Статті в журналах з теми "Grassberger -Procaccia correlation integral"

Photon emission accompanying the fracture of an epoxy and single crystal MgO is examined for evidence of deterministic chaos by means of the autocorrelation function, the Fourier transform, the correlation integral of Grassberger and Procaccia, and the fractal box dimension. A positive Lyapunov exponent is also obtained from the epoxy phE data. Each of these measures is consistent with a significant degree of deterministic chaos associated with attractors of relatively low dimension. A typical epoxy fracture surface was analyzed for fractal character by means of the slit island technique, yielding a fractal dimension of 1.32 ± 0.03. The fractal dimensions of the fracture surface and the photon emission data (box dimension) of the epoxy are in good agreement. These observations suggest that fluctuations in photon emission intensity during fracture reflect the production of fractal surface features as they are being produced and thus provide important information on the process of dynamic crack growth.

1. The fractal scaling of heart rate variability, gauged by the correlation dimension (CD), is hypothesized to be characterized by a time structure (chronome), which in health shows differences as a function of gender and age. 2. From 24 h Holter records of 44 clinically healthy male subjects in four age groups (5–10, 20–25, 40–45 and 60–65 years; n = 11 in each group), 500 s sections at 4 h intervals for 24 h were analysed for smoothed R-R intervals sampled at 4 Hz. Using an algorithm modified from Grassberger and Procaccia (Physica D 1983; 9: 189–208), the correlation integral was estimated for embedding dimensions from 1 to 20 with a 1.0 s time lag for each section. Nightly (02.00 hours-06.00 hours) ECG records were similarly analysed in 72 additional clinically healthy subjects of both genders, 5–70 years of age. The single cosinor assessed the circadian characteristics; one- and two-way analyses of variance and linear regression were used to examine changes as a function of gender and age. 3. The 24 h average of CD is largest in the 20–25-year-old men and decreases with age thereafter (P < 0.05). These changes apply in particular to the nightly CD values, which are higher in female than in male subjects (P < 0.001). Increasing age is associated with a decrease in the amplitude and an advance in the phase of the circadian rhythm in CD (P < 0.05). 4. A chaotic end-point from fractal scaling, yielding a non-linear index, such as the correlation integral, undergoes a circadian rhythm and changes with gender and age. This assessment in the chronome represents an added diagnostic tool in cardiology, and provides new end-points for the study of coherence among internal variables of autonomic mechanisms and of influences by external environmental variables upon them.

Aim - combined use of frequency and nonlinear analysis methods for obtaining hypnograms by analyzing electroencephalographic (EEG) signals during somnological studies. Methods. Frequency filtering methods were used for preliminary treatment of EEG signals before the following nonlinear analysis. As non-linear methods of analysis we used fractal methods of deterministic chaos, such as Hurst’s method of the normalized amplitude, approximate entropy method, calculation of the correlation integral by Grassberger and Procaccia’s method. For the possibility of applying the last two methods we used quasi phase space recovery method according to the Taken’s theorem. As a result of non-linear analysis we obtained hypnograms reflecting the transition between the stages of sleep in patients undergoing somnological examination. To assess the reliability of the results, they were compared to the hypnograms obtained by the classical method based on the rules of Rehchaffen and Keyls. Also the problems associated with the occurrence of various types of interference were considered and methods for reducing their influence on the final results were suggested. Results. We can conclude that using these methods with appropriate selection of the parameters, employing the necessary normalization of raw data, and averaging the results allow us to obtain hypnogram having a full match of defined phases of sleep for about half of the periods recorded by EEG. To obtain these results it is sufficient to use only one channel of EEG recording.

In this paper, we study the behavior of the correlation dimension estimated using the Grassberger–Procaccia (GP) algorithm [Grassberger & Procaccia, 1983] in the wavelet domain for functions belonging to Hölder space. We prove that, as the wavelet scale level tends to infinity, the GP correlation dimension estimate tends to zero. Applying this result to the trajectories of the fractional Brownian motion process and using basic properties of the wavelet transform, we show that, for the fractional Gaussian noise process (fGn), the correlation dimension estimated by the GP procedure converges to the zero value. As the fractional Gaussian noise is a stochastic process with 1/fα spectrum, -1 < α < 1, our results confirm Osborne and Provenzale's assertion that colored random noise leads to the convergence of the GP-based correlation dimension estimator. However, our result holds for a different range of the spectrum exponent values. Moreover, for the fGn class of random processes, we found no correspondence between the value of the scaling exponent H and the value of the correlation dimension estimated by the GP algorithm as the latter is simply zero.

