Multifractal Singularity Spectrum Research Articles

MULTIFRACTAL ANALYSIS OF EMG FOR CLASSIFICATION AND PROGRESSIVE ASSESSMENT OF BICEPS BRACHII MUSCLE STRENGTH

The proposed research demonstrates an attempt to introduce a systematic procedure for studying the multifractal dynamics of biceps brachii muscle actions during light exercises. The intrinsic patterns in the Surface Electromyogram (sEMG) signals were extracted by fruitfully exploiting the Multifractal features of the signal. The Multifractal features are derived from the multifractal singularity spectrum of the EMG signals. This multifractal feature vector could be utilized for signal characterization, which was successfully extended for the classification of EMG signals. Experimental verification has been done to validate the feature extraction and classification algorithm proposed in this article. A pilot study was conducted on signals from the Physionet database, which was then extended to a medium database developed with biceps brachii EMG signals of 32 healthy male subjects. From this study, we could validate that the Multifractal features fit as a differentiating multi-feature set and also for the progressive assessment of EMG signals of different classes. The observations of the proposed method revealed that the strength of multifractality and area under the spectrum increase as a result of fast movements of the forearm or increases in muscle fatigue. The classification is performed using well-recognized supervised classification algorithms such as k-Nearest Neighbor and Support Vector Machine (SVM) Classifiers. The performance analysis of the classifiers are studied on various measures such as Accuracy, Precision, Recall, F1 score. The statistical significance analysis of the feature vector was carried out by one-way ANOVA test.

EEG fractal dimensions predict high-level behavioral responses in minimally conscious patients

Objective. Brain-injured patients may enter a state of minimal or inconsistent awareness termed minimally conscious state (MCS). Such patient may (MCS+) or may not (MCS-) exhibit high-level behavioral responses, and the two groups retain two inherently different rehabilitative paths and expected outcomes. We hypothesized that brain complexity may be treated as a proxy of high-level cognition and thus could be used as a neural correlate of consciousness. Approach. In this prospective observational study, 68 MCS patients (MCS-: 30; women: 31) were included (median [IQR] age 69 [20]; time post-onset 83 [28]). At admission to intensive rehabilitation, 30 min resting-state closed-eyes recordings were performed together with consciousness diagnosis following international guidelines. The width of the multifractal singularity spectrum (MSS) was computed for each channel time series and entered nested cross-validated interpretable machine learning models targeting the differential diagnosis of MCS±. Main results. Frontal MSS widths (p < 0.05), as well as the ones deriving from the left centro-temporal network (C3: p = 0.018, T3: p = 0.017; T5: p = 0.003) were found to be significantly higher in the MCS+ cohort. The best performing solution was found to be the K-nearest neighbor model with an aggregated test accuracy of 75.5% (median [IQR] AuROC for 100 executions 0.88 [0.02]). Coherently, the electrodes with highest Shapley values were found to be Fz and Cz, with four out the first five ranked features belonging to the fronto-central network. Significance. MCS+ is a frequent condition associated with a notably better prognosis than the MCS-. High fractality in the left centro-temporal network results coherent with neurological networks involved in the language function, proper of MCS+ patients. Using EEG-based interpretable algorithm to complement differential diagnosis of consciousness may improve rehabilitation pathways and communications with caregivers.

