; Muñoz, P R; Valdivia, J A
2013-02-01
We study general multifractal properties of tidal gauge and long-wave time series which show a well defined transition between two states, as is the case of sea level when a tsunami arrives. We adopt a method based on discrete wavelets, called wavelet leaders, which has been successfully used in a wide range of applications from image analysis to biomedical signals. First, we analyze an empirical time series of tidal gauge from the tsunami event of 27 February 2010 in Chile. Then, we study a numerical solution of the driven-damped regularized long-wave equation (RLWE) which displays on-off intermittency. Both time series are characterized by a sudden change between two sharply distinct dynamical states. Our analysis suggests a correspondence between the pre- and post-tsunami states (ocean background) and the on state in the RLWE, and also between the tsunami state (disturbed ocean) and the off state in the RLWE. A qualitative similarity in their singularity spectra is observed, and since the RLWE is used to model shallow water dynamics, this result could imply an underlying dynamical similarity.
Exoplanetary Detection by Multifractal Spectral Analysis
Agarwal, Sahil; Del Sordo, Fabio; Wettlaufer, John S.
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 of 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.
Multifractal analysis of managed and independent float exchange rates
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.
New Suns in the Cosmos III: multifractal signature analysis
de Freitas, D B; Junior, P R V de Moraes; Lopes, C E F; Leão, I C; Chagas, M L Das; Bravo, J P; Costa, A D; Martins, B L Canto; De Medeiros, J R
2016-01-01
In present paper, we investigate the multifractality signatures in hourly time series extracted from 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 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 main source of multifractality, while heavy-tailed distribution plays a minor role in generating the multifractal effects. Our work also reveals that rotation period of stars is inherently scaled by degree of multifractality. As a result, analyzing the multifractal degree of referred series, we uncover an evolution of mul...
Gillet, J
2008-01-01
We present a comparison of two english texts, written by Lewis Carroll, one (Alice in wonderland) and the other (Through a looking glass), the former translated into esperanto, in order to observe whether natural and artificial languages significantly differ from each other. We construct one dimensional time series like signals using either word lengths or word frequencies. We use the multifractal ideas for sorting out correlations in the writings. In order to check the robustness of the methods we also write the corresponding shuffled texts. We compare characteristic functions and e.g. observe marked differences in the (far from parabolic) f(alpha) curves, differences which we attribute to Tsallis non extensive statistical features in the ''frequency time series'' and ''length time series''. The esperanto text has more extreme vallues. A very rough approximation consists in modeling the texts as a random Cantor set if resulting from a binomial cascade of long and short words (or words and blanks). This leads...
Multifractal analysis of the fracture surfaces of foamed polypropylene/polyethylene blends
Liu, Chuang; Jiang, Xiu-Lei; Liu, Tao; Zhao, Ling; Zhou, Wei-Xing; Yuan, Wei-Kang
2009-01-01
The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene (PP/PE) blends at different temperatures. Nice power-law scaling relationship between the detrended fluctuation function Fq and the scale s is observed for different orders q and the scaling exponent h(q) is found to be a nonlinear function of q, confirming the presence of multifractality in the fracture surfaces. The multifractal spectra f(α) are obtained numerically through Legendre transform. The shape of the multifractal spectrum of singularities can be well captured by the width of spectrum Δα and the difference of dimension Δf. With the increase of the PE content, the fracture surface becomes more irregular and complex, as is manifested by the facts that Δα increases and Δf decreases from positive to negative. A qualitative interpretation is provided based on the foaming process.
Application of multifractal wavelet analysis to spontaneous fermentation processes
Ibarra-Junquera, V; Escalante-Minakata, P; Rosu, H C
2007-01-01
An algorithm is presented here to get more detailed information, of mixed culture type, based exclusively on the biomass concentrations data for fermentation processes. The analysis is performed having available only the on-line measurements of the redox potential. It is a two-step procedure which includes an Artificial Neural Network (ANN) that relates the redox potential to the biomass concentrations in the first step. Next, a multifractal wavelet analysis is performed using the biomass estimates of the process. In this context, our results show that the redox potential is a valuable indicator of microorganism metabolic activity during the spontaneous fermentation. In this paper, the detailed design of the multifractal wavelet analysis is presented, as well as its direct experimental application at the laboratory level
In situ detection of small-size insect pests sampled on traps using multifractal analysis
Xia, Chunlei; Lee, Jang-Myung; Li, Yan; Chung, Bu-Keun; Chon, Tae-Soo
2012-02-01
We introduce a multifractal analysis for detecting the small-size pest (e.g., whitefly) images from a sticky trap in situ. An automatic attraction system is utilized for collecting pests from greenhouse plants. We applied multifractal analysis to segment action of whitefly images based on the local singularity and global image characteristics. According to the theory of multifractal dimension, the candidate blobs of whiteflies are initially defined from the sticky-trap image. Two schemes, fixed thresholding and regional minima obtainment, were utilized for feature extraction of candidate whitefly image areas. The experiment was conducted with the field images in a greenhouse. Detection results were compared with other adaptive segmentation algorithms. Values of F measuring precision and recall score were higher for the proposed multifractal analysis (96.5%) compared with conventional methods such as Watershed (92.2%) and Otsu (73.1%). The true positive rate of multifractal analysis was 94.3% and the false positive rate minimal level at 1.3%. Detection performance was further tested via human observation. The degree of scattering between manual and automatic counting was remarkably higher with multifractal analysis (R2=0.992) compared with Watershed (R2=0.895) and Otsu (R2=0.353), ensuring overall detection of the small-size pests is most feasible with multifractal analysis in field conditions.
Fan, Xingxing; Lin, Min
2017-08-01
The multifractal characteristics of magnitude time series of earthquakes that occurred in Southern California from 1990 to 2010 are studied in this work. A method for the scale division of the magnitude of these earthquakes based on empirical mode decomposition (EMD) and multifractal analysis is proposed. This method gains a new insight into measuring multifractal properties of the magnitude time series at multiple scales, and it reveals further information about the dynamic seismic behavior. By using EMD, a time series can be decomposed into mode time series that represent different time-frequency components. We find that time-frequency components show long-range correlation with different Hurst exponents by using R / S analysis. Based on the different fractal structures of components, we consider three different scale series: Micro-, Mid- and Macro-scale subsequences, which are superposed and reconstructed by the components. The multifractal properties of the three scale subsequences are analyzed by using multifractal detrended fluctuation analysis (MF-DFA). The results show that the three different scale subsequences have various shapes of multifractal spectra and corresponding distinct properties. The Micro-scale subsequence singularity spectrum shows left-skewed, indicating a relative dominance of the lower Hurst exponent; the Mid-scale subsequence has a right-skewed singularity spectrum; the Macro-scale subsequence exhibits the most significant persistence and shows the strongest multifractality.
Local multifractal detrended fluctuation analysis for non-stationary image's texture segmentation
Wang, Fang; Li, Zong-shou; Li, Jin-wei
2014-12-01
Feature extraction plays a great important role in image processing and pattern recognition. As a power tool, multifractal theory is recently employed for this job. However, traditional multifractal methods are proposed to analyze the objects with stationary measure and cannot for non-stationary measure. The works of this paper is twofold. First, the definition of stationary image and 2D image feature detection methods are proposed. Second, a novel feature extraction scheme for non-stationary image is proposed by local multifractal detrended fluctuation analysis (Local MF-DFA), which is based on 2D MF-DFA. A set of new multifractal descriptors, called local generalized Hurst exponent (Lhq) is defined to characterize the local scaling properties of textures. To test the proposed method, both the novel texture descriptor and other two multifractal indicators, namely, local Hölder coefficients based on capacity measure and multifractal dimension Dq based on multifractal differential box-counting (MDBC) method, are compared in segmentation experiments. The first experiment indicates that the segmentation results obtained by the proposed Lhq are better than the MDBC-based Dq slightly and superior to the local Hölder coefficients significantly. The results in the second experiment demonstrate that the Lhq can distinguish the texture images more effectively and provide more robust segmentations than the MDBC-based Dq significantly.
Multifractal modelling and 3D lacunarity analysis
Energy Technology Data Exchange (ETDEWEB)
Hanen, Akkari, E-mail: bettaieb.hanen@topnet.t [Laboratoire de biophysique, TIM, Faculte de Medecine (Tunisia); Imen, Bhouri, E-mail: bhouri_imen@yahoo.f [Unite de recherche ondelettes et multifractals, Faculte des sciences (Tunisia); Asma, Ben Abdallah, E-mail: asma.babdallah@cristal.rnu.t [Laboratoire de biophysique, TIM, Faculte de Medecine (Tunisia); Patrick, Dubois, E-mail: pdubois@chru-lille.f [INSERM, U 703, Lille (France); Hedi, Bedoui Mohamed, E-mail: medhedi.bedoui@fmm.rnu.t [Laboratoire de biophysique, TIM, Faculte de Medecine (Tunisia)
2009-09-28
This study presents a comparative evaluation of lacunarity of 3D grey level models with different types of inhomogeneity. A new method based on the 'Relative Differential Box Counting' was developed to estimate the lacunarity features of grey level volumes. To validate our method, we generated a set of 3D grey level multifractal models with random, anisotropic and hierarchical properties. Our method gives a lacunarity measurement correlated with the theoretical one and allows a better model classification compared with a classical approach.
Multifractal modelling and 3D lacunarity analysis
Hanen, Akkari; Imen, Bhouri; Asma, Ben Abdallah; Patrick, Dubois; Hédi, Bedoui Mohamed
2009-09-01
This study presents a comparative evaluation of lacunarity of 3D grey level models with different types of inhomogeneity. A new method based on the “Relative Differential Box Counting” was developed to estimate the lacunarity features of grey level volumes. To validate our method, we generated a set of 3D grey level multifractal models with random, anisotropic and hierarchical properties. Our method gives a lacunarity measurement correlated with the theoretical one and allows a better model classification compared with a classical approach.
Multifractal analysis of sentence lengths in English literary texts
Grabska-Gradzińska, Iwona; Kwapień, Jarosław; Oświ\\kecimka, Paweł; Drożdż, Stanisław
2012-01-01
This paper presents analysis of 30 literary texts written in English by different authors. For each text, there were created time series representing length of sentences in words and analyzed its fractal properties using two methods of multifractal analysis: MFDFA and WTMM. Both methods showed that there are texts which can be considered multifractal in this representation but a majority of texts are not multifractal or even not fractal at all. Out of 30 books, only a few have so-correlated lengths of consecutive sentences that the analyzed signals can be interpreted as real multifractals. An interesting direction for future investigations would be identifying what are the specific features which cause certain texts to be multifractal and other to be monofractal or even not fractal at all.
Fractal and multifractal analysis of human retinal vascular network: a review
Directory of Open Access Journals (Sweden)
Ştefan Ţălu
2011-12-01
Full Text Available The objective of this paper is to present a synthesis concerning the results obtained in fractaland multifractal analysis of vascular network geometry of the human retina. The numerical results areuseful in mathematical models based on parametric representations, used in vitreo-retinal biomechanicalstudies. The fractal and multifractal analysis of retinal vascular network provides noninvasive powerfultools that allow physicians the early detection of patients with different retinal vascular diseases.
Chen, Feier; Tian, Kang; Ding, Xiaoxu; Miao, Yuqi; Lu, Chunxia
2016-11-01
Analysis of freight rate volatility characteristics attracts more attention after year 2008 due to the effect of credit crunch and slowdown in marine transportation. The multifractal detrended fluctuation analysis technique is employed to analyze the time series of Baltic Dry Bulk Freight Rate Index and the market trend of two bulk ship sizes, namely Capesize and Panamax for the period: March 1st 1999-February 26th 2015. In this paper, the degree of the multifractality with different fluctuation sizes is calculated. Besides, multifractal detrending moving average (MF-DMA) counting technique has been developed to quantify the components of multifractal spectrum with the finite-size effect taken into consideration. Numerical results show that both Capesize and Panamax freight rate index time series are of multifractal nature. The origin of multifractality for the bulk freight rate market series is found mostly due to nonlinear correlation.
Multifractal detrended moving average analysis of global temperature records
Mali, Provash
2015-01-01
Long-range correlation and multifractal nature of the global monthly mean temperature anomaly time series over the period 1850-2012 are studied in terms of the multifractal detrended moving average (MFDMA) method. We try to address the source(s) of multifractality in the time series by comparing the results derived from the actual series with those from a set of shuffled and surrogate series. It is seen that the newly developed MFDMA method predicts a multifractal structure of the temperature anomaly time series that is more or less similar to that observed by other multifractal methods. In our analysis the major contribution of multifractality in the temperature records is found to be stemmed from long-range temporal correlation among the measurements, however the contribution of fat-tail distribution function of the records is not negligible. The results of the MFDMA analysis, which are found to depend upon the location of the detrending window, tend towards the observations of the multifractal detrended fl...
Multifractal age? Multifractal analysis of cardiac interbeat intervals in assessing of healthy aging
Makowiec, Danuta; Wdowczyk-Szulc, Joanna; Zarczynska-Buchowiecka, Marta; Gruchal, Marcin; Rynkiewicz, Andrzej
2013-01-01
24-hour Holter recordings of 124 healthy people at different age are studied. The nocturnal signals of young people reveal the presence of the multiplicative structure. This structure is significantly weaker in diurnal signals and becomes less evident for elderly people. Multifractal analysis allows us to propose qualitative and quantitative methods to estimate the advancement of the aging process for healthy humans.
A rainfall simulator based on multifractal generator
Akrour, Nawal; mallet, Cecile; barthes, Laurent; chazottes, Aymeric
2015-04-01
The Precipitations are due to complex meteorological phenomenon's and unlike other geophysical constituents such as water vapour concentration they present a relaxation behaviour leading to an alternation of dry and wet periods. Thus, precipitations can be described as intermittent process. The spatial and temporal variability of this phenomenon is significant and covers large scales. This high variability can cause extreme events which are difficult to observe properly because of their suddenness and their localized character. For all these reasons, the precipitations are therefore difficult to model. This study aims to adapt a one-dimensional time series model previously developed by the authors [Akrour et al., 2013, 2014] to a two-dimensional rainfall generator. The original time series model can be divided into 3 major steps : rain support generation, intra event rain rates generation using multifractal and finally calibration process. We use the same kind of methodology in the present study. Based on dataset obtained from meteorological radar of Météo France with a spatial resolution of 1 km x 1 km we present the used approach : Firstly, the extraction of rain support (rain/no rain area) allowing the retrieval of the rain support structure function (variogram) and fractal properties. This leads us to use either the rain support modelisation proposed by ScleissXXX [ref] or directly real rain support extracted from radar rain maps. Then, the generation (over rain areas) of rain rates is made thanks to a 2D multifractal Fractionnally Integrated Flux (FIF) model [ref]. This second stage is followed by a calibration/forcing step (forcing average rain rate per events) added in order to provide rain rate coherent with observed rain-rate distribution. The forcing process is based on a relation identified from the average rain rate of observed events and their surfaces. The presentation will first explain the different steps presented above, then some results
Multiscale multifractal time irreversibility analysis of stock markets
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.
Multifractal analysis of stock exchange crashes
Siokis, Fotios M.
2013-03-01
We analyze the complexity of rare events of the DJIA Index. We reveal that the returns of the time series exhibit strong multifractal properties meaning that temporal correlations play a substantial role. The effect of major stock market crashes can be best illustrated by the comparison of the multifractal spectra of the time series before and after the crash. Aftershock periods compared to foreshock periods exhibit richer and more complex dynamics. Compared to an average crash, calculated by taking into account the larger 5 crashes of the DJIA Index, the 1929 event exhibits significantly more increase in multifractality than the 1987 crisis.
Performance of multifractal detrended fluctuation analysis on short time series
Lopez, Juan Luis
2013-01-01
The performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono- and multifractal models. The reconstruction of the generalized Hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of the decreasing length of the series. As an application the series of the daily exchange rate between the U.S. dollar and the euro is studied.
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
Detrended cross-correlation analysis consistently extended to multifractality.
Oświecimka, Paweł; Drożdż, Stanisław; Forczek, Marcin; Jadach, Stanisław; Kwapień, Jarosław
2014-02-01
We propose an algorithm, multifractal cross-correlation analysis (MFCCA), which constitutes a consistent extension of the detrended cross-correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods, like multifractal extension, have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross-correlations when there are none. The principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments. Furthermore, we present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross-correlative structure of analyzed processes. In particular, it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized Hurst exponent and the multifractal scaling parameter λ(q). This relation provides information about the character of potential multifractality in cross-correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far. By using examples of time series from the stock market, we show that financial fluctuations typically cross-correlate multifractally only for relatively large fluctuations, whereas small fluctuations remain mutually independent even at maximum of such cross-correlations. Finally, we indicate possible utility of MFCCA to study effects of the time-lagged cross-correlations.
Introduction to multifractal detrended fluctuation analysis in matlab.
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.
Xi, Caiping; Zhang, Shuning; Xiong, Gang; Zhao, Huichang; Yang, Yonghong
2017-02-01
Many complex systems generate multifractal time series which are long-range cross-correlated. This paper introduces three multifractal cross-correlation analysis methods, such as multifractal cross-correlation analysis based on the partition function approach (MFXPF), multifractal detrended cross-correlation analysis (MFDCCA) methods based on detrended fluctuation analysis (MFXDFA) and detrended moving average analysis (MFXDMA), which only consider one moment order. We do comparative analysis of the artificial time series (binomial multiplicative cascades and Cantor sets with different probabilities) by these methods. Then we do a feasibility test of the fixed threshold target detection within sea clutter by applying the multifractal cross-correlation analysis methods to the IPIX radar sea clutter data. The results show that it is feasible to use the method of the fixed threshold based on the multifractal feature parameter Δf(α) by the MFXPF and MFXDFA-1 methods. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms, the detection parameters and the target detection methods within sea clutter in practice.
Multifractal Framework Based on Blanket Method
Paskaš, Milorad P.; Reljin, Irini S.; Reljin, Branimir D.
2014-01-01
This paper proposes two local multifractal measures motivated by blanket method for calculation of fractal dimension. They cover both fractal approaches familiar in image processing. The first two measures (proposed Methods 1 and 3) support model of image with embedded dimension three, while the other supports model of image embedded in space of dimension three (proposed Method 2). While the classical blanket method provides only one value for an image (fractal dimension) multifractal spectrum obtained by any of the proposed measures gives a whole range of dimensional values. This means that proposed multifractal blanket model generalizes classical (monofractal) blanket method and other versions of this monofractal approach implemented locally. Proposed measures are validated on Brodatz image database through texture classification. All proposed methods give similar classification results, while average computation time of Method 3 is substantially longer. PMID:24578664
Multifractal and lacunarity analysis of microvascular morphology and remodeling.
Gould, Daniel J; Vadakkan, Tegy J; Poché, Ross A; Dickinson, Mary E
2011-02-01
Classical measures of vessel morphology, including diameter and density, are employed to study microvasculature in endothelial membrane labeled mice. These measurements prove sufficient for some studies; however, they are less well suited for quantifying changes in microcirculatory networks lacking hierarchical structure. We demonstrate that automated multifractal analysis and lacunarity may be used with classical methods to quantify microvascular morphology. Using multifractal analysis and lacunarity, we present an automated extraction tool with a processing pipeline to characterize 2D representations of 3D microvasculature. We apply our analysis on four tissues and the hyaloid vasculature during remodeling. We found that the vessel networks analyzed have multifractal geometries and that kidney microvasculature has the largest fractal dimension and the lowest lacunarity compared to microvasculature networks in the cortex, skin, and thigh muscle. Also, we found that, during hyaloid remodeling, there were differences in multifractal spectra reflecting the functional transition from a space filling vasculature which nurtures the lens to a less dense vasculature as it regresses, permitting unobstructed vision. Multifractal analysis and lacunarity are valuable additions to classical measures of vascular morphology and will have utility in future studies of normal, developing, and pathological tissues. © 2011 John Wiley & Sons Ltd.
Multifractal detrended fluctuation analysis of optogenetic modulation of neural activity
Kumar, S.; Gu, L.; Ghosh, N.; Mohanty, S. K.
2013-02-01
Here, we introduce a computational procedure to examine whether optogenetically activated neuronal firing recordings could be characterized as multifractal series. Optogenetics is emerging as a valuable experimental tool and a promising approach for studying a variety of neurological disorders in animal models. The spiking patterns from cortical region of the brain of optogenetically-stimulated transgenic mice were analyzed using a sophisticated fluctuation analysis method known as multifractal detrended fluctuation analysis (MFDFA). We observed that the optogenetically-stimulated neural firings are consistent with a multifractal process. Further, we used MFDFA to monitor the effect of chemically induced pain (formalin injection) and optogenetic treatment used to relieve the pain. In this case, dramatic changes in parameters characterizing a multifractal series were observed. Both the generalized Hurst exponent and width of singularity spectrum effectively differentiates the neural activities during control and pain induction phases. The quantitative nature of the analysis equips us with better measures to quantify pain. Further, it provided a measure for effectiveness of the optogenetic stimulation in inhibiting pain. MFDFA-analysis of spiking data from other deep regions of the brain also turned out to be multifractal in nature, with subtle differences in the parameters during pain-induction by formalin injection and inhibition by optogenetic stimulation. Characterization of neuronal firing patterns using MFDFA will lead to better understanding of neuronal response to optogenetic activation and overall circuitry involved in the process.
Laser image denoising technique based on multi-fractal theory
Du, Lin; Sun, Huayan; Tian, Weiqing; Wang, Shuai
2014-02-01
The noise of laser images is complex, which includes additive noise and multiplicative noise. Considering the features of laser images, the basic processing capacity and defects of the common algorithm, this paper introduces the fractal theory into the research of laser image denoising. The research of laser image denoising is implemented mainly through the analysis of the singularity exponent of each pixel in fractal space and the feature of multi-fractal spectrum. According to the quantitative and qualitative evaluation of the processed image, the laser image processing technique based on fractal theory not only effectively removes the complicated noise of the laser images obtained by range-gated laser active imaging system, but can also maintains the detail information when implementing the image denoising processing. For different laser images, multi-fractal denoising technique can increase SNR of the laser image at least 1~2dB compared with other denoising techniques, which basically meet the needs of the laser image denoising technique.
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.
Multifractal analysis of atmospheric sub-micron particle data
Arizabalo, Rubén Darío; González-Ávalos, Eugenio; Korvin, Gabor
2015-03-01
Multifractal analysis was used to describe air pollution by sub-micrometric atmospheric particles. Atmospheric particle concentrations were studied from March 31 to April 21, 2006, as part of the MILAGRO campaign at the Jasso Station by means of an SMPS. Sixteen campaign days were selected to carry out the multifractal analysis of the experimental data through Singularity Spectra f(α). In this work, the roughness/smoothness feature of atmospheric particle distributions was studied by means of the Hölder exponent (α), which can be associated with the intensity of particle emissions through time and the randomness of the external emission sources. Multifractal analysis has been found to be a useful tool to establish intensity fluctuations of atmospheric data.
Price-volume multifractal analysis and its application in Chinese stock markets
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.
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.
Multifractal Analysis of Local Entropies for Gibbs Measures
Takens, Floris; Verbitski, Evgeni
1998-01-01
Recently a complete multifractal analysis of local dimensions, entropies and Lyapunov exponents of conformal expanding maps and surface Axion A diffeomorphisms for Gibbs measures was performed. The main goal of this was primarily the analysis of the local (pointwise) dimensions. This is an extremely
Multifractal analysis of dynamic infrared imaging of breast cancer
Gerasimova, E.; Audit, B.; Roux, S. G.; Khalil, A.; Argoul, F.; Naimark, O.; Arneodo, A.
2013-12-01
The wavelet transform modulus maxima (WTMM) method was used in a multifractal analysis of skin breast temperature time-series recorded using dynamic infrared (IR) thermography. Multifractal scaling was found for healthy breasts as the signature of a continuous change in the shape of the probability density function (pdf) of temperature fluctuations across time scales from \\sim0.3 to 3 s. In contrast, temperature time-series from breasts with malignant tumors showed homogeneous monofractal temperature fluctuations statistics. These results highlight dynamic IR imaging as a very valuable non-invasive technique for preliminary screening in asymptomatic women to identify those with risk of breast cancer.
Multifractal detrending moving-average cross-correlation analysis.
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 h(xy) 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 q0. 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 h(xy)(q) since its h(xy)(2) is closest to 0.5, as expected, and
Xi, Caiping; Zhang, Shunning; Xiong, Gang; Zhao, Huichang
2016-07-01
Multifractal detrended fluctuation analysis (MFDFA) and multifractal detrended moving average (MFDMA) algorithm have been established as two important methods to estimate the multifractal spectrum of the one-dimensional random fractal signal. They have been generalized to deal with two-dimensional and higher-dimensional fractal signals. This paper gives a brief introduction of the two-dimensional multifractal detrended fluctuation analysis (2D-MFDFA) and two-dimensional multifractal detrended moving average (2D-MFDMA) algorithm, and a detailed description of the application of the two-dimensional fractal signal processing by using the two methods. By applying the 2D-MFDFA and 2D-MFDMA to the series generated from the two-dimensional multiplicative cascading process, we systematically do the comparative analysis to get the advantages, disadvantages and the applicabilities of the two algorithms for the first time from six aspects such as the similarities and differences of the algorithm models, the statistical accuracy, the sensitivities of the sample size, the selection of scaling range, the choice of the q-orders and the calculation amount. The results provide a valuable reference on how to choose the algorithm from 2D-MFDFA and 2D-MFDMA, and how to make the schemes of the parameter settings of the two algorithms when dealing with specific signals in practical applications.
Multifractal analysis of the fat-tail PDFs observed in fully developed turbulence
Energy Technology Data Exchange (ETDEWEB)
Arimitsu, T [Graduate School of Pure and Applied Sciences, University of Tsukuba, Ibaraki 305-8571 (Japan); Arimitsu, N [Graduate School of Environment and Information Sciences, Yokohama Nat' l. University, Yokohama 240-8501 (Japan)
2005-01-01
The fundamentals of the multifractal analysis (MFA) is given, which is a unified statistical mechanical theory that treats the systems containing intermittent phenomena and representing fat-tail probability density functions (PDFs) for appropriate observables. MFA utilizes two distinct Tsallis-type MaxEnt distribution functions, one for the tail part of PDF and the other for its center part. It is shown that A and A model within MFA can explain the recently observed PDFs of turbulence in the highest accuracy superior to the analyses based on other multifractal models such as the log-normal model and the p model.
H.264/AVC Video Compressed Traces: Multifractal and Fractal Analysis
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Samčović Andreja
2006-01-01
Full Text Available Publicly available long video traces encoded according to H.264/AVC were analyzed from the fractal and multifractal points of view. It was shown that such video traces, as compressed videos (H.261, H.263, and MPEG-4 Version 2 exhibit inherent long-range dependency, that is, fractal, property. Moreover they have high bit rate variability, particularly at higher compression ratios. Such signals may be better characterized by multifractal (MF analysis, since this approach describes both local and global features of the process. From multifractal spectra of the frame size video traces it was shown that higher compression ratio produces broader and less regular MF spectra, indicating to higher MF nature and the existence of additive components in video traces. Considering individual frames (I, P, and B and their MF spectra one can approve additive nature of compressed video and the particular influence of these frames to a whole MF spectrum. Since compressed video occupies a main part of transmission bandwidth, results obtained from MF analysis of compressed video may contribute to more accurate modeling of modern teletraffic. Moreover, by appropriate choice of the method for estimating MF quantities, an inverse MF analysis is possible, that means, from a once derived MF spectrum of observed signal it is possible to recognize and extract parts of the signal which are characterized by particular values of multifractal parameters. Intensive simulations and results obtained confirm the applicability and efficiency of MF analysis of compressed video.
Salat, Hadrien; Arcaute, Elsa
2016-01-01
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within a space, they are not necessarily equivalent on a more rigorous level. This review article aims at unifying the multifractal methodology by presenting the multifractal theoretical framework and principal practical methods, namely the moment method, the histogram method, multifractal detrended fluctuation analysis (MDFA) and modulus maxima wavelet transform (MMWT), with a comparative and interpretative eye.
Multifractal analysis of weighted networks by a modified sandbox algorithm
Song, Yu-Qin; Liu, Jin-Long; Yu, Zu-Guo; Li, Bao-Gen
2015-12-01
Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks. First, we use the SBw algorithm to study the multifractal property of two families of weighted fractal networks (WFNs): “Sierpinski” WFNs and “Cantor dust” WFNs. We also discuss how the fractal dimension and generalized fractal dimensions change with the edge-weights of the WFN. From the comparison between the theoretical and numerical fractal dimensions of these networks, we can find that the proposed SBw algorithm is efficient and feasible for MFA of weighted networks. Then, we apply the SBw algorithm to study multifractal properties of some real weighted networks — collaboration networks. It is found that the multifractality exists in these weighted networks, and is affected by their edge-weights.
Fetterhoff, Dustin; Opris, Ioan; Simpson, Sean L; Deadwyler, Sam A; Hampson, Robert E; Kraft, Robert A
2015-04-15
Multifractal analysis quantifies the time-scale-invariant properties in data by describing the structure of variability over time. By applying this analysis to hippocampal interspike interval sequences recorded during performance of a working memory task, a measure of long-range temporal correlations and multifractal dynamics can reveal single neuron correlates of information processing. Wavelet leaders-based multifractal analysis (WLMA) was applied to hippocampal interspike intervals recorded during a working memory task. WLMA can be used to identify neurons likely to exhibit information processing relevant to operation of brain-computer interfaces and nonlinear neuronal models. Neurons involved in memory processing ("Functional Cell Types" or FCTs) showed a greater degree of multifractal firing properties than neurons without task-relevant firing characteristics. In addition, previously unidentified FCTs were revealed because multifractal analysis suggested further functional classification. The cannabinoid type-1 receptor (CB1R) partial agonist, tetrahydrocannabinol (THC), selectively reduced multifractal dynamics in FCT neurons compared to non-FCT neurons. WLMA is an objective tool for quantifying the memory-correlated complexity represented by FCTs that reveals additional information compared to classification of FCTs using traditional z-scores to identify neuronal correlates of behavioral events. z-Score-based FCT classification provides limited information about the dynamical range of neuronal activity characterized by WLMA. Increased complexity, as measured with multifractal analysis, may be a marker of functional involvement in memory processing. The level of multifractal attributes can be used to differentially emphasize neural signals to improve computational models and algorithms underlying brain-computer interfaces. Copyright © 2014 Elsevier B.V. All rights reserved.
Understanding the multifractality in portfolio excess returns
Chen, Cheng; Wang, Yudong
2017-01-01
The multifractality in stock returns have been investigated extensively. However, whether the autocorrelations in portfolio returns are multifractal have not been considered in the literature. In this paper, we detect multifractal behavior of returns of portfolios constructed based on two popular trading rules, size and book-to-market (BM) ratio. Using the multifractal detrended fluctuation analysis, we find that the portfolio returns are significantly multifractal and the multifractality is mainly attributed to long-range dependence. We also investigate the multifractal cross-correlation between portfolio return and market average return using the detrended cross-correlation analysis. Our results show that the cross-correlations of small fluctuations are persistent, while those of large fluctuations are anti-persistent.
Morozov, A. Yu.
2013-05-01
In their recent article ‘multifractal diffusion entropy analysis on stock volatility in financial markets’ Huang, Shang and Zhao (2012) [6] suggested a generalization of the diffusion entropy analysis method with the main goal of being able to reveal scaling exponents for multifractal times series. The main idea seems to be replacing the Shannon entropy by the Rényi entropy, which is a one-parametric family of entropies. The authors claim that based on their method they are able to separate long range and short correlations of financial market multifractal time series. In this comment I show that the suggested new method does not bring much valuable information in obtaining the correct scaling for a multifractal/mono-fractal process beyond the original diffusion entropy analysis method. I also argue that the mathematical properties of the multifractal diffusion entropy analysis should be carefully explored to avoid possible numerical artefacts when implementing the method in analysis of real sequences of data.
Super-Resolution Reconstruction of Remote Sensing Images Using Multifractal Analysis
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Mao-Gui Hu
2009-10-01
Full Text Available 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., intraurban. 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 resolutionenhanced image is generated by a fractal coding-based denoising and downscaling method. The empirical case shows that the reconstructed super-resolution image performs well indetail enhancement. This method is not only useful for remote sensing in investigating Earth, but also for other images with multifractal characteristics.
Multifractal analysis of weighted networks by a modified sandbox algorithm
Song, Yu-Qin; Yu, Zu-Guo; Li, Bao-Gen
2015-01-01
Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks.First, we use the SBw algorithm to study the multifractal property of two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor dust" WFNs. We also discuss how the fractal dimension and generalized fractal dimensions change with the edge-weights of the WFN. From the comparison between the theoretical and numerical fractal dimensions of these networks, we can find that the proposed SBw algorithm is efficient and feasible for MFA of weighted networks. Then, we apply...
Irregularities and scaling in signal and image processing: multifractal analysis
Abry, Patrice; Jaffard, Herwig; Wendt, Stéphane
2015-03-01
B. Mandelbrot gave a new birth to the notions of scale invariance, self-similarity and non-integer dimensions, gathering them as the founding corner-stones used to build up fractal geometry. The first purpose of the present contribution is to review and relate together these key notions, explore their interplay and show that they are different facets of a single intuition. Second, we will explain how these notions lead to the derivation of the mathematical tools underlying multifractal analysis. Third, we will reformulate these theoretical tools into a wavelet framework, hence enabling their better theoretical understanding as well as their efficient practical implementation. B. Mandelbrot used his concept of fractal geometry to analyze real-world applications of very different natures. As a tribute to his work, applications of various origins, and where multifractal analysis proved fruitful, are revisited to illustrate the theoretical developments proposed here.
Multifractal Detrended Fluctuation Analysis of Streamflow in the Yellow River Basin, China
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Erhui Li
2015-04-01
Full Text Available Multifractal detrended fluctuation analysis (MFDFA can provide information about inner regularity, randomness and long-range correlation of time series, promoting the knowledge of their evolution regularity. The MFDFA are applied to detect long-range correlations and multifractal behavior of streamflow series at four hydrological stations (Toudaoguai, Longmen, Huangfu and Ganguyi in the main channel and tributaries of the Yellow River. The results showed that there was one crossover point in the log−log curve of the fluctuation function Fq(s versus s. The location for the crossover point is approximately one year, implying an unchanged annual periodicity within the streamflow variations. The annual periodical feature of streamflow was removed by using seasonal trend decomposition based on locally weighted regression (STL. All the decomposed streamflow series were characterized by long-term persistence in the study areas. Strong dependence of the generalized Hurst exponent h(q on q exhibited multifractal behavior in streamflow time series at four stations in the Yellow River basin. The reduction of dependence of h(q on q for shuffled time series showed that the multifractality of streamflow series was responsible for the correlation properties, as well as the probability density function of the streamflow series.
Yang, Ge; Wang, Jun
2016-11-01
A random agent-based financial model is developed and investigated by the finite-range multitype contact dynamic system, in an attempt to reproduce and study the dynamics of financial markets. And an analysis method of detecting duration and intensity relationship in volatility series is introduced, called the volatility duration analysis. Then the auto-correlation analysis suggests that there exists evident volatility clustering feature in absolute volatility durations for the simulation data and the real data. Besides, the Lempel-Ziv complexity analysis is applied to study the complexity of the returns, the corresponding absolute returns and the volatility duration returns, which can reflect the fluctuation behaviors, the volatility behaviors and the volatility duration behaviors. At last, the multifractal phenomena of volatility durations of returns are comparatively studied for Shanghai Composite Index and the proposed model by multifractal detrended fluctuation analysis.
Mixed Multifractal Analysis of Crude Oil, Gold and Exchange Rate Series
Dai, Meifeng; Shao, Shuxiang; Gao, Jianyu; Sun, Yu; Su, Weiyi
2016-11-01
The multifractal analysis of one time series, e.g. crude oil, gold and exchange rate series, is often referred. In this paper, we apply the classical multifractal and mixed multifractal spectrum to study multifractal properties of crude oil, gold and exchange rate series and their inner relationships. The obtained results show that in general, the fractal dimension of gold and crude oil is larger than that of exchange rate (RMB against the US dollar), reflecting a fact that the price series in gold and crude oil are more heterogeneous. Their mixed multifractal spectra have a drift and the plot is not symmetric, so there is a low level of mixed multifractal between each pair of crude oil, gold and exchange rate series.
Lacunarity and multifractal analysis of the large DLA mass distribution
Rodriguez-Romo, Suemi; Sosa-Herrera, Antonio
2013-08-01
We show the methodology used to analyze fractal and mass-multifractal properties of very large Diffusion-Limited Aggregation (DLA) clusters with a maximum of 109 particles for 2D aggregates and 108 particles for 3D clusters, to support our main result; the scaling behavior obtained by our experimental results corresponds to the expected performance of monofractal objects. In order to estimate lacunarity measures for large DLA clusters, we develop a variant of the gliding-box algorithm which reduces the computer time needed to obtain experimental results. We show how our mass multifractal data have a tendency to present monofractal behavior for the mass distribution of the cases presented in this paper in the limit of very large clusters. Lacunarity analysis shows, provided we study small clusters mass distributions, data which might be interpreted as two different values of fractal dimensions while the cluster grows; however, this effect tends to vanish when the cluster size increases further, in such a way that monofractality is achieved. The outcomes of this paper lead us to conclude that the previously reported mass multifractality behavior (Vicsek et al., 1990 [13]) detected for DLA clusters is a consequence of finite size effects and floating point precision limitations and not an intrinsic feature of the phenomena, since the scaling behavior of our DLA clusters space corresponds to monofractal objects, being this situation remarkably noticeable in the limit of very large clusters.
Multifractal analysis of low-latitude geomagnetic fluctuations
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M. J. A. Bolzan
2009-02-01
Full Text Available The technique of large deviation multifractal spectrum has shown that the high-latitude (77.5° N, 69.2° W geomagnetic fluctuations can be described from direct dissipation process or loading-unloading regimes of the solar wind-magnetosphere coupling. In this paper, we analyze the H-component of low-latitude (22.4° S, 43.6° W geomagnetic field variability observed during the month of July 2000 at the Geomagnetic Observatory, Vassouras, RJ, Brazil. The variability pattern during this period is a mixture of quiet and disturbed days including the Bastille Day intense geomagnetic storm on 15 July. Due to the complexity of this data, we pursue a detailed analysis of the geomagnetic fluctuations in different time scales including a multifractal approach using the singular power spectrum deviations obtained from the wavelet transform modulus maxima (WTMM. The results suggest, as observed from high-latitude data, the occurrence of low-latitude multifractal processes driving the intermittent coupling between the solar wind-magnetosphere and geomagnetic field variations. On finer scales possible physical mechanisms in the context of nonlinear magnetosphere response are discussed.
Multifractal Detrended Fluctuation Analysis of Interevent Time Series in a Modified OFC Model
Institute of Scientific and Technical Information of China (English)
LIN Min; YAN Shuang-Xi; ZHAO Gang; WANG Gang
2013-01-01
We use multifractal detrended fluctuation analysis (MF-DFA) method to investigate the multifractal behavior of the interevent time series in a modified Olami-Feder-Christensen (OFC) earthquake model on assortative scale-free networks.We determine generalized Hurst exponent and singularity spectrum and find that these fluctuations have multifractal nature.Comparing the MF-DFA results for the original interevent time series with those for shuffled and surrogate series,we conclude that the origin of multifractality is due to both the broadness of probability density function and long-range correlation.
Multifractal Analysis of Typhoons: the case study of Bolaven (2012)
Lee, Jisun; Paz, Igor; Ichiba, Abdellah; Tchiguirinskaia, Ioulia; Schertzer, Daniel; Lee, Dong-In; Kuo, Hung-Chi
2017-04-01
Multifractals have become rather standard tools to analyze and simulate meteorological and hydrological data, especially radar data that have the rare advantage of providing space-time (3D+1) fields. However, in spite of their inherent capacity to deal with extreme multiscale phenomena like typhoons, as well as an increased availability of higher quality data, there had been not so many multifractal studies of typhoons since pioneering studies (Chygyrynsakaia et al 1994, Lazarev et al 1994), which relied on time series data obtained from 1D aircraft or balloon trajectories. This lack of new developments might have impeded significant progress in predicting typhoon evolution prediction. We therefore decided to jointly understand the dynamics and rainfall by multifractal space-time analysis with the help of the joint measurements of the Typhoon Bolaven by three Doppler S-band radars. This experimental set-up not only provided accurate estimates of the rainfall intensity, but also of the 3 components of the wind velocity. Typhoon Bolaven is one of the typhoons that caused the largest damages with severe rainfall all over Korea including Jeju Island with more than 250 mm in 2 days in 2012. It was regarded as the most powerful storm to strike the Korean Peninsula in nearly a decade, with wind gusts measured up to 186 km h-1. The three radars were respectively located in Gosan, and Seongsan, in Jeju Island, and Jindo, in southwest of Korea peninsula, i.e. all around the region where the typhoon intensity was the largest. The largest distance between the radars was approximately 100km, and the rainfall and wind velocity were estimated on a grid of 360×360×60 every ten minutes. The multifractal analysis of this large amount of data (space time Trace Method and Double Trace Method) was performed to better understand through scales the fast transformation of potential energy into kinetic energy and the premier role of convection. In particular, this analysis confirms power
Multifractal analysis of heartbeat dynamics during meditation training
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.
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Gang-Jin Wang
2014-01-01
Full Text Available We supply a new perspective to describe and understand the behavior of cross-correlations between energy and emissions markets. Namely, we investigate cross-correlations between oil and gas (Oil-Gas, oil and CO2 (Oil-CO2, and gas and CO2 (Gas-CO2 based on fractal and multifractal analysis. We focus our study on returns of the oil, gas, and CO2 during the period of April 22, 2005–April 30, 2013. In the empirical analysis, by using the detrended cross-correlation analysis (DCCA method, we find that cross-correlations for Oil-Gas, Oil-CO2, and Gas-CO2 obey a power-law and are weakly persistent. Then, we adopt the method of DCCA cross-correlation coefficient to quantify cross-correlations between energy and emissions markets. The results show that their cross-correlations are diverse at different time scales. Next, based on the multifractal DCCA method, we find that cross-correlated markets have the nonlinear and multifractal nature and that the multifractality strength for three cross-correlated markets is arranged in the order of Gas-CO2 > Oil-Gas > Oil-CO2. Finally, by employing the rolling windows method, which can be used to investigate time-varying cross-correlation scaling exponents, we analyze short-term and long-term market dynamics and find that the recent global financial crisis has a notable influence on short-term and long-term market dynamics.
Multifractal analysis of spot rates in tanker markets and their comparisons with crude oil markets
Zheng, Shiyuan; Lan, Xiangang
2016-02-01
This paper investigates the dynamic features of the spot rates for VLCC/ULCC, Suezmax, Aframax, Panamax and Handysize tanker markets by means of multifractal detrended fluctuation analysis (MF-DFA). The Hurst exponents, especially the time-dependent Hurst exponents, of the daily rate returns are calculated to capture the fractal properties of these different tanker markets. The origins of multifractility in these markets are identified by comparing their multifractal scaling exponents based on the original data, the shuffled data and the surrogate data. Furthermore, the non-periodic cycles for these markets are detected by the V-statistic. Finally, the comparisons of the fractal properties between the tanker markets and the crude oil commodity markets suggest that the tanker markets are more fractal than their upstream counterparts.
