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We propose a new paradigm for describing complex networks in terms of the spectrum of the adjacency matrix and its submatrices. We show that a variety of basic node information, such as degree, clique, and subgraph centrality, can be calculated analytically. Moreover, we find that energy of spectrum series can uncover randomness and complexity of network structure. Interestingly, it presents an universal linear growth pattern with the growth of networks. Furthermore, the spectrum series of synthetic and real networks present clearly self-similarity characteristics for which the associated scaling exponents remain constant. Our work reveals that spectrum series representation will provide an alternative perspective for studying and understanding structure and function of complex networks rather than connectivity. [ABSTRACT FROM AUTHOR]

Highlights • Urban wind speed measured at different heights from the ground are analysed. • The low frequency spectrum is power-law with a mean exponent of about 1.5. • The linear/nonlinear properties of urban wind speed are analysed. • The scaling exponent of the wind magnitude series depends on the height. • A crossover height of about 13.5 m is found. Abstract In this paper, high frequency wind time series measured at different heights from the ground (from 5.5 to 25.5 m) in an urban area were investigated. The spectrum of each series is characterized by a power-law behaviour at low frequency range, with a mean spectral exponent of about 1.5, which is rather consistent with the Kolmogorov spectrum of atmospheric turbulence. The detrended fluctuation analysis was applied on the magnitude and sign series of the increments of wind speed, in order to get information about the linear and nonlinear dynamics of the time series. Both the sign series and magnitude series are characterized by two timescale ranges; in particular the scaling exponent of the magnitude series in the high timescale range seems to be related with the height of the sensor. This study aims to understand better high frequency wind speed in urban areas and to disclose the underlying mechanism governing the wind fluctuations at different heights. [ABSTRACT FROM AUTHOR]

The combined action of physical, chemical and biological processes at different scales creates a highly complex soil architecture. At the same time, this soil pores' complexity is crucial in maintaining soil biogeochemical and biophysical processes. The development of digital image processing and a multiscaling analysis allow a better study to quantify pore complexity and evaluate pore spatial variability. This study took saline soils from coastal reclamation areas as an example and aimed to compare the multifractality of porosity series using different methods on sample cubes of 512 pixels in length extracted at different soil depths. Two measures were selected to represent the porosity series: the average grey values (AVG) of each slice and the CT-porosity (CTP) of binarized slices. The mass distribution (MD), detrended fluctuation analysis (DFA), and the moments function (K) were the methods applied in the multiscaling study. Shuffled and surrogated series were used to analyze the two possible multifractality sources, the probability distribution density function (PDF) and long-range correlations, respectively. The results showed that MD gave the minimum multifractal spectrum, which appeared as a point in AGV and a narrow concave parabola in CTP. On the other hand, both AGV and CTP showed a higher complexity, a clear and significant multifractal behaviour when DFA and K were used. The shuffled and surrogated series pointed out that the long-range correlations were the main factor of the multifractal sources of the porosity series. Both long-range correlations and PDF influenced more heavily on the multifractality of porosity in topsoil (0– 20 cm) than in the deeper soil (20– 60 cm), implying that the porosity series in topsoil had stronger multifractality. In addition, the DFA and K, combined with shuffled and surrogated series analysis, can distinguish between different factors in the multiscaling behaviour of different soil textures and time reclamation. • Multifractal analysis of binary images based on mass distribution is more worthy. • The detrended fluctuation analysis (DFA) and moments function (K) can multi-scaling characteristics of porosity series. • Long-range correlations were the main factor of the multifractal sources of porosity series. • The DFA and K, combined with shuffled and surrogated series, can distinguish factors influencing multi-scale behaviour. [ABSTRACT FROM AUTHOR]

