Detrended Fluctuation Analysis Scaling Exponent Research Articles

Fractal complexity of daily physical activity and cognitive function in a midlife cohort

High stability of fluctuation in physiological patterns across fixed time periods suggest healthy fractal complexity, while greater randomness in fluctuation patterns may indicate underlying disease processes. The importance of fractal stability in mid-life remains unexplored. We quantified fractal regulation patterns in 24-h accelerometer data and examined associations with cognitive function in midlife. Data from 5097 individuals (aged 46) from the 1970 British Cohort Study were analyzed. Participants wore thigh-mounted accelerometers for seven days and completed cognitive tests (verbal fluency, memory, processing speed; derived composite z-score). Detrended fluctuation analysis (DFA) was used to examine temporal correlations of acceleration magnitude across 25 time scales (range: 1 min–10 h). Linear regression examined associations between DFA scaling exponents (DFAe) and each standardised cognitive outcome. DFAe was normally distributed (mean ± SD: 0.90 ± 0.06; range: 0.72–1.25). In males, a 0.10 increase in DFAe was associated with a 0.30 (95% Confidence Interval: 0.14, 0.47) increase in composite cognitive z-score in unadjusted models; associations were strongest for verbal fluency (0.10 [0.04, 0.16]). Associations remained in fully-adjusted models for verbal fluency only (0.06 [0.00, 0.12]). There was no association between DFA and cognition in females. Greater fractal stability in men was associated with better cognitive function. This could indicate mechanisms through which fractal complexity may scale up to and contribute to cognitive clinical endpoints.

A simple approach to determine loss of physiological complexity in heart rate series

There are several ways to assess complexity, but no method has yet been developed for quantitatively calculating the ‘loss of fractal complexity’ under pathological or physiological states. In this paper, we aimed to quantitatively evaluate fractal complexity loss using a novel approach and new variables developed from Detrended Fluctuation Analysis (DFA) log-log graphics. Three study groups were established to evaluate the new approach: one for normal sinus rhythm (NSR), one for congestive heart failure (CHF), and white noise signal (WNS). ECG recordings of the NSR and CHF groups were obtained from PhysioNET Database and were used for analysis. For all groups Detrended Fluctuation Analysis scaling exponents (DFAα 1, DFAα 2) were determined. Scaling exponents were used to recreate the DFA log-log graph and lines. Then, the relative total logarithmic fluctuations for each sample were identified and new parameters were computed. To do this, we used a standard log-log plane to standardize the DFA log-log curves and calculated the differences between the standardized and expected areas. We quantified the total difference in standardized areas using parameters called dS1, dS2, and TdS. Our results showed that; compared to the NSR group, DFAα 1 was lower in both CHF and WNS groups. However, DFAα 2 was only reduced in the WNSgroup and not in the CHFgroup. Newly derived parameters: dS1, dS2, and TdS were significantly lowerin the NSR group compared to the CHF and WNS groups. The new parameters derived from the DFA log-log graphs are highly distinguishing for congestive heart failure and white noise signal. In addition, it may be concluded that a potential feature of our approach can be beneficial in classifying the severity of cardiac abnormalities.

Quantitative effect of musical sound on seed germination kinetics in Pisum sativum

Germination of seed is a crucial step in a plant’s life cycle. It is essential for emergence of seedling and finally producing viable offspring. Germination encompasses a wide number of events influenced by different factors and sound is not an exception. Sound is a vibration that propagates as an acoustic wave. Sound waves with different frequencies, intensities and amplitudes affect different phases of plant’s life cycle including germination. Seed germination kinetics, particularly germination speed contributes a major role in the variability of germination. This work is aimed to analyse the effect of musical sound with specific spectral characteristics mainly Detrended Fluctuation Analysis scaling exponent on seed germination kinetics in Pisum sativum. Indian Classical music and Natural music was used to stimulate Pisum sativum seeds for 72 hours. Germination kinetics was evaluated in terms of Mean Germination Time, t20 and Germination Percentage. Experimental results showed that musical sound can speed up germination process in Pisum sativum. Extremely high statistically significant differences were observed in germination kinetics after musical sound treatment (p<0.0001). This new work will be valuable for improving germination performance in Pisum sativum.

Influence of Controlled Stomatognathic Motor Activity on Sway, Control and Stability of the Center of Mass During Dynamic Steady-State Balance-An Uncontrolled Manifold Analysis.

