Detrended Fluctuation Function Research Articles

Analysis of the structural complexity of Crab Nebula observed at radio frequency using a multifractal approach

The Crab Nebula is an astrophysical system that exhibits complex morphological patterns at different observing frequencies. We carry out a systematic investigation of the structural complexity of the nebula using publicly available imaging data at radio frequency. For the analysis, we use the well-known multifractal detrended fluctuation analysis in two dimensions. We find that radio data exhibit long-range correlations, as expected from the underlying physics of the supernova explosion and evolution. The correlations follow a power-law scaling with length scales. The structural complexity is found to be multifractal in nature, as evidenced by the dependence of the generalized Hurst exponent on the order of the moments of the detrended fluctuation function. By repeating the analysis on shuffled data, we further probe the origin of the multifractality in the radio imaging data. For the radio data, we find that the probability density function is close to a Gaussian form. Hence, the multifractal behavior is due to the differing nature of long-range correlations of the large and small detrended fluctuation field values. We investigate the multifractal parameters across different partitions of the radio image and find that the structures across the image are highly heterogeneous, making the Crab Nebula a structurally complex astrophysical system. Our analysis thus provides a fresh perspective on the morphology of the Crab Nebula from a complexity science viewpoint.

Analysis of detrended fluctuation function derived from continuous glucose monitoring may assist in distinguishing latent autoimmune diabetes in adults from T2DM.

BackgroundWe aimed to explore the performance of detrended fluctuation function (DFF) in distinguishing patients with latent autoimmune diabetes in adults (LADA) from type 2 diabetes mellitus (T2DM) with glucose data derived from continuous glucose monitoring.MethodsIn total, 71 LADA and 152 T2DM patients were enrolled. Correlations between glucose parameters including time in range (TIR), mean glucose, standard deviation (SD), mean amplitude of glucose excursions (MAGE), coefficient of variation (CV), DFF and fasting and 2-hour postprandial C-peptide (FCP, 2hCP) were analyzed and compared. Receiver operating characteristics curve (ROC) analysis and 10-fold cross-validation were employed to explore and validate the performance of DFF in diabetes classification respectively.ResultsPatients with LADA had a higher mean glucose, lower TIR, greater SD, MAGE and CV than those of T2DM (P<0.001). DFF achieved the strongest correlation with FCP (r = -0.705, P<0.001) as compared with TIR (r = 0.485, P<0.001), mean glucose (r = -0.337, P<0.001), SD (r = -0.645, P<0.001), MAGE (r = -0.663, P<0.001) and CV (r = -0.639, P<0.001). ROC analysis showed that DFF yielded the greatest area under the curve (AUC) of 0.862 (sensitivity: 71.2%, specificity: 84.9%) in differentiating LADA from T2DM as compared with TIR, mean glucose, SD, MAGE and CV (AUC: 0.722, 0.650, 0.800, 0.820 and 0.807, sensitivity: 71.8%, 47.9%, 63.6%, 72.7% and 78.8%, specificity: 67.8%, 83.6%, 80.9%, 80.3% and 72.4%, respectively). The kappa test indicated a good consistency between DFF and the actual diagnosis (kappa = 0.551, P<0.001). Ten-fold cross-validation showed a stable performance of DFF with a mean AUC of 0.863 (sensitivity: 78.8%, specificity: 77.8%) in 10 training sets and a mean AUC of 0.866 (sensitivity: 80.9%, specificity: 84.1%) in 10 test sets.ConclusionsA more violent glucose fluctuation pattern was marked in patients with LADA than T2DM. We first proposed the possible role of DFF in distinguishing patients with LADA from T2DM in our study population, which may assist in diabetes classification.

Flash glucose monitoring data analysed by detrended fluctuation function on beta-cell function and diabetes classification.

We aimed to use data-driven glucose pattern analysis to unveil the correlation between the metrics reflecting glucose fluctuation and beta-cell function, and to identify the possible role of this metric in diabetes classification. In total, 78 participants with type 1 diabetes and 59 with type 2 diabetes were enrolled in this study. All participants wore a flash glucose monitoring system, and glucose data were collected. A detrended fluctuation function (DFF) was utilized to extract glucose fluctuation information from flash glucose monitoring data and a DFF-based glucose fluctuation metric was proposed. For the entire study population, a significant negative correlation between the DFF-based glucose fluctuation metric and fasting C-peptide was observed (r = -0.667; P <.001), which was larger than the correlation coefficient between the fasting C-peptide and mean amplitude of plasma glucose excursions (r = -0.639; P < .001), standard deviation (r = -0.649; P <.001), mean blood glucose (r = -0.519; P < .001) and time in range (r = 0.593; P < .001). As glucose data analysed by DFF revealed a clear bimodal distribution among the total participants, we randomly assigned the 137 participants into discovery cohorts (n = 100) and validation cohorts (n = 37) for 10 times to evaluate the consistency and effectiveness of the proposed metric for diabetes classification. The confidence interval for area under the curve according to the receiver operating characteristic analysis in the 10 discovery cohorts achieved (0.846, 0.868) and that for the 10 validation cohorts was (0.799, 0.862). In addition, the confidence intervals for sensitivity and specificity in the discovery cohorts were (75.5%, 83.0%), (81.3%, 88.5%) and (71.8%, 88.3%), (76.5%, 90.3%) in the validation cohorts, indicating the potential capacity of DFF in distinguishing type 1 and type 2 diabetes. Our study first proposed the possible role of data-driven analysis acquired glucose metric in predicting beta-cell function and diabetes classification, and a large-scale, multicentre study will be needed in the future.