Interplay of transition of floating potential fluctuations in a glow discharge plasma in the toroidal vacuum vessel of SINP tokamak has been observed. With variation in the strength of the vertical and toroidal magnetic fields, regular and inverted relaxation oscillations as well as sinusoidal oscillations are observed with the slow and fast time scale of the relaxation oscillations reversing their nature at a high value of vertical magnetic field strength. However for small value of toroidal magnetic field the transitions follow relaxation  →  chaotic oscillations with the chaotic nature prevailing at higher values of toroidal magnetic field. Evolution of associated anode fireball dynamics under the action of increasing vertical, toroidal as well as increasing vertical field at a fixed toroidal field (mixed field) of different strength has been studied. Estimation of phase coherence index for each case has been carried out to examine the evidence of finite nonlinear interaction. A comprehensive study of the dynamics of the fireball is found to be associated with the values of phase coherence index. The index is found to take maximum values for the case of toroidal, mixed field when there is an existence of power/energy concentration in a large region of frequency band. A detailed study of the scaling region using detrended fluctuation analysis (DFA) by estimating the scaling exponent has been carried out for increasing values of discharge voltage (DV), vertical, toroidal as well as the mixed field (toroidal plus vertical). A persistence long range behaviour associated with the nature of the anode glow has been investigated in case of higher values of toroidal, mixed field whereas increasing DV, vertical magnetic field lead to a perfectly correlated dynamics with values of scaling exponent greater than unity. [ABSTRACT FROM AUTHOR]

In this work, we generalize the detrended fluctuation analysis (DFA) to the multivariate case, named multivariate DFA (MVDFA). The validity of the proposed MVDFA is illustrated by numerical simulations on synthetic multivariate processes, where the cases that initial data are generated independently from the same system and from different systems as well as the correlated variate from one system are considered. Moreover, the proposed MVDFA works well when applied to the multi-scale analysis of the returns of stock indices in Chinese and US stock markets. Generally, connections between the multivariate system and the individual variate are uncovered, showing the solid performances of MVDFA and the multi-scale MVDFA. [ABSTRACT FROM AUTHOR]

In order to ascertain the dynamics of temperature variation in India, the scaling properties of the daily mean temperature time series obtained from seven different weather stations viz. Kolkata, Chennai, New Delhi, Mumbai, Bhopal, Agartala and Ahmadabad representing different geographical zones in India has been studied. Scaling properties of the temperature profile across India has been estimated from the calculation of Hurst-Exponent parameter obtained from five different scaling methods. Hurst Exponent values confirm that all temperature time series are Fractional Brownian Motion (FBM), statistically self-affine, anti-persistent and Short Range Dependent (SRD) self similar. As SRD self similarity is a common signature of a nonlinear dynamical process, further investigation has been made to discover the presence of any nonlinear behaviour of the temperature profile of Indian climate using Delay Vector Variance (DVV) method and the present calculation confirms a deterministic nonlinear profile of the same. [ABSTRACT FROM AUTHOR]

Signal decompositions such as wavelet and Gabor transforms have successfully been applied in denoising problems. Empirical mode decomposition (EMD) is a recently proposed method to analyze non-linear and non-stationary time series and may be used for noise elimination. Similar to other decomposition based denoising approaches, EMD based denoising requires a reliable threshold to determine which oscillations called intrinsic mode functions (IMFs) are noise components or noise free signal components. Here, we propose a metric based on detrended fluctuation analysis (DFA) to define a robust threshold. The scaling exponent of DFA is an indicator of statistical self-affinity. In our study, it is used to determine a threshold region to eliminate the noisy IMFs. The proposed DFA threshold and denoising by DFA-EMD are tested on different synthetic and real signals at various signal to noise ratios (SNR). The results are promising especially at 0 dB when signal is corrupted by white Gaussian noise (WGN). The proposed method outperforms soft and hard wavelet threshold method. [ABSTRACT FROM AUTHOR]

