Higuchi Method Research Articles

Inclusion Complex of Thiourea Substrate with Hydroxypropyl--cyclodextrin

To be active, a heavy metal trap substrate must possess some degree of aqueous solubility. The use of cyclodextrins molecules, which can form inclusion complexes with the hydrophobic trap substrates, has provided the required solubility through the relatively hydrophobic cavity of native cyclodextrins and their derivatives that enhances the ability to complex hydrophobic substrates of appropriate size and shape. In this study, spectrophotometry has been used to investigate the effects of cyclodextrin on the solubility, stoichiometry and stability of the substrate-CD complex formed between N-(2-ethylphenyl)-N'-(2-methylphenyl) thiourea, (a hydrophobic substrate trap) and hydroxypropyl-β-cyclodextrin (HP−β−CD). The solubility, stoichiometry and overall association constant of the complex have been determined using the Higuchi's method, the continuous variation (Job's plot) method and the Scott's method respectively.

FRACTAL ANALYSIS OF PRIME INDIAN STOCK MARKET INDICES

The purpose of the present work is to study the fractal behaviour of prime Indian stock exchanges, namely Bombay Stock Exchange Sensitivity Index (BSE Sensex) and National Stock Exchange (NSE). To analyze the monofractality of these indices we have used Higuchi method and Katz method separately. By applying Mutifractal Detrended Fluctuation Analysis (MFDFA) technique we have calculated the generalized Hurst exponents, multifractal scaling exponents and generalized multifractal dimensions for the present indices. We have deduced Hölder exponents as well as singularity spectra for BSE and NSE. It has been observed that both the stock exchanges are possessing self-similarity at different small ranges separately and inhomogeneously. By comparing the multifractal behaviour of the BSE and NSE indices, we have found that the second one exhibits a richer multifractal feature than the first one.

Fractal characteristics of the ULF emissions along a meridian profile, based on the 210 MM stations data

Fractal analysis of magnetic records (1 Hz sampling rate) of 5 stations (Guam, Moshiri, Paratunka, Magadan, and Chokurdakh) located along the 210 magnetic meridian (210 MM) has been performed using the Higuchi method. The period of 22 months (October 1992 to July 1994) that embodies the date of the strong Guam earthquake of 8 August1993 has been considered. A comparison of the ULF emissions scaling parameters (spectral exponents β and fractal dimensions D) obtained at different latitudes has been made. Dependence of β and D on the Kp index of geomagnetic activity has been analyzed for each of the 24 local time intervals. It is revealed that D decreases ( β increases) with increasing geomagnetic activity at all stations, but the rates of decrease (increase) are different at different stations and in different time intervals. It is shown that the evening, night and early morning hours are preferable to study magnetospheric effects, whereas the noon hours are the most suitable for the analysis of lithospheric effects. A possibility of using the data of the 210 MM stations as reference materials for the Guam seismically active area is discussed.

ELECTROMYOGRAPHY (EMG) SIGNAL CLASSIFICATION BASED ON DETRENDED FLUCTUATION ANALYSIS

Electromyography (EMG) signal is a useful signal in various medical and engineering applications. To extract the useful information in the EMG signal, feature extraction method should be performed. The extracted features of the EMG signal are usually calculated based on linear or statistical methods, but the EMG signal exhibits the nonlinear and more complex in the properties. With recent advances in nonlinear analysis we are proposing the study of the EMG signals from upper-limb movements using Detrended Fluctuation Analysis (DFA) method. This study used EMG signals obtained from eight upper-limb movements and five muscle positions as representative EMG signals. The usefulness of the DFA method has been proposed to discriminate the upper-limb movements. Complete comparative studies of an optimal parameter of the DFA method were performed. From the viewpoints of maximum class separability, robustness, and complexity, scaling exponent obtained from the DFA method shows the appropriateness to be used as a feature in the classification of the EMG signal. From the experimental results, an optimal DFA method is obtained under these conditions: the minimum box size is approximately four, the maximum box size is one-tenth of the signal length, the box size increment is based on a power of two, and the quadratic polynomial fits is used in the fitting procedure. Moreover, the classification performance of the DFA method is better than other existing nonlinear methods, including the Higuchi's method.