Scale-Specific Multifractal Medical Image Analysis
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Boris Braverman
2013-01-01
irregular complex tissue structures that do not lend themselves to straightforward analysis with traditional Euclidean geometry. In this study, we treat the nonfractal behaviour of medical images over large-scale ranges by considering their box-counting fractal dimension as a scale-dependent parameter rather than a single number. We describe this approach in the context of the more generalized Rényi entropy, in which we can also compute the information and correlation dimensions of images. In addition, we describe and validate a computational improvement to box-counting fractal analysis. This improvement is based on integral images, which allows the speedup of any box-counting or similar fractal analysis algorithm, including estimation of scale-dependent dimensions. Finally, we applied our technique to images of invasive breast cancer tissue from 157 patients to show a relationship between the fractal analysis of these images over certain scale ranges and pathologic tumour grade (a standard prognosticator for breast cancer. Our approach is general and can be applied to any medical imaging application in which the complexity of pathological image structures may have clinical value.
Multifractal analysis of African monsoon rain fields, taking into account the zero rain-rate problem
Verrier, S.; de Montera, L.; Barthès, L.; Mallet, C.
2010-07-01
SummaryNonlinear rain dynamics, due to strong coupling with turbulence, can be described by stochastic scale invariant (such as multifractal) models. In this study, attention is focused on the three-parameter fractionally integrated flux (FIF), based on the universal multifractal (UM) model developed by Schertzer and Lovejoy (1987). Multifractal analysis techniques were applied to experimental radar data measured during the African monsoon multidisciplinary analysis (AMMA) campaign, during the summer of 2006. The non-conservation parameter H, which has often been estimated at 0, was found to be more likely close to 0.4, meaning that rain is not a conserved cascade. Moreover, it is shown that the presence of numerous zero values in the data has an influence, which has until now been underestimated, but should in fact be accounted for. UM parameters are therefore estimated from the full dataset, and then only from maps in which almost all pixels have a non-zero value. Significant differences were found, attributed to on-off intermittency, and their role was checked by means of simulations. Finally, these results are compared with those previously based on time series, and collected by a co-localized disdrometer. The sets of parameters obtained in the spatial and time domains are found to be quite close to each other, contrary to most results published in the literature. This generally reported incoherency is believed to result mainly from the influence of on-off intermittency, whose effects are stronger for time series than for selected radar maps.
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Ana Gavrovska
2013-01-01
Full Text Available Phonocardiography has shown a great potential for developing low-cost computer-aided diagnosis systems for cardiovascular monitoring. So far, most of the work reported regarding cardiosignal analysis using multifractals is oriented towards heartbeat dynamics. This paper represents a step towards automatic detection of one of the most common pathological syndromes, so-called mitral valve prolapse (MVP, using phonocardiograms and multifractal analysis. Subtle features characteristic for MVP in phonocardiograms may be difficult to detect. The approach for revealing such features should be locally based rather than globally based. Nevertheless, if their appearances are specific and frequent, they can affect a multifractal spectrum. This has been the case in our experiment with the click syndrome. Totally, 117 pediatric phonocardiographic recordings (PCGs, 8 seconds long each, obtained from 117 patients were used for PMV automatic detection. We propose a two-step algorithm to distinguish PCGs that belong to children with healthy hearts and children with prolapsed mitral valves (PMVs. Obtained results show high accuracy of the method. We achieved 96.91% accuracy on the dataset (97 recordings. Additionally, 90% accuracy is achieved for the evaluation dataset (20 recordings. Content of the datasets is confirmed by the echocardiographic screening.
Zajić, Goran; Reljin, Irini; Reljin, Branimir
2013-01-01
Phonocardiography has shown a great potential for developing low-cost computer-aided diagnosis systems for cardiovascular monitoring. So far, most of the work reported regarding cardiosignal analysis using multifractals is oriented towards heartbeat dynamics. This paper represents a step towards automatic detection of one of the most common pathological syndromes, so-called mitral valve prolapse (MVP), using phonocardiograms and multifractal analysis. Subtle features characteristic for MVP in phonocardiograms may be difficult to detect. The approach for revealing such features should be locally based rather than globally based. Nevertheless, if their appearances are specific and frequent, they can affect a multifractal spectrum. This has been the case in our experiment with the click syndrome. Totally, 117 pediatric phonocardiographic recordings (PCGs), 8 seconds long each, obtained from 117 patients were used for PMV automatic detection. We propose a two-step algorithm to distinguish PCGs that belong to children with healthy hearts and children with prolapsed mitral valves (PMVs). Obtained results show high accuracy of the method. We achieved 96.91% accuracy on the dataset (97 recordings). Additionally, 90% accuracy is achieved for the evaluation dataset (20 recordings). Content of the datasets is confirmed by the echocardiographic screening. PMID:23762185
Detection of crossover time scales in multifractal detrended fluctuation analysis
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.
Spatial Characterization of Landscapes through Multifractal Analysis of DEM
Directory of Open Access Journals (Sweden)
P. L. Aguado
2014-01-01
Full Text Available Landscape evolution is driven by abiotic, biotic, and anthropic factors. The interactions among these factors and their influence at different scales create a complex dynamic. Landscapes have been shown to exhibit numerous scaling laws, from Horton’s laws to more sophisticated scaling of heights in topography and river network topology. This scaling and multiscaling analysis has the potential to characterise the landscape in terms of the statistical signature of the measure selected. The study zone is a matrix obtained from a digital elevation model (DEM (map 10 × 10 m, and height 1 m that corresponds to homogeneous region with respect to soil characteristics and climatology known as “Monte El Pardo” although the water level of a reservoir and the topography play a main role on its organization and evolution. We have investigated whether the multifractal analysis of a DEM shows common features that can be used to reveal the underlying patterns and information associated with the landscape of the DEM mapping and studied the influence of the water level of the reservoir on the applied analysis. The results show that the use of the multifractal approach with mean absolute gradient data is a useful tool for analysing the topography represented by the DEM.
Asymmetric multifractal detrending moving average analysis in time series of PM2.5 concentration
Zhang, Chen; Ni, Zhiwei; Ni, Liping; Li, Jingming; Zhou, Longfei
2016-09-01
In this paper, we propose the asymmetric multifractal detrending moving average analysis (A-MFDMA) method to explore the asymmetric correlation in non-stationary time series. The proposed method is applied to explore the asymmetric correlation of PM2.5 daily average concentration with uptrends or downtrends in China. In addition, shuffling and phase randomization procedures are applied to detect the sources of multifractality. The results show that existences of asymmetric correlations, and the asymmetric correlations are multifractal. Further, the multifractal scaling behavior in the Chinese PM2.5 is caused not only by long-range correlation but also by fat-tailed distribution, but the major source of multifractality is fat-tailed distribution.
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.
Sandbox algorithm for multifractal analysis of complex networks
Liu, Jin-Long; Anh, Vo
2014-01-01
Complex networks have attracted much attention in diverse areas of science and technology. Multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new algorithm --- the sandbox (SB) algorithm, for MFA of complex networks. First we compare the SB algorithm with two existing algorithms of MFA for complex networks: the compact-box-burning (CBB) algorithm proposed by Furuya and Yakubo ( Phys. Rev. E, 84 (2011) 036118), and the improved box-counting (BC) algorithm proposed by Li et al. ( J. Stat. Mech.: Theor. Exp., 2014 (2014) P02020) by calculating the mass exponents tau(q) of some deterministic model networks. We make a detailed comparison between the numerical and theoretical results of these model networks. The comparison results show that the SB algorithm is the most effective and feasible algorithm to calculate the mass exponents tau(q) and to explore the multifractal behavior of com...
Nasehnejad, M.; Gholipour Shahraki, M.; Nabiyouni, G.
2016-12-01
We used atomic force microscopy (AFM) to study surface morphology and kinetic roughening of Ag films. X-ray diffraction (XRD) technique is used to verify the films crystalline structure. The influence of film thickness on the kinetic roughening was investigated using AFM data and roughness calculation. It is revealed that the surface roughness increases with increasing the film thickness. The data also consist with a complex behavior which is called as anomalous scaling. Scaling laws analysis for Ag films presents two distinct dynamics including large local and scale roughness and indicates a power law dependency on the thickness of film. AFM images have been characterized by the multifractal analysis. This analysis shows that the self-similar and multifractal characteristics as well as anomalous scaling exist in the Ag film morphologies. Description of the quantitative growth and surface morphology was done by the multifractal spectra, f (α) - α . It is found that the multifractal spectrum shape is left hook-like (that is difference of height interval of the multifractal spectrum, Δf = f (αmin) - f (αmax) > 0). The results indicate that the surfaces having greater roughness give rise the wider multifractal spectrum width (Δα) and the greater Δf, thus, the nonuniformity of the height probabilities becomes larger. It indicates that the multifractality of the films becomes more pronounced at the higher thickness.
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 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
Rainfall Climatology of the US Based on a Multifractal Storm Model
Lepore, C.; Molini, A.; Veneziano, D.; Yoon, S.
2012-12-01
Whether the multifractal properties of rainfall are impacted by climatology and therefore deviate from universality is a vexing question in both hydrology and the climate sciences and a crucial issue for rainfall downscaling applications. In a recent paper, Veneziano and Lepore (The Scaling of Temporal Rainfall, WRR, 2012) suggested a rainfall model with alternating storms and dry inter-storm periods and beta-lognormal multifractal rainfall intensity inside the storms. The parameters of the model are the rate of storm arrivals λ , the mean value mD and coefficient of variation VD of storm duration, the mean rainfall intensity inside the storms mI, and the multifractal parameters Cβ (lacunarity), CLN (intermittency), and dmax (outer limit of the scaling range). We use this model and 200 hourly rainfall records from NOAA to describe the variability of intense rainfall over the continental US. The records are selected based on length (at least 25 years) and data quality (quantization, fraction of unavailable values, periods when rainfall is reported as aggregated total depth…). We conclude that CLN and dmax display large systematic variations in space and with season. In particular, CLN decreases as latitude increases, from 0.20-0.25 along the Gulf of Mexico to about 0.12 in New England and 0.08 in the Northwest. This spatial variation is captured in approximation by partitioning the continental US into 11 climatic regions. Seasonal analysis shows that in most regions CLN is highest in the summer and lowest in the winter, following similar variations in the frequency and intensity of convective rainfall. An exception is the Northwest region, where CLN is almost constant throughout the year. The outer scale dmax is negatively correlated with CLN and follows opposite trends. The lacunarity parameter Cβ is lowest (around 0.04) in the Northeast and highest (around 0.07) in Florida and the Midwestern region. Lacunarity tends to be higher in the spring and summer
Inverse Multifractal Analysis of Different Frame Types of Multiview 3D Video
Directory of Open Access Journals (Sweden)
A. Zeković
2014-11-01
Full Text Available In this paper, the results of multifractal characterization of multiview 3D video are presented. Analyses are performed for different views of multiview video and for different frame types of video. Multifractal analysis is performed by the histogram method. Due to the advantages of the selected method for determining the spectrum, the inverse multifractal analysis of multiview 3D video was also possible. A discussion of the results obtained by the inverse multifractal analysis of multiview 3D video is presented, taking into account the frame type and whether the original frames belong to the left or right view of multiview 3D video. In the analysis, publicly available multiview 3D video traces were used.
Institute of Scientific and Technical Information of China (English)
林近山; 陈前
2013-01-01
Gearbox fault data are usually characterized by nonstationarity and multiple scaling behaviors, a detrended fluctuation analysis ( DFA) often fails to uncover their underlying dynamical mechanism. Multifractal DFA (MF-DFA) is an extension of DFA and able to effectively reveal their underlying dynamical mechanism hidden in nonstationary data with multiple scaling behaviors. To start with, MF-DFA was used to compute the multifractal singularity spectrum of gearbox fault data. Next, four characteristic parameters including multifractal spectrum width, maximum singularity exponent, minimum singularity exponent and singularity exponent corresponding to extremum of multifractal spectrum had clear physical meaning, they could express underlying dynamical mechanism of gearbox fault data and could be employed as fault features of gearbox fault data. Consequently, a novel method for feature extraction of gearbox fault data was proposed based on MF-DFA. Besides, the proposed method together with DFA was utilized to separate the normal, the slight-worn, the medium-worn and the broken-tooth vibration data from a four-speed motorcycle gearbox. The results showed that the proposed method overcomes the deficiencies of DFA, it is sensitive to small changes of gearbox fault conditions, it can totally separate the fault patterns close to each other and is a feasible method for feature extraction of gearbox fault data.%齿轮箱故障信号通常是具有多标度行为的非平稳信号,去趋势波动分析(Detrended Fluctuation Analysis,DFA)不能准确揭示隐藏在这类信号中的动力学行为.多重分形去趋势波动分析(Multifractal Detrended Fluctuation Analysis,MF-DFA)是DFA方法的拓展,能够有效地揭示隐藏在多标度非平稳信号中的动力学行为.利用MF-DFA计算齿轮箱故障信号的多重分形奇异谱,而多重分形奇异谱的宽度、最大奇异指数、最小奇异指数和极值点对应的奇异指数都具有明确的物理意义,
An analysis of multifractal characteristics of API time series in Nanjing, China
Shen, Chen-hua; Huang, Yi; Yan, Ya-ni
2016-06-01
This paper describes multifractal characteristics of daily air pollution index (API) records in Nanjing from 2001 to 2012. The entire daily API time series is first divided into 12 parts that serve as research objects, and the generalized Hurst exponent is calculated for each series. And then, the multifractal sources are analyzed and singularity spectra are shown. Next, based on a singularity spectrum, the multifractal-characteristics parameters (maximum exponent α0, spectrum width Δ α, and asymmetry Δ αas) are introduced. The results show that the fractality of daily API for each year is multifractal. The multifractal sources originate from both a broad probability density function and different long-range correlations with small and large fluctuations. The strength of the distribution multifractality is stronger than that of the correlation multifractality. The variation in the structure of API time series with increasing years is mainly related to long-range correlations. The structure of API time series in some years is richer. These findings can provide a scientific basis for further probing into the complexity of API.
Multifractal detrended fluctuation analysis of analog random multiplicative processes
Energy Technology Data Exchange (ETDEWEB)
Silva, L.B.M.; Vermelho, M.V.D. [Instituto de Fisica, Universidade Federal de Alagoas, Maceio - AL, 57072-970 (Brazil); Lyra, M.L. [Instituto de Fisica, Universidade Federal de Alagoas, Maceio - AL, 57072-970 (Brazil)], E-mail: marcelo@if.ufal.br; Viswanathan, G.M. [Instituto de Fisica, Universidade Federal de Alagoas, Maceio - AL, 57072-970 (Brazil)
2009-09-15
We investigate non-Gaussian statistical properties of stationary stochastic signals generated by an analog circuit that simulates a random multiplicative process with weak additive noise. The random noises are originated by thermal shot noise and avalanche processes, while the multiplicative process is generated by a fully analog circuit. The resulting signal describes stochastic time series of current interest in several areas such as turbulence, finance, biology and environment, which exhibit power-law distributions. Specifically, we study the correlation properties of the signal by employing a detrended fluctuation analysis and explore its multifractal nature. The singularity spectrum is obtained and analyzed as a function of the control circuit parameter that tunes the asymptotic power-law form of the probability distribution function.
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.
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.
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.
Multifractal Analysis of Infinite Products of Stationary Jump Processes
Directory of Open Access Journals (Sweden)
Petteri Mannersalo
2010-01-01
Full Text Available There has been a growing interest in constructing stationary measures with known multifractal properties. In an earlier paper, the authors introduced the multifractal products of stochastic processes (MPSP and provided basic properties concerning convergence, nondegeneracy, and scaling of moments. This paper considers a subclass of MPSP which is determined by jump processes with i.i.d. exponentially distributed interjump times. Particularly, the information dimension and a multifractal spectrum of the MPSP are computed. As a side result it is shown that the random partitions imprinted naturally by a family of Poisson point processes are sufficient to determine the spectrum in this case.
MULTIFRACTAL ANALYSIS OF PARTICLE-FLUID SYSTEM IN A CIRCULATING FLUIDIZED BED
Institute of Scientific and Technical Information of China (English)
Liping; Ma; Weixing; Huang; Yanfu; Shi; Huarui; Yu; Jingxu; Zhu
2005-01-01
In this paper, multifractal analysis together with wavelet transform modulus maxima (WTMM) method is used to analyze the fluctuating signals of circulating fluidized bed (CFB). Singularity spectrum shows that the gas-particle flow in CFB has multifractal character. Motion behavior of the particle-fluid system of CFB can be described by singularity spectrum. Intermittency index can be used to determine the transition of flow regime from fast fluidization to pneumatic conveying.
Wei, Yu; Huang, Dengshi
2005-09-01
In this paper, high frequency (per 5 min) data of Shanghai Stock Exchange Composite index (SSEC) from January 1999 to July 2001 is analyzed by multifractal. We find that the correlation of the parameters of the multifractal spectra with the variation of daily return Z in SSEC is noticeably different from that in previous studies of Heng Seng index in Hong Kong stock market [Sun et al., Phys. A 291 (2001) 553-562; Sun et al., Phys. A 301 (2001) 473-482]. So, we suppose that there may not be a universal rule for the dependence of the parameters of the multifractal spectra with daily return of a stock index. Then, we construct a new measurement of market risk based on multifractal spectra, and test its ability of predicting index fluctuations with a more thorough method than that in Sun et al. [Phys. A 301 (2001) 473-482].
Multifractal Properties of the Ukraine Stock Market
Ganchuk, A; Solovov, V
2006-01-01
Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. We used two possible procedures of analyzing multifractal properties of a time series. The first one uses the continuous wavelet transform and extracts scaling exponents from the wavelet transform amplitudes over all scales. The second method is the multifractal version of the detrended fluctuation analysis method (MF-DFA). The multifractality of a time series we analysed by means of the difference of values singularity stregth as a suitable way to characterise multifractality. Singularity spectrum calculated from daily returns using a sliding 1000 day time window in discrete steps of 1-10 days. We discovered that changes in the multifractal spectrum display distinctive pattern around significant "drawdowns". Finally, we discuss applications to the construction of crushes precursors at the financial markets.
Multifractal analysis of high resolution solar wind proton density measurements
Sorriso-Valvo, Luca; Carbone, Francesco; Leonardis, Ersilia; Chen, Christopher H. K.; Šafránková, Jana; Němeček, Zdenek
2017-03-01
The solar wind is a highly turbulent medium, with a high level of field fluctuations throughout a broad range of scales. These include an inertial range where a turbulent cascade is assumed to be active. The solar wind cascade shows intermittency, which however may depend on the wind conditions. Recent observations have shown that ion-scale magnetic turbulence is almost self-similar, rather than intermittent. A similar result was observed for the high resolution measurements of proton density provided by the spacecraft Spektr-R. Intermittency may be interpreted as the result of the multifractal properties of the turbulent cascade. In this perspective, this paper is devoted to the description of the multifractal properties of the high resolution density measurements. In particular, we have used the standard coarse-graining technique to evaluate the generalized dimensions Dq , and from these the multifractal spectrum f (α) , in two ranges of scale. A fit with the p-model for intermittency provided a quantitative measure of multifractality. Such indicator was then compared with alternative measures: the width of the multifractal spectrum, the peak of the kurtosis, and its scaling exponent. The results indicate that the small-scale fluctuations are multifractal, and suggest that different measures of intermittency are required to fully understand the small scale cascade.
Multifractal analysis of 2D gray soil images
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
Guo, Enliang; Zhang, Jiquan; Si, Ha; Dong, Zhenhua; Cao, Tiehua; Lan, Wu
2016-08-01
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 analysis of earthquakes in Kumaun Himalaya and its surrounding region
Indian Academy of Sciences (India)
P N S Roy; S K Mondal
2012-08-01
Himalayan seismicity is related to continuing northward convergence of Indian plate against Eurasian plate. Earthquakes in this region are mainly caused due to release of elastic strain energy. The Himalayan region can be attributed to highly complex geodynamic process and therefore is best suited for multifractal seismicity analysis. Fractal analysis of earthquakes (mb ≥ 3.5) occurred during 1973–2008 led to the detection of a clustering pattern in the narrow time span. This clustering was identified in three windows of 50 events each having low spatial correlation fractal dimension () value 0.836, 0.946 and 0.285 which were mainly during the span of 1998 to 2005. This clustering may be considered as an indication of a highly stressed region. The Guttenberg Richter -value was determined for the same subsets considered for the estimation. Based on the fractal clustering pattern of events, we conclude that the clustered events are indicative of a highly stressed region of weak zone from where the rupture propagation eventually may nucleate as a strong earthquake. Multifractal analysis gave some understanding of the heterogeneity of fractal structure of the seismicity and existence of complex interconnected structure of the Himalayan thrust systems. The present analysis indicates an impending strong earthquake, which might help in better hazard mitigation for the Kumaun Himalaya and its surrounding region.
Directory of Open Access Journals (Sweden)
Stefan Tălu
2015-10-01
Full Text Available AIM:To characterize the human retinal vessel arborisation in normal and amblyopic eyes using multifractal geometry and lacunarity parameters.METHODS:Multifractal analysis using a box counting algorithm was carried out for a set of 12 segmented and skeletonized human retinal images, corresponding to both normal (6 images and amblyopia states of the retina (6 images.RESULTS:It was found that the microvascular geometry of the human retina network represents geometrical multifractals, characterized through subsets of regions having different scaling properties that are not evident in the fractal analysis. Multifractal analysis of the amblyopia images (segmented and skeletonized versions show a higher average of the generalized dimensions (Dq for q=0, 1, 2 indicating a higher degree of the tree-dimensional complexity associated with the human retinal microvasculature network whereas images of healthy subjects show a lower value of generalized dimensions indicating normal complexity of biostructure. On the other hand, the lacunarity analysis of the amblyopia images (segmented and skeletonized versions show a lower average of the lacunarity parameter Λ than the corresponding values for normal images (segmented and skeletonized versions.CONCLUSION:The multifractal and lacunarity analysis may be used as a non-invasive predictive complementary tool to distinguish amblyopic subjects from healthy subjects and hence this technique could be used for an early diagnosis of patients with amblyopia.
Tălu, Stefan; Vlăduţiu, Cristina; Lupaşcu, Carmen A
2015-01-01
To characterize the human retinal vessel arborisation in normal and amblyopic eyes using multifractal geometry and lacunarity parameters. Multifractal analysis using a box counting algorithm was carried out for a set of 12 segmented and skeletonized human retinal images, corresponding to both normal (6 images) and amblyopia states of the retina (6 images). It was found that the microvascular geometry of the human retina network represents geometrical multifractals, characterized through subsets of regions having different scaling properties that are not evident in the fractal analysis. Multifractal analysis of the amblyopia images (segmented and skeletonized versions) show a higher average of the generalized dimensions (Dq ) for q=0, 1, 2 indicating a higher degree of the tree-dimensional complexity associated with the human retinal microvasculature network whereas images of healthy subjects show a lower value of generalized dimensions indicating normal complexity of biostructure. On the other hand, the lacunarity analysis of the amblyopia images (segmented and skeletonized versions) show a lower average of the lacunarity parameter Λ than the corresponding values for normal images (segmented and skeletonized versions). The multifractal and lacunarity analysis may be used as a non-invasive predictive complementary tool to distinguish amblyopic subjects from healthy subjects and hence this technique could be used for an early diagnosis of patients with amblyopia.
Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion
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.
Multifractal Detrended Cross-Correlation Analysis of agricultural futures markets
Energy Technology Data Exchange (ETDEWEB)
He Lingyun, E-mail: lyhe@amss.ac.cn [Center for Futures and Financial Derivatives, College of Economics and Management, China Agricultural University, Beijing 100083 (China); Chen Shupeng [Center for Futures and Financial Derivatives, College of Economics and Management, China Agricultural University, Beijing 100083 (China)
2011-06-15
Highlights: > We investigated cross-correlations between China's and US agricultural futures markets. > Power-law cross-correlations are found between the geographically far but correlated markets. > Multifractal features are significant in all the markets. > Cross-correlation exponent is less than averaged GHE when q < 0 and greater than the latter when q > 0. - Abstract: We investigated geographically far but temporally correlated China's and US agricultural futures markets. We found that there exists a power-law cross-correlation between them, and that multifractal features are significant in all the markets. It is very interesting that the geographically far markets show strong cross-correlations and share much of their multifractal structure. Furthermore, we found that for all the agricultural futures markets in our studies, the cross-correlation exponent is less than the averaged generalized Hurst exponents (GHE) when q < 0 and greater than the averaged GHE when q > 0.
Are crude oil markets multifractal? Evidence from MF-DFA and MF-SSA perspectives
He, Ling-Yun; Chen, Shu-Peng
2010-08-01
In this article, we investigated the multifractality and its underlying formation mechanisms in international crude oil markets, namely, Brent and WTI, which are the most important oil pricing benchmarks globally. We attempt to find the answers to the following questions: (1) Are those different markets multifractal? (2) What are the dynamical causes for multifractality in those markets (if any)? To answer these questions, we applied both multifractal detrended fluctuation analysis (MF-DFA) and multifractal singular spectrum analysis (MF-SSA) based on the partition function, two widely used multifractality detecting methods. We found that both markets exhibit multifractal properties by means of these methods. Furthermore, in order to identify the underlying formation mechanisms of multifractal features, we destroyed the underlying nonlinear temporal correlation by shuffling the original time series; thus, we identified that the causes of the multifractality are influenced mainly by a nonlinear temporal correlation mechanism instead of a non-Gaussian distribution. At last, by tracking the evolution of left- and right-half multifractal spectra, we found that the dynamics of the large price fluctuations is significantly different from that of the small ones. Our main contribution is that we not only provided empirical evidence of the existence of multifractality in the markets, but also the sources of multifractality and plausible explanations to current literature; furthermore, we investigated the different dynamical price behaviors influenced by large and small price fluctuations.
Multi-fractal analysis of highway traffic data
Institute of Scientific and Technical Information of China (English)
Shang Peng-Jian; Shen Jin-Sheng
2007-01-01
The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwise H(o)lder exponent of a function is calculated by developing an algorithm for the numerical evaluation of H(o)lder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.
Directory of Open Access Journals (Sweden)
Todd Zorick
Full Text Available Recently, many lines of investigation in neuroscience and statistical physics have converged to raise the hypothesis that the underlying pattern of neuronal activation which results in electroencephalography (EEG signals is nonlinear, with self-affine dynamics, while scalp-recorded EEG signals themselves are nonstationary. Therefore, traditional methods of EEG analysis may miss many properties inherent in such signals. Similarly, fractal analysis of EEG signals has shown scaling behaviors that may not be consistent with pure monofractal processes. In this study, we hypothesized that scalp-recorded human EEG signals may be better modeled as an underlying multifractal process. We utilized the Physionet online database, a publicly available database of human EEG signals as a standardized reference database for this study. Herein, we report the use of multifractal detrended fluctuation analysis on human EEG signals derived from waking and different sleep stages, and show evidence that supports the use of multifractal methods. Next, we compare multifractal detrended fluctuation analysis to a previously published multifractal technique, wavelet transform modulus maxima, using EEG signals from waking and sleep, and demonstrate that multifractal detrended fluctuation analysis has lower indices of variability. Finally, we report a preliminary investigation into the use of multifractal detrended fluctuation analysis as a pattern classification technique on human EEG signals from waking and different sleep stages, and demonstrate its potential utility for automatic classification of different states of consciousness. Therefore, multifractal detrended fluctuation analysis may be a useful pattern classification technique to distinguish among different states of brain function.
Pal, Mayukha; Kiran, V. Satya; Rao, P. Madhusudana; Manimaran, P.
2016-08-01
We characterized the multifractal nature and power law cross-correlation between any pair of genome sequence through an integrative approach combining 2D multifractal detrended cross-correlation analysis and chaos game representation. In this paper, we have analyzed genomes of some prokaryotes and calculated fractal spectra h(q) and f(α) . From our analysis, we observed existence of multifractal nature and power law cross-correlation behavior between any pair of genome sequences. Cluster analysis was performed on the calculated scaling exponents to identify the class affiliation and the same is represented as a dendrogram. We suggest this approach may find applications in next generation sequence analysis, big data analytics etc.
Evidence of multifractality from emerging European stock markets.
Caraiani, Petre
2012-01-01
We test for the presence of multifractality in the daily returns of the three most important stock market indices from Central and Eastern Europe, Czech PX, Hungarian BUX and Polish WIG using the Empirical Mode Decomposition based Multifractal Detrended Fluctuation Analysis. We found that the global Hurst coefficient varies with the q coefficient and that there is multifractality evidenced through the multifractal spectrum. The exercise is replicated for the sample around the high volatility period corresponding to the last global financial crisis. Although no direct link has been found between the crisis and the multifractal spectrum, the crisis was found to influence the overall shape as quantified through the norm of the multifractal spectrum.
Evidence of multifractality from emerging European stock markets.
Directory of Open Access Journals (Sweden)
Petre Caraiani
Full Text Available We test for the presence of multifractality in the daily returns of the three most important stock market indices from Central and Eastern Europe, Czech PX, Hungarian BUX and Polish WIG using the Empirical Mode Decomposition based Multifractal Detrended Fluctuation Analysis. We found that the global Hurst coefficient varies with the q coefficient and that there is multifractality evidenced through the multifractal spectrum. The exercise is replicated for the sample around the high volatility period corresponding to the last global financial crisis. Although no direct link has been found between the crisis and the multifractal spectrum, the crisis was found to influence the overall shape as quantified through the norm of the multifractal spectrum.
Cabrelli, Carlos; Jaffard, Stephane; Molter, Ursula
2016-01-01
This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and covers both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.
Wei, Yun-Lan; Yu, Zu-Guo; Zou, Hai-Long; Anh, Vo
2017-06-01
A new method—multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA)—is proposed to investigate multifractal cross-correlations in this paper. This new method is based on multifractal temporally weighted detrended fluctuation analysis and multifractal cross-correlation analysis (MFCCA). An innovation of the method is applying geographically weighted regression to estimate local trends in the nonstationary time series. We also take into consideration the sign of the fluctuations in computing the corresponding detrended cross-covariance function. To test the performance of the MF-TWXDFA algorithm, we apply it and the MFCCA method on simulated and actual series. Numerical tests on artificially simulated series demonstrate that our method can accurately detect long-range cross-correlations for two simultaneously recorded series. To further show the utility of MF-TWXDFA, we apply it on time series from stock markets and find that power-law cross-correlation between stock returns is significantly multifractal. A new coefficient, MF-TWXDFA cross-correlation coefficient, is also defined to quantify the levels of cross-correlation between two time series.
Institute of Scientific and Technical Information of China (English)
丁凯; 方向; 张卫平; 范磊; 李兴华; 谢立军
2012-01-01
In order to improve the recognition rate of smart landmines for armored target, as the acoustic signals radiated from armored vehicles have been proved to be nonlinear, an identification model based on multifractal analysis and support vector machine (SVM) was established. 40 sample signals for each armored target( a certain type of wheeled armored vehicle and a tank) running in different speeds(2 working conditions) were collected by outdoor experiment. The generalized fractal dimension spectrums ( GFDS) for both target signals were calculated based on multifractal analysis, and the characters of GFDS under 2 working conditions were analyzed. The GFDS values were input into SVM classification model, and the optimal identification results were obtained by training the model. After an identification effect comparison between GFDS and wavelet packet energy ( WPE) method, the results show that the model based on GFDS and SVM has a recognition rate of 92. 5% , which is higher than the 85% by WPE method.%为提高智能地雷对地面装甲目标的识别率,针对地面装甲目标辐射的噪声信号具有非线性的特性,建立了一种基于多重分形和支持向量机(SVM)相结合的分类识别模型.通过野外场地实验,采集到两种装甲目标在不同工况(运行速度)下的各40组样本信号；利用多重分形分析计算得到两种目标信号的广义分形维数谱(GFDS),分析了两种目标信号在不同工况下多重分形谱的特征；将GFDS值作为目标特征向量输入SVM分类模型,经训练得到最优分类结果,并与小波包能量(WPE)法提取样本特征后输入SVM的识别效果进行了对比,结果表明前者的识别率达到92.5％,高于后者的85％的识别率.
Institute of Scientific and Technical Information of China (English)
杜文辽; 陶建峰; 巩晓赟; 贡亮; 刘成良
2016-01-01
Multifractal detrended fluctuation analysis is an effective tool for dealing with the non-uniformity and singularity of nonstationary time series. For the serious issues of the trend extraction and the ineﬃcient computation in the traditional polynomial fitting based multifractal detrended fluctuation analysis, based on the dual-tree complex wavelet transform, a novel multifractal analysis is proposed. To begin with, as the dual-tree complex wavelet transform has the anti-aliasing and nearly shift-invariance, it is first utilized to decompose the signal through the pyramid algorithm, and the scale-dependent trends and the fluctuations are extracted from the wavelet coeﬃcients. Then, using the wavelet coeﬃcients, the length of the non-overlapping segment on a corresponding time scale is computed through the Hilbert transform, and each of the extracted fluctuations is divided into a series of non-overlapping segments whose sizes are identical. Next,on each scale, the detrended fluctuation function for each segment is calculated, and the overall fluctuation function can be obtained by averaging all segments with different orders. Finally, the generalized Hurst index and scaling exponent spectrum are determined from the logarithmic relations between the overall detrended fluctuation function and the time scale and the standard partition function, respectively, and then the multifractal singularity spectrum is calculated with the help of Legendre transform. We assess the performance of the dual-tree-complex wavelet transform based multifractal detrended fluctuation analysis (MFDFA) procedure through the classic multiplicative cascading process and the fractional Brownian motions, which have the theoretical fractal measures. For the multiplicative cascading process, compared with the traditional polynomial fitting based MFDFA methods, the proposed multifractal approach defines the trends and the length of non-overlapping segments adaptively and obtains a more
Phase transitions for the multifractal analysis of self-similar measures
Testud, B.
2006-05-01
We are interested in the multifractal analysis of a class of self-similar measures with overlaps. This class, for which we obtain explicit formulae for the Lq-spectrum, τ(q), as well as the singularity spectrum f(α), is sufficiently large to point out new phenomena in the multifractal structure of self-similar measures. We show that, unlike in the classical quasi-Bernoulli case, the Lq-spectrum, τ(q), of the measures studied can have an arbitrarily large number of non-differentiability points (phase transitions). These singularities occur only for the negative values of q and yield to measures that do not satisfy the usual multifractal formalism. The weak quasi-Bernoulli property is the key point of most of the arguments.
Multifractal analysis of surface EMG signals for assessing muscle fatigue during static contractions
Institute of Scientific and Technical Information of China (English)
WANG Gang; REN Xiao-mei; LI Lei; WANG Zhi-zhong
2007-01-01
This study is aimed at assessing muscle fatigue during a static contraction using multifractal analysis and found that the surface electromyographic (SEMG) signals characterized multifractality during a static contraction. By applying the method of direct determination of the f(α) singularity spectrum, the area of the multifractal spectrum of the SEMG signals was computed. The results showed that the spectrum area significantly increased during muscle fatigue. Therefore the area could be used as an assessor of muscle fatigue. Compared with the median frequency (MDF)-the most popular indicator of muscle fatigue, the spectrum area presented here showed higher sensitivity during a static contraction. So the singularity spectrum area is considered to be a more effective indicator than the MDF for estimating muscle fatigue.
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.
Institute of Scientific and Technical Information of China (English)
温芝元; 曹乐平
2013-01-01
Plant pests and diseases image recognition is one of the key technologies of digital agricultural information collection and processing. Usually, based on pest infestation-like plant, it is carried out according to the size, shape, color, texture, etc., or a combination of several parameters. Machine recognition of diseases and insect pests needs to use digitalized characteristics without overlapping. Multi-fractal analysis of Fourier transform spectra was adopted to investigate the possibility of extraction of damage pattern characteristics for Citrus reticulata Blanco var. Ponkan. First, images of the boundary of a damaged pattern are extracted with an improved watershed algorithm and region merging. Secondly, a Discrete Fourier Transform (DFT) was applied to the damaged fruit image. With reference to the boundary of a damaged pattern, a fruit image magnitude spectrum was extracted. Thirdly, a fruit image magnitude spectrum was multi-fractiously analyzed and the multi-fractal spectrum of DFT magnitude spectrum was quadratic fitted. Height, width, and centroid coordinate of a fitting parabolic section were chosen feature values to identify the diseases and insect damage of fruits, with these three feature values as inputs of a BP neural network identifying diseases and insect damage of Ponkan, and the accuracy was up to 92.67%. Finally, the amplitude spectrum of the Fourier transform was adopted for multifractal analysis and multi-fractal spectrum of a quadratic fit;fit parabola segment height, width, and centroid coordinates were regarded as pests’ Eigen values, and then used as input variables to establish a BP citrus pest identification neural network model for pest identification. Among 5 classes of pests, in 30 groups of test samples, such as Pezothrips Kellyanus, Oxycetonia Jucunda, Oraesia Emarginata, Polyphagotarsonemus Latus, Colletotrichum Gloeoporioides Penz, the highest recognition rate was for Oraesia Emarginata, that is 96.67%, Polyphagotarsonemus
Multifractal analysis of non-uniformly contracting iterated function systems
Ye, Yuan-Ling
2017-05-01
Let X = [0,1]. Given a non-uniformly contracting conformal iterated function system (IFS) ≤ft\\{{{w}j}\\right\\}j=1m and a family of positive Dini continuous potential functions ≤ft\\{ {{p}j}\\right\\}j=1m , the triple system ≤ft(X,≤ft\\{{{w}j}\\right\\}j=1m,≤ft\\{ {{p}j}\\right\\}j=1m\\right) , under some conditions, determines uniquely a probability invariant measure, denoted by μ. In this paper, we study the pressure function of the system and multifractal structure of μ. We prove that the pressure function is Gateaux differentiable and the multifractal formalism holds, if the IFS ≤ft\\{{{w}j}\\right\\}j=1m has non-overlapping.
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.
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.
Analysis of normal human retinal vascular network architecture using multifractal geometry
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
Gierałtowski, J.; Żebrowski, J. J.; Baranowski, R.
2012-02-01
Human heart rate variability, in the form of time series of intervals between heart beats, shows complex, fractal properties. Recently, it was demonstrated many times that the fractal properties vary from point to point along the series, leading to multifractality. In this paper, we concentrate not only on the fact that the human heart rate has multifractal properties but also that these properties depend on the time scale in which the multifractality is measured. This time scale is related to the frequency band of the signal. We find that human heart rate variability appears to be far more complex than hitherto reported in the studies using a fixed time scale. We introduce a method called multiscale multifractal analysis (MMA), which allows us to extend the description of heart rate variability to include the dependence on the magnitude of the variability and time scale (or frequency band). MMA is relatively immune to additive noise and nonstationarity, including the nonstationarity due to inclusions into the time series of events of a different dynamics (e.g., arrhythmic events in sinus rhythm). The MMA method may provide new ways of measuring the nonlinearity of a signal, and it may help to develop new methods of medical diagnostics.
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.
The l1/2 law and multifractal topography: theory and analysis
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S. Lovejoy
1995-01-01
Full Text Available Over wide ranges of scale, orographic processes have no obvious scale; this has provided the justification for both deterministic and monofractal scaling models of the earth's topography. These models predict that differences in altitude (Δh vary with horizontal separation (l as Δh ≈ lH. The scaling exponent has been estimated theoretically and empirically to have the value H=1/2. Scale invariant nonlinear processes are now known to generally give rise to multifractals and we have recently empirically shown that topography is indeed a special kind of theoretically predicted "universal" multifractal. In this paper we provide a multifractal generalization of the l1/2 law, and propose two distinct multifractal models, each leading via dimensional arguments to the exponent 1/2. The first, for ocean bathymetry assumes that the orographic dynamics are dominated by heat fluxes from the earth's mantle, whereas the second - for continental topography - is based on tectonic movement and gravity. We test these ideas empirically on digital elevation models of Deadman's Butte, Wyoming.
Energy Technology Data Exchange (ETDEWEB)
Schertzer, D.; Lovejoy, S. [Univ. Pierre et Marie Curie, Paris (France)
1995-09-01
Multifractal techniques and notions are increasingly widely recognized as the most appropriate and straightforward framework within which to analyze and simulate not only the scale dependence of geophysical observables, but also their extreme variability over a wide range of scales. This is particularly the case for cloud fields and their radiative properties. Schertzer first recalled the original scalar framework of turbulent cascades, especially for the modeling and analysis of passive clouds, based on multifractal developments of the Corrsin-Obukhov spectral scaling of scalar variance. These developments are based on the scaling symmetries of the dynamical equations of both the velocity and liquid water density fields. He emphasized the power of straightforward simulation methods based on these physical arguments. Schertzer showed a video displaying a time evolution of multifractal cloud in the framework of universal multifractals. He insisted that with the aid of these tools, there is no real need to took for constructs such as bounded cascades. 6 refs.
Assessing soil surface roughness decay during simulated rainfall by multifractal analysis
Directory of Open Access Journals (Sweden)
E. Vidal Vázquez
2008-06-01
Full Text Available Understanding and describing the spatial characteristics of soil surface microrelief are required for modelling overland flow and erosion. We employed the multifractal approach to characterize topographical point elevation data sets acquired by high resolution laser scanning for assessing the effect of simulated rainfall on microrelief decay. Three soil surfaces with different initial states or composition and rather smooth were prepared on microplots and subjected to successive events of simulated rainfall. Soil roughness was measured on a 2×2 mm^{2} grid, initially, i.e. before rain, and after each simulated storm, yielding a total of thirteen data sets for three rainfall sequences. The vertical microrelief component as described by the statistical index random roughness (RR exhibited minor changes under rainfall in two out of three study cases, which was due to the imposed wet initial state constraining aggregate breakdown. The effect of cumulative rainfall on microrelief decay was also assessed by multifractal analysis performed with the box-count algorithm. Generalized dimension, D_{q}, spectra allowed characterization of the spatial variation of soil surface microrelief measured at the microplot scale. These D_{q} spectra were also sensitive to temporal changes in soil surface microrelief, so that in all the three study rain sequences, the initial soil surface and the surfaces disturbed by successive storms displayed great differences in their degree of multifractality. Therefore, Multifractal parameters best discriminate between successive soil stages under a given rain sequence. Decline of RR and multifractal parameters showed little or no association.
Joint Multifractal Analysis of penetration resistance variability in an olive orchard.
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
Assessment of petrophysical quantities inspired by joint multifractal approach
Lai, Z Koohi; Jafari, G R
2015-01-01
In this paper joint multifractal random walk approach is carried out to analyze some petrophysical quantities for characterizing the petroleum reservoir. These quantities include Gamma emission (GR), sonic transient time (DT) and Neutron porosity (NPHI) which are collected from four wells of a reservoir. To quantify mutual interaction of petrophysical quantities, joint multifractal random walk is implemented. This approach is based on the mutual multiplicative cascade notion in the multifractal formalism and in this approach $L_0$ represents a benchmark to describe the nature of cross-correlation between two series. The analysis of the petrophysical quantities revealed that GR for all wells has strongly multifractal nature due to the considerable abundance of large fluctuations in various scales. The variance of probability distribution function, $\\lambda_{\\ell}^2$, at scale $\\ell$ and its intercept determine the multifractal properties of the data sets sourced by probability density function. The value of $\\...
Multifractal Scaling of Grayscale Patterns: Lacunarity and Correlation Dimension
Roy, A.; Perfect, E.
