Multifractal analysis for grading complex fractionated electrograms in atrial fibrillation.

PubMed

Orozco-Duque, A; Novak, D; Kremen, V; Bustamante, J

2015-11-01

Complex fractionated atrial electrograms provide an important tool for identifying arrhythmogenic substrates that can be used to guide catheter ablation for atrial fibrillation (AF). However, fractionation is a phenomenon that remains unclear. This paper aims to evaluate the multifractal properties of electrograms in AF in order to propose a method based on multifractal analysis able to discriminate between different levels of fractionation. We introduce a new method, the h-fluctuation index (hFI), where h is the generalised Hurst exponent, to extract information from the shape of the multifractal spectrum. Two multifractal frameworks are evaluated: multifractal detrended fluctuation analysis and wavelet transform modulus maxima. hFI is exemplified through its application in synthetic signals, and it is evaluated in a database of electrograms labeled on the basis of four degrees of fractionation. We compare the performance of hFI with other indexes, and find that hFI outperforms them. The results of the study provide evidence that multifractal analysis is useful for studying fractionation phenomena in AF electrograms, and indicate that hFI can be proposed as a tool for grade fractionation associated with the detection of target sites for ablation in AF.

Gradual multifractal reconstruction of time-series: Formulation of the method and an application to the coupling between stock market indices and their Hölder exponents

NASA Astrophysics Data System (ADS)

Keylock, Christopher J.

2018-04-01

A technique termed gradual multifractal reconstruction (GMR) is formulated. A continuum is defined from a signal that preserves the pointwise Hölder exponent (multifractal) structure of a signal but randomises the locations of the original data values with respect to this (φ = 0), to the original signal itself(φ = 1). We demonstrate that this continuum may be populated with synthetic time series by undertaking selective randomisation of wavelet phases using a dual-tree complex wavelet transform. That is, the φ = 0 end of the continuum is realised using the recently proposed iterated, amplitude adjusted wavelet transform algorithm (Keylock, 2017) that fully randomises the wavelet phases. This is extended to the GMR formulation by selective phase randomisation depending on whether or not the wavelet coefficient amplitudes exceeds a threshold criterion. An econophysics application of the technique is presented. The relation between the normalised log-returns and their Hölder exponents for the daily returns of eight financial indices are compared. One particularly noticeable result is the change for the two American indices (NASDAQ 100 and S&P 500) from a non-significant to a strongly significant (as determined using GMR) cross-correlation between the returns and their Hölder exponents from before the 2008 crash to afterwards. This is also reflected in the skewness of the phase difference distributions, which exhibit a geographical structure, with Asian markets not exhibiting significant skewness in contrast to those from elsewhere globally.

Multifractal analysis of information processing in hippocampal neural ensembles during working memory under Δ9-tetrahydrocannabinol administration

PubMed Central

Fetterhoff, Dustin; Opris, Ioan; Simpson, Sean L.; Deadwyler, Sam A.; Hampson, Robert E.; Kraft, Robert A.

2014-01-01

Background 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. New method 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. Results 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 partial agonist, tetrahydrocannabinol (THC), selectively reduced multifractal dynamics in FCT neurons compared to non-FCT neurons. Comparison with existing methods 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. Conclusion 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. PMID:25086297

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

ERIC Educational Resources Information Center

Ihlen, Espen A. F.; Vereijken, Beatrix

2010-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Multifractal and wavelet analysis of epileptic seizures

NASA Astrophysics Data System (ADS)

Dick, Olga E.; Mochovikova, Irina A.

The aim of the study is to develop quantitative parameters of human electroencephalographic (EEG) recordings with epileptic seizures. We used long-lasting recordings from subjects with epilepsy obtained as part of their clinical investigation. The continuous wavelet transform of the EEG segments and the wavelet-transform modulus maxima method enable us to evaluate the energy spectra of the segments, to fin lines of local maximums, to gain the scaling exponents and to construct the singularity spectra. We have shown that the significant increase of the global energy with respect to background and the redistribution of the energy over the frequency range are observed in the patterns involving the epileptic activity. The singularity spectra expand so that the degree of inhomogenety and multifractality of the patterns enhances. Comparing the results gained for the patterns during different functional probes such as open and closed eyes or hyperventilation we demonstrate the high sensitivity of the analyzed parameters (the maximal global energy, the width and asymmetry of the singularity spectrum) for detecting the epileptic patterns.

The dynamic system corresponding to LOD and AAM.

NASA Astrophysics Data System (ADS)

Liu, Shida; Liu, Shikuo; Chen, Jiong

2000-02-01

Using wavelet transform, the authors can reconstruct the 1-D map of a multifractal object. The wavelet transform of LOD and AAM shows that at 20 years scale, annual scale and 2 - 3 years scale, the jump points of LOD and AAM accord with each other very well, and their reconstructing 1-D mapping dynamic system are also very similar.

Wavelet detection of coherent structures in interplanetary magnetic flux ropes and its role in the intermittent turbulence

NASA Astrophysics Data System (ADS)

Muñoz, P. R.; Chian, A. C.

2013-12-01

We implement a method to detect coherent magnetic structures using the Haar discrete wavelet transform (Salem et al., ApJ 702, 537, 2009), and apply it to an event detected by Cluster at the turbulent boundary layer of an interplanetary magnetic flux rope. The wavelet method is able to detect magnetic coherent structures and extract main features of solar wind intermittent turbulence, such as the power spectral density and the scaling exponent of structure functions. Chian and Muñoz (ApJL 733, L34, 2011) investigated the relation between current sheets, turbulence, and magnetic reconnections at the leading edge of an interplanetary coronal mass ejection measured by Cluster upstream of the Earth's bow shock on 2005 January 21. We found observational evidence of two magnetically reconnected current sheets in the vicinity of a front magnetic cloud boundary layer, where the scaling exponent of structure functions of magnetic fluctuations exhibits multifractal behavior. Using the wavelet technique, we show that the current sheets associated to magnetic reconnection are part of the set of magnetic coherent structures responsible for multifractality. By removing them using a filtering criteria, it is possible to recover a self-similar scaling exponent predicted for homogeneous turbulence. Finally, we discuss an extension of the wavelet technique to study coherent structures in two-dimensional solar magnetograms.

Frozen Fractals all Around: Solar flares, Ampere’s Law, and the Search for Units in Scale-Free Processes.

NASA Astrophysics Data System (ADS)

McAteer, R. T. James

2015-08-01

My soul is spiraling in frozen fractals all around, And one thought crystallizes like an icy blast, I'm never going back, the past is in the past.Elsa, from Disney’s Frozen, characterizes two fundamental aspects of scale-free processes in Nature: fractals are everywhere in space; fractals can be used to probe changes in time. Self-Organized Criticality provides a powerful set of tools to study scale-free processes. It connects spatial fractals (more generically, multifractals) to temporal evolution. The drawback is that this usually results in scale-free, unit-less, indices, which can be difficult to connect to everyday physics. Here, I show a novel method that connects one of the most powerful SOC tools - the wavelet transform modulus maxima approach to calculating multifractality - to one of the most powerful equations in all of physics - Ampere’s law. In doing so I show how the multifractal spectra can be expressed in terms of current density, and how current density can then be used for the prediction of future energy release from such a system.Our physical understanding of the solar magnetic field structure, and hence our ability to predict solar activity, is limited by the type of data currently available. I show that the multifractal spectrum provides a powerful physical connection between the details of photospheric magnetic gradients of current data and the coronal magnetic structure. By decomposing Ampere’s law and comparing it to the wavelet transform modulus maximum method, I show how the scale-free Holder exponent provides a direct measure of current density across all relevant sizes. The prevalence of this current density across various scales is connected to its stability in time, and hence to the ability of the magnetic structure to store and then release energy. Hence (spatial) multifractals inform us of (future) solar activity.Finally I discuss how such an approach can be used in any study of scale-free processes, and highlight the necessary key steps in identifying the nature of the mother wavelet to ensuring the viability of this powerful connection.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

NASA Astrophysics Data System (ADS)

Dashtian, Hassan; Yang, Yafan; Sahimi, Muhammad

2015-12-01

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

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

PubMed

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

2016-01-01

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

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

PubMed Central

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

2016-01-01

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

Multifractal analysis of a GCM climate

NASA Astrophysics Data System (ADS)

Carl, P.

2003-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2001-03-01

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

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

PubMed Central

Hu, Jing; Zheng, Yi; Gao, Jianbo

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

Lin, Jinshan; Chen, Qian

2013-07-01

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

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

NASA Astrophysics Data System (ADS)

Davis, A. B.; Marshak, A.

2001-12-01

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

Multifractal Analysis for Nutritional Assessment

PubMed Central

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

2013-01-01

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

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

PubMed

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Analysis of HD 73045 light curve data

NASA Astrophysics Data System (ADS)

Das, Mrinal Kanti; Bhatraju, Naveen Kumar; Joshi, Santosh

2018-04-01

In this work we analyzed the Kepler light curve data of HD 73045. The raw data has been smoothened using standard filters. The power spectrum has been obtained by using a fast Fourier transform routine. It shows the presence of more than one period. In order to take care of any non-stationary behavior, we carried out a wavelet analysis to obtain the wavelet power spectrum. In addition, to identify the scale invariant structure, the data has been analyzed using a multifractal detrended fluctuation analysis. Further to characterize the diversity of embedded patterns in the HD 73045 flux time series, we computed various entropy-based complexity measures e.g. sample entropy, spectral entropy and permutation entropy. The presence of periodic structure in the time series was further analyzed using the visibility network and horizontal visibility network model of the time series. The degree distributions in the two network models confirm such structures.

Fractal density modeling of crustal heterogeneity from the KTB deep hole

NASA Astrophysics Data System (ADS)

Chen, Guoxiong; Cheng, Qiuming

2017-03-01

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

Application of wavelet based MFDFA on Mueller matrix images for cervical pre-cancer detection

NASA Astrophysics Data System (ADS)

Zaffar, Mohammad; Pradhan, Asima

2018-02-01

A systematic study has been conducted on application of wavelet based multifractal de-trended fluctuation analysis (MFDFA) on Mueller matrix (MM) images of cervical tissue sections for early cancer detection. Changes in multiple scattering and orientation of fibers are observed by utilizing a discrete wavelet transform (Daubechies) which identifies fluctuations over polynomial trends. Fluctuation profiles, after 9th level decomposition, for all elements of MM qualitatively establish a demarcation of different grades of cancer from normal tissue. Moreover, applying MFDFA on MM images, Hurst exponent profiles for images of MM qualitatively are seen to display differences. In addition, the values of Hurst exponent increase for the diagonal elements of MM with increasing grades of the cervical cancer, while the value for the elements which correspond to linear polarizance decrease. However, for circular polarizance the value increases with increasing grades. These fluctuation profiles reveal the trend of local variation of refractive -indices and along with Hurst exponent profile, may serve as a useful biological metric in the early detection of cervical cancer. The quantitative measurements of Hurst exponent for diagonal and first column (polarizance governing elements) elements which reflect changes in multiple scattering and structural anisotropy in stroma, may be sensitive indicators of pre-cancer.

Turbulence Characteristics in an Elevated Shear Layer over Owens Valley

DTIC Science & Technology

2010-02-14

Arnéodo, G. Grasseau, Y. Gagne, E. J. Hopfinger, and U. Frisch, 1989: Wavelet analysis of turbulence reveals the multifractal nature of the Richardson...Helmholtz (KH) instability, the tur- bulence inertial subrange, turbulence intermittency, and cross -scale energy transfer over complex terrain. The...or cross -valley) and the normal (also referred to as along- valley) wind components, respectively. Figure 2 shows profiles derived from the 1800 UTC

Log-Normality and Multifractal Analysis of Flame Surface Statistics

NASA Astrophysics Data System (ADS)

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

2013-11-01

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

Statistical physics and physiology: monofractal and multifractal approaches

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

Multifractality of stock markets based on cumulative distribution function and multiscale multifractal analysis

NASA Astrophysics Data System (ADS)

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.

Joint multifractal analysis based on the partition function approach: analytical analysis, numerical simulation and empirical application

NASA Astrophysics Data System (ADS)

Xie, Wen-Jie; Jiang, Zhi-Qiang; Gu, Gao-Feng; Xiong, Xiong; Zhou, Wei-Xing

2015-10-01

Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

A picture for the coupling of unemployment and inflation

NASA Astrophysics Data System (ADS)

Safdari, H.; Hosseiny, A.; Vasheghani Farahani, S.; Jafari, G. R.

2016-02-01

The aim of this article is to illustrate the scaling features of two well heard characters in the media; unemployment and inflation. We carry out a scaling analysis on the coupling between unemployment and inflation. This work is based on the wavelet analysis as well as the detrended fluctuation analysis (DFA). Through our analysis we state that while unemployment is time scale invariant, inflation is bi-scale. We show that inflation possess a five year time scale where it experiences different behaviours before and after this scale period. This behaviour of inflation provides basis for the coupling to inherit the stated time interval. Although inflation is bi-scale, it is unemployment that shows a strong multifractality feature. Owing to the cross wavelet analysis we provide a picture that illustrates the dynamics of coupling between unemployment and inflation regarding intensity, direction, and scale. The fact of the matter is that the coupling between inflation and unemployment is not equal in one way compared to the opposite. Regarding the scaling; coupling exhibits different features in various scales. In a sense that although in one scale its correlation behaves in a positive/negative manner, at the same time it can be negative/positive for another scale.

Direct determination approach for the multifractal detrending moving average analysis

NASA Astrophysics Data System (ADS)

Xu, Hai-Chuan; Gu, Gao-Feng; Zhou, Wei-Xing

2017-11-01

In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent τ (q ) is related to the partition function and the multifractal spectrum f (α ) can be directly determined. The performances of the direct determination approach and the traditional approach of the MF-DMA are compared based on three synthetic multifractal and monofractal measures generated from the one-dimensional p -model, the two-dimensional p -model, and the fractional Brownian motions. We find that both approaches have comparable performances to unveil the fractal and multifractal nature. In other words, without loss of accuracy, the multifractal spectrum f (α ) can be directly determined using the new approach with less computation cost. We also apply the new MF-DMA approach to the volatility time series of stock prices and confirm the presence of multifractality.

Local multifractal detrended fluctuation analysis for non-stationary image's texture segmentation

NASA Astrophysics Data System (ADS)

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.

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

Davis, A.B.; Clothiaux, E.

Because of Earth`s gravitational field, its atmosphere is strongly anisotropic with respect to the vertical; the effect of the Earth`s rotation on synoptic wind patterns also causes a more subtle form of anisotropy in the horizontal plane. The authors survey various approaches to statistically robust anisotropy from a wavelet perspective and present a new one adapted to strongly non-isotropic fields that are sampled on a rectangular grid with a large aspect ratio. This novel technique uses an anisotropic version of Multi-Resolution Analysis (MRA) in image analysis; the authors form a tensor product of the standard dyadic Haar basis, where themore » dividing ratio is {lambda}{sub z} = 2, and a nonstandard triadic counterpart, where the dividing ratio is {lambda}{sub x} = 3. The natural support of the field is therefore 2{sup n} pixels (vertically) by 3{sup n} pixels (horizontally) where n is the number of levels in the MRA. The natural triadic basis includes the French top-hat wavelet which resonates with bumps in the field whereas the Haar wavelet responds to ramps or steps. The complete 2D basis has one scaling function and five wavelets. The resulting anisotropic MRA is designed for application to the liquid water content (LWC) field in boundary-layer clouds, as the prevailing wind advects them by a vertically pointing mm-radar system. Spatial correlations are notoriously long-range in cloud structure and the authors use the wavelet coefficients from the new MRA to characterize these correlations in a multifractal analysis scheme. In the present study, the MRA is used (in synthesis mode) to generate fields that mimic cloud structure quite realistically although only a few parameters are used to control the randomness of the LWC`s wavelet coefficients.« less

Understanding the multifractality in portfolio excess returns

NASA Astrophysics Data System (ADS)

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.

Scale invariance in biophysics

NASA Astrophysics Data System (ADS)

Stanley, H. Eugene

2000-06-01

In this general talk, we offer an overview of some problems of interest to biophysicists, medical physicists, and econophysicists. These include DNA sequences, brain plaques in Alzheimer patients, heartbeat intervals, and time series giving price fluctuations in economics. These problems have the common feature that they exhibit features that appear to be scale invariant. Particularly vexing is the problem that some of these scale invariant phenomena are not stationary-their statistical properties vary from one time interval to the next or form one position to the next. We will discuss methods, such as wavelet methods and multifractal methods, to cope with these problems. .

Multifractal analysis of line-edge roughness

NASA Astrophysics Data System (ADS)

Constantoudis, Vassilios; Papavieros, George; Lorusso, Gian; Rutigliani, Vito; van Roey, Frieda; Gogolides, Evangelos

2018-03-01

In this paper, we propose to rethink the issue of LER characterization on the basis of the fundamental concept of symmetries. In LER one can apply two kinds of symmetries: a) the translation symmetry characterized by periodicity and b) the scaling symmetry quantified by the fractal dimension. Up to now, a lot of work has been done on the first symmetry since the Power Spectral Density (PSD), which has been extensively studied recently, is a decomposition of LER signal into periodic edges and quantification of the `power' of each periodicity at the real LER. The aim of this paper is to focus on the second symmetry of scaling invariance. Similarly to PSD, we introduce the multifractal approach in LER analysis which generalizes the scaling analysis of standard (mono)fractal theory and decomposes LER into fractal edges characterized by specific fractal dimensions. The main benefit of multifractal analysis is that it enables the characterization of the multi-scaling contributions of different mechanisms involved in LER formation. In the first part of our work, we present concisely the multifractal theory of line edges and utilize the Box Counting method for its implementation and the extraction of the multifractal spectrum. Special emphasis is given on the explanation of the physical meaning of the obtained multifractal spectrum whose asymmetry quantifies the degree of multifractality. In addition, we propose the distinction between peak-based and valley-based multifractality according to whether the asymmetry of the multifractal spectrum is coming from the sharp line material peaks to space regions or from the cavities of line materis (edge valleys). In the second part, we study systematically the evolution of LER multifractal spectrum during the first successive steps of a multiple (quadruple) patterning lithography technique and find an interesting transition from a peak-based multifractal behavior in the first litho resist LER to a valley-based multifractality caused mainly by the effects of etch pattern transfer steps.

Comparison of Machine Learning Methods for the Arterial Hypertension Diagnostics

PubMed Central

Belo, David; Gamboa, Hugo

2017-01-01

The paper presents results of machine learning approach accuracy applied analysis of cardiac activity. The study evaluates the diagnostics possibilities of the arterial hypertension by means of the short-term heart rate variability signals. Two groups were studied: 30 relatively healthy volunteers and 40 patients suffering from the arterial hypertension of II-III degree. The following machine learning approaches were studied: linear and quadratic discriminant analysis, k-nearest neighbors, support vector machine with radial basis, decision trees, and naive Bayes classifier. Moreover, in the study, different methods of feature extraction are analyzed: statistical, spectral, wavelet, and multifractal. All in all, 53 features were investigated. Investigation results show that discriminant analysis achieves the highest classification accuracy. The suggested approach of noncorrelated feature set search achieved higher results than data set based on the principal components. PMID:28831239

Intrapartum fetal heart rate classification from trajectory in Sparse SVM feature space.

PubMed

Spilka, J; Frecon, J; Leonarduzzi, R; Pustelnik, N; Abry, P; Doret, M

2015-01-01

Intrapartum fetal heart rate (FHR) constitutes a prominent source of information for the assessment of fetal reactions to stress events during delivery. Yet, early detection of fetal acidosis remains a challenging signal processing task. The originality of the present contribution are three-fold: multiscale representations and wavelet leader based multifractal analysis are used to quantify FHR variability ; Supervised classification is achieved by means of Sparse-SVM that aim jointly to achieve optimal detection performance and to select relevant features in a multivariate setting ; Trajectories in the feature space accounting for the evolution along time of features while labor progresses are involved in the construction of indices quantifying fetal health. The classification performance permitted by this combination of tools are quantified on a intrapartum FHR large database (≃ 1250 subjects) collected at a French academic public hospital.

a Comparison Between Two Ols-Based Approaches to Estimating Urban Multifractal Parameters

NASA Astrophysics Data System (ADS)

Huang, Lin-Shan; Chen, Yan-Guang

Multifractal theory provides a new spatial analytical tool for urban studies, but many basic problems remain to be solved. Among various pending issues, the most significant one is how to obtain proper multifractal dimension spectrums. If an algorithm is improperly used, the parameter spectrums will be abnormal. This paper is devoted to investigating two ordinary least squares (OLS)-based approaches for estimating urban multifractal parameters. Using empirical study and comparative analysis, we demonstrate how to utilize the adequate linear regression to calculate multifractal parameters. The OLS regression analysis has two different approaches. One is that the intercept is fixed to zero, and the other is that the intercept is not limited. The results of comparative study show that the zero-intercept regression yields proper multifractal parameter spectrums within certain scale range of moment order, while the common regression method often leads to abnormal multifractal parameter values. A conclusion can be reached that fixing the intercept to zero is a more advisable regression method for multifractal parameters estimation, and the shapes of spectral curves and value ranges of fractal parameters can be employed to diagnose urban problems. This research is helpful for scientists to understand multifractal models and apply a more reasonable technique to multifractal parameter calculations.

Multifractal in Volatility of Family Business Stocks Listed on Casablanca STOCK Exchange

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

In this paper, we check for existence of multifractal in volatility of Moroccan family business stock returns and in volatility of Casablanca market index returns based on multifractal detrended fluctuation analysis (MF-DFA) technique. Empirical results show strong evidence of multifractal characteristics in volatility series of both family business stocks and market index. In addition, it is found that small variations in volatility of family business stocks are persistent, whilst small variations in volatility of market index are anti-persistent. However, large variations in family business volatility and market index volatility are both anti-persistent. Furthermore, multifractal spectral analysis based results show strong evidence that volatility in Moroccan family business companies exhibits more multifractality than volatility in the main stock market. These results may provide insightful information for risk managers concerned with family business stocks.

BOOK REVIEW: The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

NASA Astrophysics Data System (ADS)

Ng, J.; Kingsbury, N. G.

2004-02-01

This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar wavelet. The second half of the chapter groups together miscellaneous points about the discrete wavelet transform, including coefficient manipulation for signal denoising and smoothing, a description of Daubechies’ wavelets, the properties of translation invariance and biorthogonality, the two-dimensional discrete wavelet transforms and wavelet packets. The fourth chapter is dedicated to wavelet transform methods in the author’s own specialty, fluid mechanics. Beginning with a definition of wavelet-based statistical measures for turbulence, the text proceeds to describe wavelet thresholding in the analysis of fluid flows. The remainder of the chapter describes wavelet analysis of engineering flows, in particular jets, wakes, turbulence and coherent structures, and geophysical flows, including atmospheric and oceanic processes. The fifth chapter describes the application of wavelet methods in various branches of engineering, including machining, materials, dynamics and information engineering. Unlike previous chapters, this (and subsequent) chapters are styled more as literature reviews that describe the findings of other authors. The areas addressed in this chapter include: the monitoring of machining processes, the monitoring of rotating machinery, dynamical systems, chaotic systems, non-destructive testing, surface characterization and data compression. The sixth chapter continues in this vein with the attention now turned to wavelets in the analysis of medical signals. Most of the chapter is devoted to the analysis of one-dimensional signals (electrocardiogram, neural waveforms, acoustic signals etc.), although there is a small section on the analysis of two-dimensional medical images. The seventh and final chapter of the book focuses on the application of wavelets in three seemingly unrelated application areas: fractals, finance and geophysics. The treatment on wavelet methods in fractals focuses on stochastic fractals with a short section on multifractals. The treatment on finance touches on the use of wavelets by other authors in studying stock prices, commodity behaviour, market dynamics and foreign exchange rates. The treatment on geophysics covers what was omitted from the fourth chapter, namely, seismology, well logging, topographic feature analysis and the analysis of climatic data. The text concludes with an assortment of other application areas which could only be mentioned in passing. Unlike most other publications in the subject, this book does not treat wavelet transforms in a mathematically rigorous manner but rather aims to explain the mechanics of the wavelet transform in a way that is easy to understand. Consequently, it serves as an excellent overview of the subject rather than as a reference text. Keeping the mathematics to a minimum and omitting cumbersome and detailed proofs from the text, the book is best-suited to those who are new to wavelets or who want an intuitive understanding of the subject. Such an audience may include graduate students in engineering and professionals and researchers in engineering and the applied sciences.

Characterizing multi-scale self-similar behavior and non-statistical properties of fluctuations in financial time series

NASA Astrophysics Data System (ADS)

Ghosh, Sayantan; Manimaran, P.; Panigrahi, Prasanta K.

2011-11-01

We make use of wavelet transform to study the multi-scale, self-similar behavior and deviations thereof, in the stock prices of large companies, belonging to different economic sectors. The stock market returns exhibit multi-fractal characteristics, with some of the companies showing deviations at small and large scales. The fact that, the wavelets belonging to the Daubechies’ (Db) basis enables one to isolate local polynomial trends of different degrees, plays the key role in isolating fluctuations at different scales. One of the primary motivations of this work is to study the emergence of the k-3 behavior [X. Gabaix, P. Gopikrishnan, V. Plerou, H. Stanley, A theory of power law distributions in financial market fluctuations, Nature 423 (2003) 267-270] of the fluctuations starting with high frequency fluctuations. We make use of Db4 and Db6 basis sets to respectively isolate local linear and quadratic trends at different scales in order to study the statistical characteristics of these financial time series. The fluctuations reveal fat tail non-Gaussian behavior, unstable periodic modulations, at finer scales, from which the characteristic k-3 power law behavior emerges at sufficiently large scales. We further identify stable periodic behavior through the continuous Morlet wavelet.

Are crude oil markets multifractal? Evidence from MF-DFA and MF-SSA perspectives

NASA Astrophysics Data System (ADS)

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.

Financial liberalization and stock market cross-correlation: MF-DCCA analysis based on Shanghai-Hong Kong Stock Connect

NASA Astrophysics Data System (ADS)

Ruan, Qingsong; Zhang, Shuhua; Lv, Dayong; Lu, Xinsheng

2018-02-01

Based on the implementation of Shanghai-Hong Kong Stock Connect in China, this paper examines the effects of financial liberalization on stock market comovement using both multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DCCA) methods. Results based on MF-DFA confirm the multifractality of Shanghai and Hong Kong stock markets, and the market efficiency of Shanghai stock market increased after the implementation of this connect program. Besides, analysis based on MF-DCCA has verified the existence of persistent cross-correlation between Shanghai and Hong Kong stock markets, and the cross-correlation gets stronger after the launch of this liberalization program. Finally, we find that fat-tail distribution is the main source of multifractality in the cross-correlations before the stock connect program, while long-range correlation contributes to the multifractality after this program.

Finite-size effect and the components of multifractality in transport economics volatility based on multifractal detrending moving average method

NASA Astrophysics Data System (ADS)

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 Fluctuation Analysis of Regional Precipitation Sequences Based on the CEEMDAN-WPT

NASA Astrophysics Data System (ADS)

Liu, Dong; Cheng, Chen; Fu, Qiang; Liu, Chunlei; Li, Mo; Faiz, Muhammad Abrar; Li, Tianxiao; Khan, Muhammad Imran; Cui, Song

2018-03-01

In this paper, the complete ensemble empirical mode decomposition with the adaptive noise (CEEMDAN) algorithm is introduced into the complexity research of precipitation systems to improve the traditional complexity measure method specific to the mode mixing of the Empirical Mode Decomposition (EMD) and incomplete decomposition of the ensemble empirical mode decomposition (EEMD). We combined the CEEMDAN with the wavelet packet transform (WPT) and multifractal detrended fluctuation analysis (MF-DFA) to create the CEEMDAN-WPT-MFDFA, and used it to measure the complexity of the monthly precipitation sequence of 12 sub-regions in Harbin, Heilongjiang Province, China. The results show that there are significant differences in the monthly precipitation complexity of each sub-region in Harbin. The complexity of the northwest area of Harbin is the lowest and its predictability is the best. The complexity and predictability of the middle and Midwest areas of Harbin are about average. The complexity of the southeast area of Harbin is higher than that of the northwest, middle, and Midwest areas of Harbin and its predictability is worse. The complexity of Shuangcheng is the highest and its predictability is the worst of all the studied sub-regions. We used terrain and human activity as factors to analyze the causes of the complexity of the local precipitation. The results showed that the correlations between the precipitation complexity and terrain are obvious, and the correlations between the precipitation complexity and human influence factors vary. The distribution of the precipitation complexity in this area may be generated by the superposition effect of human activities and natural factors such as terrain, general atmospheric circulation, land and sea location, and ocean currents. To evaluate the stability of the algorithm, the CEEMDAN-WPT-MFDFA was compared with the equal probability coarse graining LZC algorithm, fuzzy entropy, and wavelet entropy. The results show that the CEEMDAN-WPT-MFDFA was more stable than 3 contrast methods under the influence of white noise and colored noise, which proves that the CEEMDAN-WPT-MFDFA has a strong robustness under the influence of noise.

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

NASA Astrophysics Data System (ADS)

Zhou, Weijie; Dang, Yaoguo; Gu, Rongbao

2013-03-01

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

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

NASA Astrophysics Data System (ADS)

Zhu, Huijian; Zhang, Weiguo

2018-01-01

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

Magnetic resonance image segmentation using multifractal techniques

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

Coupling detrended fluctuation analysis for multiple warehouse-out behavioral sequences

NASA Astrophysics Data System (ADS)

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.

Mueller matrix approach for probing multifractality in the underlying anisotropic connective tissue

NASA Astrophysics Data System (ADS)

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.

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

PubMed Central

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

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

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

PubMed

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

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

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

PubMed Central

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

2012-01-01

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

Variations in the Parameters of Background Seismic Noise during the Preparation Stages of Strong Earthquakes in the Kamchatka Region

NASA Astrophysics Data System (ADS)

Kasimova, V. A.; Kopylova, G. N.; Lyubushin, A. A.