Using nonlinear features for fetal heart rate classification

Highlights • We analyzed fetal heart rate of normal and acidemic fetuses. • We used conventional and nonlinear features for the signal analysis. • Addition of nonlinear features improves accuracy of classification. • The best nonlinear features are: Lempel Ziv complexity and Sample entropy. • Combination of conventional and nonlinear features provides the best accuracy. Abstract Fetal heart rate (FHR) is used to evaluate fetal well-being and enables clinicians to detect ongoing hypoxia during delivery. Routine clinical evaluation of intrapartum FHR is based on macroscopic morphological features visible to the naked eye. In this paper we evaluated conventional features and compared them to the nonlinear ones in the task of intrapartum FHR classification. The experiments were performed using a database of 217 FHR records with objective annotations, i.e. pH measurement. We have proven that the addition of nonlinear features improves accuracy of classification. The best classification results were achieved using a combination of conventional and nonlinear features with sensitivity of 73.4%, specificity of 76.3%, and F-measure of 71.9%. The best selected nonlinear features were: Lempel Ziv complexity, Sample entropy, and fractal dimension estimated by Higuchi method. Since the results of automatic signal evaluation are easily reproducible, the process of FHR evaluation can become more objective and may enable clinicians to focus on additional non-cardiotocography parameters influencing the fetus during delivery.

SIGNAL CHARACTERIZATION USING FRACTAL DIMENSION

Fractal Dimensions (FD) are one of the popular measures used for characterizing signals. They have been used as complexity measures of signals in various fields including speech and biomedical applications. However, proper interpretation of such analyses has not been thoroughly addressed. In this paper, we study the effect of various signal properties on FD and interpret results in terms of classical signal processing concepts such as amplitude, frequency, number of harmonics, noise power and signal bandwidth. We have used Higuchi's method for estimating FDs. This study may help in gaining a better understanding of the FD complexity measure itself, and for interpreting changing structural complexity of signals in terms of FD. Our results indicate that FD is a useful measure in quantifying structural changes in signal properties.

A COMPARATIVE STUDY OF VALIDITY RANGES OF SOME FRACTAL METHODS OF TIME SERIES ANALYSIS

Each fractal method of time series analysis gives origin to a parameter that characterizes them. For example, β is the resulting parameter of the application of spectral analysis, α for detrended fluctuation analysis (DFA), D for Higuchi's method and Ha for semivariogram, to mention only some of them. Diverse linear relations between the mentioned parameters have been reported; some of these relations have been obtained from theoretical approaches by assuming time series properties such as their self-similarity. The obtained relations are linear in all cases; nevertheless, these relations only have a limited validity range. In this work, we determine the relation between each one of the parameters ß, α and D for a suitable value range. This is done by means of numerical experiments, consisting of the generation of self-affine and fractal synthetic series. Each one of these sets has a minimum of 500 series with pre-established values of ß, D and Ha. In addition, these are constructed in a suitable value range for each generation method. Later, we apply fractal methods to each one of the three sets of series and the relations between the parameters are obtained. It is observed that all the relations have a linear part as it is expected, but there exist differences in the validity range depending on the generation method.

Sensorimotor cortical response during motion reflecting audiovisual stimulation: evidence from fractal EEG analysis

Sensorimotor activity in response to motion reflecting audiovisual titillation is studied in this article. EEG recordings, and especially the Mu-rhythm over the sensorimotor cortex (C3, CZ, and C4 electrodes), were acquired and explored. An experiment was designed to provide auditory (Modest Mussorgsky's "Promenade" theme) and visual (synchronized human figure walking) stimuli to advanced music students (AMS) and non-musicians (NM) as a control subject group. EEG signals were analyzed using fractal dimension (FD) estimation (Higuchi's, Katz's and Petrosian's algorithms) and statistical methods. Experimental results from the midline electrode (CZ) based on the Higuchi method showed significant differences between the AMS and the NM groups, with the former displaying substantial sensorimotor response during auditory stimulation and stronger correlation with the acoustic stimulus than the latter. This observation was linked to mirror neuron system activity, a neurological mechanism that allows trained musicians to detect action-related meanings underlying the structural patterns in musical excerpts. Contrarily, the response of AMS and NM converged during audiovisual stimulation due to the dominant presence of human-like motion in the visual stimulus. These findings shed light upon music perception aspects, exhibiting the potential of FD to respond to different states of cortical activity.