We propose an extension of the detrended cross-correlation analysis (DCCA) for signals with highly inhomogeneous structure. The proposed approach evaluates two scaling exponents, one of which characterizes the detrended covariance, and the second exponent quantifies the effects of nonstationarity caused by the distribution of local fluctuations of signal profiles from the trend. Using simulated datasets produced by a system of coupled Lorenz models, we describe entrainment phenomena associated with chaotic synchronization and the role of nonstationarity in their description. The processing of experimental data related to cerebral blood flow in neighboring vessels of different size confirm the general conclusion of this study and shows the possible advantages of the proposed extension of the DCCA-method for diagnosing changes in cooperative dynamics in physiological systems, where the combined effects of dynamics, nonstationarity and noise may occur. • An extension of the detrended cross-correlation analysis is proposed. • Characterization of nonstationarity effects is performed in models and experiments. • Advantages of the proposed extension of the DCCA-method are shown. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes a recurrence plot (RP) approach to the analysis of non-stationary transition patterns of IP-network traffic. To get a quantitative measure of dynamical transition patterns of IP-network traffic, we used the values of determinism (DET) defined by the recurrence quantification analysis (RQA). Also, when evaluating the fractal-based properties of IP-network traffic, we focused on two parameters: (i) the long-range dependence (LRD)-related scaling parameter α derived from the detrended fluctuation analysis (DFA) and (ii) the range of the generalized fractal dimension. In applying this method to traffic analysis, we performed two kinds of traffic measurement in Tokyo, Japan, and derived the values of DET and fractal-based parameters of IP-network traffic over time. In checking the measured network traffic, we found that the characteristic with respect to DET and self-similarity seen in the measured network traffic fluctuated over time, with different time-variation patterns for two measurement locations. Results also confirmed that a larger value of DET or accumulated DET reflected increases in the degree of LRD of IP-network traffic and that the accumulated DET reflected the decreases in the degree of multi-fractality of IP-network traffic. As a result, we confirmed that RP-based measures can be effective for evaluating the non-stationary transition patterns of IP-network traffic in terms of quantitative fractal-based properties. [Copyright &y& Elsevier]

Abstract: This paper presents an approach to the assessment of IP-network traffic in terms of the time variation of self-similarity. To get a comprehensive view in analyzing the degree of long-range dependence (LRD) of IP-network traffic, we use a hierarchical clustering scheme, which provides a way to classify high-dimensional data with a tree-like structure. Also, in the LRD-based analysis, we employ detrended fluctuation analysis (DFA), which is applicable to the analysis of long-range power-law correlations or LRD in non-stationary time-series signals. Based on sequential measurements of IP-network traffic at two locations, this paper derives corresponding values for the LRD-related parameter α that reflects the degree of LRD of measured data. In performing the hierarchical clustering scheme, we use three parameters: the α value, average throughput, and the proportion of network traffic that exceeds 80% of network bandwidth for each measured data set. We visually confirm that the traffic data can be classified in accordance with the network traffic properties, resulting in that the combined depiction of the LRD and other factors can give us an effective assessment of network conditions at different times. [Copyright &y& Elsevier]

Abstract: The fire-induced variability in vegetation dynamics was analyzed by means of a fluctuation analysis applied to a time series of satellite SPOT-VEGETATION normalized difference of vegetation index (NDVI) data from 1998 to 2003. We used the detrended fluctuation analysis (DFA), which allows capturing persistent behavior in nonstationary signals. We analyzed four vegetation sites, two affected and the other two not affected by fires. Our results point out that the persistence of vegetation dynamics is significantly increased by the occurrence of fires. [Copyright &y& Elsevier]

Abstract: The long-range scaling behaviours of human colonic pressure activities under normal physiological conditions are studied by using the method of detrended fluctuation analysis (DFA). The DFA is an effective period representation with a single quantitative scaling exponent α to accurately quantify long-range correlations naturally presented in a complex non-stationary time series. The method shows that the colonic activities of the healthy subjects exhibit long-range power-law correlations; however such correlations either will be destroyed if we randomly shuffle the original data or will cease to be of a power-law form if we chop some high-amplitude spikes off. These facts indicate that the colonic tissue or enteric nervous system (ENS) with a good functional motility has a good memory to its past behaviours and generates well-organized colonic spikes; however such good memory becomes too long to be remembered for the colonic activity of the slow transit constipation (STC) patient and colonic dysmotility occurs. [Copyright &y& Elsevier]