2018-03-01

The results of the long (2011-2016) investigation of background seismic noise (BSN) in Kamchatka by the method suggested by Doct. Sci. (Phys.-Math.) A.A. Lyubushin with the use of the data from the network of broadband seismic stations of the Geophysical Survey of the Russian Academy of Sciences are presented. For characterizing the BSN field and its variability, continuous time series of the statistical parameters of the multifractal singularity spectra and wavelet expansion calculated from the records at each station are used. These parameters include the generalized Hurst exponent α*, singularity spectrum support width Δα, wavelet spectral exponent β, minimal normalized entropy of wavelet coefficients En, and spectral measure of their coherent behavior. The peculiarities in the spatiotemporal distribution of the BSN parameters as a probable response to the earthquakes with M w = 6.8-8.3 that occurred in Kamchatka in 2013 and 2016 are considered. It is established that these seismic events were preceded by regular variations in the BSN parameters, which lasted for a few months and consisted in the reduction of the median and mean α*, Δα, and β values estimated over all the stations and in the increase of the En values. Based on the increase in the spectral measure of the coherent behavior of the four-variate time series of the median and mean values of the considered statistics, the effect of the enhancement of the synchronism in the joint (collective) behavior of these parameters during a certain period prior to the mantle earthquake in the Sea of Okhotsk (May 24, 2013, M w = 8.3) is diagnosed. The procedures for revealing the precursory effects in the variations of the BSN parameters are described and the examples of these effects are presented.

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

NASA Astrophysics Data System (ADS)

Laib, Mohamed; Telesca, Luciano; Kanevski, Mikhail

2018-03-01

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

Quantifying two-dimensional nonstationary signal with power-law correlations by detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Fan, Qingju; Wu, Yonghong

2015-08-01

In this paper, we develop a new method for the multifractal characterization of two-dimensional nonstationary signal, which is based on the detrended fluctuation analysis (DFA). By applying to two artificially generated signals of two-component ARFIMA process and binomial multifractal model, we show that the new method can reliably determine the multifractal scaling behavior of two-dimensional signal. We also illustrate the applications of this method in finance and physiology. The analyzing results exhibit that the two-dimensional signals under investigation are power-law correlations, and the electricity market consists of electricity price and trading volume is multifractal, while the two-dimensional EEG signal in sleep recorded for a single patient is weak multifractal. The new method based on the detrended fluctuation analysis may add diagnostic power to existing statistical methods.

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

NASA Technical Reports Server (NTRS)

Wiscombe, W.

1999-01-01

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

Multifractal Value at Risk model

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

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

NASA Astrophysics Data System (ADS)

Wei, Yu; Chen, Wang; Lin, Yu

2013-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Multifractal Fluctuations of Jiuzhaigou Tourists Before and after Wenchuan Earthquake

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Cross-correlation detection and analysis for California's electricity market based on analogous multifractal analysis

NASA Astrophysics Data System (ADS)

Wang, Fang; Liao, Gui-ping; Li, Jian-hui; Zou, Rui-biao; Shi, Wen

2013-03-01

A novel method, which we called the analogous multifractal cross-correlation analysis, is proposed in this paper to study the multifractal behavior in the power-law cross-correlation between price and load in California electricity market. In addition, a statistic ρAMF -XA, which we call the analogous multifractal cross-correlation coefficient, is defined to test whether the cross-correlation between two given signals is genuine or not. Our analysis finds that both the price and load time series in California electricity market express multifractal nature. While, as indicated by the ρAMF -XA statistical test, there is a huge difference in the cross-correlation behavior between the years 1999 and 2000 in California electricity markets.

Cross-correlation detection and analysis for California's electricity market based on analogous multifractal analysis.

PubMed

Wang, Fang; Liao, Gui-ping; Li, Jian-hui; Zou, Rui-biao; Shi, Wen

2013-03-01

A novel method, which we called the analogous multifractal cross-correlation analysis, is proposed in this paper to study the multifractal behavior in the power-law cross-correlation between price and load in California electricity market. In addition, a statistic ρAMF-XA, which we call the analogous multifractal cross-correlation coefficient, is defined to test whether the cross-correlation between two given signals is genuine or not. Our analysis finds that both the price and load time series in California electricity market express multifractal nature. While, as indicated by the ρAMF-XA statistical test, there is a huge difference in the cross-correlation behavior between the years 1999 and 2000 in California electricity markets.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Investigation of multifractality in the Brazilian stock market

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Super-Resolution Reconstruction of Remote Sensing Images Using Multifractal Analysis

PubMed Central

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

2009-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Automatic lithofacies segmentation from well-logs data. A comparative study between the Self-Organizing Map (SOM) and Walsh transform

NASA Astrophysics Data System (ADS)

Aliouane, Leila; Ouadfeul, Sid-Ali; Rabhi, Abdessalem; Rouina, Fouzi; Benaissa, Zahia; Boudella, Amar

2013-04-01

The main goal of this work is to realize a comparison between two lithofacies segmentation techniques of reservoir interval. The first one is based on the Kohonen's Self-Organizing Map neural network machine. The second technique is based on the Walsh transform decomposition. Application to real well-logs data of two boreholes located in the Algerian Sahara shows that the Self-organizing map is able to provide more lithological details that the obtained lithofacies model given by the Walsh decomposition. Keywords: Comparison, Lithofacies, SOM, Walsh References: 1)Aliouane, L., Ouadfeul, S., Boudella, A., 2011, Fractal analysis based on the continuous wavelet transform and lithofacies classification from well-logs data using the self-organizing map neural network, Arabian Journal of geosciences, doi: 10.1007/s12517-011-0459-4 2) Aliouane, L., Ouadfeul, S., Djarfour, N., Boudella, A., 2012, Petrophysical Parameters Estimation from Well-Logs Data Using Multilayer Perceptron and Radial Basis Function Neural Networks, Lecture Notes in Computer Science Volume 7667, 2012, pp 730-736, doi : 10.1007/978-3-642-34500-5_86 3)Ouadfeul, S. and Aliouane., L., 2011, Multifractal analysis revisited by the continuous wavelet transform applied in lithofacies segmentation from well-logs data, International journal of applied physics and mathematics, Vol01 N01. 4) Ouadfeul, S., Aliouane, L., 2012, Lithofacies Classification Using the Multilayer Perceptron and the Self-organizing Neural Networks, Lecture Notes in Computer Science Volume 7667, 2012, pp 737-744, doi : 10.1007/978-3-642-34500-5_87 5) Weisstein, Eric W. "Fast Walsh Transform." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/FastWalshTransform.html

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

Stochastic multifractal forecasts: from theory to applications in radar meteorology

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Decomposing Multifractal Crossovers

PubMed Central

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2011-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-11-01

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

Multifractal analysis of mobile social networks

NASA Astrophysics Data System (ADS)

Zheng, Wei; Zhang, Zifeng; Deng, Yufan

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

Karaca, Yeliz; Cattani, Carlo

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

The human genome: a multifractal analysis

PubMed Central

2011-01-01

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

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

PubMed

Marri, Kiran; Swaminathan, Ramakrishnan

2016-06-23

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

Multifractal Omori law for earthquake triggering: new tests on the California, Japan and worldwide catalogues

NASA Astrophysics Data System (ADS)

Ouillon, G.; Sornette, D.; Ribeiro, E.

2009-07-01

The Multifractal Stress-Activated model is a statistical model of triggered seismicity based on mechanical and thermodynamic principles. It predicts that, above a triggering magnitude cut-off M0, the exponent p of the Omori law for the time decay of the rate of aftershocks is a linear increasing function p(M) = a0M + b0 of the main shock magnitude M. We previously reported empirical support for this prediction, using the Southern California Earthquake Center (SCEC) catalogue. Here, we confirm this observation using an updated, longer version of the same catalogue, as well as new methods to estimate p. One of this methods is the newly defined Scaling Function Analysis (SFA), adapted from the wavelet transform. This method is able to measure a mathematical singularity (hence a p-value), erasing the possible regular part of a time-series. The SFA also proves particularly efficient to reveal the coexistence and superposition of several types of relaxation laws (typical Omori sequences and short-lived swarms sequences) which can be mixed within the same catalogue. Another new method consists in monitoring the largest aftershock magnitude observed in successive time intervals, and thus shortcuts the problem of missing events with small magnitudes in aftershock catalogues. The same methods are used on data from the worldwide Harvard Centroid Moment Tensor (CMT) catalogue and show results compatible with those of Southern California. For the Japan Meteorological Agency (JMA) catalogue, we still observe a linear dependence of p on M, but with a smaller slope. The SFA shows however that results for this catalogue may be biased by numerous swarm sequences, despite our efforts to remove them before the analysis.

Multifractal analysis of white matter structural changes on 3D magnetic resonance imaging between normal aging and early Alzheimer’s disease

NASA Astrophysics Data System (ADS)

Ni, Huang-Jing; Zhou, Lu-Ping; Zeng, Peng; Huang, Xiao-Lin; Liu, Hong-Xing; Ning, Xin-Bao

2015-07-01

Applications of multifractal analysis to white matter structure changes on magnetic resonance imaging (MRI) have recently received increasing attentions. Although some progresses have been made, there is no evident study on applying multifractal analysis to evaluate the white matter structural changes on MRI for Alzheimer’s disease (AD) research. In this paper, to explore multifractal analysis of white matter structural changes on 3D MRI volumes between normal aging and early AD, we not only extend the traditional box-counting multifractal analysis (BCMA) into the 3D case, but also propose a modified integer ratio based BCMA (IRBCMA) algorithm to compensate for the rigid division rule in BCMA. We verify multifractal characteristics in 3D white matter MRI volumes. In addition to the previously well studied multifractal feature, Δα, we also demonstrated Δf as an alternative and effective multifractal feature to distinguish NC from AD subjects. Both Δα and Δf are found to have strong positive correlation with the clinical MMSE scores with statistical significance. Moreover, the proposed IRBCMA can be an alternative and more accurate algorithm for 3D volume analysis. Our findings highlight the potential usefulness of multifractal analysis, which may contribute to clarify some aspects of the etiology of AD through detection of structural changes in white matter. Project supported by the National Natural Science Foundation of China (Grant No. 61271079), the Vice Chancellor Research Grant in University of Wollongong, and the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

PubMed Central

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

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

Ruan, Qingsong; Yang, Bingchan; Ma, Guofeng

2017-02-01

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

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

PubMed Central

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

2016-01-01

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

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

PubMed

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

2016-01-01

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

Mammographic evidence of microenvironment changes in tumorous breasts.

PubMed

Marin, Zach; Batchelder, Kendra A; Toner, Brian C; Guimond, Lyne; Gerasimova-Chechkina, Evgeniya; Harrow, Amy R; Arneodo, Alain; Khalil, Andre

2017-04-01

The microenvironment of breast tumors plays a critical role in tumorigenesis. As long as the structural integrity of the microenvironment is upheld, the tumor is suppressed. If tissue structure is lost through disruptions in the normal cell cycle, the microenvironment may act as a tumor promoter. Therefore, the properties that distinguish between healthy and tumorous tissues may not be solely in the tumor characteristics but rather in surrounding non-tumor tissue. The goal of this paper was to show preliminary evidence that tissue disruption and loss of homeostasis in breast tissue microenvironment and breast bilateral asymmetry can be quantitatively and objectively assessed from mammography via a localized, wavelet-based analysis of the whole breast. A wavelet-based multifractal formalism called the 2D Wavelet Transform Modulus Maxima (WTMM) method was used to quantitate density fluctuations from mammographic breast tissue via the Hurst exponent (H). Each entire mammogram was cut in hundreds of 360 × 360 pixel subregions in a gridding scheme of overlapping sliding windows, with each window boundary separated by 32 pixels. The 2D WTMM method was applied to each subregion individually. A data mining approach was set up to determine which metrics best discriminated between normal vs. cancer cases. These same metrics were then used, without modification, to discriminate between normal vs. benign and benign vs. cancer cases. The density fluctuations in healthy mammographic breast tissue are either monofractal anti-correlated (H < 1/2) for fatty tissue or monofractal long-range correlated (H>1/2) for dense tissue. However, tissue regions with H~1/2, as well as left vs. right breast asymetries, were found preferably in tumorous (benign or cancer) breasts vs. normal breasts, as quantified via a combination metric yielding a P-value ~ 0.0006. No metric considered showed significant differences between cancer vs. benign breasts. Since mammographic tissue regions associated with uncorrelated (H~1/2) density fluctuations were predominantly in tumorous breasts, and since the underlying physical processes associated with a H~1/2 signature are those of randomness, lack of spatial correlation, and free diffusion, it is hypothesized that this signature is also associated with tissue disruption and loss of tissue homeostasis. © 2017 American Association of Physicists in Medicine.

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

NASA Astrophysics Data System (ADS)

Chen, Shu-Peng; He, Ling-Yun

2010-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-02-01

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

Scaling and Multifractality in Road Accidental Distances

NASA Astrophysics Data System (ADS)

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

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

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

NASA Astrophysics Data System (ADS)

Gu, Rongbao; Chen, Hongtao; Wang, Yudong

2010-07-01

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

Multifractal cross-correlations between crude oil and tanker freight rate

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Multifractal vector fields and stochastic Clifford algebra.

PubMed

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2015-12-01

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

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

NASA Astrophysics Data System (ADS)

Yang, Liansheng; Zhu, Yingming; Wang, Yudong

2016-06-01

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

Dynamic Singularity Spectrum Distribution of Sea Clutter

NASA Astrophysics Data System (ADS)

Xiong, Gang; Yu, Wenxian; Zhang, Shuning

2015-12-01

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

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

PubMed

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

2009-03-13

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

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

NASA Astrophysics Data System (ADS)

Lin, D. C.; Sharif, A.

2010-06-01

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

Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates

NASA Astrophysics Data System (ADS)

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

2001-12-01

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

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

NASA Astrophysics Data System (ADS)

Kadum, Hawwa; Ali, Naseem; Cal, Raúl

2016-11-01

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

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

NASA Astrophysics Data System (ADS)

Melgarejo, Miguel; Obregon, Nelson

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

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

NASA Astrophysics Data System (ADS)

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

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

Changes in multifractal properties for stable angina pectoris

NASA Astrophysics Data System (ADS)

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

2005-12-01

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

Multifractal texture estimation for detection and segmentation of brain tumors.

PubMed

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

2013-11-01

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

Multifractal Texture Estimation for Detection and Segmentation of Brain Tumors

PubMed Central

Islam, Atiq; Reza, Syed M. S.

2016-01-01

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

Complexity measures of music

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

Zhuang, Xiaoyang; Wei, Yu; Ma, Feng

2015-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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

PubMed

Czechowski, Zbigniew; Lovallo, Michele; Telesca, Luciano

2016-02-01

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

Anti-correlation and multifractal features of Spain electricity spot market

NASA Astrophysics Data System (ADS)

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

2007-07-01

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

MULTIFRACTAL STRUCTURES DETECTED BY VOYAGER 1 AT THE HELIOSPHERIC BOUNDARIES

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

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

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

Passive microrheology of normal and cancer cells after ML7 treatment by atomic force microscopy

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

Lyapunova, Elena, E-mail: lyapunova@icmm.ru; Ural Federal University, Kuibyishev Str. 48, Ekaterinburg, 620000; Nikituk, Alexander, E-mail: nas@icmm.ru

Mechanical properties of living cancer and normal thyroidal cells were investigated by atomic force microscopy (AFM). Cell mechanics was compared before and after treatment with ML7, which is known to reduce myosin activity and induce softening of cell structures. We recorded force curves with extended dwell time of 6 seconds in contact at maximum forces from 500 pN to 1 nN. Data were analyzed within different frameworks: Hertz fit was applied in order to evaluate differences in Young’s moduli among cell types and conditions, while the fluctuations of the cantilever in contact with cells were analyzed with both conventional algorithmsmore » (probability density function and power spectral density) and multifractal detrended fluctuation analysis (MF-DFA). We found that cancer cells were softer than normal cells and ML7 had a substantial softening effect on normal cells, but only a marginal one on cancer cells. Moreover, we observed that all recorded signals for normal and cancer cells were monofractal with small differences between their scaling parameters. Finally, the applicability of wavelet-based methods of data analysis for the discrimination of different cell types is discussed.« less

Multifractal analysis of managed and independent float exchange rates

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

NEW SUNS IN THE COSMOS. III. MULTIFRACTAL SIGNATURE ANALYSIS

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

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

2016-11-01

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

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

NASA Astrophysics Data System (ADS)

Wang, Jun; Ning, Xinbao; Chen, Ying

2003-05-01

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

Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

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

2009-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

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

NASA Astrophysics Data System (ADS)

Wei, Yu; Wang, Yudong; Huang, Dengshi

2011-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-06-01

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

Multifractal Analysis of Asian Foreign Exchange Markets and Financial Crisis

NASA Astrophysics Data System (ADS)

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

2012-02-01

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

A multifractal analysis of Asian foreign exchange markets

NASA Astrophysics Data System (ADS)

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

2012-06-01

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

Determination of key parameters of vector multifractal vector fields

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Distinguishing cognitive state with multifractal complexity of hippocampal interspike interval sequences

PubMed Central

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

2015-01-01

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

Enhancing seismic P phase arrival picking based on wavelet denoising and kurtosis picker

NASA Astrophysics Data System (ADS)

Shang, Xueyi; Li, Xibing; Weng, Lei

2018-01-01

P phase arrival picking of weak signals is still challenging in seismology. A wavelet denoising is proposed to enhance seismic P phase arrival picking, and the kurtosis picker is applied on the wavelet-denoised signal to identify P phase arrival. It has been called the WD-K picker. The WD-K picker, which is different from those traditional wavelet-based pickers on the basis of a single wavelet component or certain main wavelet components, takes full advantage of the reconstruction of main detail wavelet components and the approximate wavelet component. The proposed WD-K picker considers more wavelet components and presents a better P phase arrival feature. The WD-K picker has been evaluated on 500 micro-seismic signals recorded in the Chinese Yongshaba mine. The comparison between the WD-K pickings and manual pickings shows the good picking accuracy of the WD-K picker. Furthermore, the WD-K picking performance has been compared with the main detail wavelet component combining-based kurtosis (WDC-K) picker, the single wavelet component-based kurtosis (SW-K) picker, and certain main wavelet component-based maximum kurtosis (MMW-K) picker. The comparison has demonstrated that the WD-K picker has better picking accuracy than the other three-wavelet and kurtosis-based pickers, thus showing the enhanced ability of wavelet denoising.

Forecasting volatility of SSEC in Chinese stock market using multifractal analysis

NASA Astrophysics Data System (ADS)

Wei, Yu; Wang, Peng

2008-03-01

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

Multi-fractality in aeroelastic response as a precursor to flutter

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Complex multifractal nature in Mycobacterium tuberculosis genome

PubMed Central

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

2017-01-01

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

Complex multifractal nature in Mycobacterium tuberculosis genome

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

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

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

Submicron scale tissue multifractal anisotropy in polarized laser light scattering

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Multifractal analysis and the NYHA index

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

Asymmetric multiscale multifractal analysis of wind speed signals

NASA Astrophysics Data System (ADS)

Zhang, Xiaonei; Zeng, Ming; Meng, Qinghao

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

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

NASA Astrophysics Data System (ADS)

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

2012-10-01

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

On the multifractal effects generated by monofractal signals

NASA Astrophysics Data System (ADS)

Grech, Dariusz; Pamuła, Grzegorz

2013-12-01

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

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

NASA Astrophysics Data System (ADS)

Verrier, Sébastien; Crépon, Michel; Thiria, Sylvie

2014-09-01

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

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

ERIC Educational Resources Information Center

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

2018-01-01

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

Multifractal structures for the Russian stock market

NASA Astrophysics Data System (ADS)

Ikeda, Taro

2018-02-01

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

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

PubMed

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

2017-07-01

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

Multi-fractal detrended texture feature for brain tumor classification

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Multifractal analysis of heartbeat dynamics during meditation training

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

Detrending moving average algorithm for multifractals

NASA Astrophysics Data System (ADS)

Gu, Gao-Feng; Zhou, Wei-Xing

2010-07-01

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

Multifractal detrended fluctuation analysis of sheep livestock prices in origin

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

Price-volume multifractal analysis of the Moroccan stock market

NASA Astrophysics Data System (ADS)

El Alaoui, Marwane

2017-11-01

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

An Integrated Nonlinear Analysis library - (INA) for solar system plasma turbulence

NASA Astrophysics Data System (ADS)

Munteanu, Costel; Kovacs, Peter; Echim, Marius; Koppan, Andras

2014-05-01

We present an integrated software library dedicated to the analysis of time series recorded in space and adapted to investigate turbulence, intermittency and multifractals. The library is written in MATLAB and provides a graphical user interface (GUI) customized for the analysis of space physics data available online like: Coordinated Data Analysis Web (CDAWeb), Automated Multi Dataset Analysis system (AMDA), Planetary Science Archive (PSA), World Data Center Kyoto (WDC), Ulysses Final Archive (UFA) and Cluster Active Archive (CAA). Three main modules are already implemented in INA : the Power Spectral Density (PSD) Analysis, the Wavelet and Intemittency Analysis and the Probability Density Functions (PDF) analysis.The layered structure of the software allows the user to easily switch between different modules/methods while retaining the same time interval for the analysis. The wavelet analysis module includes algorithms to compute and analyse the PSD, the Scalogram, the Local Intermittency Measure (LIM) or the Flatness parameter. The PDF analysis module includes algorithms for computing the PDFs for a range of scales and parameters fully customizable by the user; it also computes the Flatness parameter and enables fast comparison with standard PDF profiles like, for instance, the Gaussian PDF. The library has been already tested on Cluster and Venus Express data and we will show relevant examples. Research supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 313038/STORM, and a grant of the Romanian Ministry of National Education, CNCS UEFISCDI, project number PN-II-ID PCE-2012-4-0418.

Multifractal Turbulence in the Heliosphere

NASA Astrophysics Data System (ADS)

Macek, Wieslaw M.; Wawrzaszek, Anna

2010-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Multifractal diffusion entropy analysis: Optimal bin width of probability histograms

NASA Astrophysics Data System (ADS)

Jizba, Petr; Korbel, Jan

2014-11-01

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

Multifractal Characteristics of Axisymmetric Jet Turbulence Intensity from Rans Numerical Simulation

NASA Astrophysics Data System (ADS)

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

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, A.

2005-01-01

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

Multifractal to monofractal evolution of the London street network.

PubMed

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

2015-12-01

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

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

NASA Astrophysics Data System (ADS)

Green, Elena; Hanan, William; Heffernan, Daniel

2014-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

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

PubMed

Dong, Qingli; Wang, Yong; Li, Peizhi

2017-03-01

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

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

NASA Astrophysics Data System (ADS)

Abramenko, Valentyna

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

High-performance wavelet engine

NASA Astrophysics Data System (ADS)

Taylor, Fred J.; Mellot, Jonathon D.; Strom, Erik; Koren, Iztok; Lewis, Michael P.

1993-11-01

Wavelet processing has shown great promise for a variety of image and signal processing applications. Wavelets are also among the most computationally expensive techniques in signal processing. It is demonstrated that a wavelet engine constructed with residue number system arithmetic elements offers significant advantages over commercially available wavelet accelerators based upon conventional arithmetic elements. Analysis is presented predicting the dynamic range requirements of the reported residue number system based wavelet accelerator.

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

NASA Technical Reports Server (NTRS)

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

2010-01-01

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

Dependence and risk assessment for oil prices and exchange rate portfolios: A wavelet based approach

NASA Astrophysics Data System (ADS)

Aloui, Chaker; Jammazi, Rania

2015-10-01

In this article, we propose a wavelet-based approach to accommodate the stylized facts and complex structure of financial data, caused by frequent and abrupt changes of markets and noises. Specifically, we show how the combination of both continuous and discrete wavelet transforms with traditional financial models helps improve portfolio's market risk assessment. In the empirical stage, three wavelet-based models (wavelet-EGARCH with dynamic conditional correlations, wavelet-copula, and wavelet-extreme value) are considered and applied to crude oil price and US dollar exchange rate data. Our findings show that the wavelet-based approach provides an effective and powerful tool for detecting extreme moments and improving the accuracy of VaR and Expected Shortfall estimates of oil-exchange rate portfolios after noise is removed from the original data.

Long-range memory and multifractality in gold markets

NASA Astrophysics Data System (ADS)

Mali, Provash; Mukhopadhyay, Amitabha

2015-03-01

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

Value-at-risk estimation with wavelet-based extreme value theory: Evidence from emerging markets

NASA Astrophysics Data System (ADS)

Cifter, Atilla

2011-06-01

This paper introduces wavelet-based extreme value theory (EVT) for univariate value-at-risk estimation. Wavelets and EVT are combined for volatility forecasting to estimate a hybrid model. In the first stage, wavelets are used as a threshold in generalized Pareto distribution, and in the second stage, EVT is applied with a wavelet-based threshold. This new model is applied to two major emerging stock markets: the Istanbul Stock Exchange (ISE) and the Budapest Stock Exchange (BUX). The relative performance of wavelet-based EVT is benchmarked against the Riskmetrics-EWMA, ARMA-GARCH, generalized Pareto distribution, and conditional generalized Pareto distribution models. The empirical results show that the wavelet-based extreme value theory increases predictive performance of financial forecasting according to number of violations and tail-loss tests. The superior forecasting performance of the wavelet-based EVT model is also consistent with Basel II requirements, and this new model can be used by financial institutions as well.

Wavelet based free-form deformations for nonrigid registration

NASA Astrophysics Data System (ADS)

Sun, Wei; Niessen, Wiro J.; Klein, Stefan

2014-03-01

In nonrigid registration, deformations may take place on the coarse and fine scales. For the conventional B-splines based free-form deformation (FFD) registration, these coarse- and fine-scale deformations are all represented by basis functions of a single scale. Meanwhile, wavelets have been proposed as a signal representation suitable for multi-scale problems. Wavelet analysis leads to a unique decomposition of a signal into its coarse- and fine-scale components. Potentially, this could therefore be useful for image registration. In this work, we investigate whether a wavelet-based FFD model has advantages for nonrigid image registration. We use a B-splines based wavelet, as defined by Cai and Wang.1 This wavelet is expressed as a linear combination of B-spline basis functions. Derived from the original B-spline function, this wavelet is smooth, differentiable, and compactly supported. The basis functions of this wavelet are orthogonal across scales in Sobolev space. This wavelet was previously used for registration in computer vision, in 2D optical flow problems,2 but it was not compared with the conventional B-spline FFD in medical image registration problems. An advantage of choosing this B-splines based wavelet model is that the space of allowable deformation is exactly equivalent to that of the traditional B-spline. The wavelet transformation is essentially a (linear) reparameterization of the B-spline transformation model. Experiments on 10 CT lung and 18 T1-weighted MRI brain datasets show that wavelet based registration leads to smoother deformation fields than traditional B-splines based registration, while achieving better accuracy.

Wavelet analysis techniques applied to removing varying spectroscopic background in calibration model for pear sugar content

NASA Astrophysics Data System (ADS)

Liu, Yande; Ying, Yibin; Lu, Huishan; Fu, Xiaping

2005-11-01

A new method is proposed to eliminate the varying background and noise simultaneously for multivariate calibration of Fourier transform near infrared (FT-NIR) spectral signals. An ideal spectrum signal prototype was constructed based on the FT-NIR spectrum of fruit sugar content measurement. The performances of wavelet based threshold de-noising approaches via different combinations of wavelet base functions were compared. Three families of wavelet base function (Daubechies, Symlets and Coiflets) were applied to estimate the performance of those wavelet bases and threshold selection rules by a series of experiments. The experimental results show that the best de-noising performance is reached via the combinations of Daubechies 4 or Symlet 4 wavelet base function. Based on the optimization parameter, wavelet regression models for sugar content of pear were also developed and result in a smaller prediction error than a traditional Partial Least Squares Regression (PLSR) mode.

Wavelet transforms with discrete-time continuous-dilation wavelets

NASA Astrophysics Data System (ADS)

Zhao, Wei; Rao, Raghuveer M.

1999-03-01

Wavelet constructions and transforms have been confined principally to the continuous-time domain. Even the discrete wavelet transform implemented through multirate filter banks is based on continuous-time wavelet functions that provide orthogonal or biorthogonal decompositions. This paper provides a novel wavelet transform construction based on the definition of discrete-time wavelets that can undergo continuous parameter dilations. The result is a transformation that has the advantage of discrete-time or digital implementation while circumventing the problem of inadequate scaling resolution seen with conventional dyadic or M-channel constructions. Examples of constructing such wavelets are presented.

Long memory and multifractality: A joint test

NASA Astrophysics Data System (ADS)

Goddard, John; Onali, Enrico

2016-06-01

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

Hydrothermal mineralising systems as critical systems

NASA Astrophysics Data System (ADS)

Hobbs, Bruce

2015-04-01

Hydrothermal mineralising systems as critical systems. Bruce E Hobbs1,2, Alison Ord1 and Mark A. Munro1. 1. Centre for Exploration Targeting, The University of Western Australia, M006, 35 Stirling Highway, Crawley, WA 6009, Australia. 2. CSIRO Earth and Resource Engineering, Bentley, WA, Australia Hydrothermal mineralising systems are presented as large, open chemical reactors held far from equilibrium during their life-time by the influx of heat, fluid and dissolved chemical species. As such they are nonlinear dynamical systems and need to be analysed using the tools that have been developed for such systems. Hydrothermal systems undergo a number of transitions during their evolution and this paper focuses on methods for characterising these transitions in a quantitative manner and establishing whether they resemble first or second (critical) phase transitions or whether they have some other kind of nature. Critical phase transitions are characterised by long range correlations for some parameter characteristic of the system, power-law probability distributions so that there is no characteristic length scale and a high sensitivity to perturbations; as one approaches criticality, characteristic parameters for the system scale in a power law manner with distance from the critical point. The transitions undergone in mineralised hydrothermal systems are: (i) widespread, non-localised mineral alteration involving exothermic mineral reactions that produce hydrous silicate phases, carbonates and iron-oxides, (ii) strongly localised veining, brecciation and/or stock-work formation, (iii) a series of endothermic mineral reactions involving the formation of non-hydrous silicates, sulphides and metals such as gold, (iv) multiple repetitions of transitions (ii) and (iii). We have quantified aspects of these transitions in gold deposits from the Yilgarn craton of Western Australia using wavelet transforms. This technique is convenient and fast. It enables one to establish if the transition is multifractal (and if so, quantify the multifractal spectrum) and determine the scale dependence of long range correlations or anti-correlations. The availability of long drill holes with detailed chemical analyses and mineral abundances derived from hyperspectral data enables individual ore bodies to be characterised in a quantitative manner and constraints placed on whether the various transition are possibly critical or of some other form. We also present some simple nonlinear models that produce the multifractal character and correlation scaling relations observed in these data sets,

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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

NASA Astrophysics Data System (ADS)

Ruan, Qingsong; Yang, Bingchan

2017-10-01

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

Graphic analysis and multifractal on percolation-based return interval series

NASA Astrophysics Data System (ADS)

Pei, A. Q.; Wang, J.