Research on Multifractal Characteristics of Vehicle Driving Cycles

Vehicle driving cycles have complex characteristics, but there are few publicly reported methods for their quantitative characterization. This paper innovatively investigates their multifractal characteristics using the fractal theory to characterize their complex properties, laying the foundation for applications such as vehicle driving cycle feature identification, vehicle energy management strategies (EMS), and so on. To explore the scale-invariance of the vehicle driving cycles, the four vehicle driving cycles were analyzed using the Multifractal Detrended Fluctuation Analysis (MF-DFA) method, three of which are standard vehicle test cycles: the New European Driving Cycle (NEDC), the World-wide harmonized Light-duty Test Cycle (WLTC) and the China Light-duty Vehicle Test Cycle for Passenger Car (CLTC-P), and the other is the Urban Road Real Driving Cycle (URRDC), which was obtained by analyzing and processing vehicle driving data collected in actual urban driving conditions. The fluctuation functions, the generalized Hurst exponents, the mass exponent spectra, the multifractal singularity spectra, and the multifractal characteristic parameters were calculated to verify the multifractal characteristics, and to quantify the fluctuation singularities of different driving cycles as the time series. The results show that the fluctuations of all four driving cycles have long-range anticorrelations and exhibit significant multifractal characteristics. The results can provide a basis for the analysis of the complexity of the vehicle driving cycles.

Wave-function extreme value statistics in Anderson localization

We consider a disordered one-dimensional tight-binding model with power-law decaying hopping amplitudes to disclose wavefunction maximum distributions related to the Anderson localization phenomenon. Deeply in the regime of extended states, the wavefunction intensities follow the Porter-Thomas distribution while their maxima assume the Gumbel distribution. At the critical point, distinct scaling laws govern the regimes of small and large wavefunction intensities with a multifractal singularity spectrum. The distribution of maxima deviates from the usual Gumbel form and some characteristic finite-size scaling exponents are reported. Well within the localization regime, the wavefunction intensity distribution is shown to develop a sequence of pre-power-law, power-law, exponential and anomalous localized regimes. Their values are strongly correlated, which significantly affects the emerging extreme values distribution.

Use of multifractal parameters to determine soil particle size distribution and erodibility of a physical soil crust in the Loess Plateau, China

Understanding the knowledge of multifractal analysis on particle size distribution (PSD) of soil physical crusts is indispensable for progressing soil surface erosion mode. In this study, hoeing tillage (20 cm long × 15 cm wide × 5 cm deep) were conducted to simulate classic tillage mode in Yangling, China to obtain physical crusts under artificial rainfall (60 mm h−1 intensity with three durations (5, 15, and 30 min)). We defined crusts formed in ridges as structural crust (Cst), formed by infiltration of runoff in hoes as sediment-containing depositional crust (Cscd), and formed by the extraction of runoff as sediment-free depositional crust (Csfd). Soil stratification methods were used to explore physical crust particle sorting. Results represented that the sand content of Cst, Cscd, and Csfd decreased, whereas clay and silt contents increased after rainfall compared to undisturbed soil. There was no significant difference between Cscd and Csfd under short rainfall duration. Three crust types became gradually concentrated in areas with higher density with increasing rainfall duration according to six common parameters in the generalised dimension spectrum (D0, D1, D2, D1/D0, Dv(D-10–D0), and Ds(D0–D10)). Multifractal singularity spectrum (α0, Av, Fv) showed that PSD was most symmetrical in Csfd, followed by Cscd and Cst. Erodibility index KEPIC was largest for Cst, followed by Csfd then Cscd. The relationship between KEPIC and multifractal parameters were significant. Spatial difference caused by tillage activities and rainfall events determine the heterogeneous formation mode, particle size distribution and erodibility of physical crust.

Investigation of the Global Seismic Noise Properties in Connection to Strong Earthquakes

The global seismic noise, recorded on a network of 229 broadband seismic stations located around the globe for 25 years, from the beginning of 1997 to the end of 2021, has been investigated. To study the noise properties a set of statistics estimated daily have been used: the multifractal singularity spectrum support width, the minimum entropy of the squared wavelet coefficients, and the wavelet-based Donoho-Johnstone (DJ) index. It is shown that the time points of local extrema of the average values of the analyzed noise properties (minima for singularity spectrum support width and DJ-index and maxima for entropy) tend to occur before strong earthquakes. The time interval from the middle of 2002 to the middle of 2003 is determined, when the trend of decreasing the average coherence of the noise properties in the auxiliary network of 50 reference points changed to an increase. Along with an increase in the average coherence, there is an increase in the radius of the spatial maximum coherences of noise properties. Both of these trends continue until the end of 2021, which is interpreted as a general sign of an increase in the degree of criticality of the state of the planet and, as a result, an increase in global seismic danger. After two mega-earthquakes close in time: 27 February 2010, M=8.8 in Chile and 11 March 2011, M=9.1 in Japan, there was an increase in the spatial scales of the strong coherence of noise parameters, which is a sign of an increase in the critical state. The response of seismic noise properties to variations in the length of the day (LOD) has been studied. An estimate of the correlation function between the mean values of the response to LOD and the logarithm of the released seismic energy in a time window of 1 year indicates a delay in energy release with respect to the maxima of the response of noise properties to LOD with a delay time of about 500 days. In connection with this result, an additional intrigue is the extreme increase in the average value of the response to LOD in 2021.