A note on fractal dimensions of biomedical waveforms

In this paper, we study performance of Katz method of computing fractal dimension of waveforms, and its estimation accuracy is compared with Higuchi's method. The study is performed on four synthetic parametric fractal waveforms for which true fractal dimensions can be calculated, and real sleep electroencephalogram. The dependence of Katz's fractal dimension on amplitude, frequency and sampling frequency of waveforms is noted. Even though the Higuchi's method has given more accurate estimation of fractal dimensions, the study suggests that the results of Katz's based fractal dimension analysis of biomedical waveforms have to be carefully interpreted.

Extracting complexity waveforms from one-dimensional signals

BackgroundNonlinear methods provide a direct way of estimating complexity of one-dimensional sampled signals through calculation of Higuchi's fractal dimension (1<FD<2). In most cases the signal is treated as being characterized by one value of FD and consequently analyzed as one epoch or, if divided into more epochs, often only mean and standard deviation of epoch FD are calculated. If its complexity variation (or running fractal dimension), FD(t), is to be extracted, a moving window (epoch) approach is needed. However, due to low-pass filtering properties of moving windows, short epochs are preferred. Since Higuchi's method is based on consecutive reduction of signal sampling frequency, it is not suitable for estimating FD of very short epochs (N < 100 samples).ResultsIn this work we propose a new and simple way to estimate FD for N < 100 by introducing 'normalized length density' of a signal epoch,where yn(i) represents the ith signal sample after amplitude normalization. The actual calculation of signal FD is based on construction of a monotonic calibration curve, FD = f(NLD), on a set of Weierstrass functions, for which FD values are given theoretically. The two existing methods, Higuchi's and consecutive differences, applied simultaneously on signals with constant FD (white noise and Brownian motion), showed that standard deviation of calculated window FD (FDw) increased sharply as the epoch became shorter. However, in case of the new NLD method a considerably lower scattering was obtained, especially for N < 30, at the expense of some lower accuracy in calculating average FDw. Consequently, more accurate reconstruction of FD waveforms was obtained when synthetic signals were analyzed, containig short alternating epochs of two or three different FD values. Additionally, scatter plots of FDw of an occipital human EEG signal for 10 sample epochs demontrated that Higuchi's estimations for some epochs exceeded the theoretical FD limits, while NLD-derived values did not.ConclusionThe presented approach was more accurate than the existing two methods in FD(t) extraction for very short epochs and could be used in physiological signals when FD is expected to change abruptly, such as short phasic phenomena or transient artefacts, as well as in other fields of science.

Estimating long-range dependence in time series: An evaluation of estimators implemented in R

Recent studies have shown that many physiological and behavioral processes can be characterized by long-range correlations. The Hurst exponent H of fractal analysis and the fractional-differencing parameter d of the ARFIMA methodology are useful for capturing serial correlations. In this study, we report on different estimators of H and d implemented in R, a popular and freely available software package. By means of Monte Carlo simulations, we analyzed the performance of (1) the Geweke-Porter-Hudak estimator, (2) the approximate maximum likelihood algorithm, (3) the smoothed periodogram approach, (4) the Whittle estimator, (5) rescaled range analysis, (6) a modified periodogram, (7) Higuchi's method, and (8) detrended fluctuation analysis. The findings-confined to ARFIMA (0, d, 0) models and fractional Gaussian noise-identify the best estimators for persistent and antipersistent series. Two examples combining these results with the step-by-step procedure proposed by Delignières et al. (2006) demonstrate how this evaluation can be used as a guideline in a typical research situation.

Variations in the fractal dimension of fluctuations of the ionospheric F2 layer critical frequency

The 40-year period of observations of short-term variations (with characteristic times of up to 1–2 days) in the critical frequency of the ionospheric F2 layer (foF2) is analyzed. The continuous (with a step of 1 h) series of fluctuations (F) of the foF2 critical frequency (with eliminated daily variations) has been calculated using the hourly variations in foF2 at Moscow stations. The fractal dimension (FRH) of the fluctuations, characterizing short-term variations in foF2, has been determined and analyzed on a 30-day interval, using the Higuchi method. It has been established that FRH estimates substantially change in time. The 11-year cycle, which is in antiphase with the solar cycle, and the total annual and semiannual variations, similar to the variations observed in the normalized critical frequency of the E region and in the electron density of the D region, are clearly defined in these changes. Thus, the parameters of fast variations in the ionospheric F2 layer are affected by the phase of the 11-year solar cycle and by the position of the Earth in the orbit or seasonal variations in the atmosphere.