2015-05-01

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

Multifractal detrended cross-correlation analysis for two nonstationary signals.

PubMed

Zhou, Wei-Xing

2008-06-01

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

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

NASA Astrophysics Data System (ADS)

Lu, Xinsheng; Sun, Xinxin; Ge, Jintian

2017-05-01

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

PULSAR SIGNAL DENOISING METHOD BASED ON LAPLACE DISTRIBUTION IN NO-SUBSAMPLING WAVELET PACKET DOMAIN

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

Wenbo, Wang; Yanchao, Zhao; Xiangli, Wang

2016-11-01

In order to improve the denoising effect of the pulsar signal, a new denoising method is proposed in the no-subsampling wavelet packet domain based on the local Laplace prior model. First, we count the true noise-free pulsar signal’s wavelet packet coefficient distribution characteristics and construct the true signal wavelet packet coefficients’ Laplace probability density function model. Then, we estimate the denosied wavelet packet coefficients by using the noisy pulsar wavelet coefficients based on maximum a posteriori criteria. Finally, we obtain the denoisied pulsar signal through no-subsampling wavelet packet reconstruction of the estimated coefficients. The experimental results show that the proposed method performs better when calculating the pulsar time of arrival than the translation-invariant wavelet denoising method.

Statistical classifiers on multifractal parameters for optical diagnosis of cervical cancer

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

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

Long-range correlation in cosmic microwave background radiation.

PubMed

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

2011-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

PubMed

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

2014-10-01

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

Wavelet-based 3-D inversion for frequency-domain airborne EM data

NASA Astrophysics Data System (ADS)

Liu, Yunhe; Farquharson, Colin G.; Yin, Changchun; Baranwal, Vikas C.

2018-04-01

In this paper, we propose a new wavelet-based 3-D inversion method for frequency-domain airborne electromagnetic (FDAEM) data. Instead of inverting the model in the space domain using a smoothing constraint, this new method recovers the model in the wavelet domain based on a sparsity constraint. In the wavelet domain, the model is represented by two types of coefficients, which contain both large- and fine-scale informations of the model, meaning the wavelet-domain inversion has inherent multiresolution. In order to accomplish a sparsity constraint, we minimize an L1-norm measure in the wavelet domain that mostly gives a sparse solution. The final inversion system is solved by an iteratively reweighted least-squares method. We investigate different orders of Daubechies wavelets to accomplish our inversion algorithm, and test them on synthetic frequency-domain AEM data set. The results show that higher order wavelets having larger vanishing moments and regularity can deliver a more stable inversion process and give better local resolution, while the lower order wavelets are simpler and less smooth, and thus capable of recovering sharp discontinuities if the model is simple. At last, we test this new inversion algorithm on a frequency-domain helicopter EM (HEM) field data set acquired in Byneset, Norway. Wavelet-based 3-D inversion of HEM data is compared to L2-norm-based 3-D inversion's result to further investigate the features of the new method.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Optimal wavelets for biomedical signal compression.

PubMed

Nielsen, Mogens; Kamavuako, Ernest Nlandu; Andersen, Michael Midtgaard; Lucas, Marie-Françoise; Farina, Dario

2006-07-01

Signal compression is gaining importance in biomedical engineering due to the potential applications in telemedicine. In this work, we propose a novel scheme of signal compression based on signal-dependent wavelets. To adapt the mother wavelet to the signal for the purpose of compression, it is necessary to define (1) a family of wavelets that depend on a set of parameters and (2) a quality criterion for wavelet selection (i.e., wavelet parameter optimization). We propose the use of an unconstrained parameterization of the wavelet for wavelet optimization. A natural performance criterion for compression is the minimization of the signal distortion rate given the desired compression rate. For coding the wavelet coefficients, we adopted the embedded zerotree wavelet coding algorithm, although any coding scheme may be used with the proposed wavelet optimization. As a representative example of application, the coding/encoding scheme was applied to surface electromyographic signals recorded from ten subjects. The distortion rate strongly depended on the mother wavelet (for example, for 50% compression rate, optimal wavelet, mean+/-SD, 5.46+/-1.01%; worst wavelet 12.76+/-2.73%). Thus, optimization significantly improved performance with respect to previous approaches based on classic wavelets. The algorithm can be applied to any signal type since the optimal wavelet is selected on a signal-by-signal basis. Examples of application to ECG and EEG signals are also reported.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Multifractal Characterization of Geologic Noise for Improved UXO Detection and Discrimination

DTIC Science & Technology

2008-03-01

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

Multifractality and Network Analysis of Phase Transition

PubMed Central

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Manimaran, P.; Narayana, A. C.

2018-07-01

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

Multifractal detrended cross-correlation analysis in the MENA area

NASA Astrophysics Data System (ADS)

El Alaoui, Marwane; Benbachir, Saâd

2013-12-01

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

Iterated oversampled filter banks and wavelet frames

NASA Astrophysics Data System (ADS)

Selesnick, Ivan W.; Sendur, Levent

2000-12-01

This paper takes up the design of wavelet tight frames that are analogous to Daubechies orthonormal wavelets - that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case. The oversampled dyadic DWT considered in this paper is based on a single scaling function and tow distinct wavelets. Having more wavelets than necessary gives a closer spacing between adjacent wavelets within the same scale. As a result, the transform is nearly shift-invariant, and can be used to improve denoising. Because the associated time- frequency lattice preserves the dyadic structure of the critically sampled DWT it can be used with tree-based denoising algorithms that exploit parent-child correlation.

Multifractal Behaviors in Foreign Exchange Markets

NASA Astrophysics Data System (ADS)

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

2008-03-01

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

Fractal and multifractal analyses of bipartite networks

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Fractal and multifractal analyses of bipartite networks.

PubMed

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

2017-03-31

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

Fractal and multifractal analyses of bipartite networks

PubMed Central

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

EEG analysis using wavelet-based information tools.

PubMed

Rosso, O A; Martin, M T; Figliola, A; Keller, K; Plastino, A

2006-06-15

Wavelet-based informational tools for quantitative electroencephalogram (EEG) record analysis are reviewed. Relative wavelet energies, wavelet entropies and wavelet statistical complexities are used in the characterization of scalp EEG records corresponding to secondary generalized tonic-clonic epileptic seizures. In particular, we show that the epileptic recruitment rhythm observed during seizure development is well described in terms of the relative wavelet energies. In addition, during the concomitant time-period the entropy diminishes while complexity grows. This is construed as evidence supporting the conjecture that an epileptic focus, for this kind of seizures, triggers a self-organized brain state characterized by both order and maximal complexity.

Approximated maximum likelihood estimation in multifractal random walks

NASA Astrophysics Data System (ADS)

Løvsletten, O.; Rypdal, M.

2012-04-01

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

Strict parabolicity of the multifractal spectrum at the Anderson transition

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

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

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

Applying wavelet transforms to analyse aircraft-measured turbulence and turbulent fluxes in the atmospheric boundary layer over eastern Siberia

NASA Astrophysics Data System (ADS)

Strunin, M. A.; Hiyama, T.

2004-11-01

The wavelet spectral method was applied to aircraft-based measurements of atmospheric turbulence obtained during joint Russian-Japanese research on the atmospheric boundary layer near Yakutsk (eastern Siberia) in April-June 2000. Practical ways to apply Fourier and wavelet methods for aircraft-based turbulence data are described. Comparisons between Fourier and wavelet transform results are shown and they demonstrate, in conjunction with theoretical and experimental restrictions, that the Fourier transform method is not useful for studying non-homogeneous turbulence. The wavelet method is free from many disadvantages of Fourier analysis and can yield more informative results. Comparison of Fourier and Morlet wavelet spectra showed good agreement at high frequencies (small scales). The quality of the wavelet transform and corresponding software was estimated by comparing the original data with restored data constructed with an inverse wavelet transform. A Haar wavelet basis was inappropriate for the turbulence data; the mother wavelet function recommended in this study is the Morlet wavelet. Good agreement was also shown between variances and covariances estimated with different mathematical techniques, i.e. through non-orthogonal wavelet spectra and through eddy correlation methods.

A new wavelet transform to sparsely represent cortical current densities for EEG/MEG inverse problems.

PubMed

Liao, Ke; Zhu, Min; Ding, Lei

2013-08-01

The present study investigated the use of transform sparseness of cortical current density on human brain surface to improve electroencephalography/magnetoencephalography (EEG/MEG) inverse solutions. Transform sparseness was assessed by evaluating compressibility of cortical current densities in transform domains. To do that, a structure compression method from computer graphics was first adopted to compress cortical surface structure, either regular or irregular, into hierarchical multi-resolution meshes. Then, a new face-based wavelet method based on generated multi-resolution meshes was proposed to compress current density functions defined on cortical surfaces. Twelve cortical surface models were built by three EEG/MEG softwares and their structural compressibility was evaluated and compared by the proposed method. Monte Carlo simulations were implemented to evaluate the performance of the proposed wavelet method in compressing various cortical current density distributions as compared to other two available vertex-based wavelet methods. The present results indicate that the face-based wavelet method can achieve higher transform sparseness than vertex-based wavelet methods. Furthermore, basis functions from the face-based wavelet method have lower coherence against typical EEG and MEG measurement systems than vertex-based wavelet methods. Both high transform sparseness and low coherent measurements suggest that the proposed face-based wavelet method can improve the performance of L1-norm regularized EEG/MEG inverse solutions, which was further demonstrated in simulations and experimental setups using MEG data. Thus, this new transform on complicated cortical structure is promising to significantly advance EEG/MEG inverse source imaging technologies. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Fault Diagnosis for Micro-Gas Turbine Engine Sensors via Wavelet Entropy

PubMed Central

Yu, Bing; Liu, Dongdong; Zhang, Tianhong

2011-01-01

Sensor fault diagnosis is necessary to ensure the normal operation of a gas turbine system. However, the existing methods require too many resources and this need can’t be satisfied in some occasions. Since the sensor readings are directly affected by sensor state, sensor fault diagnosis can be performed by extracting features of the measured signals. This paper proposes a novel fault diagnosis method for sensors based on wavelet entropy. Based on the wavelet theory, wavelet decomposition is utilized to decompose the signal in different scales. Then the instantaneous wavelet energy entropy (IWEE) and instantaneous wavelet singular entropy (IWSE) are defined based on the previous wavelet entropy theory. Subsequently, a fault diagnosis method for gas turbine sensors is proposed based on the results of a numerically simulated example. Then, experiments on this method are carried out on a real micro gas turbine engine. In the experiment, four types of faults with different magnitudes are presented. The experimental results show that the proposed method for sensor fault diagnosis is efficient. PMID:22163734

Fault diagnosis for micro-gas turbine engine sensors via wavelet entropy.

PubMed

Yu, Bing; Liu, Dongdong; Zhang, Tianhong

2011-01-01

Sensor fault diagnosis is necessary to ensure the normal operation of a gas turbine system. However, the existing methods require too many resources and this need can't be satisfied in some occasions. Since the sensor readings are directly affected by sensor state, sensor fault diagnosis can be performed by extracting features of the measured signals. This paper proposes a novel fault diagnosis method for sensors based on wavelet entropy. Based on the wavelet theory, wavelet decomposition is utilized to decompose the signal in different scales. Then the instantaneous wavelet energy entropy (IWEE) and instantaneous wavelet singular entropy (IWSE) are defined based on the previous wavelet entropy theory. Subsequently, a fault diagnosis method for gas turbine sensors is proposed based on the results of a numerically simulated example. Then, experiments on this method are carried out on a real micro gas turbine engine. In the experiment, four types of faults with different magnitudes are presented. The experimental results show that the proposed method for sensor fault diagnosis is efficient.

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

USGS Publications Warehouse

Bultman, Mark W.

2013-01-01

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

Testing for multifractality of Islamic stock markets

NASA Astrophysics Data System (ADS)

Saâdaoui, Foued

2018-04-01

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

Introduction to multifractal detrended fluctuation analysis in matlab.

PubMed

Ihlen, Espen A F

2012-01-01

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

Introduction to Multifractal Detrended Fluctuation Analysis in Matlab

PubMed Central

Ihlen, Espen A. F.

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

Hasan, Rashid; Mohammed Salim, M.

2017-05-01

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

Multifractal analysis of Moroccan family business stock returns

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2017-11-01

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

Daily water level forecasting using wavelet decomposition and artificial intelligence techniques

NASA Astrophysics Data System (ADS)

Seo, Youngmin; Kim, Sungwon; Kisi, Ozgur; Singh, Vijay P.

2015-01-01

Reliable water level forecasting for reservoir inflow is essential for reservoir operation. The objective of this paper is to develop and apply two hybrid models for daily water level forecasting and investigate their accuracy. These two hybrid models are wavelet-based artificial neural network (WANN) and wavelet-based adaptive neuro-fuzzy inference system (WANFIS). Wavelet decomposition is employed to decompose an input time series into approximation and detail components. The decomposed time series are used as inputs to artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS) for WANN and WANFIS models, respectively. Based on statistical performance indexes, the WANN and WANFIS models are found to produce better efficiency than the ANN and ANFIS models. WANFIS7-sym10 yields the best performance among all other models. It is found that wavelet decomposition improves the accuracy of ANN and ANFIS. This study evaluates the accuracy of the WANN and WANFIS models for different mother wavelets, including Daubechies, Symmlet and Coiflet wavelets. It is found that the model performance is dependent on input sets and mother wavelets, and the wavelet decomposition using mother wavelet, db10, can further improve the efficiency of ANN and ANFIS models. Results obtained from this study indicate that the conjunction of wavelet decomposition and artificial intelligence models can be a useful tool for accurate forecasting daily water level and can yield better efficiency than the conventional forecasting models.

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

PubMed Central

Bhaduri, Anirban; Ghosh, Dipak

2016-01-01

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

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

PubMed

Bhaduri, Anirban; Ghosh, Dipak

2016-01-01

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

Multifractality of laser beam spatial intensity in a turbulent medium

NASA Astrophysics Data System (ADS)

Barille, Régis; Lapenna, Paolo

2006-05-01

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

A comparative analysis of alternative approaches for quantifying nonlinear dynamics in cardiovascular system.

PubMed

Chen, Yun; Yang, Hui

2013-01-01

Heart rate variability (HRV) analysis has emerged as an important research topic to evaluate autonomic cardiac function. However, traditional time and frequency-domain analysis characterizes and quantify only linear and stationary phenomena. In the present investigation, we made a comparative analysis of three alternative approaches (i.e., wavelet multifractal analysis, Lyapunov exponents and multiscale entropy analysis) for quantifying nonlinear dynamics in heart rate time series. Note that these extracted nonlinear features provide information about nonlinear scaling behaviors and the complexity of cardiac systems. To evaluate the performance, we used 24-hour HRV recordings from 54 healthy subjects and 29 heart failure patients, available in PhysioNet. Three nonlinear methods are evaluated not only individually but also in combination using three classification algorithms, i.e., linear discriminate analysis, quadratic discriminate analysis and k-nearest neighbors. Experimental results show that three nonlinear methods capture nonlinear dynamics from different perspectives and the combined feature set achieves the best performance, i.e., sensitivity 97.7% and specificity 91.5%. Collectively, nonlinear HRV features are shown to have the promise to identify the disorders in autonomic cardiovascular function.

Segmentation-based wavelet transform for still-image compression

NASA Astrophysics Data System (ADS)

Mozelle, Gerard; Seghier, Abdellatif; Preteux, Francoise J.

1996-10-01

In order to address simultaneously the two functionalities, content-based scalability required by MPEG-4, we introduce a segmentation-based wavelet transform (SBWT). SBWT takes into account both the mathematical properties of multiresolution analysis and the flexibility of region-based approaches for image compression. The associated methodology has two stages: 1) image segmentation into convex and polygonal regions; 2) 2D-wavelet transform of the signal corresponding to each region. In this paper, we have mathematically studied a method for constructing a multiresolution analysis (VjOmega)j (epsilon) N adapted to a polygonal region which provides an adaptive region-based filtering. The explicit construction of scaling functions, pre-wavelets and orthonormal wavelets bases defined on a polygon is carried out by using scaling functions is established by using the theory of Toeplitz operators. The corresponding expression can be interpreted as a location property which allow defining interior and boundary scaling functions. Concerning orthonormal wavelets and pre-wavelets, a similar expansion is obtained by taking advantage of the properties of the orthogonal projector P(V(j(Omega )) perpendicular from the space Vj(Omega ) + 1 onto the space (Vj(Omega )) perpendicular. Finally the mathematical results provide a simple and fast algorithm adapted to polygonal regions.

Statistical properties of the yuan exchange rate index

NASA Astrophysics Data System (ADS)

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

2012-06-01

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

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

NASA Astrophysics Data System (ADS)

Lamy, Hervé; Echim, Marius; Chang, Tom

2014-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-02-01

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

A wavelet-based Gaussian method for energy dispersive X-ray fluorescence spectrum.

PubMed

Liu, Pan; Deng, Xiaoyan; Tang, Xin; Shen, Shijian

2017-05-01

This paper presents a wavelet-based Gaussian method (WGM) for the peak intensity estimation of energy dispersive X-ray fluorescence (EDXRF). The relationship between the parameters of Gaussian curve and the wavelet coefficients of Gaussian peak point is firstly established based on the Mexican hat wavelet. It is found that the Gaussian parameters can be accurately calculated by any two wavelet coefficients at the peak point which has to be known. This fact leads to a local Gaussian estimation method for spectral peaks, which estimates the Gaussian parameters based on the detail wavelet coefficients of Gaussian peak point. The proposed method is tested via simulated and measured spectra from an energy X-ray spectrometer, and compared with some existing methods. The results prove that the proposed method can directly estimate the peak intensity of EDXRF free from the background information, and also effectively distinguish overlap peaks in EDXRF spectrum.

Multifractal spectra in shear flows

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Multifractality and value-at-risk forecasting of exchange rates

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

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

PubMed

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

2009-01-01

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

Multifractals of investor behavior in stock market

NASA Astrophysics Data System (ADS)

Oh, Gabjin

2017-07-01

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

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

NASA Astrophysics Data System (ADS)

Lu, Yunfan; Wang, Jun; Niu, Hongli

2015-10-01

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

Multifractality as a Measure of Complexity in Solar Flare Activity

NASA Astrophysics Data System (ADS)

Sen, Asok K.

2007-03-01

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

Multiscale multifractal time irreversibility analysis of stock markets

NASA Astrophysics Data System (ADS)

Jiang, Chenguang; Shang, Pengjian; Shi, Wenbin

2016-11-01

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

Understanding the source of multifractality in financial markets

NASA Astrophysics Data System (ADS)

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

2012-09-01

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

Coupling detrended fluctuation analysis of Asian stock markets

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

Khan, Shaista; Ahmad, Shakeel

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

Dynamical Mechanism of Scaling Behaviors in Multifractal Structure

NASA Astrophysics Data System (ADS)

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

2010-03-01

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

Wavelet-based compression of pathological images for telemedicine applications

NASA Astrophysics Data System (ADS)

Chen, Chang W.; Jiang, Jianfei; Zheng, Zhiyong; Wu, Xue G.; Yu, Lun

2000-05-01

In this paper, we present the performance evaluation of wavelet-based coding techniques as applied to the compression of pathological images for application in an Internet-based telemedicine system. We first study how well suited the wavelet-based coding is as it applies to the compression of pathological images, since these images often contain fine textures that are often critical to the diagnosis of potential diseases. We compare the wavelet-based compression with the DCT-based JPEG compression in the DICOM standard for medical imaging applications. Both objective and subjective measures have been studied in the evaluation of compression performance. These studies are performed in close collaboration with expert pathologists who have conducted the evaluation of the compressed pathological images and communication engineers and information scientists who designed the proposed telemedicine system. These performance evaluations have shown that the wavelet-based coding is suitable for the compression of various pathological images and can be integrated well with the Internet-based telemedicine systems. A prototype of the proposed telemedicine system has been developed in which the wavelet-based coding is adopted for the compression to achieve bandwidth efficient transmission and therefore speed up the communications between the remote terminal and the central server of the telemedicine system.

Comparison between deterministic and statistical wavelet estimation methods through predictive deconvolution: Seismic to well tie example from the North Sea

NASA Astrophysics Data System (ADS)

de Macedo, Isadora A. S.; da Silva, Carolina B.; de Figueiredo, J. J. S.; Omoboya, Bode

2017-01-01

Wavelet estimation as well as seismic-to-well tie procedures are at the core of every seismic interpretation workflow. In this paper we perform a comparative study of wavelet estimation methods for seismic-to-well tie. Two approaches to wavelet estimation are discussed: a deterministic estimation, based on both seismic and well log data, and a statistical estimation, based on predictive deconvolution and the classical assumptions of the convolutional model, which provides a minimum-phase wavelet. Our algorithms, for both wavelet estimation methods introduce a semi-automatic approach to determine the optimum parameters of deterministic wavelet estimation and statistical wavelet estimation and, further, to estimate the optimum seismic wavelets by searching for the highest correlation coefficient between the recorded trace and the synthetic trace, when the time-depth relationship is accurate. Tests with numerical data show some qualitative conclusions, which are probably useful for seismic inversion and interpretation of field data, by comparing deterministic wavelet estimation and statistical wavelet estimation in detail, especially for field data example. The feasibility of this approach is verified on real seismic and well data from Viking Graben field, North Sea, Norway. Our results also show the influence of the washout zones on well log data on the quality of the well to seismic tie.

Analysis of normal human retinal vascular network architecture using multifractal geometry

PubMed Central

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

2017-01-01

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

Measuring efficiency of international crude oil markets: A multifractality approach

NASA Astrophysics Data System (ADS)

Niere, H. M.

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

Li, Qingchen; Cao, Guangxi; Xu, Wei

2018-01-01

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

Adjusting Wavelet-based Multiresolution Analysis Boundary Conditions for Robust Long-term Streamflow Forecasting Model

NASA Astrophysics Data System (ADS)

Maslova, I.; Ticlavilca, A. M.; McKee, M.

2012-12-01

There has been an increased interest in wavelet-based streamflow forecasting models in recent years. Often overlooked in this approach are the circularity assumptions of the wavelet transform. We propose a novel technique for minimizing the wavelet decomposition boundary condition effect to produce long-term, up to 12 months ahead, forecasts of streamflow. A simulation study is performed to evaluate the effects of different wavelet boundary rules using synthetic and real streamflow data. A hybrid wavelet-multivariate relevance vector machine model is developed for forecasting the streamflow in real-time for Yellowstone River, Uinta Basin, Utah, USA. The inputs of the model utilize only the past monthly streamflow records. They are decomposed into components formulated in terms of wavelet multiresolution analysis. It is shown that the model model accuracy can be increased by using the wavelet boundary rule introduced in this study. This long-term streamflow modeling and forecasting methodology would enable better decision-making and managing water availability risk.

The 4D hyperspherical diffusion wavelet: A new method for the detection of localized anatomical variation.

PubMed

Hosseinbor, Ameer Pasha; Kim, Won Hwa; Adluru, Nagesh; Acharya, Amit; Vorperian, Houri K; Chung, Moo K

2014-01-01

Recently, the HyperSPHARM algorithm was proposed to parameterize multiple disjoint objects in a holistic manner using the 4D hyperspherical harmonics. The HyperSPHARM coefficients are global; they cannot be used to directly infer localized variations in signal. In this paper, we present a unified wavelet framework that links Hyper-SPHARM to the diffusion wavelet transform. Specifically, we will show that the HyperSPHARM basis forms a subset of a wavelet-based multiscale representation of surface-based signals. This wavelet, termed the hyperspherical diffusion wavelet, is a consequence of the equivalence of isotropic heat diffusion smoothing and the diffusion wavelet transform on the hypersphere. Our framework allows for the statistical inference of highly localized anatomical changes, which we demonstrate in the first-ever developmental study on the hyoid bone investigating gender and age effects. We also show that the hyperspherical wavelet successfully picks up group-wise differences that are barely detectable using SPHARM.

The 4D Hyperspherical Diffusion Wavelet: A New Method for the Detection of Localized Anatomical Variation

PubMed Central

Hosseinbor, A. Pasha; Kim, Won Hwa; Adluru, Nagesh; Acharya, Amit; Vorperian, Houri K.; Chung, Moo K.

2014-01-01

Recently, the HyperSPHARM algorithm was proposed to parameterize multiple disjoint objects in a holistic manner using the 4D hyperspherical harmonics. The HyperSPHARM coefficients are global; they cannot be used to directly infer localized variations in signal. In this paper, we present a unified wavelet framework that links HyperSPHARM to the diffusion wavelet transform. Specifically, we will show that the HyperSPHARM basis forms a subset of a wavelet-based multiscale representation of surface-based signals. This wavelet, termed the hyperspherical diffusion wavelet, is a consequence of the equivalence of isotropic heat diffusion smoothing and the diffusion wavelet transform on the hypersphere. Our framework allows for the statistical inference of highly localized anatomical changes, which we demonstrate in the firstever developmental study on the hyoid bone investigating gender and age effects. We also show that the hyperspherical wavelet successfully picks up group-wise differences that are barely detectable using SPHARM. PMID:25320783

Effect of spatial averaging on multifractal properties of meteorological time series

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

EnvironmentalWaveletTool: Continuous and discrete wavelet analysis and filtering for environmental time series

NASA Astrophysics Data System (ADS)

Galiana-Merino, J. J.; Pla, C.; Fernandez-Cortes, A.; Cuezva, S.; Ortiz, J.; Benavente, D.

2014-10-01

A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of several environmental time series, particularly focused on the analyses of cave monitoring data. The continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform have been implemented to provide a fast and precise time-period examination of the time series at different period bands. Moreover, statistic methods to examine the relation between two signals have been included. Finally, the entropy of curves and splines based methods have also been developed for segmenting and modeling the analyzed time series. All these methods together provide a user-friendly and fast program for the environmental signal analysis, with useful, practical and understandable results.

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

NASA Astrophysics Data System (ADS)

Dutta, Srimonti; Ghosh, Dipak; Chatterjee, Sucharita

2016-12-01

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

On the Daubechies-based wavelet differentiation matrix

NASA Technical Reports Server (NTRS)

Jameson, Leland

1993-01-01

The differentiation matrix for a Daubechies-based wavelet basis is constructed and superconvergence is proven. That is, it will be proven that under the assumption of periodic boundary conditions that the differentiation matrix is accurate of order 2M, even though the approximation subspace can represent exactly only polynomials up to degree M-1, where M is the number of vanishing moments of the associated wavelet. It is illustrated that Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small-scale structure is present.

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

NASA Astrophysics Data System (ADS)

Siokis, Fotios M.

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

Speckle noise reduction in quantitative optical metrology techniques by application of the discrete wavelet transformation

NASA Astrophysics Data System (ADS)

Furlong, Cosme; Pryputniewicz, Ryszard J.

2002-06-01

Effective suppression of speckle noise content in interferometric data images can help in improving accuracy and resolution of the results obtained with interferometric optical metrology techniques. In this paper, novel speckle noise reduction algorithms based on the discrete wavelet transformation are presented. The algorithms proceed by: (a) estimating the noise level contained in the interferograms of interest, (b) selecting wavelet families, (c) applying the wavelet transformation using the selected families, (d) wavelet thresholding, and (e) applying the inverse wavelet transformation, producing denoised interferograms. The algorithms are applied to the different stages of the processing procedures utilized for generation of quantitative speckle correlation interferometry data of fiber-optic based opto-electronic holography (FOBOEH) techniques, allowing identification of optimal processing conditions. It is shown that wavelet algorithms are effective for speckle noise reduction while preserving image features otherwise faded with other algorithms.

Target Detection and Classification Using Seismic and PIR Sensors

DTIC Science & Technology

2012-06-01

time series analysis via wavelet - based partitioning,” Signal Process...regard, this paper presents a wavelet - based method for target detection and classification. The proposed method has been validated on data sets of...The work reported in this paper makes use of a wavelet - based feature extraction method , called Symbolic Dynamic Filtering (SDF) [12]–[14]. The

Wavelet Types Comparison for Extracting Iris Feature Based on Energy Compaction

NASA Astrophysics Data System (ADS)

Rizal Isnanto, R.