Scaling properties of particle-size distributions of purple soils in a small agricultural watershed: A multifractal analysis

The particle-size distribution (PSD) of soils is a basic physical attribute that affects edaphic hydrological, chemical, and biological properties as well as soil quality and land productivity. Purple soil, as an early weathering product of purple mudstone, is a valuable resource for agricultural development in southwestern China. However, little is known regarding PSDs of purple soil, especially in small agricultural watersheds with diverse land-use types. The present study aimed to elucidate the scaling properties of purple soil PSDs by applying multifractal characterization. Results indicate that the PSDs of purple soils demonstrate clear multifractal behaviour, with generalised dimension and multifractal singularity spectra showing sigma and left-deviating unimodal convex-up curves, respectively. By comparing with soils under other land-use types, the present study found that forestland purple soil is characterised by coarser granularity and more complex PSD, and has the minimum volumetric fractal dimension and the maximum generalised dimensions. No statistically significant correlation was observed between multifractal parameters and soil texture separates, except for that between the Hölder exponent of order zero and the clay fraction (p < 0.05). In addition, most of the multifractal parameters do not exhibit statistically significant differences among soils under different land-use types (p < 0.05). The findings of the present study highlight that the effect of current land use on purple soil PSDs is limited and complex at a small watershed scale, and that the legacy effect of historical land use also plays a role in the evolution of purple soil PSDs. Overall, our findings can provide a reference for comprehensive understanding the influence of land use on purple soil quality.

Multifractality via Stochasticity in Atmospheric Dynamics Description Validated through Remote Sensing Data

In the present paper, correlations between multifractality and stochasticity in atmospheric dynamics are investigated. Starting with two descriptions of atmospheric scenarios, one based on scale relativity theory and another based on stochastic theory, correspondences between parameters and variables belonging to both scenarios are found. In such a context, by replacing an atmospheric conservative passive additive with a non-differentiable component of the atmospheric multifractal velocity, stochastic evolution equations are found for this component, which reveal the multifractal variational transport coefficient and the multifractal molecular diffusion coefficient, along with the multifractal inhomogeneity variation. Furthermore, equations which describe a multifractal Reynolds number and singularity spectrum are also found. Finally, these theoretical results are validated through remote sensing data obtained with the aid of a ceilometer platform.

Adsorption behaviors of near-critical carbon dioxide on organic-rich shales: Modeling, multifractality, and kinetics