Empirical Mode Decomposition based Detrended Fluctuation Analysis of Uterine Electromyography Signals in Term Conditions

In this study, an attempt has been made to analyze uterine Electromyography (uEMG) signals during Term conditions (pregnancy duration more than 37 weeks of gestational age) using Empirical Mode Decomposition based Detrended Fluctuation Analysis (EMD-DFA). The Term delivery signals are considered from a publicly available database, grouped as T1 (26 weeks gestational age) and T2 (≥26 weeks gestational age) based on the time of recording, and are subjected to an EMD-DFA algorithm. The double logarithmic plot of the detrended fluctuation function against the scale is analyzed, and the Hurst exponent feature is computed for both groups. The features are statistically analyzed using the Student’s t-test. Results show that the EMD-DFA method is able to capture the variations in the fluctuations of uEMG signals under these conditions. The Hurst exponent feature is found to be statistically significant (p-value 0.005) for both groups. There is an increase in the Hurst exponent feature value in the T2 group, which indicates that T2 signals possess smoother characteristics than T1 signals. Hence, it appears that the proposed approach could aid in investigating variations in the fluctuations of Term delivery signals, differentiating T1 and T2 conditions.

Predictive Value of Flash Glucose Monitoring Data Analyzed by Detrended Fluctuation Function on Beta Cell Function and Diabetes Classification

Predictive Value of Flash Glucose Monitoring Data Analyzed by Detrended Fluctuation Function on Beta Cell Function and Diabetes Classification

Dual-tree complex wavelet transform based multifractal detrended fluctuation analysis for nonstationary time series

Multifractal detrended fluctuation analysis is an effective tool for dealing with the non-uniformity and singularity of nonstationary time series. For the serious issues of the trend extraction and the inefficient computation in the traditional polynomial fitting based multifractal detrended fluctuation analysis, based on the dual-tree complex wavelet transform, a novel multifractal analysis is proposed. To begin with, as the dual-tree complex wavelet transform has the anti-aliasing and nearly shift-invariance, it is first utilized to decompose the signal through the pyramid algorithm, and the scale-dependent trends and the fluctuations are extracted from the wavelet coefficients. Then, using the wavelet coefficients, the length of the non-overlapping segment on a corresponding time scale is computed through the Hilbert transform, and each of the extracted fluctuations is divided into a series of non-overlapping segments whose sizes are identical. Next, on each scale, the detrended fluctuation function for each segment is calculated, and the overall fluctuation function can be obtained by averaging all segments with different orders. Finally, the generalized Hurst index and scaling exponent spectrum are determined from the logarithmic relations between the overall detrended fluctuation function and the time scale and the standard partition function, respectively, and then the multifractal singularity spectrum is calculated with the help of Legendre transform. We assess the performance of the dual-tree-complex wavelet transform based multifractal detrended fluctuation analysis (MFDFA) procedure through the classic multiplicative cascading process and the fractional Brownian motions, which have the theoretical fractal measures. For the multiplicative cascading process, compared with the traditional polynomial fitting based MFDFA methods, the proposed multifractal approach defines the trends and the length of non-overlapping segments adaptively and obtains a more precise result, while for the traditional MFDFA method, for the negative orders, no matter the generalized Hurst index, scaling exponents spectrum, or the multifractal singularity spectrum, the acquired results each have a significant deviation from the theoretical one. For the time series with different sizes, the proposed method can also give a stable result. Compared with the other adaptive method such as maximal overlap discrete wavelet transform based MFDFA and the discrete wavelet transfrom based MFDFA, the proposed approach obtains a very accurate result and has a fast calculation speed. For another time series of fractional Brownian motions with different Hurst indexes of 0.4, 0.5 and 0.6, which represent the anticorrelated, uncorrelated, correlated process, respectively, the results of the proposed method are consistent with those analytical results, while the results of the polynomial fitting based MFDFA methods are most greatly affected by the order of the fitting polynomial. The method in this article provides a valuable reference for how to use the dual-tree complex wavelet transform to realize the multifractal detrended fluctuation analysis, and we can benefit from the signal self-adaptive trend extraction and the high computation efficiency.