2015-06-01

Human iris has a very unique pattern which is possible to be used as a biometric recognition. To identify texture in an image, texture analysis method can be used. One of method is wavelet that extract the image feature based on energy. Wavelet transforms used are Haar, Daubechies, Coiflets, Symlets, and Biorthogonal. In the research, iris recognition based on five mentioned wavelets was done and then comparison analysis was conducted for which some conclusions taken. Some steps have to be done in the research. First, the iris image is segmented from eye image then enhanced with histogram equalization. The features obtained is energy value. The next step is recognition using normalized Euclidean distance. Comparison analysis is done based on recognition rate percentage with two samples stored in database for reference images. After finding the recognition rate, some tests are conducted using Energy Compaction for all five types of wavelets above. As the result, the highest recognition rate is achieved using Haar, whereas for coefficients cutting for C(i) < 0.1, Haar wavelet has a highest percentage, therefore the retention rate or significan coefficient retained for Haaris lower than other wavelet types (db5, coif3, sym4, and bior2.4)

Wavelet tree structure based speckle noise removal for optical coherence tomography

NASA Astrophysics Data System (ADS)

Yuan, Xin; Liu, Xuan; Liu, Yang

2018-02-01

We report a new speckle noise removal algorithm in optical coherence tomography (OCT). Though wavelet domain thresholding algorithms have demonstrated superior advantages in suppressing noise magnitude and preserving image sharpness in OCT, the wavelet tree structure has not been investigated in previous applications. In this work, we propose an adaptive wavelet thresholding algorithm via exploiting the tree structure in wavelet coefficients to remove the speckle noise in OCT images. The threshold for each wavelet band is adaptively selected following a special rule to retain the structure of the image across different wavelet layers. Our results demonstrate that the proposed algorithm outperforms conventional wavelet thresholding, with significant advantages in preserving image features.

Spatially adaptive bases in wavelet-based coding of semi-regular meshes

NASA Astrophysics Data System (ADS)

Denis, Leon; Florea, Ruxandra; Munteanu, Adrian; Schelkens, Peter

2010-05-01

In this paper we present a wavelet-based coding approach for semi-regular meshes, which spatially adapts the employed wavelet basis in the wavelet transformation of the mesh. The spatially-adaptive nature of the transform requires additional information to be stored in the bit-stream in order to allow the reconstruction of the transformed mesh at the decoder side. In order to limit this overhead, the mesh is first segmented into regions of approximately equal size. For each spatial region, a predictor is selected in a rate-distortion optimal manner by using a Lagrangian rate-distortion optimization technique. When compared against the classical wavelet transform employing the butterfly subdivision filter, experiments reveal that the proposed spatially-adaptive wavelet transform significantly decreases the energy of the wavelet coefficients for all subbands. Preliminary results show also that employing the proposed transform for the lowest-resolution subband systematically yields improved compression performance at low-to-medium bit-rates. For the Venus and Rabbit test models the compression improvements add up to 1.47 dB and 0.95 dB, respectively.

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

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

Multifractal analysis of time series generated by discrete Ito equations

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

Telesca, Luciano; Czechowski, Zbigniew; Lovallo, Michele

2015-06-15

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

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

NASA Technical Reports Server (NTRS)

Kurdila, Andrew J.; Sharpley, Robert C.

1999-01-01

This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.

Watermarking on 3D mesh based on spherical wavelet transform.

PubMed

Jin, Jian-Qiu; Dai, Min-Ya; Bao, Hu-Jun; Peng, Qun-Sheng

2004-03-01

In this paper we propose a robust watermarking algorithm for 3D mesh. The algorithm is based on spherical wavelet transform. Our basic idea is to decompose the original mesh into a series of details at different scales by using spherical wavelet transform; the watermark is then embedded into the different levels of details. The embedding process includes: global sphere parameterization, spherical uniform sampling, spherical wavelet forward transform, embedding watermark, spherical wavelet inverse transform, and at last resampling the mesh watermarked to recover the topological connectivity of the original model. Experiments showed that our algorithm can improve the capacity of the watermark and the robustness of watermarking against attacks.

A lung sound classification system based on the rational dilation wavelet transform.

PubMed

Ulukaya, Sezer; Serbes, Gorkem; Sen, Ipek; Kahya, Yasemin P

2016-08-01

In this work, a wavelet based classification system that aims to discriminate crackle, normal and wheeze lung sounds is presented. While the previous works related with this problem use constant low Q-factor wavelets, which have limited frequency resolution and can not cope with oscillatory signals, in the proposed system, the Rational Dilation Wavelet Transform, whose Q-factors can be tuned, is employed. Proposed system yields an accuracy of 95 % for crackle, 97 % for wheeze, 93.50 % for normal and 95.17 % for total sound signal types using energy feature subset and proposed approach is superior to conventional low Q-factor wavelet analysis.

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

PubMed

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

2014-02-15

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

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

PubMed

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

2012-10-01

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

Wavelet detection of singularities in the presence of fractal noise

NASA Astrophysics Data System (ADS)

Noel, Steven E.; Gohel, Yogesh J.; Szu, Harold H.

1997-04-01

Here we detect singularities with generalized quadrature processing using the recently developed Hermitian Hat wavelet. Our intended application is radar target detection for the optimal fuzzing of ship self-defense munitions. We first develop a wavelet-based fractal noise model to represent sea clutter. We then investigate wavelet shrinkage as a way to reduce and smooth the noise before attempting wavelet detection. Finally, we use the complex phase of the Hermitian Hat wavelet to detect a simulated target singularity in the presence of our fractal noise.

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

NASA Astrophysics Data System (ADS)

Deng, Wei; Wang, Jun

2015-06-01

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

Multifractal Analysis of Human Heartbeat in Sleep

NASA Astrophysics Data System (ADS)

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

2007-07-01

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

Spherical 3D isotropic wavelets

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2012-04-01

Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html

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

NASA Astrophysics Data System (ADS)

Saakian, David B.

2012-03-01

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

[Recognition of landscape characteristic scale based on two-dimension wavelet analysis].

PubMed

Gao, Yan-Ni; Chen, Wei; He, Xing-Yuan; Li, Xiao-Yu

2010-06-01

Three wavelet bases, i. e., Haar, Daubechies, and Symlet, were chosen to analyze the validity of two-dimension wavelet analysis in recognizing the characteristic scales of the urban, peri-urban, and rural landscapes of Shenyang. Owing to the transform scale of two-dimension wavelet must be the integer power of 2, some characteristic scales cannot be accurately recognized. Therefore, the pixel resolution of images was resampled to 3, 3.5, 4, and 4.5 m to densify the scale in analysis. It was shown that two-dimension wavelet analysis worked effectively in checking characteristic scale. Haar, Daubechies, and Symle were the optimal wavelet bases to the peri-urban landscape, urban landscape, and rural landscape, respectively. Both Haar basis and Symlet basis played good roles in recognizing the fine characteristic scale of rural landscape and in detecting the boundary of peri-urban landscape. Daubechies basis and Symlet basis could be also used to detect the boundary of urban landscape and rural landscape, respectively.

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

NASA Astrophysics Data System (ADS)

Lee, Hyun-Jung; Kim, Ki-Seok

2018-04-01

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

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

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

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

2014-11-15

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

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

NASA Astrophysics Data System (ADS)

Argyroudis, G.; Siokis, F.

2018-04-01

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

Multifractality and freezing phenomena in random energy landscapes: An introduction

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.

2010-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2010-10-01

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

Efficacy Evaluation of Different Wavelet Feature Extraction Methods on Brain MRI Tumor Detection

NASA Astrophysics Data System (ADS)

Nabizadeh, Nooshin; John, Nigel; Kubat, Miroslav

2014-03-01

Automated Magnetic Resonance Imaging brain tumor detection and segmentation is a challenging task. Among different available methods, feature-based methods are very dominant. While many feature extraction techniques have been employed, it is still not quite clear which of feature extraction methods should be preferred. To help improve the situation, we present the results of a study in which we evaluate the efficiency of using different wavelet transform features extraction methods in brain MRI abnormality detection. Applying T1-weighted brain image, Discrete Wavelet Transform (DWT), Discrete Wavelet Packet Transform (DWPT), Dual Tree Complex Wavelet Transform (DTCWT), and Complex Morlet Wavelet Transform (CMWT) methods are applied to construct the feature pool. Three various classifiers as Support Vector Machine, K Nearest Neighborhood, and Sparse Representation-Based Classifier are applied and compared for classifying the selected features. The results show that DTCWT and CMWT features classified with SVM, result in the highest classification accuracy, proving of capability of wavelet transform features to be informative in this application.

Extracting fingerprint of wireless devices based on phase noise and multiple level wavelet decomposition

NASA Astrophysics Data System (ADS)

Zhao, Weichen; Sun, Zhuo; Kong, Song

2016-10-01

Wireless devices can be identified by the fingerprint extracted from the signal transmitted, which is useful in wireless communication security and other fields. This paper presents a method that extracts fingerprint based on phase noise of signal and multiple level wavelet decomposition. The phase of signal will be extracted first and then decomposed by multiple level wavelet decomposition. The statistic value of each wavelet coefficient vector is utilized for constructing fingerprint. Besides, the relationship between wavelet decomposition level and recognition accuracy is simulated. And advertised decomposition level is revealed as well. Compared with previous methods, our method is simpler and the accuracy of recognition remains high when Signal Noise Ratio (SNR) is low.

Skin image retrieval using Gabor wavelet texture feature.

PubMed

Ou, X; Pan, W; Zhang, X; Xiao, P

2016-12-01

Skin imaging plays a key role in many clinical studies. We have used many skin imaging techniques, including the recently developed capacitive contact skin imaging based on fingerprint sensors. The aim of this study was to develop an effective skin image retrieval technique using Gabor wavelet transform, which can be used on different types of skin images, but with a special focus on skin capacitive contact images. Content-based image retrieval (CBIR) is a useful technology to retrieve stored images from database by supplying query images. In a typical CBIR, images are retrieved based on colour, shape, texture, etc. In this study, texture feature is used for retrieving skin images, and Gabor wavelet transform is used for texture feature description and extraction. The results show that the Gabor wavelet texture features can work efficiently on different types of skin images. Although Gabor wavelet transform is slower compared with other image retrieval techniques, such as principal component analysis (PCA) and grey-level co-occurrence matrix (GLCM), Gabor wavelet transform is the best for retrieving skin capacitive contact images and facial images with different orientations. Gabor wavelet transform can also work well on facial images with different expressions and skin cancer/disease images. We have developed an effective skin image retrieval method based on Gabor wavelet transform, that it is useful for retrieving different types of images, namely digital colour face images, digital colour skin cancer and skin disease images, and particularly greyscale skin capacitive contact images. Gabor wavelet transform can also be potentially useful for face recognition (with different orientation and expressions) and skin cancer/disease diagnosis. © 2016 Society of Cosmetic Scientists and the Société Française de Cosmétologie.

Wavelet transforms as solutions of partial differential equations

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

Zweig, G.

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Wavelet transforms are useful in representing transients whose time and frequency structure reflect the dynamics of an underlying physical system. Speech sound, pressure in turbulent fluid flow, or engine sound in automobiles are excellent candidates for wavelet analysis. This project focused on (1) methods for choosing the parent wavelet for a continuous wavelet transform in pattern recognition applications and (2) the more efficient computation of continuous wavelet transforms by understanding the relationship between discrete wavelet transforms and discretized continuousmore » wavelet transforms. The most interesting result of this research is the finding that the generalized wave equation, on which the continuous wavelet transform is based, can be used to understand phenomena that relate to the process of hearing.« less

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Detecting Multifractal Properties in Asset Returns:

NASA Astrophysics Data System (ADS)

Lux, Thomas

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

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

PubMed

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

2003-09-01

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

Running wavelet archetype aids the determination of heart rate from the video photoplethysmogram during motion.

PubMed

Addison, Paul S; Foo, David M H; Jacquel, Dominique

2017-07-01

The extraction of heart rate from a video-based biosignal during motion using a novel wavelet-based ensemble averaging method is described. Running Wavelet Archetyping (RWA) allows for the enhanced extraction of pulse information from the time-frequency representation, from which a video-based heart rate (HRvid) can be derived. This compares favorably to a reference heart rate derived from a pulse oximeter.

Wavelet-based fMRI analysis: 3-D denoising, signal separation, and validation metrics

PubMed Central

Khullar, Siddharth; Michael, Andrew; Correa, Nicolle; Adali, Tulay; Baum, Stefi A.; Calhoun, Vince D.

2010-01-01

We present a novel integrated wavelet-domain based framework (w-ICA) for 3-D de-noising functional magnetic resonance imaging (fMRI) data followed by source separation analysis using independent component analysis (ICA) in the wavelet domain. We propose the idea of a 3-D wavelet-based multi-directional de-noising scheme where each volume in a 4-D fMRI data set is sub-sampled using the axial, sagittal and coronal geometries to obtain three different slice-by-slice representations of the same data. The filtered intensity value of an arbitrary voxel is computed as an expected value of the de-noised wavelet coefficients corresponding to the three viewing geometries for each sub-band. This results in a robust set of de-noised wavelet coefficients for each voxel. Given the decorrelated nature of these de-noised wavelet coefficients; it is possible to obtain more accurate source estimates using ICA in the wavelet domain. The contributions of this work can be realized as two modules. First, the analysis module where we combine a new 3-D wavelet denoising approach with better signal separation properties of ICA in the wavelet domain, to yield an activation component that corresponds closely to the true underlying signal and is maximally independent with respect to other components. Second, we propose and describe two novel shape metrics for post-ICA comparisons between activation regions obtained through different frameworks. We verified our method using simulated as well as real fMRI data and compared our results against the conventional scheme (Gaussian smoothing + spatial ICA: s-ICA). The results show significant improvements based on two important features: (1) preservation of shape of the activation region (shape metrics) and (2) receiver operating characteristic (ROC) curves. It was observed that the proposed framework was able to preserve the actual activation shape in a consistent manner even for very high noise levels in addition to significant reduction in false positives voxels. PMID:21034833

Energy-Based Wavelet De-Noising of Hydrologic Time Series

PubMed Central

Sang, Yan-Fang; Liu, Changming; Wang, Zhonggen; Wen, Jun; Shang, Lunyu

2014-01-01

De-noising is a substantial issue in hydrologic time series analysis, but it is a difficult task due to the defect of methods. In this paper an energy-based wavelet de-noising method was proposed. It is to remove noise by comparing energy distribution of series with the background energy distribution, which is established from Monte-Carlo test. Differing from wavelet threshold de-noising (WTD) method with the basis of wavelet coefficient thresholding, the proposed method is based on energy distribution of series. It can distinguish noise from deterministic components in series, and uncertainty of de-noising result can be quantitatively estimated using proper confidence interval, but WTD method cannot do this. Analysis of both synthetic and observed series verified the comparable power of the proposed method and WTD, but de-noising process by the former is more easily operable. The results also indicate the influences of three key factors (wavelet choice, decomposition level choice and noise content) on wavelet de-noising. Wavelet should be carefully chosen when using the proposed method. The suitable decomposition level for wavelet de-noising should correspond to series' deterministic sub-signal which has the smallest temporal scale. If too much noise is included in a series, accurate de-noising result cannot be obtained by the proposed method or WTD, but the series would show pure random but not autocorrelation characters, so de-noising is no longer needed. PMID:25360533

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

NASA Astrophysics Data System (ADS)

Nakashima, Yoshito; Komatsubara, Junko

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

Use of the Morlet mother wavelet in the frequency-scale domain decomposition technique for the modal identification of ambient vibration responses

NASA Astrophysics Data System (ADS)

Le, Thien-Phu

2017-10-01

The frequency-scale domain decomposition technique has recently been proposed for operational modal analysis. The technique is based on the Cauchy mother wavelet. In this paper, the approach is extended to the Morlet mother wavelet, which is very popular in signal processing due to its superior time-frequency localization. Based on the regressive form and an appropriate norm of the Morlet mother wavelet, the continuous wavelet transform of the power spectral density of ambient responses enables modes in the frequency-scale domain to be highlighted. Analytical developments first demonstrate the link between modal parameters and the local maxima of the continuous wavelet transform modulus. The link formula is then used as the foundation of the proposed modal identification method. Its practical procedure, combined with the singular value decomposition algorithm, is presented step by step. The proposition is finally verified using numerical examples and a laboratory test.

Quality of reconstruction of compressed off-axis digital holograms by frequency filtering and wavelets.

PubMed

Cheremkhin, Pavel A; Kurbatova, Ekaterina A

2018-01-01

Compression of digital holograms can significantly help with the storage of objects and data in 2D and 3D form, its transmission, and its reconstruction. Compression of standard images by methods based on wavelets allows high compression ratios (up to 20-50 times) with minimum losses of quality. In the case of digital holograms, application of wavelets directly does not allow high values of compression to be obtained. However, additional preprocessing and postprocessing can afford significant compression of holograms and the acceptable quality of reconstructed images. In this paper application of wavelet transforms for compression of off-axis digital holograms are considered. The combined technique based on zero- and twin-order elimination, wavelet compression of the amplitude and phase components of the obtained Fourier spectrum, and further additional compression of wavelet coefficients by thresholding and quantization is considered. Numerical experiments on reconstruction of images from the compressed holograms are performed. The comparative analysis of applicability of various wavelets and methods of additional compression of wavelet coefficients is performed. Optimum parameters of compression of holograms by the methods can be estimated. Sizes of holographic information were decreased up to 190 times.

Wavelet entropy characterization of elevated intracranial pressure.

PubMed

Xu, Peng; Scalzo, Fabien; Bergsneider, Marvin; Vespa, Paul; Chad, Miller; Hu, Xiao

2008-01-01

Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.

Time-frequency analysis of phonocardiogram signals using wavelet transform: a comparative study.

PubMed

Ergen, Burhan; Tatar, Yetkin; Gulcur, Halil Ozcan

2012-01-01

Analysis of phonocardiogram (PCG) signals provides a non-invasive means to determine the abnormalities caused by cardiovascular system pathology. In general, time-frequency representation (TFR) methods are used to study the PCG signal because it is one of the non-stationary bio-signals. The continuous wavelet transform (CWT) is especially suitable for the analysis of non-stationary signals and to obtain the TFR, due to its high resolution, both in time and in frequency and has recently become a favourite tool. It decomposes a signal in terms of elementary contributions called wavelets, which are shifted and dilated copies of a fixed mother wavelet function, and yields a joint TFR. Although the basic characteristics of the wavelets are similar, each type of the wavelets produces a different TFR. In this study, eight real types of the most known wavelets are examined on typical PCG signals indicating heart abnormalities in order to determine the best wavelet to obtain a reliable TFR. For this purpose, the wavelet energy and frequency spectrum estimations based on the CWT and the spectra of the chosen wavelets were compared with the energy distribution and the autoregressive frequency spectra in order to determine the most suitable wavelet. The results show that Morlet wavelet is the most reliable wavelet for the time-frequency analysis of PCG signals.

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

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

Pesin, Y.; Weiss, H.

1997-01-01

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

Multi-resolution analysis for ear recognition using wavelet features

NASA Astrophysics Data System (ADS)

Shoaib, M.; Basit, A.; Faye, I.

2016-11-01

Security is very important and in order to avoid any physical contact, identification of human when they are moving is necessary. Ear biometric is one of the methods by which a person can be identified using surveillance cameras. Various techniques have been proposed to increase the ear based recognition systems. In this work, a feature extraction method for human ear recognition based on wavelet transforms is proposed. The proposed features are approximation coefficients and specific details of level two after applying various types of wavelet transforms. Different wavelet transforms are applied to find the suitable wavelet. Minimum Euclidean distance is used as a matching criterion. Results achieved by the proposed method are promising and can be used in real time ear recognition system.

A Hybrid Wavelet-Based Method for the Peak Detection of Photoplethysmography Signals.

PubMed

Li, Suyi; Jiang, Shanqing; Jiang, Shan; Wu, Jiang; Xiong, Wenji; Diao, Shu

2017-01-01

The noninvasive peripheral oxygen saturation (SpO 2 ) and the pulse rate can be extracted from photoplethysmography (PPG) signals. However, the accuracy of the extraction is directly affected by the quality of the signal obtained and the peak of the signal identified; therefore, a hybrid wavelet-based method is proposed in this study. Firstly, we suppressed the partial motion artifacts and corrected the baseline drift by using a wavelet method based on the principle of wavelet multiresolution. And then, we designed a quadratic spline wavelet modulus maximum algorithm to identify the PPG peaks automatically. To evaluate this hybrid method, a reflective pulse oximeter was used to acquire ten subjects' PPG signals under sitting, raising hand, and gently walking postures, and the peak recognition results on the raw signal and on the corrected signal were compared, respectively. The results showed that the hybrid method not only corrected the morphologies of the signal well but also optimized the peaks identification quality, subsequently elevating the measurement accuracy of SpO 2 and the pulse rate. As a result, our hybrid wavelet-based method profoundly optimized the evaluation of respiratory function and heart rate variability analysis.

A Hybrid Wavelet-Based Method for the Peak Detection of Photoplethysmography Signals

PubMed Central

Jiang, Shanqing; Jiang, Shan; Wu, Jiang; Xiong, Wenji

2017-01-01

The noninvasive peripheral oxygen saturation (SpO2) and the pulse rate can be extracted from photoplethysmography (PPG) signals. However, the accuracy of the extraction is directly affected by the quality of the signal obtained and the peak of the signal identified; therefore, a hybrid wavelet-based method is proposed in this study. Firstly, we suppressed the partial motion artifacts and corrected the baseline drift by using a wavelet method based on the principle of wavelet multiresolution. And then, we designed a quadratic spline wavelet modulus maximum algorithm to identify the PPG peaks automatically. To evaluate this hybrid method, a reflective pulse oximeter was used to acquire ten subjects' PPG signals under sitting, raising hand, and gently walking postures, and the peak recognition results on the raw signal and on the corrected signal were compared, respectively. The results showed that the hybrid method not only corrected the morphologies of the signal well but also optimized the peaks identification quality, subsequently elevating the measurement accuracy of SpO2 and the pulse rate. As a result, our hybrid wavelet-based method profoundly optimized the evaluation of respiratory function and heart rate variability analysis. PMID:29250135

Content Based Image Retrieval based on Wavelet Transform coefficients distribution

PubMed Central

Lamard, Mathieu; Cazuguel, Guy; Quellec, Gwénolé; Bekri, Lynda; Roux, Christian; Cochener, Béatrice

2007-01-01

In this paper we propose a content based image retrieval method for diagnosis aid in medical fields. We characterize images without extracting significant features by using distribution of coefficients obtained by building signatures from the distribution of wavelet transform. The research is carried out by computing signature distances between the query and database images. Several signatures are proposed; they use a model of wavelet coefficient distribution. To enhance results, a weighted distance between signatures is used and an adapted wavelet base is proposed. Retrieval efficiency is given for different databases including a diabetic retinopathy, a mammography and a face database. Results are promising: the retrieval efficiency is higher than 95% for some cases using an optimization process. PMID:18003013

Design of almost symmetric orthogonal wavelet filter bank via direct optimization.

PubMed

Murugesan, Selvaraaju; Tay, David B H

2012-05-01

It is a well-known fact that (compact-support) dyadic wavelets [based on the two channel filter banks (FBs)] cannot be simultaneously orthogonal and symmetric. Although orthogonal wavelets have the energy preservation property, biorthogonal wavelets are preferred in image processing applications because of their symmetric property. In this paper, a novel method is presented for the design of almost symmetric orthogonal wavelet FB. Orthogonality is structurally imposed by using the unnormalized lattice structure, and this leads to an objective function, which is relatively simple to optimize. The designed filters have good frequency response, flat group delay, almost symmetric filter coefficients, and symmetric wavelet function.

Wavelets and molecular structure

NASA Astrophysics Data System (ADS)

Carson, Mike

1996-08-01

The wavelet method offers possibilities for display, editing, and topological comparison of proteins at a user-specified level of detail. Wavelets are a mathematical tool that first found application in signal processing. The multiresolution analysis of a signal via wavelets provides a hierarchical series of `best' lower-resolution approximations. B-spline ribbons model the protein fold, with one control point per residue. Wavelet analysis sets limits on the information required to define the winding of the backbone through space, suggesting a recognizable fold is generated from a number of points equal to 1/4 or less the number of residues. Wavelets applied to surfaces and volumes show promise in structure-based drug design.

The design and implementation of signal decomposition system of CL multi-wavelet transform based on DSP builder

NASA Astrophysics Data System (ADS)

Huang, Yan; Wang, Zhihui

2015-12-01

With the development of FPGA, DSP Builder is widely applied to design system-level algorithms. The algorithm of CL multi-wavelet is more advanced and effective than scalar wavelets in processing signal decomposition. Thus, a system of CL multi-wavelet based on DSP Builder is designed for the first time in this paper. The system mainly contains three parts: a pre-filtering subsystem, a one-level decomposition subsystem and a two-level decomposition subsystem. It can be converted into hardware language VHDL by the Signal Complier block that can be used in Quartus II. After analyzing the energy indicator, it shows that this system outperforms Daubenchies wavelet in signal decomposition. Furthermore, it has proved to be suitable for the implementation of signal fusion based on SoPC hardware, and it will become a solid foundation in this new field.

Digital transceiver implementation for wavelet packet modulation

NASA Astrophysics Data System (ADS)

Lindsey, Alan R.; Dill, Jeffrey C.

1998-03-01

Current transceiver designs for wavelet-based communication systems are typically reliant on analog waveform synthesis, however, digital processing is an important part of the eventual success of these techniques. In this paper, a transceiver implementation is introduced for the recently introduced wavelet packet modulation scheme which moves the analog processing as far as possible toward the antenna. The transceiver is based on the discrete wavelet packet transform which incorporates level and node parameters for generalized computation of wavelet packets. In this transform no particular structure is imposed on the filter bank save dyadic branching, and a maximum level which is specified a priori and dependent mainly on speed and/or cost considerations. The transmitter/receiver structure takes a binary sequence as input and, based on the desired time- frequency partitioning, processes the signal through demultiplexing, synthesis, analysis, multiplexing and data determination completely in the digital domain - with exception of conversion in and out of the analog domain for transmission.

Extreme values and fat tails of multifractal fluctuations

NASA Astrophysics Data System (ADS)

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

2006-06-01

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

Dependency structure and scaling properties of financial time series are related

PubMed Central

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

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

Siokis, Fotios M.

2014-02-01

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

Empirical method to measure stochasticity and multifractality in nonlinear time series

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Dependency structure and scaling properties of financial time series are related

NASA Astrophysics Data System (ADS)

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

2014-04-01

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

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

NASA Astrophysics Data System (ADS)

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

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

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Wavelet based detection of manatee vocalizations

NASA Astrophysics Data System (ADS)

Gur, Berke M.; Niezrecki, Christopher

2005-04-01

The West Indian manatee (Trichechus manatus latirostris) has become endangered partly because of watercraft collisions in Florida's coastal waterways. Several boater warning systems, based upon manatee vocalizations, have been proposed to reduce the number of collisions. Three detection methods based on the Fourier transform (threshold, harmonic content and autocorrelation methods) were previously suggested and tested. In the last decade, the wavelet transform has emerged as an alternative to the Fourier transform and has been successfully applied in various fields of science and engineering including the acoustic detection of dolphin vocalizations. As of yet, no prior research has been conducted in analyzing manatee vocalizations using the wavelet transform. Within this study, the wavelet transform is used as an alternative to the Fourier transform in detecting manatee vocalizations. The wavelet coefficients are analyzed and tested against a specified criterion to determine the existence of a manatee call. The performance of the method presented is tested on the same data previously used in the prior studies, and the results are compared. Preliminary results indicate that using the wavelet transform as a signal processing technique to detect manatee vocalizations shows great promise.

Multifractal Properties of Process Control Variables

NASA Astrophysics Data System (ADS)

Domański, Paweł D.

2017-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2003-08-01

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

Estimation of Handgrip Force from SEMG Based on Wavelet Scale Selection.

PubMed

Wang, Kai; Zhang, Xianmin; Ota, Jun; Huang, Yanjiang

2018-02-24

This paper proposes a nonlinear correlation-based wavelet scale selection technology to select the effective wavelet scales for the estimation of handgrip force from surface electromyograms (SEMG). The SEMG signal corresponding to gripping force was collected from extensor and flexor forearm muscles during the force-varying analysis task. We performed a computational sensitivity analysis on the initial nonlinear SEMG-handgrip force model. To explore the nonlinear correlation between ten wavelet scales and handgrip force, a large-scale iteration based on the Monte Carlo simulation was conducted. To choose a suitable combination of scales, we proposed a rule to combine wavelet scales based on the sensitivity of each scale and selected the appropriate combination of wavelet scales based on sequence combination analysis (SCA). The results of SCA indicated that the scale combination VI is suitable for estimating force from the extensors and the combination V is suitable for the flexors. The proposed method was compared to two former methods through prolonged static and force-varying contraction tasks. The experiment results showed that the root mean square errors derived by the proposed method for both static and force-varying contraction tasks were less than 20%. The accuracy and robustness of the handgrip force derived by the proposed method is better than that obtained by the former methods.

An efficient coding algorithm for the compression of ECG signals using the wavelet transform.

PubMed

Rajoub, Bashar A

2002-04-01

A wavelet-based electrocardiogram (ECG) data compression algorithm is proposed in this paper. The ECG signal is first preprocessed, the discrete wavelet transform (DWT) is then applied to the preprocessed signal. Preprocessing guarantees that the magnitudes of the wavelet coefficients be less than one, and reduces the reconstruction errors near both ends of the compressed signal. The DWT coefficients are divided into three groups, each group is thresholded using a threshold based on a desired energy packing efficiency. A binary significance map is then generated by scanning the wavelet decomposition coefficients and outputting a binary one if the scanned coefficient is significant, and a binary zero if it is insignificant. Compression is achieved by 1) using a variable length code based on run length encoding to compress the significance map and 2) using direct binary representation for representing the significant coefficients. The ability of the coding algorithm to compress ECG signals is investigated, the results were obtained by compressing and decompressing the test signals. The proposed algorithm is compared with direct-based and wavelet-based compression algorithms and showed superior performance. A compression ratio of 24:1 was achieved for MIT-BIH record 117 with a percent root mean square difference as low as 1.08%.

An innovative approach for characteristic analysis and state-of-health diagnosis for a Li-ion cell based on the discrete wavelet transform

NASA Astrophysics Data System (ADS)

Kim, Jonghoon; Cho, B. H.

