Detrended fluctuation analysis and the difference between external drifts and intrinsic diffusionlike nonstationarity

Inferring long memory using extreme events

Many natural and physical processes display long memory and extreme events. In these systems, the measured time series is invariably contaminated by noise and/or missing data. As the extreme events display a large deviation from the mean behavior, noise and/or missing data do not affect the extreme events as much as it affects the typical values. Since the extreme events also carry the information about correlations in the full-time series, we can use them to infer the correlation properties of the latter. In this work, we construct three modified time series using only the extreme events from a given time series. We show that the correlations in the original time series and in the modified time series are related, as measured by the exponent obtained from the detrended fluctuation analysis technique. Hence, the correlation exponents for a long memory time series can be inferred from its extreme events alone. We demonstrate this approach for several empirical time series.

Characterizing variability and predictability for air pollutants with stochastic models

We investigate the dynamics of particulate matter, nitrogen oxides, and ozone concentrations in Hong Kong. Using fluctuation functions as a measure for their variability, we develop several simple data models and test their predictive power. We discuss two relevant dynamical properties, namely, the scaling of fluctuations, which is associated with long memory, and the deviations from the Gaussian distribution. While the scaling of fluctuations can be shown to be an artifact of a relatively regular seasonal cycle, the process does not follow a normal distribution even when corrected for correlations and non-stationarity due to random (Poissonian) spikes. We compare predictability and other fitted model parameters between stations and pollutants.

Sulprostone-Induced Gastric Dysrhythmia in the Ferret: Conventional and Advanced Analytical Approaches

Nausea and emesis resulting from disease or drug treatment may be associated with disrupted gastric myoelectric activity (GMA). Conventional analytical techniques can determine the relative degrees of brady-, normo-, and tachygastric power, but lose information relative to the basic slow wave shape. The aim of the present study was to investigate the application of advanced analytical techniques in the analysis of disrupted GMA recorded after administration of sulprostone, a prostaglandin E_3/1 agonist, in ferrets. Ferrets were implanted with radiotelemetry devices to record GMA, blood pressure, heart rate (HR) and core body temperature 1 week before the administration of sulprostone (30 μg/kg) or vehicle (saline, 0.5 mL/kg). GMA was initially analyzed using fast Fourier transformations (FFTs) and a conventional power partitioning. Detrended fluctuation analysis (DFA) was also applied to the GMA recordings to reveal information relative to the fluctuation of signals around local trends. Sample entropy (SampEn) analysis was used for examining the regularity of signals. Conventional signal processing techniques revealed that sulprostone increased the dominant frequency (DF) of slow waves, with an increase in the percentage power of the tachygastric range and a decrease in the percentage power of the normogastric range. DFA revealed that sulprostone decreased the fluctuation function, indicative of a loss of the variability of GMA fluctuations around local trends. Sulprostone increased SampEn values, indicating a loss of regularity in the GMA data. Behaviorally, sulprostone induced emesis and caused defecation. It also increased blood pressure and elevated HR, with an associated decrease in HR variability (HRV). Further analysis of HRV revealed a decrease in both low-frequency (LF) and high-frequency (HF) components, with an overall increase in the LF/HF ratio. Sulprostone did not affect core body temperature. In conclusion, DFA and SampEn permit a detailed analysis of GMA, which is necessary to understand the action of sulprostone to modulate gastric function. The action to decrease HRV and increase the LF/HF ratio may be consistent with a shift toward sympathetic nervous system dominance, commonly seen during nausea.

Probabilistic properties of detrended fluctuation analysis for Gaussian processes

Detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range dependence in time series. Although DFA has found many interesting applications and has been shown to be one of the best performing detrending methods, its probabilistic foundations are still unclear. In this paper, we study probabilistic properties of DFA for Gaussian processes. Our main attention is paid to the distribution of the squared error sum of the detrended process. We use a probabilistic approach to derive general formulas for the expected value and the variance of the squared fluctuation function of DFA for Gaussian processes. We also get analytical results for the expected value of the squared fluctuation function for particular examples of Gaussian processes, such as Gaussian white noise, fractional Gaussian noise, ordinary Brownian motion, and fractional Brownian motion. Our analytical formulas are supported by numerical simulations. The results obtained can serve as a starting point for analyzing the statistical properties of DFA-based estimators for the fluctuation function and long-memory parameter.