Multiple sensory signals from visual, somatosensory and vestibular systems are used for human postural control. To maintain postural stability, the central nervous system keeps the center of mass (CoM) within the base of support. The influence of the stomatognathic motor system on postural control has been established under static conditions, but it has not yet been investigated during dynamic steady-state balance. The purpose of the study was to investigate the effects of controlled stomatognathic motor activity on the control and stability of the CoM during dynamic steady-state balance. A total of 48 physically active and healthy adults were assigned to three groups with different stomatognathic motor conditions: jaw clenching, tongue pressing and habitual stomatognathic behavior. Dynamic steady-state balance was assessed using an oscillating platform and the kinematic data were collected with a 3D motion capturing system. The path length (PL) of the 3D CoM trajectory was used for quantifying CoM sway. Temporal dynamics of the CoM movement was assessed with a detrended fluctuation analysis (DFA). An uncontrolled manifold (UCM) analysis was applied to assess the stability and control of the CoM with a subject-specific anthropometric 3D model. The statistical analysis revealed that the groups did not differ significantly in PL, DFA scaling exponents or UCM parameters. The results indicated that deliberate jaw clenching or tongue pressing did not seem to affect the sway, control or stability of the CoM on an oscillating platform significantly. Because of the task-specificity of balance, further research investigating the effects of stomatognathic motor activities on dynamic steady-state balance with different movement tasks are needed. Additionally, further analysis by use of muscle synergies or co-contractions may reveal effects on the level of muscles, which were not visible on the level of kinematics. This study can contribute to the understanding of postural control mechanisms, particularly in relation to stomatognathic motor activities and under dynamic conditions.

Persistence of Rainfall Time Series: Kırşehir Case Study

This study examines the persistence and long-term correlation of monthly and seasonal rainfall time series of Kırşehir for the period of 1960-2019, with widely used Hurst exponent and Detrended Fluctuation Analysis (DFA) analyses. Both Hurst exponent and DFA analyses could be used to detect the long-term memory and correlation that can be assessed as a reference of predictability. To support the analyses results Augmented Dickey Fuller and Mann-Kendall tests also applied to time series. Within various rainfall series, evidence of persistence and long-term correlation was identified. According to H exponent values of simple R/S and corrected R/S methods, 10 out of 12 months and winter, spring (only simple R/S), summer (only corrected R/S) and autumn season and according to DFA scaling exponent values 4 out of 12 months and winter and autumn seasons exhibit long term correlation. On the other hand, when the H exponent and DFA scaling exponent values compared only four monthly and two seasonal rainfall series concluded to be consistent with both H exponent and DFA scaling exponent results.

Effects of arm swing amplitude and lower limb asymmetry on motor variability patterns during treadmill gait

Motor variability is a fundamental feature of gait. Altered arm swing and lower limb asymmetry (LLA) may be contributing factors having been shown to affect the magnitude and dynamics of variability in spatiotemporal and trunk motion. However, the effects on lower limb joints remain unclear.Full-body kinematics of 15 healthy young adults were recorded during treadmill walking using the Computer-Assisted Rehabilitation Environment system. Participants completed six trials, combining three arm swing (AS) amplitude (normal, active, held) and two LLA (symmetrical, asymmetrical) conditions. The mean standard deviation (meanSD), maximum Lyapunov exponent (λmax), detrended fluctuation analysis scaling exponent of range of motion (DFAα), and sample entropy (SaEn) were computed for tridimensional trunk, pelvis, and lower limb joint angles, and compared using repeated-measures ANOVAs.Relative to normal AS, active AS increased meanSD of all joint angles, λmax of frontal plane hip and ankle angles, and SaEn of sagittal plane ankle angles. Active AS, however, did not affect λmax or SaEn of trunk or pelvis angles. LLA increased meanSD of sagittal plane joint angles, λmax of Euclidean norm trunk angle and of lower limb joint angles, and SaEn of ankle dorsiflexion/ plantarflexion, but decreased SaEn of tridimensional trunk angles and hip rotation in the slower moving leg.Alterations in lower limb variability with active AS and LLA suggest that young adults actively exploit their lower limb redundancies to maintain gait. This appears to preserve trunk stability and regularity during active AS but not during LLA.