2014-08-01

This paper introduces an innovative approach to analyze electrochemical characteristics and state-of-health (SOH) diagnosis of a Li-ion cell based on the discrete wavelet transform (DWT). In this approach, the DWT has been applied as a powerful tool in the analysis of the discharging/charging voltage signal (DCVS) with non-stationary and transient phenomena for a Li-ion cell. Specifically, DWT-based multi-resolution analysis (MRA) is used for extracting information on the electrochemical characteristics in both time and frequency domain simultaneously. Through using the MRA with implementation of the wavelet decomposition, the information on the electrochemical characteristics of a Li-ion cell can be extracted from the DCVS over a wide frequency range. Wavelet decomposition based on the selection of the order 3 Daubechies wavelet (dB3) and scale 5 as the best wavelet function and the optimal decomposition scale is implemented. In particular, this present approach develops these investigations one step further by showing low and high frequency components (approximation component An and detail component Dn, respectively) extracted from variable Li-ion cells with different electrochemical characteristics caused by aging effect. Experimental results show the clearness of the DWT-based approach for the reliable diagnosis of the SOH for a Li-ion cell.

An Automated Parallel Image Registration Technique Based on the Correlation of Wavelet Features

NASA Technical Reports Server (NTRS)

LeMoigne, Jacqueline; Campbell, William J.; Cromp, Robert F.; Zukor, Dorothy (Technical Monitor)

2001-01-01

With the increasing importance of multiple platform/multiple remote sensing missions, fast and automatic integration of digital data from disparate sources has become critical to the success of these endeavors. Our work utilizes maxima of wavelet coefficients to form the basic features of a correlation-based automatic registration algorithm. Our wavelet-based registration algorithm is tested successfully with data from the National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR) and the Landsat/Thematic Mapper(TM), which differ by translation and/or rotation. By the choice of high-frequency wavelet features, this method is similar to an edge-based correlation method, but by exploiting the multi-resolution nature of a wavelet decomposition, our method achieves higher computational speeds for comparable accuracies. This algorithm has been implemented on a Single Instruction Multiple Data (SIMD) massively parallel computer, the MasPar MP-2, as well as on the CrayT3D, the Cray T3E and a Beowulf cluster of Pentium workstations.

Multidimensional, mapping-based complex wavelet transforms.

PubMed

Fernandes, Felix C A; van Spaendonck, Rutger L C; Burrus, C Sidney

2005-01-01

Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce multidimensional, mapping-based, complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, nonredundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and nonredundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we exploit this flexibility to create the complex double-density DWT: a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3M - 1)/(2M - 1) in M dimensions. No other transform achieves all these properties at a lower redundancy, to the best of our knowledge. By exploiting the advantages of our multidimensional, mapping-based complex wavelet transforms in seismic signal-processing applications, we have demonstrated state-of-the-art results.

Phase synchronization based on a Dual-Tree Complex Wavelet Transform

NASA Astrophysics Data System (ADS)

Ferreira, Maria Teodora; Domingues, Margarete Oliveira; Macau, Elbert E. N.

2016-11-01

In this work, we show the applicability of our Discrete Complex Wavelet Approach (DCWA) to verify the phenomenon of phase synchronization transition in two coupled chaotic Lorenz systems. DCWA is based on the phase assignment from complex wavelet coefficients obtained by using a Dual-Tree Complex Wavelet Transform (DT-CWT). We analyzed two coupled chaotic Lorenz systems, aiming to detect the transition from non-phase synchronization to phase synchronization. In addition, we check how good is the method in detecting periods of 2π phase-slips. In all experiments, DCWA is compared with classical phase detection methods such as the ones based on arctangent and Hilbert transform showing a much better performance.

Denoising embolic Doppler ultrasound signals using Dual Tree Complex Discrete Wavelet Transform.

PubMed

Serbes, Gorkem; Aydin, Nizamettin

2010-01-01

Early and accurate detection of asymptomatic emboli is important for monitoring of preventive therapy in stroke-prone patients. One of the problems in detection of emboli is the identification of an embolic signal caused by very small emboli. The amplitude of the embolic signal may be so small that advanced processing methods are required to distinguish these signals from Doppler signals arising from red blood cells. In this study instead of conventional discrete wavelet transform, the Dual Tree Complex Discrete Wavelet Transform was used for denoising embolic signals. Performances of both approaches were compared. Unlike the conventional discrete wavelet transform discrete complex wavelet transform is a shift invariant transform with limited redundancy. Results demonstrate that the Dual Tree Complex Discrete Wavelet Transform based denoising outperforms conventional discrete wavelet denoising. Approximately 8 dB improvement is obtained by using the Dual Tree Complex Discrete Wavelet Transform compared to the improvement provided by the conventional Discrete Wavelet Transform (less than 5 dB).

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

NASA Astrophysics Data System (ADS)

Macek, W. M.; Wawrzaszek, A.

2011-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Multifractal scaling of the kinetic energy flux in solar wind turbulence

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Dynamic Bayesian wavelet transform: New methodology for extraction of repetitive transients

NASA Astrophysics Data System (ADS)

Wang, Dong; Tsui, Kwok-Leung

2017-05-01

Thanks to some recent research works, dynamic Bayesian wavelet transform as new methodology for extraction of repetitive transients is proposed in this short communication to reveal fault signatures hidden in rotating machine. The main idea of the dynamic Bayesian wavelet transform is to iteratively estimate posterior parameters of wavelet transform via artificial observations and dynamic Bayesian inference. First, a prior wavelet parameter distribution can be established by one of many fast detection algorithms, such as the fast kurtogram, the improved kurtogram, the enhanced kurtogram, the sparsogram, the infogram, continuous wavelet transform, discrete wavelet transform, wavelet packets, multiwavelets, empirical wavelet transform, empirical mode decomposition, local mean decomposition, etc.. Second, artificial observations can be constructed based on one of many metrics, such as kurtosis, the sparsity measurement, entropy, approximate entropy, the smoothness index, a synthesized criterion, etc., which are able to quantify repetitive transients. Finally, given artificial observations, the prior wavelet parameter distribution can be posteriorly updated over iterations by using dynamic Bayesian inference. More importantly, the proposed new methodology can be extended to establish the optimal parameters required by many other signal processing methods for extraction of repetitive transients.

The application of super wavelet finite element on temperature-pressure coupled field simulation of LPG tank under jet fire

NASA Astrophysics Data System (ADS)

Zhao, Bin

2015-02-01

Temperature-pressure coupled field analysis of liquefied petroleum gas (LPG) tank under jet fire can offer theoretical guidance for preventing the fire accidents of LPG tank, the application of super wavelet finite element on it is studied in depth. First, review of related researches on heat transfer analysis of LPG tank under fire and super wavelet are carried out. Second, basic theory of super wavelet transform is studied. Third, the temperature-pressure coupled model of gas phase and liquid LPG under jet fire is established based on the equation of state, the VOF model and the RNG k-ɛ model. Then the super wavelet finite element formulation is constructed using the super wavelet scale function as interpolating function. Finally, the simulation is carried out, and results show that the super wavelet finite element method has higher computing precision than wavelet finite element method.

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

Intelligent Gearbox Diagnosis Methods Based on SVM, Wavelet Lifting and RBR

PubMed Central

Gao, Lixin; Ren, Zhiqiang; Tang, Wenliang; Wang, Huaqing; Chen, Peng

2010-01-01

Given the problems in intelligent gearbox diagnosis methods, it is difficult to obtain the desired information and a large enough sample size to study; therefore, we propose the application of various methods for gearbox fault diagnosis, including wavelet lifting, a support vector machine (SVM) and rule-based reasoning (RBR). In a complex field environment, it is less likely for machines to have the same fault; moreover, the fault features can also vary. Therefore, a SVM could be used for the initial diagnosis. First, gearbox vibration signals were processed with wavelet packet decomposition, and the signal energy coefficients of each frequency band were extracted and used as input feature vectors in SVM for normal and faulty pattern recognition. Second, precision analysis using wavelet lifting could successfully filter out the noisy signals while maintaining the impulse characteristics of the fault; thus effectively extracting the fault frequency of the machine. Lastly, the knowledge base was built based on the field rules summarized by experts to identify the detailed fault type. Results have shown that SVM is a powerful tool to accomplish gearbox fault pattern recognition when the sample size is small, whereas the wavelet lifting scheme can effectively extract fault features, and rule-based reasoning can be used to identify the detailed fault type. Therefore, a method that combines SVM, wavelet lifting and rule-based reasoning ensures effective gearbox fault diagnosis. PMID:22399894

Intelligent gearbox diagnosis methods based on SVM, wavelet lifting and RBR.

PubMed

Gao, Lixin; Ren, Zhiqiang; Tang, Wenliang; Wang, Huaqing; Chen, Peng

2010-01-01

Given the problems in intelligent gearbox diagnosis methods, it is difficult to obtain the desired information and a large enough sample size to study; therefore, we propose the application of various methods for gearbox fault diagnosis, including wavelet lifting, a support vector machine (SVM) and rule-based reasoning (RBR). In a complex field environment, it is less likely for machines to have the same fault; moreover, the fault features can also vary. Therefore, a SVM could be used for the initial diagnosis. First, gearbox vibration signals were processed with wavelet packet decomposition, and the signal energy coefficients of each frequency band were extracted and used as input feature vectors in SVM for normal and faulty pattern recognition. Second, precision analysis using wavelet lifting could successfully filter out the noisy signals while maintaining the impulse characteristics of the fault; thus effectively extracting the fault frequency of the machine. Lastly, the knowledge base was built based on the field rules summarized by experts to identify the detailed fault type. Results have shown that SVM is a powerful tool to accomplish gearbox fault pattern recognition when the sample size is small, whereas the wavelet lifting scheme can effectively extract fault features, and rule-based reasoning can be used to identify the detailed fault type. Therefore, a method that combines SVM, wavelet lifting and rule-based reasoning ensures effective gearbox fault diagnosis.

Risk management of a fund for natural disasters

NASA Astrophysics Data System (ADS)

Flores, C.

2003-04-01

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

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

NASA Astrophysics Data System (ADS)

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2016-04-01

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

Multifractal detrending moving-average cross-correlation analysis

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Zhou, Wei-Xing

2011-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Harmonic analysis of electric locomotive and traction power system based on wavelet singular entropy

NASA Astrophysics Data System (ADS)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, the locomotive and traction power system has become the main harmonic source of China's power grid. In response to this phenomenon, the system's power quality issues need timely monitoring, assessment and governance. Wavelet singular entropy is an organic combination of wavelet transform, singular value decomposition and information entropy theory, which combines the unique advantages of the three in signal processing: the time-frequency local characteristics of wavelet transform, singular value decomposition explores the basic modal characteristics of data, and information entropy quantifies the feature data. Based on the theory of singular value decomposition, the wavelet coefficient matrix after wavelet transform is decomposed into a series of singular values that can reflect the basic characteristics of the original coefficient matrix. Then the statistical properties of information entropy are used to analyze the uncertainty of the singular value set, so as to give a definite measurement of the complexity of the original signal. It can be said that wavelet entropy has a good application prospect in fault detection, classification and protection. The mat lab simulation shows that the use of wavelet singular entropy on the locomotive and traction power system harmonic analysis is effective.

A wavelet-based statistical analysis of FMRI data: I. motivation and data distribution modeling.

PubMed

Dinov, Ivo D; Boscardin, John W; Mega, Michael S; Sowell, Elizabeth L; Toga, Arthur W

2005-01-01

We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural magnetic resonance imaging (MRI) and fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and spatial locations. An anatomical subvolume probabilistic atlas is used to tessellate the structural and functional signals into smaller regions each of which is processed separately. A frequency-adaptive wavelet shrinkage scheme is employed to obtain essentially optimal estimations of the signals in the wavelet space. The empirical distributions of the signals on all the regions are computed in a compressed wavelet space. These are modeled by heavy-tail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that the Cauchy, Bessel K Forms, and Pareto distributions provide the most accurate asymptotic models for the distribution of the wavelet coefficients of the data. Finally, we propose a new model for statistical analysis of functional MRI data using this atlas-based wavelet space representation. In the second part of our investigation, we will apply this technique to analyze a large fMRI dataset involving repeated presentation of sensory-motor response stimuli in young, elderly, and demented subjects.

Research on artificial neural network intrusion detection photochemistry based on the improved wavelet analysis and transformation

NASA Astrophysics Data System (ADS)

Li, Hong; Ding, Xue

2017-03-01

This paper combines wavelet analysis and wavelet transform theory with artificial neural network, through the pretreatment on point feature attributes before in intrusion detection, to make them suitable for improvement of wavelet neural network. The whole intrusion classification model gets the better adaptability, self-learning ability, greatly enhances the wavelet neural network for solving the problem of field detection invasion, reduces storage space, contributes to improve the performance of the constructed neural network, and reduces the training time. Finally the results of the KDDCup99 data set simulation experiment shows that, this method reduces the complexity of constructing wavelet neural network, but also ensures the accuracy of the intrusion classification.

Coupled uncertainty provided by a multifractal random walker

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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

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

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

2010-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Spatial analysis of cities using Renyi entropy and fractal parameters

NASA Astrophysics Data System (ADS)

Chen, Yanguang; Feng, Jian

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

An Intelligent Pattern Recognition System Based on Neural Network and Wavelet Decomposition for Interpretation of Heart Sounds

DTIC Science & Technology

2001-10-25

wavelet decomposition of signals and classification using neural network. Inputs to the system are the heart sound signals acquired by a stethoscope in a...Proceedings. pp. 415–418, 1990. [3] G. Ergun, “An intelligent diagnostic system for interpretation of arterpartum fetal heart rate tracings based on ANNs and...AN INTELLIGENT PATTERN RECOGNITION SYSTEM BASED ON NEURAL NETWORK AND WAVELET DECOMPOSITION FOR INTERPRETATION OF HEART SOUNDS I. TURKOGLU1, A

Distributed Compressive Sensing

DTIC Science & Technology

2009-01-01

example, smooth signals are sparse in the Fourier basis, and piecewise smooth signals are sparse in a wavelet basis [8]; the commercial coding standards MP3...including wavelets [8], Gabor bases [8], curvelets [35], etc., are widely used for representation and compression of natural signals, images, and...spikes and the sine waves of a Fourier basis, or the Fourier basis and wavelets . Signals that are sparsely represented in frames or unions of bases can

Wavelet-Based Signal and Image Processing for Target Recognition

NASA Astrophysics Data System (ADS)

Sherlock, Barry G.

2002-11-01

The PI visited NSWC Dahlgren, VA, for six weeks in May-June 2002 and collaborated with scientists in the G33 TEAMS facility, and with Marilyn Rudzinsky of T44 Technology and Photonic Systems Branch. During this visit the PI also presented six educational seminars to NSWC scientists on various aspects of signal processing. Several items from the grant proposal were completed, including (1) wavelet-based algorithms for interpolation of 1-d signals and 2-d images; (2) Discrete Wavelet Transform domain based algorithms for filtering of image data; (3) wavelet-based smoothing of image sequence data originally obtained for the CRITTIR (Clutter Rejection Involving Temporal Techniques in the Infra-Red) project. The PI visited the University of Stellenbosch, South Africa to collaborate with colleagues Prof. B.M. Herbst and Prof. J. du Preez on the use of wavelet image processing in conjunction with pattern recognition techniques. The University of Stellenbosch has offered the PI partial funding to support a sabbatical visit in Fall 2003, the primary purpose of which is to enable the PI to develop and enhance his expertise in Pattern Recognition. During the first year, the grant supported publication of 3 referred papers, presentation of 9 seminars and an intensive two-day course on wavelet theory. The grant supported the work of two students who functioned as research assistants.

Short-term data forecasting based on wavelet transformation and chaos theory

NASA Astrophysics Data System (ADS)

Wang, Yi; Li, Cunbin; Zhang, Liang

2017-09-01

A sketch of wavelet transformation and its application was given. Concerning the characteristics of time sequence, Haar wavelet was used to do data reduction. After processing, the effect of “data nail” on forecasting was reduced. Chaos theory was also introduced, a new chaos time series forecasting flow based on wavelet transformation was proposed. The largest Lyapunov exponent was larger than zero from small data sets, it verified the data change behavior still met chaotic behavior. Based on this, chaos time series to forecast short-term change behavior could be used. At last, the example analysis of the price from a real electricity market showed that the forecasting method increased the precision of the forecasting more effectively and steadily.

Wavelet analysis for wind fields estimation.

PubMed

Leite, Gladeston C; Ushizima, Daniela M; Medeiros, Fátima N S; de Lima, Gilson G

2010-01-01

Wind field analysis from synthetic aperture radar images allows the estimation of wind direction and speed based on image descriptors. In this paper, we propose a framework to automate wind direction retrieval based on wavelet decomposition associated with spectral processing. We extend existing undecimated wavelet transform approaches, by including à trous with B(3) spline scaling function, in addition to other wavelet bases as Gabor and Mexican-hat. The purpose is to extract more reliable directional information, when wind speed values range from 5 to 10 ms(-1). Using C-band empirical models, associated with the estimated directional information, we calculate local wind speed values and compare our results with QuikSCAT scatterometer data. The proposed approach has potential application in the evaluation of oil spills and wind farms.

Wavelet Transform Based Filter to Remove the Notches from Signal Under Harmonic Polluted Environment

NASA Astrophysics Data System (ADS)

Das, Sukanta; Ranjan, Vikash

2017-12-01

The work proposes to annihilate the notches present in the synchronizing signal required for converter operation appearing due to switching of semiconductor devices connected to the system in the harmonic polluted environment. The disturbances in the signal are suppressed by wavelet based novel filtering technique. In the proposed technique, the notches in the signal are determined and eliminated by the wavelet based multi-rate filter using `Daubechies4' (db4) as mother wavelet. The computational complexity of the adapted technique is very less as compared to any other conventional notch filtering techniques. The proposed technique is developed in MATLAB/Simulink and finally validated with dSPACE-1103 interface. The recovered signal, thus obtained, is almost free of the notches.

On the wavelet optimized finite difference method

NASA Technical Reports Server (NTRS)

Jameson, Leland

1994-01-01

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

Automatic epileptic seizure detection in EEGs using MF-DFA, SVM based on cloud computing.

PubMed

Zhang, Zhongnan; Wen, Tingxi; Huang, Wei; Wang, Meihong; Li, Chunfeng

2017-01-01

Epilepsy is a chronic disease with transient brain dysfunction that results from the sudden abnormal discharge of neurons in the brain. Since electroencephalogram (EEG) is a harmless and noninvasive detection method, it plays an important role in the detection of neurological diseases. However, the process of analyzing EEG to detect neurological diseases is often difficult because the brain electrical signals are random, non-stationary and nonlinear. In order to overcome such difficulty, this study aims to develop a new computer-aided scheme for automatic epileptic seizure detection in EEGs based on multi-fractal detrended fluctuation analysis (MF-DFA) and support vector machine (SVM). New scheme first extracts features from EEG by MF-DFA during the first stage. Then, the scheme applies a genetic algorithm (GA) to calculate parameters used in SVM and classify the training data according to the selected features using SVM. Finally, the trained SVM classifier is exploited to detect neurological diseases. The algorithm utilizes MLlib from library of SPARK and runs on cloud platform. Applying to a public dataset for experiment, the study results show that the new feature extraction method and scheme can detect signals with less features and the accuracy of the classification reached up to 99%. MF-DFA is a promising approach to extract features for analyzing EEG, because of its simple algorithm procedure and less parameters. The features obtained by MF-DFA can represent samples as well as traditional wavelet transform and Lyapunov exponents. GA can always find useful parameters for SVM with enough execution time. The results illustrate that the classification model can achieve comparable accuracy, which means that it is effective in epileptic seizure detection.

ICER-3D: A Progressive Wavelet-Based Compressor for Hyperspectral Images

NASA Technical Reports Server (NTRS)

Kiely, A.; Klimesh, M.; Xie, H.; Aranki, N.

2005-01-01

ICER-3D is a progressive, wavelet-based compressor for hyperspectral images. ICER-3D is derived from the ICER image compressor. ICER-3D can provide lossless and lossy compression, and incorporates an error-containment scheme to limit the effects of data loss during transmission. The three-dimensional wavelet decomposition structure used by ICER-3D exploits correlations in all three dimensions of hyperspectral data sets, while facilitating elimination of spectral ringing artifacts. Correlation is further exploited by a context modeler that effectively exploits spectral dependencies in the wavelet-transformed hyperspectral data. Performance results illustrating the benefits of these features are presented.

Objective research of auscultation signals in Traditional Chinese Medicine based on wavelet packet energy and support vector machine.

PubMed

Yan, Jianjun; Shen, Xiaojing; Wang, Yiqin; Li, Fufeng; Xia, Chunming; Guo, Rui; Chen, Chunfeng; Shen, Qingwei

2010-01-01

This study aims at utilising Wavelet Packet Transform (WPT) and Support Vector Machine (SVM) algorithm to make objective analysis and quantitative research for the auscultation in Traditional Chinese Medicine (TCM) diagnosis. First, Wavelet Packet Decomposition (WPD) at level 6 was employed to split more elaborate frequency bands of the auscultation signals. Then statistic analysis was made based on the extracted Wavelet Packet Energy (WPE) features from WPD coefficients. Furthermore, the pattern recognition was used to distinguish mixed subjects' statistical feature values of sample groups through SVM. Finally, the experimental results showed that the classification accuracies were at a high level.

Medical Image Compression Based on Vector Quantization with Variable Block Sizes in Wavelet Domain

PubMed Central

Jiang, Huiyan; Ma, Zhiyuan; Hu, Yang; Yang, Benqiang; Zhang, Libo

2012-01-01

An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited; for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD) was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified K-means approach which is based on energy function was used in the codebook training phase. At last, vector quantization coding was implemented in different types of sub-blocks. In order to verify the effectiveness of the proposed algorithm, JPEG, JPEG2000, and fractal coding approach were chosen as contrast algorithms. Experimental results show that the proposed method can improve the compression performance and can achieve a balance between the compression ratio and the image visual quality. PMID:23049544

Medical image compression based on vector quantization with variable block sizes in wavelet domain.

PubMed

Jiang, Huiyan; Ma, Zhiyuan; Hu, Yang; Yang, Benqiang; Zhang, Libo

2012-01-01

An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited; for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD) was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified K-means approach which is based on energy function was used in the codebook training phase. At last, vector quantization coding was implemented in different types of sub-blocks. In order to verify the effectiveness of the proposed algorithm, JPEG, JPEG2000, and fractal coding approach were chosen as contrast algorithms. Experimental results show that the proposed method can improve the compression performance and can achieve a balance between the compression ratio and the image visual quality.

Alcoholism detection in magnetic resonance imaging by Haar wavelet transform and back propagation neural network

NASA Astrophysics Data System (ADS)

Yu, Yali; Wang, Mengxia; Lima, Dimas

2018-04-01

In order to develop a novel alcoholism detection method, we proposed a magnetic resonance imaging (MRI)-based computer vision approach. We first use contrast equalization to increase the contrast of brain slices. Then, we perform Haar wavelet transform and principal component analysis. Finally, we use back propagation neural network (BPNN) as the classification tool. Our method yields a sensitivity of 81.71±4.51%, a specificity of 81.43±4.52%, and an accuracy of 81.57±2.18%. The Haar wavelet gives better performance than db4 wavelet and sym3 wavelet.

Wavelet-based polarimetry analysis

NASA Astrophysics Data System (ADS)

Ezekiel, Soundararajan; Harrity, Kyle; Farag, Waleed; Alford, Mark; Ferris, David; Blasch, Erik

2014-06-01

Wavelet transformation has become a cutting edge and promising approach in the field of image and signal processing. A wavelet is a waveform of effectively limited duration that has an average value of zero. Wavelet analysis is done by breaking up the signal into shifted and scaled versions of the original signal. The key advantage of a wavelet is that it is capable of revealing smaller changes, trends, and breakdown points that are not revealed by other techniques such as Fourier analysis. The phenomenon of polarization has been studied for quite some time and is a very useful tool for target detection and tracking. Long Wave Infrared (LWIR) polarization is beneficial for detecting camouflaged objects and is a useful approach when identifying and distinguishing manmade objects from natural clutter. In addition, the Stokes Polarization Parameters, which are calculated from 0°, 45°, 90°, 135° right circular, and left circular intensity measurements, provide spatial orientations of target features and suppress natural features. In this paper, we propose a wavelet-based polarimetry analysis (WPA) method to analyze Long Wave Infrared Polarimetry Imagery to discriminate targets such as dismounts and vehicles from background clutter. These parameters can be used for image thresholding and segmentation. Experimental results show the wavelet-based polarimetry analysis is efficient and can be used in a wide range of applications such as change detection, shape extraction, target recognition, and feature-aided tracking.

Acoustic emission detection for mass fractions of materials based on wavelet packet technology.

PubMed

Wang, Xianghong; Xiang, Jianjun; Hu, Hongwei; Xie, Wei; Li, Xiongbing

2015-07-01

Materials are often damaged during the process of detecting mass fractions by traditional methods. Acoustic emission (AE) technology combined with wavelet packet analysis is used to evaluate the mass fractions of microcrystalline graphite/polyvinyl alcohol (PVA) composites in this study. Attenuation characteristics of AE signals across the composites with different mass fractions are investigated. The AE signals are decomposed by wavelet packet technology to obtain the relationships between the energy and amplitude attenuation coefficients of feature wavelet packets and mass fractions as well. Furthermore, the relationship is validated by a sample. The larger proportion of microcrystalline graphite will correspond to the higher attenuation of energy and amplitude. The attenuation characteristics of feature wavelet packets with the frequency range from 125 kHz to 171.85 kHz are more suitable for the detection of mass fractions than those of the original AE signals. The error of the mass fraction of microcrystalline graphite calculated by the feature wavelet packet (1.8%) is lower than that of the original signal (3.9%). Therefore, AE detection base on wavelet packet analysis is an ideal NDT method for evaluate mass fractions of composite materials. Copyright © 2015 Elsevier B.V. All rights reserved.

Detailed Analysis of the Interoccurrence Time Statistics in Seismic Activity

NASA Astrophysics Data System (ADS)

Tanaka, Hiroki; Aizawa, Yoji

2017-02-01

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

Multifractal-based nuclei segmentation in fish images.

PubMed

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

2017-09-01

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

Wavelet SVM in Reproducing Kernel Hilbert Space for hyperspectral remote sensing image classification

NASA Astrophysics Data System (ADS)

Du, Peijun; Tan, Kun; Xing, Xiaoshi

2010-12-01

Combining Support Vector Machine (SVM) with wavelet analysis, we constructed wavelet SVM (WSVM) classifier based on wavelet kernel functions in Reproducing Kernel Hilbert Space (RKHS). In conventional kernel theory, SVM is faced with the bottleneck of kernel parameter selection which further results in time-consuming and low classification accuracy. The wavelet kernel in RKHS is a kind of multidimensional wavelet function that can approximate arbitrary nonlinear functions. Implications on semiparametric estimation are proposed in this paper. Airborne Operational Modular Imaging Spectrometer II (OMIS II) hyperspectral remote sensing image with 64 bands and Reflective Optics System Imaging Spectrometer (ROSIS) data with 115 bands were used to experiment the performance and accuracy of the proposed WSVM classifier. The experimental results indicate that the WSVM classifier can obtain the highest accuracy when using the Coiflet Kernel function in wavelet transform. In contrast with some traditional classifiers, including Spectral Angle Mapping (SAM) and Minimum Distance Classification (MDC), and SVM classifier using Radial Basis Function kernel, the proposed wavelet SVM classifier using the wavelet kernel function in Reproducing Kernel Hilbert Space is capable of improving classification accuracy obviously.

Onboard image compression schemes for modular airborne imaging spectrometer (MAIS) based on wavelet transform

NASA Astrophysics Data System (ADS)

Zhu, Zhenyu; Wang, Jianyu

1996-11-01

In this paper, two compression schemes are presented to meet the urgent needs of compressing the huge volume and high data rate of imaging spectrometer images. According to the multidimensional feature of the images and the high fidelity requirement of the reconstruction, both schemes were devised to exploit the high redundancy in both spatial and spectral dimension based on the mature wavelet transform technology. Wavelet transform was applied here in two ways: First, with the spatial wavelet transform and the spectral DPCM decorrelation, a ratio up to 84.3 with PSNR > 48db's near-lossless result was attained. This is based ont he fact that the edge structure among all the spectral bands are similar while WT has higher resolution in high frequency components. Secondly, with the wavelet's high efficiency in processing the 'wideband transient' signals, it was used to transform the raw nonstationary signals in the spectral dimension. A good result was also attained.

Block-based scalable wavelet image codec

NASA Astrophysics Data System (ADS)

Bao, Yiliang; Kuo, C.-C. Jay

1999-10-01

This paper presents a high performance block-based wavelet image coder which is designed to be of very low implementational complexity yet with rich features. In this image coder, the Dual-Sliding Wavelet Transform (DSWT) is first applied to image data to generate wavelet coefficients in fixed-size blocks. Here, a block only consists of wavelet coefficients from a single subband. The coefficient blocks are directly coded with the Low Complexity Binary Description (LCBiD) coefficient coding algorithm. Each block is encoded using binary context-based bitplane coding. No parent-child correlation is exploited in the coding process. There is also no intermediate buffering needed in between DSWT and LCBiD. The compressed bit stream generated by the proposed coder is both SNR and resolution scalable, as well as highly resilient to transmission errors. Both DSWT and LCBiD process the data in blocks whose size is independent of the size of the original image. This gives more flexibility in the implementation. The codec has a very good coding performance even the block size is (16,16).

Analysis of embolic signals with directional dual tree rational dilation wavelet transform.