This paper reports on the application of the correlation dimension in large rotating machinery fault diagnosis. The Grassberger-Procaccia algorithm and its modified version are introduced. Some important influencing factors relating directly to the computational precision of the correlation dimension are discussed. Industrial vibration signals measured from large rotating machinery with different faults are researched using the above-mentioned methods. The results show that the correlation dimension can provide some intrinsic information on an underlying dynamic system and can be used to classify different faults intelligently.

The correlation dimension D(2) as a characteristic measure of the regular or chaotic behaviour of the solar dynamical system has been calculated. The algorithm suggested by Grassberger and Procaccia (1983) has been applied to time series of relative sunspot numbers and of areas of sunspots and faculae. In the first case, a correlation dimension D(2) ≃ 1.5 has been found; in the other two cases, the algorithm was not convergent, the results obtained being not relevant, due to the too short series of data available.

Abstract. Understanding the complexity of natural systems, such as climate systems, is critical for various research and application purposes. A range of techniques have been developed to quantify system complexity, among which the Grassberger–Procaccia (G-P) algorithm has been used the most. However, the use of this method is still not adaptive and the choice of scaling regions relies heavily on subjective criteria. To this end, an improved G-P algorithm was proposed, which integrated the normal-based K-means clustering technique and random sample consensus (RANSAC) algorithm for computing correlation dimensions. To test its effectiveness for computing correlation dimensions, the proposed algorithm was compared with traditional methods using the classical Lorenz and Henon chaotic systems. The results revealed that the new method outperformed traditional algorithms in computing correlation dimensions for both chaotic systems, demonstrating the improvement made by the new method. Based on the new algorithm, the complexity of precipitation, and air temperature in the Hai River basin (HRB) in northeastern China was further evaluated. The results showed that there existed considerable regional differences in the complexity of both climatic variables across the HRB. Specifically, precipitation was shown to become progressively more complex from the mountainous area in the northwest to the plain area in the southeast, whereas the complexity of air temperature exhibited an opposite trend, with less complexity in the plain area. Overall, the spatial patterns of the complexity of precipitation and air temperature reflected the influence of the dominant climate system in the region.

ABSTRACT .The correlation fractal dimension of strange at tractors of southwest monsoon rainfall of all the 35 Indian meteorological sub-divisions and India as a whole and nonh-east monsoon rainfall of 4 meteorological sub-divisions of peninsular India are estimated using the Grassberger and Procaccia algorithm (1983-). The fractal dimensions provide us the primary information on the number of parameters that are required to understand the dynamics underlying the monsoon dynamic system. The fractal dimensions varied between 2.9 and 7.1 and the saturation occurred between 14 and 21 ~ dimensions. In 5 sub-divisions the fractal dimension could not be determined.

This paper is mainly devoted to the investigation of discrete-time fractional systems in three aspects. Firstly, the fractional Bogdanov map with memory effect in Riemann–Liouville sense is obtained. Then, via constructing suitable controllers, the fractional Bogdanov map is shown to undergo a transition from regular state to chaotic one. Meanwhile, the positive largest Lyapunov exponent is calculated by the Jacobian matrix algorithm to distinguish the chaotic areas. Finally, the Grassberger–Procaccia algorithm is employed to evaluate the correlation dimension of the controlled fractional Bogdanov system under different parameters. The main results show that the correlation dimension converges to a fixed value as the embedding dimension increases for the controlled fractional Bogdanov map in chaotic state, which also coincides with the conclusion driven by the largest Lyapunov exponent. Moreover, three-dimensional fractional Stefanski map is considered to further verify the effectiveness and generality of the obtained results.