Studies on the near-critical carbon dioxide (NC-CO2) adsorption behavior of organic-rich shales are important for shallow shale gas exploration and hydrocarbon recovery enhancement of liquid CO2 fracturing, which further contributes to geological CO2 sequestration and global carbon neutrality. We performed CO2 isothermal adsorption and kinetic experiments on six organic-rich shale samples at a temperature of 303.15 K and pressures of up to 5 MPa to investigate the modeling, multifractality, and kinetics of NC-CO2 adsorption behavior on shales. The equilibrium data were fitted to the Langmuir, Freundlich, BET, modified BET (M−BET), DA, DR, and OK adsorption models; the multifractality of the isotherms was analyzed; and pseudo-first-order, pseudo-second-order, Elovich, and Avrami's fractional-order models were adopted to analyze the adsorption kinetics. Furthermore, an error analysis technique was employed to compare the accuracies of various models for fitting the experimental data. The results showed that various adsorption models presented different fitting effects; however, the M−BET, Freundlich, and DA adsorption models performed better over the entire studied pressure range. The fitting results of the M−BET model indicated that the number of adsorption layers ranged from 2.528 to 4.663 and had a multilayer adsorption mechanism. The multifractality of the adsorption behavior was described by the generalized fractal dimension and multifractal singularity spectra; we demonstrated that some multifractal parameters characterize the NC-CO2 adsorption behavior on shales well. Additionally, the TOC, clay, and quartz contents show close covariations with the isothermal adsorption and multifractal parameters. Moreover, the adsorption process was TOC-dependent and subject to Avrami's fractional-order model. Finally, we propose conceptual three-stage adsorption and geological storage models to understand the nature of the NC-CO2 adsorption behavior of shales.

Multifractal point processes and the spatial distribution of wildfires in French Mediterranean regions

We introduce a simple and wide class of multifractal spatial point patterns as Cox processes which intensity is multifractal, i.e., the class of Poisson processes with a stochastic intensity corresponding to a random multifractal measure. We then propose a maximum likelihood approach by means of a standard Expectation–Maximization procedure in order to estimate the distribution of these intensities at all scales. This provides, as validated on various numerical examples, a simple framework to estimate the scaling laws and therefore the multifractal properties for this class of spatial point processes. The wildfire distribution gathered in the Prométhée French Mediterranean wildfire database is investigated within this approach that notably allows us to compute the statistical moments associated with the spatial distribution of annual likelihood of fire event occurrence. We show that for each order q, these moments display a well defined scaling behavior with a non-linear spectrum of scaling exponents ζq. From our study, it thus appears that the spatial distribution of the wildfire ignition annual risk can be described by a non-trivial, multifractal singularity spectrum and that this risk cannot be reduced to providing a number of events per km2. Our analysis is confirmed by a direct spatial correlation estimation of the intensity logarithms whose the peculiar slowly decreasing shape corresponds to the hallmark of multifractal cascades. The multifractal features appear to be constant over time and similar over the three regions that are studied.

Multifractal features of the particle-size distribution of suspended sediment in the Three Gorges Reservoir, China

The Three Gorges Reservoir (TGR) in China is the largest hydroelectric project in the world, but the threat of sediment affecting ecological sustainability of the reservoir is a topic of concern. Sediment particle-size distribution (PSD) is informative in understanding sediment transport dynamics and biochemical functions. It is, therefore, important to quantitatively characterize the distribution of sediment particles. In the current study, fractal theory is applied to determine the PSD of suspended sediment in the TGR. The results show that the volumetric fractal dimension (Dv) exhibits a significant seasonal difference (p < 0.05), reflecting sediment source and hydrodynamic sorting control the granularity of suspended sediment in the TGR. More specifically, suspended sediment particles are coarser in the wet season than in the dry season for the Yangtze River, and the opposite is true for the Ruxi River, an important tributary. The generalized dimension spectrum, D(q)–q, and multifractal singularity spectrum, f[α(q)]–α(q), were calculated for each suspended sediment sample. Thereafter, the parameters, D(0), D(1), D(2), α(0), Δα(q), and Δf[α(q)], were determined to characterize the PSD. As a result, the coarser suspended sediment during the wet season is characterised by a more complex PSD pattern, with a wider range of particle sizes, greater heterogeneity, and greater homogeneity of distribution over the measurement interval. However, the multifractal structure of the PSD of suspended sediment is more complex during the dry season than during the wet season, with higher local dispersion and variability. The findings of the current study highlight that multifractal analysis provides important insight for understanding the PSD of suspended sediment in the TGR.