2012-12-01
While fractal models can characterize self-similarity in binary fields, comprised solely of 0's and 1's, the concept of multifractals is needed to quantify scaling behavior in non-binary grayscale fields made up of fractional values. Multifractals are characterized by a spectrum of non-integer dimensions, Dq (-∞ lacunarity, L, which characterizes the distribution of gaps or spaces in patterns, fractals, multifractals or otherwise, as a function of scale (or box-size, x). In the case of 2-dimensional multifractal fields, L has been shown to be theoretically related to the correlation dimension, D2, by dlog(L)/dlog(x) = D2 - 2. Therefore, it is hypothesized that lacunarity analysis can help in delineating multifractal behavior in grayscale patterns. In testing this hypothesis, a set of 2-dimensional multifractal grayscale patterns was generated with known D2 values, and then analyzed for lacunarity by employing the gliding-box algorithm. The D2 values computed using this analysis gave a 1:1 relationship with the known D2 values, thus empirically validating the theoretical relationship between L and D2. Lacunarity analysis was further used to evaluate the multifractal nature of natural grayscale images in the form of soil thin sections that had been previously classified as multifractals based on the standard box counting method. The results indicated that lacunarity analysis is a more sensitive indicator of multifractal behavior in natural grayscale patterns than the box counting approach. A weighted mean of the log-transformed lacunarity values at different scales was employed for differentiating between grayscale patterns with various degrees of scale dependent clustering attributes. This new measure, which expresses lacunarity as a single number, should prove useful to researchers who want to explore the correlative influence of texture on, for instance, flow and transport parameters. The advantage of using lacunarity instead of D2 in this context is that it can
Energy Technology Data Exchange (ETDEWEB)
Humeau, Anne; Buard, Benjamin; Chapeau-Blondeau, Francois; Rousseau, David [Laboratoire d' Ingenierie des Systemes Automatises (LISA), Universite d' Angers, 62 avenue Notre Dame du Lac, 49000 Angers (France); Mahe, Guillaume; Abraham, Pierre, E-mail: anne.humeau@univ-angers.f [Laboratoire de Physiologie et d' Explorations Vasculaires, UMR CNRS 6214-INSERM 771, Centre Hospitalier Universitaire d' Angers, 49033 Angers cedex 01 (France)
2010-10-21
To contribute to the understanding of the complex dynamics in the cardiovascular system (CVS), the central CVS has previously been analyzed through multifractal analyses of heart rate variability (HRV) signals that were shown to bring useful contributions. Similar approaches for the peripheral CVS through the analysis of laser Doppler flowmetry (LDF) signals are comparatively very recent. In this direction, we propose here a study of the peripheral CVS through a multifractal analysis of LDF fluctuations, together with a comparison of the results with those obtained on HRV fluctuations simultaneously recorded. To perform these investigations concerning the biophysics of the CVS, first we have to address the problem of selecting a suitable methodology for multifractal analysis, allowing us to extract meaningful interpretations on biophysical signals. For this purpose, we test four existing methodologies of multifractal analysis. We also present a comparison of their applicability and interpretability when implemented on both simulated multifractal signals of reference and on experimental signals from the CVS. One essential outcome of the study is that the multifractal properties observed from both the LDF fluctuations (peripheral CVS) and the HRV fluctuations (central CVS) appear very close and similar over the studied range of scales relevant to physiology.
Humeau, Anne; Buard, Benjamin; Mahé, Guillaume; Chapeau-Blondeau, François; Rousseau, David; Abraham, Pierre
2010-10-01
To contribute to the understanding of the complex dynamics in the cardiovascular system (CVS), the central CVS has previously been analyzed through multifractal analyses of heart rate variability (HRV) signals that were shown to bring useful contributions. Similar approaches for the peripheral CVS through the analysis of laser Doppler flowmetry (LDF) signals are comparatively very recent. In this direction, we propose here a study of the peripheral CVS through a multifractal analysis of LDF fluctuations, together with a comparison of the results with those obtained on HRV fluctuations simultaneously recorded. To perform these investigations concerning the biophysics of the CVS, first we have to address the problem of selecting a suitable methodology for multifractal analysis, allowing us to extract meaningful interpretations on biophysical signals. For this purpose, we test four existing methodologies of multifractal analysis. We also present a comparison of their applicability and interpretability when implemented on both simulated multifractal signals of reference and on experimental signals from the CVS. One essential outcome of the study is that the multifractal properties observed from both the LDF fluctuations (peripheral CVS) and the HRV fluctuations (central CVS) appear very close and similar over the studied range of scales relevant to physiology.
THE APPLICATION OF WAVELET-MULTIFRACTAL ANALYSIS IN PROBLEMS OF METAL STRUCTURE
Directory of Open Access Journals (Sweden)
VOLCHUK V. N.
2015-09-01
Full Text Available Raising of problem. In order to obtain acceptable results of the evaluation of the metal structure developed methodology should include the use of both classical and modern methods of its evaluation and the properties of the produced goods. Thus, to establish the relationship between mechanical properties and structural elements of metal to use multifractal theory. The proposed method is the most appropriate to quantify the majority of real structures, which are integral approximation figures Euclid introduces some uncertainty, and therefore not always acceptable in practical problems of modern materials science. According to the proposed method, each of heterogeneous objects, which are the structures most metals can be characterized by variety of statistical Renyi dimensions. The range of dimensions multifractals interpreted as some of the physical laws, which have a separate statistical properties that make it possible to their financial performance. Application of statistical dimensions of the structural elements for the assessment of qualitative characteristics of metal contributes to their formalization as a function of the fractal dimension. This in turn makes it possible to identify and anticipate the physical and mechanical properties of the metal without producing special mechanical tests. Purpose obtain information about the possible application of wavelet-multifractal analysis to assess the microstructure of the metal. Conclusion. Using the methods of wavelet multifractal analysis, a statistical evaluation of the structural elements of steel St3ps. An analysis of the characteristics of uniformity, consistency and regularity of the structural elements has shown that most of the change observed in the samples subjected to accelerated cooling water in the temperature range of the intermediate (bainitic conversion 550 – 4500С, less - in samples cooled in the temperature range 650 pearlite transformation 6000С and the smallest
MULTIFRACTAL ANALYSIS OF PROTEIN AGGREGATES TO DERIVE PROTEIN-SPECIFIC SIGNATURE
Hrishikesh Mishra, Tapobrata Lahiri*
2010-01-01
Deriving a property of a protein that is unique to it has well known significance since the study on ab initio model based derivation of protein structure where uniqueness of protein sequence is taken as the source of specificity of protein structure. In this direction, Heat denatured protein aggregates (HDPA) of proteins were studied with an objective to derive some multi-fractal markers specific to constituent protein that may be further utilized to extract information of the seed protein. ...
Vitanov, N K; Vitanov, Nikolay K.; Yankulova, Elka D.
2006-01-01
Time series of heartbeat activity of humans can exhibit long-range correlations. In this paper we show that such kind of correlations can exist for the heartbeat activity of much simpler species like Drosophila melanogaster. By means of the method of multifractal detrended fluctuation analysis (MFDFA) we calculate fractal spectra $f(\\alpha)$ and $h(q)$ and investigate the correlation properties of heartbeat activity of Drosophila with genetic hearth defects for three consequent generations of species. We observe that opposite to the case of humans the time series of the heartbeat activity of healtly Drosophila do not have scaling properties. Time series from flies with genetic defects can be long-range correllated and can have multifractal properties. The fractal heartbeat dynamics of Drosophila is transferred from generation to generation.
Predictability of multifractal analysis of Hang Seng stock index in Hong Kong
Sun, Xia; Chen, Huiping; Yuan, Yongzhuang; Wu, Ziqin
2001-12-01
In this paper, the daily Hang Seng index in Hong Kong stock market is studied by multifractal analysis. The main parameter of multifractal spectra used is Δ f, which can be used to characterize the ratio of number of highest index moments to that of lowest ones. The dependence of today's gain probability ( G%) and the day's index increase probability ( n%) with Δ f of the previous 3 days are studied. It is found that G% and n% can reach 70-80% at the large positive Δ f region and can be very close to 20% at the big negative Δ f region. The predictability decreases with the increasing number of the previous days.
Designing thermal diode and heat pump based on DNA nanowire: Multifractal approach
Energy Technology Data Exchange (ETDEWEB)
Behnia, S., E-mail: s.behnia@iaurmia.ac.ir; Panahinia, R.
2017-07-12
The management of heat flow in DNA nano wire was considered. Thermal diode effect in DNA and the domain of its appearance dependent to system parameters have been detected. The appearance of directed thermal flow in thermodynamic sizes proposes the possibility of designing the macroscopic thermal rectifier. By applying driven force, pumping effect has been also observed. The resonance frequency of DNA and threshold amplitudes of driving force for attaining permanent pumping effect have been detected. Forasmuch as detecting negative differential thermal resistance (NDTR) phenomenon, DNA can act as a thermal transistor. By using an analytical parallel investigation based on Rényi spectrum analysis, threshold values to transition to NDTR and pumping regimes have been detected. - Highlights: • The control and management of heat current in DNA have been investigated. • Directed thermal flow and NDTR in DNA have been identified. • By increasing the system size, the reversed thermal rectification appeared. So, it is proposed the possibility of designing the macroscopic thermal rectifier. • Pumping effect accompanied with detection of resonance frequency of DNA has been observed. • To verify the results, we did a parallel analysis based on multifractal concept to detect threshold values for transition to pumping state and NDTR regime.
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.
Forecasting volatility of SSEC in Chinese stock market using multifractal analysis
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.
He, Shuilong; Chen, Jinglong; Zhou, Zitong; Zi, Yanyang; Wang, Yanxue; Wang, Xiaodong
2016-08-01
Compound-fault diagnosis of mechanical equipment is still challenging at present because of its complexity, multiplicity and non-stationarity. In this work, an adaptive redundant multiwavelet packet (ARMP) method is proposed for the compound-fault diagnosis. Multiwavelet transform has two or more base functions and many excellent properties, making it suitable for detecting all the features of compound-fault simultaneously. However, on the other hand, the fixed basis function used in multiwavelet transform may decrease the accuracy of fault extraction; what's more, the multi-resolution analysis of multiwavelet transform in low frequency band may also leave out the useful features. Thus, the minimum sum of normalized multifractal entropy is adopted as the optimization criteria for the proposed ARMP method, while the relative energy ratio of the characteristic frequency is utilized as an effective way in automatically selecting the sensitive frequency bands. Then, The ARMP technique combined with Hilbert transform demodulation analysis is then applied to detect the compound-fault of bevel gearbox and planetary gearbox. The results verify that the proposed method can effectively identify and detect the compound-fault of mechanical equipment.
Multifractal analysis of the strength of Fe-Cu paragenetic relationships in eastern Tianshan, China
Zhao, Jie; Wang, Wenlei; Cheng, Qiuming
2016-04-01
Paragenetic association of elements is a natural and important geological phenomenon reflecting the geochemical behavior of elements during various geo-processes. Because of intrinsic characteristics, different elements of paragenetic association may also be generated. As a result, the respective material sources could be shifted from the original locations, and the strength of paragenetic association of elements could be declined. Therefore, study of paragenetic association of elements can help in locating material source, characterizing migration form, and indicating precipitation conditions. Resulted from complicated and cascade geo-processes, the strength of paragenetic relationship between elements presents variations in space. To examine influences of the strength of paragenetic association of elements on polymetallic mineralization, the current research proposes a data processing procedure that includes non-linear regression and multifractal analysis of the resulting regression coefficients. This procedure is currently tested in the eastern Tianshan mineral district, China, and encouraging results are being derived. In this research, geographically weighted regression (GWR), which is a non-linear statistical method, is used to examine the relationship between Fe and Cu concentrations in eastern Tianshan mineral district, China. This local regression method allows calculation of coefficients for Fe and Cu concentrations at every individual location. Therefore, the variation of the strength of Fe-Cu paragenetic association across the study area can be derived. Furthermore, a multifractal method, spectrum-area (S-A) analysis is applied to the regression coefficient map in order to delineate locations strong associated with Fe-Cu mineralization. Anomalies indicating very strong paragenetic association are separated from background. In addition, noise indicating locations with strong paragenetic relationships but that are not suitable for Fe-Cu mineralization are
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.
Multifractals theory and applications
Harte, David
2001-01-01
Although multifractals are rooted in probability, much of the related literature comes from the physics and mathematics arena. Multifractals: Theory and Applications pulls together ideas from both these areas using a language that makes them accessible and useful to statistical scientists. It provides a framework, in particular, for the evaluation of statistical properties of estimates of the Renyi fractal dimensions.The first section provides introductory material and different definitions of a multifractal measure. The author then examines some of the various constructions for describing multifractal measures. Building from the theory of large deviations, he focuses on constructions based on lattice coverings, covering by point-centered spheres, and cascades processes. The final section presents estimators of Renyi dimensions of integer order two and greater and discusses their properties. It also explores various applications of dimension estimation and provides a detailed case study of spatial point patte...
Beyond Fractals and 1/f Noise: Multifractal Analysis of Complex Physiological Time Series
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.
Institute of Scientific and Technical Information of China (English)
张林
2014-01-01
The market dynamics exhibits extremely turbulent behaviors around the financial crisis point. The correct locating of financial crisis point is the key step of distinguishing the multifractal properties of stock mar-ket both before and after financial crisis. Comparing with other methods,the wavelet transform modulus maxi-ma(WTMM)method has its advantages in detecting the outliers and indentifying the multifractal properties in financial markets. The time points of financial crisis are identified though the maxima lines of DJI and TPX in-dices,which are estimated by WTMM. The multifractal analysis of DJI is further performed around the time points where the outliers are detected. From our analysis,the WTMM is found to be capable of not only on correctly locating the time point of financial crisis,but also characterizing the evolution of the multifractal fea-tures both before and after financial crisis. Our empirical results also verify the Fractal Market Hypothesis (FMH)on the causes of market crash and provide a new idea for financial risk management.%在金融危机时点前后，市场的动力学会呈现出异常剧烈的波动。准确定位金融危机时点是区分出金融危机前后股市多重分形特性的关键步骤。与其他方法相比，小波变换模极大值法（WTMM）的优势在于它可以侦测出突变点并对金融市场的多重分形特性进行分析。研究通过小波变换模极大值法（WTMM）所建立的模极大值线将道琼斯工业指数（DJI）与东京证交所股价指数（TPX）的金融危机时点定位出来，随后基于所侦测出来的道琼斯工业指数（DJI）突变点对该指数进行多重分形分析。分析发现：小波变换模极大值法（WTMM）不仅可以准确定位金融危机发生的时点，还可以刻画出多重分形特征在金融危机前后的演化。实证结果验证了分形市场假说（FMH）关于市场发生崩溃的起因，也为金融风险管理提供了一个新思路。
Milazzo, Lorenzo
2016-01-01
A multifractal analysis (MFA) is performed on three-dimensional grayscale images associated with natural porous structures (soil samples). First, computed tomography (CT) scans are carried out on the samples to generate 3D grayscale images. Then, a preliminary analysis is conducted to evaluate key quantities associated with the porosity, such as void fraction, pore volume, connectivity, and surface area. Finally, the samples are successfully identified and separated into two different structure families by using the MFA. A new software (Munari) to carry out the MFA of 3D grayscale images is also presented.
Directory of Open Access Journals (Sweden)
Anirban eBhaduri
2016-02-01
Full Text Available Abstract: Abstract: 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.
Martin, Victor Manuel San
2016-01-01
A method for segmenting water bodies in optical and synthetic aperture radar (SAR) satellite images is proposed. It makes use of the textural features of the different regions in the image for segmentation. The method consists in a multiscale analysis of the images, which allows us to study the images regularity both, locally and globally. As results of the analysis, coarse multifractal spectra of studied images and a group of images that associates each position (pixel) with its corresponding value of local regularity (or singularity) spectrum are obtained. Thresholds are then applied to the multifractal spectra of the images for the classification. These thresholds are selected after studying the characteristics of the spectra under the assumption that water bodies have larger local regularity than other soil types. Classifications obtained by the multifractal method are compared quantitatively with those obtained by neural networks trained to classify the pixels of the images in covered against uncovered b...
When Van Gogh meets Mandelbrot: Multifractal Classification of Painting's Texture
Abry, Patrice; Wendt, Herwig; Jaffard, Stéphane
2013-01-01
International audience; In a recent past, there has been a growing interest for examining the po- tential of Image Processing tools to assist Art Investigation. Simultaneously, several research works showed the interest of using multifractal analysis for the description of homogeneous textures in images. In this context, the goal of the present contribution is to study the benefits of using the wavelet leader based multifractal formalism to characterize paintings. To that end, after a brief r...
Directory of Open Access Journals (Sweden)
Zhike Zhao
2014-07-01
Full Text Available This paper is to propose a novel fault diagnosis method for broken rotor bars in squirrel-cage induction motor of hoister, which is based on duffing oscillator and multifractal dimension. Firstly, based on the analysis of the structure and performance of modified duffing oscillator, the end of transitional slope from chaotic area to large-scale cycle area is selected as the optimal critical threshold of duffing oscillator by bifurcation diagrams and Lyapunov exponent. Secondly, the phase transformation duffing oscillator from chaos to intermittent chaos is sensitive to the signals, whose frequency difference is quite weak from the reference signal. The spectrums of the largest Lyapunov exponents and bifurcation diagrams of the duffing oscillator are utilized to analyze the variance in different parameters of frequency. Finally, this paper is to analyze the characteristics of both single fractal (box-counting dimension and multifractal and make a comparison between them. Multifractal detrended fluctuation analysis is applied to detect extra frequency component of current signal. Experimental results reveal that the method is effective for early detection of broken rotor bars in squirrel-cage induction motor of hoister.
A space-time multifractal analysis on radar rainfall sequences from central Poland
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
Computational approach to multifractal music
Oświęcimka, Paweł; Celińska, Iwona; Drożdż, Stanisław; Rak, Rafał
2011-01-01
In this work we perform a fractal analysis of 160 pieces of music belonging to six different genres. We show that the majority of the pieces reveal characteristics that allow us to classify them as physical processes called the 1/f (pink) noise. However, this is not true for classical music represented here by Frederic Chopin's works and for some jazz pieces that are much more correlated than the pink noise. We also perform a multifractal (MFDFA) analysis of these music pieces. We show that all the pieces reveal multifractal properties. The richest multifractal structures are observed for pop and rock music. Also the viariably of multifractal features is best visible for popular music genres. This can suggest that, from the multifractal perspective, classical and jazz music is much more uniform than pieces of the most popular genres of music.
Directory of Open Access Journals (Sweden)
VOLCHUK V. M.
2015-10-01
Full Text Available Problem statement. At present , to implement a deterministic method of assessment of the mechanical features is not possible based on the analysis of causalit links, because they are influenced with a large number of variables that are highly correlated with each other, and some part of them are changing in a wide range of unpredictable ways. Especially, this problem is in assessing the mechanical properties of metal constructions and products of special purpose in the process of their expluatation: oil pipes, carcasses of residential buildings, etc. In these cases, mechanical testing is the problem is not always technically feasible, and out of variety of express methods of non-destructive control are used often in practice in verbal or semiquantitative. The difficulty is that under the impact of various factors: temperature, corrosive environments, etc., structural changes occur far from thermodynamic equilibrium, and as result the mixed structures are got, including widmanshtatten structure. Use of classical methods of metallography is not always possible to quantify such structures with the precision that may be necessary for practical purposes. In this regard, considerable interest is the search for new approaches to assess the metal structure with a purpose of prognosis of its mechanical properties. Purpose. To obtain information about the possible application of wavelet-multifractal analysis to assess the mechanical properties of metal. Conclusion. Sensitiveness between strength properties and uniformity is set with regularity of structure elements of bainite-perlite group, and also between the viscous properties and uniformity, a regularity of element of the ferrite group. The results suggest that the realization of this method allows in the minimal and possible cost for the real tests to provide the necessary accuracy for practical purposes.
Multifractal analysis of slacken surface in hydrocarbon molecules through fuel additives
Directory of Open Access Journals (Sweden)
G. Arockia Prabakar
2014-09-01
Full Text Available This paper investigates the effect of organic fuel additives (Bio-Glycerol on fuel savings, emission reduction and extend engine life. Using this enzyme, a motor cycle is tested five times. The test report shows the reduction in the release of carbon monoxide (CO and hydrocarbon upto 60%. The use of organic fuel additives in diesel vehicles for different periods of time reveals the reduction in air pollution by 55%. Finally, we have experimented scanning electron microscope (SEM test for organic fuel additives with biodiesel. The SEM image shows the existence of molecules of hydrocarbons. The analysis elucidated the complex morphology of molecules of hydrocarbons in fuel additives with biodiesel. The hydrocarbon molecules are slackened and irregular as it refers to the fractal form. SEM Photograph images are analyzed by multifractal analysis. MFA (multifractal analysis is carried out according to the method of moments, i.e., the probability distribution is estimated for moments which differ from -150
Dam management and multifractal downscaling
Biaou, A.; Hubert, P.; Schertzer, D.; Hendrickx, F.; Tchiguirinskaia, I.
2003-04-01
In order to get a more efficient production management of reservoirs, it would be helpful to apply long-term meteorological forecasts to hydrological models. Unfortunately, the explicit scales of present meteorological models are quite larger than those of hydrological models. Therefore it is indispensable to proceed to a downscaling of the output of the former in order to obtain an input for the latter. In this paper, we discuss a multifractal downscaling procedure. This type of procedure was motivated because it deals with scaling variability of the fields. The site of the study is the region of the Doubs, but we make an extension on the whole France for the multifractale analysis to take into account well the spatial variabilities. We first present the results of a detailed multifractal analysis of various data bases. Concerning the development of our downscaling model, we show how to develop a scaling space-time cascade, which takes into account the distinct space and time scaling. We will present it first in the framework of the pedagogical b-model and a-model, then in the framework of universal multifractal models. The obtained results can be the object of an relief and microclimate conditioning before being compared with the real values.
MULTIFRACTAL ANALYSIS OF PROTEIN AGGREGATES TO DERIVE PROTEIN-SPECIFIC SIGNATURE
Directory of Open Access Journals (Sweden)
Hrishikesh Mishra, Tapobrata Lahiri*
2010-11-01
Full Text Available Deriving a property of a protein that is unique to it has well known significance since the study on ab initio model based derivation of protein structure where uniqueness of protein sequence is taken as the source of specificity of protein structure. In this direction, Heat denatured protein aggregates (HDPA of proteins were studied with an objective to derive some multi-fractal markers specific to constituent protein that may be further utilized to extract information of the seed protein. Since Ordinary microscopic images of aggregates were analyzed to extract Intensity Level-based Multifractal Dimension (ILMFD features. ILMFD features include four different features, perimeter fractal dimension (ILMFDP, perimeter-area relationship (ILMFDPAR, Area fractal dimension (ILMFDA and Perimeter-area fractal dimension (ILMFDPA that were calculated using fractal computations considering perimeter, and area of aggregate images. Feed forward backpropagation network was used to classify the proteins using different ILMFD parameters. It was found that ILMFD features could discriminate the proteins used in our study, that points to their potential to serve as unique property or marker of a protein. Further to validate the results, the outputs from ANN were clustered, and the outputs clustered in the largest cluster were found to significantly improve the result in class decision given by ANN.
Digital Repository Service at National Institute of Oceanography (India)
Haris, K.; Chakraborty, B.
location (Fig. 1b). Depth-dependent correction Apart from the processing steps described in the preceding subsection, the echo-envelope data require an additional cor- rection for the sonar footprint dimension prior to stochas- tic multifractal analyses... ensemble averaged to obtain a representative stable acous- tic signal (at each location) prior to multifractal analyses. be multifractal over various ranges (Lovejoy and Schertzer, 2007a). However, in the specific case of echo envelopes, the power...
An Airborne Radar Clutter Tracking Algorithm Based on Multifractal and Fuzzy C-Mean Cluster
Institute of Scientific and Technical Information of China (English)
Wei Zhang; Sheng-Lin Yu; Gong Zhang
2007-01-01
For an airborne lookdown radar, clutter power often changes dynamically about 80 dB with wide distributions as the platform moves. Therefore, clutter tracking techniques are required to guide the selection of const false alarm rate (CFAR) schemes. In this work, clutter tracking is done in image domain and an algorithm combining multifractal and fuzzy C-mean (FCM) cluster is proposed. The clutter with large dynamic distributions in power density is converted to steady distributions of multifractal exponents by the multifractal transformation with the optimum moment. Then, later, the main lobe and side lobe are tracked from the multifractal exponents by FCM clustering method.
Decomposing Multifractal Crossovers
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
Decomposing Multifractal Crossovers
Directory of Open Access Journals (Sweden)
Zoltan Nagy
2017-07-01
Full Text Available 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 f
Multifractal diffusion entropy analysis on stock volatility in financial markets
Huang, Jingjing; Shang, Pengjian; Zhao, Xiaojun
2012-11-01
This paper introduces a generalized diffusion entropy analysis method to analyze long-range correlation then applies this method to stock volatility series. The method uses the techniques of the diffusion process and Rényi entropy to focus on the scaling behaviors of regular volatility and extreme volatility respectively in developed and emerging markets. It successfully distinguishes their differences where regular volatility exhibits long-range persistence while extreme volatility reveals anti-persistence.
Fractal and Multifractal Time Series
Kantelhardt, Jan W
2008-01-01
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling relation over several orders of magnitude, allowing for a characterisation of the data and the generating complex system by fractal (or multifractal) scaling exponents. In addition, fractal and multifractal approaches can be used for modelling time series and deriving predictions regarding extreme events. This review article describes and exemplifies several methods originating from Statistical Physics and Applied Mathematics, which have been used for fractal and multifractal time series analysis.
Multifractal analysis and instability index of prior-to-crash market situations
Piacquadio, M
2009-01-01
We take prior-to-crash market prices (NASDAQ, Dow Jones Industrial Average) as a signal, a function of time, we project these discrete values onto a vertical axis, thus obtaining a Cantordust. We study said cantordust with the tools of multifractal analysis, obtaining spectra by definition and by lagrangian coordinates. These spectra have properties that typify the prior-to-crash market situation. Any of these spectra entail elaborate processing of the raw signal data. With the unprocessed raw data we obtain an instability index, also with properties that typify the prior-to-crisis market situation. Both spectra and the instability index agree in characterizing such crashes, and in giving an early warning of them.
Multifractal analysis of sEMG signal of the complex muscle activity
Trybek, Paulina; Nowakowski, Michal; Machura, Lukasz
2014-01-01
The neuro--muscular activity while working on laparoscopic trainer is the example of the complex (and complicated) movement. This class of problems are still waiting for the proper theory which will be able to describe the actual properties of the muscle performance. Here we consider the signals obtained from three states of muscle activity: at maximum contraction, during complex movements (at actual work) and in the completely relaxed state. In addition the difference between a professional and an amateur is presented. The Multifractal Detrended Fluctuation Analysis was used in description of the properties the kinesiological surface electromyographic signals (sEMG). We demonstrate the dissimilarity between each state of work for the selected group of muscles as well as between trained and untrained individuals.
SELECTION OF SCALE OF PICTURE OF STRUCTURE FOR ITS MULTIFRACTAL ANALYSIS
Directory of Open Access Journals (Sweden)
VOLCHUK V. N.
2015-11-01
Full Text Available Problem statement. Each scale level detectesthe new features of the structure of the material describing of it quality. For example, features of the grain structure are revealed in different kind of steel on microstruc ture level, and its parameters greatly influences on the strength properties of the metal. Thus, to select the scale of representation of a fractal object, for instance the elements of structure of roll iron or steel is necessary to determine the interval (1, where observed its self-similarity, and on this interval should be selected the scale, the use of which will allow him to choose adequate fractal dimension. For optimal scale structure of repose is taken one in which at least two adjacent points of the series (2, the fractal dimension is minimal differences between them. This is explained by the fact that this is best observed property of self-similarity structure. An example of the selection of the scale representation of the structure of cast iron rolls execution of SPHN (a and execution SSHN (b is shown on interval of increases in the range of x 100 to x1000 with a predetermined pitch Δl = 100. The implementation of this phase of research allowed to determine experimentally the optimal scale of representation of structure of iron roll with increasing x 200 for multifractal analysis of its elements: inclusion of the plate and nodular graphit, carbides. Purpose To determine the optimal scale structure representation for iron roll multifractal analysis of its elements: inclusion of the plate and nodular carbides. Conclusion. It was found that the fractal dimension of the structural elements of the test ranged from experimental error 5÷7%, which testifies to the universality of this assessment, and therefore reliability and economic benefits, in terms of the equipping of laboratories expensive metallurgical microscopes with higher resolution.
Multifractal Value at Risk model
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.
Multifractal vector fields and stochastic Clifford algebra
Energy Technology Data Exchange (ETDEWEB)
Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr [University Paris-Est, Ecole des Ponts ParisTech, Hydrology Meteorology and Complexity HM& Co, Marne-la-Vallée (France)
2015-12-15
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.
Multifractal vector fields and stochastic Clifford algebra.
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.
Institute of Scientific and Technical Information of China (English)
WANG Zheng-Ying; SHU Qiao-Sheng; XIE Li-Ya; LIU Zuo-Xin; B.C.SI
2011-01-01
Soil water-retention characteristics at measurement scales are generally different from those at application scales, and there is scale disparity between them and soil physical properties. The relationships between two water-retention parameters,the scaling parameter related to the inverse of the air-entry pressure (αvG, cm-1) and the curve shape factor related to soil pore-size distribution (n) of the van Genuchten water-retention equation, and soil texture (sand, silt, and clay contents)were examined at multiple scales. One hundred twenty-eight undisturbed soil samples were collected from a 640-m transect located in Fuxin, China. Soil water-retention curves were measured and the van Genuchten parameters were obtained by curve fitting. The relationships between the two parameters and soil texture at the observed scale and at multiple scales were evaluated using Pearson correlation and joint multifractal analyses, respectively. The results of Pearson correlation analysis showed that the parameter αvG was significantly correlated with sand, silt, and clay contents at the observed scale. Joint multifractal analyses, however, indicated that the parameter αvG was not correlated with silt and sand contents at multiple scales. The parameter n was positively correlated with clay content at multiple scales. Sand content was significantly correlated with the parameter n at the observed scale but not at multiple scales. Clay contents were strongly correlated to both water-retention parameters because clay content was relatively low in the soil studied, indicating that water retention was dominated by clay content in the field of this study at all scales. These suggested that multiple-scale analyses were necessary to fully grasp the spatial variability of soil water-retention characteristics.
Tokinaga, Shozo; Ikeda, Yoshikazu
In investments, it is not easy to identify traders'behavior from stock prices, and agent systems may help us. This paper deals with discriminant analyses of stock prices using multifractality of time series generated via multi-agent systems and interpolation based on Wavelet Transforms. We assume five types of agents where a part of agents prefer forecast equations or production rules. Then, it is shown that the time series of artificial stock price reveals as a multifractal time series whose features are defined by the Hausedorff dimension D(h). As a result, we see the relationship between the reliability (reproducibility) of multifractality and D(h) under sufficient number of time series data. However, generally we need sufficient samples to estimate D(h), then we use interpolations of multifractal times series based on the Wavelet Transform.
On the multifractal effects generated by monofractal signals
Grech, Dariusz
2013-01-01
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 $\\Delta h$ or a threshold in the width of multifractal spectrum $\\Delta \\alpha$ below which multifractal properties of the system are only apparent, i.e. do not exist, despite $\\Delta\\alpha\
Wawrzaszek, A.; Krupiński, M.; Drzewiecki, W.; Aleksandrowicz, S.
2015-12-01
Research presented in this paper is focused on the efficiency assessment of multifractal description as a tool for Image Information Mining. Large datasets of very high spatial resolution satellite images (WorldView-2 and EROS-A) have been analysed. The results have confirmed the superiority of multifractals as global image descriptors in comparison to monofractals. Moreover, their usefulness in image classification by using decision trees classifiers was confirmed, also in comparison with textural features. Filtration process preceding fractal and multifractal features estimations was also proved to improve classification results. Additionally, airborne hyperspectral data have been initially analysed. Fractal dimension shows high potential for the description of hyperspectral data. To summarise all conducted tests indicate the usefulness of multifractal formalism in various aspects of remote sensing. Prepared methodology can be further developed and used for more specific tasks, for example in change detection or in the description of hyperspectal data complexity.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Multifractal spectrum, autocorrelation/semivariogram and power spectrum are three dif- ferent functions characterizing a field or measure from different aspects. These functions are interre- lated in such that the autocorrelation/semivariogram and power spectrum are related to the low order statistical moments (0 to 2 nd) which may determine the local multifractality (τ"(1)) of a multifractal measure. A better understanding of the interrelationships among these three functions is important because, on one hand, the multifractal modelling characterizes a multifractal measure in a more de- tailed manner since it involves moments of all orders. On the other hand, the commonly used semivariogram and power spectrum functions can be used as alternatives to study the dominant mul- tifractal properties around the mean measure. Moreover, semivariogram and power-spectrum func- tions provide spatial and spectral information, which is highly valued in geological applications. A new fractal relation found between area and power-spectrum will be useful for investigation of new meth- ods of spatial-spectral analysis for pattern recognition, anomaly separation, classification, etc. These results have been demonstrated with the case study of modelling gamma ray spectrometer data from the mineral district, southwestern Nova Scotia, Canada. The results have shown that the values of uranium (U), thorium (Th) and potassium (K) may possess monofractal properties whereas the ratios of these values show high multifractality. The values of the ratios U/K and U/Th show relatively large variances and may provide more information for distinguishing the distinct phases of the granites, country rocks as well as possible gold mineralization-associated regional hydrothermal alteration zones. In addition, the power spectra for U, Th, K, U/Th and U/K consistently show two distinct power-law relationships for two ranges of wave number 12≤ω≤160 km and 0≤ω≤12 km. These properties might
A Mixed Generalized Multifractal Formalism For Vector Valued Measures
Mabrouk, Anouar Ben
2012-01-01
We introduce a mixed generalized multifractal formalism which extends the mixed multifractal formalism introduced by L. Olsen based on generalizations of the Hausdorff and packing measures. The validity of such a formalism is proved in some special cases.
Institute of Scientific and Technical Information of China (English)
李彦明; 杜文辽; 叶鹏飞; 刘成良
2013-01-01
Mechanical vibration signal is a typical non-linear, nonstationary signal, and multifractal features are powerful tool to express the geometry features of such signals. The traditional multifractal features extraction methods require complex computation, which limit their application. Wavelet leaders-based multifractal analysis has solid supports of mathematical theories and can be calculate easily. A multifractal features extraction method is presented based on wavelet leaders, which is applied to the gears vibration signals under normal and pitting conditions. An optimization algorithm is given to conform the block length of bootstrap technology , and then a validity testing method is presented to test the characteristic variables obtained from vibration signals with wavelet leaders-based multifractal features extraction. The result shows that the geometry features of vibration signal can be reflected with wavelet leaders multifractal features, and the block bootstrap method can be used to analyze the statistical performance of multifractal features, which provides an effective approach for condition monitoring and fault diagnosis of mechanical equipment.%机械振动信号一般具有非线性、非平稳特性,多重分形特征是表示振动信号几何结构特征的一种重要手段.传统的多重分形特征计算方法计算量大,限制了多重分形特征的应用.小波leaders多重分形分析方法具有坚实的数学基础,且计算简便.针对齿轮正常状态和点蚀故障状态,提出基于小波leaders的多重分形振动信号特征提取及表示方法,提出基于bootstrap技术的最优块长求解算法,并建立振动信号小波leaders多重分形特征的统计性能分析方法.研究结果表明,小波leaders多重分形特征能够很好反映振动信号的几何结构特征,基于块bootstrap方法能有效分析多重分形特征统计性能,为机械设备状态监控和故障诊断提供了一种有效的选择.
Monte Carlo Analysis of the Lévy Stability and Multi-fractal Spectrum in e+e- Collisions
Institute of Scientific and Technical Information of China (English)
陈刚; 刘连寿
2002-01-01
The Lévy stability analysis is carried out for e+e- collisions at Z0 mass using the Monte Carlo method. The Lévy index μ is found to be μ = 1.701 ± 0.043. The self-slmilar generalized dimensions D(q) and multi-fractal spectrum f(а) are presented. The Rényi dimension D(q) decreases with increasing q. The self-similar multifractal spectrum is a convex curve with a maximum at q = 0, а = 1.169 ± 0.011. The right-hand side of the spectrum, corresponding to negative values of q, is obtained through analytical continuation.
Cumbrera, Ramiro; Millán, Humberto; Martín-Sotoca, Juan Jose; Pérez Soto, Luis; Sanchez, Maria Elena; Tarquis, Ana Maria
2016-04-01
Soil moisture distribution usually presents extreme variation at multiple spatial scales. Image analysis could be a useful tool for investigating these spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to describe the local scaling of apparent soil moisture distribution and (ii) to define apparent soil moisture patterns from vertical planes of Vertisol pit images. Two soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. One was excavated in April/2011 and the other pit was established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. For more details see Cumbrera et al. (2012). Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, using the concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012). This method is based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. We have applied it to each soil image. The results show that, in spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used to study the dynamical change of soil moisture sampling in agreement with previous results (Millán et al., 2016). REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and
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.
Multifractal analysis of radar rainfall fields over the area of Rome
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G. Calenda
2005-01-01
Full Text Available A scale-invariance analysis of space and time rainfall events monitored by meteorological radar over the area of Rome (Italy is proposed. The study of the scale-invariance properties of intense precipitation storms, particularly important in flood forecast and risk mitigation, allows to transfer rainfall information from the large scale predictive meteorological models to the small scale hydrological rainfall-runoff models. Precipitation events are monitored using data collected by the polarimetric Doppler radar Polar 55C (ISAC-CNR, located 15 km Southeast from downtown. The meteorological radar provides the estimates of rainfall intensity over an area of about 10 000 km2 at a resolution of 2×2 km2 in space and 5 min in time. Many precipitation events have been observed from autumn 2001 up to now. A scale-invariance analysis is performed on some of these events with the aim at exploring the multifractal properties and at understanding their dependence on the meteorological large-scale conditions.
Du, Haibo; Wu, Zhengfang; Zong, Shengwei; Meng, Xiangjun; Wang, Lei
2013-06-01
Extreme climate events have inflicted severe and adverse effects on human life, social economy, and natural ecosystems. In this study, the precipitation time series from a network of 90 weather stations in Northeast China (NEC) and for the period of 1961-2009 are used. An objective method, the multifractal detrended fluctuation analysis method, is applied to determine the thresholds of extreme events. Notable occurrence frequency and strong intensity of extreme precipitation (EP) mainly occur in Liaoning Province and the piedmont regions in Changbai Mountains and Xiao Hinggan Mountains. Generally, EP frequency shows a nonsignificant negative trend, whereas EP intensity has a weak and nonsignificant positive trend for the entire NEC in the period of 1961-2009. To assess EP severity, we propose an EP severity index (EPSI) combining both EP frequency and intensity, rather than separately analyze the EP frequency or intensity. Spatial gradients of EPSI are observed in northeast-southwest and northwest-southeast directions over NEC. The EPSI in northwestern and southeastern NEC are low (0.02-0.3), whereas high EPSI (0.34-0.83) occurs in the southwestern and northeastern portions of the region. Higher EPSI (0.4-0.83) occurs in southern Liaoning Province, which decreases along the southwest-northeast direction. The spatial patterns of EPSI are associated with the circulation over East Asia. Areas that have a short distance from sea and that locate in the windward slope of mountain will probably accompany high EP severity over NEC.
Doroudiani, Saeed
2013-01-01
I read interest the article "Multifractal analysis of the fracture surfaces of foamed polypropylene/polyethylene blends" by Chuang Liu et al. published in Applied Surface Science (vol. 255, pp. 4239-4245, 2009; http://dx.doi.org/10.1016/j.apsusc.2008.11.014). I found a number of problems and limitations in this article that I believe have significant impact on its quality and validity. I would like to make the following comments and draw the attention of the authors to certain concerns, listed below: In the Introduction section, it was stated "can offer some unique properties that conventional foams do not possess, such as higher impact strength, higher toughness, higher stiffness-to-weight ratio, higher fatigue life, higher thermal stability, lower dielectric constant, and lower thermal conductivity" and was cited to references 3-6. The authors needed to provide specific reference for each item in the sentence-bulk citation is not effective and clear. Moreover, the provided references are about supercritical carbon dioxide as a green solvent for processing of polymer melts, not about fatigue and toughness matters of cellular solids. The authors could easily find papers directly related to these subjects [1,2]. The same problem was observed in the next sentence.
Multifractals of central place systems: models, dimension spectrums, and empirical analysis
Chen, Yanguang
2013-01-01
Central place systems have been demonstrated to possess self-similar patterns in both the theoretical and empirical perspectives. A central place fractal can be treated as a monofractal with a single scaling process. However, in the real world, a system of human settlements is a complex network with multi-scaling processes. The simple fractal central place models are not enough to interpret the spatial patterns and evolutive processes of urban systems. It is necessary to construct multi-scaling fractal models of urban places. Based on the postulate of intermittent space filling, two typical multifractal models of central places are proposed in this paper. One model is put forward to reflect the process of spatial convergence (aggregation), and the generalized correlation dimension varies from 0.7306 to 1.3181; the other model is presented to describe the process of spatial divergence (diffusion), the generalized correlation dimension ranges from 1.6523 to 1.7118. As a case study, an analogy is drawn between t...
MIXED SELF-CONFORMAL MULTIFRACTAL MEASURES
Institute of Scientific and Technical Information of China (English)
Meifeng Dai
2009-01-01
Mixed multifractal analysis studies the simultaneous scaling behavior of finitely many measures. A self-conformal measure is a measure invariant under a set of conformal mappings. In this paper, we provide a description of the mixed multifractal theory of finitely many self-conformal measures.
Lacunarity Analyses of Multifractal and Natural Grayscale Patterns
Roy, Ankur; Perfect, Edmund
2014-09-01
Lacunarity (L) is a scale (r)-dependent parameter that was developed for quantifying clustering in fractals and has subsequently been employed to characterize various natural patterns. For multifractals it can be shown analytically that L is related to the correlation dimension, D2, by: dlog(L)/dlog(r) = D2 - 2. We empirically tested this equation using two-dimensional multifractal grayscale patterns with known correlation dimensions. These patterns were analyzed for their lacunarity using the gliding-box algorithm. D2 values computed from the dlog(L)/dlog(r) analysis gave a 1:1 relationship with the known D2 values. Lacunarity analysis was also employed in discriminating between multifractal grayscale patterns with the same D2 values, but different degrees of scale-dependent clustering. For this purpose, a new lacunarity parameter, , was formulated based on the weighted mean of the log-transformed lacunarity values at different scales. This approach was further used to evaluate scale-dependent clustering in soil thin section grayscale images that had previously been classified as multifractals based on standard method of moments box-counting. Our results indicate that lacunarity analysis may be a more sensitive indicator of multifractal behavior in natural grayscale patterns than the standard approach. Thus, multifractal behavior can be checked without having to compute the whole spectrum of non-integer dimensions, Dq(-∞ parameter should be useful to researchers who want to explore the correlative influence of clustering on flow and transport in grayscale representations of soil aggregates and heterogeneous aquifers.
Multifractal Analysis of Morphology of TiO2 Nano-films
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The SEM and AFM images of three TiO2 nano-films prepared at different conditions were obtained and transformed into digital format.The multifractal analyses for three films were made using height from a depth of thickness of film B and q from 55 to -55.The scale- invariance is very good for all lnχq(ε)～ln( plots and τ(q)～q plots at least close to three orders of magnitude.But the multifractal spectra f(a) of the films are quite distinct due to their different height distribution.
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.