Scaling Properties and Persistence of Long-Term Solar Activity

The long-range correlations associated with the presence of persistence are investigated by applying the detrended fluctuation analysis (DFA) on three different proxies of long-term solar activity. The considered datasets are a sunspot number reconstruction (SNR04) obtained from the atmospheric activity of the cosmogenic isotope 14C derived from tree rings, a total solar irradiance reconstruction (TSIR12) obtained from several 10Be ice core records from Greenland and Antarctica in combination with the global record of 14C in tree rings and a new multi-proxy sunspot number reconstruction (SNR18), also derived from 10Be datasets and the global 14C production series. The DFA scaling exponents found for the three time series are similar (lying in the range between 0.70 and 0.77) and the scaling ranges are comparable. These results indicate the presence of long-range correlations with persistence, in substantial agreement with the findings of previous studies carried out on other solar activity indices and proxies.

Use of Virtual Reality to Assess Dynamic Posturography and Sensory Organization: Instrument Validation Study.

BackgroundThe Equitest system (Neurocom) is a computerized dynamic posturography device used by health care providers and clinical researchers to safely test an individual’s postural control. While the Equitest system has evaluative and rehabilitative value, it may be limited owing to its cost, lack of portability, and reliance on only sagittal plane movements. Virtual reality (VR) provides an opportunity to reduce these limitations by providing more mobile and cost-effective tools while also observing a wider array of postural characteristics.ObjectiveThis study aimed to test the plausibility of using VR as a feasible alternative to the Equitest system for conducting a sensory organization test.MethodsA convenience sample of 20 college-aged healthy individuals participated in the study. Participants completed the sensory organization test using the Equitest system as well as using a VR environment while standing atop a force plate (Bertec Inc). The Equitest system measures the equilibrium index. During VR trials, the estimated equilibrium index, 95% ellipse area, path length, and anterior-posterior detrended fluctuation analysis scaling exponent alpha were calculated from center of pressure data. Pearson correlation coefficients were used to assess the relationship between the equilibrium index and center of pressure–derived balance measures. Intraclass correlations for absolute agreement and consistency were calculated to compare the equilibrium index and estimated equilibrium index.ResultsIntraclass correlations demonstrated moderate consistency and absolute agreement (0.5 < intraclass correlation coefficient < 0.75) between the equilibrium index and estimated equilibrium index from the Equitest and VR sensory organization test (SOT), respectively, in four of six tested conditions. Additionally, weak to moderate correlations between force plate measurements and the equilibrium index were noted in several of the conditions.ConclusionsThis research demonstrated the plausibility of using VR as an alternative method to conduct the SOT. Ongoing development and testing of virtual environments are necessary before employing the technology as a replacement to current clinical tests.

Multiparametric statistical and dynamical analysis of angular high-frequency wind speed time series

High frequency data from the city of Petrolina, Northeast Brazil, are used to find the wind speed projection series at different angles, which are then analyzed by using several statistical tools: detrended fluctuation analysis (DFA), multifractal detrended fluctuation analysis (MFDFA) and Fisher–Shannon analysis (FSA). It is found that α, the DFA scaling exponent, varies between 0.6 (indicating weak persistence) and unity (strong persistence), at different time frames and at different projection angles. At lower projection angles wind speed is characterized by higher heterogeneity, lower disorder, higher organization and relative dominance of small fluctuations. The statistical analysis of wind speed with varying the direction could contribute to enrich the knowledge of the dynamics of wind speed.

How persons with transtibial amputation regulate lateral stepping while walking in laterally destabilizing environments

BackgroundPersons with lower limb amputation often experience decreased physical capacity, difficulty walking, and increased fall risk. To either prevent or recover from a loss of balance, one must effectively regulate their stepping movements. It is therefore critical to identify how well persons with amputation regulate stepping. Here, we used a multi-objective control framework based on Goal Equivalent Manifolds to identify how persons with transtibial amputation (TTA) regulate lateral stepping while walking without and with lateral perturbations. Research questionWhen walking in destabilizing environments, do otherwise healthy persons with TTA exhibit greater difficulty regulating lateral stepping due to impaired control? Or do they instead continue to use similar strategies to regulate lateral stepping despite their amputation? MethodsEight persons with unilateral TTA and thirteen able-bodied (AB) controls walked in a virtual environment under three conditions: no perturbations, laterally oscillating visual field, and laterally oscillating treadmill platform. We analyzed step-to-step time series of step widths and absolute lateral body positions. We computed means, standard deviations and Detrended Fluctuation Analysis scaling exponents for each time series and computed how much participants directly corrected step width and position deviations at each step. We compared our results to computational predictions to identify the underlying causes of our experimental findings. ResultsAll participants exhibited significantly increased variability, decreased scaling exponents, and tighter direct control when perturbed. Simulations from our stepping regulation models revealed that people responded to the increased variability produced by the imposed perturbations by tightening their control of both step width and lateral position. Participants with TTA exhibited only a few minor differences from AB in lateral stepping regulation, even when subjected to substantially destabilizing lateral perturbations. SignificanceSince control of stepping is intrinsically multi-objective, developing effective interventions to reduce fall risk in persons with amputation will likely require strategies that adopt multi-objective approaches.