PubMed

Serbes, Gorkem; Aydin, Nizamettin

2016-08-01

The dyadic discrete wavelet transform (dyadic-DWT), which is based on fixed integer sampling factor, has been used before for processing piecewise smooth biomedical signals. However, the dyadic-DWT has poor frequency resolution due to the low-oscillatory nature of its wavelet bases and therefore, it is less effective in processing embolic signals (ESs). To process ESs more effectively, a wavelet transform having better frequency resolution than the dyadic-DWT is needed. Therefore, in this study two ESs, containing micro-emboli and artifact waveforms, are analyzed with the Directional Dual Tree Rational-Dilation Wavelet Transform (DDT-RADWT). The DDT-RADWT, which can be directly applied to quadrature signals, is based on rational dilation factors and has adjustable frequency resolution. The analyses are done for both low and high Q-factors. It is proved that, when high Q-factor filters are employed in the DDT-RADWT, clearer representations of ESs can be attained in decomposed sub-bands and artifacts can be successfully separated.

Simultaneous compression and encryption for secure real-time secure transmission of sensitive video transmission

NASA Astrophysics Data System (ADS)

Al-Hayani, Nazar; Al-Jawad, Naseer; Jassim, Sabah A.

2014-05-01

Video compression and encryption became very essential in a secured real time video transmission. Applying both techniques simultaneously is one of the challenges where the size and the quality are important in multimedia transmission. In this paper we proposed a new technique for video compression and encryption. Both encryption and compression are based on edges extracted from the high frequency sub-bands of wavelet decomposition. The compression algorithm based on hybrid of: discrete wavelet transforms, discrete cosine transform, vector quantization, wavelet based edge detection, and phase sensing. The compression encoding algorithm treats the video reference and non-reference frames in two different ways. The encryption algorithm utilized A5 cipher combined with chaotic logistic map to encrypt the significant parameters and wavelet coefficients. Both algorithms can be applied simultaneously after applying the discrete wavelet transform on each individual frame. Experimental results show that the proposed algorithms have the following features: high compression, acceptable quality, and resistance to the statistical and bruteforce attack with low computational processing.

Spectral information enhancement using wavelet-based iterative filtering for in vivo gamma spectrometry.

PubMed

Paul, Sabyasachi; Sarkar, P K

2013-04-01

Use of wavelet transformation in stationary signal processing has been demonstrated for denoising the measured spectra and characterisation of radionuclides in the in vivo monitoring analysis, where difficulties arise due to very low activity level to be estimated in biological systems. The large statistical fluctuations often make the identification of characteristic gammas from radionuclides highly uncertain, particularly when interferences from progenies are also present. A new wavelet-based noise filtering methodology has been developed for better detection of gamma peaks in noisy data. This sequential, iterative filtering method uses the wavelet multi-resolution approach for noise rejection and an inverse transform after soft 'thresholding' over the generated coefficients. Analyses of in vivo monitoring data of (235)U and (238)U were carried out using this method without disturbing the peak position and amplitude while achieving a 3-fold improvement in the signal-to-noise ratio, compared with the original measured spectrum. When compared with other data-filtering techniques, the wavelet-based method shows the best results.

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

PubMed Central

Lin, D. C.; Sharif, A.

2012-01-01

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

Gait recognition based on Gabor wavelets and modified gait energy image for human identification

NASA Astrophysics Data System (ADS)

Huang, Deng-Yuan; Lin, Ta-Wei; Hu, Wu-Chih; Cheng, Chih-Hsiang

2013-10-01

This paper proposes a method for recognizing human identity using gait features based on Gabor wavelets and modified gait energy images (GEIs). Identity recognition by gait generally involves gait representation, extraction, and classification. In this work, a modified GEI convolved with an ensemble of Gabor wavelets is proposed as a gait feature. Principal component analysis is then used to project the Gabor-wavelet-based gait features into a lower-dimension feature space for subsequent classification. Finally, support vector machine classifiers based on a radial basis function kernel are trained and utilized to recognize human identity. The major contributions of this paper are as follows: (1) the consideration of the shadow effect to yield a more complete segmentation of gait silhouettes; (2) the utilization of motion estimation to track people when walkers overlap; and (3) the derivation of modified GEIs to extract more useful gait information. Extensive performance evaluation shows a great improvement of recognition accuracy due to the use of shadow removal, motion estimation, and gait representation using the modified GEIs and Gabor wavelets.

Noise adaptive wavelet thresholding for speckle noise removal in optical coherence tomography.

PubMed

Zaki, Farzana; Wang, Yahui; Su, Hao; Yuan, Xin; Liu, Xuan

2017-05-01

Optical coherence tomography (OCT) is based on coherence detection of interferometric signals and hence inevitably suffers from speckle noise. To remove speckle noise in OCT images, wavelet domain thresholding has demonstrated significant advantages in suppressing noise magnitude while preserving image sharpness. However, speckle noise in OCT images has different characteristics in different spatial scales, which has not been considered in previous applications of wavelet domain thresholding. In this study, we demonstrate a noise adaptive wavelet thresholding (NAWT) algorithm that exploits the difference of noise characteristics in different wavelet sub-bands. The algorithm is simple, fast, effective and is closely related to the physical origin of speckle noise in OCT image. Our results demonstrate that NAWT outperforms conventional wavelet thresholding.

Analysis on Behaviour of Wavelet Coefficient during Fault Occurrence in Transformer

NASA Astrophysics Data System (ADS)

Sreewirote, Bancha; Ngaopitakkul, Atthapol

2018-03-01

The protection system for transformer has play significant role in avoiding severe damage to equipment when disturbance occur and ensure overall system reliability. One of the methodology that widely used in protection scheme and algorithm is discrete wavelet transform. However, characteristic of coefficient under fault condition must be analyzed to ensure its effectiveness. So, this paper proposed study and analysis on wavelet coefficient characteristic when fault occur in transformer in both high- and low-frequency component from discrete wavelet transform. The effect of internal and external fault on wavelet coefficient of both fault and normal phase has been taken into consideration. The fault signal has been simulate using transmission connected to transformer experimental setup on laboratory level that modelled after actual system. The result in term of wavelet coefficient shown a clearly differentiate between wavelet characteristic in both high and low frequency component that can be used to further design and improve detection and classification algorithm that based on discrete wavelet transform methodology in the future.

Multifractality of cerebral blood flow

NASA Astrophysics Data System (ADS)

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

2003-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Multiscale multifractal detrended cross-correlation analysis of financial time series

NASA Astrophysics Data System (ADS)

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

2014-06-01

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

Cross-correlations between RMB exchange rate and international commodity markets

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Fast, large-scale hologram calculation in wavelet domain

NASA Astrophysics Data System (ADS)

Shimobaba, Tomoyoshi; Matsushima, Kyoji; Takahashi, Takayuki; Nagahama, Yuki; Hasegawa, Satoki; Sano, Marie; Hirayama, Ryuji; Kakue, Takashi; Ito, Tomoyoshi

2018-04-01

We propose a large-scale hologram calculation using WAvelet ShrinkAge-Based superpositIon (WASABI), a wavelet transform-based algorithm. An image-type hologram calculated using the WASABI method is printed on a glass substrate with the resolution of 65 , 536 × 65 , 536 pixels and a pixel pitch of 1 μm. The hologram calculation time amounts to approximately 354 s on a commercial CPU, which is approximately 30 times faster than conventional methods.

Evolution of Multiscale Multifractal Turbulence in the Heliosphere

NASA Astrophysics Data System (ADS)

Macek, W. M.; Wawrzaszek, A.

2009-04-01

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

Automatic Image Registration of Multimodal Remotely Sensed Data with Global Shearlet Features

NASA Technical Reports Server (NTRS)

Murphy, James M.; Le Moigne, Jacqueline; Harding, David J.

2015-01-01

Automatic image registration is the process of aligning two or more images of approximately the same scene with minimal human assistance. Wavelet-based automatic registration methods are standard, but sometimes are not robust to the choice of initial conditions. That is, if the images to be registered are too far apart relative to the initial guess of the algorithm, the registration algorithm does not converge or has poor accuracy, and is thus not robust. These problems occur because wavelet techniques primarily identify isotropic textural features and are less effective at identifying linear and curvilinear edge features. We integrate the recently developed mathematical construction of shearlets, which is more effective at identifying sparse anisotropic edges, with an existing automatic wavelet-based registration algorithm. Our shearlet features algorithm produces more distinct features than wavelet features algorithms; the separation of edges from textures is even stronger than with wavelets. Our algorithm computes shearlet and wavelet features for the images to be registered, then performs least squares minimization on these features to compute a registration transformation. Our algorithm is two-staged and multiresolution in nature. First, a cascade of shearlet features is used to provide a robust, though approximate, registration. This is then refined by registering with a cascade of wavelet features. Experiments across a variety of image classes show an improved robustness to initial conditions, when compared to wavelet features alone.

Automatic Image Registration of Multi-Modal Remotely Sensed Data with Global Shearlet Features

PubMed Central

Murphy, James M.; Le Moigne, Jacqueline; Harding, David J.

2017-01-01

Automatic image registration is the process of aligning two or more images of approximately the same scene with minimal human assistance. Wavelet-based automatic registration methods are standard, but sometimes are not robust to the choice of initial conditions. That is, if the images to be registered are too far apart relative to the initial guess of the algorithm, the registration algorithm does not converge or has poor accuracy, and is thus not robust. These problems occur because wavelet techniques primarily identify isotropic textural features and are less effective at identifying linear and curvilinear edge features. We integrate the recently developed mathematical construction of shearlets, which is more effective at identifying sparse anisotropic edges, with an existing automatic wavelet-based registration algorithm. Our shearlet features algorithm produces more distinct features than wavelet features algorithms; the separation of edges from textures is even stronger than with wavelets. Our algorithm computes shearlet and wavelet features for the images to be registered, then performs least squares minimization on these features to compute a registration transformation. Our algorithm is two-staged and multiresolution in nature. First, a cascade of shearlet features is used to provide a robust, though approximate, registration. This is then refined by registering with a cascade of wavelet features. Experiments across a variety of image classes show an improved robustness to initial conditions, when compared to wavelet features alone. PMID:29123329

Improved medical image fusion based on cascaded PCA and shift invariant wavelet transforms.

PubMed

Reena Benjamin, J; Jayasree, T

2018-02-01

In the medical field, radiologists need more informative and high-quality medical images to diagnose diseases. Image fusion plays a vital role in the field of biomedical image analysis. It aims to integrate the complementary information from multimodal images, producing a new composite image which is expected to be more informative for visual perception than any of the individual input images. The main objective of this paper is to improve the information, to preserve the edges and to enhance the quality of the fused image using cascaded principal component analysis (PCA) and shift invariant wavelet transforms. A novel image fusion technique based on cascaded PCA and shift invariant wavelet transforms is proposed in this paper. PCA in spatial domain extracts relevant information from the large dataset based on eigenvalue decomposition, and the wavelet transform operating in the complex domain with shift invariant properties brings out more directional and phase details of the image. The significance of maximum fusion rule applied in dual-tree complex wavelet transform domain enhances the average information and morphological details. The input images of the human brain of two different modalities (MRI and CT) are collected from whole brain atlas data distributed by Harvard University. Both MRI and CT images are fused using cascaded PCA and shift invariant wavelet transform method. The proposed method is evaluated based on three main key factors, namely structure preservation, edge preservation, contrast preservation. The experimental results and comparison with other existing fusion methods show the superior performance of the proposed image fusion framework in terms of visual and quantitative evaluations. In this paper, a complex wavelet-based image fusion has been discussed. The experimental results demonstrate that the proposed method enhances the directional features as well as fine edge details. Also, it reduces the redundant details, artifacts, distortions.

Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields

NASA Technical Reports Server (NTRS)

Baxes, Gregory A. (Inventor); Linger, Timothy C. (Inventor)

2011-01-01

Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.

Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields

NASA Technical Reports Server (NTRS)

Baxes, Gregory A. (Inventor)

2010-01-01

Systems and methods are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. A method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Software products that implement these methods are provided.

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

NASA Astrophysics Data System (ADS)

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

2007-09-01

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

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

NASA Astrophysics Data System (ADS)

Cajueiro, Daniel O.; Tabak, Benjamin M.

2007-01-01

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

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

PubMed Central

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

2017-01-01

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

Multifractality and heteroscedastic dynamics: An application to time series analysis

NASA Astrophysics Data System (ADS)

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

2008-01-01

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

The weather and climate: emergent laws and multifractal cascades

NASA Astrophysics Data System (ADS)

Lovejoy, Shaun; Schertzer, Daniel

2013-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Application of wavelet transformation and adaptive neighborhood based modified backpropagation (ANMBP) for classification of brain cancer

NASA Astrophysics Data System (ADS)

Werdiningsih, Indah; Zaman, Badrus; Nuqoba, Barry

2017-08-01

This paper presents classification of brain cancer using wavelet transformation and Adaptive Neighborhood Based Modified Backpropagation (ANMBP). Three stages of the processes, namely features extraction, features reduction, and classification process. Wavelet transformation is used for feature extraction and ANMBP is used for classification process. The result of features extraction is feature vectors. Features reduction used 100 energy values per feature and 10 energy values per feature. Classifications of brain cancer are normal, alzheimer, glioma, and carcinoma. Based on simulation results, 10 energy values per feature can be used to classify brain cancer correctly. The correct classification rate of proposed system is 95 %. This research demonstrated that wavelet transformation can be used for features extraction and ANMBP can be used for classification of brain cancer.

Wavelet Analysis for Wind Fields Estimation

PubMed Central

Leite, Gladeston C.; Ushizima, Daniela M.; Medeiros, Fátima N. S.; de Lima, Gilson G.

2010-01-01

Wind field analysis from synthetic aperture radar images allows the estimation of wind direction and speed based on image descriptors. In this paper, we propose a framework to automate wind direction retrieval based on wavelet decomposition associated with spectral processing. We extend existing undecimated wavelet transform approaches, by including à trous with B3 spline scaling function, in addition to other wavelet bases as Gabor and Mexican-hat. The purpose is to extract more reliable directional information, when wind speed values range from 5 to 10 ms−1. Using C-band empirical models, associated with the estimated directional information, we calculate local wind speed values and compare our results with QuikSCAT scatterometer data. The proposed approach has potential application in the evaluation of oil spills and wind farms. PMID:22219699

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

NASA Astrophysics Data System (ADS)

Monthus, Cécile; Garel, Thomas

2011-04-01

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

Paradigms of Complexity: Fractals and Structures in the Sciences

NASA Astrophysics Data System (ADS)

Novak, Miroslav M.

The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic Dynamics of Elastic-Plastic Beams * The Riemann Non-Differentiable Function and Identities for the Gaussian Sums * Revealing the Multifractal Nature of Failure Sequence * The Fractal Nature of wood Revealed by Drying * Squaring the Circle: Diffusion Volume and Acoustic Behaviour of a Fractal Structure * Relationship Between Acupuncture Holographic Units and Fetus Development; Fractal Features of Two Acupuncture Holographic Unit Systems * The Fractal Properties of the Large-Scale Magnetic Fields on the Sun * Fractal Analysis of Tide Gauge Data * Author Index

Modular continuous wavelet processing of biosignals: extracting heart rate and oxygen saturation from a video signal

PubMed Central

2016-01-01

A novel method of extracting heart rate and oxygen saturation from a video-based biosignal is described. The method comprises a novel modular continuous wavelet transform approach which includes: performing the transform, undertaking running wavelet archetyping to enhance the pulse information, extraction of the pulse ridge time–frequency information [and thus a heart rate (HRvid) signal], creation of a wavelet ratio surface, projection of the pulse ridge onto the ratio surface to determine the ratio of ratios from which a saturation trending signal is derived, and calibrating this signal to provide an absolute saturation signal (SvidO2). The method is illustrated through its application to a video photoplethysmogram acquired during a porcine model of acute desaturation. The modular continuous wavelet transform-based approach is advocated by the author as a powerful methodology to deal with noisy, non-stationary biosignals in general. PMID:27382479

An improved wavelet-Galerkin method for dynamic response reconstruction and parameter identification of shear-type frames

NASA Astrophysics Data System (ADS)

Bu, Haifeng; Wang, Dansheng; Zhou, Pin; Zhu, Hongping

2018-04-01

An improved wavelet-Galerkin (IWG) method based on the Daubechies wavelet is proposed for reconstructing the dynamic responses of shear structures. The proposed method flexibly manages wavelet resolution level according to excitation, thereby avoiding the weakness of the wavelet-Galerkin multiresolution analysis (WGMA) method in terms of resolution and the requirement of external excitation. IWG is implemented by this work in certain case studies, involving single- and n-degree-of-freedom frame structures subjected to a determined discrete excitation. Results demonstrate that IWG performs better than WGMA in terms of accuracy and computation efficiency. Furthermore, a new method for parameter identification based on IWG and an optimization algorithm are also developed for shear frame structures, and a simultaneous identification of structural parameters and excitation is implemented. Numerical results demonstrate that the proposed identification method is effective for shear frame structures.

Denoising time-domain induced polarisation data using wavelet techniques

NASA Astrophysics Data System (ADS)

Deo, Ravin N.; Cull, James P.

2016-05-01

Time-domain induced polarisation (TDIP) methods are routinely used for near-surface evaluations in quasi-urban environments harbouring networks of buried civil infrastructure. A conventional technique for improving signal to noise ratio in such environments is by using analogue or digital low-pass filtering followed by stacking and rectification. However, this induces large distortions in the processed data. In this study, we have conducted the first application of wavelet based denoising techniques for processing raw TDIP data. Our investigation included laboratory and field measurements to better understand the advantages and limitations of this technique. It was found that distortions arising from conventional filtering can be significantly avoided with the use of wavelet based denoising techniques. With recent advances in full-waveform acquisition and analysis, incorporation of wavelet denoising techniques can further enhance surveying capabilities. In this work, we present the rationale for utilising wavelet denoising methods and discuss some important implications, which can positively influence TDIP methods.

Application of improved wavelet total variation denoising for rolling bearing incipient fault diagnosis

NASA Astrophysics Data System (ADS)

Zhang, W.; Jia, M. P.

2018-06-01

When incipient fault appear in the rolling bearing, the fault feature is too small and easily submerged in the strong background noise. In this paper, wavelet total variation denoising based on kurtosis (Kurt-WATV) is studied, which can extract the incipient fault feature of the rolling bearing more effectively. The proposed algorithm contains main steps: a) establish a sparse diagnosis model, b) represent periodic impulses based on the redundant wavelet dictionary, c) solve the joint optimization problem by alternating direction method of multipliers (ADMM), d) obtain the reconstructed signal using kurtosis value as criterion and then select optimal wavelet subbands. This paper uses overcomplete rational-dilation wavelet transform (ORDWT) as a dictionary, and adjusts the control parameters to achieve the concentration in the time-frequency plane. Incipient fault of rolling bearing is used as an example, and the result shows that the effectiveness and superiority of the proposed Kurt- WATV bearing fault diagnosis algorithm.

3-D surface profilometry based on modulation measurement by applying wavelet transform method

NASA Astrophysics Data System (ADS)

Zhong, Min; Chen, Feng; Xiao, Chao; Wei, Yongchao

2017-01-01

A new analysis of 3-D surface profilometry based on modulation measurement technique by the application of Wavelet Transform method is proposed. As a tool excelling for its multi-resolution and localization in the time and frequency domains, Wavelet Transform method with good localized time-frequency analysis ability and effective de-noizing capacity can extract the modulation distribution more accurately than Fourier Transform method. Especially for the analysis of complex object, more details of the measured object can be well remained. In this paper, the theoretical derivation of Wavelet Transform method that obtains the modulation values from a captured fringe pattern is given. Both computer simulation and elementary experiment are used to show the validity of the proposed method by making a comparison with the results of Fourier Transform method. The results show that the Wavelet Transform method has a better performance than the Fourier Transform method in modulation values retrieval.

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

NASA Technical Reports Server (NTRS)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Continuous time wavelet entropy of auditory evoked potentials.

PubMed

Cek, M Emre; Ozgoren, Murat; Savaci, F Acar

2010-01-01

In this paper, the continuous time wavelet entropy (CTWE) of auditory evoked potentials (AEP) has been characterized by evaluating the relative wavelet energies (RWE) in specified EEG frequency bands. Thus, the rapid variations of CTWE due to the auditory stimulation could be detected in post-stimulus time interval. This approach removes the probability of missing the information hidden in short time intervals. The discrete time and continuous time wavelet based wavelet entropy variations were compared on non-target and target AEP data. It was observed that CTWE can also be an alternative method to analyze entropy as a function of time. 2009 Elsevier Ltd. All rights reserved.

Cell edge detection in JPEG2000 wavelet domain - analysis on sigmoid function edge model.

PubMed

Punys, Vytenis; Maknickas, Ramunas

2011-01-01

Big virtual microscopy images (80K x 60K pixels and larger) are usually stored using the JPEG2000 image compression scheme. Diagnostic quantification, based on image analysis, might be faster if performed on compressed data (approx. 20 times less the original amount), representing the coefficients of the wavelet transform. The analysis of possible edge detection without reverse wavelet transform is presented in the paper. Two edge detection methods, suitable for JPEG2000 bi-orthogonal wavelets, are proposed. The methods are adjusted according calculated parameters of sigmoid edge model. The results of model analysis indicate more suitable method for given bi-orthogonal wavelet.

A wavelet analysis of co-movements in Asian gold markets

NASA Astrophysics Data System (ADS)

Das, Debojyoti; Kannadhasan, M.; Al-Yahyaee, Khamis Hamed; Yoon, Seong-Min

2018-02-01

This study assesses the cross-country co-movements of gold spot returns among the major gold consuming countries in Asia using wavelet-based analysis for a dataset spanning over 26 years. Wavelet-based analysis is used since it allows measuring co-movements in a time-frequency space. The results suggest intense and positive co-movements in Asia after the Asian financial crisis of 1997 at all frequencies. In addition, the Asian gold spot markets depict a state of impending perfect market integration. Finally, Thailand emerges as the potential market leader in all wavelet scales except one, which is led by India. The study has important implications for international diversification of a single-asset (gold) portfolio.

Numerical solution of the Black-Scholes equation using cubic spline wavelets

NASA Astrophysics Data System (ADS)

Černá, Dana

2016-12-01

The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.

Detection method of flexion relaxation phenomenon based on wavelets for patients with low back pain

NASA Astrophysics Data System (ADS)

Nougarou, François; Massicotte, Daniel; Descarreaux, Martin

2012-12-01

The flexion relaxation phenomenon (FRP) can be defined as a reduction or silence of myoelectric activity of the lumbar erector spinae muscle during full trunk flexion. It is typically absent in patients with chronic low back pain (LBP). Before any broad clinical utilization of this neuromuscular response can be made, effective, standardized, and accurate methods of identifying FRP limits are needed. However, this phenomenon is clearly more difficult to detect for LBP patients than for healthy patients. The main goal of this study is to develop an automated method based on wavelet transformation that would improve time point limits detection of surface electromyography signals of the FRP in case of LBP patients. Conventional visual identification and proposed automated methods of time point limits detection of relaxation phase were compared on experimental data using criteria of accuracy and repeatability based on physiological properties. The evaluation demonstrates that the use of wavelet transform (WT) yields better results than methods without wavelet decomposition. Furthermore, methods based on wavelet per packet transform are more effective than algorithms employing discrete WT. Compared to visual detection, in addition to demonstrating an obvious saving of time, the use of wavelet per packet transform improves the accuracy and repeatability in the detection of the FRP limits. These results clearly highlight the value of the proposed technique in identifying onset and offset of the flexion relaxation response in LBP subjects.

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

PubMed

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

2013-11-01

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

Wavelet based de-noising of breath air absorption spectra profiles for improved classification by principal component analysis

NASA Astrophysics Data System (ADS)

Kistenev, Yu. V.; Shapovalov, A. V.; Borisov, A. V.; Vrazhnov, D. A.; Nikolaev, V. V.; Nikiforova, O. Yu.

2015-11-01

The comparison results of different mother wavelets used for de-noising of model and experimental data which were presented by profiles of absorption spectra of exhaled air are presented. The impact of wavelets de-noising on classification quality made by principal component analysis are also discussed.

Multiadaptive Bionic Wavelet Transform: Application to ECG Denoising and Baseline Wandering Reduction

NASA Astrophysics Data System (ADS)

Sayadi, Omid; Shamsollahi, Mohammad B.

2007-12-01

We present a new modified wavelet transform, called the multiadaptive bionic wavelet transform (MABWT), that can be applied to ECG signals in order to remove noise from them under a wide range of variations for noise. By using the definition of bionic wavelet transform and adaptively determining both the center frequency of each scale together with the[InlineEquation not available: see fulltext.]-function, the problem of desired signal decomposition is solved. Applying a new proposed thresholding rule works successfully in denoising the ECG. Moreover by using the multiadaptation scheme, lowpass noisy interference effects on the baseline of ECG will be removed as a direct task. The method was extensively clinically tested with real and simulated ECG signals which showed high performance of noise reduction, comparable to those of wavelet transform (WT). Quantitative evaluation of the proposed algorithm shows that the average SNR improvement of MABWT is 1.82 dB more than the WT-based results, for the best case. Also the procedure has largely proved advantageous over wavelet-based methods for baseline wandering cancellation, including both DC components and baseline drifts.

MRS3D: 3D Spherical Wavelet Transform on the Sphere

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2011-12-01

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. We present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We tested the 3D wavelet transform and as a toy-application, applied a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and found we can successfully remove noise without much loss to the large scale structure. The new spherical 3D isotropic wavelet transform, called MRS3D, is ideally suited to analysing and denoising future 3D spherical cosmological surveys; it uses a novel discrete spherical Fourier-Bessel Transform. MRS3D is based on two packages, IDL and Healpix and can be used only if these two packages have been installed.

Research on the fault diagnosis of bearing based on wavelet and demodulation

NASA Astrophysics Data System (ADS)

Li, Jiapeng; Yuan, Yu

2017-05-01

As a most commonly-used machine part, antifriction bearing is extensively used in mechanical equipment. Vibration signal analysis is one of the methods to monitor and diagnose the running status of antifriction bearings. Therefore, using wavelet analysis for demising is of great importance in the engineering practice. This paper firstly presented the basic theory of wavelet analysis to study the transformation, decomposition and reconstruction of wavelet. In addition, edition software LabVIEW was adopted to conduct wavelet and demodulation upon the vibration signal of antifriction bearing collected. With the combination of Hilbert envelop demodulation analysis, the fault character frequencies of the demised signal were extracted to conduct fault diagnosis analysis, which serves as a reference for the wavelet and demodulation of the vibration signal in engineering practice.

Perceptual compression of magnitude-detected synthetic aperture radar imagery

NASA Technical Reports Server (NTRS)

Gorman, John D.; Werness, Susan A.

1994-01-01

A perceptually-based approach for compressing synthetic aperture radar (SAR) imagery is presented. Key components of the approach are a multiresolution wavelet transform, a bit allocation mask based on an empirical human visual system (HVS) model, and hybrid scalar/vector quantization. Specifically, wavelet shrinkage techniques are used to segregate wavelet transform coefficients into three components: local means, edges, and texture. Each of these three components is then quantized separately according to a perceptually-based bit allocation scheme. Wavelet coefficients associated with local means and edges are quantized using high-rate scalar quantization while texture information is quantized using low-rate vector quantization. The impact of the perceptually-based multiresolution compression algorithm on visual image quality, impulse response, and texture properties is assessed for fine-resolution magnitude-detected SAR imagery; excellent image quality is found at bit rates at or above 1 bpp along with graceful performance degradation at rates below 1 bpp.

Wavelet-based segmentation of renal compartments in DCE-MRI of human kidney: initial results in patients and healthy volunteers.

PubMed

Li, Sheng; Zöllner, Frank G; Merrem, Andreas D; Peng, Yinghong; Roervik, Jarle; Lundervold, Arvid; Schad, Lothar R

2012-03-01

Renal diseases can lead to kidney failure that requires life-long dialysis or renal transplantation. Early detection and treatment can prevent progression towards end stage renal disease. MRI has evolved into a standard examination for the assessment of the renal morphology and function. We propose a wavelet-based clustering to group the voxel time courses and thereby, to segment the renal compartments. This approach comprises (1) a nonparametric, discrete wavelet transform of the voxel time course, (2) thresholding of the wavelet coefficients using Stein's Unbiased Risk estimator, and (3) k-means clustering of the wavelet coefficients to segment the kidneys. Our method was applied to 3D dynamic contrast enhanced (DCE-) MRI data sets of human kidney in four healthy volunteers and three patients. On average, the renal cortex in the healthy volunteers could be segmented at 88%, the medulla at 91%, and the pelvis at 98% accuracy. In the patient data, with aberrant voxel time courses, the segmentation was also feasible with good results for the kidney compartments. In conclusion wavelet based clustering of DCE-MRI of kidney is feasible and a valuable tool towards automated perfusion and glomerular filtration rate quantification. Copyright © 2011 Elsevier Ltd. All rights reserved.

A de-noising method using the improved wavelet threshold function based on noise variance estimation

NASA Astrophysics Data System (ADS)

Liu, Hui; Wang, Weida; Xiang, Changle; Han, Lijin; Nie, Haizhao

2018-01-01

The precise and efficient noise variance estimation is very important for the processing of all kinds of signals while using the wavelet transform to analyze signals and extract signal features. In view of the problem that the accuracy of traditional noise variance estimation is greatly affected by the fluctuation of noise values, this study puts forward the strategy of using the two-state Gaussian mixture model to classify the high-frequency wavelet coefficients in the minimum scale, which takes both the efficiency and accuracy into account. According to the noise variance estimation, a novel improved wavelet threshold function is proposed by combining the advantages of hard and soft threshold functions, and on the basis of the noise variance estimation algorithm and the improved wavelet threshold function, the research puts forth a novel wavelet threshold de-noising method. The method is tested and validated using random signals and bench test data of an electro-mechanical transmission system. The test results indicate that the wavelet threshold de-noising method based on the noise variance estimation shows preferable performance in processing the testing signals of the electro-mechanical transmission system: it can effectively eliminate the interference of transient signals including voltage, current, and oil pressure and maintain the dynamic characteristics of the signals favorably.