Research on the relationships among tectonics, micropores, microfractures, and coalbed methane (CBM) content is important for the optimal selection of CBM production areas. In this study, micropore-microfracture structural parameters of coal samples from the Guojiahe coalfield are determined through the use of X-ray photography, an image recognition algorithm, and a liquid nitrogen adsorption method. The relationship between the micropore-microfracture characteristics of the reservoir and the gas content is quantitatively assessed using the Grassberger and Procaccia (GP) algorithm to calculate the correlation dimension of the parameters. Micropore-microfracture development varies in different tectonic zones. Additionally, the CBM content varies according to the characteristic parameters of hysteresis loops and the pore diameter. The correlation dimension is an effective indicator of the nonlinear relationship between reservoir micropore-microfracture characteristics and the gas content.

The search for low-dimensional chaos in ocean surface waves is nowadays a very active field. The interpretation of the results, however, is not always straightforward. The issue addressed in this paper is how time series analysis tools from dynamical systems theory behave for a class of Gaussian processes often used in the study of ocean surface waves. The study includes the largest Lyapunov exponent, the Grassberger and Procaccia correlation dimension and the self-similarity properties. Surprisingly, for certain parameter ranges, the correlation dimension is found to be finite, the largest Lyapunov exponent is found to be positive and structure appears on all time scales. These results suggest that improved techniques and data analysis procedures may be required in order to study chaos properties of ocean surface waves or of other Gaussian processes with similar power spectra.

Forecasting surface temperature and pressure to a reasonable degree of accuracy atleast 3 hours ahead of the scheduled departure of an aircraft helps the aircrew to make the optimum planning for the payload and cargo load. The method of generalised Adaptive Filter (AF) algorithm as suggested by Makridakis and Wheelright (1978) has been used to forecast temperature and pressure over Madras airport and the forecast efficiency is compared with that obtained through method of persistency, auto regressive processes and other statistical techniques. The dimensions of attractors of the phase space trajectories of these variables have been estimated using the Grassberger and Procaccia (1983) algorithm of correlation fractal dimension with a view to find out the predictability of these variables and the minimum and maximum number of parameters needed for modelling these variables.

The non-geometric and irregular objects are considered as complex patterns. The geometric complexity is measured as space lling capacity by a factor known as a fractal dimension. Dierent techniques are proposed to nd this complexity measure according to the properties of the pattern. This paper is aimed to introduce a method for counting the dimension of the lled Julia fractal set generated by the Escape Time Algorithm using the method of spreading the points inside the proposed window. The resulted dimension is called Escape Time dimension. A new method to compute a correlation dimension of the Filled Julia fractal set is also proposed based on the Grassberger-Procaccia algorithm by computing the correlation function. A log-log graph of the correlation function versus the distances between every pair of points in the lled Julia fractal set is an approximation of the correlation dimension. Finally, a comparison between these two fractal dimensions of the led Julia fractal set which is generated by the Escape Time Algorithm is presented to show the efficiency of the proposed method.