Effect of annealing on the micromorphology and corrosion properties of Ti/SS thin films

Abstract Ti and TiN thin films were deposited by means of electron beam evaporation on stainless steel substrates, and subsequently annealed at different temperatures (650, 750 and 850 °C) in a nitrogen atmosphere. The surface morphology of the films studied by atomic force microscopy (AFM), was found to exhibit specific multifractal properties depending on the annealing temperature. It turned out that the width of the multifractal singularity spectra, f(α), decreased as the annealing temperature increased up to 750 °C, but it increased when the temperature was kept at 750 and 850 °C accompanied by the rapid development of the surface objects. The generalized fractal dimension followed a similar trend. On the other hand, the corrosion resistance of the specimens was studied bythe potentiodynamic polarization test in 3.5% NaCl solution at room temperature, observing improved corrosion protection of the films remarkably due to the presence of very thin titanium nitride outer layer.

Identification of healthy and pathological heartbeat dynamics based on ECG-waveform using multifractal spectrum

Human body surface electrocardiogram (ECG) is non-stationary and frequency-varying by nature that belongs to a typical nonlinear signal. Therefore, traditional linear and time–frequency​ analysis methods cannot fully disclose its nonlinear nature. Meanwhile, physiological complexity of heartbeat signal may vary with age, diseases, drug administrations, or even behavioral modifiers. To test the intrinsic relationships among them, we first put forward a theoretical model for nonlinear time series analysis and then took the generally accepted multifractal sets to verify it. Upon that, we then investigated the multifractal singularity spectrum areas of synchronous 12-lead ECG signals taken from crowds with different age stages, healthy conditions and drug medications. Our results suggested that aging and diseases can not only decrease multifractal complexity of the signals, but also increase inhomogeneity of it. With aging and deepening lesion, fractal-like structure of the heartbeat system is damaged or even structurally changed, which lead to the declination of physiological complexity and at the same time the increasement of irregularity and anisotropy of ECG signal’s propagation. In addition, the mean value of multifractal spectrum area of human 12-lead ECG signals also reflect the self-discipline regulation of human autonomic nervous system. The value descends with age growing or drug intervention to restrain sympathetic nerves. That suggest self-discipline control function weakens when people are getting old, or they are under repressed heartbeat activities with lower heart rate and lower blood pressure. Then, complexity of heartbeat signal declines and even tends to turn from multifractality to monofractality, which means drops off of human individual adaptability.

Connection of Seismic Noise Properties in Japan and California with Irregularity of Earth’s Rotation

The problem of the relationship of the properties of seismic noise with the irregular rotation of the Earth is considered. We study the median daily values of the multifractal singularity spectrum support width, the generalized Hurst exponent, and the seismic noise wavelet-based entropy on the networks of broadband seismic stations in Japan and California for the time interval 1997–2019. The first principal components of the noise properties in a half year moving time window are calculated. The coherence spectra are estimated both between the principal noise components in two regions and each principal component with a time series of the length of day (LOD). It has been shown that an increase in the power of high-frequency pulsations of LOD (for periods less than 6 days) is accompanied by a decrease in the coherence between the properties of seismic noise in Japan and California. The degree of synchronization of the response of changes in the properties of seismic noise in Japan and California to the irregularity of Earth’s rotation in a “long” moving time window of 5 years is estimated. For this purpose, the correlation coefficient and the “secondary” coherence spectrum between synchronous variations of the “primary” coherence spectra between the LOD and each of the main noise components obtained in the “short” half-year window, as well as their mutual correlation function, were calculated.

The institutional characteristics of multifractal spectrum of China’s stock market

This paper investigates the fractal structure of China’s stock market by calculating the multifractal singularity spectrum and comparing the scaling behavior of the bubble phase of eight abnormal volatilities with that of normal fluctuation on the timeline. We find robust evidence that the Shanghai Stock Exchange Composite Index has multifractal features in the bubble and normal fluctuation periods, where the higher multifractality is associated with a bubble and more unstable market. The short-sighted administrative policies cause over-supply of intervention, which enhances the multifractality and increases the instability of the stock market. The multifractal parameter set (α0,Δα,−B) might be used as a quantifier to characterize the status of the stock market. A policy aimed to improve the stability of the stock market should be devoted to optimizing the parameter set.