A high-performance seizure detection algorithm based on Discrete Wavelet Transform (DWT) and EEG

PubMed Central

Chen, Duo; Wan, Suiren; Xiang, Jing; Bao, Forrest Sheng

2017-01-01

In the past decade, Discrete Wavelet Transform (DWT), a powerful time-frequency tool, has been widely used in computer-aided signal analysis of epileptic electroencephalography (EEG), such as the detection of seizures. One of the important hurdles in the applications of DWT is the settings of DWT, which are chosen empirically or arbitrarily in previous works. The objective of this study aimed to develop a framework for automatically searching the optimal DWT settings to improve accuracy and to reduce computational cost of seizure detection. To address this, we developed a method to decompose EEG data into 7 commonly used wavelet families, to the maximum theoretical level of each mother wavelet. Wavelets and decomposition levels providing the highest accuracy in each wavelet family were then searched in an exhaustive selection of frequency bands, which showed optimal accuracy and low computational cost. The selection of frequency bands and features removed approximately 40% of redundancies. The developed algorithm achieved promising performance on two well-tested EEG datasets (accuracy >90% for both datasets). The experimental results of the developed method have demonstrated that the settings of DWT affect its performance on seizure detection substantially. Compared with existing seizure detection methods based on wavelet, the new approach is more accurate and transferable among datasets. PMID:28278203

Identification of large geomorphological anomalies based on 2D discrete wavelet transform

NASA Astrophysics Data System (ADS)

Doglioni, A.; Simeone, V.

2012-04-01

The identification and analysis based on quantitative evidences of large geomorphological anomalies is an important stage for the study of large landslides. Numerical geomorphic analyses represent an interesting approach to this kind of studies, allowing for a detailed and pretty accurate identification of hidden topographic anomalies that may be related to large landslides. Here a geomorphic numerical analyses of the Digital Terrain Model (DTM) is presented. The introduced approach is based on 2D discrete wavelet transform (Antoine et al., 2003; Bruun and Nilsen, 2003, Booth et al., 2009). The 2D wavelet decomposition of the DTM, and in particular the analysis of the detail coefficients of the wavelet transform can provide evidences of anomalies or singularities, i.e. discontinuities of the land surface. These discontinuities are not very evident from the DTM as it is, while 2D wavelet transform allows for grid-based analysis of DTM and for mapping the decomposition. In fact, the grid-based DTM can be assumed as a matrix, where a discrete wavelet transform (Daubechies, 1992) is performed columnwise and linewise, which basically represent horizontal and vertical directions. The outcomes of this analysis are low-frequency approximation coefficients and high-frequency detail coefficients. Detail coefficients are analyzed, since their variations are associated to discontinuities of the DTM. Detailed coefficients are estimated assuming to perform 2D wavelet transform both for the horizontal direction (east-west) and for the vertical direction (north-south). Detail coefficients are then mapped for both the cases, thus allowing to visualize and quantify potential anomalies of the land surface. Moreover, wavelet decomposition can be pushed to further levels, assuming a higher scale number of the transform. This may potentially return further interesting results, in terms of identification of the anomalies of land surface. In this kind of approach, the choice of a proper mother wavelet function is a tricky point, since it conditions the analysis and then their outcomes. Therefore multiple levels as well as multiple wavelet analyses are guessed. Here the introduced approach is applied to some interesting cases study of south Italy, in particular for the identification of large anomalies associated to large landslides at the transition between Apennine chain domain and the foredeep domain. In particular low Biferno valley and Fortore valley are here analyzed. Finally, the wavelet transforms are performed on multiple levels, thus trying to address the problem of which is the level extent for an accurate analysis fit to a specific problem. Antoine J.P., Carrette P., Murenzi R., and Piette B., (2003), Image analysis with two-dimensional continuous wavelet transform, Signal Processing, 31(3), pp. 241-272, doi:10.1016/0165-1684(93)90085-O. Booth A.M., Roering J.J., and Taylor Perron J., (2009), Automated landslide mapping using spectral analysis and high-resolution topographic data: Puget Sound lowlands, Washington, and Portland Hills, Oregon, Geomorphology, 109(3-4), pp. 132-147, doi:10.1016/j.geomorph.2009.02.027. Bruun B.T., and Nilsen S., (2003), Wavelet representation of large digital terrain models, Computers and Geoscience, 29(6), pp. 695-703, doi:10.1016/S0098-3004(03)00015-3. Daubechies, I. (1992), Ten lectures on wavelets, SIAM.

Multi-source feature extraction and target recognition in wireless sensor networks based on adaptive distributed wavelet compression algorithms

NASA Astrophysics Data System (ADS)

Hortos, William S.

2008-04-01

Proposed distributed wavelet-based algorithms are a means to compress sensor data received at the nodes forming a wireless sensor network (WSN) by exchanging information between neighboring sensor nodes. Local collaboration among nodes compacts the measurements, yielding a reduced fused set with equivalent information at far fewer nodes. Nodes may be equipped with multiple sensor types, each capable of sensing distinct phenomena: thermal, humidity, chemical, voltage, or image signals with low or no frequency content as well as audio, seismic or video signals within defined frequency ranges. Compression of the multi-source data through wavelet-based methods, distributed at active nodes, reduces downstream processing and storage requirements along the paths to sink nodes; it also enables noise suppression and more energy-efficient query routing within the WSN. Targets are first detected by the multiple sensors; then wavelet compression and data fusion are applied to the target returns, followed by feature extraction from the reduced data; feature data are input to target recognition/classification routines; targets are tracked during their sojourns through the area monitored by the WSN. Algorithms to perform these tasks are implemented in a distributed manner, based on a partition of the WSN into clusters of nodes. In this work, a scheme of collaborative processing is applied for hierarchical data aggregation and decorrelation, based on the sensor data itself and any redundant information, enabled by a distributed, in-cluster wavelet transform with lifting that allows multiple levels of resolution. The wavelet-based compression algorithm significantly decreases RF bandwidth and other resource use in target processing tasks. Following wavelet compression, features are extracted. The objective of feature extraction is to maximize the probabilities of correct target classification based on multi-source sensor measurements, while minimizing the resource expenditures at participating nodes. Therefore, the feature-extraction method based on the Haar DWT is presented that employs a maximum-entropy measure to determine significant wavelet coefficients. Features are formed by calculating the energy of coefficients grouped around the competing clusters. A DWT-based feature extraction algorithm used for vehicle classification in WSNs can be enhanced by an added rule for selecting the optimal number of resolution levels to improve the correct classification rate and reduce energy consumption expended in local algorithm computations. Published field trial data for vehicular ground targets, measured with multiple sensor types, are used to evaluate the wavelet-assisted algorithms. Extracted features are used in established target recognition routines, e.g., the Bayesian minimum-error-rate classifier, to compare the effects on the classification performance of the wavelet compression. Simulations of feature sets and recognition routines at different resolution levels in target scenarios indicate the impact on classification rates, while formulas are provided to estimate reduction in resource use due to distributed compression.

Detection of small bowel tumors in capsule endoscopy frames using texture analysis based on the discrete wavelet transform.

PubMed

Barbosa, Daniel J C; Ramos, Jaime; Lima, Carlos S

2008-01-01

Capsule endoscopy is an important tool to diagnose tumor lesions in the small bowel. The capsule endoscopic images possess vital information expressed by color and texture. This paper presents an approach based in the textural analysis of the different color channels, using the wavelet transform to select the bands with the most significant texture information. A new image is then synthesized from the selected wavelet bands, trough the inverse wavelet transform. The features of each image are based on second-order textural information, and they are used in a classification scheme using a multilayer perceptron neural network. The proposed methodology has been applied in real data taken from capsule endoscopic exams and reached 98.7% sensibility and 96.6% specificity. These results support the feasibility of the proposed algorithm.

Element analysis: a wavelet-based method for analysing time-localized events in noisy time series.

PubMed

Lilly, Jonathan M

2017-04-01

A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized 'events'. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima. The distribution of events in general power-law noise is determined in order to establish significance based on an expected false detection rate. Finally, an expression for an event's 'region of influence' within the wavelet transform permits the formation of a criterion for rejecting spurious maxima due to numerical artefacts or other unsuitable events. Signals can then be reconstructed based on a small number of isolated points on the time/scale plane. This method, termed element analysis , is applied to the identification of long-lived eddy structures in ocean currents as observed by along-track measurements of sea surface elevation from satellite altimetry.

3D High Resolution Mesh Deformation Based on Multi Library Wavelet Neural Network Architecture

NASA Astrophysics Data System (ADS)

Dhibi, Naziha; Elkefi, Akram; Bellil, Wajdi; Amar, Chokri Ben

2016-12-01

This paper deals with the features of a novel technique for large Laplacian boundary deformations using estimated rotations. The proposed method is based on a Multi Library Wavelet Neural Network structure founded on several mother wavelet families (MLWNN). The objective is to align features of mesh and minimize distortion with a fixed feature that minimizes the sum of the distances between all corresponding vertices. New mesh deformation method worked in the domain of Region of Interest (ROI). Our approach computes deformed ROI, updates and optimizes it to align features of mesh based on MLWNN and spherical parameterization configuration. This structure has the advantage of constructing the network by several mother wavelets to solve high dimensions problem using the best wavelet mother that models the signal better. The simulation test achieved the robustness and speed considerations when developing deformation methodologies. The Mean-Square Error and the ratio of deformation are low compared to other works from the state of the art. Our approach minimizes distortions with fixed features to have a well reconstructed object.

Wavelet Transforms in Parallel Image Processing

DTIC Science & Technology

1994-01-27

NUMBER OF PAGES Object Segmentation, Texture Segmentation, Image Compression, Image 137 Halftoning , Neural Network, Parallel Algorithms, 2D and 3D...Vector Quantization of Wavelet Transform Coefficients ........ ............................. 57 B.1.f Adaptive Image Halftoning based on Wavelet...application has been directed to the adaptive image halftoning . The gray information at a pixel, including its gray value and gradient, is represented by

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

NASA Astrophysics Data System (ADS)

Hidajatullah-Maksoed, Widastra

2015-04-01

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

Generalization of multifractal theory within quantum calculus

NASA Astrophysics Data System (ADS)

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

2010-03-01

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

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

NASA Astrophysics Data System (ADS)

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

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

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

PubMed

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

2017-04-01

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

Volatility of linear and nonlinear time series

NASA Astrophysics Data System (ADS)

Kalisky, Tomer; Ashkenazy, Yosef; Havlin, Shlomo

2005-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Numerical Simulation of Monitoring Corrosion in Reinforced Concrete Based on Ultrasonic Guided Waves

PubMed Central

Zheng, Zhupeng; Lei, Ying; Xue, Xin

2014-01-01

Numerical simulation based on finite element method is conducted to predict the location of pitting corrosion in reinforced concrete. Simulation results show that it is feasible to predict corrosion monitoring based on ultrasonic guided wave in reinforced concrete, and wavelet analysis can be used for the extremely weak signal of guided waves due to energy leaking into concrete. The characteristic of time-frequency localization of wavelet transform is adopted in the corrosion monitoring of reinforced concrete. Guided waves can be successfully used to identify corrosion defects in reinforced concrete with the analysis of suitable wavelet-based function and its scale. PMID:25013865

The generalized Morse wavelet method to determine refractive index dispersion of dielectric films

NASA Astrophysics Data System (ADS)

Kocahan, Özlem; Özcan, Seçkin; Coşkun, Emre; Özder, Serhat

2017-04-01

The continuous wavelet transform (CWT) method is a useful tool for the determination of refractive index dispersion of dielectric films. Mother wavelet selection is an important factor for the accuracy of the results when using CWT. In this study, generalized Morse wavelet (GMW) was proposed as the mother wavelet because of having two degrees of freedom. The simulation studies, based on error calculations and Cauchy Coefficient comparisons, were presented and also the noisy signal was tested by CWT method with GMW. The experimental validity of this method was checked by D263 T schott glass having 100 μm thickness and the results were compared to those from the catalog value.

Photoacoustic signals denoising of the glucose aqueous solutions using an improved wavelet threshold method

NASA Astrophysics Data System (ADS)

Ren, Zhong; Liu, Guodong; Xiong, Zhihua

2016-10-01

The photoacoustic signals denoising of glucose is one of most important steps in the quality identification of the fruit because the real-time photoacoustic singals of glucose are easily interfered by all kinds of noises. To remove the noises and some useless information, an improved wavelet threshld function were proposed. Compared with the traditional wavelet hard and soft threshold functions, the improved wavelet threshold function can overcome the pseudo-oscillation effect of the denoised photoacoustic signals due to the continuity of the improved wavelet threshold function, and the error between the denoised signals and the original signals can be decreased. To validate the feasibility of the improved wavelet threshold function denoising, the denoising simulation experiments based on MATLAB programmimg were performed. In the simulation experiments, the standard test signal was used, and three different denoising methods were used and compared with the improved wavelet threshold function. The signal-to-noise ratio (SNR) and the root-mean-square error (RMSE) values were used to evaluate the performance of the improved wavelet threshold function denoising. The experimental results demonstrate that the SNR value of the improved wavelet threshold function is largest and the RMSE value is lest, which fully verifies that the improved wavelet threshold function denoising is feasible. Finally, the improved wavelet threshold function denoising was used to remove the noises of the photoacoustic signals of the glucose solutions. The denoising effect is also very good. Therefore, the improved wavelet threshold function denoising proposed by this paper, has a potential value in the field of denoising for the photoacoustic singals.

Statistical and Multifractal Evaluation of Soil Compaction in a Vineyard

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Experimental study on Statistical Damage Detection of RC Structures based on Wavelet Packet Analysis

NASA Astrophysics Data System (ADS)

Zhu, X. Q.; Law, S. S.; Jayawardhan, M.

2011-07-01

A novel damage indicator based on wavelet packet transform is developed in this study for structural health monitoring. The response signal of a structure under an impact load is normalized and then decomposed into wavelet packet components. Energies of these wavelet packet components are then calculated to obtain the energy distribution. A statistical indicator is developed to describe the damage extent of the structure. This approach is applied to the test results from simply supported reinforced concrete beams in the laboratory. Cases with single damage are created from static loading, and accelerations of the structure from under impact loads are analyzed. Results show that the method can be used for the damage monitoring and assessment of the structure.

Application of based on improved wavelet algorithm in fiber temperature sensor

NASA Astrophysics Data System (ADS)

Qi, Hui; Tang, Wenjuan

2018-03-01

It is crucial point that accurate temperature in distributed optical fiber temperature sensor. In order to solve the problem of temperature measurement error due to weak Raman scattering signal and strong noise in system, a new based on improved wavelet algorithm is presented. On the basis of the traditional modulus maxima wavelet algorithm, signal correlation is considered to improve the ability to capture signals and noise, meanwhile, combined with wavelet decomposition scale adaptive method to eliminate signal loss or noise not filtered due to mismatch scale. Superiority of algorithm filtering is compared with others by Matlab. At last, the 3km distributed optical fiber temperature sensing system is used for verification. Experimental results show that accuracy of temperature generally increased by 0.5233.

Detection of spontaneous vesicle release at individual synapses using multiple wavelets in a CWT-based algorithm.

PubMed

Sokoll, Stefan; Tönnies, Klaus; Heine, Martin

2012-01-01

In this paper we present an algorithm for the detection of spontaneous activity at individual synapses in microscopy images. By employing the optical marker pHluorin, we are able to visualize synaptic vesicle release with a spatial resolution in the nm range in a non-invasive manner. We compute individual synaptic signals from automatically segmented regions of interest and detect peaks that represent synaptic activity using a continuous wavelet transform based algorithm. As opposed to standard peak detection algorithms, we employ multiple wavelets to match all relevant features of the peak. We evaluate our multiple wavelet algorithm (MWA) on real data and assess the performance on synthetic data over a wide range of signal-to-noise ratios.

A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs

NASA Astrophysics Data System (ADS)

Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin

2018-05-01

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

A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs

NASA Astrophysics Data System (ADS)

Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin

2018-04-01

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

Data series embedding and scale invariant statistics.

PubMed

Michieli, I; Medved, B; Ristov, S

2010-06-01

Data sequences acquired from bio-systems such as human gait data, heart rate interbeat data, or DNA sequences exhibit complex dynamics that is frequently described by a long-memory or power-law decay of autocorrelation function. One way of characterizing that dynamics is through scale invariant statistics or "fractal-like" behavior. For quantifying scale invariant parameters of physiological signals several methods have been proposed. Among them the most common are detrended fluctuation analysis, sample mean variance analyses, power spectral density analysis, R/S analysis, and recently in the realm of the multifractal approach, wavelet analysis. In this paper it is demonstrated that embedding the time series data in the high-dimensional pseudo-phase space reveals scale invariant statistics in the simple fashion. The procedure is applied on different stride interval data sets from human gait measurements time series (Physio-Bank data library). Results show that introduced mapping adequately separates long-memory from random behavior. Smaller gait data sets were analyzed and scale-free trends for limited scale intervals were successfully detected. The method was verified on artificially produced time series with known scaling behavior and with the varying content of noise. The possibility for the method to falsely detect long-range dependence in the artificially generated short range dependence series was investigated. (c) 2009 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Cao, Guangxi; Zhao, Yingchao; Han, Yan

2015-05-01

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

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

PubMed Central

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

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

EEG Artifact Removal Using a Wavelet Neural Network

NASA Technical Reports Server (NTRS)

Nguyen, Hoang-Anh T.; Musson, John; Li, Jiang; McKenzie, Frederick; Zhang, Guangfan; Xu, Roger; Richey, Carl; Schnell, Tom

2011-01-01

!n this paper we developed a wavelet neural network. (WNN) algorithm for Electroencephalogram (EEG) artifact removal without electrooculographic (EOG) recordings. The algorithm combines the universal approximation characteristics of neural network and the time/frequency property of wavelet. We. compared the WNN algorithm with .the ICA technique ,and a wavelet thresholding method, which was realized by using the Stein's unbiased risk estimate (SURE) with an adaptive gradient-based optimal threshold. Experimental results on a driving test data set show that WNN can remove EEG artifacts effectively without diminishing useful EEG information even for very noisy data.

An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

NASA Astrophysics Data System (ADS)

Alam Khan, Najeeb; Razzaq, Oyoon Abdul

2016-03-01

In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

Real-time modeling of primitive environments through wavelet sensors and Hebbian learning

NASA Astrophysics Data System (ADS)

Vaccaro, James M.; Yaworsky, Paul S.

1999-06-01

Modeling the world through sensory input necessarily provides a unique perspective for the observer. Given a limited perspective, objects and events cannot always be encoded precisely but must involve crude, quick approximations to deal with sensory information in a real- time manner. As an example, when avoiding an oncoming car, a pedestrian needs to identify the fact that a car is approaching before ascertaining the model or color of the vehicle. In our methodology, we use wavelet-based sensors with self-organized learning to encode basic sensory information in real-time. The wavelet-based sensors provide necessary transformations while a rank-based Hebbian learning scheme encodes a self-organized environment through translation, scale and orientation invariant sensors. Such a self-organized environment is made possible by combining wavelet sets which are orthonormal, log-scale with linear orientation and have automatically generated membership functions. In earlier work we used Gabor wavelet filters, rank-based Hebbian learning and an exponential modulation function to encode textural information from images. Many different types of modulation are possible, but based on biological findings the exponential modulation function provided a good approximation of first spike coding of `integrate and fire' neurons. These types of Hebbian encoding schemes (e.g., exponential modulation, etc.) are useful for quick response and learning, provide several advantages over contemporary neural network learning approaches, and have been found to quantize data nonlinearly. By combining wavelets with Hebbian learning we can provide a real-time front-end for modeling an intelligent process, such as the autonomous control of agents in a simulated environment.

Wavelet method for CT colonography computer-aided polyp detection.

PubMed

Li, Jiang; Van Uitert, Robert; Yao, Jianhua; Petrick, Nicholas; Franaszek, Marek; Huang, Adam; Summers, Ronald M

2008-08-01

Computed tomographic colonography (CTC) computer aided detection (CAD) is a new method to detect colon polyps. Colonic polyps are abnormal growths that may become cancerous. Detection and removal of colonic polyps, particularly larger ones, has been shown to reduce the incidence of colorectal cancer. While high sensitivities and low false positive rates are consistently achieved for the detection of polyps sized 1 cm or larger, lower sensitivities and higher false positive rates occur when the goal of CAD is to identify "medium"-sized polyps, 6-9 mm in diameter. Such medium-sized polyps may be important for clinical patient management. We have developed a wavelet-based postprocessor to reduce false positives for this polyp size range. We applied the wavelet-based postprocessor to CTC CAD findings from 44 patients in whom 45 polyps with sizes of 6-9 mm were found at segmentally unblinded optical colonoscopy and visible on retrospective review of the CT colonography images. Prior to the application of the wavelet-based postprocessor, the CTC CAD system detected 33 of the polyps (sensitivity 73.33%) with 12.4 false positives per patient, a sensitivity comparable to that of expert radiologists. Fourfold cross validation with 5000 bootstraps showed that the wavelet-based postprocessor could reduce the false positives by 56.61% (p <0.001), to 5.38 per patient (95% confidence interval [4.41, 6.34]), without significant sensitivity degradation (32/45, 71.11%, 95% confidence interval [66.39%, 75.74%], p=0.1713). We conclude that this wavelet-based postprocessor can substantially reduce the false positive rate of our CTC CAD for this important polyp size range.

Scaling properties of Polish rain series

NASA Astrophysics Data System (ADS)

Licznar, P.

2009-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Adaptive zero-tree structure for curved wavelet image coding

NASA Astrophysics Data System (ADS)

Zhang, Liang; Wang, Demin; Vincent, André

2006-02-01

We investigate the issue of efficient data organization and representation of the curved wavelet coefficients [curved wavelet transform (WT)]. We present an adaptive zero-tree structure that exploits the cross-subband similarity of the curved wavelet transform. In the embedded zero-tree wavelet (EZW) and the set partitioning in hierarchical trees (SPIHT), the parent-child relationship is defined in such a way that a parent has four children, restricted to a square of 2×2 pixels, the parent-child relationship in the adaptive zero-tree structure varies according to the curves along which the curved WT is performed. Five child patterns were determined based on different combinations of curve orientation. A new image coder was then developed based on this adaptive zero-tree structure and the set-partitioning technique. Experimental results using synthetic and natural images showed the effectiveness of the proposed adaptive zero-tree structure for encoding of the curved wavelet coefficients. The coding gain of the proposed coder can be up to 1.2 dB in terms of peak SNR (PSNR) compared to the SPIHT coder. Subjective evaluation shows that the proposed coder preserves lines and edges better than the SPIHT coder.

Wavelet-based analysis of circadian behavioral rhythms.

PubMed

Leise, Tanya L

2015-01-01

The challenging problems presented by noisy biological oscillators have led to the development of a great variety of methods for accurately estimating rhythmic parameters such as period and amplitude. This chapter focuses on wavelet-based methods, which can be quite effective for assessing how rhythms change over time, particularly if time series are at least a week in length. These methods can offer alternative views to complement more traditional methods of evaluating behavioral records. The analytic wavelet transform can estimate the instantaneous period and amplitude, as well as the phase of the rhythm at each time point, while the discrete wavelet transform can extract the circadian component of activity and measure the relative strength of that circadian component compared to those in other frequency bands. Wavelet transforms do not require the removal of noise or trend, and can, in fact, be effective at removing noise and trend from oscillatory time series. The Fourier periodogram and spectrogram are reviewed, followed by descriptions of the analytic and discrete wavelet transforms. Examples illustrate application of each method and their prior use in chronobiology is surveyed. Issues such as edge effects, frequency leakage, and implications of the uncertainty principle are also addressed. © 2015 Elsevier Inc. All rights reserved.

Local wavelet transform: a cost-efficient custom processor for space image compression

NASA Astrophysics Data System (ADS)

Masschelein, Bart; Bormans, Jan G.; Lafruit, Gauthier

2002-11-01

Thanks to its intrinsic scalability features, the wavelet transform has become increasingly popular as decorrelator in image compression applications. Throuhgput, memory requirements and complexity are important parameters when developing hardware image compression modules. An implementation of the classical, global wavelet transform requires large memory sizes and implies a large latency between the availability of the input image and the production of minimal data entities for entropy coding. Image tiling methods, as proposed by JPEG2000, reduce the memory sizes and the latency, but inevitably introduce image artefacts. The Local Wavelet Transform (LWT), presented in this paper, is a low-complexity wavelet transform architecture using a block-based processing that results in the same transformed images as those obtained by the global wavelet transform. The architecture minimizes the processing latency with a limited amount of memory. Moreover, as the LWT is an instruction-based custom processor, it can be programmed for specific tasks, such as push-broom processing of infinite-length satelite images. The features of the LWT makes it appropriate for use in space image compression, where high throughput, low memory sizes, low complexity, low power and push-broom processing are important requirements.

Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam

NASA Astrophysics Data System (ADS)

Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa

2017-08-01

In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.

An improved method based on wavelet coefficient correlation to filter noise in Doppler ultrasound blood flow signals

NASA Astrophysics Data System (ADS)

Wan, Renzhi; Zu, Yunxiao; Shao, Lin

2018-04-01

The blood echo signal maintained through Medical ultrasound Doppler devices would always include vascular wall pulsation signal .The traditional method to de-noise wall signal is using high-pass filter, which will also remove the lowfrequency part of the blood flow signal. Some scholars put forward a method based on region selective reduction, which at first estimates of the wall pulsation signals and then removes the wall signal from the mixed signal. Apparently, this method uses the correlation between wavelet coefficients to distinguish blood signal from wall signal, but in fact it is a kind of wavelet threshold de-noising method, whose effect is not so much ideal. In order to maintain a better effect, this paper proposes an improved method based on wavelet coefficient correlation to separate blood signal and wall signal, and simulates the algorithm by computer to verify its validity.

Noise Reduction in Breath Sound Files Using Wavelet Transform Based Filter

NASA Astrophysics Data System (ADS)

Syahputra, M. F.; Situmeang, S. I. G.; Rahmat, R. F.; Budiarto, R.

2017-04-01

The development of science and technology in the field of healthcare increasingly provides convenience in diagnosing respiratory system problem. Recording the breath sounds is one example of these developments. Breath sounds are recorded using a digital stethoscope, and then stored in a file with sound format. This breath sounds will be analyzed by health practitioners to diagnose the symptoms of disease or illness. However, the breath sounds is not free from interference signals. Therefore, noise filter or signal interference reduction system is required so that breath sounds component which contains information signal can be clarified. In this study, we designed a filter called a wavelet transform based filter. The filter that is designed in this study is using Daubechies wavelet with four wavelet transform coefficients. Based on the testing of the ten types of breath sounds data, the data is obtained in the largest SNRdB bronchial for 74.3685 decibels.

Wavelet energy-guided level set-based active contour: a segmentation method to segment highly similar regions.

PubMed

Achuthan, Anusha; Rajeswari, Mandava; Ramachandram, Dhanesh; Aziz, Mohd Ezane; Shuaib, Ibrahim Lutfi

2010-07-01

This paper introduces an approach to perform segmentation of regions in computed tomography (CT) images that exhibit intra-region intensity variations and at the same time have similar intensity distributions with surrounding/adjacent regions. In this work, we adapt a feature computed from wavelet transform called wavelet energy to represent the region information. The wavelet energy is embedded into a level set model to formulate the segmentation model called wavelet energy-guided level set-based active contour (WELSAC). The WELSAC model is evaluated using several synthetic and CT images focusing on tumour cases, which contain regions demonstrating the characteristics of intra-region intensity variations and having high similarity in intensity distributions with the adjacent regions. The obtained results show that the proposed WELSAC model is able to segment regions of interest in close correspondence with the manual delineation provided by the medical experts and to provide a solution for tumour detection. Copyright 2010 Elsevier Ltd. All rights reserved.

Improving liquid chromatography-tandem mass spectrometry determinations by modifying noise frequency spectrum between two consecutive wavelet-based low-pass filtering procedures.

PubMed

Chen, Hsiao-Ping; Liao, Hui-Ju; Huang, Chih-Min; Wang, Shau-Chun; Yu, Sung-Nien

2010-04-23

This paper employs one chemometric technique to modify the noise spectrum of liquid chromatography-tandem mass spectrometry (LC-MS/MS) chromatogram between two consecutive wavelet-based low-pass filter procedures to improve the peak signal-to-noise (S/N) ratio enhancement. Although similar techniques of using other sets of low-pass procedures such as matched filters have been published, the procedures developed in this work are able to avoid peak broadening disadvantages inherent in matched filters. In addition, unlike Fourier transform-based low-pass filters, wavelet-based filters efficiently reject noises in the chromatograms directly in the time domain without distorting the original signals. In this work, the low-pass filtering procedures sequentially convolve the original chromatograms against each set of low pass filters to result in approximation coefficients, representing the low-frequency wavelets, of the first five resolution levels. The tedious trials of setting threshold values to properly shrink each wavelet are therefore no longer required. This noise modification technique is to multiply one wavelet-based low-pass filtered LC-MS/MS chromatogram with another artificial chromatogram added with thermal noises prior to the other wavelet-based low-pass filter. Because low-pass filter cannot eliminate frequency components below its cut-off frequency, more efficient peak S/N ratio improvement cannot be accomplished using consecutive low-pass filter procedures to process LC-MS/MS chromatograms. In contrast, when the low-pass filtered LC-MS/MS chromatogram is conditioned with the multiplication alteration prior to the other low-pass filter, much better ratio improvement is achieved. The noise frequency spectrum of low-pass filtered chromatogram, which originally contains frequency components below the filter cut-off frequency, is altered to span a broader range with multiplication operation. When the frequency range of this modified noise spectrum shifts toward the high frequency regimes, the other low-pass filter is able to provide better filtering efficiency to obtain higher peak S/N ratios. Real LC-MS/MS chromatograms, of which typically less than 6-fold peak S/N ratio improvement achieved with two consecutive wavelet-based low-pass filters remains the same S/N ratio improvement using one-step wavelet-based low-pass filter, are improved to accomplish much better ratio enhancement 25-folds to 40-folds typically when the noise frequency spectrum is modified between two low-pass filters. The linear standard curves using the filtered LC-MS/MS signals are validated. The filtered LC-MS/MS signals are also reproducible. The more accurate determinations of very low concentration samples (S/N ratio about 7-9) are obtained using the filtered signals than the determinations using the original signals. Copyright 2010 Elsevier B.V. All rights reserved.