MULTIFRACTAL STRUCTURE OF CENTRAL AND EASTERN EUROPEAN FOREIGN EXCHANGE MARKETS
Directory of Open Access Journals (Sweden)
Cn#259;pun#351;an Rn#259;zvan
2012-07-01
Full Text Available It is well known that empirical data coming from financial markets, like stock market indices, commodities, interest rates, traded volumes and foreign exchange rates have a multifractal structure. Multifractals were introduced in the field of economics to surpass the shortcomings of classical models like the fractional Brownian motion or GARCH processes. In this paper we investigate the multifractal behavior of Central and Eastern European foreign exchange rates, namely the Czech koruna, Croatian kuna, Hungarian forint, Polish zlot, Romanian leu and Russian rouble with respect to euro from January 13, 2000 to February 29, 2012. The dynamics of exchange rates is of interest for investors and traders, monetary and fiscal authorities, economic agents or policy makers. The exchange rate movements affect the international balance of payments, trade flows, and allocation of the resources in national and international economy. The empirical results from the multifractal detrending fluctuation analysis algorithm show that the six exchange rate series analysed display significant multifractality. Moreover, generating shuffled and surrogate time series, we analyze the sources of multifractality, long-range correlations and heavy-tailed distributions, and we find that this multifractal behavior can be mainly attributed to the latter. Finally, we propose a foreign exchange market inefficiency ranking by considering the multifractality degree as a measure of inefficiency. The regulators, through policy instruments, aim to improve the informational inefficiency of the markets, to reduce the associated risks and to ensure economic stabilization. Evaluation of the degree of information efficiency of foreign exchange markets, for Central and Eastern Europe countries, is important to assess to what extent these countries are prepared for the transition towards fully monetary integration. The weak form efficiency implies that the past exchange rates cannot help to
Z.R. Struzik; A.P.J.M. Siebes (Arno)
2002-01-01
textabstractWe present a method of detecting and localising outliers in financial time series and other stochastic processes. The method checks the internal consistency of the scaling behaviour of the process within the paradigm of the multifractal spectrum. Deviation from the expected spectrum is i
Suleymanov, M K; Zborovský, I
2003-01-01
Using three different Monte Carlo generators of high energy proton-proton collisions (HIJING, NEXUS, and PSM) we study the energy dependence of multiplicity distributions of charged particles including the LHC energy range. Results are used for calculation of the information entropy, Renyi's dimensions and other multifractal characteristics of particle production.
Multifractal analysis and topological properties of a new family of weighted Koch networks
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.
Energy Technology Data Exchange (ETDEWEB)
Meson, Alejandro M., E-mail: meson@iflysib.unlp.edu.ar; Vericat, Fernando, E-mail: vericat@iflysib.unlp.edu.ar [CONICET-UNLP, Instituto de Fisica de Liquidos y Sistemas Biologicos (IFLYSIB) (Argentina)
2011-12-15
We analyze when a multifractal spectrum can be used to recover the potential. This phenomenon is known as multifractal rigidity. We prove that for a certain class of potentials the multifractal spectrum of local entropies uniquely determines their equilibrium states. This leads to a classification which identifies two systems up to a change of variables.
Li, Qingmou
Mineralization is often intertwined with other processes spatially. This makes it difficult to extract features for mineral exploration. However, the existing techniques are far from adequate in support of this purpose. A series of multifractal feature extraction techniques in spatial, Walsh, eigenspace domains and other methods were developed in a GIS environment for mineral prospecting in this thesis. Techniques in spatial domain including spatial moments, gradient parameters, and local singularity are reviewed and implemented with the emphases on singularity analysis which extracts features on the basis of local self-similarity and spatial association property. A new multifractal method (W-A) was developed in the Walsh domain. W-A model is demonstrated to be advantageous for extracting abruptly change features. This advantage comes from its square wave functions of Walsh transformation (WT). A new multifractal singular-value decomposition (MSVD) model is developed on the basis of scale invariance in eigen-space for features extraction. The eigenimage and power spectrum structure of the studied area are investigated. The extracted feature using MSVD method characterizes rich textures, particularly capable of extracting weak and subtle features from data with strong influence of background and (fault) sharp change values. New Gauss inversion (GI) and hierarchical decomposition methods have been developed for distinguishing probability density function (PDF) from mixing populations. The forward modeling, the least square (LS) segmentation, and the GI are compared. These methods were used in estimating the spatial and entropy distributions. These features have rich textures portraying underground intrusions that are related with the hydrothermal mineral alteration in the study area. The data from southwestern Nova Scotia, Canada, were processed. The results have shown that the features extracted using the techniques developed are associated with a prior mineral
Zhang, Yuanzhi; Ge, Erjia
2013-01-01
The rise in global sea levels has been recognized by many scientists as an important global research issue. The process of sea-level change has demonstrated a complex scaling behavior in space and time. Large numbers of tide gauge stations have been built to measure sea-level change in the North Pacific Ocean, Indian Ocean, North Atlantic Ocean, and Antarctic Ocean. Extensive studies have been devoted to exploring sea-level variation in Asia concerning the Bohai Gulf (China), the Yellow Sea (China), the Mekong Delta (Thailand), and Singapore. Hong Kong, however, a mega city with a population of over 7 million situated in the mouth of the Pear River Estuary in the west and the South China Sea in the east, has yet to be studied, particularly in terms of the temporal scaling behavior of sea-level change. This article presents an approach to studying the temporal scaling behavior of sea-level change over multiple time scales by analyzing the time series of sea-level change in Tai Po Kou, Tsim Bei Tsui, and Quarry Bay from the periods of 1964-2010, 1974-2010, and 1986-2010, respectively. The detection of long-range correlation and multi-fractality of sea-level change seeks answers to the following questions: (1) Is the current sea-level rise associated with and responsible for the next rise over time? (2) Does the sea-level rise have specific temporal patterns manifested by multi-scaling behaviors? and (3) Is the sea-level rise is temporally heterogeneous in the different parts of Hong Kong? Multi-fractal temporally weighted de-trended fluctuation analysis (MF-TWDFA), an extension of multi-fractal de-trended fluctuation analysis (MF-DFA), has been applied in this study to identify long-range correlation and multi-scaling behavior of the sea-level rise in Hong Kong. The experimental results show that the sea-level rise is long-range correlated and multi-fractal. The temporal patterns are heterogeneous over space. This finding implies that mechanisms associated with the
Complex multifractal nature in Mycobacterium tuberculosis genome
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.
Multifractal analysis of the branch structure of diffusion-limited aggregates
Hanan, W. G.; Heffernan, D. M.
2012-02-01
We examine the branch structure of radial diffusion-limited aggregation (DLA) clusters for evidence of multifractality. The lacunarity of DLA clusters is measured and the generalized dimensions D(q) of their mass distribution is estimated using the sandbox method. We find that the global n-fold symmetry of the aggregates can induce anomalous scaling behavior into these measurements. However, negating the effects of this symmetry, standard scaling is recovered.
Detrending moving average algorithm for multifractals
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.
Breki, Christina-Marina; Hassel, Jessica; Theoharis, Theoharis; Sachpekidis, Christos; Pan, Leyun; Provata, Astero
2016-01-01
PET/CT with F-18-Fluorodeoxyglucose (FDG) images of patients suffering from metastatic melanoma have been analysed using fractal and multifractal analysis to assess the impact of monoclonal antibody ipilimumab treatment with respect to therapy outcome. Our analysis shows that the fractal dimensions which describe the tracer dispersion in the body decrease consistently with the deterioration of the patient therapeutic outcome condition. In 20 out-of 24 cases the fractal analysis results match those of the medical records, while 7 cases are considered as special cases because the patients have non-tumour related medical conditions or side effects which affect the results. The decrease in the fractal dimensions with the deterioration of the patient conditions (in terms of disease progression) are attributed to the hierarchical localisation of the tracer which accumulates in the affected lesions and does not spread homogeneously throughout the body. Fractality emerges as a result of the migration patterns which t...
Variability of multifractal parameters in an urban precipitation monitoring network
Licznar, Paweł; De Michele, Carlo; Dżugaj, Dagmara; Niesobska, Maria
2014-05-01
Precipitation especially over urban areas is considered a highly non-linear process, with wide variability over a broad range of temporal and spatial scales. Despite obvious limitations of rainfall gauges location at urban sites, rainfall monitoring by gauge networks is a standard solution of urban hydrology. Often urban precipitation gauge networks are formed by modern electronic gauges and connected to control units of centralized urban drainage systems. Precipitation data, recorded online through these gauge networks, are used in so called Real-Time-Control (RTC) systems for the development of optimal strategies of urban drainage outflows management. As a matter of fact, the operation of RTC systems is motivated mainly by the urge of reducing the severity of urban floods and combined sewerage overflows, but at the same time, it creates new valuable precipitation data sources. The variability of precipitation process could be achieved by investigating multifractal behavior displayed by the temporal structure of precipitation data. There are multiply scientific communications concerning multifractal properties of point-rainfall data from different worldwide locations. However, very little is known about the close variability of multifractal parameters among closely located gauges, at the distances of single kilometers. Having this in mind, here we assess the variability of multifractal parameters among gauges of the urban precipitation monitoring network in Warsaw, Poland. We base our analysis on the set of 1-minute rainfall time series recorded in the period 2008-2011 by 25 electronic weighing type gauges deployed around the city by the Municipal Water Supply and Sewerage Company in Warsaw as a part of local RTC system. The presence of scale invariance and multifractal properties in the precipitation process was investigated with spectral analysis, functional box counting method and studying the probability distributions and statistical moments of the rainfall
MULTIFRACTAL STRUCTURES DETECTED BY VOYAGER 1 AT THE HELIOSPHERIC BOUNDARIES
Energy Technology Data Exchange (ETDEWEB)
Macek, W. M. [Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University, Wóycickiego 1/3, 01-938 Warsaw (Poland); Wawrzaszek, A. [Space Research Centre, Polish Academy of Sciences, Bartycka 18 A, 00-716 Warszawa (Poland); Burlaga, L. F., E-mail: macek@cbk.waw.pl, E-mail: anna.wawrzaszek@cbk.waw.pl, E-mail: lburlagahsp@verizon.net [NASA Goddard Space Flight Center, Code 673, Greenbelt, MD 20771 (United States)
2014-10-01
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 heliocentric 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.
Schertzer, Daniel; Tchiguirinskaia, Ioula
2017-04-01
Multifractal fields have opened a new approach in geophysics to explore "spatial chaos", i.e. processes that are not only complex in time but also in space, because their definition is rather independent of their domain dimension. However multifractals have been for too long restricted to be scalar valued, i.e. to have one-dimensional codomains. This has prevented to deal with the key question of complex component interactions of vector fields and their non trivial symmetries. On the theoretical level, this is resolved by considering the Lie algebra of stochastic generators of cascade processes with arbitrarily large codomains, e.g. flows of vector fields over large dimensional manifolds. We recently investigated the neat example of stable Levy generators on Clifford algebra that provide both universal statistical and robust algebraic properties to the basic symmetries of the corresponding fields (Schertzer and Tchiguirinskaia, 2015). This presentation will focus on the concrete analysis of observation data and their simulation in the Levy-Clifford algebra framework. This correspond to a wide and innovative generalisation of classical multifractal methodologies. Schertzer, D. & Tchiguirinskaia, I., 2015. Multifractal vector fields and stochastic Clifford algebra. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p.123127.
Wang, Yucheng; Wang, Yancheng; Chen, Shu
2016-11-01
We study the spectral and wavefunction properties of a one-dimensional incommensurate system with p-wave pairing and unveil that the system demonstrates a series of particular properties in its ciritical region. By studying the spectral statistics, we show that the bandwidth distribution and level spacing distribution in the critical region follow inverse power laws, which however break down in the extended and localized regions. By performing a finite-size scaling analysis, we can obtain some critical exponents of the system and find these exponents fulfilling a hyperscaling law in the whole critical region. We also carry out a multifractal analysis on system's wavefuntions by using a box-counting method and unveil the wavefuntions displaying different behaviors in the critical, extended and localized regions.
Multifractal analyses of music sequences
Su, Zhi-Yuan; Wu, Tzuyin
2006-09-01
Multifractal analysis is applied to study the fractal property of music. In this paper, a method is proposed to transform both the melody and rhythm of a music piece into individual sets of distributed points along a one-dimensional line. The structure of the musical composition is thus manifested and characterized by the local clustering pattern of these sequences of points. Specifically, the local Hölder exponent and the multifractal spectrum are calculated for the transformed music sequences according to the multifractal formalism. The observed fluctuations of the Hölder exponent along the music sequences confirm the non-uniformity feature in the structures of melodic and rhythmic motions of music. Our present result suggests that the shape and opening width of the multifractal spectrum plot can be used to distinguish different styles of music. In addition, a characteristic curve is constructed by mapping the point sequences converted from the melody and rhythm of a musical work into a two-dimensional graph. Each different pieces of music has its own unique characteristic curve. This characteristic curve, which also exhibits a fractal trait, unveils the intrinsic structure of music.
Fractal And Multi-fractal Analysis Of The Hydraulic Property Variations Of Karst Aquifers
Majone, B.; Bellin, A.; Borsato, A.
Karst aquifers are very heterogeneous systems with hydraulic property variations acting at several continuous and discrete scales, as a result of the fact that macro- structural elements, such as faults and karst channels, and fractures are intertwined in a complex, and largely unknown, manner. Many experimental studies on karst springs showed that the recession limb of the typical storm hydrograph can be divided into several regions with different decreasing rate, suggesting that the discharge is com- posed of contributions experiencing different travel times. Despite the importance of karst aquifers as a source of fresh water for most Mediterranean countries fostered the attention of scientists and practitioners, the mechanisms controlling runoff production in such a complex subsurface environment need to be further explored. A detailed sur- vey, lasting for one year and conducted by the Museo Tridentino di Scienze Naturali of Trento, represents a unique opportunity to analyze the imprint of hydraulic prop- erty variations on the hydrological signal recorded at the spring of Prese Val, located in the Dolomiti group near Trento. Data include water discharge (Q), temperature (T) and electric conductivity of water (E). Analysis of the data revealed that the power spectrum of E scales as 1/f, with slightly, but significantly, smaller than 1. The scaling nature of the E-signal has been confirmed by rescaled range analysis of the time series. Since the electric conductivity is proportional to the concentration of ions in the spring water, which increases with the residence time, one may conclude that the fractal structure of the E signal is the consequence of a similar structure in the hydraulic property variations. This finding confirms previous results of Kirchner et al. (2000), who reported a similar behavior for chloride concentration in the streamflow of three small Welsh catchments. A more detailed analysis revealed that E and T are both multifractal signals
Common multifractality in the heart rate variability and brain activity of healthy humans
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.
Chacón-Cardona, C. A.; Casas-Miranda, R. A.
2012-12-01
We investigate from a fractal viewpoint the way in which dark matter is grouped at z = 0 in the Millennium dark matter cosmological simulation. Determination of the crossing point to homogeneity in the Millennium Simulation data is described with regard to the behaviour of the fractal dimension and lacunarity. We use the sliding-window technique to calculate the fractal mass-radius dimension, the pre-factor F and the lacunarity of this fractal relation. Additionally, we determine the multifractal dimension and the lacunarity spectrum, including their dependence on radial distance. The calculations show a radial distance dependence of all fractal quantities, with heterogeneous clustering of dark matter haloes up to depths of 100 Mpc h-1. Dark matter halo clustering in the Millennium Simulation shows a radial distance dependence, with two regions clearly defined. The lacunarity spectrum for values of the structure parameter q ≥ 1 shows regions with relative maxima, revealing the formation of clusters and voids in the dark matter halo distribution. With use of the multifractal dimension and the lacunarity spectrum, the transition to homogeneity at depths between 100 Mpc h-1 and 120 Mpc h-1 for Millennium Simulation dark matter haloes is detected.
Multifractal cross-correlations between crude oil and tanker freight rate
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.
A robust method for estimating the multifractal wavelet spectrum in geophysical images
Nicolis, Orietta; Porro, Francesco
2013-04-01
The description of natural phenomena by an analysis of the statistical scaling laws is always a popular topic. Many studies aim to identify the fractal feature by estimating the self-similar parameter H, considered constant at different scales of observation. However, most real world data exhibit a multifractal structure, that is, the self-similarity parameter varies erratically with time. The multifractal spectrum provide an efficient tool for characterizing the scaling and singularity structures in signals and images, proving useful in numerous applications such as fluid dynamics, internet network traffic, finance, image analysis, texture synthesis, meteorology, and geophysics. In recent years, the multifractal formalism has been implemented with wavelets. The advantages of using the wavelet-based multifractal spectrum are: the availability of fast algorithms for wavelet transform, the locality of wavelet representations in both time and scale, and intrinsic dyadic self-similarity of basis functions. In this work we propose a robust Wavelet-based Multifractal Spectrum Estimator for the analysis of geophysical signals and satellite images. Finally, a simulation study and examples are considered to test the performances of the estimator.
Mueller matrix approach for probing multifractality in the underlying anisotropic connective tissue
Das, Nandan Kumar; Dey, Rajib; Ghosh, Nirmalya
2016-09-01
Spatial variation of refractive index (RI) in connective tissues exhibits multifractality, which encodes useful morphological and ultrastructural information about the disease. We present a spectral Mueller matrix (MM)-based approach in combination with multifractal detrended fluctuation analysis (MFDFA) to exclusively pick out the signature of the underlying connective tissue multifractality through the superficial epithelium layer. The method is based on inverse analysis on selected spectral scattering MM elements encoding the birefringence information on the anisotropic connective tissue. The light scattering spectra corresponding to the birefringence carrying MM elements are then subjected to the Born approximation-based Fourier domain preprocessing to extract ultrastructural RI fluctuations of anisotropic tissue. The extracted RI fluctuations are subsequently analyzed via MFDFA to yield the multifractal tissue parameters. The approach was experimentally validated on a simple tissue model comprising of TiO2 as scatterers of the superficial isotropic layer and rat tail collagen as an underlying anisotropic layer. Finally, the method enabled probing of precancer-related subtle alterations in underlying connective tissue ultrastructural multifractality from intact tissues.
Directory of Open Access Journals (Sweden)
Evgeniya Gerasimova-Chechkina
2016-08-01
Full Text Available 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 itself become a promoter of 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 the temporal fluctuations of breast skin temperature collected with an IR thermography camera in patients with breast cancer. This study reveals that the multifractal complexity of temperature fluctuations about the 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.
Institute of Scientific and Technical Information of China (English)
王访; 廖桂平; 王晓乔; 李建辉; 李锦卫; 施文
2013-01-01
为描述油菜缺素叶片图像的特征，该文提出了一种基于多重分形去趋势波动分析方法，即局部多重分形去趋势波动分析。该方法确定的hij(q)指数能有效刻画叶片图像每个像素点的多重分形特征，并以所有像素点hij(q)的平均值Lhq表征每幅图像的多重分形特征。选取4种油菜缺素叶片图像进行试验，结果表明所提取局部多重分形去趋势波动平均指数Lhq能很好地区分叶片，并通过方差分析指出当q={-10,-9,-8,-7,-6}时的Lhq区分效果最好。最后基于每个像素点的hij(q)指数利用模糊C均值聚类对缺镁油菜叶片图像进行模糊分割，并与传统的灰度值分割及经典的基于容量测度的Hölder指数分割进行了对比试验，结果表明以上述hij(q)为特征具有最佳的分割效果。%Fertilization levels play a critical role in crops’ growth. As a vital organ of rapeseed, leaves can well reflect the nutritional level, and their images are always processed and analyzed by a computer vision system. The texture feature of the leaves’ images is very important to become a key indicator to describe the nutritional status for the rapeseeds. In recent years, multifractal methods were used to extract its features for describing a texture image. The traditional type of multifractal analysis (MFA) was calculated based on the standard partition function multifractal formalism, which describes stationary measurements. For a crop image collected in field crops, the surface itself is hardly stationary and whose gray scale volatility is likely to be more bizarre. By this token, this is not always a valid choice to analysis them based on MFA. A novel method: local multifractal detrended fluctuation (LMF-DFA) analysis was proposed in this paper to extract texture feature of every pixel for a self-similar surface based on the method of 2-D multifractal detrended fluctuation analysis (MF-DFA), which can well portray
Chacón-Cardona, César A
2012-01-01
We investigate from the fractal viewpoint the way in which the dark matter is grouped at z = 0 in the Millennium dark matter cosmological simulation. The determination of the cross to homogeneity in the Millennium Simulation data is described from the behaviour of the fractal dimension and the lacunarity. We use the sliding window technique to calculate the fractal mass-radius dimension, the pre-factor F and the lacunarity of this fractal relation. Besides, we determinate the multi-fractal dimension and the lacunarity spectrum, including their dependence with radial distance. This calculations show a radial distance dependency of all the fractal quantities, with heterogeneity clustering of dark matter haloes up to depths of 100 Mpc/h. The dark matter haloes clustering in the Millennium Simulation shows a radial distance dependency, with two regions clearly defined. The lacunarity spectrum for values of the structure parameter q >= 1 shows regions with relative maxima, revealing the formation of clusters and v...
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.
Wavelet Leaders: A new method to estimate the multifractal singularity spectra
Serrano, E.; Figliola, A.
2009-07-01
Wavelet Leaders is a novel alternative based on wavelet analysis for estimating the Multifractal Spectrum. It was proposed by Jaffard and co-workers improving the usual wavelet methods. In this work, we analyze and compare it with the well known Multifractal Detrended Fluctuation Analysis. The latter is a comprehensible and well adapted method for natural and weakly stationary signals. Alternatively, Wavelet Leaders exploits the wavelet self-similarity structures combined with the Multiresolution Analysis scheme. We give a brief introduction on the multifractal formalism and the particular implementation of the above methods and we compare their effectiveness. We expose several cases: Cantor measures, Binomial Multiplicative Cascades and also natural series from a tonic-clonic epileptic seizure. We analyze the results and extract the conclusions.
Modelling and control of broadband trafﬁc using multiplicative multifractal cascades
Indian Academy of Sciences (India)
P Murali Krishna; Vikram M Gadre; Uday B Desai
2002-12-01
We present the results on the modelling and synthesis of broadband trafﬁc processes namely ethernet inter-arrival times using the VVGM (variable variance gaussian multiplier) multiplicative multifractal model. This model is shown to be more appropriate for modelling network trafﬁc which possess time varying scaling/self-similarity and burstiness. The model gives a simple and efﬁcient technique to synthesise Ethernet inter-arrival times. The results of the detailed statistical and multifractal analysis performed on the original and the synthesised traces are presented and the performance is compared with other models in the literature, such as the Poisson process, and the Multifractal Wavelet Model (MWM) process. It is also shown empirically that a single server queue preserves the multifractal character of the process by analysing its inter-departure process when fed with the multifractal traces. The result of the existence of a global-scaling exponent for multifractal cascades and its application in queueing theory are discussed. We propose tracking and control algorithms for controlling network congestion with bursty trafﬁc modelled by multifractal cascade processes, characterised by the Holder exponents, the value of which at an interval indicates the burstiness in the trafﬁc at that point. This value has to be estimated and used for the estimation of the congestion and predictive control of the trafﬁc in broadband networks. The estimation can be done by employing wavelet transforms and a Kalman ﬁlter based predictor for predicting the burstiness of the trafﬁc.
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 Analysis of Local Packing Entropies for Recurrence Time%局部回归时间Packing熵的重分形分析
Institute of Scientific and Technical Information of China (English)
郭春霞
2014-01-01
We consider the multifractal analysis of local packing entropies for recurrence time.Futhermore we show the connections between the packing topological entropy and (q,τ)-Packing entropy for level set Kα.%利用packing维数这一工具定义水平集Kα的(q，τ)-packing熵，并给出对于水平集Kα的packing熵与(q，τ)-packing二者之间的关系。
Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions
Cheng, Q.
2014-04-01
The concepts and models of multifractals have been employed in various fields in the geosciences to characterize singular fields caused by nonlinear geoprocesses. Several indices involved in multifractal models, i.e., asymmetry, multifractality, and range of singularity, are commonly used to characterize nonlinear properties of multifractal fields. An understanding of how these indices are related to the processes involved in the generation of multifractal fields is essential for multifractal modeling. In this paper, a five-parameter binomial multiplicative cascade model is proposed based on the anisotropic partition processes. Each partition divides the unit set (1-D length or 2-D area) into h equal subsets (segments or subareas) and m1 of them receive d1 (> 0) and m2 receive d2 (> 0) proportion of the mass in the previous subset, respectively, where m1+m2 ≤ h. The model is demonstrated via several examples published in the literature with asymmetrical fractal dimension spectra. This model demonstrates the various properties of asymmetrical multifractal distributions and multifractal indices with explicit functions, thus providing insight into and an understanding of the properties of asymmetrical binomial multifractal distributions.
Dutta, Srimonti; Ghosh, Dipak; Samanta, Shukla
2016-04-01
This paper studies the human gait pattern of normal people and patients suffering from Parkinson's disease using the MFDXA (Multifractal Detrended Cross-correlation Analysis) methodology. The auto correlation and cross correlation of the time series of the total force under the left foot and right foot were studied. The study reveals that the degree of multifractality (W) and degree of correlation (γ) are generally more for normal patients than the diseased set. It is also observed that the values of W and γ are nearly same for left foot and right. It is also observed that the study of autocorrelation alone is not sufficient, cross correlations should also be studied to get a better concept of neurodegenerative diseases.
Multifractal analysis on gold market with MF-DFA method%基于MF-DFA方法的黄金市场多重分形分析
Institute of Scientific and Technical Information of China (English)
曹建军; 顾荣宝
2011-01-01
This paper analyzes the daily return series of Shanghai gold market and London gold market with multifractal and dispeling tendency fluctuation analysis (MF-DFA ) method. A conclusion is drawn that both of the two markets have multifractal characters. Meanwhile, the multifractal character of Shanghai gold market is more salient than the latter. The analysis provides a new method to realize and research the complex structure of gold markets.%运用多重分形消除趋势波动分析(MF-DFA)方法对上海黄金市场和伦敦黄金市场日收益率数据进行实证研究.分析结果表明:两个黄金市场均表现出多重分形特征,其中上海黄金市场的多重分形特征更为显著,风险性也相对较大.该分析结果为更好地认识和研究黄金市场的复杂结构,提供了新的思路.
Statistical Properties and Multifractal Behaviors of Market Returns by Ising Dynamic Systems
Fang, Wen; Wang, Jun
An interacting-agent model of speculative activity explaining price formation in financial markets is considered in the present paper, which based on the stochastic Ising model and the mean field theory. The model describes the interaction strength among the agents as well as an external field, and the corresponding random logarithmic price return process is investigated. According to the empirical research of the model, the time series formed by this Ising model exhibits the bursting typical of volatility clustering, the fat-tail phenomenon, the power-law distribution tails and the long-time memory. The statistical properties of the returns of Hushen 300 Index, Shanghai Stock Exchange (SSE) Composite Index and Shenzhen Stock Exchange (SZSE) Component Index are also studied for comparison between the real time series and the simulated ones. Further, the multifractal detrended fluctuation analysis is applied to investigate the time series returns simulated by Ising model have the distribution multifractality as well as the correlation multifractality.
On the long-term correlations and multifractal properties of electric arc furnace time series
Livi, Lorenzo; Rizzi, Antonello; Sadeghian, Alireza
2015-01-01
In this paper, we study long-term correlations and multifractal properties elaborated from time series of three-phase current signals coming from an industrial electric arc furnace plant. Implicit sinusoidal trends are suitably detected in the scaling of the fluctuation function of such time series. Time series are then initially filtered via a Fourier based analysis, removing hence such strong periodicities. In the filtered time series we detected long-term, positive correlations. The presence of persistent correlations is in agreement with the typical V--I characteristic (hysteresis) of the electric arc furnace, justifying thus the memory effects found in the current time series. The multifractal signature is strong enough in the filtered time series to be effectively classified as multifractal.
Directory of Open Access Journals (Sweden)
G. Ouillon
1995-01-01
Full Text Available The classical method of statistical physics deduces the macroscopic behaviour of a system from the organization and interactions of its microscopical constituents. This kind of problem can often be solved using procedures deduced from the Renormalization Group Theory, but in some cases, the basic microscopic rail are unknown and one has to deal only with the intrinsic geometry. The wavelet analysis concept appears to be particularly adapted to this kind of situation as it highlights details of a set at a given analyzed scale. As fractures and faults generally define highly anisotropic fields, we defined a new renormalization procedure based on the use of anisotropic wavelets. This approach consists of finding an optimum filter will maximizes wavelet coefficients at each point of the fie] Its intrinsic definition allows us to compute a rose diagram of the main structural directions present in t field at every scale. Scaling properties are determine using a multifractal box-counting analysis improved take account of samples with irregular geometry and finite size. In addition, we present histograms of fault length distribution. Our main observation is that different geometries and scaling laws hold for different rang of scales, separated by boundaries that correlate well with thicknesses of lithological units that constitute the continental crust. At scales involving the deformation of the crystalline crust, we find that faulting displays some singularities similar to those commonly observed in Diffusion- Limited Aggregation processes.
Distributed-order diffusion equations and multifractality: Models and solutions
Sandev, Trifce; Chechkin, Aleksei V.; Korabel, Nickolay; Kantz, Holger; Sokolov, Igor M.; Metzler, Ralf
2015-10-01
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Multi-scale and multi-fractal analysis of pressure fluctuation in slurry bubble column bed reactor
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The Daubechies second order wavelet was applied to decompose pressure fluctuation signals with the gas flux varying from 0.18 to 0.90 m3/h and the solid mass fraction from 0 to 20% and scales 1-9 detail signals and the 9th scale approximation signals. The pressure signals were studied by multi-scale and R/S analysis method. Hurst analysis method was applied to analyze multi-fractal characteristics of different scale signals. The results show that the characteristics of mono-fractal under scale 1 and scale 2, and bi-fractal under scale 3-9 are effective in deducing the hydrodynamics in slurry bubbling flow system. The measured pressure signals are decomposed to micro-scale signals, meso-scale signals and macro-scale signals. Micro-scale and macro-scale signals are of mono-fractal characteristics, and meso-scale signals are of bi-fractal characteristics. By analyzing energy distribution of different scale signals, it is shown that pressure fluctuations mainly reflects meso-scale interaction between the particles and the bubble.
Regularities of Multifractal Measures
Indian Academy of Sciences (India)
Hun Ki Baek
2008-05-01
First, we prove the decomposition theorem for the regularities of multifractal Hausdorff measure and packing measure in $\\mathbb{R}^d$. This decomposition theorem enables us to split a set into regular and irregular parts, so that we can analyze each separately, and recombine them without affecting density properties. Next, we give some properties related to multifractal Hausdorff and packing densities. Finally, we extend the density theorem in [6] to any measurable set.
Institute of Scientific and Technical Information of China (English)
李秋生; 袁新娣; 管立新
2012-01-01
The multifractal feature of the conventional radar return signal from aircraft targets offers the fine description of the dynamic characteristics which induce the target's echo structure, therefore it can provide a new way to the aircraft target classification and its recognition in the conventional radar. On the basis of introducing the research methods for the multifractal as well as the mathematical model of aircraft returns in the conventional radar, by means of the multifractal measure analysis, the multifractal characteristic curves of the aircraft returns such as the mass index and the multifractal singularity spectrum were analyzed in detail, and several multifractal characteristic parameters such as the symmetry degree Rτ of the mass index, the multifractal singularity spectrum width Δδ, the multifractal singularity spectrum asymmetric index Rσ and etc. , were defined. The experimental analysis showed that the conventional radar returns from three types of aircraft targets containing jets, propeller aircrafts and helicopters, had significantly different multifractal characteristic curves, and the three multifractal characteristic parameters could be used as effective features for aircraft target classification and recognition in the conventional radar. '%常规雷达飞机目标回波的多重分形特性提供了对产生目标回波结构动力学特征的精细描述,为常规雷达飞机目标的分类和识别提供了新的途径.在介绍多重分形的研究方法以及常规雷达飞机目标回波数学模型的基础上,利用多重分形测度分析手段,详细分析常规雷达飞机目标回波的质量指数和多重分形奇异谱等多重分形特性曲线,并定义质量指数对称度Rr、多重分形谱宽度Aσ和非对称指数Rσ等多重分形特征参数.实验结果表明:喷气式飞机、螺旋桨飞机和直升机这3类飞机目标的常规雷达回波数据具有显著不同的多重分形特征,所定义的3种多重
Multifractal to monofractal evolution of the London's street network
Murcio, Roberto; Arcaute, Elsa; Batty, Michael
2015-01-01
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 su ce 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, that can be described in terms of a multifractal, to a homogeneous one, that converges to monofractality. We argue that London's multifractal to monofracal 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 di usion limited aggregation, evolve towards monofractality if their growth is constrained by a non-permeable boundary.
Chacón-Cardona, César A
2012-01-01
In this work, we develop a statistical analysis of the large-scale clustering of matter in the Universe from the fractal point of view using galaxies from the Ninth Sloan Digital Sky Survey (SDSS) Data Release (DR9). From the total set of galaxies, a magnitude-limited sample of galaxies with redshifts in the range 0 < z < 0.15 was created. The sample covers the largest completely connected area of the celestial sphere within the catalogue, with limits in right ascension from 120 to 240 degrees and declination from 0 to 60 degrees, which is a region that includes the largest galactic samples that have been studied from the fractal viewpoint to date. The sample contains 164,168 galaxies. Using the sliding-window technique, the multifractal dimension spectrum and its dependence on radial distance are determined. This generalisation of the concept of fractal dimension is used to analyse large-scale clustering of matter in complex systems. Likewise, the lacunarity spectrum, which is a quantity that complemen...
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.
Multifractal approach for seafloor characterization
Digital Repository Service at National Institute of Oceanography (India)
Chakraborty, B.; Haris, K.; Latha, G.; Maslov, N.; Menezes, A.A.A.
to characterize the seafloor. Two distinct multifractal formalisms are applied to determine the characteristics. The first formalism employs data analyses using generalized dimension D(q) and multifractal singularity spectrum f(alpha) linked shape parameters...
Jia, Zhanliang; Cui, Meilan; Li, Handong
2012-02-01
We examine the multifractal properties of the realized volatility (RV) and realized bipower variation (RBV) series in the Shanghai Stock Exchange Composite Index (SSECI) by using the multifractal detrended fluctuation analysis (MF-DFA) method. We find that there exist distinct multifractal characteristics in the volatility series. The contributions of two different types of source of multifractality, namely, fat-tailed probability distributions and nonlinear temporal correlations, are studied. By using the unit root test, we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive.
Cao, Guangxi; Xu, Wei
2016-02-01
This paper investigates the nonlinear structure between carbon and energy markets by employing the maximum overlap wavelet transform (MODWT) as well as the multifractal detrended cross-correlation analysis based on maximum overlap wavelet transform (MFDCCA-MODWT). Based on the MODWT multiresolution analysis and the statistic Qcc(m) significance, relatively significant cross-correlations are obtained between carbon and energy future markets either on different time scales or on the whole. The result of the Granger causality test indicates bidirectional Granger causality between carbon and electricity future markets, although the Granger causality relationship between the carbon and oil price is not evident. The existence of multifractality for the returns between carbon and energy markets is proven with the MFDCCA-MODWT algorithm. In addition, results of investigating the origin of multifractality demonstrate that both long-range correlations and fat-tailed distributions play important roles in the contributions of multifractality.
Multifractality and intermittency in the solar wind
Directory of Open Access Journals (Sweden)
W. M. Macek
2007-11-01
Full Text Available Within the complex dynamics of the solar wind's fluctuating plasma parameters, there is a detectable, hidden order described by a chaotic strange attractor which has a multifractal structure. The multifractal spectrum has been investigated using Voyager (magnetic field data in the outer heliosphere and using Helios (plasma data in the inner heliosphere. We have also analyzed the spectrum for the solar wind attractor. The spectrum is found to be consistent with that for the multifractal measure of the self-similar one-scale weighted Cantor set with two parameters describing uniform compression and natural invariant probability measure of the attractor of the system. In order to further quantify the multifractality, we also consider a generalized weighted Cantor set with two different scales describing nonuniform compression. We investigate the resulting multifractal spectrum depending on two scaling parameters and one probability measure parameter, especially for asymmetric scaling. We hope that this generalized model will also be a useful tool for analysis of intermittent turbulence in space plasmas.
Multifractal analysis of different hydrological products of X-band radar
Skouri-Plakali, Ilektra; Da Silva Rocha Paz, Igor; Ichiba, Abdellah; Gires, Auguste; Tchiguirinskaia, Ioulia; Schertzer, Daniel
2017-04-01
Rainfall is widely considered as the hydrological process that triggers all the others. Its accurate measurements are crucial especially when they are used afterwards for the hydrological modeling of urban and peri-urban catchments for decision-making. Rainfall is a complex process and is scale dependent in space and time. Hence a high spatial and temporal resolution of the data is more appropriate for urban modeling. Therefore, a great interest of high-resolution measurements of precipitation in space and time is manifested. Radar technologies have not stopped evolving since their first appearance about the mid-twentieth. Indeed, the turning point work by Marshall-Palmer (1948) has established the Z - R power-law relation that has been widely used, with major scientific efforts being devoted to find "the best choice" of the two associated parameters. Nowadays X-band radars, being provided with dual-polarization and Doppler means, offer more accurate data of higher resolution. The fact that drops are oblate induces a differential phase shift between the two polarizations. The quantity most commonly used for the rainfall rate computation is actually the specific differential phase shift, which is the gradient of the differential phase shift along the radial beam direction. It is even stronger correlated to the rain rate R than reflectivity Z. Hence the rain rate can be computed with a different power-law relation, which again depends on only two parameters. Furthermore, an attenuation correction is needed to adjust the loss of radar energy due to the absorption and scattering as it passes through the atmosphere. Due to natural variations of reflectivity with altitude, vertical profile of reflectivity should be corrected as well. There are some other typical radar data filtering procedures, all resulting in various hydrological products. In this work, we use the Universal Multifractal framework to analyze and to inter-compare different products of X-band radar
Multifractal detrended cross-correlations between the Chinese exchange market and stock market
Cao, Guangxi; Xu, Longbing; Cao, Jie
2012-10-01
Based on the daily price data of the Chinese Yuan (RMB)/US dollar exchange rate and the Shanghai Stock Composite Index, we conducted an empirical analysis of the cross-correlations between the Chinese exchange market and stock market using the multifractal cross-correlation analysis method. The results demonstrate the overall significance of the cross-correlation based on the analysis of a statistic. Multifractality exists in cross-correlations, and the cross-correlated behavior of small fluctuations is more persistent than that of large fluctuations. Moreover, using the rolling windows method, we find that the cross-correlations between the Chinese exchange market and stock market vary with time and are especially sensitive to the reform of the RMB exchange rate regime. The previous reduction in the flexibility of the RMB exchange rate in July 2008 strengthened the persistence of cross-correlations and decreased the degree of multifractality, whereas the enhancement of the flexibility of the RMB exchange rate in June 2010 weakened the persistence of cross-correlations and increased the multifractality. Finally, several relevant discussions are provided to verify the robustness of our empirical analysis.
Coupling detrended fluctuation analysis for multiple warehouse-out behavioral sequences
Yao, Can-Zhong; Lin, Ji-Nan; Zheng, Xu-Zhou
2017-01-01
Interaction patterns among different warehouses could make the warehouse-out behavioral sequences less predictable. We firstly take a coupling detrended fluctuation analysis on the warehouse-out quantity, and find that the multivariate sequences exhibit significant coupling multifractal characteristics regardless of the types of steel products. Secondly, we track the sources of multifractal warehouse-out sequences by shuffling and surrogating original ones, and we find that fat-tail distribution contributes more to multifractal features than the long-term memory, regardless of types of steel products. From perspective of warehouse contribution, some warehouses steadily contribute more to multifractal than other warehouses. Finally, based on multiscale multifractal analysis, we propose Hurst surface structure to investigate coupling multifractal, and show that multiple behavioral sequences exhibit significant coupling multifractal features that emerge and usually be restricted within relatively greater time scale interval.
Multifractals of investor behavior in stock market
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 characteristics of titanium nitride thin films
Directory of Open Access Journals (Sweden)
Ţălu Ştefan
2015-09-01
Full Text Available The study presents a multi-scale microstructural characterization of three-dimensional (3-D micro-textured surface of titanium nitride (TiN thin films prepared by reactive DC magnetron sputtering in correlation with substrate temperature variation. Topographical characterization of the surfaces, obtained by atomic force microscopy (AFM analysis, was realized by an innovative multifractal method which may be applied for AFM data. The surface micromorphology demonstrates that the multifractal geometry of TiN thin films can be characterized at nanometer scale by the generalized dimensions Dq and the singularity spectrum f(α. Furthermore, to improve the 3-D surface characterization according with ISO 25178-2:2012, the most relevant 3-D surface roughness parameters were calculated. To quantify the 3-D nanostructure surface of TiN thin films a multifractal approach was developed and validated, which can be used for the characterization of topographical changes due to the substrate temperature variation.
Computational approach to multifractal music
Oświęcimka, Paweł; Kwapień, Jarosław; Celińska, Iwona; Drożdż, Stanisław; Rak, Rafał
2011-01-01
In this work we perform a fractal analysis of 160 pieces of music belonging to six different genres. We show that the majority of the pieces reveal characteristics that allow us to classify them as physical processes called the 1/f (pink) noise. However, this is not true for classical music represented here by Frederic Chopin's works and for some jazz pieces that are much more correlated than the pink noise. We also perform a multifractal (MFDFA) analysis of these music pieces. We show that a...
di, Baofeng; Shi, Kai; Zhang, Kaishan; Svirchev, Laurence; Hu, Xiaoxi
2016-02-01
In this paper, a GIS-based method was developed to extract the real-time traffic information (RTTI) from the Google Maps system for city roads. The method can be used to quantify both congested and free-flow traffic conditions. The roadway length was defined as congested length (CL) and free-flow length (FFL). Chengdu, the capital of Sichuan Province in the southwest of China, was chosen as a case study site. The RTTI data were extracted from the Google real-time maps in May 12-17, 2013 and were used to derive the CL and FFL for the study areas. The Multifractal Detrended Fluctuation Analysis (MFDFA) was used to characterize the long-term correlations of CL and FFL time series and their corresponding multifractal properties. Analysis showed that CL and FFL had demonstrated time nonlinearity and long-term correlations and both characteristics differed significantly. A shuffling procedure and a phase randomization procedure were further integrated with multifractal detrending moving average (MFDMA) to identify the major sources of multifractality of these two time series. The results showed that a multifractal process analysis could be used to characterize complex traffic data. Traffic data collected and methods developed in this paper will help better understand the complex traffic systems.
Multifractal behavior of commodity markets: Fuel versus non-fuel products
Delbianco, Fernando; Tohmé, Fernando; Stosic, Tatijana; Stosic, Borko
2016-09-01
We investigate multifractal properties of commodity time series using multifractal detrended fluctuation analysis (MF-DFA). We find that agricultural and energy-related commodities exhibit very similar behavior, while the multifractal behavior of daily and monthly commodity series is rather different. Daily series demonstrate overall uncorrelated behavior, lower degree of multifractality and the dominance of small fluctuations. On the other hand, monthly commodity series show overall persistent behavior, higher degree of multifractality and the dominance of large fluctuations. After shuffling the series, we find that the multifractality is due to a broad probability density function for daily commodities series, while for monthly commodities series multifractality is caused by both a broad probability density function and long term correlations.
Directory of Open Access Journals (Sweden)
M. J. A. Bolzan
2013-01-01
Full Text Available This paper analyses the multifractal aspects of the GPS data (measured during a period of low solar activity obtained from two Brazilian stations: Belém (01.3° S, 48.3° W and São José dos Campos (SJC (23.2° S, 45.9° W. The results show that the respective geographic sites show important scaling differences as well as similarities when their multifractal signatures for vertical total electron content (VTEC are compared. The f(α spectra have a narrow shape for great scales, which indicates the predominance of deterministic phenomena, such as solar rotation (27 days over intermittent phenomena. Furthermore, the f(α spectra for both sites have a strong multifractality degree at small scales. This strong multifractality degree observed at small scales (1 to 12 h at both sites is because the ionosphere over Brazil is a non-equilibrium system. The differences found were that Belém presented a stronger multifractality at small scales (1 h to 12 h compared with SJC, particularly in 2006. The reason for this behaviour may be associated with the location of Belém, near the geomagnetic equator, where at this location the actions of X-rays, ultraviolet, and another wavelength from the Sun are more direct, strong, and constant throughout the whole year. Although the SJC site is near ionospheric equatorial anomaly (IEA peaks, this interpretation could explain the higher values found for the intermittent parameter μ for Belém compared with SJC. Belém also showed the presence of one or two flattening regions for f(α spectra at the same scales mentioned before. These differences and similarities also were interpreted in terms of the IEA content, where this phenomenon is an important source of intermittence due the presence of the VTEC peaks at ±20° geomagnetic latitudes.