Abstract: The depth of anesthesia estimation has been of great interest in recent decades. In this paper, we present a new methodology to quantify the levels of consciousness. Our algorithm takes advantage of the fractal and self-similarity properties of the electroencephalogram (EEG) signal. We have studied the effect of anesthetic agents on the rate of the signal fluctuations. By translating these fluctuations with detrended fluctuation analysis (DFA) algorithm to fractal exponent, we could describe the dynamics of brain during anesthesia. We found the optimum fractal-scaling exponent by selecting the best domain of box sizes, which have meaningful changes with different depth of anesthesia. Experimental results confirm that the optimal fractal-scaling exponent on the raw EEG data can clearly discriminate between awake to moderate and deep anesthesia levels and have robust relation with the well-known depth of anesthesia index (BIS). When the patient''s cerebral states change from awake to moderate and deep anesthesia, the fractal-scaling exponent increases from 0.8 to 2 approximately. Moreover, our new algorithm significantly reduces computational complexity and produces faster reaction to transients in patients’ consciousness levels compared to other algorithms and technologies. [Copyright &y& Elsevier]

• Responses of cerebral circulation to an abrupt increase in blood pressure are studied. • Different types of reactions of veins and capillaries are reported. • Efficiency of a combined MWA&DFA approach is shown. The responses of cerebral circulation to an abrupt increase in blood pressure caused by pharmacologically induced hypertension are compared by means of multiresolution wavelet analysis (MWA), which uses standard deviations of expansion coefficients as diagnostic criteria, and an enhanced approach, combining MWA with analysis of long-range power-law correlations in the wavelet domain. We discuss how applying both of these approaches elicits different types of reactions of large blood vessels in the brain and capillary network and show that the use of simple statistical measures limits the information that can be extracted during data processing. Taking into account the correlation features in addition to the width of the probability density is a possible way to improve the characterization of the effects produced by "jumps" in blood pressure. [ABSTRACT FROM AUTHOR]

Abstract: Improvement in time resolution sometimes introduces fast (short-range) random noises into temporal data sequences. These noises affect the results of power-spectrum analyses and the detrended fluctuation analysis (DFA). The DFA is one of useful methods for analyzing long-range correlations in non-stationary sequences. The effects of noises are discussed based on artificial temporal sequences. Short-range noises prevent power-spectrum analyses from detecting long-range correlations. The DFA can extract long-range correlations from noisy time sequences. The DFA also gives the threshold time length, under which the noises dominate. [Copyright &y& Elsevier]

• Permeability of the blood-brain barrier is studied in terms of long-range correlations. • Changes in rat electroencephalograms are characterized by DFA and its extension. • Improvement of diagnostics with the extended DFA is shown. We discuss the problem of revealing structural changes in rat electroencephalograms (EEG) caused by activation of the brain lymphatic drainage function due to a sound-induced stress. For this purpose, we apply the detrended fluctuation analysis (DFA) with its extended version to characterize long-range power-law correlations associated with the slow-wave dynamics of the electrical activity of the brain. The proposed extended DFA (EDFA) provided a stronger separation of groups of rats with different permeability of the blood-brain barrier (BBB) compared to the conventional DFA technique. We argue that such abilities of this tool can be useful in other diagnostic-related studies. [ABSTRACT FROM AUTHOR]

• Reactions of cerebral blood circulation to "jumps" in peripheral arterial pressure are studied. • An extension of the conventional DFA approach is proposed. • Significant distinctions in the responses of cerebral blood vessels are reported. We study scaling features in the reactions of cereral blood vessel network to sudden "jumps" in peripheral arterial pressure in rats. Using laser speckle contrast imaging (LSCI) to measure the relative velocity of cerebral blood flow (CBF) and detrended fluctuation analysis (DFA) for processing experimental data, we investigate distinctions in the responses of veins and capillaries. To quantify short-term reactions associated with transients, we propose an extension of the conventional DFA approach, which estimates an additional scaling exponent reflecting the effect of nonstationarity. We also consider the ability of characterizing vascular dynamics with multifractal DFA in terms of the degree of multiscality. Based on statistical analysis, we report significant distinctions in the responses of small network of microcerebral blood vessels compared to veins such as the sagittal sinus, which are quite insensitive to variations in peripheral blood circulation. [ABSTRACT FROM AUTHOR]