Risk estimation of CSI 300 index spot and futures in China from a new perspective

We investigate the statistical behavior and application in risk estimation of recurrence intervals between high-frequency returns that are either larger than a given positive threshold or smaller than a negative threshold for the stock index and stock index futures markets in China. By studying the probability density function of recurrence intervals, we find symmetric profiles for both the positive and negative occurrence thresholds, which can be fitted with stretched exponential functions. The probability density function further scales with the mean interval as the unified functional form for different thresholds. We further study the dependence of the conditional probability density function and the scaled mean condition recurrence interval on the previous recurrence interval, and demonstrate the existence of short memory in recurrence intervals. The result from detrended fluctuation analysis exhibits long-term correlations, where the detrended fluctuation function decays as an exponential function, with an exponent between 0.5 and 1. Based on the results of the analysis of recurrence intervals, we construct a hazard function and define a loss probability in order to evaluate risk in financial markets. To our surprise, a crossover is found in the loss probability plot of the stock index and its futures market, which sheds light on the issue of value at risk (VaR) overestimation (underestimation) based on recurrence interval analysis of complex financial markets. The study would enable one to improve risk estimation and is useful for management of risks in financial markets.

The spatial scale dependence of water vapor variability inferred from observations from a very tall tower

AbstractRecent studies have established that atmospheric water vapor fields exhibit spatial spectra that take the form of power laws and hence can be compactly characterized by scaling exponents. The power law scaling exponents have been shown to exhibit substantial vertical variability. In this work, Taylor's frozen turbulence hypothesis is used to infer the first‐order spatial structure function and generalized detrended fluctuation function scaling exponents for scales between 1 km and 100 km. Both methods are used to estimate the Hurst exponent (H) using 10 Hz time series of water vapor measured at 396 m altitude from an Ameriflux tower in Wisconsin. Due to the diurnal cycle in the boundary layer height at the 396 m observational level, H may be estimated for both the daytime convective mixed layer and the nocturnal residual layer. Values of are obtained for the convective mixed layer, while values of apply in the nocturnal residual layer. The results are shown to be remarkably consistent with a similar analysis from satellite‐based observations as reported in Pressel and Collins (2012).

Multifractal detrended fluctuation analysis for clustering structures of electricity price periods

A new model is proposed to investigate the structure of electricity price in different time periods. A popular method — the multifractal detrended fluctuation analysis (MF-DFA) method is employed to analyze the features achieved from three types of electricity price data after filtering some trends by Fourier detrended fluctuation function. Twelve multifractal parameters are calculated and selected as the characteristic indicators for comparison. Moreover, the minimum number of indicators is determined so that the discriminant accuracy reaches maximum based on Fisher’s linear discriminant algorithm (Fisher’s LDA) for each time period. These indicators form a multi-dimensional space, in which each point represents a price time series. This allows us to cluster the three price time periods, namely, the low price time periods, the average price time periods and the peak price time periods. Fisher’s LDA is employed to evaluate the discriminant accuracy on these three kinds of time periods. Our analysis is then applied to the data in California1999–2000 and PJM2001–2002 electricity markets to demonstrate the applicability of our methods.

Recurrence interval analysis of trading volumes

We study the statistical properties of the recurrence intervals τ between successive trading volumes exceeding a certain threshold q. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period from January 2000 to May 2009, and two Chinese indices from January 2003 to April 2009. Similar to the recurrence interval distribution of the price returns, the tail of the recurrence interval distribution of the trading volumes follows a power-law scaling, and the results are verified by the goodness-of-fit tests using the Kolmogorov-Smirnov (KS) statistic, the weighted KS statistic and the Cramér-von Mises criterion. The measurements of the conditional probability distribution and the detrended fluctuation function show that both short-term and long-term memory effects exist in the recurrence intervals between trading volumes. We further study the relationship between trading volumes and price returns based on the recurrence interval analysis method. It is found that large trading volumes are more likely to occur following large price returns, and the comovement between trading volumes and price returns is more pronounced for large trading volumes.

Multifractal analysis of the fracture surfaces of foamed polypropylene/polyethylene blends

The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene (PP/PE) blends at different temperatures. Nice power-law scaling relationship between the detrended fluctuation function F q and the scale s is observed for different orders q and the scaling exponent h ( q ) is found to be a nonlinear function of q, confirming the presence of multifractality in the fracture surfaces. The multifractal spectra f ( α ) are obtained numerically through Legendre transform. The shape of the multifractal spectrum of singularities can be well captured by the width of spectrum Δ α and the difference of dimension Δ f . With the increase of the PE content, the fracture surface becomes more irregular and complex, as is manifested by the facts that Δ α increases and Δ f decreases from positive to negative. A qualitative interpretation is provided based on the foaming process.