Introduction. Non-linear methods of analysis have found widespread use in the Heart Rate Variability (HRV) technology, when the long-term HRV records are available. Using one of the effective nonlinear methods of analysis of HRV correlation dimension D2 for the standard 5-min HRV records is suppressed by unsatisfactory accuracy of available methods in case of short records (usually, doctors have about 500 RRs during standard 5-min HRV record), as well as complexity and ambiguity of choosing additional parameters for known methods of calculating D2. The purpose of the work. Building a robust estimator for calculating correlation dimension D2 with high accuracy for limited se-ries of RR-intervals observed in a standard 5-minute HRV record, i. e. with N  500. As well as demonstrating the capabilities of the D2 formula on a well known attractors (Lorenz, Duffing, Hennon and etc.) and in applications for Normal Sinus Rhythm (NSR), Congestive Heart Failure (CHF) and Atrial Fibrillation (AF). Materials and Methods. We used MIT-BIH long-term HRV records for normal sinus rhythm, congestive heart failure and atrial fibrillation. In order to analyze the accuracy of new robust estimator for D2, we used the known theoretical values for some famous attractors (Lorenz, Duffing, Hennon and etc.) and the most popular Grassberger-Procaccia (G-P) algorithm for D2. The results of the study. We have shown the effectiveness of the developed D2 formula for time series of limited length (N = 500–1000) by some famous attractors (Lorenz, Duffing, Hennon and etc.) and with the most popular Grassberger-Procaccia (G-P) algorithm for D2. It was demonstrated statistically significant difference of D2 for normal sinus rhythm and congestive heart failure by standard 5 min HRV segments from MIT-BIH database. The promised technology for early prediction of atrial fibrillation episodes by current D2 algorithm was shown for standard 5 min HRV segments from MIT-BIH Atrial Fibrillation database. Conclusion. Robust correlation dimension D2 estimator suggested in the article allows for time series of limited length (N ≈ 500) to calculate D2 value that differs at mean from a precise one by 5 ± 4%, as demonstrated for various well known attractors (Lorenz, Duffing, Hennon and etc.). We have shown on the standard 5-min segments from MIT-BIH database of HRV records: - the statistically significant difference of D2 for cases of normal sinus rhythm and congestive heart failure; - D2 drop significantly for the about 30 min. before of AF and D2 growth drastically under AF there was shown for HRV records with Atrial Fibrillation (AF) episodes. The suggested robust correlation dimension D2 estimator is perfect suitable for real time HRV monitoring as accurate, fast and non-consuming for computing resources. Key words: Hearth rate variability; Correlation dimension; Congestive heart failure; Atrial fibrillation.

Vibration signals extracted from rotating parts of machinery carry a lot of useful information about the condition of operating machine. Due to the strong non-linear, complex and non-stationary characteristics of vibration signals from working bearings, an accurate and reliable health assessment method for bearing is necessary. This paper proposes to utilize the selected chaotic characteristics of vibration signal for health assessment of a bearing by using self-organizing map (SOM). Both Grassberger-Procaccia algorithm and Takens' theory are employed to calculate the characteristic vector which includes three chaotic characteristics, such as correlation dimension, largest Lyapunov exponent and Kolmogorov entropy. After that, SOM is used to map the three corresponding characteristics into a confidence value (CV) which represents the health state of the bearing. Finally, a case study based on vibration datasets of a group of testing bearings was conducted to demonstrate that the proposed method can reliably assess the health state of bearing.

To effectively identify network rumors and block their spread, this paper uses fractal theory to analyze a network rumor spreading situation time series, reveal its inner regularity, extract features, and establish a network rumor recognition model. The model is based on an empirical mode decomposition (EMD) correlation dimension and K-nearest neighbor (KNN) approach. Firstly, a partition function is used to determine if the time series of the rumor spreading situation is a uniform fractal process. Secondly, the rumor spreading situation is subjected to EMD to obtain a series of intrinsic mode functions (IMFs), construct the IMF1–IMF6 components containing effective feature information as the principal components, and reconstruct the phase space of the principal components, respectively. Finally, the correlation dimensions of the principal components IMF1–IMF6 as obtained by the Grassberger-Procaccia algorithm are used as feature parameters and are imported into the KNN model for rumor recognition. The experimental results show that the correlation dimension of a spreading situation can better reflect the characteristic information; as combined with the KNN model for identifying rumors, the recognition rate reaches 87.5%. This result verifies the effectiveness of fractal theory in network rumors recognition, expands the thinking for the research of rumors recognition, and provides theoretical support for rumor governance.

In this paper, the method of measuring the porosity of electrostatic nanofiber membrane by VC++ and Matlab is introduced. It is found that the ratio of the calculated porosity to the porosity measured by the mercury intrusion method accords with the famous Feigenbaum constant (α=2.5029078750957⋯). The porosity distribution of nanofiber membranes was studied by VC++ and Matlab based on the image obtained by using a scanning electron microscope. The porosity distribution calculated by using a computer is magnified by eα times which was named as relative porosity distribution. According to the relative porosity distribution, we use the algorithm proposed by Grassberger and Procaccia (briefly referred to as the G-P algorithm) to calculate the correlation fractal dimension. The correlation fractal dimension calculated from the relative porosity distribution series was between 1 and 2, consistent with geometric characteristics of coincidence samples. The fractal meaning of the Feigenbaum constant was verified again. In the end, we obtained the relationship between the associated fractal dimension and the filtration resistance by fitting in accordance with the secondary function relationship and reached the maximum correlation fractal dimension when the filtration resistance was 15–20 pa.