Levy Stability Index from Multifractal Spectrum
Yuan, H B; Lian Shou Liu; Yuan, Hu; Meiling, Yu; Lianshou, Liu
1999-01-01
A method for extracting the Levy stability index $\\mu$ from the multi-fractal spectrum $f(\\alpha)$ in high energy multiparticle production is proposed. This index is an important parameter, characterizing the non-linear behaviour of dynamical fluctuations in high energy collisions. Using the random cascading that this method, basing on a linear fit, is consistent with and more accurate than the usual method of fitting the ratio of $q$th to 2nd order multi-fractal (Rényi) dimensions to the Peschanski formula.
Multifractal properties of resistor diode percolation.
Stenull, Olaf; Janssen, Hans-Karl
2002-03-01
Focusing on multifractal properties we investigate electric transport on random resistor diode networks at the phase transition between the nonpercolating and the directed percolating phase. Building on first principles such as symmetries and relevance we derive a field theoretic Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of the current distribution that are governed by a family of critical exponents [psi(l)]. We calculate the family [psi(l)] to two-loop order in a diagrammatic perturbation calculation augmented by renormalization group methods.
Designing thermal diode and heat pump based on DNA nanowire: Multifractal approach
Behnia, S.; Panahinia, R.
2017-07-01
The management of heat flow in DNA nano wire was considered. Thermal diode effect in DNA and the domain of its appearance dependent to system parameters have been detected. The appearance of directed thermal flow in thermodynamic sizes proposes the possibility of designing the macroscopic thermal rectifier. By applying driven force, pumping effect has been also observed. The resonance frequency of DNA and threshold amplitudes of driving force for attaining permanent pumping effect have been detected. Forasmuch as detecting negative differential thermal resistance (NDTR) phenomenon, DNA can act as a thermal transistor. By using an analytical parallel investigation based on Rényi spectrum analysis, threshold values to transition to NDTR and pumping regimes have been detected.
A new measure to characterize multifractality of sleep electroencephalogram
Institute of Scientific and Technical Information of China (English)
MA Qianli; NING Xinbao; WANG Jun; BIAN Chunhua
2006-01-01
Traditional methods for nonlinear dynamic analysis, such as correlation dimension,Lyapunov exponent, approximate entropy, detrended fluctuation analysis, using a single parameter, cannot fully describe the extremely sophisticated behavior of electroencephalogram (EEG). The multifractal formalism reveals more "hidden" information of EEG by using singularity spectrum to characterize its nonlinear dynamics. In this paper, the zero-crossing time intervals of sleep EEG were studied using multifractal analysis. A new multifractal measure △asα was proposed to describe the asymmetry of singularity spectrum, and compared with the singularity strength range △α that was normally used as a degree indicator of multifractality. One-way analysis of variance and multiple comparison tests showed that the new measure we proposed gave better discrimination of sleep stages, especially in the discrimination between sleep and awake, and between sleep stages 3and 4.
Wu, C.; Chang, T.
2010-12-01
A new method in describing the multifractal characteristics of intermittent events was introduced by Cheng and Wu [Chang T. and Wu C.C., Physical Rev, E77, 045401(R), 2008]. The procedure provides a natural connection between the rank-ordered spectrum and the idea of one-parameter scaling for monofractals. This technique has been demonstrated using results obtained from a 2D MHD simulation. It has also been successfully applied to in-situ solar wind observations [Chang T., Wu, C.C. and Podesta, J., AIP Conf Proc. 1039, 75, 2008], and the broadband electric field oscillations from the auroral zone [Tam, S.W.Y. et al., Physical Rev, E81, 036414, 2010]. We take the next step in this procedure. By using the ROMA spectra and the scaled probability distribution functions (PDFs), raw PDFs can be calculated, which can be compared directly with PDFs from observations or simulation results. In addition to 2D MHD simulation results and in-situ solar wind observation, we show clearly using the ROMA analysis the multifractal character of the 3D fluid simulation data obtained from the JHU turbulence database cluster at http://turbulence.pha.jhu.edu. In particular, we show the scaling of the non-symmetrical PDF for the parallel-velocity fluctuations of this 3D fluid data.
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.
Daily extreme temperature multifractals in Catalonia (NE Spain)
Energy Technology Data Exchange (ETDEWEB)
Burgueño, A. [Departament d' Astronomia i Meteorologia, Universitat de Barcelona, Barcelona (Spain); Lana, X., E-mail: francisco.javier.lana@upc.edu [Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Barcelona (Spain); Serra, C. [Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Barcelona (Spain); Martínez, M.D. [Departament de Física Aplicada, Universitat Politècnica de Catalunya, Barcelona (Spain)
2014-02-01
The multifractal character of the daily extreme temperatures in Catalonia (NE Spain) is analyzed by means of the multifractal detrended fluctuation analysis (MF-DFA) applied to 65 thermometric records covering years 1950–2004. Although no clear spatial patterns of the multifractal spectrum parameters appear, factor scores deduced from Principal Component analysis indicate some signs of spatial gradients. Additionally, the daily extreme temperature series are classified depending on their complex time behavior, through four multifractal parameters (Hurst exponent, Hölder exponent with maximum spectrum, spectrum asymmetry and spectrum width). As a synthesis of the three last parameters, a basic measure of complexity is proposed through a normalized Complexity Index. Its regional behavior is found to be free of geographical dependences. This index represents a new step towards the description of the daily extreme temperatures complexity.
Multifractal properties of Chinese stock market in Shanghai
Du, Guoxiong; Ning, Xuanxi
2008-01-01
In this article, we apply three methods of multifractal analysis, partition function method, singular spectrum method and multifractal detrended fluctuation analysis method, to analyze the closing index fluctuations of Shanghai stock market during the past seven years. We have found that Shanghai stock market has weak multifractal features and there are long-range power-law correlations between index series. The shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten. But when the orders of partition function increase, the strengths of multifractal increase, the singular spectrums become rougher and the general Hurst exponents decrease. These results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation.
Estimation of the global regularity of a multifractional Brownian motion
DEFF Research Database (Denmark)
Lebovits, Joachim; Podolskij, Mark
This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional Brownian motion at two different frequencies. We show...... that a logarithmic transformation of this statistic converges in probability to the minimum of the Hurst functional parameter, which is, under weak assumptions, identical to the global regularity index of the path....
Ouadfeul, S.-A.; Aliouane, L.; Tourtchine, V.
2013-09-01
In this paper, we use the so-called the Wavelet Transform Modulus Maxima lines (WTMM) technique for estimation of the capacity, the information and the correlation fractal dimensions of the Intermagnet Observatories time series. Analysis of Hermanus, Baker-Lake, Kakioka, Albibag and Wingst observatories data shows that the correlation and the information dimensions can be used a supplementary indexes for geomagnetic disturbances identification.
Energy Technology Data Exchange (ETDEWEB)
Ţălu, Ştefan, E-mail: stefan_ta@yahoo.com [Technical University of Cluj-Napoca, Faculty of Mechanical Engineering, Department of AET, Discipline of Descriptive Geometry and Engineering Graphics, 103-105 B-dul Muncii St., Cluj-Napoca 400641, Cluj (Romania); Stach, Sebastian, E-mail: sebastian.stach@us.edu.pl [University of Silesia, Faculty of Computer Science and Materials Science, Institute of Informatics, Department of Biomedical Computer Systems, Będzińska 39, 41-205 Sosnowiec (Poland); Lainović, Tijana, E-mail: tijana.lainovic@gmail.com [University of Novi Sad, Faculty of Medicine, School of Dentistry, Hajduk Veljkova 3, 21000 Novi Sad (Serbia); Vilotić, Marko, E-mail: markovil@uns.ac.rs [University of Novi Sad, Faculty of Technical Sciences, Department for Production Engineering, Trg Dositeja Obradovića 6, 21000 Novi Sad (Serbia); Blažić, Larisa, E-mail: larisa.blazic@gmail.com [University of Novi Sad, Faculty of Medicine, School of Dentistry, Clinic of Dentistry of Vojvodina, Department of Restorative Dentistry and Endodontics, Hajduk Veljkova 3, 21000 Novi Sad (Serbia); Alb, Sandu Florin, E-mail: albflorin@yahoo.com [“Iuliu Haţieganu” University of Medicine and Pharmacy, Faculty of Dentistry, Department of Periodontology, 8 Victor Babeş St., 400012 Cluj-Napoca (Romania); Kakaš, Damir, E-mail: kakasdam@uns.ac.rs [University of Novi Sad, Faculty of Technical Sciences, Department for Production Engineering, Trg Dositeja Obradovića 6, 21000 Novi Sad (Serbia)
2015-03-01
Graphical abstract: - Highlights: • Multifractals are good indicators of polished dental composites 3-D surface structure. • The nanofilled composite had superior 3-D surface properties than the nanohybrid one. • Composite polishing with diamond paste created improved 3-D multifractal structure. • Recommendation: polish the composite with diamond paste if using the one-step tool. • Multifractal analysis could become essential in designing new dental surfaces. - Abstract: The objective of this study was to determine the effect of different dental polishing methods on surface texture parameters of dental nanocomposites. The 3-D surface morphology was investigated by atomic force microscopy (AFM) and multifractal analysis. Two representative dental resin-based nanocomposites were investigated: a nanofilled and a nanohybrid composite. The samples were polished by two dental polishing protocols using multi-step and one-step system. Both protocols were then followed by diamond paste polishing. The 3-D surface roughness of samples was studied by AFM on square areas of topography on the 80 × 80 μm{sup 2} scanning area. The multifractal spectrum theory based on computational algorithms was applied for AFM data and multifractal spectra were calculated. The generalized dimension D{sub q} and the singularity spectrum f(α) provided quantitative values that characterize the local scale properties of dental nanocomposites polished by four different dental polishing protocols at nanometer scale. The results showed that the larger the spectrum width Δα (Δα = α{sub max} − α{sub min}) of the multifractal spectra f(α), the more non-uniform was the surface morphology. Also, the 3-D surface topography was described by statistical parameters, according to ISO 25178-2:2012. The 3-D surface of samples had a multifractal nature. Nanofilled composite had lower values of height parameters than nanohybrid composites, due to its composition. Multi-step polishing protocol
Target classification by surveillance radar based on multifractal features%基于多重分形特征的防空雷达目标分类方法
Institute of Scientific and Technical Information of China (English)
李秋生; 谢维信
2013-01-01
On basis of introducing the mathematical model of aircraft returns in the conventional radar, by means of the multi-fractal measure analysis, this paper analyzed the multifractal characteristic of the aircraft returns as well as the extraction method of their multifractal signatures, and proposed the classification method for three types of aircraft containing jets, propeller aircrafts and helicopters from the angle of pattern recognition. The experimental analysis shows, the conventional radar returns from three types of aircraft targets, containing jets, propeller aircrafts and helicopters, have significantly different multifractal characteristic curves, and the defined multifractal characteristic parameters can be used as effective features for aircraft target classification and recognition. The simulation validated the validity of the proposed method.%在介绍常规雷达飞机目标回波数学模型的基础上,利用多重分形测度分析手段,分析了常规雷达飞机目标回波的多重分形特性及其多重分形特征的提取方法,并从模式分类的角度,提出了利用多重分形特征对喷气式飞机、螺旋桨飞机和直升机等三类飞机目标进行分类的方法.实验表明,上述三类飞机的目标回波数据具有显著不同的多重分形特征,所定义的多重分形特征参数可以作为飞机目标分类和识别的有效特征,仿真实验验证了所提方法的有效性.
Epileptic Seizure Detection in Eeg Signals Using Multifractal Analysis and Wavelet Transform
Uthayakumar, R.; Easwaramoorthy, D.
2013-06-01
This paper explores the three different methods to explicitly recognize the healthy and epileptic EEG signals: Modified, Improved, and Advanced forms of Generalized Fractal Dimensions (GFD). The newly proposed scheme is based on GFD and the discrete wavelet transform (DWT) for analyzing the EEG signals. First EEG signals are decomposed into approximation and detail coefficients using DWT and then GFD values of the original EEGs, approximation and detail coefficients are computed. Significant differences are observed among the GFD values of the healthy and epileptic EEGs allowing us to classify seizures with high accuracy. It is shown that the classification rate is very less accurate without DWT as a preprocessing step. The proposed idea is illustrated through the graphical and statistical tools. The EEG data is further tested for linearity by using normal probability plot and we proved that epileptic EEG had significant nonlinearity whereas healthy EEG distributed normally and similar to Gaussian linear process. Therefore, we conclude that the GFD and the wavelet decomposition through DWT are the strong indicators of the state of illness of epileptic patients.
Multifractal properties of ECG patterns of patients suffering from congestive heart failure
Dutta, Srimonti
2010-12-01
The multifractal properties of two-channel ECG patterns of patients suffering from severe congestive heart failure (New York Heart Association (NYHA) classes III-IV) are studied and are compared with those for normal healthy people using the multifractal detrended fluctuation analysis methodology. Ivanov et al (1999 Nature 399 461) have studied the multifractality of human heart rate dynamics using the wavelet transformation modulus maxima (WTMM) methodology. But it has been observed by several scientists that multifractal detrended fluctuation analysis (MFDFA) works better than the WTMM method in the detection of monofractal and multifractal characteristics of the data. Galaska et al (2008 Ann. Noninvasive Electrocardiol. 13 155) have observed that MFDFA is more sensitive compared to the WTMM method in the differentiation between multifractal properties of the heart rate in healthy subjects and patients with left ventricular systolic dysfunction. In the present work the variation of two parameters of the multifractal spectrum—its width W (related to the degree of multifractality) and the value of the Hölder exponent α0—for the healthy and congestive heart failure patients is studied. α0 is a measure of the degree of correlation. The degree of multifractality varies appreciably (85-90% C.L.) for the normal and the CHF sets for channel I. For channel II no significant change in the values is observed. The degree of correlation is found to be comparatively high for the normal healthy people compared to those suffering from CHF.
Turbulence in magnetized plasmas and financial markets: comparative study of multifractal statistics
Budaev, V. P.
2004-12-01
The turbulence in magnetized plasma and financial data of Russian market have been studied in terms of the multifractal formalism revisited with wavelets. The multifractal formalism based on wavelet calculations allows one to study the scaling properties of turbulent fluctuations. It is observed that both plasma edge turbulence in fusion devices and Russian financial markets demonstrate multifractal statistics, i.e., the scaling behaviour of absolute moments is described by a convex function. Multifractality parameter defined in multiplicative cacade model, seems to be of the same magnitude for the plasma and financial time series considered in this paper.
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
Box Counting Multifractal Analysis
1992-06-01
and Jan Tobochnik, Computers in Physics Vol. 4, 1990, p. 202. 4. William H. Press, Brian P. Flannery, Saul A. Teukolsky and William T. Vetterling...27709-2211 MIAC/ CINDAS PURDUE UNIVERSITY DIRECTOR 2595 YEAGER ROAD US NAVAL RESEARCH LAB WEST LAFAYETTE, IN 47905 ATTN: MATERIALS SCI & TECH DIVISION 1
Wavelets and Multifractal Analysis
2004-07-01
however, routes to chaos emerge. It has been suggested that since chaos - control methods prove effective for removing such behavior, the heartbeat...A. Garfinkel, J. N. Weiss, W. L. Ditto, and M. L. Spano, “ Chaos control of cardiac arrhythmias,” Trends Cardiovasc. Med., vol. 5, pp. 76–80, 1995. 62...Controlling nonchaotic neuronal noise using chaos control techniques,” Phys. Rev. Lett., vol. 75, pp. 2782–2785, 1995. [89] H. C. Tuckwell, Stochastic
Statistical and Multifractal Evaluation of Soil Compaction in a Vineyard
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
Correlation Fractal and Multifractal Characteristics of Seismic Activity in the Taiwan Area, China
Institute of Scientific and Technical Information of China (English)
XU Jiandong; HUANG Jianfa; WEI Fuquan; YAN Yunpeng; LI Yaping; LIN Chien-te
2005-01-01
Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan area is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions Dq andf(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan area. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattem of Dq variation with time is a good indicator for predicting strong earthquake events.
A copula-multifractal volatility hedging model for CSI 300 index futures
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.
Measuring efficiency of international crude oil markets: A multifractality approach
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
Effect of spatial averaging on multifractal properties of meteorological time series
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
Entropy Function for Multifractal Thermodynamics
Institute of Scientific and Technical Information of China (English)
QiuhuaZENG
1999-01-01
The theory on multifractal thermodynamics has been studied by the method of series expansion.The method is able to overcome the shortages of Kohmoto's steepest desent method and the results have general meanings.
Defining urban and rural regions by multifractal spectrums of urbanization
Chen, Yanguang
2015-01-01
The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper is devoted to defining urban and rural regions using ideas from fractals. A basic postulate is that human geographical systems are of self-similar patterns associated with recursive processes. Then multifractal geometry can be employed to describe or define the urban and rural terrain with the level of urbanization. A space-filling index of urban-rural region based on the generalized correlation dimension is presented to reflect the degree of geo-spatial utilization in terms of urbanization. The census data of America and China are adopted to show how to make empirical analyses of urban-rural multifractals. This work is not so much a positive analysis as a normative study, but it proposes a new way of investigating urban and rural regional systems using fractal theory.
Multifractality in dilute magnetorheological fluids under an oscillating magnetic field.
Moctezuma, R E; Arauz-Lara, J L; Donado, F
2014-12-01
A study of the multifractal characteristics of the structure formed by magnetic particles in a dilute magnetorheological fluid is presented. A quasi-two-dimensional magnetorheological fluid sample is simultaneously subjected to a static magnetic field and a sinusoidal magnetic field transverse to each other. We analyzed the singularity spectrum f(α) and the generalized dimension D(q) of the whole structure to characterize the distribution of the aggregates under several conditions of particle concentration, magnetic field intensities, and liquid viscosity. We also obtained the fractal dimension D(g), calculated from the radius of gyration of the chains, to describe the internal distribution of the particles. We present a thermodynamic interpretation of the multifractal analysis, and based on this, we discussed the characteristics of the structure formed by the particles and its relation with previous studies of the average chain length. We have found that this method is useful to quantitatively describe the structure of magnetorheological fluids, especially in systems with high particle concentration where the aggregates are more complex than simple chains or columns.
Multifractality and heart rate variability
Sassi, Roberto; Signorini, Maria Gabriella; Cerutti, Sergio
2009-06-01
In this paper, we participate to the discussion set forth by the editor of Chaos for the controversy, "Is the normal heart rate chaotic?" Our objective was to debate the question, "Is there some more appropriate term to characterize the heart rate variability (HRV) fluctuations?" We focused on the ≈24 h RR series prepared for this topic and tried to verify with two different techniques, generalized structure functions and wavelet transform modulus maxima, if they might be described as being multifractal. For normal and congestive heart failure subjects, the hq exponents showed to be decreasing for increasing q with both methods, as it should be for multifractal signals. We then built 40 surrogate series to further verify such hypothesis. For most of the series (≈75%-80% of cases) multifractality stood the test of the surrogate data employed. On the other hand, series coming from patients in atrial fibrillation showed a small, if any, degree of multifractality. The population analyzed is too small for definite conclusions, but the study supports the use of multifractal series to model HRV. Also it suggests that the regulatory action of autonomous nervous system might play a role in the observed multifractality.
Multifractals embedded in short time series: An unbiased estimation of probability moment
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.
Multifractality in fidelity sequences of optimized Toffoli gates
Moqadam, Jalil Khatibi; Welter, Guilherme S.; Esquef, Paulo A. A.
2016-11-01
We analyze the multifractality in the fidelity sequences of several engineered Toffoli gates. Using quantum control methods, we consider several optimization problems whose global solutions realize the gate in a chain of three qubits with XY Heisenberg interaction. Applying a minimum number of control pulses assuring a fidelity above 99 % in the ideal case, we design stable gates that are less sensitive to variations in the interqubits couplings. The most stable gate has the fidelity above 91 % with variations about 0.1 %, for up to 10 % variation in the nominal couplings. We perturb the system by introducing a single source of 1 / f noise that affects all the couplings. In order to quantify the performance of the proposed optimized gates, we calculate the fidelity of a large set of optimized gates under prescribed levels of coupling perturbation. Then, we run multifractal analysis on the sequence of attained fidelities. This way, gate performance can be assessed beyond mere average results, since the chosen multifractality measure (the width of the multifractal spectrum) encapsulates into a single performance indicator the spread of fidelity values around the mean and the presence of outliers. The higher the value of the performance indicator the more concentrated around the mean the fidelity values are and rarer is the occurrence of outliers. The results of the multifractal analysis on the fidelity sequences demonstrate the effectiveness of the proposed optimized gate implementations, in the sense they are rendered less sensitive to variations in the interqubits coupling strengths.
Ţălu, Ştefan; Stach, Sebastian; Lainović, Tijana; Vilotić, Marko; Blažić, Larisa; Alb, Sandu Florin; Kakaš, Damir
2015-03-01
The objective of this study was to determine the effect of different dental polishing methods on surface texture parameters of dental nanocomposites. The 3-D surface morphology was investigated by atomic force microscopy (AFM) and multifractal analysis. Two representative dental resin-based nanocomposites were investigated: a nanofilled and a nanohybrid composite. The samples were polished by two dental polishing protocols using multi-step and one-step system. Both protocols were then followed by diamond paste polishing. The 3-D surface roughness of samples was studied by AFM on square areas of topography on the 80 × 80 μm2 scanning area. The multifractal spectrum theory based on computational algorithms was applied for AFM data and multifractal spectra were calculated. The generalized dimension Dq and the singularity spectrum f(α) provided quantitative values that characterize the local scale properties of dental nanocomposites polished by four different dental polishing protocols at nanometer scale. The results showed that the larger the spectrum width Δα (Δα = αmax - αmin) of the multifractal spectra f(α), the more non-uniform was the surface morphology. Also, the 3-D surface topography was described by statistical parameters, according to ISO 25178-2:2012. The 3-D surface of samples had a multifractal nature. Nanofilled composite had lower values of height parameters than nanohybrid composites, due to its composition. Multi-step polishing protocol created a better finished surface, for both tested materials, than one-step polishing protocol, even when it was followed by diamond paste polishing. Diamond paste polishing created smooth surface and reduced roughness of tested materials.
Institute of Scientific and Technical Information of China (English)
张德园; 王雪飞
2014-01-01
以美国西德克萨斯轻质原油现货价格（WTI）、英国北海布伦特原油现货价格（Brent）、中东迪拜原油现货价格（Dubai）和中国大庆原油现货价格（Daq）为代表性的研究对象，运用耦合消除趋势波动分析法（CDFA）对国内外原油市场之间耦合关系的多重分形特征进行实证分析。实证结果表明：原油市场之间的耦合关系具有明显的多重分形特征；厚尾分布和长记忆性是产生多重分形特征的主要原因；无论就长记忆性而言，还是就厚尾分布而言，WTI 对原油市场耦合关系多重分形特征的影响最为突出。%Coupling Detrended Fluctuation Analysis (CDFA)is used to analyze the multifractal characteristic of coupling relationship between domestic and international crude oil markets,which draw upon WTI,Brent and Dubai crude oil spot prices typical of international crude oil markets and Chinese Daqing crude oil spot prices (Daq)typical of domestic crude oil markets. The empirical results demonstrate that the coupling relationship between four crude oil markets are multifractal and main reasons for the multifractal characteristic are heavy tailed distribution and long memory;for both long memory and heavy tailed distribution,WTI has a significant influence on multifractal property of coupling relationship in crude oil markets.
Fitton, G. F.; Tchiguirinskaia, I.; Schertzer, D. J.; Lovejoy, S.
2012-12-01
Under various physical conditions (mean temperature and velocity gradients, stratification and rotation) atmospheric turbulent flows remain intrinsically anisotropic. The immediate vicinity of physical boundaries rises to a greater complexity of the anisotropy effects. In this paper we address the issue of the scaling anisotropy of the wind velocity fields within the atmospheric boundary layer (ABL). Under the universal multifractal (UM) framework we compare the small time-scale (0.1 to 1,000 seconds) boundary-layer characteristics of the wind for two different case studies. The first case study consisted of a single mast located within a wind farm in Corsica, France. Three sonic anemometers were installed on the mast at 22, 23 and 43m, measuring three-dimensional wind velocity data at 10Hz. Wakes, complex terrain and buoyancy forces influenced the measurements. The second case study (GROWIAN experiment in Germany) consisted of an array of propeller anemometers measuring wind speed inflow data at 2.5Hz over flat terrain. The propeller anemometers were positioned vertically at 10, 50, 75, 100, 125 and 150m with four horizontal measurements taken at 75, 100 and 125m. The spatial distribution allowed us to calculate the horizontal and vertical shear structure functions of the horizontal wind. Both case studies are within a kilometre from the sea. For the first case study (10Hz measurements in a wind farm test site) the high temporal resolution of the data meant we observed Kolmogorov scaling from 0.2 seconds (with intermittency correction) right up to 1,000 seconds at which point a scaling break occurred. After the break we observed a scaling power law of approximately 2, which is in agreement with Bolgiano-Obukhov scaling theory with intermittency correction. However, for the second case study (2.5Hz on flat terrain) we only observed Kolmogorov scaling from 6.4 seconds (also with intermittency correction). The spectra of horizontal velocity components remain
Jiménez-Hornero, Francisco J.; Ariza-Villaverde, Ana B.; de Ravé, Eduardo Gutiérrez
2013-03-01
The spatial description of flows in porous media is a main issue due to their influence on processes that take place inside. In addition to descriptive statistics, the multifractal analysis based on the Box-Counting fixed-size method has been used during last decade to study some porous media features. However, this method gives emphasis to domain regions containing few data points that spark the biased assessment of generalized fractal dimensions for negative moment orders. This circumstance is relevant when describing the flow velocity field in idealised three-dimensional porous media. The application of the Sandbox method is explored in this work as an alternative to the Box-Counting procedure for analyzing flow velocity magnitude simulated with the lattice model approach for six media with different porosities. According to the results, simulated flows have multiscaling behaviour. The multifractal spectra obtained with the Sandbox method reveal more heterogeneity as well as the presence of some extreme values in the distribution of high flow velocity magnitudes as porosity decreases. This situation is not so evident for the multifractal spectra estimated with the Box-Counting method. As a consequence, the description of the influence of porous media structure on flow velocity distribution provided by the Sandbox method improves the results obtained with the Box-Counting procedure.
Directory of Open Access Journals (Sweden)
Dustin eFetterhoff
2015-09-01
Full Text Available 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.
Automatic detection of microcalcifications with multi-fractal spectrum.
Ding, Yong; Dai, Hang; Zhang, Hang
2014-01-01
For improving the detection of micro-calcifications (MCs), this paper proposes an automatic detection of MC system making use of multi-fractal spectrum in digitized mammograms. The approach of automatic detection system is based on the principle that normal tissues possess certain fractal properties which change along with the presence of MCs. In this system, multi-fractal spectrum is applied to reveal such fractal properties. By quantifying the deviations of multi-fractal spectrums between normal tissues and MCs, the system can identify MCs altering the fractal properties and finally locate the position of MCs. The performance of the proposed system is compared with the leading automatic detection systems in a mammographic image database. Experimental results demonstrate that the proposed system is statistically superior to most of the compared systems and delivers a superior performance.
Solar system plasma Turbulence: Observations, inteRmittency and Multifractals
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
Apparent scale correlations in a random multifractal process
DEFF Research Database (Denmark)
Cleve, Jochen; Schmiegel, Jürgen; Greiner, Martin
2008-01-01
We discuss various properties of a homogeneous random multifractal process, which are related to the issue of scale correlations. By design, the process has no built-in scale correlations. However, when it comes to observables like breakdown coefficients, which are based on a coarse......-graining of the multifractal field, scale correlations do appear. In the log-normal limit of the model process, the conditional distributions and moments of breakdown coefficients reproduce the observations made in fully developed small-scale turbulence. These findings help to understand several puzzling empirical details...
Variable bit rate video traffic modeling by multiplicative multifractal model
Institute of Scientific and Technical Information of China (English)
Huang Xiaodong; Zhou Yuanhua; Zhang Rongfu
2006-01-01
Multiplicative multifractal process could well model video traffic. The multiplier distributions in the multiplicative multifractal model for video traffic are investigated and it is found that Gaussian is not suitable for describing the multipliers on the small time scales. A new statistical distribution-symmetric Pareto distribution is introduced. It is applied instead of Gaussian for the multipliers on those scales. Based on that, the algorithm is updated so that symmetric pareto distribution and Gaussian distribution are used to model video traffic but on different time scales. The simulation results demonstrate that the algorithm could model video traffic more accurately.
Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes
Energy Technology Data Exchange (ETDEWEB)
Lim, S C [Faculty of Engineering, Multimedia University, Jalan Multimedia, Cyberjaya 63100, Selangor Darul Ehsan (Malaysia); Teo, L P [Faculty of Information Technology, Multimedia University, Jalan Multimedia, Cyberjaya, 63100, Selangor Darul Ehsan (Malaysia)
2007-06-08
This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established.
Multifractal model of asset returns with leverage effect
Eisler, Z.; Kertész, J.
2004-11-01
Multifractal processes are a relatively new tool of stock market analysis. Their power lies in the ability to take multiple orders of autocorrelations into account explicitly. In the first part of the paper we discuss the framework of the Lux model and refine the underlying phenomenological picture. We also give a procedure of fitting all parameters to empirical data. We present a new approach to account for the effective length of power-law memory in volatility. The second part of the paper deals with the consequences of asymmetry in returns. We incorporate two related stylized facts, skewness and leverage autocorrelations into the model. Then from Monte Carlo measurements we show, that this asymmetry significantly increases the mean squared error of volatility forecasts. Based on a filtering method we give evidence on similar behavior in empirical data.
Energy Technology Data Exchange (ETDEWEB)
Souza, Jeferson de [Laboratorio de Analise de Bacias e Petrofisica, Departamento de Geologia, Universidade Federal do Parana, Centro Politecnico - Jardim das Americas, Caixa Postal 19001, 81531-990 Curitiba-PR (Brazil); Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ (Brazil)], E-mail: jdesouza@ufpr.br; Duarte Queiros, Silvio M. [Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ (Brazil)], E-mail: sdqueiro@googlemail.com
2009-11-30
In this manuscript we present a comprehensive study on the multifractal properties of high-frequency price fluctuations and instantaneous volatility of the equities that compose the Dow Jones Industrial Average. The analysis consists about the quantification of the influence of dependence and non-Gaussianity on the multifractal character of financial quantities. Our results point out an equivalent importance of dependence and non-Gaussianity on the multifractality of time series. Moreover, we analyse l-diagrams of price fluctuations. In the latter case, we show that the fractal dimension of these maps is basically independent of the lag between price fluctuations that we assume.
Shaw, Pankaj Kumar; Saha, Debajyoti; Ghosh, Sabuj; Janaki, M. S.; Iyengar, A. N. Sekar
2017-03-01
In this paper, multifractal detrended fluctuation analysis (MF-DFA) has been used to analyze the floating potential fluctuations obtained with a Langmuir probe from a dc glow discharge magnetized plasma device. The generalized Hurst exponents (h(q)) , local fluctuation function (Fq(s)) , the Rényi exponents (τ(q)) and the multifractal spectrum F(α) have been calculated by applying the MF-DFA method. The result of the MF-DFA shows the multifractal nature of these fluctuations. We have investigated the influence of magnetic field on the multifractal nature of the fluctuations and it is seen that degree of multifractality is reduced with the increase in the magnetic field strength. The values of h(q) have been restricted between 0.7 and 1 for the magnetized fluctuations. This result is evidence of the existence of long-range correlations in the fluctuations. Furthermore, we employed shuffle and surrogate approaches to analyze the origins of multifractality. Comparing the MF-DFA results for the data set to those for shuffled and surrogate series, we have found that its multifractal nature is due to the existence of significant long-term correlation.
Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.
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.
Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.
Directory of Open Access Journals (Sweden)
Xu Shanhua
Full Text Available 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.
Nonlinear dynamics of wind waves: multifractal phase/time effects
Directory of Open Access Journals (Sweden)
R. H. Mellen
1994-01-01
Full Text Available In addition to the bispectral coherence method, phase/time analysis of analytic signals is another promising avenue for the investigation of phase effects in wind waves. Frequency spectra of phase fluctuations obtained from both sea and laboratory experiments follow an F-β power law over several decades, suggesting that a fractal description is appropriate. However, many similar natural phenomena have been shown to be multifractal. Universal multifractals are quantified by two additional parameters: the Lévy index 0 α 2 for the type of multifractal and the co-dimension 0 C1 1 for intermittence. The three parameters are a full statistical measure the nonlinear dynamics. Analysis of laboratory flume data is reported here and the results indicate that the phase fluctuations are 'hard multifractal' (α > 1. The actual estimate is close to the limiting value α = 2, which is consistent with Kolmogorov's lognormal model for turbulent fluctuations. Implications for radar and sonar backscattering from the sea surface are briefly considered.
Influence of urban morphology on total noise pollution: multifractal description.
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.
Multifractals, random walks and Arctic sea ice
Agarwal, Sahil; Wettlaufer, John
We examine the long-term correlations and multifractal properties of daily satellite retrievals of Arctic sea ice albedo, extent, and ice velocity for decadal periods. The approach harnesses a recent development called Multifractal Temporally Weighted Detrended Fluctuation Analysis (MF-TWDFA), which exploits the intuition that points closer in time are more likely to be related than distant points. In both data sets we extract multiple crossover times, as characterized by generalized Hurst exponents, ranging from synoptic to decadal. The method goes beyond treatments that assume a single decay scale process, such as a first-order autoregression, which cannot be justifiably fit to these observations. The ice extent data exhibits white noise behavior from seasonal to bi-seasonal time scales, whereas the clear fingerprints of the short (weather) and long (~ 7 and 9 year) time scales remain, the latter associated with the recent decay in the ice cover. Thus, long term persistence is reentrant beyond the seasonal scale and it is not possible to distinguish whether a given ice extent minimum/maximum will be followed by a minimum/maximum that is larger or smaller in magnitude. The ice velocity data show long term persistence in auto covariance. NASA Grant NNH13ZDA001N-CRYO and Swedish Research Council Grant No. 638-2013-9243.
Multifractal Simulation of Geochemical Map Patterns
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.
Revisiting the multifractality in stock returns and its modeling implications
He, Shanshan; Wang, Yudong
2017-02-01
In this paper, we investigate the multifractality of Chinese and the U.S. stock markets using a multifractal detrending moving average algorithm. The results show that stock returns in both markets are multifractal at a similar extent. We detect the source of multifractality and find that long-range correlations are one of the major sources of multifractality in the US market but not in the Chinese market. Fat-tailed distribution plays a crucial role in multifractality of both markets. As an innovation, we quantify the effect of extreme events on multifractality and find the strong evidence of their contribution to multifractality. Furthermore, we investigate the usefulness of popular ARFIMA-GARCH models with skew-t distribution in capturing multifractality. Our results indicate that these models can capture only a fraction of multifractality. More complex models do not necessarily perform better than simple GARCH models in describing multifractality in stock returns.
Das, Nandan Kumar; Dey, Rajib; Chakraborty, Semanti; Panigrahi, P. K.; Ghosh, Nirmalya
2016-12-01
Fourier domain low coherence interferometry is a promising method for quantification of the depth distribution of the refractive index in a layered scattering medium such as biological tissue. Here, we have explored backscattering spectral interferometric measurement in combination with multifractal detrended fluctuation analysis to probe and quantify multifractality in depth distribution of the refractive index in tissue. The depth resolution of the experimental system was validated on model systems comprising of polystyrene microspheres and mica sheet, and was initially tested on turbid collagen layer, the main building blocks of the connective tissue. Following successful evaluation, the method was applied on ex vivo tissues of human cervix. The derived multifractal parameters of depth-resolved index fluctuations of tissue, namely, the generalized Hurst exponent and the width of the singularity spectrum showed interesting differences between tissues having different grades of precancers. The depth-resolved index fluctuations exhibited stronger multifractality with increasing pathological grades, demonstrating its promise as a potential biomarker for precancer detection.
Bayesian estimation of the multifractality parameter for image texture using a Whittle approximation
Combrexelle, Sébastien; Dobigeon, Nicolas; Tourneret, Jean-Yves; McLaughlin, Steve; Abry, Patrice
2014-01-01
Texture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a challenge. This is due in the main to the fact that current estimation procedures consist of performing linear regressions across frequency scales of the two-dimensional (2D) dyadic wavelet transform, for which only a few such scales are computable for images. The strongly non-Gaussian nature of multifractal processes, combined with their complicated dependence structure, makes it difficult to develop suitable models for parameter estimation. Here, we propose a Bayesian procedure that addresses the difficulties in the estimation of the multifractality parameter. The originality of the procedure is threefold: The construction of a generic semi-parametric statistical model for the logarithm of wavelet leaders; the formulation of Bayesian estimators that are associated with this ...
Surface characterization of proteins using multi-fractal property of heat-denatured aggregates
Lahiri, Tapobrata; Mishra, Hrishikesh; Sarkar, Subrata; Misra, Krishna
2008-01-01
Multi-fractal property of heat-denatured protein aggregates (HDPA) is characteristic of its individual form. The visual similarity between digitally generated microscopic images of HDPA with that of surface-image of its individual X-ray structures in protein databank (PDB) displayed using Visual Molecular Dynamics (VMD) viewer is the basis of the study. We deigned experiments to view the fractal nature of proteins at different aggregate scales. Intensity based multi-fractal dimensions (ILMFD)...
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.
Lorentz violations in multifractal spacetimes
Calcagni, Gianluca
2016-01-01
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 manifest 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 $E_*>10^{14}\\,\\text{GeV}$ (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...
Lorentz violations in multifractal spacetimes
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2017-05-15
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{sub *} > 10{sup 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{sub *} > 10{sup 17} GeV or greater. (orig.)
Lorentz violations in multifractal spacetimes
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.
Nonlinear multi-analysis of agent-based financial market dynamics by epidemic system
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.
Nonlinear multi-analysis of agent-based financial market dynamics by epidemic system.
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.
Diffusion and scattering in multifractal clouds
Energy Technology Data Exchange (ETDEWEB)
Lovejoy, S. [McGill Univ., Montreal, Quebec (Canada); Schertzer, D. [Universite Pierre et Marie Curie, Paris (France); Waston, B. [St. Lawrence Univ., Canton, NY (United States)] [and others
1996-04-01
This paper describes investigations of radiative properties of multifractal clouds using two different approaches. In the first, diffusion is considered by examining the scaling properties of one dimensional random walks on media with multifractal diffusivities. The second approach considers the scattering statistics associated with radiative transport.
Institute of Scientific and Technical Information of China (English)
张冬梅; 龚小胜; 戴光明
2011-01-01
Current model-based multi-objective evolutionary algorithms use linear modeling approach such as PCA and local PCA, which has deficiencies that the model fitting result is not satisfactory and is sensitive to modeling parameters. In this paper, a multi-objective evolutionary optimization algorithm based on multifractal principal curve (MFPC-MOEA) is proposed. The algorithm uses principal curve to build nonlinear modeling on the distribution of the solution set and to establish the probability model on the individual distribution of population, which can generate the individuals distributed evenly in the objective space and ensure the diversity of optimization results. The start and stop criteria for the algorithm modeling are two important aspects of modeling multi-objective algorithm. In this paper, we analyze the distribution of individuals in the solution space with multifractal spectrum, and design the start criteria of the modeling for the model of multi-objective evolutionary algorithm, which is used as initial conditions of model. Furthermore, multifractal approach is used for assessing the convergence degree of algorithm, in order to design a stop criteria of the multi-objective evolutionary optimization algorithm. Moreover, we adopt internationally recognized testing functions such as ZDT, DTLZ, etc, to conduct the comparison experiment with NSGA-II, MOEA/D, PAES, SPEA2, MFPC-MOEA and other classical multi-objective evolutionary optimization algorithms. The simulation results show that the proposed algorithm performs better on the performance indicators of HV, SPREAD, IGD and EPS1LON, which indicates that through the introduction of multifractal modeling strategy and principal curve method, the quality of solution is improved in a certain extent. A new idea to solve multi-objective optimization problems (MOPs) is provided.%为了克服目前模型多目标演化算法多采用PCA,local PCA等线性建模方法,存在模型拟合效果不理想、对建模
Sondhiya, Deepak Kumar; Gwal, Ashok Kumar; Verma, Shivali; Kasde, Satish Kumar; Sonakia, Anjana
In this work Wavelet Transform Modulus Maxima (WTMM) based multifractal analysis method is used to extracts the earthquake precursory signatures from scaling characteristics of subionospheric Very Low Frequency (VLF) signals. We found specific dynamics of their fractal characteristics before the earthquake, appearance of the spike in the signal and increase of the fractal dimension. We analyze VLF signals of famous Turkey Bafa transmitter (N 370 24’, E 27019’) recorded by sudden Ionospheric Disturbance (SID) monitoring station located at South of France during the Earthquake occurred at Greece during the year 2011-2012. The analysis of VLF signal during some days before and after the occurrence of earthquake has been done. Keywords: Multifractal analysis, VLF signal, Sudden Ionospheric disturbances
Multifractional Spacetimes, Asymptotic Safety and HOŘAVA-LIFSHITZ Gravity
Calcagni, Gianluca
2013-07-01
We compare the recently formulated multifractional spacetimes with field theories of quantum gravity based on the renormalization group (RG), such as asymptotic safety and Hořava-Lifshitz gravity. The change of spacetime dimensionality with the probed scale is realized in both cases by an adaptation of the measurement tools ("rods") to the scale, but in different ways. In the multifractional case, by an adaptation of the position-space measure, which can be encoded into an explicit scale dependence of effective coordinates. In the case of RG-based theories, by an adaptation of the momenta. The two pictures are mapped into each other, thus presenting the fractal structure of spacetime in RG-based theories under an alternative perspective.
Using multifractals to evaluate oceanographic model skill
Skákala, Jozef; Cazenave, Pierre W.; Smyth, Timothy J.; Torres, Ricardo
2016-08-01
We are in an era of unprecedented data volumes generated from observations and model simulations. This is particularly true from satellite Earth Observations (EO) and global scale oceanographic models. This presents us with an opportunity to evaluate large-scale oceanographic model outputs using EO data. Previous work on model skill evaluation has led to a plethora of metrics. The paper defines two new model skill evaluation metrics. The metrics are based on the theory of universal multifractals and their purpose is to measure the structural similarity between the model predictions and the EO data. The two metrics have the following advantages over the standard techniques: (a) they are scale-free and (b) they carry important part of information about how model represents different oceanographic drivers. Those two metrics are then used in the paper to evaluate the performance of the FVCOM model in the shelf seas around the south-west coast of the UK.
On multifractality of high-latitude geomagnetic fluctuations
Directory of Open Access Journals (Sweden)
Z. Vörös
model are observed when the influence of the solar wind fluctuations is examined. On this basis it is expected that an extended multifractal analysis of the singularity structure of near-Earth plasma system fluctuations would lead to improved geomagnetic diagnosis of the magnetospheric dynamics.
Key words: Magnetospheric physics (magnetosphere-ionosphere interaction; solar wind-magnetosphere interactions; storms and substorms
Seismic Interevent Time: A Spatial Scaling and Multifractality
Molchan, G
2005-01-01
The optimal scaling problem for the time t(LxL) between two successive events in a seismogenic cell of size L is considered. The quantity t(LxL) is defined for a random cell of a grid covering a seismic region G. We solve that problem in terms of a multifractal characteristic of epicenters in G known as the tau-function or generalized fractal dimensions; the solution depends on the type of cell randomization. Our theoretical deductions are corroborated by California seismicity with magnitude M>2. In other words, the population of waiting time distributions for L = 10-100 km provides positive information on the multifractal nature of seismicity, which impedes the population to be converted into a unified law by scaling. This study is a follow-up of our analysis of power/unified laws for seismicity (see PAGEOPH 162 (2005), 1135 and GJI 162 (2005), 899).