Nonparametric time series summary statistics for high-frequency accelerometry data from individuals with advanced dementia

Accelerometry data has been widely used to measure activity and the circadian rhythm of individuals across the health sciences, in particular with people with advanced dementia. Modern accelerometers can record continuous observations on a single individual for several days at a sampling frequency of the order of one hertz. Such rich and lengthy data sets provide new opportunities for statistical insight, but also pose challenges in selecting from a wide range of possible summary statistics, and how the calculation of such statistics should be optimally tuned and implemented. In this paper, we build on existing approaches, as well as propose new summary statistics, and detail how these should be implemented with high frequency accelerometry data. We test and validate our methods on an observed data set from 26 recordings from individuals with advanced dementia and 14 recordings from individuals without dementia. We study four metrics: Interdaily stability (IS), intradaily variability (IV), the scaling exponent from detrended fluctuation analysis (DFA), and a novel nonparametric estimator which we call the proportion of variance (PoV), which calculates the strength of the circadian rhythm using spectral density estimation. We perform a detailed analysis indicating how the time series should be optimally subsampled to calculate IV, and recommend a subsampling rate of approximately 5 minutes for the dataset that has been studied. In addition, we propose the use of the DFA scaling exponent separately for daytime and nighttime, to further separate effects between individuals. We compare the relationships between all these methods and show that they effectively capture different features of the time series.

Detrended cross correlation analysis (DCCA) of radon, thoron, temperature and pressure time series data

Non-linear processes evolving within earth crust and in atmosphere gives complex time series and extracting meaningful physical information from such data is not easy without development and practice of modern computational techniques. Detrended fluctuation analysis (DFA), and detrended cross correlation analysis (DCCA), are used to explore long-range correlations and characterization of correlated data of more than one non-stationary time series. We present results of DFA, and DCCA techniques applied on radon, thoron, temperature and pressure time series. Time series data of each series have been decomposed for each season and seasonal periodicities have been removed. DFA and DCCA techniques have been employed on the deseasonalized data. For all four seasons, DFA scaling exponent () and correlation exponent () have been calculated for radon, thoron, temperature and pressure time series. The results of ‘’ and ‘r’, for each of the time series have been used for finding the existence of persistency in processes and investigation of long-range correlations. Largely, these results indicate that the cross-correlation relationship between observed times series for each season is not of simply power-law type. Detrended Cross Correlation Analysis between different time series shows persistent behavior. In order to quantify the level of cross-correlations, we computed the DCCA cross-correlation coefficient

Noise suppression for magnetotelluric using variational mode decomposition and detrended fluctuation analysis

Noise suppression is significant for magnetotelluric (MT) data analysis, especially in the face of strong human electromagnetic interference. Variational mode decomposition (VMD) is a novel signal processing method, and the selection of proper decomposition layers plays a key role in its signal processing effects. In view of the fact that detrended fluctuation analysis (DFA) is an evaluation criterion capable of selecting the appropriate number of sub-signals, we propose a noise suppression method for MT by combing VMD with DFA. We firstly estimate the scaling exponent range of MT noisy data and decompose it into a given series of K-order intrinsic mode functions (IMFs). Then, a criterion based on DFA is designed to select the mode number K with the purpose to improve the decomposition accuracy of VMD. The scaling exponent of DFA is used to define the relevant modes for the construction of filtered signals. In this research, the MT data is collected from Qinghai test site and added with strong interference for comprehensive analysis by the remote reference method, VMD method, and the proposed VMD-DFA method. The results have shown that the proposed method could greatly improve the accuracy of signal decomposition and the reliability of the reconstructed signal by adaptively selecting suitable K-order IMFs for different types of interference. Consequently, strong interference is effectively eliminated, and the obtained apparent resistivity-phase curve is stable and smooth. Moreover, the denoised MT data will further strengthen the interpretability of geoelectric information.