In the present study, our aim was to evaluate the applicability of the nonlinear technique to the investigation of cardiovascular control. We applied an approach known as the “surrogate data method” to test for nonlinear components in the blood pressure (BP) signal. Our results strongly indicate that there are nonlinear components in the BP time series taken from a Wistar-Kyoto rat (WKY), suggesting that the use of nonlinear methods may provide new information about the BP control system. We developed a procedure appropriate for the stable and reliable calculation of the Grassberger-Procaccia correlation dimension (D) of the arterial BP signal. The saturation value D was 5.48 +/- 0.30 for the WKY group and 5.92 +/- 0.26 for the spontaneously hypertensive rat (SHR) group, with P < 0.001. We also found that in the WKY group D displays a significant response to complete alpha 1 blockade and bleeding, whereas no response is observed in the SHR group. These results imply that differences in the control mechanisms may be detected by the nonlinear dynamics approach both under baseline conditions and when interfering with cardiovascular control.

Acoustic emission (AE) series on time and location distributions on space are all fractal during the failure process of rock material. In this paper, AE signals of heated rock samples at different temperature under uniaxial compression were captured, and the correlation fractal dimensions (CFDs) of AE counts series at different stress level were calculated using Grassberger-Procaccia algorithm. The temperature effect on AE fractal behavior was revealed. The results show that as the heat temperature increases, the total AE counts are more, while the peak value is less. With the increase of external loading, the AE CFD increases fast to a peak at first and then decreases to a bottom and, after that, increases again but within a narrow range. 200°C and 800°C are two thresholds. As the heat temperature rises, the maximum CFD value and the corresponding stress level both increase from 25°C to 200°C and decrease from 200°C to 800°C and then increase again from 800°C to 1200°C. The CFD value at the failure point shows polynomial decline with rising heat temperature.

Abstract. A detailed nonlinear time series analysis has been made of two daytime geomagnetic pulsation events being recorded at L'Aquila (Italy, L ≈ 1.6) and Niemegk (Germany, L ≈ 2.3). Grassberger and Procaccia algorithm has been used to investigate the dimensionality of physical processes. Surrogate data test and self affinity (fractal) test have been used to exclude coloured noise with power law spectra. Largest Lyapunow exponents have been estimated using the methods of Wolf et al. The problems of embedding, stability of estimations, spurious correlations and nonlinear noise reduction have also been discussed. The main conclusions of this work, which include some new results on the geomagnetic pulsations, are (1) that the April 26, 1991 event, represented by two observatory time series LAQ1 and NGK1 is probably due to incoherent waves; no finite correlation dimension was found in this case, and (2) that the June 18, 1991 event represented by observatory time series LAQ2 and NGK2, is due to low dimensional nonlinear dynamics, which include deterministic chaos with correlation dimension D2(NGK2) = 2.25 ± 0.05 and D2(NDK2) = 2.02 ± 0.03, and with positive Lyapunov exponents λmax (LAQ2) = 0.055 ± 0.003 bits/s and λmax (NGK2) = 0.052 ± 0.003 bits/s; the predictability time in both cases is ≈ 13 s.

Variability in individual pain sensitivity is a major problem in pain assessment. There have been studies reported using pain-event related potential (pain-ERP) for evaluating pain perception. However, none of them has achieved high accuracy in estimating multiple pain perception levels. A major reason lies in the lack of investigation of feature extraction. The goal of this study is to assess four different pain perception levels through classification of pain-ERP, elicited by transcutaneous electrical stimulation on healthy subjects. Nonlinear methods: Higuchi’s fractal dimension, Grassberger-Procaccia correlation dimension, with auto-correlation, and moving variance functions were introduced into the feature extraction. Fisher score was used to select the most discriminative channels and features. As a result, the correlation dimension with a moving variance without channel selection achieved the best accuracies of 100% for both the two-level and the three-level classification but degraded to 75% for the four-level classification. The best combined feature group is the variance-based one, which achieved accuracy of 87.5% and 100% for the four-level and three-level classification, respectively. Moreover, the features extracted from less than 20 trials could not achieve sensible accuracy, which makes it difficult for an instantaneous pain perception levels evaluation. These results show strong evidence on the possibility of objective pain assessment using nonlinear feature-based classification of pain-ERP.