Динамика морфологии поверхности вольфрамовой фольги под нагрузкой

Morphology dynamics of recrystallized tungsten foil surface under uniaxial stretching was investigated in situ by LEED, Auger, AFM, SEM an X-Ray fluorescent analysis. It has been found that before the rupture of the sample the transition from multifractality to monofractality occurs in a few stages: narrowing of the width of multifractal singularity spectrum of surface defects, turn of structural blocks of dominating face W (112) and transition of the lattice of dominating face into diffractive disordered state.

Multifractal analysis and evolution rules of micro-fractures in brittle tectonically deformed coals of Yangquan mining area

Micro-fractures act as a bridge between pores and macro-fractures and directly affect the permeability of coal reservoirs. Understanding the micro-fracture heterogeneity and its relationships with deformation can enrich our knowledge on the gas transportation behavior of tectonically deformed coals. The multifractal theory was applied to characterize the variations and heterogeneity of micro-fractures in high-rank brittle tectonically deformed coals. The results indicated that the micro-fractures exhibit multifractal behavior at e = 1–1/16 (e being the size of the boxes considered), and that the obtained generalized dimension spectra Dq-q, multifractal singularity spectrum f(α)-α, and characteristic parameters, including the capacity dimension D0, information dimension D1, correlation dimension D2, D1/D0, the width of multifractal spectrum Δα, and the difference of the fractal dimensions Δf(α), can be applied to accurately describe the differences and variations of the micro-fracture distributions and scales. Moreover, the deformation has a significant influence on the variation and heterogeneity of micro-fracture distributions and scales, as demonstrated by the change rules of the characteristic parameters. The D1, D2, and D1/D0 increased with the increase of deformation degree, while Δα and Δf(α) decreased. Consequently, the deformation leads to higher density, more uniform distributions, and more dispersed and complex scales in the micro-fractures of brittle tectonically deformed coals, and controls the permeability of coal reservoirs.

RESEARCH ON THE FRACTAL STATISTICAL CHARACTERISTICS AS POSSIBLE PROGNOSTIC PARAMETERS FOR EARTHQUAKES, GENERATED IN THE SEISMIC ZONE OF VRANCEA, IN THE PERIOD BETWEEN 01.08.2016 AND 30.12.2016

&#x0D; &#x0D; &#x0D; Using fractal analysis is an excellent alternative method for decode the seismic noise structure. Fractal analysis of microseismic noise could also be an appropriate method to detect earthquake indicators. The scientific goal is to detect standard signals, based on different earthquakes’ focal mechanisms, separating the "individual" behavior of the elements of the monitoring systems.The method for describing low-frequency microseismic noise from the network of seismic stations in a seismically active region of the Vrancea used. Seismic records of twenty-three broadband stations were analyzed, situated at distances of 20 to 500 km from the Vrancea earthquakes whit magnitudes Mw=5.7 and Mw=5.6 on September 23 and December 27, 2016, respectively. The daily assessment values of three multifractal parameters (characteristics of the multifractal singularity spectra of the waveform) from each station used for the description.The present paper is a continuation of previous work [Oynakov et al., 2019], where the effects of synchronization in the low-frequency microseismic field were found before the Vrancea earthquake with magnitude Mp=5.6 on October 28, 2019.The study shows that the noise coherence measure increased for stations, closer to the epicenter. However, the question of the source of this coherence remains open.&#x0D; &#x0D; &#x0D;

The complexity of ECG signal based on multifractal theories and its nonlinear dynamical mechanism