Complexity analysis of EEG in patients with schizophrenia using fractal dimension

We computed Higuchi's fractal dimension (FD) of resting, eyes closed EEG recorded from 30 scalp locations in 18 male neuroleptic-naïve, recent-onset schizophrenia (NRS) subjects and 15 male healthy control (HC) subjects, who were group-matched for age. Schizophrenia patients showed a diffuse reduction of FD except in the bilateral temporal and occipital regions, with the reduction being most prominent bifrontally. The positive symptom (PS) schizophrenia subjects showed FD values similar to or even higher than HC in the bilateral temporo-occipital regions, along with a co-existent bifrontal FD reduction as noted in the overall sample of NRS. In contrast, this increase in FD values in the bilateral temporo-occipital region was absent in the negative symptom (NS) subgroup. The regional differences in complexity suggested by these findings may reflect the aberrant brain dynamics underlying the pathophysiology of schizophrenia and its symptom dimensions. Higuchi's method of measuring FD directly in the time domain provides an alternative for the more computationally intensive nonlinear methods of estimating EEG complexity.

ULF geomagnetic anomalous changes possibly associated with 2004–2005 Sumatra earthquakes

Anomalous ULF geomagnetic field change is considered to be one of the most convincing and promising phenomena among earthquake-related electromagnetic effects, because we expect emissions from the crust of the source region. There has been a great deal of accumulated and convincing evidence of ULF magnetic signatures before large earthquakes as reported in the previous studies. In order to verify these phenomena preceding large earthquakes and to clarify the relationship between electromagnetic phenomena and possible physical mechanism, we have investigated the data of ULF geomagnetic observations at Kototabang and Biak stations associated with the 2004/2005 Sumatra earthquakes. A case study is carried out in this work to investigate the pre-earthquake ULF geomagnetic anomalies during the Sumatra–Andaman earthquake on December 26, 2004 (magnitude Mw = 9.0 and depth = 30 km from USGS catalog), and Sumatra–Nias earthquake on March 28, 2005 (Mw = 8.7 and depth = 30 km). For the aim of finding any precursors, we have adopted the spectral density ratio analysis and transfer functions analysis based on wavelet transform method. Results of the spectral density analysis indicate similar variations to those of amplitude for the induction arrow in transfer function analysis. Both of these variations at Kototabang exhibit strange or anomalous changes from a few weeks before the Sumatra–Andaman earthquake to July 2005, while there are no apparent changes at remote station of Biak. To make these results more convincing, the fractal analysis based on a Higuchi method has been applied to the same observed data, which also show a significant change (or decrease) in mono-fractal dimension a few weeks before the earthquakes. This result would lend a further support to those by the spectral density ratio and transfer function analyses. So, we can conclude that the anomalous change as observed simultaneously by the three methods, might be a possible signature related with the earthquake preparation phase of Sumatra earthquakes.

Thermodynamic Study of Cyclodextrins Complexation with Benzimidazolic Antihelmintics in Different Reaction Media

The main purpose of this work was to accomplish a comparative study about cyclodextrins complexation equilibria with three benzimidazolic antihelmintics: albendazole (Alb), mebendazole (Meb) and thiabendazole (Thiab). The complexation process with four different cyclodextrins (alpha-, beta-, gamma-, and HP-beta-CDs) was investigated under various temperatures and different reaction media (aqueous solution buffered at pH 7.5, dimethylsulfoxide (DMSO) and DMSO/water at 25/75, 50/50, 75/50 (w/w) mixtures). It was studied by electronic absorption and 1H NMR (NOESY) spectroscopy. Binding constants were determined by electronic absorption spectroscopic method, the DeltaH and DeltaS complexation values were evaluated and discussed according to the diverse factors that affect the chemical interactions in these systems. Solubility has also been determined by the Higuchi and Connors method. In general, albendazole and mebendazole exhibit similar complexation behavior, while thiabendazole acts differently. Classic and non-classic solvophobic effects are mainly the driving and stabilizing forces for complex formation, with the exception in some Thiab-CDs interactions. In all cases, DMSO, an aprotic solvent, should be considered as an active component of the reaction systems.