Calculations of two types of fractal dimension are reported, regarding the elastic-plastic response of a two-degree-of-freedom beam model to short pulse loading. The first is Mandelbrot’s (1982) self-similarity dimension, expressing independence of scale of a figure showing the final displacement as function of the force in the pulse loading; these calculations were made with light damping. These results are equivalent to a microscopic examination in which the magnification is increased by factors of 102; 104; and 106. It is found that the proportion and distribution of negative final displacements remain nearly constant, independent of magnification. This illustrates the essentially unlimited sensitivity to the load parameter, and implies that the final displacement in this range of parameters is unpredictable. The second fractal number is the correlation dimension of Grassberger and Procaccia (1983), derived from plots of Poincare intersection points of solution trajectories computed for the undamped model. This fractional number for strongly chaotic cases underlies the random and discontinuous selection by the solution trajectory of the potential well leading to the final rest state, in the case of the lightly damped model.

We examine the photon emission accompanying rapid crack growth in an unfilled epoxy resin and in the same resin filled with alumina particles. The alumina particles substantially increase the toughness of the material and increase the photon emission intensities at least tenfold. We attribute the increased photon emission in the filled material to high densities of broken bonds near the alumina particles. The photon emission signals from both filled and unfilled materials show nonintegral (fractal) dimensions which are insensitive to the presence of the particles at the level of precision employed. Fractal dimension measurements of the fracture surfaces are likewise relatively insensitive to the presence of the filler, despite marked variations in apparent surface roughness. The photon emission signals were examined for the presence of chaos. Computations of the correlation exponent of Grassberger and Procaccia indicate that the photon emission fluctuations are not noise-like in character, and suggest deterministic chaos. Lyapunov exponent estimates on photon emission signals confirm the presence of chaotic processes. X-ray photoelectron spectroscopy and electron microscopy of the fracture surface indicate very little interfacial failure; i.e., fracture proceeds predominantly through the epoxy matrix in both filled and unfilled materials. Consequently, the character of the polymer matrix dominates the fracture process and therefore determines the fractal nature of the surface and the chaotic nature of the photon emission intensities in each material.

To determine whether arterial pressure (AP) and renal blood flow (RBF) are nonlinear dynamic processes (chaotic), we measured resting AP and RBF over 4 h in six conscious dogs. A catheter was placed in the aorta, and transit-time flowmeters were positioned around the renal artery. The average AP was 102 +/- 3 mmHg, and the mean RBF was 318 +/- 42 ml/min. We applied four analytic procedures to test the nature of AP and RBF time series, i.e., to determine if these variables are controlled randomly, if they consist of periodic oscillations, or whether they are best characterized as nonlinear dynamic processes. To this end, a fast Fourier transform was performed to quantify the amount of distinct periodic oscillations and nonperiodic variability in the very low frequency domain (< 0.01 Hz). The power spectrum of AP and RBF revealed broad band noise with no distinct peaks, which is commonly referred to as “1/f noise.” As a second procedure, time-delayed phase return maps were constructed, and as a third approach the correlation dimensions were estimated via the Grassberger-Procaccia algorithm. The correlation dimensions of RBF and AP were similar (RBF 3.3 +/- 0.37 vs. AP 3.6 +/- 0.23; P = 0.2). The fourth method determined sensitive dependence on initial conditions, a hallmark of nonlinear “chaotic” dynamics. We determined the maximal Lyapunov exponents and found them to be positive for AP (0.1 +/- 0.01) and for RBF (0.04 +/- 0.01) indicating that they both are nonlinear dynamic processes.(ABSTRACT TRUNCATED AT 250 WORDS)