Multifractal Model of Soil Water Erosion
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
Directory of Open Access Journals (Sweden)
Lei Jiang
2013-01-01
Full Text Available The temporal scaling properties of the daily 0 cm average ground surface temperature (AGST records obtained from four selected sites over China are investigated using multifractal detrended fluctuation analysis (MF-DFA method. Results show that the AGST records at all four locations exhibit strong persistence features and different scaling behaviors. The differences of the generalized Hurst exponents are very different for the AGST series of each site reflecting the different scaling behaviors of the fluctuation. Furthermore, the strengths of multifractal spectrum are different for different weather stations and indicate that the multifractal behaviors vary from station to station over China.
Multifractality and herding behavior in the Japanese stock market
Energy Technology Data Exchange (ETDEWEB)
Cajueiro, Daniel O. [Universidade Catolica de Brasilia, Doutorado em Economia de Empresas, SGAN 916, Modulo B, Asa Norte, DF 70790-160 (Brazil); Tabak, Benjamin M. [Banco Central do Brasil, SBS Quadra 3, Bloco B, 9 andar, DF 70074-900 (Brazil)], E-mail: benjamin@ucb.br
2009-04-15
In this paper we present evidence of multifractality and herding behavior for a large set of Japanese stocks traded in the Tokyo Stock Exchange. We find evidence that herding behavior occurs in periods of extreme market movements. Therefore, based on the intuition behind the tests to detect herding phenomenon developed, for instance, in Christie and Huang [Christie W, Huang R. Following the pied pier: do individual returns herd around the market? Financ Analysts J 1995;51:31-7] and Chang et al. [Chang EC, Cheng JW, Khorana A. Examination of herd behavior in equity markets: an international perspective. J Bank Finance 2000;24:1651-99], we suggest that herding behavior may be one of the causes of multifractality.
Multifractal comparison of the painting techniques of adults and children
Mureika, J. R.; Fairbanks, M. S.; Taylor, R. P.
2010-02-01
Statistical analysis of art, particularly of the abstract genre, is becoming an increasingly important tool for understanding the image creation process. We present a multifractal clustering analysis of non-representational images painted by adults and children using a 'pouring' technique. The effective dimensions (D0) are measured for each, as is the associated multifractal depth ▵D = D0 - DOO. It is shown that children create paintings whose dimensions D0 are less than those created by adults. The effective dimensions for adult painters tend to cluster around 1.8, while those for children assume typical values of 1.6. In a similar fashion, the multifractal depths for images painted by adults and children show statistically-significant differences in their values. Adult paintings show a relatively shallow depth (▵D ~ 0.02), while children's paintings show a much greater depth (▵D ~ 0.1). Given that the 'pouring' technique reflects the body motions of the artist, the results suggest that the differences in the paintings' fractal characteristics are potential indicators of artist physiology.
基于多分形理论的动态VaR预测模型研究%Forecasting Model for Dynamic Value-at-Risk Based on Multifractal Theories
Institute of Scientific and Technical Information of China (English)
魏宇
2012-01-01
经济物理学（econophysics）的大量研究表明，金融市场的波动具有复杂的多分形（multifractal）特征，因此准确地测度和预测市场波动，对金融风险管理工作的意义重大。在已有多分形波动率（multifractal volatility）测度及其模型应用基础上，以上证综指10年的高频数据为对象，提出了基于多分形波动率的样本外动态风险价值（out-of-sample dynamic VaR）预测法。通过两种规范的后验分析（backtesting）结果表明，与8种主流的线性和非线性GARCH族模型相比，在高风险水平上，基于多分形波动率测度的VaR模型明显具有更高的样本外动态风险预测精度。%Much literature in Econophysics reveals that the volatility in financial markets presents multi- fractal features. Thus, measuring and forecasting the market volatility accurately is very important for fi- nancial risk management. Based on the earlier research of multifractal volatility and its model, an out-of-sample dynamic VaR forecasting method is proposed in this paper. The empirical results on two backtesting techniques show that, on high-risk levels, VaR fnodel based on multifractal volatility produces much better out-of-sample VaR forecasts than eight popular linear and nonlinear GARCH models.
Multifractal dimension and lacunarity of yolk sac vasculature after exposure to magnetic field.
Costa, Edbhergue Ventura Lola; Nogueira, Romildo de Albuquerque
2015-05-01
Several studies have reported about the effects of magnetic fields (MFs) on vascular tissue. Extremely low frequency magnetic fields (ELF-MFs) can promote either inhibition or stimulation of vasculogenesis and angiogenesis, depending upon the intensity and time of exposure to the MF. To investigate the possible effects of ELF-MF on vascular processes, it is necessary to employ methods that allow parameterization of the vascular network. Vascular network is a structure with fractal geometry; therefore, fractal methods have been used to evaluate its morphometric complexity. Here, we used the lacunarity parameter (complementary method of fractal analysis) and multifractal analyses to investigate angiogenesis and vasculogenesis in the embryonic yolk sac membrane (YSM) of Japanese quails (Coturnix japonica) with and without exposure to an external MF of 1 mT and 60 Hz. Lacunarity results showed that the vascular density was lower for the group exposed to the magnetic field for 9 h/day. In addition, multifractal analysis showed reduced vascularization in the experimental groups (6 h/day and 9 h/day of exposure to MF). Furthermore, multifractal analysis showed difference between the groups exposed for 12 and 24 h/day. Using multifractal methods (generalized dimensions and singularity spectrum), it was possible to characterize the vascular network of the quail embryo YSM as a multifractal object, therefore proving this method to be a more appropriate application than the traditional monofractal methods. Copyright © 2015 Elsevier Inc. All rights reserved.
Scaling and multifractal fields in the solid earth and topography
Directory of Open Access Journals (Sweden)
S. Lovejoy
2007-08-01
Full Text Available Starting about thirty years ago, new ideas in nonlinear dynamics, particularly fractals and scaling, provoked an explosive growth of research both in modeling and in experimentally characterizing geosystems over wide ranges of scale. In this review we focus on scaling advances in solid earth geophysics including the topography. To reduce the review to manageable proportions, we restrict our attention to scaling fields, i.e. to the discussion of intensive quantities such as ore concentrations, rock densities, susceptibilities, and magnetic and gravitational fields.
We discuss the growing body of evidence showing that geofields are scaling (have power law dependencies on spatial scale, resolution, over wide ranges of both horizontal and vertical scale. Focusing on the cases where both horizontal and vertical statistics have both been estimated from proximate data, we argue that the exponents are systematically different, reflecting lithospheric stratification which – while very strong at small scales – becomes less and less pronounced at larger and larger scales, but in a scaling manner. We then discuss the necessity for treating the fields as multifractals rather than monofractals, the latter being too restrictive a framework. We discuss the consequences of multifractality for geostatistics, we then discuss cascade processes in which the same dynamical mechanism repeats scale after scale over a range. Using the binomial model first proposed by de Wijs (1951 as an example, we discuss the issues of microcanonical versus canonical conservation, algebraic ("Pareto" versus long tailed (e.g. lognormal distributions, multifractal universality, conservative and nonconservative multifractal processes, codimension versus dimension formalisms. We compare and contrast different scaling models (fractional Brownian motion, fractional Levy motion, continuous (in scale cascades, showing that they are all based on fractional integrations of noises
MULTIFRACTAL STRUCTURE AND PRODUCT OF MATRICES
Institute of Scientific and Technical Information of China (English)
Lau Ka-sing
2003-01-01
There is a well established multifractal theory for self-similar measures generated by non-overlapping contractive similutudes.Our report here concerns those with overlaps.In particular we restrict our attention to the important classes of self-similar measures that have matrix representations.The dimension spectra and the Lq-spectra are analyzed through the product of matrices.There are abnormal behaviors on the multifrac-tal structure and they will be discussed in detail.
Multifractal Models, Intertrade Durations and Return Volatility
Segnon, Mawuli Kouami
2015-01-01
This thesis covers the application of multifractal processes in modeling financial time series. It aims to demonstrate the capacity and the robustness of the multifractal processes to better model return volatility and ultra high frequency financial data than both the generalized autoregressive conditional heteroscedasticity (GARCH)-type and autoregressive conditional duration (ACD) models currently used in research and practice. The thesis is comprised of four main parts that ...
Stochastic Calculus with respect to multifractional Brownian motion
Lebovits, Joachim
2011-01-01
Stochastic calculus with respect to fractional Brownian motion (fBm) has attracted a lot of interest in recent years, motivated in particular by applications in finance and Internet traffic modeling. Multifractional Brownian motion (mBm) is a Gaussian extension of fBm that allows to control the pointwise regularity of the paths of the process and to decouple it from its long range dependence properties. This generalization is obtained by replacing the constant Hurst parameter H of fBm by a function h(t). Multifractional Brownian motion has proved useful in many applications, including the ones just mentioned. In this work we extend to mBm the construction of a stochastic integral with respect to fBm. This stochastic integral is based on white noise theory, as originally proposed in [15], [6], [4] and in [5]. In that view, a multifractional white noise is defined, which allows to integrate with respect to mBm a large class of stochastic processes using Wick products. It\\^o formulas (both for tempered distribut...
Multifractals and Entropy Computing
Slomczynski, W; Zyczkowski, K; Slomczynski, Wojciech; Kwapien, Jaroslaw; Zyczkowski, Karol
1998-01-01
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their shown that with certain dynamical systems one can associate the corresponding IFSs in such a way that their generalized entropies are equal. We use this method to compute entropy of some classical and quantum dynamical systems. Numerical techniques are based on integration over fractal measures.
Fractal and multifractal analyses of bipartite networks.
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
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
Fractal and multifractal analyses of bipartite networks
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.
Multifractal network generator.
Palla, Gergely; Lovász, László; Vicsek, Tamás
2010-04-27
We introduce a new approach to constructing networks with realistic features. Our method, in spite of its conceptual simplicity (it has only two parameters) is capable of generating a wide variety of network types with prescribed statistical properties, e.g., with degree or clustering coefficient distributions of various, very different forms. In turn, these graphs can be used to test hypotheses or as models of actual data. The method is based on a mapping between suitably chosen singular measures defined on the unit square and sparse infinite networks. Such a mapping has the great potential of allowing for graph theoretical results for a variety of network topologies. The main idea of our approach is to go to the infinite limit of the singular measure and the size of the corresponding graph simultaneously. A very unique feature of this construction is that with the increasing system size the generated graphs become topologically more structured. We present analytic expressions derived from the parameters of the--to be iterated--initial generating measure for such major characteristics of graphs as their degree, clustering coefficient, and assortativity coefficient distributions. The optimal parameters of the generating measure are determined from a simple simulated annealing process. Thus, the present work provides a tool for researchers from a variety of fields (such as biology, computer science, biology, or complex systems) enabling them to create a versatile model of their network data.
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
Directory of Open Access Journals (Sweden)
D. Schertzer
1994-01-01
Full Text Available 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
Chatzigeorgiou, M.; Constantoudis, V.; Diakonos, F.; Karamanos, K.; Papadimitriou, C.; Kalimeri, M.; Papageorgiou, H.
2017-03-01
During the last years, several methods from the statistical physics of complex systems have been applied to the study of natural language written texts. They have mostly been focused on the detection of long-range correlations, multifractal analysis and the statistics of the content word positions. In the present paper, we show that these statistical aspects of language series are not independent but may exhibit strong interrelations. This is done by means of a two-step investigation. First, we calculate the multifractal spectra using the word-length representation of huge parallel corpora from ten European languages and compare with the shuffled data to assess the contribution of long-range correlations to multifractality. In the second step, the detected multifractal correlations are shown to be related to the scale-dependent clustering of the long, highly informative content words. Furthermore, exploiting the language sensitivity of the used word-length representation, we demonstrate the consistent impact of the classification of languages into families on the multifractal correlations and long-word clustering patterns.
Multifractal Geophysical Extremes: Nonstationarity and Long Range Correlations
Tchiguirinskaia, I.; Schertzer, D.; Lovejoy, S.
2012-04-01
Throughout the world, extremes in environmental sciences are of prime importance. They are key variables not only for risk assessments and engineering designs (e.g. of dams and bridges), but also for resource management (e.g. water and energy) and for land use. A better understanding of them is more and more indispensable in settling the debate on their possible climatological evolution. Whereas it took decades before a uniform technique for estimating flow frequencies within a stationary framework, it is often claimed that « stationarity is dead ! ». The fact that geophysical and environmental fields are variable over a wider range of scales than previously thought require to go beyond the limits of the (classical) Extreme Value Theory (EVT). Indeed, long-range correlations are beyond the scope of the classical EVT theory. We show that multifractal concepts and techniques are particularly appealing because they can effectively deal with a cascade of interactions concentrating for instance energy, liquid water, etc. into smaller and smaller space-time domains. Furthermore, a general outcome of these cascade processes -which surprisingly was realized only rather recently- is that rather independently of their details they yield probability distributions with power-law fall-offs, often called (asymptotic) Pareto or Zipf laws. We discuss the corresponding probability distributions of their maxima and its relationship with the Frechet law. We use these multifractal techniques to investigate the possibility of using very short or incomplete data records for reliable statistical predictions of the extremes. In particular we assess the multifractal parameter uncertainty with the help of long synthetic multifractal series and their sub-samples, in particular to obtain an approximation of confidence intervals that would be particularly important for the predictions of multifractal extremes. We finally illustrate the efficiency of this approach with its application to
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
Hierarchical multifractal representation of symbolic sequences and application to human chromosomes
Provata, A.; Katsaloulis, P.
2010-02-01
The two-dimensional density correlation matrix is constructed for symbolic sequences using contiguous segments of arbitrary size. The multifractal spectrum obtained from this matrix motif is shown to characterize the correlations in the symbolic sequences. This method is applied to entire human chromosomes, shuffled human chromosomes, reconstructed human genomic sequences and to artificial random sequences. It is shown that all human chromosomes have common characteristics in their multifractal spectrum and deviate substantially from random and uncorrelated sequences of the same size. Small deviations are observed between the longer and the shorter chromosomes, especially for the higher (in absolute values) statistical moments. The correlations are crucial for the form of the multifractal spectrum; surrogate shuffled chromosomes present randomlike spectrum, distinctly different from the actual chromosomes. Analytical approaches based on hierarchical superposition of tensor products show that retaining pair correlations in the sequences leads to a closer representation of the genomic multifractal spectra, especially in the region of negative exponents, due to the underrepresentation of various functional units (such as the cytosine-guanine CG combination and its complementary GC complex). Retaining higher-order correlations in the construction of the tensor products is a way to approach closer the structure of the multifractal spectra of the actual genomic sequences. This hierarchical approach is generic and is applicable to other correlated symbolic sequences.
Improved moment scaling estimation for multifractal signals
Directory of Open Access Journals (Sweden)
D. Veneziano
2009-11-01
Full Text Available A fundamental problem in the analysis of multifractal processes is to estimate the scaling exponent K(q of moments of different order q from data. Conventional estimators use the empirical moments μ^_{r}^{q}=⟨ | ε_{r}(τ|^{q}⟩ of wavelet coefficients ε_{r}(τ, where τ is location and r is resolution. For stationary measures one usually considers "wavelets of order 0" (averages, whereas for functions with multifractal increments one must use wavelets of order at least 1. One obtains K^(q as the slope of log( μ^_{r}^{q} against log(r over a range of r. Negative moments are sensitive to measurement noise and quantization. For them, one typically uses only the local maxima of | ε_{r}(τ| (modulus maxima methods. For the positive moments, we modify the standard estimator K^(q to significantly reduce its variance at the expense of a modest increase in the bias. This is done by separately estimating K(q from sub-records and averaging the results. For the negative moments, we show that the standard modulus maxima estimator is biased and, in the case of additive noise or quantization, is not applicable with wavelets of order 1 or higher. For these cases we propose alternative estimators. We also consider the fitting of parametric models of K(q and show how, by splitting the record into sub-records as indicated above, the accuracy of standard methods can be significantly improved.
Energy Technology Data Exchange (ETDEWEB)
Yadav, R. P.; Mittal, A. K. [Department of Physics, University of Allahabad, Allahabad 211002 (India); Kumar, Manvendra, E-mail: kmanav@gmail.com; Pandey, A. C. [Nanotechnology Application Centre, University of Allahabad, Allahabad 211002 (India)
2015-08-15
Fractal and multifractal characteristics of self-affine surfaces of BaF{sub 2} thin films, deposited on crystalline Si 〈1 1 1〉 substrate at room temperature, were studied. Self-affine surfaces were prepared by irradiation of 120 MeV Ag{sup 9+} ions which modified the surface morphology at nanometer scale. The surface morphology of virgin thin film and those irradiated with different ion fluences are characterized by atomic force microscopy technique. The surface roughness (interface width) shows monotonic decrease with ion fluences, while the other parameters, such as lateral correlation length, roughness exponent, and fractal dimension, did not show either monotonic decrease or increase in nature. The self-affine nature of the films is further confirmed by autocorrelation function. The power spectral density of thin films surfaces exhibits inverse power law variation with spatial frequency, suggesting the existence of fractal component in surface morphology. The multifractal detrended fluctuation analysis based on the partition function approach is also performed on virgin and irradiated thin films. It is found that the partition function exhibits the power law behavior with the segment size. Moreover, it is also seen that the scaling exponents vary nonlinearly with the moment, thereby exhibiting the multifractal nature.
Self-Affine Multifractal Spectrum and Levy Stability Index from NA27 Data
Institute of Scientific and Technical Information of China (English)
王韶舜; 吴冲
2001-01-01
A self-affine analysis of multiparticle production in pp collisions at 400 GeV/c was performed by using the method of continuously varying scale and the method of the factorial moments of continuous order. The self-affine generalized fractal dimensions and multifractal spectrum have been obtained. The self-affine multifractal spectrum is concave downward with a maximum at q ＝ 0, f(α(0)) ＝ D(0) ＝ 1. D(q) decreases with increasing q showing that there is self-affine multifractal behaviour in multiparticle production at the 400GeV/c pp collisions. The Levy index μ ＞ 1 indicates that a non-thermal phase transition may exist in the pp collisions at 400 GeV/c.
Multifractal modelling of runoffs of karstic springs
Márkus, L.
2003-04-01
A new multifractal stochastic process, Terdik and Iglói call the Limit of the Integrated Superposition of Diffusion processes with Linear differential Generator (LISDLG) , has been defined for modelling network traffic multifractality. The process is stationary, and exhibits long range dependency or long memory. Its characteristic property is that its bispectrum is real. It serves as the basis of distinction e.g. from the superposition of Levy-processes driven Ornstein-Uhlenbeck processes. Its further appealing property is that its finite dimensional distribution stems from multivariate Gamma, therefore it is inherently positive and skewed (and hence non-Gaussian). All together, this makes it a very promising candidate for modelling e.g. runoff data of springs or river flows. Quite recently Labat et al. (2002, J. of Hydrology, Vol 256, pp.176-195) pointed out multifractal properties of the runoff time series of French karstic springs. We show that runoff data of karstic springs in north-east Hungary possesses multifractal and cumulant-multifractal property as well as long range dependency and fit the above described LISDLG process, to model the phenomenon. Acknowledgement: This research was supported by the Nat. Sci. Research Fund OTKA, grant No.: T 032725.
Munro, Mark; Ord, Alison; Hobbs, Bruce
2015-04-01
A range of factors controls the location of hydrothermal alteration and gold mineralisation in the Earth's crust. These include the broad-scale lithospheric architecture, availability of fluid sources, fluid composition and pH, pressure-temperature conditions, microscopic to macroscopic structural development, the distribution of primary lithologies, and the extent of fluid-rock interactions. Consequently, the spatial distribution of alteration and mineralization in hydrothermal systems is complex and often considered highly irregular. However, despite this, do they organize themselves in a configuration that can be documented and quantified? Wavelets, mathematical functions representing wave-like oscillations, are commonly used in digital signals analysis. Wavelet-based multifractal analysis involves incrementally scanning a wavelet across the dataset multiple times (varying its scale) and recording its degree of fit to the signal at each interval. This approach (the wavelet transform modulus maxima method) highlights patterns of self-similarity present in the dataset and addresses the range of scales over which these patterns replicate themselves (expressed by their range in 'fractal dimension'). Focusing on seven gold ore bodies in the Archaean Yilgarn craton of Western Australia, this study investigates whether different aspects of hydrothermal gold systems evolve to organize themselves spatially as multifractals. Four ore bodies were selected from the Sunrise Dam deposit (situated in the Laverton tectonic zone of the Kurnalpi terrane) in addition to the Imperial, Majestic and Salt Creek gold prospects, situated in the Yindarlgooda dome of the Mount Monger goldfield (approximately 40km due east of Kalgoorlie). The Vogue, GQ, Cosmo East and Astro ore bodies at Sunrise Dam were chosen because they exhibit different structural geometries and relationships between gold and associated host-rock alteration styles. Wavelet-based analysis was conducted on 0.5m and 1m
de Freitas, D. B.; Nepomuceno, M. M. F.; Gomes de Souza, M.; Leão, I. C.; Das Chagas, M. L.; Costa, A. D.; Canto Martins, B. L.; De Medeiros, J. R.
2017-07-01
In the present study, we investigate the multifractal nature of a long-cadence time series observed by the Kepler mission for a sample of 34 M dwarf stars and the Sun in its active phase. Using the Multifractal Detrending Moving Average algorithm, which enables the detection of multifractality in nonstationary time series, we define a set of multifractal indices based on the multifractal spectrum profile as a measure of the level of stellar magnetic activity. This set of indices is given by the (A, {{Δ }}α , C, H)-quartet, where A, {{Δ }}α , and C are related to geometric features from the multifractal spectrum and the global Hurst exponent H describes the global structure and memorability of time series dynamics. As a test, we measure these indices and compare them with a magnetic index defined as S ph and verify the degree of correlation among them. First, we apply the Poincaré plot method and find a strong correlation between the index and one of the descriptors that emerges from this method. As a result, we find that this index is strongly correlated with long-term features of the signal. From the multifractal perspective, the index is also strongly linked to the geometric properties of the multifractal spectrum except for the H index. Furthermore, our results emphasize that the rotation period of stars is scaled by the H index, which is consistent with Skumanich’s relationship. Finally, our approach suggests that the H index may be related to the evolution of stellar angular momentum and a star’s magnetic properties.
Changes in multifractal properties for stable angina pectoris
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.
To be and not to be: scale correlations in random multifractal processes
DEFF Research Database (Denmark)
Cleve, Jochen; Schmiegel, Jürgen; Greiner, Martin
We discuss various properties of a random multifractal process, which are related to the issue of scale correlations. By design, the process is homogeneous, non-conservative and has no built-in scale correlations. However, when it comes to observables like breakdown coefficients, which are based...... on a coarse-graining of the multifractal field, scale correlations do appear. In the log-normal limit of the model process, the conditional distributions and moments of breakdown coefficients reproduce the observations made in fully developed small-scale turbulence. These findings help to understand several...
Can economic policy uncertainty help to forecast the volatility: A multifractal perspective
Liu, Zhicao; Ye, Yong; Ma, Feng; Liu, Jing
2017-09-01
In this study, we investigate whether economic policy uncertainty (EPU) can impact on future volatility based on the multifractal insight. Our estimation results show that the impact of EPU on future volatility is significantly positive, which indicate that EPU can aggravate the future market risk. Moreover, Out-of-sample results tell us that adding EPU as explanatory variable to volatility models can indeed improve the forecasting performance. Furthermore, we also find evidence that the multifractal volatility models can beat the GARCH-class models in forecasting.
Deformed symmetries in noncommutative and multifractional spacetimes
Calcagni, Gianluca
2016-01-01
We clarify the relation between noncommutative spacetimes and multifractional geometries where the spacetime dimension changes with the probed scale. In the absence of curvature and comparing the symmetries of both position and momentum space, we show that $\\kappa$-Minkowski spacetime and the commutative multifractional theory with $q$-derivatives are physically inequivalent but they admit several contact points that allow one to describe certain aspects of $\\kappa$-Minkowski noncommutative geometry as a multifractional theory and vice versa. Contrary to previous literature, this result holds without assuming any specific measure for $\\kappa$-Minkowski. More generally, no well-defined $\\star$-product can be constructed from the $q$-theory, although the latter does admit a natural noncommutative extension with a given deformed Poincar\\'e algebra. A similar no-go theorem may be valid for all multiscale theories with factorizable measures. Turning gravity on, we write the algebras of gravitational first-class co...
Unveiling the Multi-fractal Structure of Complex Networks
Jalan, Sarika; Sarkar, Camellia; Boccaletti, Stefano
2016-01-01
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding method for revealing changes in the fractal behavior of networks, and particularly for allowing distinction between mono-fractal, quasi mono-fractal, and multi-fractal structures. We show that degree homogeneity plays a crucial role in determining the fractal nature of the underlying network, and report on six different protein-protein interaction networks along with their corresponding random networks. Our analysis allows to identify varying levels of complexity in the species.
Multifractal spectrum and lacunarity as measures of complexity of osseointegration.
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
Approximated maximum likelihood estimation in multifractal random walks
Løvsletten, Ola
2011-01-01
We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 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.
Multifractal characteristics of Nitrogen adsorption isotherms from tropical soils
Vidal Vázquez, Eva; Paz Ferreiro, Jorge
2010-05-01
One of the primary methods used to characterize a wide range of porous materials, including soils, are gas adsorption isotherms. An adsorption isotherm is a function relating the amount of adsorbed gas or vapour to the respective equilibrium pressure, during pressure increase at constant temperature. Adsorption data allow easily estimates of specific surface area and also can provide a characterization of pore surface heterogeneity. Most of the properties and the reactivity of soil colloids are influenced by their specific surface area and by parameters describing the surface heterogeneity. For a restricted scale range, linearity between applied pressure and volume of adsorbate holds, which is the basis for current estimations of specific surface area. However, adsorption isotherms contain also non-linear segments of pressure versus volume so that evidence of multifractal scale has been demonstrated. The aim of this study was to analyze the multifractal behaviour of nitrogen adsorption isotherms from a set of tropical soils. Samples were collected form 54 horizons belonging to 19 soil profiles in the state of Minas Gerais, Brazil. The most frequent soil type was Oxisol, according to the Soil Survey Staff, equivalent to Latossolo in the Brazilian soil classification system. Nitrogen adsorption isotherms at standard 77 K were measured using a Thermo Finnigan Sorptomatic 1990 gas sorption analyzer (Thermo Scientific, Waltham, MA). From the raw data a distributions of mass along a support was obtained to perform multifractal analysis. The probability distribution was constructed by dividing the values of the measure in a given segment by the sum of the measure in the whole scale range. The box-counting method was employed to perform multifractal analysis. All the analyzed N2 adsorption isotherms behave like a multifractal system. The singularity spectra, f(α), showed asymmetric concave down parabolic shapes, with a greater tendency toward the left side, where moments
Speech emotion recognition based on multifractal%多重分形在语音情感识别中的研究
Institute of Scientific and Technical Information of China (English)
叶吉祥; 王聪慧
2012-01-01
为了克服语音情感线性参数在刻画不同情感类型特征上的不足,将多重分形理论引入语音情感识别中来,通过分析不同语音情感状态下的多重分形特征,提取多重分形谱参数和广义Hurst指数作为新的语音情感特征参数,并结合传统语音声学特征采用支持向量机(SVM)进行语音情感识别.实验结果表明,通过非线性参数的介入,与仅使用传统语音线性特征的识别方法相比,识别系统的准确率和稳定性得到有效提高,因此为语音情感识别提供了一个新的思路.%In order to overcome the inadequate of emotional conventional linear argument at depicting different types of character sentiments, this paper takes the multiple fractals theory into the sound emotional identify, by analyzing the multiple fractal features on the different sound emotional state, and proposes multifractal spectrum parameters and generalizes hurst index as emotional conventional parameters, combines with traditional voice acoustic features and using Support Vector Machine (SVM) for speech emotion recognition. The results show that the accuracy and stability of the recognition system are improved effectively through using non-linear parameters, compared with the linear features of traditional voice recognition method, so it provides a new idea for voice emotion recognition.
Deformed symmetries in noncommutative and multifractional spacetimes
Calcagni, Gianluca; Ronco, Michele
2017-02-01
We clarify the relation between noncommutative spacetimes and multifractional geometries, two quantum-gravity-related approaches where the fundamental description of spacetime is not given by a classical smooth geometry. Despite their different conceptual premises and mathematical formalisms, both research programs allow for the spacetime dimension to vary with the probed scale. This feature and other similarities led to ask whether there is a duality between these two independent proposals. In the absence of curvature and comparing the symmetries of both position and momentum space, we show that κ -Minkowski spacetime and the commutative multifractional theory with q -derivatives are physically inequivalent but they admit several contact points that allow one to describe certain aspects of κ -Minkowski noncommutative geometry as a multifractional theory and vice versa. Contrary to previous literature, this result holds without assuming any specific measure for κ -Minkowski. More generally, no well-defined ⋆-product can be constructed from the q -theory, although the latter does admit a natural noncommutative extension with a given deformed Poincaré algebra. A similar no-go theorem may be valid for all multiscale theories with factorizable measures. Turning gravity on, we write the algebras of gravitational first-class constraints in the multifractional theories with q - and weighted derivatives and discuss their differences with respect to the deformed algebras of κ -Minkowski spacetime and of loop quantum gravity.
Institute of Scientific and Technical Information of China (English)
吴栩; 宋光辉; 董艳
2014-01-01
不同市场的相互关系是金融中的热点问题，现有研究常常仅从风险或者收益的角度加以讨论，忽视了股票市场风险与收益不可分割性的特征。基于此，本文从沪深股市的夏普比率的角度分析了两个市场的相互关系。结果表明，两个市场间的协整不明显，其相关性呈现多重分形波动。%The relationship between different stock markets is the hot issue in financial.The past research often only discussed the relationship from the angle of risks or earnings.They neglected that the benefits and risks of the stock market characteristics cannot be separated.Based on this situation,this paper added the literature on the angle of the Sharpe ratio by examining the relationship between Shanghai and Shenzhen stock market.The empirical result reveals that the co-integration relationship between the two stock markets is not obvious,and the correlation between the two stock markets presents multi-fractal fluctuations.
Multifractal Solar EUV Intensity Fluctuations and their Implications for Coronal Heating Models
Cadavid, A. C.; Rivera, Y. J.; Lawrence, J. K.; Christian, D. J.; Jennings, P. J.; Rappazzo, A. F.
2016-11-01
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 minutes 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.
Multifractal Solar EUV Intensity Fluctuations and their Implications for Coronal Heating Models
Cadavid, Ana Cristina Cadavid; Lawrence, John K; Christian, Damian J; Jennings, Peter J; Rappazzo, A Franco
2016-01-01
We investigate the scaling properties of the long-range temporal evolution and intermittency of SDO/AIA intensity observations in four solar environments: 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 Angstrom 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 15-45 min is multifractal, and the time series are anti-persistent on the average. The degree of anti-correlation in the TR time series is greater than for coronal emission. The multifractality stems from long term correlations in the data rather than the wide distribution of intensities. Observations in the 335 Angstrom waveband can be described in terms of a multifractal with ...
Multifractal characterization of morphology of human red blood cells membrane skeleton.
Ţălu, Ş; Stach, S; Kaczmarska, M; Fornal, M; Grodzicki, T; Pohorecki, W; Burda, K
2016-04-01
The purpose of this paper is to show applicability of multifractal analysis in investigations of the morphological changes of ultra-structures of red blood cells (RBCs) membrane skeleton measured using atomic force microscopy (AFM). Human RBCs obtained from healthy and hypertensive donors as well as healthy erythrocytes irradiated with neutrons (45 μGy) were studied. The membrane skeleton of the cells was imaged using AFM in a contact mode. Morphological characterization of the three-dimensional RBC surfaces was realized by a multifractal method. The nanometre scale study of human RBCs surface morphology revealed a multifractal geometry. The generalized dimensions Dq and the singularity spectrum f(α) provided quantitative values that characterize the local scale properties of their membrane skeleton organization. Surface characterization was made using areal ISO 25178-2: 2012 topography parameters in combination with AFM topography measurement. The surface structure of human RBCs is complex with hierarchical substructures resulting from the organization of the erythrocyte membrane skeleton. The analysed AFM images confirm a multifractal nature of the surface that could be useful in histology to quantify human RBC architectural changes associated with different disease states. In case of very precise measurements when the red cell surface is not wrinkled even very fine differences can be uncovered as was shown for the erythrocytes treated with a very low dose of ionizing radiation.
Determination of multifractal dimensions of complex networks by means of the sandbox algorithm
Liu, Jin-Long; Yu, Zu-Guo; Anh, Vo
2015-02-01
Complex networks have attracted much attention in diverse areas of science and technology. Multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we employ the sandbox (SB) algorithm proposed by Tél et al. (Physica A 159, 155-166 (1989)), for MFA of complex networks. First, we compare the SB algorithm with two existing algorithms of MFA for complex networks: the compact-box-burning algorithm proposed by Furuya and Yakubo (Phys. Rev. E 84, 036118 (2011)), and the improved box-counting algorithm proposed by Li et al. (J. Stat. Mech.: Theor. Exp. 2014, P02020 (2014)) by calculating the mass exponents τ(q) of some deterministic model networks. We make a detailed comparison between the numerical and theoretical results of these model networks. The comparison results show that the SB algorithm is the most effective and feasible algorithm to calculate the mass exponents τ(q) and to explore the multifractal behavior of complex networks. Then, we apply the SB algorithm to study the multifractal property of some classic model networks, such as scale-free networks, small-world networks, and random networks. Our results show that multifractality exists in scale-free networks, that of small-world networks is not obvious, and it almost does not exist in random networks.
Serinaldi, F.
2010-12-01
Discrete multiplicative random cascade (MRC) models were extensively studied and applied to disaggregate rainfall data, thanks to their formal simplicity and the small number of involved parameters. Focusing on temporal disaggregation, the rationale of these models is based on multiplying the value assumed by a physical attribute (e.g., rainfall intensity) at a given time scale L, by a suitable number b of random weights, to obtain b attribute values corresponding to statistically plausible observations at a smaller L/b time resolution. In the original formulation of the MRC models, the random weights were assumed to be independent and identically distributed. However, for several studies this hypothesis did not appear to be realistic for the observed rainfall series as the distribution of the weights was shown to depend on the space-time scale and rainfall intensity. Since these findings contrast with the scale invariance assumption behind the MRC models and impact on the applicability of these models, it is worth studying their nature. This study explores the possible presence of dependence of the parameters of two discrete MRC models on rainfall intensity and time scale, by analyzing point rainfall series with 5-min time resolution. Taking into account a discrete microcanonical (MC) model based on beta distribution and a discrete canonical beta-logstable (BLS), the analysis points out that the relations between the parameters and rainfall intensity across the time scales are detectable and can be modeled by a set of simple functions accounting for the parameter-rainfall intensity relationship, and another set describing the link between the parameters and the time scale. Therefore, MC and BLS models were modified to explicitly account for these relationships and compared with the continuous in scale universal multifractal (CUM) model, which is used as a physically based benchmark model. Monte Carlo simulations point out that the dependence of MC and BLS
Directory of Open Access Journals (Sweden)
F. Serinaldi
2010-12-01
Full Text Available Discrete multiplicative random cascade (MRC models were extensively studied and applied to disaggregate rainfall data, thanks to their formal simplicity and the small number of involved parameters. Focusing on temporal disaggregation, the rationale of these models is based on multiplying the value assumed by a physical attribute (e.g., rainfall intensity at a given time scale L, by a suitable number b of random weights, to obtain b attribute values corresponding to statistically plausible observations at a smaller L/b time resolution. In the original formulation of the MRC models, the random weights were assumed to be independent and identically distributed. However, for several studies this hypothesis did not appear to be realistic for the observed rainfall series as the distribution of the weights was shown to depend on the space-time scale and rainfall intensity. Since these findings contrast with the scale invariance assumption behind the MRC models and impact on the applicability of these models, it is worth studying their nature. This study explores the possible presence of dependence of the parameters of two discrete MRC models on rainfall intensity and time scale, by analyzing point rainfall series with 5-min time resolution. Taking into account a discrete microcanonical (MC model based on beta distribution and a discrete canonical beta-logstable (BLS, the analysis points out that the relations between the parameters and rainfall intensity across the time scales are detectable and can be modeled by a set of simple functions accounting for the parameter-rainfall intensity relationship, and another set describing the link between the parameters and the time scale. Therefore, MC and BLS models were modified to explicitly account for these relationships and compared with the continuous in scale universal multifractal (CUM model, which is used as a physically based benchmark model. Monte Carlo simulations point out
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).
Detrended cross-correlation analysis on RMB exchange rate and Hang Seng China Enterprises Index
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.
Multifractality and value-at-risk forecasting of exchange rates
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.
Defining Urban and Rural Regions by Multifractal Spectrums of Urbanization
Chen, Yanguang
2016-03-01
The spatial pattern of the urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper is devoted to defining urban and rural regions using ideas from fractals. A basic postulate is that human geographical systems are of self-similar patterns correlated with recursive processes. Then multifractal geometry can be employed to describe or define the urban and rural terrain with the level of urbanization. A space-filling index of urban-rural region based on a generalized correlation dimension is presented to reflect the degree of geo-spatial utilization in terms of urbanism. The census data of America and China are used to show how to make empirical analyses of urban-rural multifractals. This work is a normative study rather than a positive study, and it proposes a new way of investigating urban and rural regional systems using fractal theory.
Multifractal characteristics of NDVI maps in space and time in the Community of Madrid (Spain)
Sotoca, Juan J. Martin; Saa-Requejo, Antonio; Grau, Juan B.; Tarquis, Ana M.
2015-04-01
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
Directory of Open Access Journals (Sweden)
Michael James Lewis
2013-05-01
Full Text Available Multifractal properties of electrocardiographic inter-beat (RR time-series offer insight into its long-term correlation structure, independently of RR variability. Here we quantify multifractal characteristics of RR data during 24-hour diurnal-nocturnal activity in healthy participants. We tested the hypotheses that (1 age, gender and aerobic fitness influence RR multifractal properties, and that (2 these are influenced by circadian variation.Seventy adults (39 males aged 19-58 years and of various fitness levels were monitored using 24-hour ECG. Participants were dichotomised by median age and fitness for sub-group analysis. Gender and fitness were independent of age (p=0.1, p>0.5. Younger/older group ages were substantially different (p<0.0005 and were independent of gender and fitness. Multifractality was quantified using the probability spectrum of Hölder exponents (h, from which modal h (h* and the full-width and half-widths at half-maximum measures (FWHM, HWHM+ and HWHM- were derived. FWHM decreased (p=0.004 and h* increased (p=0.011 in older people, indicating diminished long-range RR correlations and weaker anti-persistent behavior. Anti-persistent correlation (h* was strongest in the youngest/fittest individuals and weakest in the oldest/least fit individuals (p=0.015. Long-range correlation (HWHM+/FWHM was strongest in the fittest males and weakest in the least fit females (p=0.007-0.033.Multifractal RR characteristics in our healthy participants showed strong age-dependence with diminished long-range anti-persistent correlation in older people. Circadian variation of these characteristics was influenced by fitness and gender: fitter males and females of all ages had the greatest degree of multifractality or long-range order. Multifractal characterisation appears to be a useful method for exploring the physiological basis of long-term correlation structure in RR time-series as well as the benefits thereon of physical fitness training.
Particle-physics constraints on multifractal spacetimes
Calcagni, Gianluca; Rodríguez-Fernández, David
2016-01-01
We study electroweak interactions in the multiscale theory with $q$-derivatives, a framework where spacetime has the typical features of a multifractal. In the simplest case with only one characteristic time, length and energy scale $t_*$, $\\ell_*$, and $E_*$, we consider (i) the muon decay rate and (ii) the Lamb shift in the hydrogen atom, and constrain the corrections to the ordinary results. We obtain the independent absolute upper bounds (i) $t_* 35\\,\\text{MeV}$. Under some mild theoretical assumptions, the Lamb shift alone yields the even tighter ranges $t_*450\\,\\text{GeV}$. To date, these are the first robust constraints on the scales at which the multifractal features of the geometry can become important in a physical process.
A multifractal formalism for countable alphabet subshifts
Energy Technology Data Exchange (ETDEWEB)
Meson, Alejandro [Instituto de Fisica de Liquidos y Sistemas Biologicos (IFLYSIB), CONICET-UNLP-CICPBA and Grupo de Aplicaciones Matematicas y Estadisticas de la Facultad de Ingenieria (GAMEFI) UNLP, La Plata (Argentina)], E-mail: vericat@gw-iflysib.iflysib.unlp.edu.ar; Vericat, Fernando [Instituto de Fisica de Liquidos y Sistemas Biologicos (IFLYSIB), CONICET-UNLP-CICPBA and Grupo de Aplicaciones Matematicas y Estadisticas de la Facultad de Ingenieria (GAMEFI) UNLP, La Plata (Argentina)], E-mail: meson@iflysib.unlp.edu.ar
2009-01-15
We study here the multifractal spectrum of local entropies for subshifts with an infinite alphabet. The description of this spectrum is obtained from the Legendre transform of a free energy map and Gibbs states associated with adequate potentials. The lack of compactness in the symbolic space necessitates modifications to the description for the compact case, i.e. for finite alphabet. In particular, the class of potentials must be restricted to a narrower one than that considered for the compact case.
Multifractal properties of ball milling dynamics
Energy Technology Data Exchange (ETDEWEB)
Budroni, M. A., E-mail: mabudroni@uniss.it; Pilosu, V.; Rustici, M. [Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, Via Vienna 2, Sassari 07100 (Italy); Delogu, F. [Dipartimento di Ingegneria Meccanica, Chimica, e dei Materiali, Università degli Studi di Cagliari, via Marengo 2, Cagliari 09123 (Italy)
2014-06-15
This work focuses on the dynamics of a ball inside the reactor of a ball mill. We show that the distribution of collisions at the reactor walls exhibits multifractal properties in a wide region of the parameter space defining the geometrical characteristics of the reactor and the collision elasticity. This feature points to the presence of restricted self-organized zones of the reactor walls where the ball preferentially collides and the mechanical energy is mainly dissipated.
Multifractal properties of ball milling dynamics
Energy Technology Data Exchange (ETDEWEB)
Budroni, M. A., E-mail: mabudroni@uniss.it; Pilosu, V.; Rustici, M. [Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, Via Vienna 2, Sassari 07100 (Italy); Delogu, F. [Dipartimento di Ingegneria Meccanica, Chimica, e dei Materiali, Università degli Studi di Cagliari, via Marengo 2, Cagliari 09123 (Italy)
2014-06-15
This work focuses on the dynamics of a ball inside the reactor of a ball mill. We show that the distribution of collisions at the reactor walls exhibits multifractal properties in a wide region of the parameter space defining the geometrical characteristics of the reactor and the collision elasticity. This feature points to the presence of restricted self-organized zones of the reactor walls where the ball preferentially collides and the mechanical energy is mainly dissipated.
Fractal Analysis Based on Hierarchical Scaling in Complex Systems
Chen, Yanguang
2016-01-01
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and spatial network proved to be associated with one another. This paper is devoted to exploring the theory of fractal analysis of complex systems by means of hierarchical scaling. Two research methods are utilized to make this study, including logic analysis method and empirical analysis method. The main results are as follows. First, a fractal system such as Cantor set is described from the hierarchical angle of view; based on hierarchical structure, three approaches are proposed to estimate fractal dimension. Second, the hierarchical scaling can be generalized to describe multifractals, fractal complementary sets, and self-similar curve such as logarithmic spiral. Third, complex systems such as urban system are demonstrated to be a self-similar hierarchy. The human settlements i...
The origin of an increasing or decreasing multifractal spectrum.
Opheusden, van J.H.J.
1998-01-01
The multifractal dimensionality Dq as a function of q expresses the distribution of measure over space. When all the moments scale with resolution in exactly the same way, we have a flat spectrum, and a single monofractal dimensionality. We argue that for multifractal spectra the scaling of the
Econophysics vs Cardiophysics: the Dual Face of Multifractality
Struzik, Z.R.