The nonlinear dynamical analysis of biomedical signals has always been the research focus in academic fields. It better uncovers the essential rules in life activities than conventional linear and time-frequency analysis methods. Human body surface electrocardiogram (ECG) signal is non-stationary and frequency-varying by nature, which belongs to a typical nonlinear signal. Therefore, traditional linear analysis methods cannot completely disclose its nonlinear nature. The existing nonlinear dynamic tools, such as correlation dimension (D2), Lyapunov exponent, entropy, detrended fluctuation analysis, multifractal singularity spectrum etc., have already been applied to the studies on heart electrical signals, which proved that this signal has definite chaotic characteristic. The aforementioned nonlinear methods perform better in the analysis of deterministic stochastic signals. In our viewpoints, because all the probabilities in the original data set can be exactly expressed by the corresponding points in the multifractal singularity spectrum f ( α ), the area of the spectrum must comprise the total information of the data. This two-dimensional expression is more accurate than the computation of spectral width Δ α in analyzing the heartbeat signal. With regard to ECG time series, the areas of singularity spectrum should include all the information about the heartbeat dynamics. Considering the irregularity and anisotropy of the heartbeat electrical signal propagation, we investigated the arithmetic mean and dispersing degree of the area calculated from synchronous 12-lead ECG signals obtained from a large number of subjects, who were under different physiological and pathological conditions. The 12-lead ECG records were obtained from 12 sensors positioned on body surfaces, including the limb and chest leads. In addition, the ECG signals were in high frequency section (HFECG), whose frequency components were above 100 Hz (approximately 100 Hz–2 kHz). Some early heart diseases can first be reflected by high-frequency ECG signals, which are often associated with sharp notches and slurs in the time domain. Furthermore, we set sampling frequency of HFECG signal to 1 kHz so that all the components below 500 Hz could be analyzed according to the sampling theorem. Thereafter, by the virtue of the multifractal theory, we investigated the arithmetic mean and dispersing degree computed from singularity spectrum area of synchronous 12-lead ECG signals obtained from different crowds of human subjects. Variance analysis tests revealed all 12-lead ECG signals from above cohorts were statistically identifiable using these two indicators. The experimental results suggest that the arithmetic mean of the area of the 12-lead ECG signals was apparently large for healthy young but small for myocardial infarction (MI) sufferers. Besides, the dispersing degree of the area of the 12-lead ECG signals was obviously small for healthy young but large for MI sufferers. For the other cohorts, such as ischemia sufferers and healthy elderly, these two values were of middle magnitudes. This indicates that with deeper lesions, the fractal-like structure of the heartbeat system is damaged or structurally changed, which may lead to decline in the nonlinear complexity of the system and concomitant increase in the irregularity and anisotropic propagation of ECG signal. In addition, we found that the 12-lead mean value of singularity spectrum area of human ECG signals can reflect the self-discipline control status of human autonomic nerve to some degree. This value gradually decreased with aging. These findings suggest that the self-discipline control of the human autonomic nervous system weakens with aging. The nonlinear complexity of ECG signal then descends and tends to turn from multifractality to monofractality, implying weakened human individual adaptabilities. Our studies on the nonlinear dynamical features of heart electrical signals and ECG variations with age, disease, and human autonomic nerve control, demonstrate theoretical and diagnostic significances.

Distribution of Air Temperature Multifractal Characteristics Over Greece

In this study, Multifractal Detrended Fluctuation Analysis (MF-DFA) is applied to daily temperature time series (mean, maximum and minimum values) from 22 Greek meteorological stations with the purpose of examining firstly their scaling behavior and then checking if there are any differences in their multifractal characteristics. The results showed that the behavior is the same at almost all stations, i.e., time series are positive long-term correlated and their multifractal structure is insensitive to local fluctuations with large magnitude. Moreover, this study deals with the spatial distribution of the main characteristics of multifractal (singularity) spectrum: the dominant Hurst exponent, the width of the spectrum, the asymmetry and the truncation type of the spectrum. The spatial distributions are discussed in terms of possible effects from various climatic features. In general, local atmospheric circulation and weather conditions are found to affect the shape of the spectrum and the corresponding spatial distributions. Furthermore, the intercorrelation of the main multifractal spectrum parameters resulted in a well-defined group of stations sharing similar multifractal characteristics. The results indicate the usefulness of the non-linear analysis in climate research due to the complex interactions among the natural processes.