To investigate how arterial baroreceptors affect the dynamic properties of short-term blood pressure control, we determined Lyapunov exponents and correlation dimensions of blood pressure. Two groups of conscious dogs were studied: a control group (n = 7) and a group subjected to total sinoaortic and cardiopulmonary baroreceptor denervation (n = 7). As a measure of variability, standard deviation was determined and power spectra were calculated. In the lower frequency range (f < 0.1 Hz) power density was inversely related to frequency in both groups, indicating "1/f noise." Estimating the correlation dimension via the Grassberger-Procaccia algorithm as a quantification of complexity revealed a decrease after baroreceptor denervation (1.74 +/- 0.2 vs. 3.05 +/- 0.23 control; P < 0.05). Determination of the largest Lyapunov exponents lambda 1, which indicates the sensitive dependence on initial conditions, a hallmark of chaos, also yielded a diminution after denervation (lambda 1 = 0.74 +/- 0.08 vs. 1.85 +/- 0.18, P < 0.01). The results were cross-checked with surrogate data statistics. The null hypothesis, that there is no nonlinear structure in arterial blood pressure time series, was rejected. This shows that after baroreceptor denervation, blood pressure control is less complex and less sensitive to initial conditions ("chaos"). In contrast, variability (standard deviation) is increased (22.2 +/- 3.1 denervation vs. 8.3 +/- 1.4 control; P < 0.05). It is concluded that under physiological conditions, arterial and cardiopulmonary baroreceptors reduce variability of blood pressure, however, at the cost of blood pressure being less predictable. Thus the regulation is more sensitive depending on initial conditions.(ABSTRACT TRUNCATED AT 250 WORDS)

Abstract. We analyse the seismic noise recorded at the Colima Volcano (Mexico) in the period December 2005–May 2006 by four broadband three-component seismic stations. Specifically, we characterize the spectral content of the signal and follow its time evolution along all the data set. Moreover, we infer the properties of the attractor in the phase space by false nearest neighbours analysis and Grassberger–Procaccia algorithm, and adopt a time-domain decomposition method (independent component analysis) to find the basic constituents (independent components) of the system. Constraints on the seismic wavefield are inferred by the polarization analysis. We find two states of the background seismicity visible in different time-intervals that are Phase A and Phase B. Phase A has a spectrum with two peaks at 0.15 Hz and 0.3 Hz, with the latter dominating, an attractor of correlation dimension close to 3, three quasi-monochromatic independent components, and a relevant fraction of crater-pointing polarization solutions in the near-field. In Phase B, the spectrum is preserved but with the highest peak at 0.15 Hz, the attractor has a correlation dimension close to 2, two independent components are extracted, and the polarization solutions are dominated by Rayleigh waves incoming from the southwest direction. We depict two sources acting on the background seismicity that are the microseismic noise loading on the Pacific coastline and a low-energy volcanic tremor. A change in the amplitude of the microseismic noise can induce the switching from a state of the system to the other.

Sea level variations collected in several areas in the world have been analyzed trying to infer their non linear characteristics. Analyzed data were acquired in several sites in West and East coasts of the North American continent, in the Hawaii and Bermuda islands, representing oceanic sites, and in Adriatic sea, representing a well known basin type. Data have been analyzed through Independent Component Analysis, False Nearest Neighbours and the estimation of correlation dimension using Grasberger and Procaccia integral. Results show a clear non linear features in all the sites, characterized by second and third order Landau mode.