Diagnostic methodology for incipient system disturbance based on a neural wavelet approach

NASA Astrophysics Data System (ADS)

Won, In-Ho

Since incipient system disturbances are easily mixed up with other events or noise sources, the signal from the system disturbance can be neglected or identified as noise. Thus, as available knowledge and information is obtained incompletely or inexactly from the measurements; an exploration into the use of artificial intelligence (AI) tools to overcome these uncertainties and limitations was done. A methodology integrating the feature extraction efficiency of the wavelet transform with the classification capabilities of neural networks is developed for signal classification in the context of detecting incipient system disturbances. The synergistic effects of wavelets and neural networks present more strength and less weakness than either technique taken alone. A wavelet feature extractor is developed to form concise feature vectors for neural network inputs. The feature vectors are calculated from wavelet coefficients to reduce redundancy and computational expense. During this procedure, the statistical features based on the fractal concept to the wavelet coefficients play a role as crucial key in the wavelet feature extractor. To verify the proposed methodology, two applications are investigated and successfully tested. The first involves pump cavitation detection using dynamic pressure sensor. The second pertains to incipient pump cavitation detection using signals obtained from a current sensor. Also, through comparisons between three proposed feature vectors and with statistical techniques, it is shown that the variance feature extractor provides a better approach in the performed applications.

A Wavelet-Based Methodology for Grinding Wheel Condition Monitoring

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

Liao, T. W.; Ting, C.F.; Qu, Jun

2007-01-01

Grinding wheel surface condition changes as more material is removed. This paper presents a wavelet-based methodology for grinding wheel condition monitoring based on acoustic emission (AE) signals. Grinding experiments in creep feed mode were conducted to grind alumina specimens with a resinoid-bonded diamond wheel using two different conditions. During the experiments, AE signals were collected when the wheel was 'sharp' and when the wheel was 'dull'. Discriminant features were then extracted from each raw AE signal segment using the discrete wavelet decomposition procedure. An adaptive genetic clustering algorithm was finally applied to the extracted features in order to distinguish differentmore » states of grinding wheel condition. The test results indicate that the proposed methodology can achieve 97% clustering accuracy for the high material removal rate condition, 86.7% for the low material removal rate condition, and 76.7% for the combined grinding conditions if the base wavelet, the decomposition level, and the GA parameters are properly selected.« less

Design and application of discrete wavelet packet transform based multiresolution controller for liquid level system.

PubMed

Paul, Rimi; Sengupta, Anindita

2017-11-01

A new controller based on discrete wavelet packet transform (DWPT) for liquid level system (LLS) has been presented here. This controller generates control signal using node coefficients of the error signal which interprets many implicit phenomena such as process dynamics, measurement noise and effect of external disturbances. Through simulation results on LLS problem, this controller is shown to perform faster than both the discrete wavelet transform based controller and conventional proportional integral controller. Also, it is more efficient in terms of its ability to provide better noise rejection. To overcome the wind up phenomenon by considering the saturation due to presence of actuator, anti-wind up technique is applied to the conventional PI controller and compared to the wavelet packet transform based controller. In this case also, packet controller is found better than the other ones. This similar work has been extended for analogous first order RC plant as well as second order plant also. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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

I. W. Ginsberg

Multiresolutional decompositions known as spectral fingerprints are often used to extract spectral features from multispectral/hyperspectral data. In this study, the authors investigate the use of wavelet-based algorithms for generating spectral fingerprints. The wavelet-based algorithms are compared to the currently used method, traditional convolution with first-derivative Gaussian filters. The comparison analyses consists of two parts: (a) the computational expense of the new method is compared with the computational costs of the current method and (b) the outputs of the wavelet-based methods are compared with those of the current method to determine any practical differences in the resulting spectral fingerprints. The resultsmore » show that the wavelet-based algorithms can greatly reduce the computational expense of generating spectral fingerprints, while practically no differences exist in the resulting fingerprints. The analysis is conducted on a database of hyperspectral signatures, namely, Hyperspectral Digital Image Collection Experiment (HYDICE) signatures. The reduction in computational expense is by a factor of about 30, and the average Euclidean distance between resulting fingerprints is on the order of 0.02.« less

Wavelets and the squeezed states of quantum optics

NASA Technical Reports Server (NTRS)

Defacio, B.

1992-01-01

Wavelets are new mathematical objects which act as 'designer trigonometric functions.' To obtain a wavelet, the original function space of finite energy signals is generalized to a phase-space, and the translation operator in the original space has a scale change in the new variable adjoined to the translation. Localization properties in the phase-space can be improved and unconditional bases are obtained for a broad class of function and distribution spaces. Operators in phase space are 'almost diagonal' instead of the traditional condition of being diagonal in the original function space. These wavelets are applied to the squeezed states of quantum optics. The scale change required for a quantum wavelet is shown to be a Yuen squeeze operator acting on an arbitrary density operator.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

NASA Astrophysics Data System (ADS)

Niu, Hongli; Wang, Jun

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

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

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

Multi-level basis selection of wavelet packet decomposition tree for heart sound classification.

PubMed

Safara, Fatemeh; Doraisamy, Shyamala; Azman, Azreen; Jantan, Azrul; Abdullah Ramaiah, Asri Ranga

2013-10-01

Wavelet packet transform decomposes a signal into a set of orthonormal bases (nodes) and provides opportunities to select an appropriate set of these bases for feature extraction. In this paper, multi-level basis selection (MLBS) is proposed to preserve the most informative bases of a wavelet packet decomposition tree through removing less informative bases by applying three exclusion criteria: frequency range, noise frequency, and energy threshold. MLBS achieved an accuracy of 97.56% for classifying normal heart sound, aortic stenosis, mitral regurgitation, and aortic regurgitation. MLBS is a promising basis selection to be suggested for signals with a small range of frequencies. Copyright © 2013 The Authors. Published by Elsevier Ltd.. All rights reserved.

A comparative study on book shelf structure based on different domain modal analysis

NASA Astrophysics Data System (ADS)

Sabamehr, Ardalan; Roy, Timir Baran; Bagchi, Ashutosh

2017-04-01

Structural Health Monitoring (SHM) based on the vibration of structures has been very attractive topic for researchers in different fields such as: civil, aeronautical and mechanical engineering. The aim of this paper is to compare three most common modal identification techniques such as Frequency Domain Decomposition (FDD), Stochastic Subspace Identification (SSI) and Continuous Wavelet Transform (CWT) to find modal properties (such as natural frequency, mode shape and damping ratio) of three story book shelf steel structure which was built in Concordia University Lab. The modified Complex Morlet wavelet have been selected for wavelet in order to use asymptotic signal rather than real one with variable bandwidth and wavelet central frequency. So, CWT is able to detect instantaneous modulus and phase by use of local maxima ridge detection.

Analysis of photonic Doppler velocimetry data based on the continuous wavelet transform

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

Liu Shouxian; Wang Detian; Li Tao

2011-02-15

The short time Fourier transform (STFT) cannot resolve rapid velocity changes in most photonic Doppler velocimetry (PDV) data. A practical analysis method based on the continuous wavelet transform (CWT) was presented to overcome this difficulty. The adaptability of the wavelet family predicates that the continuous wavelet transform uses an adaptive time window to estimate the instantaneous frequency of signals. The local frequencies of signal are accurately determined by finding the ridge in the spectrogram of the CWT and then are converted to target velocity according to the Doppler effects. A performance comparison between the CWT and STFT is demonstrated bymore » a plate-impact experiment data. The results illustrate that the new method is automatic and adequate for analysis of PDV data.« less

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

NASA Astrophysics Data System (ADS)

Yang, Yujun; Li, Jianping; Yang, Yimei

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

Cao, Guangxi; Zhang, Minjia

2015-10-01

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

Analysis of the tennis racket vibrations during forehand drives: Selection of the mother wavelet.

PubMed

Blache, Y; Hautier, C; Lefebvre, F; Djordjevic, A; Creveaux, T; Rogowski, I

2017-08-16

The time-frequency analysis of the tennis racket and hand vibrations is of great interest for discomfort and pathology prevention. This study aimed to (i) to assess the stationarity of the vibratory signal of the racket and hand and (ii) to identify the best mother wavelet to perform future time-frequency analysis, (iii) to determine if the stroke spin, racket characteristics and impact zone can influence the selection of the best mother wavelet. A total of 2364 topspin and flat forehand drives were performed by fourteen male competitive tennis players with six different rackets. One tri-axial and one mono-axial accelerometer were taped on the racket throat and dominant hand respectively. The signal stationarity was tested through the wavelet spectrum test. Eighty-nine mother wavelet were tested to select the best mother wavelet based on continuous and discrete transforms. On average only 25±17%, 2±5%, 5±7% and 27±27% of the signal tested respected the hypothesis of stationarity for the three axes of the racket and the hand respectively. Regarding the two methods for the detection of the best mother wavelet, the Daubechy 45 wavelet presented the highest average ranking. No effect of the stroke spin, racket characteristics and impact zone was observed for the selection of the best mother wavelet. It was concluded that alternative approach to Fast Fourier Transform should be used to interpret tennis vibration signals. In the case where wavelet transform is chosen, the Daubechy 45 mother wavelet appeared to be the most suitable. Copyright © 2017 Elsevier Ltd. All rights reserved.

Fingerprint recognition of wavelet-based compressed images by neuro-fuzzy clustering

NASA Astrophysics Data System (ADS)

Liu, Ti C.; Mitra, Sunanda

1996-06-01

Image compression plays a crucial role in many important and diverse applications requiring efficient storage and transmission. This work mainly focuses on a wavelet transform (WT) based compression of fingerprint images and the subsequent classification of the reconstructed images. The algorithm developed involves multiresolution wavelet decomposition, uniform scalar quantization, entropy and run- length encoder/decoder and K-means clustering of the invariant moments as fingerprint features. The performance of the WT-based compression algorithm has been compared with JPEG current image compression standard. Simulation results show that WT outperforms JPEG in high compression ratio region and the reconstructed fingerprint image yields proper classification.

Texture Analysis of Recurrence Plots Based on Wavelets and PSO for Laryngeal Pathologies Detection.

PubMed

Souza, Taciana A; Vieira, Vinícius J D; Correia, Suzete E N; Costa, Silvana L N C; de A Costa, Washington C; Souza, Micael A

2015-01-01

This paper deals with the discrimination between healthy and pathological speech signals using recurrence plots and wavelet transform with texture features. Approximation and detail coefficients are obtained from the recurrence plots using Haar wavelet transform, considering one decomposition level. The considered laryngeal pathologies are: paralysis, Reinke's edema and nodules. Accuracy rates above 86% were obtained by means of the employed method.

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Mouse EEG spike detection based on the adapted continuous wavelet transform

NASA Astrophysics Data System (ADS)

Tieng, Quang M.; Kharatishvili, Irina; Chen, Min; Reutens, David C.

2016-04-01

Objective. Electroencephalography (EEG) is an important tool in the diagnosis of epilepsy. Interictal spikes on EEG are used to monitor the development of epilepsy and the effects of drug therapy. EEG recordings are generally long and the data voluminous. Thus developing a sensitive and reliable automated algorithm for analyzing EEG data is necessary. Approach. A new algorithm for detecting and classifying interictal spikes in mouse EEG recordings is proposed, based on the adapted continuous wavelet transform (CWT). The construction of the adapted mother wavelet is founded on a template obtained from a sample comprising the first few minutes of an EEG data set. Main Result. The algorithm was tested with EEG data from a mouse model of epilepsy and experimental results showed that the algorithm could distinguish EEG spikes from other transient waveforms with a high degree of sensitivity and specificity. Significance. Differing from existing approaches, the proposed approach combines wavelet denoising, to isolate transient signals, with adapted CWT-based template matching, to detect true interictal spikes. Using the adapted wavelet constructed from a predefined template, the adapted CWT is calculated on small EEG segments to fit dynamical changes in the EEG recording.

ECG compression using non-recursive wavelet transform with quality control

NASA Astrophysics Data System (ADS)

Liu, Je-Hung; Hung, King-Chu; Wu, Tsung-Ching

2016-09-01

While wavelet-based electrocardiogram (ECG) data compression using scalar quantisation (SQ) yields excellent compression performance, a wavelet's SQ scheme, however, must select a set of multilevel quantisers for each quantisation process. As a result of the properties of multiple-to-one mapping, however, this scheme is not conducive for reconstruction error control. In order to address this problem, this paper presents a single-variable control SQ scheme able to guarantee the reconstruction quality of wavelet-based ECG data compression. Based on the reversible round-off non-recursive discrete periodised wavelet transform (RRO-NRDPWT), the SQ scheme is derived with a three-stage design process that first uses genetic algorithm (GA) for high compression ratio (CR), followed by a quadratic curve fitting for linear distortion control, and the third uses a fuzzy decision-making for minimising data dependency effect and selecting the optimal SQ. The two databases, Physikalisch-Technische Bundesanstalt (PTB) and Massachusetts Institute of Technology (MIT) arrhythmia, are used to evaluate quality control performance. Experimental results show that the design method guarantees a high compression performance SQ scheme with statistically linear distortion. This property can be independent of training data and can facilitate rapid error control.

Element analysis: a wavelet-based method for analysing time-localized events in noisy time series

PubMed Central

2017-01-01

A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized ‘events’. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima. The distribution of events in general power-law noise is determined in order to establish significance based on an expected false detection rate. Finally, an expression for an event’s ‘region of influence’ within the wavelet transform permits the formation of a criterion for rejecting spurious maxima due to numerical artefacts or other unsuitable events. Signals can then be reconstructed based on a small number of isolated points on the time/scale plane. This method, termed element analysis, is applied to the identification of long-lived eddy structures in ocean currents as observed by along-track measurements of sea surface elevation from satellite altimetry. PMID:28484325

Application of wavelet-based multi-model Kalman filters to real-time flood forecasting

NASA Astrophysics Data System (ADS)

Chou, Chien-Ming; Wang, Ru-Yih

2004-04-01

This paper presents the application of a multimodel method using a wavelet-based Kalman filter (WKF) bank to simultaneously estimate decomposed state variables and unknown parameters for real-time flood forecasting. Applying the Haar wavelet transform alters the state vector and input vector of the state space. In this way, an overall detail plus approximation describes each new state vector and input vector, which allows the WKF to simultaneously estimate and decompose state variables. The wavelet-based multimodel Kalman filter (WMKF) is a multimodel Kalman filter (MKF), in which the Kalman filter has been substituted for a WKF. The WMKF then obtains M estimated state vectors. Next, the M state-estimates, each of which is weighted by its possibility that is also determined on-line, are combined to form an optimal estimate. Validations conducted for the Wu-Tu watershed, a small watershed in Taiwan, have demonstrated that the method is effective because of the decomposition of wavelet transform, the adaptation of the time-varying Kalman filter and the characteristics of the multimodel method. Validation results also reveal that the resulting method enhances the accuracy of the runoff prediction of the rainfall-runoff process in the Wu-Tu watershed.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

Maksoed, Wh-

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

Linear and Nonlinear Statistical Characterization of DNA

NASA Astrophysics Data System (ADS)

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

2002-03-01

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

Wavelet-based study of valence-arousal model of emotions on EEG signals with LabVIEW.

PubMed

Guzel Aydin, Seda; Kaya, Turgay; Guler, Hasan

2016-06-01

This paper illustrates the wavelet-based feature extraction for emotion assessment using electroencephalogram (EEG) signal through graphical coding design. Two-dimensional (valence-arousal) emotion model was studied. Different emotions (happy, joy, melancholy, and disgust) were studied for assessment. These emotions were stimulated by video clips. EEG signals obtained from four subjects were decomposed into five frequency bands (gamma, beta, alpha, theta, and delta) using "db5" wavelet function. Relative features were calculated to obtain further information. Impact of the emotions according to valence value was observed to be optimal on power spectral density of gamma band. The main objective of this work is not only to investigate the influence of the emotions on different frequency bands but also to overcome the difficulties in the text-based program. This work offers an alternative approach for emotion evaluation through EEG processing. There are a number of methods for emotion recognition such as wavelet transform-based, Fourier transform-based, and Hilbert-Huang transform-based methods. However, the majority of these methods have been applied with the text-based programming languages. In this study, we proposed and implemented an experimental feature extraction with graphics-based language, which provides great convenience in bioelectrical signal processing.

Identification Method of Mud Shale Fractures Base on Wavelet Transform

NASA Astrophysics Data System (ADS)

Xia, Weixu; Lai, Fuqiang; Luo, Han

2018-01-01

In recent years, inspired by seismic analysis technology, a new method for analysing mud shale fractures oil and gas reservoirs by logging properties has emerged. By extracting the high frequency attribute of the wavelet transform in the logging attribute, the formation information hidden in the logging signal is extracted, identified the fractures that are not recognized by conventional logging and in the identified fracture segment to show the “cycle jump”, “high value”, “spike” and other response effect is more obvious. Finally formed a complete wavelet denoising method and wavelet high frequency identification fracture method.

Privacy Preserving Technique for Euclidean Distance Based Mining Algorithms Using a Wavelet Related Transform

NASA Astrophysics Data System (ADS)

Kadampur, Mohammad Ali; D. v. L. N., Somayajulu

Privacy preserving data mining is an art of knowledge discovery without revealing the sensitive data of the data set. In this paper a data transformation technique using wavelets is presented for privacy preserving data mining. Wavelets use well known energy compaction approach during data transformation and only the high energy coefficients are published to the public domain instead of the actual data proper. It is found that the transformed data preserves the Eucleadian distances and the method can be used in privacy preserving clustering. Wavelets offer the inherent improved time complexity.

Wavelet Applications for Flight Flutter Testing

NASA Technical Reports Server (NTRS)

Lind, Rick; Brenner, Marty; Freudinger, Lawrence C.

1999-01-01

Wavelets present a method for signal processing that may be useful for analyzing responses of dynamical systems. This paper describes several wavelet-based tools that have been developed to improve the efficiency of flight flutter testing. One of the tools uses correlation filtering to identify properties of several modes throughout a flight test for envelope expansion. Another tool uses features in time-frequency representations of responses to characterize nonlinearities in the system dynamics. A third tool uses modulus and phase information from a wavelet transform to estimate modal parameters that can be used to update a linear model and reduce conservatism in robust stability margins.

Highly efficient codec based on significance-linked connected-component analysis of wavelet coefficients

NASA Astrophysics Data System (ADS)

Chai, Bing-Bing; Vass, Jozsef; Zhuang, Xinhua

1997-04-01

Recent success in wavelet coding is mainly attributed to the recognition of importance of data organization. There has been several very competitive wavelet codecs developed, namely, Shapiro's Embedded Zerotree Wavelets (EZW), Servetto et. al.'s Morphological Representation of Wavelet Data (MRWD), and Said and Pearlman's Set Partitioning in Hierarchical Trees (SPIHT). In this paper, we propose a new image compression algorithm called Significant-Linked Connected Component Analysis (SLCCA) of wavelet coefficients. SLCCA exploits both within-subband clustering of significant coefficients and cross-subband dependency in significant fields. A so-called significant link between connected components is designed to reduce the positional overhead of MRWD. In addition, the significant coefficients' magnitude are encoded in bit plane order to match the probability model of the adaptive arithmetic coder. Experiments show that SLCCA outperforms both EZW and MRWD, and is tied with SPIHT. Furthermore, it is observed that SLCCA generally has the best performance on images with large portion of texture. When applied to fingerprint image compression, it outperforms FBI's wavelet scalar quantization by about 1 dB.

Characteristic Analysis of Air-gun Source Wavelet based on the Vertical Cable Data

NASA Astrophysics Data System (ADS)

Xing, L.

2016-12-01

Air guns are important sources for marine seismic exploration. Far-field wavelets of air gun arrays, as a necessary parameter for pre-stack processing and source models, plays an important role during marine seismic data processing and interpretation. When an air gun fires, it generates a series of air bubbles. Similar to onshore seismic exploration, the water forms a plastic fluid near the bubble; the farther the air gun is located from the measurement, the more steady and more accurately represented the wavelet will be. In practice, hydrophones should be placed more than 100 m from the air gun; however, traditional seismic cables cannot meet this requirement. On the other hand, vertical cables provide a viable solution to this problem. This study uses a vertical cable to receive wavelets from 38 air guns and data are collected offshore Southeast Qiong, where the water depth is over 1000 m. In this study, the wavelets measured using this technique coincide very well with the simulated wavelets and can therefore represent the real shape of the wavelets. This experiment fills a technology gap in China.

Regional-specific Stochastic Simulation of Spatially-distributed Ground-motion Time Histories using Wavelet Packet Analysis

NASA Astrophysics Data System (ADS)

Huang, D.; Wang, G.

2014-12-01

Stochastic simulation of spatially distributed ground-motion time histories is important for performance-based earthquake design of geographically distributed systems. In this study, we develop a novel technique to stochastically simulate regionalized ground-motion time histories using wavelet packet analysis. First, a transient acceleration time history is characterized by wavelet-packet parameters proposed by Yamamoto and Baker (2013). The wavelet-packet parameters fully characterize ground-motion time histories in terms of energy content, time- frequency-domain characteristics and time-frequency nonstationarity. This study further investigates the spatial cross-correlations of wavelet-packet parameters based on geostatistical analysis of 1500 regionalized ground motion data from eight well-recorded earthquakes in California, Mexico, Japan and Taiwan. The linear model of coregionalization (LMC) is used to develop a permissible spatial cross-correlation model for each parameter group. The geostatistical analysis of ground-motion data from different regions reveals significant dependence of the LMC structure on regional site conditions, which can be characterized by the correlation range of Vs30 in each region. In general, the spatial correlation and cross-correlation of wavelet-packet parameters are stronger if the site condition is more homogeneous. Using the regional-specific spatial cross-correlation model and cokriging technique, wavelet packet parameters at unmeasured locations can be best estimated, and regionalized ground-motion time histories can be synthesized. Case studies and blind tests demonstrated that the simulated ground motions generally agree well with the actual recorded data, if the influence of regional-site conditions is considered. The developed method has great potential to be used in computational-based seismic analysis and loss estimation in a regional scale.

Identification of the subthalamic nucleus in deep brain stimulation surgery with a novel wavelet-derived measure of neural background activity.

PubMed

Snellings, André; Sagher, Oren; Anderson, David J; Aldridge, J Wayne

2009-10-01

The authors developed a wavelet-based measure for quantitative assessment of neural background activity during intraoperative neurophysiological recordings so that the boundaries of the subthalamic nucleus (STN) can be more easily localized for electrode implantation. Neural electrophysiological data were recorded in 14 patients (20 tracks and 275 individual recording sites) with dopamine-sensitive idiopathic Parkinson disease during the target localization portion of deep brain stimulator implantation surgery. During intraoperative recording, the STN was identified based on audio and visual monitoring of neural firing patterns, kinesthetic tests, and comparisons between neural behavior and the known characteristics of the target nucleus. The quantitative wavelet-based measure was applied offline using commercially available software to measure the magnitude of the neural background activity, and the results of this analysis were compared with the intraoperative conclusions. Wavelet-derived estimates were also compared with power spectral density measurements. The wavelet-derived background levels were significantly higher in regions encompassed by the clinically estimated boundaries of the STN than in the surrounding regions (STN, 225 +/- 61 microV; ventral to the STN, 112 +/- 32 microV; and dorsal to the STN, 136 +/- 66 microV). In every track, the absolute maximum magnitude was found within the clinically identified STN. The wavelet-derived background levels provided a more consistent index with less variability than measurements with power spectral density. Wavelet-derived background activity can be calculated quickly, does not require spike sorting, and can be used to identify the STN reliably with very little subjective interpretation required. This method may facilitate the rapid intraoperative identification of STN borders.

Identification of the subthalamic nucleus in deep brain stimulation surgery with a novel wavelet-derived measure of neural background activity

PubMed Central

Snellings, André; Sagher, Oren; Anderson, David J.; Aldridge, J. Wayne

2016-01-01

Object A wavelet-based measure was developed to quantitatively assess neural background activity taken during surgical neurophysiological recordings to localize the boundaries of the subthalamic nucleus during target localization for deep brain stimulator implant surgery. Methods Neural electrophysiological data was recorded from 14 patients (20 tracks, n = 275 individual recording sites) with dopamine-sensitive idiopathic Parkinson’s disease during the target localization portion of deep brain stimulator implant surgery. During intraoperative recording the STN was identified based upon audio and visual monitoring of neural firing patterns, kinesthetic tests, and comparisons between neural behavior and known characteristics of the target nucleus. The quantitative wavelet-based measure was applied off-line using MATLAB software to measure the magnitude of the neural background activity, and the results of this analysis were compared to the intraoperative conclusions. Wavelet-derived estimates were compared to power spectral density measures. Results The wavelet-derived background levels were significantly higher in regions encompassed by the clinically estimated boundaries of the STN than in surrounding regions (STN: 225 ± 61 μV vs. ventral to STN: 112 ± 32 μV, and dorsal to STN: 136 ± 66 μV). In every track, the absolute maximum magnitude was found within the clinically identified STN. The wavelet-derived background levels provided a more consistent index with less variability than power spectral density. Conclusions The wavelet-derived background activity assessor can be calculated quickly, requires no spike sorting, and can be reliably used to identify the STN with very little subjective interpretation required. This method may facilitate rapid intraoperative identification of subthalamic nucleus borders. PMID:19344225

Classification of arterial and venous cerebral vasculature based on wavelet postprocessing of CT perfusion data.

PubMed

Havla, Lukas; Schneider, Moritz J; Thierfelder, Kolja M; Beyer, Sebastian E; Ertl-Wagner, Birgit; Reiser, Maximilian F; Sommer, Wieland H; Dietrich, Olaf

2016-02-01

The purpose of this study was to propose and evaluate a new wavelet-based technique for classification of arterial and venous vessels using time-resolved cerebral CT perfusion data sets. Fourteen consecutive patients (mean age 73 yr, range 17-97) with suspected stroke but no pathology in follow-up MRI were included. A CT perfusion scan with 32 dynamic phases was performed during intravenous bolus contrast-agent application. After rigid-body motion correction, a Paul wavelet (order 1) was used to calculate voxelwise the wavelet power spectrum (WPS) of each attenuation-time course. The angiographic intensity A was defined as the maximum of the WPS, located at the coordinates T (time axis) and W (scale/width axis) within the WPS. Using these three parameters (A, T, W) separately as well as combined by (1) Fisher's linear discriminant analysis (FLDA), (2) logistic regression (LogR) analysis, or (3) support vector machine (SVM) analysis, their potential to classify 18 different arterial and venous vessel segments per subject was evaluated. The best vessel classification was obtained using all three parameters A and T and W [area under the curve (AUC): 0.953 with FLDA and 0.957 with LogR or SVM]. In direct comparison, the wavelet-derived parameters provided performance at least equal to conventional attenuation-time-course parameters. The maximum AUC obtained from the proposed wavelet parameters was slightly (although not statistically significantly) higher than the maximum AUC (0.945) obtained from the conventional parameters. A new method to classify arterial and venous cerebral vessels with high statistical accuracy was introduced based on the time-domain wavelet transform of dynamic CT perfusion data in combination with linear or nonlinear multidimensional classification techniques.

Textural characterization of histopathological images for oral sub-mucous fibrosis detection.

PubMed

Krishnan, M Muthu Rama; Shah, Pratik; Choudhary, Anirudh; Chakraborty, Chandan; Paul, Ranjan Rashmi; Ray, Ajoy K

2011-10-01

In the field of quantitative microscopy, textural information plays a significant role very often in tissue characterization and diagnosis, in addition to morphology and intensity. The aim of this work is to improve the classification accuracy based on textural features for the development of a computer assisted screening of oral sub-mucous fibrosis (OSF). In fact, a systematic approach is introduced in order to grade the histopathological tissue sections into normal, OSF without dysplasia and OSF with dysplasia, which would help the oral onco-pathologists to screen the subjects rapidly. In totality, 71 textural features are extracted from epithelial region of the tissue sections using various wavelet families, Gabor-wavelet, local binary pattern, fractal dimension and Brownian motion curve, followed by preprocessing and segmentation. Wavelet families contribute a common set of 9 features, out of which 8 are significant and other 61 out of 62 obtained from the rest of the extractors are also statistically significant (p<0.05) in discriminating the three stages. Based on mean distance criteria, the best wavelet family (i.e., biorthogonal3.1 (bior3.1)) is selected for classifier design. support vector machine (SVM) is trained by 146 samples based on 69 textural features and its classification accuracy is computed for each of the combinations of wavelet family and rest of the extractors. Finally, it has been investigated that bior3.1 wavelet coefficients leads to higher accuracy (88.38%) in combination with LBP and Gabor wavelet features through three-fold cross validation. Results are shown and discussed in detail. It is shown that combining more than one texture measure instead of using just one might improve the overall accuracy. Copyright © 2011 Elsevier Ltd. All rights reserved.

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

PubMed Central

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

2014-01-01

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

Nonlinear temperature effects on multifractal complexity of metabolic rate of mice

PubMed Central

Bogdanovich, Jose M.; Bozinovic, Francisco

2016-01-01

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

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

PubMed

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

2016-01-01

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

Dual-induced multifractality in online viewing activity.

PubMed

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2008-09-01

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

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

NASA Astrophysics Data System (ADS)

Li, Zhihui; Lu, Xinsheng

2012-08-01

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

Dual-induced multifractality in online viewing activity

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2009-07-01

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

Lorentz violations in multifractal spacetimes

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca

2017-05-01

Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E_{*}>10^{14} {GeV} (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E_{*}> 10^{17} {GeV} or greater.