2003-01-01
Multifractality in physiological time series and notably in human adult heart rate has been primarily attributed to the Fourier phase ordering of the signal [1]. In contrast, the primary cause for the width of the multifractal spectrum in financial time series has recently been connected with fat-ta
Scale-free networks emerging from multifractal time series
Budroni, Marcello A.; Baronchelli, Andrea; Pastor-Satorras, Romualdo
2017-05-01
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterization of empirical data. Here we investigate the effects of the (multi)fractal properties of a signal, common in time series arising from chaotic dynamics or strange attractors, on the topology of a suitably projected network. Relying on the box-counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology and validate our findings with extensive numerical simulations. We finally present a numerical analysis on the properties of weighted and directed network projections.
Scale-free networks emerging from multifractal time series.
Budroni, Marcello A; Baronchelli, Andrea; Pastor-Satorras, Romualdo
2017-05-01
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterization of empirical data. Here we investigate the effects of the (multi)fractal properties of a signal, common in time series arising from chaotic dynamics or strange attractors, on the topology of a suitably projected network. Relying on the box-counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology and validate our findings with extensive numerical simulations. We finally present a numerical analysis on the properties of weighted and directed network projections.
Dual-induced multifractality of human online activity
Qin, Yuhao; Cai, Shimin; Gao, Liang
2014-01-01
Recent discoveries of human activity reveal the existence of long-term correlation and its relation with the fat-tailed distribution of inter-event times, which imply that there exists the fractality of human activity. However, works further analyzing the type of fractality and its origin still lack. Herein, DFA and MFDFA methods are applied in the analysis of time series of online reviewing activity from Movielens and Netflix. Results show the long-term correlation at individual and whole community level, while the strength of such correlation at individual level is restricted to activity level. Such long-term correlation reveals the fractality of online reviewing activity. In our further investigation of this fractality, we \\emph{first} demonstrate it is multifractality, which results from the dual effect of broad probability density function and long-term correlation of time series in online reviewing activity. This result is also verified by three synthesized series. Therefore, we conclude that the combin...
Complexity Induced Lifshitz Ordering with Multifractal Antiscreening/Screening (CILOMAS)
Energy Technology Data Exchange (ETDEWEB)
Chang, Tom T.S., E-mail: tom.tschang@gmail.com
2016-04-08
We demonstrate that renormalization-group effects of scale-running propagator-coupling constants due to classical fluctuations can induce antiscreening/screening and multifractal symmetry breakings among various helical and other ordered states of generalized Lifshitz character leading to novel phase-transition associated complexities in condensed matter physics and gravitational evolution. Such phenomenon can exhibit the sporadic and localized appearance of virtual particles and in the context of cosmological evolution, the coarse-grained scale-running of the gravitational constant G due to classical fluctuations may provide a partial explanation to the dark matter mystery. - Highlights: • An innovative theory in phase transitions related to complex helical orderings. • The phenomenon is induced by the “running” of the propagator-coupling constant. • The calculations are based on the exact renormalization group. • An example of gravitational evolution is described. • CILOMAS discusses Lifshitz points and virtual particles such as dark matter.
Gu, G.-F.; Chen, W.; Zhou, W.-X.
2007-05-01
The statistical properties of the bid-ask spread of a frequently traded Chinese stock listed on the Shenzhen Stock Exchange are investigated using the limit-order book data. Three different definitions of spread are considered based on the time right before transactions, the time whenever the highest buying price or the lowest selling price changes, and a fixed time interval. The results are qualitatively similar no matter linear prices or logarithmic prices are used. The average spread exhibits evident intraday patterns consisting of a big L-shape in morning transactions and a small L-shape in the afternoon. The distributions of the spread with different definitions decay as power laws. The tail exponents of spreads at transaction level are well within the interval (2,3) and that of average spreads are well in line with the inverse cubic law for different time intervals. Based on the detrended fluctuation analysis, we found the evidence of long memory in the bid-ask spread time series for all three definitions, even after the removal of the intraday pattern. Using the classical box-counting approach for multifractal analysis, we show that the time series of bid-ask spread do not possess multifractal nature.
Institute of Scientific and Technical Information of China (English)
CEN Wei; YANG ShiFeng; XUE Rong; XU RiWei; YU DingSheng
2007-01-01
Surface morphologies of supported polyethylene (PE) catalysts are investigated by an approach combining fractal with wavelet. The multiscale edge (detail) pictures of catalyst surface are extracted by wavelet transform modulus maxima (WTMM) method. And, the distribution of edge points on the edge image at every scale is studied with fractal and multifractal method. Furthermore, the singularity intensity distribution of edge points in the PE catalyst is analyzed by multifractal spectrum based on WTMM. The results reveal that the fractal dimension values and multifractal spectrums of edge images at small scales have a good relation with the activity and surface morphology of PE catalyst. Meanwhile the catalyst exhibiting the higher activity shows the wider singular strength span of multifractal spectrum based on WTMM, as well as the more edge points with the higher singular intensity. The research on catalyst surface morphology with hybrid fractal and wavelet method exerts the superiorities of wavelet and fractal theories and offers a thought for studying solid surfaces morphologies.
Nonlinear extensions of a fractal-multifractal approach for environmental modeling
Energy Technology Data Exchange (ETDEWEB)
Cortis, A.; Puente, C.E.; Sivakumar, B.
2008-10-15
We present the extension of a deterministic fractal geometric procedure aimed at representing the complexity of the spatio-temporal patterns encountered in environmental applications. The original procedure, which is based on transformations of multifractal distributions via fractal functions, is extended through the introduction of nonlinear perturbations to the underlying iterated linear maps. We demonstrate how the nonlinear perturbations generate yet a richer collection of patterns by means of various simulations that include evolutions of patterns based on changes in their parameters and in their statistical and multifractal properties. It is shown that the nonlinear extensions yield structures that closely resemble complex hydrologic temporal data sets, such as rainfall and runoff time series, and width-functions of river networks as a function of distance from the basin outlet. The implications of this nonlinear approach for environmental modeling and prediction are discussed.
MOF-derived multifractal porous carbon with ultrahigh lithium-ion storage performance
Ang Li; Yan Tong; Bin Cao; Huaihe Song; Zhihong Li; Xiaohong Chen; Jisheng Zhou; Gen Chen; Hongmei Luo
2017-01-01
Porous carbon is one of the most promising alternatives to traditional graphite materials in lithium-ion batteries. This is not only attributed to its advantages of good safety, stability and electrical conductivity, which are held by all the carbon-based electrodes, but also especially ascribed to its relatively high capacity and excellent cycle stability. Here we report the design and synthesis of a highly porous pure carbon material with multifractal structures. This material is prepared b...
ROMA (Rank-Ordered Multifractal Analyses of intermittency in space plasmas – a brief tutorial review
Directory of Open Access Journals (Sweden)
T. Chang
2010-10-01
Full Text Available Intermittent fluctuations are the consequence of the dynamic interactions of multiple coherent or pseudo-coherent structures of varied sizes in the stochastic media (Chang, 1999. We briefly review here a recently developed technique, the Rank-Ordered Multifractal Analysis (ROMA, which is both physically explicable and quantitatively accurate in deciphering the multifractal characteristics of such intermittent structures (Chang and Wu, 2008.
The utility of the method is demonstrated using results obtained from large-scale 2-D MHD simulations as well as in-situ observations of magnetic field fluctuations from the interplanetary and magnetospheric cusp regions, and the broadband electric field oscillations from the auroral zone.
Raiesdana, Somayeh
2017-01-01
It is thought that the critical brain dynamics in sleep is modulated during frequent periods of wakefulness. This paper utilizes the capacity of EEG based scaling analysis to quantify sleep fragmentation in patients with obstructive sleep apnea. The scale-free (fractal) behavior refers to a state where no characteristic scale dominates the dynamics of the underlying process which is evident as long range correlations in a time series. Here, Multiscaling (multifractal) spectrum is utilized to quantify the disturbed dynamic of an OSA brain with fragmented sleep. The whole night multichannel sleep EEG recordings of 18 subjects were employed to compute and quantify variable power-law long-range correlations and singularity spectra. Based on this characteristic, a new marker for sleep fragmentation named ``scaling based sleep fragmentation'' was introduced. This measure takes into account the sleep run length and stage transition quality within a fuzzy inference system to improve decisions made on sleep fragmentation. The proposed index was implemented, validated with sleepiness parameters and compared to some common indexes including sleep fragmentation index, arousal index, sleep diversity index, and sleep efficiency index. Correlations were almost significant suggesting that the sleep characterizing measure, based on singularity spectra range, could properly detect fragmentations and quantify their rate. This method can be an alternative for quantifying the sleep fragmentation in clinical practice after being approved experimentally. Control of sleep fragmentation and, subsequently, suppression of excessive daytime sleepiness will be a promising outlook of this kind of researches.
Interleaving distribution of multifractal strength of 16-channel EEG signals
Institute of Scientific and Technical Information of China (English)
WANG Wei; NING Xinbao; WANG Jun; ZHANG Sheng; CHEN Jie; LI Lejia
2003-01-01
Multifractal characteristics of 16-channel human electroencephalogram (EEG) signals under eye-closed rest are analyzed for the first time. The result shows that the EEGs from the different sites on the scalp have different multifractal characteristics and the multifractal strength value Δα exhibits a kind of interleaving and left-right opposite distribution on scalp. This distribution rule is consistent with the localization of function and the lateralization theory in physiology. SoΔα can become an effective parameter to describe the brain potential character. And such a Δα stable distribution rule on sites of the scalp means a classic cerebral cortex active state.
Multifractal Model of Asset Returns versus real stock market dynamics
Oswiecimka, P; Drozdz, S; Górski, A Z; Rak, R
2006-01-01
There is more and more empirical evidence that multifractality constitutes another and perhaps the most significant financial stylized fact. A realistic model of the financial dynamics should therefore incorporate this effect. The most promising in this respect is the Multifractal Model of Asset Returns (MMAR) introduced by Mandelbrot in which multifractality is carried by time deformation. In our study we focus on the Lux extension to MMAR and empirical data from Warsaw Stock Exchange. We show that this model is able to reproduce relevant aspects of the real stock market dynamics.
Empirical Study on the Multifractal Phenomenon of Chinese Stock Market
Institute of Scientific and Technical Information of China (English)
魏宇; 黄登仕
2003-01-01
Many recent researches with empirical data have demonstrated that financial data have multifractal properties. To study the properties of Chinese stock market, the Shanghai Stock Exchange Composite Index (SSECI) from January 1999 to July 2001 (a quotation taken every 5 min) is analyzed using multifractal theories, and it is found that the return volatility correlations are of power-laws with a non-unique scaling exponent. It is verified that Chinese stock market is quite similar to foreign financial markets in terms of multifractal properties.
Ouillon, G; Sornette, D
2006-01-01
The Multifractal Stress-Activated (MSA) model is a statistical model of triggered seismicity based on mechanical and thermodynamic principles. It predicts that, above a triggering magnitude cut-off $M_0$, the exponent $p$ of the Omori-Utsu law for the seismic decay of aftershocks is a linear increasing function $p(M) =a M+b$ of the mainshock magnitude $M$ [Ouillon and Sornette, 2005]. First empirical support for this prediction has been presented for the Southern California SCEC catalog. Here, we confirm this law on the worlwide Harvard CMT and the Japanese JMA catalogs, with similar ranges of variation from $p(M=3)=0.7 \\pm 0.1$ to $p(M=8)=1.1 \\pm 0.2$. However, the statistically significant differences of the slopes $a$, intercepts $b$ and cut-offs $M_0$ suggest different multifractal properties of the three catalogs, likely associated with different thermal and mechanical properties.
Surface characterization of proteins using multi-fractal property of heat-denatured aggregates
Lahiri, Tapobrata; Mishra, Hrishikesh; Sarkar, Subrata; Misra, Krishna
2008-01-01
Multi-fractal property of heat-denatured protein aggregates (HDPA) is characteristic of its individual form. The visual similarity between digitally generated microscopic images of HDPA with that of surface-image of its individual X-ray structures in protein databank (PDB) displayed using Visual Molecular Dynamics (VMD) viewer is the basis of the study. We deigned experiments to view the fractal nature of proteins at different aggregate scales. Intensity based multi-fractal dimensions (ILMFD) extracted from various planes of digital microscopic images of protein aggregates were used to characterize HDPA into different classes. Moreover, the ILMFD parameters extracted from aggregates show similar classification pattern to digital images of protein surface displayed by VMD viewer using PDB entry. We discuss the use of irregular patterns of heat-denatured aggregate proteins to understand various surface properties in native proteins. PMID:18795110
Nonlinear temperature effects on multifractal complexity of metabolic rate of mice
Directory of Open Access Journals (Sweden)
Fabio A. Labra
2016-10-01
Full Text Available 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 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.
Nonlinear temperature effects on multifractal complexity of metabolic rate of mice
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 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.
Leonardis, E; Chapman, S C; Daughton, W; Roytershteyn, V; Karimabadi, H
2013-05-17
Recent fully nonlinear, kinetic three-dimensional simulations of magnetic reconnection [W. Daughton et al., Nat. Phys. 7, 539 (2011)] evolve structures and exhibit dynamics on multiple scales, in a manner reminiscent of turbulence. These simulations of reconnection are among the first to be performed at sufficient spatiotemporal resolution to allow formal quantitative analysis of statistical scaling, which we present here. We find that the magnetic field fluctuations generated by reconnection are anisotropic, have nontrivial spatial correlation, and exhibit the hallmarks of finite range fluid turbulence: they have non-Gaussian distributions, exhibit extended self-similarity in their scaling, and are spatially multifractal. Furthermore, we find that the rate at which the fields do work on the particles, J · E, is also multifractal, so that magnetic energy is converted to plasma kinetic energy in a manner that is spatially intermittent. This suggests that dissipation in this sense in collisionless reconnection on kinetic scales has an analogue in fluidlike turbulent phenomenology, in that it proceeds via multifractal structures generated by an intermittent cascade.
Multifractal spectra of laser Doppler flowmetry signals in healthy and sleep apnea syndrome subjects
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.
Zhang, Qian; Lu, Wenxi; Chen, Sheming; Liang, Xiujuan
2016-08-01
Drought is a recurrent disaster that occurs in virtually all climatic zones of the world. However, drought characteristics vary substantially among different climatic regions. In this study, multifractal and wavelet analyses are used to characterize drought based on monthly precipitation. The rainfall data of 28 precipitation stations from 1958 to 2011 in Jilin province were collected to calculate the standardized precipitation index (SPI), and the negative monthly SPI time-series is used in a multiscaling approach to determine drought characteristics in Jilin province. Simple scaling and multiscaling analyses show significant variations in monthly droughts in the region. Morlet wavelet analysis also shows that significant cycles and multiple time-scales of drought exist in all stations. Cross wavelet analysis shows that drought occurrence in the region is mainly influenced by different climatic factor scales. However, different factors have different degrees of influence at different regions. The enduring influence of medium and long-term climatic patterns (such as El Niño events) may lead to the simple scaling behavior of drought for some regions.
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.
Dynamically multilayered visual system of the multifractal fly.
Baptista, M S; Grebogi, Celso; Köberle, Roland
2006-10-27
We dynamically analyze our experimental results on the motion sensitive spiking H1 neuron of the fly's visual system. We find that the fly uses an alphabet composed of a few letters to encode the information contained in the stimulus. The alphabet dynamics is multifractal both with and without stimulus, though the multifractality increases with the stimulus entropy. This is in sharp contrast to models generating independent spike intervals, whose dynamics is monofractal.
Direct Evidence for Inversion Formula in Multifractal Financial Volatility Measure
Institute of Scientific and Technical Information of China (English)
JIANG Zhi-Qiang; ZHOU Wei-Xing
2009-01-01
The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. We propose to verify the inversion formula using high-frequency 1982 to 1999 and its inverse measure of exit time. Both the direct and inverse measures exhibit nice multifractal nature, whose scaling ranges are not irrelevant. Empirical investigation shows that the inversion formula holds in financial markets.
Financial market volatility and contagion effect: A copula-multifractal volatility approach
Chen, Wang; Wei, Yu; Lang, Qiaoqi; Lin, Yu; Liu, Maojuan
2014-03-01
In this paper, we propose a new approach based on the multifractal volatility method (MFV) to study the contagion effect between the U.S. and Chinese stock markets. From recent studies, which reveal that multifractal characteristics exist in both developed and emerging financial markets, according to the econophysics literature we could draw conclusions as follows: Firstly, we estimate volatility using the multifractal volatility method, and find out that the MFV method performs best among other volatility models, such as GARCH-type and realized volatility models. Secondly, we analyze the tail dependence structure between the U.S. and Chinese stock market. The estimated static copula results for the entire period show that the SJC copula performs best, indicating asymmetric characteristics of the tail dependence structure. The estimated dynamic copula results show that the time-varying t copula achieves the best performance, which means the symmetry dynamic t copula is also a good choice, for it is easy to estimate and is able to depict both the upper and lower tail dependence structure. Finally, with the results of the previous two steps, we analyze the contagion effect between the U.S. and Chinese stock markets during the subprime mortgage crisis. The empirical results show that the subprime mortgage crisis started in the U.S. and that its stock market has had an obvious contagion effect on the Chinese stock market. Our empirical results should/might be useful for investors allocating their portfolios.
Hu, Shaobin; Wang, Enyuan; Li, Zhonghui; Shen, Rongxi; Liu, Jie
2014-09-01
Dynamic collapses of deeply mined coal rocks are severe threats to miners. To predict the collapses more accurately using electromagnetic radiation (EMR), we investigate the time-varying multifractal characteristics and formation mechanism of EMR induced by underground coal mining. A series of uniaxial compression and multi-stage loading experiments with coal samples of different mechanical properties were carried out. The EMR signals during their damage evolution were monitored in real-time; the inherent law of EMR time series was analyzed by fractal theory. The results show that the time-varying multifractal characteristics of EMR are determined by damage evolutions process, the dissipated energy caused by damage evolutions such as crack propagation, fractal sliding and shearing can be regard as the fingerprint of various EMR micro-mechanics. Based on the Irreversible thermodynamics and damage mechanics, we introduced the damage internal variable, constructed the dissipative potential function and established the coupled model of the EMR and the dissipative energy, which revealed the nature of dynamic nonlinear characteristics of EMR. Dynamic multifractal spectrum is the objective response of EMR signals, thus it can be used to evaluate the coal deformation and fracture process.
Energy Technology Data Exchange (ETDEWEB)
Zakariaee, R [Physics Department, University of British Columbia, Vancouver, BC (Canada); Brown, C J; Hamarneh, G [School of Computing Science, Simon Fraser University, Burnaby, BC (Canada); Parsons, C A; Spadinger, I [British Columbia Cancer Agency, Vancouver, BC (Canada)
2014-08-15
Dosimetric parameters based on dose-volume histograms (DVH) of contoured structures are routinely used to evaluate dose delivered to target structures and organs at risk. However, the DVH provides no information on the spatial distribution of the dose in situations of repeated fractions with changes in organ shape or size. The aim of this research was to develop methods to more accurately determine geometrically localized, cumulative dose to the bladder wall in intracavitary brachytherapy for cervical cancer. The CT scans and treatment plans of 20 cervical cancer patients were used. Each patient was treated with five high-dose-rate (HDR) brachytherapy fractions of 600cGy prescribed dose. The bladder inner and outer surfaces were delineated using MIM Maestro software (MIM Software Inc.) and were imported into MATLAB (MathWorks) as 3-dimensional point clouds constituting the “bladder wall”. A point-set registration toolbox for MATLAB, Coherent Point Drift (CPD), was used to non-rigidly transform the bladder-wall points from four of the fractions to the coordinate system of the remaining (reference) fraction, which was chosen to be the emptiest bladder for each patient. The doses were accumulated on the reference fraction and new cumulative dosimetric parameters were calculated. The LENT-SOMA toxicity scores of these patients were studied against the cumulative dose parameters. Based on this study, there was no significant correlation between the toxicity scores and the determined cumulative dose parameters.
Institute of Scientific and Technical Information of China (English)
李晓晖; 袁峰; 贾蔡; 张明明; 周涛发
2012-01-01
This paper took Cu element of Tongling Ore Cluster area as an example, studied on the effect of inverse distance weighted interpolation method and Kriging interpolation method on the multifractal filtering method. The research showed that, compared with raw inverse distance weighted interpolation method and Kriging interpolation method, whether based on inverse distance weighted interpolation method and Kriging interpolation method, the Cu element anomaly field which is decomposed by multifractal filtering (S-A) method could indicate the Cu ore field more accurately. The anomaly field based on the Kriging interpolation result a-chieved better results than that base on the inverse distance weighted interpolation result, the former was more significantly correlated with the distribution of Cu deposits, which is decomposed by multifractal filtering (S-A) method would have the application value for metallogenic prediction at deposit scale.%本文以铜陵矿集区土壤Cu元素含量数据为例,对比研究反距离加权插值法和克里格插值法对S-A多重分形滤波的影响.与单纯的反距离加权插值和克里格插值结果相比,无论是基于反距离加权插值还是克里格插值,多重分形滤波(S-A)方法分解得到的铜陵矿集区Cu元素异常场对已知Cu矿田的指示均更加准确.基于克里格插值结果的异常场相比于基于反距离加权插值结果的异常场,具有更好的异常识别效果,与铜陵矿集区已知Cu矿床分布的空间相关性更加显著,具有矿田尺度的成矿预测价值.
Multifractal properties of the random resistor network
Barthelemy; Buldyrev; Havlin; Stanley
2000-04-01
We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small i as P(i) approximately 1/i, where i is the current. As a consequence, the moments of i of order q
Study on Fault Diagnosis of Rolling Bearing Based on Time-Frequency Generalized Dimension
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Yu Yuan
2015-01-01
Full Text Available The condition monitoring technology and fault diagnosis technology of mechanical equipment played an important role in the modern engineering. Rolling bearing is the most common component of mechanical equipment which sustains and transfers the load. Therefore, fault diagnosis of rolling bearings has great significance. Fractal theory provides an effective method to describe the complexity and irregularity of the vibration signals of rolling bearings. In this paper a novel multifractal fault diagnosis approach based on time-frequency domain signals was proposed. The method and numerical algorithm of Multi-fractal analysis in time-frequency domain were provided. According to grid type J and order parameter q in algorithm, the value range of J and the cut-off condition of q were optimized based on the effect on the dimension calculation. Simulation experiments demonstrated that the effective signal identification could be complete by multifractal method in time-frequency domain, which is related to the factors such as signal energy and distribution. And the further fault diagnosis experiments of bearings showed that the multifractal method in time-frequency domain can complete the fault diagnosis, such as the fault judgment and fault types. And the fault detection can be done in the early stage of fault. Therefore, the multifractal method in time-frequency domain used in fault diagnosis of bearing is a practicable method.
Edenhofer, Peter; Ulamec, Stephan
2015-04-01
The paper is devoted to results of doctoral research work at University of Bochum as applied to the radar transmission experiment CONSERT of the ESA cometary mission Rosetta. This research aims at achieving the limits of optimum spatial (and temporal) resolution for radar remote sensing by implementation of covariance informations concerned with error-balanced control as well as coherence of wave propagation effects through random composite media involved (based on Joel Franklin's approach of extended stochastic inversion). As a consequence the well-known inherent numerical instabilities of remote sensing are significantly reduced in a robust way by increasing the weight of main diagonal elements of the resulting composite matrix to be inverted with respect to off-diagonal elements following synergy relations as to the principle of correlation receiver in wireless telecommunications. It is shown that the enhancement of resolution for remote sensing holds for an integral and differential equation approach of inversion as well. In addition to that the paper presents a discussion on how the efficiency of inversion for radar data gets achieved by an overall optimization of inversion due to a novel neuro-genetic approach. Such kind of approach is in synergy with the priority research program "Organic Computing" of DFG / German Research Organization. This Neuro-Genetic Optimization (NGO) turns out, firstly, to take into account more detailed physical informations supporting further improved resolution such as the process of accretion for cometary nucleus, wave propagation effects from rough surfaces, ground clutter, nonlinear focusing, etc. as well as, secondly, to accelerate the computing process of inversion in a really significantly enhanced and fast way, e.g., enabling online-control of autonomous processes such as detection of unknown objects, navigation, etc. The paper describes in some detail how this neuro-genetic approach of optimization is incorporated into the
Institute of Scientific and Technical Information of China (English)
罗平平; 王兰甫; 范波; 张芳
2012-01-01
In order to study the influence of aperture distribution on the infiltration in a single fracture, based on the fractal theory of multi-fractional Brownian motion（MBM）, four groups of fracture surfaces at different regularization dimensions are constructed, all of which more realistically reflect the asymptotic self-similarity of aperture distribution of natural fracture surface. From the numerical simulation of grouting in a single random aperture fracture, it is indicated that pressure contours show twists and turns spreading over time, which reflects the distinct non-uniform characteristics. The distribution of closed area has a tendency that is from dot-like scatter to focused plane with the regularization dimensions tending to reduce, and its spatial location has obvious influence on the pressure and grouting time. As the development of percolation, there appears a tendency that the node pressure is from monotonically rapid increase to stepwise stability, and the more the node approaching the percolation border, the shorter the grouting time used in the case of reaching the steady pressure. Moreover, there is a power relationship between the node pressure and the grouting time. In view of this rule, empirical equations with different parameters are also obtained by fitting curves.%为了研究单裂隙面隙宽分布对浆液渗透的影响,基于多重分数布朗运动（MBM）分形理论构建出4种不同规则维数下的随机隙宽单裂隙几何模型,从而较真实的反应了天然裂隙面隙宽分布的局部渐进自相似性。通过注浆数值模拟研究发现,压力等值线随时间延续呈现曲折扩散形式,反映了其非均匀渗透特征。裂隙面闭合区分布形态随规则维数降低由点状散布趋向面状集中,其空间位置对浆液后期渗透压力和全程注浆时间影响很大;并且随着浆液入渗发展,节点压力由前期的较快单调增长到后期逐步趋于稳定,越靠近入渗边界的节点
Directory of Open Access Journals (Sweden)
W. M. Macek
2011-05-01
Full Text Available 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.
The effects of common risk factors on stock returns: A detrended cross-correlation analysis
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.
The cross-correlation analysis of multi property of stock markets based on MM-DFA
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.
Beyond multi-fractals: surrogate time series and fields
Venema, V.; Simmer, C.
2007-12-01
Most natural complex are characterised by variability on a large range of temporal and spatial scales. The two main methodologies to generate such structures are Fourier/FARIMA based algorithms and multifractal methods. The former is restricted to Gaussian data, whereas the latter requires the structure to be self-similar. This work will present so-called surrogate data as an alternative that works with any (empirical) distribution and power spectrum. The best-known surrogate algorithm is the iterative amplitude adjusted Fourier transform (IAAFT) algorithm. We have studied six different geophysical time series (two clouds, runoff of a small and a large river, temperature and rain) and their surrogates. The power spectra and consequently the 2nd order structure functions were replicated accurately. Even the fourth order structure function was more accurately reproduced by the surrogates as would be possible by a fractal method, because the measured structure deviated too strong from fractal scaling. Only in case of the daily rain sums a fractal method could have been more accurate. Just as Fourier and multifractal methods, the current surrogates are not able to model the asymmetric increment distributions observed for runoff, i.e., they cannot reproduce nonlinear dynamical processes that are asymmetric in time. Furthermore, we have found differences for the structure functions on small scales. Surrogate methods are especially valuable for empirical studies, because the time series and fields that are generated are able to mimic measured variables accurately. Our main application is radiative transfer through structured clouds. Like many geophysical fields, clouds can only be sampled sparsely, e.g. with in-situ airborne instruments. However, for radiative transfer calculations we need full 3-dimensional cloud fields. A first study relating the measured properties of the cloud droplets and the radiative properties of the cloud field by generating surrogate cloud
Qian, Xi-Yuan; Gu, Gao-Feng; Zhou, Wei-Xing
2011-11-01
Detrended fluctuation analysis (DFA) is a simple but very efficient method for investigating the power-law long-term correlations of non-stationary time series, in which a detrending step is necessary to obtain the local fluctuations at different timescales. We propose to determine the local trends through empirical mode decomposition (EMD) and perform the detrending operation by removing the EMD-based local trends, which gives an EMD-based DFA method. Similarly, we also propose a modified multifractal DFA algorithm, called an EMD-based MFDFA. The performance of the EMD-based DFA and MFDFA methods is assessed with extensive numerical experiments based on fractional Brownian motion and multiplicative cascading process. We find that the EMD-based DFA method performs better than the classic DFA method in the determination of the Hurst index when the time series is strongly anticorrelated and the EMD-based MFDFA method outperforms the traditional MFDFA method when the moment order q of the detrended fluctuations is positive. We apply the EMD-based MFDFA to the 1 min data of Shanghai Stock Exchange Composite index, and the presence of multifractality is confirmed. We also analyze the daily Austrian electricity prices and confirm its anti-persistence.
Multifractal spatial patterns and diversity in an ecological succession.
Saravia, Leonardo Ariel; Giorgi, Adonis; Momo, Fernando
2012-01-01
We analyzed the relationship between biodiversity and spatial biomass heterogeneity along an ecological succession developed in the laboratory. Periphyton (attached microalgae) biomass spatial patterns at several successional stages were obtained using digital image analysis and at the same time we estimated the species composition and abundance. We show that the spatial pattern was self-similar and as the community developed in an homogeneous environment the pattern is self-organized. To characterize it we estimated the multifractal spectrum of generalized dimensions D(q). Using D(q) we analyze the existence of cycles of heterogeneity during succession and the use of the information dimension D(1) as an index of successional stage. We did not find cycles but the values of D(1) showed an increasing trend as the succession developed and the biomass was higher. D(1) was also negatively correlated with Shannon's diversity. Several studies have found this relationship in different ecosystems but here we prove that the community self-organizes and generates its own spatial heterogeneity influencing diversity. If this is confirmed with more experimental and theoretical evidence D(1) could be used as an index, easily calculated from remote sensing data, to detect high or low diversity areas.
Multifractal spatial patterns and diversity in an ecological succession.
Directory of Open Access Journals (Sweden)
Leonardo Ariel Saravia
Full Text Available We analyzed the relationship between biodiversity and spatial biomass heterogeneity along an ecological succession developed in the laboratory. Periphyton (attached microalgae biomass spatial patterns at several successional stages were obtained using digital image analysis and at the same time we estimated the species composition and abundance. We show that the spatial pattern was self-similar and as the community developed in an homogeneous environment the pattern is self-organized. To characterize it we estimated the multifractal spectrum of generalized dimensions D(q. Using D(q we analyze the existence of cycles of heterogeneity during succession and the use of the information dimension D(1 as an index of successional stage. We did not find cycles but the values of D(1 showed an increasing trend as the succession developed and the biomass was higher. D(1 was also negatively correlated with Shannon's diversity. Several studies have found this relationship in different ecosystems but here we prove that the community self-organizes and generates its own spatial heterogeneity influencing diversity. If this is confirmed with more experimental and theoretical evidence D(1 could be used as an index, easily calculated from remote sensing data, to detect high or low diversity areas.
Scale-free avalanches in the multifractal random walk
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.
The high order dispersion analysis based on first-passage-time probability in financial markets
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.
Coupled uncertainty provided by a multifractal random walker
Energy Technology Data Exchange (ETDEWEB)
Koohi Lai, Z. [Department of Physics, Firoozkooh Branch, Islamic Azad University, Firoozkooh (Iran, Islamic Republic of); Vasheghani Farahani, S. [Department of Physics, Tafresh University, P.O. Box 39518-79611, Tafresh (Iran, Islamic Republic of); Movahed, S.M.S. [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of); The Abdus Salam International Centre for Theoretical Physics, Strada Costiera, 11, Trieste 34151 (Italy); Jafari, G.R., E-mail: g_jafari@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of)
2015-10-09
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. - Highlights: • The coupled criticality between two systems is modeled by the bivariate multifractal random walk. • This coupled criticality is generally directed. • This coupled criticality is inversely proportional to the criticality of either of the systems. • The coupled criticality can emerge when at least one of the systems posses a Gaussian distribution.
Multi-Fraction Bayesian Sediment Transport Model
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Mark L. Schmelter
2015-09-01
Full Text Available A Bayesian approach to sediment transport modeling can provide a strong basis for evaluating and propagating model uncertainty, which can be useful in transport applications. Previous work in developing and applying Bayesian sediment transport models used a single grain size fraction or characterized the transport of mixed-size sediment with a single characteristic grain size. Although this approach is common in sediment transport modeling, it precludes the possibility of capturing processes that cause mixed-size sediments to sort and, thereby, alter the grain size available for transport and the transport rates themselves. This paper extends development of a Bayesian transport model from one to k fractional dimensions. The model uses an existing transport function as its deterministic core and is applied to the dataset used to originally develop the function. The Bayesian multi-fraction model is able to infer the posterior distributions for essential model parameters and replicates predictive distributions of both bulk and fractional transport. Further, the inferred posterior distributions are used to evaluate parametric and other sources of variability in relations representing mixed-size interactions in the original model. Successful OPEN ACCESS J. Mar. Sci. Eng. 2015, 3 1067 development of the model demonstrates that Bayesian methods can be used to provide a robust and rigorous basis for quantifying uncertainty in mixed-size sediment transport. Such a method has heretofore been unavailable and allows for the propagation of uncertainty in sediment transport applications.
Perez, Dario G; Morille, Yohann; Zielinska, Sonia; Ortyl, Ewelina
2014-01-01
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 C2 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.
Multifractal properties of solar wind turbulence: theory and observations.
Milovanov, A. V.; Avanov, L. A.; Zastenker, G. N.; Zelenyj, L. M.
1996-10-01
A fractal model of the solar wind is presented. This model treats fluctuations of the solar wind velocity from the viewpoint of nonlinear processes originating in the convective region and photosphere of the Sun. The multifractal structure of proton velocity fluctuations in a region of heliocentric distances from 0.2 to 0.8 AU is a result of these processes. Continuous measurements of solar wind velocity aboard the ISEE-3 spacecraft during one month were used to compare the theoretical and experimental results. It is shown that fluctuations of proton velocity have a multifractal structure in a frequency range of 10-5 - 10-3Hz.
Coupled uncertainty provided by a multifractal random walker
Lai, Z Koohi; Movahed, S M S; Jafari, G R
2015-01-01
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.
The Application of Multifractal in EMG Pattern Recognition%多重分形分析在肌电信号模式识别中的应用
Institute of Scientific and Technical Information of China (English)
张启忠; 席旭刚; 罗志增
2013-01-01
为提高肢体运动模式识别率,论文提出了一种经验模态分解与多重分形分析相结合的模式识别方法.先用经验模态分解得到代表肌电信号细节的多层内在模态函数,然后在内在模态函数上进行多重分形分析,提取其广义维数谱,作为肌电信号多模式识别的特征向量.最后以改进的K最近邻分类方法-KNN模型增量学习算法,实现对动作模式的识别.在对张开、合拢及腕内旋、腕外旋4个动作的识别实验中,正确识别率达到了93.0％.结果表明,方法具备一定的实用性,可用于遥操作机器人系统中操作者手腕运动模式识别.%In order to improve the pattern recognition rate of physical movement, a new pattern recognition method has been proposed through the combination of empirical mode decomposition ( EMD) and multifractal analysis. Firstly,multilayer intrinsic mode functions(IMF) , which represent the details of surface electromyography(sEMG) , are obtained using EMD. Then multifractal spectrum, which can be used as eigenvector in pattern recognition of sEMG.is extracted from IMF by multifractal analysis. Finally,the improved K nearest neighbor method-KNN model based incremental learning method is used to recognize various movements of hand. The experiment, designed to classify four hand gestures including hand open, hand grasp, wrist pronation and wrist supination, shows that by using this method,the recognition rate has reached 93. 0% ,which demonstrates the practicality of this approach and its possible application in the pattern recognition of manipulator's wrist movement.
Turiel, A.; Perez-Vicente, C.
The application of the multifractal formalism to the study of some time series with scale invariant evolution has given rise to a rich framework of models and processing tools for the analysis of these signals. The formalism has been successfully exploited in different ways and with different goals: to obtain the effective variables governing the evolution of the series, to predict its future evolution, to estimate in which regime the series are, etc. In this paper, we discuss on the capabilities of a new, powerful processing tool, namely the computation of dynamical sources. With the aid of the source field, we will separate the fast, chaotic dynamics defined by the multifractal structure from a new, so-far unknown slow dynamics which concerns long cycles in the series. We discuss the results on the perspective of detection of sharp dynamic changes and forecasting.
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.
Multifraction separation in countercurrent chromatography (MCSGP).
Krättli, Martin; Müller-Späth, Thomas; Morbidelli, Massimo
2013-09-01
The multicolumn countercurrent solvent gradient purification (MCSGP) process is a continuous countercurrent multicolumn chromatography process capable of performing three fraction separations while applying a linear gradient of some modifier. This process can then be used either for the purification of a single species from a multicomponent mixture or to separate a three component mixture in one single operation. In this work, this process is extended to the separation of multifractions, in principle with no limitation. To achieve this goal the MCSGP standard process is extended by introducing one extra separation section per extra fraction to be isolated. Such an extra separation section is realized in this work through a single additional column, so that a n fraction MCSGP process can be realized using a minimum of n columns. Two separation processes were considered to experimentally demonstrate the possibility of realizing a four-fraction MCSGP unit able to purify two intermediate products in a given multicomponent mixture. The first one was a model mixture containing four different proteins. The two proteins eluting in the center of the chromatogram were purified with yields equal to 95% for the early eluting and 92% for the later eluting one. The corresponding purities were 94% and 97%, respectively. Such performance was well superior to that of the batch operation with the same modifier gradient which for the same purity values could not achieve yields larger than 67% and 81%, respectively. Similar performance improvements were found for the second separation where two out of seven charge variants which constitute the mAb Cetuximab currently available on the market have been purified in one single operation using a four-fraction MCSGP unit. In this case, yields of 81% and 65% were obtained with purities of 90% and 89%, respectively. These data compare well with the corresponding data from batch chromatography where with the same gradient and for the same
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.
Selection of Multifractal Scaling Breaks and Separation of Geochemical and Geophysical Anomaly
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Spatially superimposed multiple processes such as multiplicative cascade processes often generate multifractal measures possessing so-called self-similarity or self-affinity that can be described by power-law type of functions within certain scale ranges. The multifractalities can be estimated by applying multifractal modeling to the measures reflecting the characteristics of the physical processes such as the element concentration values analyzed in rock and soil samples and caused by the underlying mineralization processes and the other geological processes. The local and regional geological processes may result in geochemical patterns with distinct multifractalities as well as variable scaling ranges. Separation of these multifractal measures on the basis of both the distinct multifractalities and the scaling ranges will be significant for both theoretical studies of multifractal modeling and its applications. Multifractal scaling breaks have been observed from various multifractal patterns. This paper introduces a technique for separating multifractal measures on the basis of scaling breaks. It has been demonstrated that the method is effective for decomposing geochemical and geophysical anomalies required for mineral exploration. A dataset containing the element concentration values of potassium and phosphorus in soil samples was employed for demonstrating the application of the method for studying the fertilizer and yield optimization in agriculture.
A NOTE ON MULTIFRACTAL PACKING DIMENSION OF MEASURES
Institute of Scientific and Technical Information of China (English)
Jinjun Li
2009-01-01
The relations between the multifractal packing dimension of Borel probability measures and the asymptotic behavior of the function φ*(x)=lim sup/r→0 logv(V(x, r))-qlogμ(B(x, r))/logr are discussed and some applications are given.
Multifractal Decomposition of Statistically Self-Similar Sets
Institute of Scientific and Technical Information of China (English)
Jing Hu YU; Di He HU
2001-01-01
Let K be a statistically self-similar set defined by Graf. In this paper, we construct arandom measure p which is supported by K and study the multifractal decomposition for K with p.Under such a decomposition, we obtain the expression of the spectrum function f(α).
Directory of Open Access Journals (Sweden)
José L. Valencia
2015-11-01
Full Text Available Rainfall, one of the most important climate variables, is commonly studied due to its great heterogeneity, which occasionally causes negative economic, social, and environmental consequences. Modeling the spatial distributions of rainfall patterns over watersheds has become a major challenge for water resources management. Multifractal analysis can be used to reproduce the scale invariance and intermittency of rainfall processes. To identify which factors are the most influential on the variability of multifractal parameters and, consequently, on the spatial distribution of rainfall patterns for different time scales in this study, universal multifractal (UM analysis—C1, α, and γs UM parameters—was combined with non-parametric statistical techniques that allow spatial-temporal comparisons of distributions by gradients. The proposed combined approach was applied to a daily rainfall dataset of 132 time-series from 1931 to 2009, homogeneously spatially-distributed across a 25 km × 25 km grid covering the Ebro River Basin. A homogeneous increase in C1 over the watershed and a decrease in α mainly in the western regions, were detected, suggesting an increase in the frequency of dry periods at different scales and an increase in the occurrence of rainfall process variability over the last decades.
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.
Muniandy, S V; Lim, S C
2001-04-01
Fractional Brownian motion (FBM) is widely used in the modeling of phenomena with power spectral density of power-law type. However, FBM has its limitation since it can only describe phenomena with monofractal structure or a uniform degree of irregularity characterized by the constant Holder exponent. For more realistic modeling, it is necessary to take into consideration the local variation of irregularity, with the Holder exponent allowed to vary with time (or space). One way to achieve such a generalization is to extend the standard FBM to multifractional Brownian motion (MBM) indexed by a Holder exponent that is a function of time. This paper proposes an alternative generalization to MBM based on the FBM defined by the Riemann-Liouville type of fractional integral. The local properties of the Riemann-Liouville MBM (RLMBM) are studied and they are found to be similar to that of the standard MBM. A numerical scheme to simulate the locally self-similar sample paths of the RLMBM for various types of time-varying Holder exponents is given. The local scaling exponents are estimated based on the local growth of the variance and the wavelet scalogram methods. Finally, an example of the possible applications of RLMBM in the modeling of multifractal time series is illustrated.
Institute of Scientific and Technical Information of China (English)
陈桂娟; 王金东; 刘耀芳; 赵海洋
2013-01-01
This paper presents an intelligent fault diagnosis fault technique based on multifractal and singularity value decomposition for reciprocating compressor,according to the complex structure and scattered fault location of reciprocating compressor and difficulty to diagnose multiple faults by single measurement point.The generalized fractal dimension can characterize local scale behavior of signal more appropriately,so an initial feature matrix was built by calculating the generalized fractal dimension of vibration signal for multiple measurement points.The matrix was compressed by singular value decomposition method,and the eigenvalue of matrix was taken as feature vector.Taken reciprocating compressor transmission mechanism as research object,feature vectors of common faults were extracted.Support vector machine was established as pattern classifier to identify faults.Compared with results of single measurement point multifractal method and multiple measurement points fractal method,the validity of this method is proved.%针对往复压缩机结构复杂,故障位置不集中,单一测点信号难以准确诊断多类故障等特点,提出一套基于多重分形与奇异值分解的往复压缩机智能故障诊断技术.广义分形维数能够更精细的刻画信号的局部尺度行为,以此计算多测点振动信号广义分形维数构成初始特征矩阵,应用奇异值分解法进行数据压缩,提取矩阵特征值作为特征向量.以往复压缩机传动机构为对象,提取常见故障特征向量,建立支持向量模式分类器诊断识别故障,与单一测点多重分形法和多测点单重分形法进行对比分析,验证了该方法的有效性.