A comparison of ground geoelectric activity between three regions of different level of seismicity

Abstract. In this work, we present a statistical study of geoelectric time series from three Mexican regions with recognized different levels of seismicity. This study is made by means of both the Higuchi's method and the detrended fluctuation analysis for the detection of fractal behavior. With these methods we present scatter plots corresponding to scaling exponents for short and large lags arisen from crossover points in the geoelectric data. Through these scatter plots we observe a reasonable segregation of clouds of points corresponding to the three mentioned regions. These results permit to suggest that a different level of characteristic seismicity in one region is translated into a different level of geoelectric activity.

Application of different signal analysis methods to the ULF data for the 1993 Guam earthquake

Abstract. Two different analysis methods; (1) mono-fractal analysis (based on Higuchi method) and (2) flicker noise spectroscopy, have been applied to the same ULF (frequency less than 10 Hz) electromagnetic data observed at Guam during 3 years including the 1993 August Guam earthquake. The results by these two methods are found to be very consistent with each other; that is, some precursory effects seem to start about 3 months before the earthquake. This gives us a strong support to the self-organizing critical process before the Guam earthquake.

Non-random fluctuations in power output during self-paced exercise

Objectives: To analyse the power output measured during a self-paced 20-km cycling time trial, during which power output was free to vary, in order to assess the level and characteristics...

태양주기별 흑점수의 프랙탈 차원과 최대흑점수의 상관관계

프랙탈 차원은 연속적으로 관측된 불규칙한 자료의 성질을 정량적으로 표현하는 파라메터이다. 본 연구에서는 프랙탈 차원을 이용하여 태양 흑점수의 불규칙한 변동을 분석하고 다가오는 태양주기의 최대흑점수를 예측하였다. 이를 위하여 우리는 SIDC(Solar Influences Data analysis Center)에서 제공하는 1850년부터 2004년까지의 일일흑점수를 이용하여 Higuchi의 방법으로 각 태양주기의 프랙탈 차원을 결정하고 같은 태양주기 동안의 최대 월평균 흑점수와 비교하였다. 그 결과 프랙탈 차원과 최대 월평균 흑점수는 강한 역비례 관계를 보였다. 이러한 관계를 이용하여 태양활동 극소기부터 활동이 증가되는 기간인 4년동안의 흑점수만을 이용하여 프랙탈 차원을 구하고 다가올 극대기의 최대 월평균 흑점수를 예측한 결과 관측된 최대흑점수와 0.89의 좋은 상관관계를 보였다. The fractal dimension is a quantitative parameter describing the characteristics of irregular time series. In this study, we use this parameter to analyze the irregular aspects of solar activity and to predict the maximum sunspot number in the following solar cycle by examining time series of the sunspot number. For this, we considered the daily sunspot number since 1850 from SIDC (Solar Influences Data analysis Center) and then estimated cycle variation of the fractal dimension by using Higuchi's method. We examined the relationship between this fractal dimension and the maximum monthly sunspot number in each solar cycle. As a result, we found that there is a strong inverse relationship between the fractal dimension and the maximum monthly sunspot number. By using this relation we predicted the maximum sunspot number in the solar cycle from the fractal dimension of the sunspot numbers during the solar activity increasing phase. The successful prediction is proven by a good correlation (r=0.89) between the observed and predicted maximum sunspot numbers in the solar cycles.

Fractal analysis for the ULF data during the 1993 Guam earthquake to study prefracture criticality

Abstract. An extremely large earthquake (with magnitude of 8.2) happened on 8 August 1993 near the Guam island, and ultra-low-frequency (ULF) (frequency less than 1 Hz) electromagnetic fields were measured by 3-axis induction magnetometers at an observing station (with the epicentral distance of 65 km) with sampling frequency of 1 Hz. In order to study electromagnetic signature of prefracture criticality, we have undertaken the fractal (mono-fractal) analysis by means of the Higuchi's method for the ULF data during the 1993 Guam earthquake. Then, it is found that the fractal dimension exhibits five maxima 99, 75, 52, 21, and 9–4 days before the earthquake main shock, which suggests the ULF electromagnetic signature of nonlinear evolution (in the sense of self-organized criticality) taking place in the lithosphere just before the 1993 large Guam earthquake. That is, there take place step-like changes in the lithosphere during the long-term of the order of several months before the main shock.