The random first order transition theory (RFOT) describing the transition from a supercooled liquid to an ideal glass has been actively developed over the last twenty years. This theory is formulated in a way that allows a description of the transition from the initial equilibrium state to the final metastable state without considering any kinetic processes. The RFOT and its applications for real molecular systems (multicomponent liquids with various intermolecular potentials, gel systems, etc.) are widely represented in English-language sources. However, these studies are practically not described in any Russian sources. This paper presents an overview of the studies carried out in this field. REFERENCES 1. Sanditov D. S., Ojovan M. I. Relaxation aspectsof the liquid—glass transition. Uspekhi FizicheskihNauk. 2019;189(2): 113–133. DOI: https://doi.org/10.3367/ufnr.2018.04.0383192. Tsydypov Sh. B., Parfenov A. N., Sanditov D. S.,Agrafonov Yu. V., Nesterov A. S. 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The aim of this paper is to investigate the discrete-time fractional systems from the following aspects. First, the discrete-time fractional unified system in Caputo sense is established with the help of Euler’s discretization method. Furthermore, the dynamic behaviors of the discrete-time fractional Lü system (DFLS) which is deemed as a representative for unified system are observed. Then, the correlation dimension ([Formula: see text]) and Kaplan–Yorke dimension ([Formula: see text]) of the DFLS are evaluated by the aid of Grassberger–Procaccia algorithm and the Lyapunov exponent spectrum, respectively. Finally, the intrinsic connections between [Formula: see text] and [Formula: see text] are analyzed by the statistical modeling idea when the DFLS is in chaotic vibrations. The main results show that [Formula: see text] shares a positive correlation with [Formula: see text] for the chaotic DFLS, while the differences between [Formula: see text] and [Formula: see text] are not only related to the ratio of the largest and smallest Lyapunov exponents, but also closely tied up with the fractional order [Formula: see text] itself.

AbstractTo investigate the effect of water on the mechanical properties and acoustic emission (AE) characteristics of coal in the failure and deformation processes. Coal samples of different content were subjected to uniaxial compression tests and AE signals were monitored. The characteristics of the AE signals were further analyzed using fractal analysis. The results show that saturated coal samples have substantially reduced mechanical properties such as uniaxial compressive strength (UCS), dissipation energy, peak stress, and elastic modulus. Under loading, stress–strain curves are characterized by five distinct stages: (1) compaction; (2) linear elastic; (3) crack stable propagation; (4) crack accelerating propagation; and (5) post-peak and residual stages. Using phase-space theory, a novel Grassberger Procaccia (GP) algorithm was utilized to find the AE fractal characteristics of coal samples in different stages. It is significant to note that AE energy does not exhibit fractal characteristics in either the first or second stages. Contrary to the first two stages, the third stage showed obvious fractal characteristics. Fractal analysis of AE time sequences indicates that fractal dimension values change as stress increases, indicating the initiation of complex microcracks in coal. In the fourth stage, the fractal dimension rapidly declines as the strength reaches its limit, indicating the occurrence of macrocracks. However, fractal dimensions continued to decrease further or increased slightly in the fifth stage. Consequently, the coal begins to collapse, potentially resulting in a disaster and failure. It is, therefore, possible to accurately predict coal and rock dynamic failures and microcrack mechanisms by observing the subsequent sudden drop in the correlation dimension of the AE signals in response to different stages of loading.

Bearing multi-fault detection from stochastic vibration signal is still a thorny task to dispose of because of the complex interplay between different fault components under severe noise interference. In such case, conventional techniques such as filter processing and envelope demodulation may cause undesired results. To overcome the limitation, this article explores a filtering-free technique combined probabilistic principal component analysis denoising with the Higuchi fractal dimension transformation to diagnose the bearing multi-faults. Fractal theory is used to optimize the model parameters and stabilize the random vibrational signal for fast Fourier transform spectrum analysis. Noise interference in the Higuchi transformation is capped using a probabilistic principal component analysis model whose parameters are optimized through embedding dimension Cao algorithm and correlation dimension Grassberger and Procaccia algorithm. The fault diagnostic scheme mainly falls into three steps. First, the original vibration signal is truncated into a series of sub-signal segments by moving window whose length is determined as twice the value of maximum time delay that is provided by examining the steady Higuchi fractal dimension value of a raw signal in a process of plotting the fractal dimension over a range of time delay. Then, the Higuchi approach is used to estimate the average fractal dimension for each segment to create a quasi-stationary Higuchi fractal dimension sequence on which, finally, the fault features are straightforwardly extracted by the fast Fourier transform algorithm. The effectiveness of the proposed method is validated using simulated and experimental compound bearing fault vibration signals. Some fault components may be clouded if applied Higuchi fractal dimension alone because of the noise interference, but using the probabilistic principal component analysis–Higuchi fractal dimension method leads to clear diagnostic results. It indicates that the proposed approach can be incorporated into bearing multi-fault extraction from raw vibration signals.