Gould, Daniel J; Reece, Gregory P
2012-10-01
One important contributor to tissue graft viability is angiogenic maturation of the graft tissue bed. This study uses scale-invariant microvascular morphological quantification to track vessel maturation and remodeling in a split-thickness skin-grafting model over 21 days, comparing the results to classical techniques. Images from a previous study of split-thickness skin grafting in rats were analyzed. Microvascular morphology (fractal and multifractal dimensions, lacunarity, and vessel density) within fibrin interfaces of samples over time was quantified using classical semi-automated methods and automated multifractal and lacunarity analyses. Microvessel morphology increased in density and complexity, from three to seven days after engraftment and then regressed by 21 days. Vessel density increased from 0.07 on day 3 to 0.20 on day 7 and then decreased to 0.06 on day 21. A similar trend was seen for the fractal dimension that increased from 1.56 at three days to 1.77 at seven days then decreased to 1.57 by 21 days. Vessel diameters did not change whereas complexity and density did, signaling remodeling. This new automated analysis identified design parameters for tissue engraftment and could be used in other models of graft vessel biology to track proliferation and pruning of complex vessel beds. © 2012 John Wiley & Sons Ltd.
Multifractal analyis of soil invertebrates along a transect under different land uses
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.
Pagliaro, Antonio; D'Alí Staiti, G.; D'Anna, F.
2011-03-01
We present a new method for the identification of extensive air showers initiated by different primaries. The method uses the multiscale concept and is based on the analysis of multifractal behaviour and lacunarity of secondary particle distributions together with a properly designed and trained artificial neural network. In the present work the method is discussed and applied to a set of fully simulated vertical showers, in the experimental framework of ARGO-YBJ, to obtain hadron to gamma primary separation. We show that the presented approach gives very good results, leading, in the 1-10 TeV energy range, to a clear improvement of the discrimination power with respect to the existing figures for extended shower detectors.
Energy Technology Data Exchange (ETDEWEB)
Pagliaro, Antonio, E-mail: pagliaro@ifc.inaf.it [Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo - Istituto Nazionale di Astrofisica, Via Ugo La Malfa 153, 90146 Palermo (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Viale A. Doria 6, 95125 Catania (Italy); D' Ali Staiti, G. [Universita degli Studi di Palermo, Dipartimento di Fisica e Tecnologie Relative, Viale delle Scienze, Edificio 18, 90128 Palermo (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Viale A. Doria 6, 95125 Catania (Italy); D' Anna, F. [Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo - Istituto Nazionale di Astrofisica, Via Ugo La Malfa 153, 90146 Palermo (Italy)
2011-03-15
We present a new method for the identification of extensive air showers initiated by different primaries. The method uses the multiscale concept and is based on the analysis of multifractal behaviour and lacunarity of secondary particle distributions together with a properly designed and trained artificial neural network. In the present work the method is discussed and applied to a set of fully simulated vertical showers, in the experimental framework of ARGO-YBJ, to obtain hadron to gamma primary separation. We show that the presented approach gives very good results, leading, in the 1-10 TeV energy range, to a clear improvement of the discrimination power with respect to the existing figures for extended shower detectors.
Site effect classification based on microtremor data analysis using concentration–area fractal model
Directory of Open Access Journals (Sweden)
A. Adib
2014-07-01
Full Text Available 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.
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
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.
Multifractal heart rate dynamics in human cardiovascular model
Kotani, Kiyoshi; Takamasu, Kiyoshi; Safonov, Leonid; Yamamoto, Yoshiharu
2003-05-01
Human cardiovascular and/or cardio-respiratory systems are shown to exhibit both multifractal and synchronous dynamics, and we recently developed a nonlinear, physiologically plausible model for the synchronization between heartbeat and respiration (Kotani, et al. Phys. Rev. E 65: 051923, 2002). By using the same model, we now show the multifractality in the heart rate dynamics. We find that beat-to-beat monofractal noise (fractional Brownian motion) added to the brain stem cardiovascular areas results in significantly broader singularity spectra for heart rate through interactions between sympathetic and parasympathetic nervous systems. We conclude that the model proposed here would be useful in studying the complex cardiovascular and/or cardio- respiratory dynamics in humans.
Multifractal modeling of the production of concentrated sugar syrup crystal
Sheng, Bi; Jianbo, Gao
2016-07-01
High quality, concentrated sugar syrup crystal is produced in a critical step in cane sugar production: the clarification process. It is characterized by two variables: the color of the produced sugar and its clarity degree. We show that the temporal variations of these variables follow power-law distributions and can be well modeled by multiplicative cascade multifractal processes. These interesting properties suggest that the degradation in color and clarity degree has a system-wide cause. In particular, the cascade multifractal model suggests that the degradation in color and clarity degree can be equivalently accounted for by the initial “impurities” in the sugarcane. Hence, more effective cleaning of the sugarcane before the clarification stage may lead to substantial improvement in the effect of clarification.
On the spin wave multifractal spectra in magnetic multilayers
Bezerra, C. G.; Albuquerque, E. L.; , E. Nogueira, Jr.
The multifractal properties of spin wave bandwidths in quasiperiodic magnetic multilayers are studied. The profiles of the bandwidths are analyzed and the f( α) function is calculated for different values of the dimensionless in-plane wave vector kxa and for four different sequences: Fibonacci, double-period, Thue-Morse and Rudin-Shapiro. We note that the f( α) spectra is qualitatively the same for different values of kxa.
Multifractal Measure of Post Distribution in Post System
Institute of Scientific and Technical Information of China (English)
CHEN Li; HUANG Deng-shi
2009-01-01
In order to investigate the true post distribution in the whole society, microelasticity (MIE) and macroelasticity (MAE) were defined by regarding all posts as a system. On this basis, the method for measuring post distribution was proposed. Using the Legendre dual transformation between MIE and MAE to highlight the probabilities of different levels, the post distribution were analyzed hierarchically. The two-scale Cantor model verified that the multifractal measure is applicable to the post distribution evolution process.
From fractional Brownian motion to multifractional and multistable motion
Falconer, Kenneth
2015-03-01
Fractional Brownian motion, introduced by Benoit Mandelbrot and John Van Ness in 1968, has had a major impact on stochastic processes and their applications. We survey a few of the many developments that have stemmed from their ideas. In particular we discuss the local structure of fractional and multifractional Brownian, stable and multistable processes, emphasising the `diagonal' construction of such processes. In all this, the ubiquity and centrality of fractional Brownian motion is striking.
Intermittency and multifractional Brownian character of geomagnetic time series
Directory of Open Access Journals (Sweden)
G. Consolini
2013-07-01
Full Text Available The Earth's magnetosphere exhibits a complex behavior in response to the solar wind conditions. This behavior, which is described in terms of mutifractional Brownian motions, could be the consequence of the occurrence of dynamical phase transitions. On the other hand, it has been shown that the dynamics of the geomagnetic signals is also characterized by intermittency at the smallest temporal scales. Here, we focus on the existence of a possible relationship in the geomagnetic time series between the multifractional Brownian motion character and the occurrence of intermittency. In detail, we investigate the multifractional nature of two long time series of the horizontal intensity of the Earth's magnetic field as measured at L'Aquila Geomagnetic Observatory during two years (2001 and 2008, which correspond to different conditions of solar activity. We propose a possible double origin of the intermittent character of the small-scale magnetic field fluctuations, which is related to both the multifractional nature of the geomagnetic field and the intermittent character of the disturbance level. Our results suggest a more complex nature of the geomagnetic response to solar wind changes than previously thought.
Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors
Energy Technology Data Exchange (ETDEWEB)
Stephen, Damian G., E-mail: foovian@gmail.co [Wyss Institute for Biologically Inspired Engineering, Harvard University, 3 Blackfan Circle, Floor 5, Boston, MA 02115 (United States); Dixon, James A. [Department of Psychology, University of Connecticut, 406 Babbidge Rd., Unit 1020, Storrs, CT 06269-1020 (United States); Haskins Laboratories, 300 George St., New Haven, CT 06511 (United States)
2011-01-15
Research highlights: We investigated anticipatory behaviors in response to chaotic metronomes. We assessed multifractal structure in tap intervals and onset intervals. Strength of multifractality in tap intervals appears to match that in onset intervals. - Abstract: Previous research on anticipatory behaviors has found that the fractal scaling of human behavior may attune to the fractal scaling of an unpredictable signal [Stephen DG, Stepp N, Dixon JA, Turvey MT. Strong anticipation: Sensitivity to long-range correlations in synchronization behavior. Physica A 2008;387:5271-8]. We propose to explain this attunement as a case of multifractal cascade dynamics [Schertzer D, Lovejoy S. Generalised scale invariance in turbulent phenomena. Physico-Chem Hydrodyn J 1985;6:623-5] in which perceptual-motor fluctuations are coordinated across multiple time scales. This account will serve to sharpen the contrast between strong and weak anticipation: whereas the former entails a sensitivity to the intermittent temporal structure of an unpredictable signal, the latter simply predicts sensitivity to an aggregate description of an unpredictable signal irrespective of actual sequence. We pursue this distinction through a reanalysis of Stephen et al.'s data by examining the relationship between the widths of singularity spectra for intertap interval time series and for each corresponding interonset interval time series. We find that the attunement of fractal scaling reported by Stephen et al. was not the trivial result of sensitivity to temporal structure in aggregate but reflected a subtle sensitivity to the coordination across multiple time scales of fluctuation in the unpredictable signal.
Symmetry relations for multifractal spectra at random critical points
Monthus, Cécile; Berche, Bertrand; Chatelain, Christophe
2009-12-01
Random critical points are generically characterized by multifractal properties. In the field of Anderson localization, Mirlin et al (2006 Phys. Rev. Lett. 97 046803) have proposed that the singularity spectrum f(α) of eigenfunctions satisfies the exact symmetry f(2d-α) = f(α)+d-α. In the present paper, we analyze the physical origin of this symmetry in relation to the Gallavotti-Cohen fluctuation relations of large deviation functions that are well known in the field of non-equilibrium dynamics: the multifractal spectrum of the disordered model corresponds to the large deviation function of the rescaling exponent γ = (α-d) along a renormalization trajectory in the effective time t = lnL. We conclude that the symmetry discovered for the specific example of Anderson transitions should actually be satisfied at many other random critical points after an appropriate translation. For many-body random phase transitions, where the critical properties are usually analyzed in terms of the multifractal spectrum H(a) and of the moment exponents X(N) of the two-point correlation function (Ludwig 1990 Nucl. Phys. B 330 639), the symmetry becomes H(2X(1)-a) = H(a)+a-X(1), or equivalently Δ(N) = Δ(1-N) for the anomalous parts \\Delta (N) \\equiv X(N)-NX(1) . We present numerical tests favoring this symmetry for the 2D random Q-state Potts model with varying Q.
Wavelet Based Fractal Analysis of Airborne Pollen
Degaudenzi, M E
1999-01-01
The most abundant biological particles in the atmosphere are pollen grains and spores. Self protection of pollen allergy is possible through the information of future pollen contents in the air. In spite of the importance of airborne pol len concentration forecasting, it has not been possible to predict the pollen concentrations with great accuracy, and about 25% of the daily pollen forecasts have resulted in failures. Previous analysis of the dynamic characteristics of atmospheric pollen time series indicate that the system can be described by a low dimensional chaotic map. We apply the wavelet transform to study the multifractal characteristics of an a irborne pollen time series. We find the persistence behaviour associated to low pollen concentration values and to the most rare events of highest pollen co ncentration values. The information and the correlation dimensions correspond to a chaotic system showing loss of information with time evolution.
Moskvin, P. P.; Krizhanovskii, V. B.; Rashkovetskii, L. V.; Vuichik, N. V.
2016-05-01
Multifractal (MF) analysis is used to describe the volume of space forms on the surfaces of structures in the solid solution of a Zn x Cd1- x Te-Si(111) substrate. AFM images of film surfaces have been are used for MF analysis. The parameters of MF spectra are determined for the distribution of volume of surface nanoforms. Based on the formal approach and data on the parameters of the fractal state for the volume and surfaces of nanoforms, an equation is proposed that considers the contribution from the fractal structure of the surface to its surface energy. The behavior of the system's surface energy, depending on fractal parameters that describe states of the volume and surfaces of nanoforms is discussed.
MOF-derived multifractal porous carbon with ultrahigh lithium-ion storage performance
Li, Ang; Tong, Yan; Cao, Bin; Song, Huaihe; Li, Zhihong; Chen, Xiaohong; Zhou, Jisheng; Chen, Gen; Luo, Hongmei
2017-01-01
Porous carbon is one of the most promising alternatives to traditional graphite materials in lithium-ion batteries. This is not only attributed to its advantages of good safety, stability and electrical conductivity, which are held by all the carbon-based electrodes, but also especially ascribed to its relatively high capacity and excellent cycle stability. Here we report the design and synthesis of a highly porous pure carbon material with multifractal structures. This material is prepared by the vacuum carbonization of a zinc-based metal-organic framework, which demonstrates an ultrahigh lithium storage capacity of 2458 mAh g‑1 and a favorable high-rate performance. The associations between the structural features and the lithium storage mechanism are also revealed by small-angle X-ray scattering (SAXS), especially the closed pore effects on lithium-ion storage.
Livi, Lorenzo
2015-01-01
In this paper, we analyze 48 signals of rest tremor velocity related to 12 distinct subjects affected by Parkinson's disease. The subjects belong to two different groups, formed by four and eight subjects with, respectively, high- and low-amplitude rest tremors. Each subject is tested in four settings, given by combining the use of deep brain stimulation and L-DOPA medication. We develop two main feature-based representations of such signals, which are obtained by considering (i) the long-term correlations and multifractal properties, and (ii) the power spectra. The feature-based representations are initially utilized for the purpose of characterizing the subjects under different settings. In agreement with previous studies, we show that deep brain stimulation does not significantly characterize neither of the two groups, regardless of the adopted representation. On the other hand, the medication effect yields statistically significant differences in both high- and low-amplitude tremor groups. We successively...
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.
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.
Moskvin, Pavel; Kryzhanivskyy, Vyacheslav; Lytvyn, Petro; Rashkovetskyi, Liubomyr
2016-09-01
Multifractal (MF) analysis is used to describe volumes of spatial forms that are formed on the surface of thin layers of ZnxCd1-xTe solid solution grown on the Si (111) substrate. MF analysis is performed on the basis of AFM images of the solid solution surface. The parameters of the MF spectrums for the distribution of volumes of the spatial forms, which formed the surface relief, were found. On the basis of a formal approach and data on the multifractal parameters for the volume and the area of the surface spatial forms the mathematic expression which takes into account the contribution of the fractal surface structure in its surface energy were proposed. The behavior of the surface energy of the system depending on the fractal parameters that describe the volume and the area of the spatial forms on the fractal surface were discussed.
Redondo Apraiz, José Manuel; Platonov, A.; Grau Barceló, Joan
2009-01-01
The interaction between multiple scales in nature and mainly in turbulent flows produces fractals or multifractal structures. We use multi-fractal analysis to investigate the scales and influence of stratification in different types of surface eddies in the ocean, and specially, near the coastline. We will also show and discuss the structure and residence time in oil spills and slicks in the ocean surface. This method, of multifractal analysis on the intensity SAR signals, as an example will ...
A comparison of multifractal behavior in galaxy samples from SDSS
García-Farieta, J. E.; Casas-Miranda, R. A.
2017-07-01
We studied the spatial distribution of galaxies with samples from the Sloan Digital Sky Survey (SDSS) including observational holes in the masks. From a multifractal formalism and using the sliding window technique for each sample, we have determined the fractal dimension and the lacunarity spectrum. Aditionally, the scale of homogeneity was determined for each struture parameter. Our results show that the galaxy clustering exhibits a behavior that depends on the radial distance, revealing that the hierarchical distribution is not a fractal at large-scales, with a transition to homogeneity on large scales below 130 Mpc/h.
Multifractional Fourier Transform Method and Its Applications to Image Encryption
Institute of Scientific and Technical Information of China (English)
RANQiwen; WANGQi; MAJing; TANLiying
2003-01-01
The multiplicity of the fractional Fourier transform(FRFT),which is intrinsic in any fractional operator,has been claimed by several authors,but never across-the-board developed.Particularly,the weight-type FRFT(WFRFT) has not been investigated.Starting with defining the multifractional Fourier transform (MFRFT),we gained the generalization permutation matrix group (GPMG)representation and multiplicity of the MFRFT,and the relationships among the MFRFT the standard WFRFT and the standard CFRFT.Finally,as a application,a novel image encryption method hased on the MFRFT is propounded.Similation results show that this method is safe,practicable and impactful.
A Renormalization-Group Interpretation of the Connection between Criticality and Multifractals
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.
Directory of Open Access Journals (Sweden)
L. Yao
2011-03-01
Full Text Available Relations between mineralization and certain geological processes are established mostly by geologist's knowledge of field observations. However, these relations are descriptive and a quantitative model of how certain geological processes strengthen or hinder mineralization is not clear, that is to say, the mechanism of the interactions between mineralization and the geological framework has not been thoroughly studied. The dynamics behind these interactions are key in the understanding of fractal or multifractal formations caused by mineralization, among which singularities arise due to anomalous concentration of metals in narrow space. From a statistical point of view, we think that cascade dynamics play an important role in mineralization and studying them can reveal the nature of the various interactions throughout the process. We have constructed a multiplicative cascade model to simulate these dynamics. The probabilities of mineral deposit occurrences are used to represent direct results of mineralization. Multifractal simulation of probabilities of mineral potential based on our model is exemplified by a case study dealing with hydrothermal gold deposits in southern Nova Scotia, Canada. The extent of the impacts of certain geological processes on gold mineralization is related to the scale of the cascade process, especially to the maximum cascade division number n_{max}. Our research helps to understand how the singularity occurs during mineralization, which remains unanswered up to now, and the simulation may provide a more accurate distribution of mineral deposit occurrences that can be used to improve the results of the weights of evidence model in mapping mineral potential.
Tweedie convergence: A mathematical basis for Taylor's power law, 1/f noise, and multifractality
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.
Multifractals in Western Major STOCK Markets Historical Volatilities in Times of Financial Crisis
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.
The SARD variety of multi-fractality of ventricular epicardial mapping during ischemia
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
We have analyzed cardiac ischemia-reperfusion in an animal model using epicardial electropotential mapping. We investigated the relationship between ischemia and variability of multifractality in epicardial electrograms. We present a new parameter called the singularity spectrum area reference dispersion (SARD) that clearly demonstrates the change in multifractility with the extent of myocardiaischemia. By contrasting the 3D ventricular epicardial SARD map with the activation map, we conclude that myocardial ischemia significantly influences the variety of multifractality of ventricular epicardium electrograms and the SARD parameter is useful in correlating multifractality of epicardial elec- trograms with location of ischemia closely.
Stenull, O; Janssen, H K
2001-03-01
We study the multifractal moments of the current distribution in randomly diluted resistor networks near the percolation threshold. When an external current is applied between two terminals x and x(') of the network, the lth multifractal moment scales as M((l))(I)(x,x(')) approximately equal /x-x'/(psi(l)/nu), where nu is the correlation length exponent of the isotropic percolation universality class. By applying our concept of master operators [Europhys. Lett. 51, 539 (2000)] we calculate the family of multifractal exponents [psi(l)] for l>or=0 to two-loop order. We find that our result is in good agreement with numerical data for three dimensions.
Directory of Open Access Journals (Sweden)
L. F. Burlaga
2004-01-01
Full Text Available During 2002, the Voyager 1 spacecraft was in the heliosphere between 83.4 and 85.9AU (1AU is the mean distance from the Sun to Earth at 34° N heliographic latitude. The magnetic field strength profile observed in this region had a multifractal structure in the range of scales from 2 to 16 days. The multifractal spectrum observed near 85AU is similar to that observed near 40AU, indicating relatively little evolution of the multifractal structure of the magnetic field with increasing distance in the distant heliosphere in the epoch near solar maximum.
ABC of multi-fractal spacetimes and fractional sea turtles
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2016-04-15
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. (orig.)
Cosmic microwave background and inflation in multi-fractional spacetimes
Calcagni, Gianluca; Tsujikawa, Shinji
2016-01-01
We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with $q$-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, then information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBs). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These ...
Cosmic microwave background and inflation in multi-fractional spacetimes
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia,CSIC, Serrano 121, 28006 Madrid (Spain); Kuroyanagi, Sachiko [Department of Physics, Nagoya University,Chikusa, Nagoya 464-8602 (Japan); Institute for Advanced Research, Nagoya University,Chikusa, Nagoya 464-8602 (Japan); Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science,1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2016-08-18
We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with q-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBs). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These results complete the scan and reduction of the parameter space of the theory. Black-body bounds are obtained also for the theory with weighted derivatives.
ABC of multi-fractal spacetimes and fractional sea turtles
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.
ABC of multi-fractal spacetimes and fractional sea turtles
Calcagni, Gianluca
2016-01-01
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 behaviour 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 ...
Cosmic microwave background and inflation in multi-fractional spacetimes
Calcagni, Gianluca; Kuroyanagi, Sachiko; Tsujikawa, Shinji
2016-08-01
We use FIRAS and PLANCK 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with q-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBs). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These results complete the scan and reduction of the parameter space of the theory. Black-body bounds are obtained also for the theory with weighted derivatives.
Directory of Open Access Journals (Sweden)
E. Vidal Vázquez
2010-10-01
Full Text Available Most of the indices currently employed for assessing soil surface micro-topography, such as random roughness (RR, are merely descriptors of its vertical component. Recently, multifractal analysis provided a new insight for describing the spatial configuration of soil surface roughness. The main objective of this study was to test the ability of multifractal parameters to assess in field conditions the decay of initial surface roughness induced by natural rainfall under different soil tillage systems. In addition, we evaluated the potential of the joint use of multifractal indices plus RR to improve predictions of water storage in depressions of the soil surface (MDS. Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil. Six tillage treatments, namely, disc harrow, disc plough, chisel plough, disc harrow + disc level, disc plough + disc level and chisel plough + disc level were tested. In each treatment soil surface micro-topography was measured four times, with increasing amounts of natural rainfall, using a pin meter. The sampling scheme was a square grid with 25 × 25 mm point spacing and the plot size was 1350 × 1350 mm (≈1.8 m^{2}, 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. MDS was estimated from grid elevation data with a depression-filling algorithm. Multifractal analysis was performed for experimental data sets as well as for oriented and random surface conditions obtained from the former by removing slope and slope plus tillage marks, respectively. All the investigated microplots exhibited multifractal behaviour, irrespective of surface condition, but the degree of multifractality showed wide differences between them. Multifractal parameters provided valuable information for characterizing the spatial features of soil micro-topography as they were able to
Directory of Open Access Journals (Sweden)
E. Vidal Vázquez
2010-03-01
Full Text Available Most of the indices currently employed for assessing soil surface micro-topography, such as random roughness (RR, are merely descriptors of its vertical component. Recently, multifractal analysis provided a new insight for describing the spatial configuration of soil surface roughness. The main objective of this study was to test the ability of multifractal parameters to assess decay of initial surface roughness induced by natural rainfall under different soil tillage systems in field conditions. In addition, we evaluated the potential of the joint use of multifractal indices plus RR to improve predictions of water storage in depressions of the soil surface (MDS. Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil. Six tillage treatments, namely, disc harrow, disc plough, chisel plough, disc harrow + disc level, disc plough + disc level and chisel plough + disc level were tested. In each treatment soil surface micro-topography was measured four times, with increasing amounts of natural rainfall, using a pin meter. The sampling scheme was a square grid with 25×25 mm point spacing and the plot size was 1350×1350 mm (≈1.8 m^{2}, 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. MDS was estimated from grid elevation data with a depression-filling algorithm. Multifractal analysis was performed for experimental data sets as well as for oriented and random surface conditions obtained from the former by removing slope and slope plus tillage marks, respectively. All the investigated microplots exhibited multifractal behaviour, irrespective of surface condition, but the degree of multifractality showed wide differences between them. Multifractal parameters provided valuable information for characterizing the spatial features of soil micro-topography as they were able to discriminate data
Indian Academy of Sciences (India)
Sunil Kumar; Nivedita Deo
2015-02-01
We apply random matrix theory (RMT) to investigate the structure of cross-correlation in 20 global financial time series after the global financial crisis of 2008. We find that the largest eigenvalue deviates from the RMT prediction and is sensitive to the financial crisis. We find that the components of eigenvectors corresponding to the second largest eigenvalue changes sign in response to the crisis. We show that 20 global financial indices exhibit multifractality. We find that the origin of multifractality is due to the long-range correlations as well as broad probability function in the financial indices, with the exception of the index of Taiwan, as in all other indices the multifractal degree for shuffled and surrogate series is weaker than the original series. We fit the binomial multifractal model to the global financial indices.
(Quantum) Fractional Brownian Motion and Multifractal Processes under the Loop of a Tensor Networks
Descamps, Benoît
2016-01-01
We derive fractional Brownian motion and stochastic processes with multifractal properties using a framework of network of Gaussian conditional probabilities. This leads to the derivation of new representations of fractional Brownian motion. These constructions are inspired from renormalization. The main result of this paper consists of constructing each increment of the process from two-dimensional gaussian noise inside the light-cone of each seperate increment. Not only does this allows us to derive fractional Brownian motion, we can introduce extensions with multifractal flavour. In another part of this paper, we discuss the use of the multi-scale entanglement renormalization ansatz (MERA), introduced in the study critical systems in quantum spin lattices, as a method for sampling integrals with respect to such multifractal processes. After proper calibration, a MERA promises the generation of a sample of size $N$ of a multifractal process in the order of $O(N\\log(N))$, an improvement over the known method...
Shaobin, H.; Enyuan, W.; Xiaofei, L.
2014-04-01
Dynamic collapses of deeply mined coal rocks are severe threats to miners, in order to predict the collapses more accurately using electromagnetic radiation (EMR), we investigate the spatiotemporal multifractal characteristics and formation mechanism of EMR induced by underground coal mining. Coal rock in the burst-prone zone often exchanges materials and energy with its environment and gradually transits from its original stable equilibrium structure to a non-equilibrium dissipative structure with implicit spatiotemporal complexity or multifractal structures, resulting in temporal variation in multifractal EMR. The inherent law of EMR time series during damage evolution was analyzed by using time-varying multifractal theory. Results show that the time-varying multifractal characteristics of EMR are determined by damage evolutions process, the dissipated energy caused by damage evolutions such as crack propagation, fractal sliding and shearing can be regarded as the fingerprint of various EMR micro-mechanics. Dynamic spatiotemporal multifractal spectrum of EMR considers both spatial (multiple fractures) and temporal (dynamic evolution) characteristics of coal rocks, and records the dynamic evolution processes of rock bursts. Thus, it can be used to evaluate the coal deformation and fracture process. The study is of significance for us to in-depth understand EMR mechanism and to increase the accuracy of applying the EMR method to forecast dynamic disasters.
Hu, S.; Wang, E.; Liu, X.
2014-08-01
Dynamic collapses of deeply mined coal rocks are severe threats to miners; in order to predict collapses more accurately using electromagnetic radiation (EMR), we investigate the spatiotemporal multifractal characteristics and formation mechanism of EMR induced by underground coal mining. Coal rock in the burst-prone zone often exchanges materials (gas, water and coal) and energy with its environment and gradually transitions from its original stable equilibrium structure to a nonequilibrium dissipative structure with implicit spatiotemporal complexity or multifractal structures, resulting in temporal variation in multifractal EMR. The inherent law of EMR time series during damage evolution was analyzed by using time-varying multifractal theory. Results show that the time-varying multifractal characteristics of EMR are determined by damage evolution processes. Moreover, the dissipated energy caused by the damage evolutions, such as crack propagation, fractal sliding and shearing, can be regarded as the fingerprint of various EMR micro-mechanics. The dynamic spatiotemporal multifractal spectrum of EMR considers both spatial (multiple fractures) and temporal (dynamic evolution) characteristics of coal rocks and records the dynamic evolution processes of rock bursts. Thus, it can be used to evaluate the coal deformation and fracture process. The study is of significance for us to understand the EMR mechanism in detail and to increase the accuracy of the EMR method in forecasting dynamic disasters.
Directory of Open Access Journals (Sweden)
H. Shaobin
2014-04-01
Full Text Available Dynamic collapses of deeply mined coal rocks are severe threats to miners, in order to predict the collapses more accurately using electromagnetic radiation (EMR, we investigate the spatiotemporal multifractal characteristics and formation mechanism of EMR induced by underground coal mining. Coal rock in the burst-prone zone often exchanges materials and energy with its environment and gradually transits from its original stable equilibrium structure to a non-equilibrium dissipative structure with implicit spatiotemporal complexity or multifractal structures, resulting in temporal variation in multifractal EMR. The inherent law of EMR time series during damage evolution was analyzed by using time-varying multifractal theory. Results show that the time-varying multifractal characteristics of EMR are determined by damage evolutions process, the dissipated energy caused by damage evolutions such as crack propagation, fractal sliding and shearing can be regarded as the fingerprint of various EMR micro-mechanics. Dynamic spatiotemporal multifractal spectrum of EMR considers both spatial (multiple fractures and temporal (dynamic evolution characteristics of coal rocks, and records the dynamic evolution processes of rock bursts. Thus, it can be used to evaluate the coal deformation and fracture process. The study is of significance for us to in-depth understand EMR mechanism and to increase the accuracy of applying the EMR method to forecast dynamic disasters.
Energy Technology Data Exchange (ETDEWEB)
Bisht, R; Kale, S; Gopishankar, N; Rath, G; Julka, P; Agarwal, D; Singh, M; Garg, A; Kumar, P; Thulkar, S; Sharma, B [All India Institute of Medical Sciences, New Delhi (India)
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 head 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
Scaling in cognitive performance reflects multiplicative multifractal cascade dynamics.
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.
Scaling in cognitive performance reflects multiplicative multifractal cascade dynamics
Directory of Open Access Journals (Sweden)
Damian G. Stephen
2012-04-01
Full Text Available Self-organized criticality purports to build multi-scaled structures, such as those supporting life, 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.
Generalized scale invariance, clouds and radiative transfer on multifractal clouds
Energy Technology Data Exchange (ETDEWEB)
Lovejoy, S.; Schertzer, D. [Univ. Pierre et Marie Curie, Paris (France)
1995-09-01
Recent systematic satellite studies (LANDSAT, AVHRR, METEOSAT) of cloud radiances using (isotropic) energy spectra have displayed excellent scaling from at least about 300m to about 4000km, even for individual cloud pictures. At first sight, this contradicts the observed diversity of cloud morphology, texture and type. The authors argue that the explanation of this apparent paradox is that the differences are due to anisotropy, e.g. differential stratification and rotation. A general framework for anisotropic scaling expressed in terms of isotropic self-similar scaling and fractals and multifractals is needed. Schertzer and Lovejoy have proposed Generalized Scale Invariance (GSI) in response to this need. In GSI, the statistics of the large and small scales of system can be related to each other by a scale changing operator T{sub {lambda}} which depends only on the scale ratio {lambda}{sub i} there is no characteristic size. 3 refs., 1 fig.
2007-11-02
S) AND ADDRESS(ES) DCW Industries, Inc. 5354 Palm Drive La Canada, CA 91011 8. PERFORMING ORGANIZATION...REPORT NUMBER DCW -38-R-05 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) U. S. Army Research Office...Turbulence Modeling for CFD, Second Edition, DCW Industries, Inc., La Cañada, CA. Wilcox, D. C. (2001), “Projectile Base Flow Analysis,” DCW
Liu, Yue; Zhou, Kefa; Cheng, Qiuming
2017-08-01
Singularity analysis is one of the most important models in the fractal/multifractal family that has been demonstrated as an efficient tool for identifying hybrid distribution patterns of geochemical data, such as normal and multifractal distributions. However, the question of how to appropriately separate these patterns using reasonable thresholds has not been well answered. In the present study, a new method termed singularity-quantile (S-Q) analysis was proposed to separate multiple geochemical anomaly populations based on integrating singularity analysis and quantile-quantile plot (QQ-plot) analysis. The new method provides excellent abilities for characterizing frequency distribution patterns of singularity indices by plotting singularity index quantiles vs. standard normal quantiles. From a perspective of geochemical element enrichment processes, distribution patterns of singularity indices can be evidently separated into three groups by means of the new method, corresponding to element enrichment, element generality and element depletion, respectively. A case study for chromitite exploration based on geochemical data in the western Junggar region (China), was employed to examine the potential application of the new method. The results revealed that the proposed method was very sensitive to the changes of singularity indices with three segments when it was applied to characterize geochemical element enrichment processes. And hence, the S-Q method can be considered as an efficient and powerful tool for separating hybrid geochemical anomalies on the basis of statistical and inherent fractal/multifractal properties.
MF-DFA Based Stock Time Series Clustering Analysis and Its Applications%基于MF-DFA的股票时间序列聚类分析及其应用
Institute of Scientific and Technical Information of China (English)
袁杰; 薛永坚; 肖宏旺
2013-01-01
多重分形消除趋势波动分析法（MF-DFA）不仅能够去除股票时间序列的长期趋势波动，还能够精确反应股票时间序列的多重分形特性。首先利用MF-DFA方法对股票时间序列进行多重分形分析，结果表明，相比标准多重分析，MF-DFA方法更能反映时间序列的多重分形特性。其次，定义一种以多重分形谱参数作为相似性度量函数的聚类方法对股票时间序列进行聚类。最后，在Markowitz提出的“期望均值收益-收益方差”（M-V）模型的基础上，把聚类结果运用股票投资组合当中。采用上海证券市场28支股票进行实验验证表明，在给定的收益率下，采用基于多重分形谱参数的聚类方法的股票组合可以得到比随机组合更小的风险水平。%The method of multi-fractal detrended fluctuation analysis (MF-DFA) can not only be able to remove the fluctuations of the long-term trend in the stock market time series, but also be able to describe the multi-fractal characteristics. First of all, this paper uses the MF-DFA to analyze the multi-fractal characteristics of the stock market time series and the result shows that the method of MF-DFA is more efficient. Secondly, it defines a similarity measure function of clustering which use the parameters of multi-fractal spectrum as their parameters on the stock time series clustering. Finally, based on the Markowitz proposed the rule of expected mean and the variance of return (M-V rule), it applies the clustering results into the stock portfolio. According to the experiment result, a portfolio with more return and lower risk is reached.
Institute of Scientific and Technical Information of China (English)
苏涛; 王志刚; 刘昌明; 徐增丙; 但斌斌
2015-01-01
考虑到耐火材料损伤声发射信号模式识别困难，提出一种结合经验模态分解（EM D ）、多重分形谱参数和支持向量机的耐火材料损伤形式分类方法。首先对耐火材料损伤声发射信号进行ED M 分解得到若干本征模态函数（IM F ）分量，并取前4个分量作为研究对象，然后将整个信号的多重分形谱宽及各IM F分量的多重分形谱宽组成的特征向量输入支持向量机进行学习训练，最后实现耐火材料损伤模式识别。研究结果表明，采用由原信号及各IM F分量的多重分形谱宽值组成的特征向量能够有效进行损伤信号的特征提取。该方法对耐火材料界面相损伤的分类准确率为99％，对其基质相损伤的分类准确率为89％。%Considering the difficulty of pattern recognition of the acoustic emission signals of refractory damage ,this paper proposes a classification method for refractory damage pattern based on empirical mode decomposition (EMD) ,multi‐fractal spectrum parameters and support vector machine .First , the acoustic emission signals are decomposed into several intrinsic mode function (IM F) components by EDM ,and the first four components are taken as the research objects .Second ,a feature vector formed by multi‐fractal spectrum width values of the entire signal and IMF components is used in learning and training of support vector machine (SVM ) .Then the refractory damage pattern classifi‐cation is completed by SVM .The results show that the constructed feature vector is efficient in fea‐ture extraction of damage signals .The classification accuracy of this method for interface damage and matrix damage of refractory can reach up to 99% and 89% ,respectively .
Analysis of reservoir properties based on X-ray computed tomography of sludge
Kadyrov, Rail
2017-04-01
Modern methods of oil fields developing require drilling with coring, but the cost of such operations is very high. In contrast, sludge drilling allows reducing the cost of the work more than two times. Core is used for the standard geological and technical research, especially it is important for definition of porosity and permeability. However, the same result can be achieved using X-ray computed tomography of sludge. In the course of the research, experiments on the comparison of porosity achieved by standard method of liquid saturation and X-Ray computed tomography in different resolutions were done. The best porosity representation scales depends on rock type and its minimal permeable for liquid pore size. It is shown that the porosity of the sample is due to matrix porosity generally. Another problem solved in the research was a destruction of strongly fractured, friable and fine lithotypes in a well and crumbling of drilled rocks. Statistical analysis of geometrical properties of porous space, such as multifractal parameters, allowed distinguishing the samples from different levels. The same pores are responsible for permeability in the investigated range 100-10 μm, regardless to the observation scale. Permeability was computed using digital 3D models and correlated with data obtained by water permeability testing system. Thus, the technology of reservoir properties analysis based on X-Ray computed tomography of sludge was developed.
Directory of Open Access Journals (Sweden)
Qiuming Cheng
2007-06-01
Full Text Available The patterns shown on two-dimensional images (fields used in geosciences reflect the end products of geo-processes that occurred on the surface and in the subsurface of the Earth. Anisotropy of these types of patterns can provide information useful for interpretation of geo-processes and identification of features in the mapped area. Quantification of the anisotropy property is therefore essential for image processing and interpretation. This paper introduces several techniques newly developed on the basis of multifractal modeling in space, Fourier frequency, and eigen domains, respectively. A singularity analysis method implemented in the space domain can be used to quantify the intensity and anisotropy of local singularities. The second method, called S-A, characterizes the generalized scale invariance property of a field in the Fourier frequency domain. The third method characterizes the field using a power-law model on the basis of eigenvalues and eigenvectors of the field. The applications of these methods are demonstrated with a case study of Environment Scan Electric Microscope (ESEM microimages for identification of sphalerite (ZnS ore minerals from the Jinding Pb/Zn/Ag mineral deposit in Shangjiang District, Yunnan Province, China.
Mensuration of microstructure multi-fractal spectra of calcined limestone particle surfaces
Institute of Scientific and Technical Information of China (English)
Jianyu Shang; Songling Wang; Chunbo Wang; Chunchang Song
2010-01-01
The microstructure of the surface of a calcined limestone particle is multi-fractal.We develop an analytic method that surveys the boundary curve multi-fractal dimensions with SEM,gets a three-dimensional surface structure α-f(α)curve via zero-sets,and finally calculates the multi-fractal spectrum values of the particle surface's microstructural topography.After analyzing two spectra from limestone particles calcined at 850 ℃ and 900 ℃,it was shown that the microstructural topographies of the surfaces of calcined limestone multi-particle system have some degree of self-similarity.This mensuration method is proposed to describe the multi-fractal characteristics of a micro-scale particle's surface topography.
Multifractality at non-Anderson disorder-driven transitions in Weyl semimetals and other systems
Syzranov, S. V.; Gurarie, V.; Radzihovsky, L.
2016-10-01
Systems with the power-law quasiparticle dispersion ɛk ∝kα exhibit non-Anderson disorder-driven transitions in dimensions d > 2 α, as exemplified by Weyl semimetals, 1D and 2D arrays of ultracold ions with long-range interactions, quantum kicked rotors, and semiconductor models in high dimensions. We study the wavefunction structure in such systems and demonstrate that at these transitions they exhibit fractal behaviour with an infinite set of multifractal exponents. The multifractality persists even when the wavefunction localisation is forbidden by symmetry or topology and occurs as a result of elastic scattering between all momentum states in the band on length scales shorter than the mean free path. We calculate explicitly the multifractal spectra in semiconductors and Weyl semimetals using one-loop and two-loop renormalisation-group approaches slightly above the marginal dimension d = 2 α.
Nouri, Reza; Jafari, Mohammad Reza; Arian, Mehran; Feizi, Faranak; Afzal, Peyman
2013-10-01
The Tarom 1: 100,000 sheet is located within the Cenozoic Tarom-Hashtjin volcano-plutonic belt, NW Iran. Reconstruction of the tectonic and structural setting of the hydrothermal deposits is fundamental to predictive models of different ore deposits. Since fractal/multifractal modelling is an effective instrument for separation of geological and mineralized zones from background, therefore Concentration-Distance to Major Fault (C-DMF) fractal model and distribution of Cu anomalies were used to classify Cu mineralizations according to their distance to major faults. Application of the C-DMF model for the classification of Cu mineralization in the Tarom 1: 100,000 sheet reveals that the main copper mineralizations have a strong correlation with their distance to major faults in the area. The distances of known copper mineralizations having Cu values higher than 2.2 % to major faults are less than 10 km showing a positive correlation between Cu mineralization and tectonic events. Moreover, extreme and high Cu anomalies based on stream sediments and lithogeochemical data were identified by the Number-Size (N-S) fractal model. These anomalies have distances to major faults less than 10 km and validate the results derived via the C-DMF fractal model. The C-DMF fractal modelling can be utilized for the reconnaissance and prospecting of magmatic and hydrothermal deposits.
Directory of Open Access Journals (Sweden)
A. Turiel
2009-01-01
Full Text Available Nowadays Earth observation satellites provide information about many relevant variables of the ocean-climate system, such as temperature, moisture, aerosols, etc. However, to retrieve the velocity field, which is the most relevant dynamical variable, is still a technological challenge, specially in the case of oceans. New processing techniques, emerged from the theory of turbulent flows, have come to assist us in this task. In this paper, we show that multifractal techniques applied to new Sea Surface Temperature satellite products opens the way to build maps of ocean currents with unprecedented accuracy. With the application of singularity analysis, we show that global ocean circulation patterns can be retrieved in a daily basis. We compare these results with high-quality altimetry-derived geostrophic velocities, finding a quite good correspondence of the observed patterns both qualitatively and quantitatively. The implications of this findings from the perspective both of theory and of operational applications are discussed.
Scale-free avalanches in the multifractal random walk
Bartolozzi, M
2007-01-01
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 ...
New empirical tests of the multifractal Omori law for Taiwan
Tsai, Ching-Yi; Sornette, Didier
2011-01-01
We report new tests on the Taiwan earthquake catalog of the prediction by the Multifractal Stress Activation (MSA) model that the p-value of the Omori law for the rate of aftershocks following a mainshock is an increasing function of its magnitude Mm. This effort is motivated by the quest to validate this crucial prediction of the MSA model and to investigate its possible dependence on local tectonic conditions. With careful attention to the long-term as well as short-term time-dependent magnitude completeness of the Taiwan catalog, and with the use of three different declustering techniques, we confirm the universality of the prediction p(Mm) = (0.09 \\pm 0.03) \\times Mm + (0.47 \\pm 0.10), valid for the SCEC Southern California catalog, the Harvard-CMT worldwide catalog, the JMA Japan catalog and the Taiwan catalog. The observed deviations of the two coefficients of the p(Mm) linear dependence on Mm from catalog to catalog are not significant enough to correlate meaningfully with any tectonic features.
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
Directory of Open Access Journals (Sweden)
J. Lévy Véhel
2013-09-01
Full Text Available Multifractional Brownian motion (mBm has proved to be a useful tool in various areas of geophysical modelling. Although a versatile model, mBm is of course not always an adequate one. We present in this work several other stochastic processes which could potentially be useful in geophysics. The first alternative type is that of self-regulating processes: these are models where the local regularity is a function of the amplitude, in contrast to mBm where it is tuned exogenously. We demonstrate the relevance of such models for digital elevation maps and for temperature records. We also briefly describe two other types of alternative processes, which are the counterparts of mBm and of self-regulating processes when the intensity of local jumps is considered in lieu of local regularity: multistable processes allow one to prescribe the local intensity of jumps in space/time, while this intensity is governed by the amplitude for self-stabilizing processes.
FractalAnalyzer: A MATLAB Application for Multifractal Seismicity Analysis
Roy, P.N.S.; Gupta, D.K.
2015-01-01
Earthquakes are seismic phenomena caused by the sudden release of energy in the Earth’s crust. Their effects range from ground shaking to faulting. Geological and geophysical studies, especially in light of plate tectonic theory have been used to explain the occurrence of earthquakes. Thus from the