Scale Features of a Network Echo Mechanism: Case Study for the Different Internet Paths

We have investigated dynamics of the Internet performance through the assessment of scaling features of a network ICMP echo mechanism or pinging. Time series of round-trip times (RTT) from the host computer to 5 destination hosts and back, recorded during three consecutive days and nights, have been used. To assess correlation and scaling features of network echo mechanism, we used method of detrended fluctuation analysis (DFA) for RTT data sets. It was shown that for different, 10 minute long periods of day and night observations, RTT data sets mostly fluctuate within a narrow range, though sometimes we observe strong sharp spikes. RTT variations mostly reveal persistent behavior. DFA fluctuation curves often are characterized by crossovers indication stronger or lesser changes in the dynamics of network performance. Distribution function of DFA scaling exponents of considered RTT time series mostly was asymmetric with long tail on the right hand side. Dynamical changes occurring in the scaling features of Internet network as assessed by RTT fluctuations do not depend on the location of the host and destination nodes. Larger delays in round-trip time responses make the scaling behavior of the RTT series complicated and strongly influence their long range correlation features.

Long-Time Memory in Drought via Detrended Fluctuation Analysis

The persistence of drought events largely determines the severity of socioeconomic and ecological impacts, unfortunately the performance of current weather forecasting models (WFM) to simulate such events is subject to great uncertainties. This study is investigating time-domain characteristics of drought persistence over Turkey by applying the detrended fluctuation analysis (DFA) method to the Palmer drought severity index (PDSI). The existence of long-range power-law correlation in PDSI fluctuations is demonstrated for time scales ranging from monthly to decadal. Understanding of such statistical patterns in PDSI values can definitely be a step forward in drought predictability. From a climatological point of view, it is found that the areas with high level DFA scaling exponent (generalized Hurst) indicate the areas of higher sensitivity to droughts and associated risks. Furthermore, the characteristics of the persistence of the PDSI in climate zones have also been examined by applying the Holdridge Life Zones (HLZ) classification. HLZ classification over Turkey leads to two climate-zones: cool-temperate and warm-temperate. In addition, when topography is taken in account, montane (cool-temperate) and lower-montane (warm-temperate) climate zones can be treated as two different zones. It has been observed that the predictable index (PI) of the PDSI derived from the DFA Hurst exponent is relatively high in the cool-temperate and montane climate zones compared to others. In fact, very different PI values were also obtained in a few HLZ climate classes within the same climate zone and with same vegetation index (i.e. steppe, dry-forest, warm-forest etc.).

Sex-Specific Dependence of Linear and Nonlinear Postural Control Metrics on Anthropometrics During Clinical Balance Tests in Healthy Young Adults.

Previous work suggests that balance behavior is a sex-dependent, complex process that can be characterized by linear and nonlinear metrics. Although a certain degree of center of pressure variability may be expected based on sexual dimorphism, there is evidence to suggest that these effects are obscured by potential interactions between sex and anthropometric factors. To date, no study has accounted for such interactive effects using both linear and nonlinear measures. This investigation sought to analyze interactive models featuring sex, height, and weight as predictors of linear and nonlinear aspects of postural control. Cross-sectional study. Controlled laboratory. A total of 26 males (23.80 [3.44]y, 177.87 [6.44]cm, 81.70 [10.80]kg) and 28 females (21.14 [2.03]y, 169.57 [8.80]cm, 64.48 [8.86]kg) were sampled from a healthy university population. Linear (range [RNG], velocity [VEL], and SD) and nonlinear (detrended fluctuation analysis scaling exponent, multivariate multiscale sample entropy [MMSECI]) summary metrics of center of pressure time series. Participants stood on a force plate for 20 seconds in 3 conditions: double (D), single (S), and tandem (T) stance. Data for each stance condition were analyzed using regression models with interaction terms for sex × height and sex × weight. In D, weight had a positive, significant main effect on VELy, MMSECId, and MMSECIv. In men, height was observed to have a positive effect on SDy (S), RNGy (S), and RNGx (T) and a negative effect on MMSECIv (T). In women, weight was observed to have a positive effect on SDy and VELx (both T). Our findings suggest that men and women differ with respect to certain linear and nonlinear aspects of balance behavior, and that these differences may reflect sex-specific behavioral patterns in addition to effects related to sexual dimorphism.