Characterization of personal solar ultraviolet radiation exposure using detrended fluctuation analysis

Studies of personal solar ultraviolet radiation (pUVR) exposure are important to identify populations at-risk of excess and insufficient exposure given the negative and positive health impacts, respectively, of time spent in the sun. Electronic UVR dosimeters measure personal solar UVR exposure at high frequency intervals generating large datasets. Sophisticated methods are needed to analyze these data. Previously, wavelet transform (WT) analysis was applied to high-frequency personal recordings collected by electronic UVR dosimeters. Those findings showed scaling behavior in the datasets that changed from uncorrelated to long-range correlated with increasing duration of time spent in the sun. We hypothesized that the WT slope would be influenced by the duration of time that a person spends in continuum outside. In this study, we address this hypothesis by using an experimental study approach. We aimed to corroborate this hypothesis and to characterize the extent and nature of influence time a person spends outside has on the shape of statistical functions that we used to analyze individual UVR exposure patterns. Detrended fluctuation analysis (DFA) was applied to personal sun exposure data. We analyzed sun exposure recordings from skiers (on snow) and hikers in Europe, golfers in New Zealand and outdoor workers in South Africa. Results confirmed validity of the DFA superposition rule for assessment of pUVR data and showed that pUVR scaling is determined by personal patterns of exposure on lower scales. We also showed that this dominance ends at the range of time scales comparable to the maximal duration of continuous exposure to solar UVR during the day; in this way the superposition rule can be used to quantify behavioral patterns, particularly accurate if it is determined on WT curves. These findings confirm a novel way in which large datasets of personal UVR data may be analyzed to inform messaging regarding safe sun exposure for human health.

Theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average

We present a bottom-up derivation of fluctuation analysis with detrending for the detection of long-range correlations in the presence of additive trends or intrinsic nonstationarities. While the well-known detrended fluctuation analysis (DFA) and detrending moving average (DMA) were introduced ad hoc, we claim basic principles for such methods where DFA and DMA are then shown to be specific realizations. The mean-squared displacement of the summed time series contains the same information about long-range correlations as the autocorrelation function but has much better statistical properties for large time lags. However, the scaling exponent of its estimator on a single time series is affected not only by trends on the data but also by intrinsic nonstationarities. We therefore define the fluctuation function as mean-squared displacement with weighting kernel. We require that its estimator be unbiased and exhibit the correct scaling behavior for the random component of a signal, which is only achieved if the weighting kernel implies detrending. We show how DFA and DMA satisfy these requirements and we extract their kernel weights.

Experimental investigations and phase-field simulations of triple-phase-separation kinetics within liquid ternary Co-Cu-Pb immiscible alloys

The phase-separation kinetics and microstructure evolution mechanisms of liquid ternary Co_{43}Cu_{40}Pb_{17} immiscible alloys are investigated by both the drop tube technique and phase-field method. Two successive phase separations take place during droplet falling and lead to the formation of a three-phase three-layer core-shell structure composed of a Co-rich core, a Cu-rich middle layer, and a Pb-rich shell. The Pb-rich shell becomes more and more conspicuous as droplet diameter decreases. Meanwhile, the Co-rich core center gradually moves away from the core-shell center. Theoretical analyses show that a larger temperature gradient inside a smaller alloy droplet induces the accelerated growth of the surface segregation shell during triple-phase separation. The residual Stokes motion and the asymmetric Marangoni convection result in the appearance of an eccentric Co-rich core and the core deviation degree is closely related to the droplet size and initial velocity. A three-dimensional phase-field model of ternary immiscible alloys, which considers the successive phase separations under the combined effects of Marangoni convection and surface segregation, is proposed to explore the formation mechanisms of three-phase core-shell structures. The simulated core-shell morphologies are consistent with the experimental observations, which verifies the model's validity in reproducing the core-shell dynamic evolution. Numerical results reveal that the development of three-phase three-layer core-shell structures can be attributed to the primary and then secondary phase separations dominated simultaneously by Marangoni convection and surface segregation. Furthermore, the effects of droplet temperature gradient on the growth kinetics of the surface segregation shell are analyzed in the light of phase-field theory.