Detrended Fluctuation, Coherence, and Spectral Power Analysis of Activation Rearrangement in EEG Dynamics During Cognitive Workload.

In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1–5.8 Hz), θ2 (5.9–7.4 Hz), β1 (13–19.9 Hz), and β2 (20–25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future.

Short communication: Assessment of disbudding pain in dairy calves using nonlinear measures of heart rate variability

The purpose of this study was to evaluate whether pain-related stress caused by disbudding could be detected using nonlinear measures of heart rate variability (HRV). Twenty-five female Holstein calves (4-7 wk of age) were randomly assigned to 1 of 3 treatments: (1) sham disbud (SHAM; n = 9), (2) disbud with lidocaine-meloxicam pain mitigation (MED; n = 8), or (3) disbud without pain mitigation (NoMED; n = 8). Heart rate variability (sample entropy, percentage determinism, percentage recurrence, or mean length of diagonal lines in a recurrence plot) was recorded on d -1, 0, 1, 3, and 5 relative to the experimental procedure, with disbudding taking place on d 0. The short-term detrended fluctuation analysis scaling exponent was greater in MED calves than in SHAM calves, indicating a greater stress response to the disbudding procedure regardless of pain mitigation. These results indicate that calves in the MED group may have experienced pain-related stress as a result of the disbudding procedure. The remaining nonlinear HRV measures did not differ by treatment. Future research on this topic should address additional potential confounding factors, such as the effect of pain-mitigating drugs on autonomic function or the influence of the autonomic nervous system on wound healing, that may prohibit HRV measurement as an indicator of disbudding pain severity.

Pre-processing of Photoplethysmographic Waveform for Amplitude Regularization

This study is aimed to develop a post-processing method to regularize amplitude of PPG waveforms and evaluate the performance of the algorithm. The proposed procedure for regularizing amplitude consists of extracting the signal envelopes based on time-domain filtering, generating a compensation curve, and reconstructing the waveform. The proposed technique was evaluated with respect to dispersion and waveform fluctuation by means of coefficients of variation (CV) and a scaling exponent of detrended fluctuation analysis (DFA). Other criteria included the detection performances of major features such as upper and lower fiducial points and maximum dV/dt. In developing this method, we used a clinical dataset that comprised 74,225 beats. By applying reconstruction algorithm, the %CV and the scaling exponent of DFA were significantly decreased from 115.4 to 71.4 and from 1.029 to 0.836, respectively in peak amplitude. In valley amplitude, they were also decreased from 38.3 to 13.2 and from 0.993 to 0.713, respectively. Moreover, sensitivity of maximum dV/dt point, upper and lower peak detection are increased by 8.50, 2.72 and 5.21% after reconstruction, respectively. Our results clearly showed that the proposed reconstruction technique could reduce amplitude fluctuation and improve detection of fiducial points.

A new methodology for local cross-correlation between two nonstationary time series

To measure the degree of local cross-correlation between two nonstationary time series, a new approach with a locally weighted Pearson correlation coefficient based on a simple locally weighted linear regression model was proposed. In this approach, a Gaussian decay-based function is selected as a weighting function. An appropriate bandwidth is selected using an alternative criterion. Some factors influencing the local cross-correlation degree, including long-range exponent estimated by means of a detrended fluctuation analysis (DFA) and seasonal change in the series, are discussed. Artificial and real-world datasets are analyzed. The results show that the proposed method can measure the degree of a locally intrinsic cross-correlation between two series. The contribution of this locally intrinsic cross-correlation is attributed to original input excitation sources and DFA scaling exponents. The effects of seasonal change with a high-frequency in the series on a locally intrinsic cross-correlation are significant. The effects of a low-frequency seasonal change are insignificant. A positive local cross-correlation between a synchronous wind speed and air pollution index series in Nanjing, China is observed, which is related to externally imported air pollution sources. Consistent results are obtained by comparing the new method with the detrended cross-correlation coefficientρDCCA. Therefore, the proposed approach is reliable, reasonable, and applicable, and can examine the degree of the local intrinsic cross-correlation between two nonstationary time series.