Interpretation of scaling properties of electroencephalographic fluctuations via spectral analysis and underlying physiology

[Formula: see text]-[Formula: see text]: A Nonparametric Model for Neural Power Spectra Decomposition

The power spectra estimated from the brain recordings are the mixed representation of aperiodic transient activity and periodic oscillations, i.e., aperiodic component (AC) and periodic component (PC). Quantitative neurophysiology requires precise decomposition preceding parameterizing each component. However, the shape, statistical distribution, scale, and mixing mechanism of AC and PCs are unclear, challenging the effectiveness of current popular parametric models such as FOOOF, IRASA, BOSC, etc. Here, ξ- π was proposed to decompose the neural spectra by embedding the nonparametric spectra estimation with penalized Whittle likelihood and the shape language modeling into the expectation maximization framework. ξ- π was validated on the synthesized spectra with loss statistics and on the sleep EEG and the large sample iEEG with evaluation metrics and neurophysiological evidence. Compared to FOOOF, both the simulation presenting shape irregularities and the batch simulation with multiple isolated peaks indicated that ξ- π improved the fit of AC and PCs with less loss and higher F1-score in recognizing the centering frequencies and the number of peaks; the sleep EEG revealed that ξ- π produced more distinguishable AC exponents and improved the sleep state classification accuracy; the iEEG showed that ξ- π approached the clinical findings in peak discovery. Overall, ξ- π offered good performance in the spectra decomposition, which allows flexible parameterization using descriptive statistics or kernel functions. ξ- π is a seminal tool for brain signal decoding in fields such as cognitive neuroscience, brain-computer interface, neurofeedback, and brain diseases.

A pattern of cognitive resource disruptions in childhood psychopathology

The Hurst exponent (H) isolated in fractal analyses of neuroimaging time series is implicated broadly in cognition. Within this literature, H is associated with multiple mental disorders, suggesting that H is transdimensionally associated with psychopathology. Here, we unify these results and demonstrate a pattern of decreased H with increased general psychopathology and attention-deficit/hyperactivity factor scores during a working memory task in 1,839 children. This pattern predicts current and future cognitive performance in children and some psychopathology in 703 adults. This pattern also defines psychological and functional axes associating psychopathology with an imbalance in resource allocation between fronto-parietal and sensorimotor regions, driven by reduced resource allocation to fronto-parietal regions. This suggests the hypothesis that impaired working memory function in psychopathology follows from a reduced cognitive resource pool and a reduction in resources allocated to the task at hand.

NREM Sleep EEG Characteristics Correlate to the Mild Cognitive Impairment in Patients with Parkinsonism

Early identification and diagnosis of mild cognitive impairment (MCI) in patients with parkinsonism (PDS) are critical. The aim of this study was to identify biomarkers of MCI in PDS using conventional electroencephalogram (EEG) power spectral analysis and detrended fluctuation analysis (DFA). In this retrospective study, patients with PDS who underwent an overnight polysomnography (PSG) study in our hospital from 2019 to 2020 were enrolled. Patients with PDS assessed by clinical examination and questionnaires were divided into two groups: the PDS with normal cognitive function (PDS-NC) group and the PDS with MCI (PDS-MCI) group. Sleep EEG signals were extracted and purified from the PSG and subjected to a conventional power spectral analysis, as well as detrended fluctuation analysis (DFA) during wakefulness, nonrapid eye movement (NREM) sleep, and rapid eye movement (REM) sleep. Forty patients with PDS were enrolled, including 25 with PDS-NC and 15 with PDS-MCI. Results revealed that compared with PDS-NC patients, patients with PDS-MCI had a reduced fast ratio ((alpha + beta)/(delta + theta)) and increased DFA during NREM sleep. DFA during NREM was diagnostic of PDS-MCI, with an area under the receiver operating characteristic curve of 0.753 (95% CI: 0.592-0.914) (p < 0.05). Mild cognitive dysfunction was positively correlated with NREM-DFA (r = 0.426, p = 0.007) and negatively correlated with an NREM-fast ratio (r = -0.524, p = 0.001). This suggested that altered EEG activity during NREM sleep is associated with MCI in patients with PDS. NREM sleep EEG characteristics of the power spectral analysis and DFA correlate to MCI. Slowing of EEG activity during NREM sleep may reflect contribution to the decline in NREM physiological function and is therefore a marker in patients with PDS-MCI.

Methods for classifying depression in single channel EEG using linear and nonlinear signal analysis

BACKGROUND AND OBJECTIVE

Depressive disorder is one of the leading causes of burden of disease today and it is presumed to take the first place in the world in 2030. Early detection of depression requires a patient-friendly inexpensive method based on easily measurable objective indicators. This study aims to compare various single-channel electroencephalographic (EEG) measures in application for detection of depression.

METHODS

The EEG recordings were performed on a group of 13 medication-free depressive outpatients and 13 gender and age matched controls. The recorded 30-channel EEG signal was analysed using linear methods spectral asymmetry index, alpha power variability and relative gamma power and nonlinear methods Higuchi's fractal dimension, detrended fluctuation analysis and Lempel-Ziv complexity. Classification accuracy between depressive and control subjects was calculated using logistic regression analysis with leave-one-out cross-validation. Calculations were performed separately for each EEG channel.

RESULTS

All calculated measures indicated increase with depression. Maximal testing accuracy using a single measure was 81% for linear and 77% for nonlinear measures. Combination of two linear measures provides the accuracy of 88% and two nonlinear measures of 85%. Maximal classification accuracy of 92% was indicated using mixed combination of three linear and three nonlinear measures.

CONCLUSIONS

The results of this preliminary study confirm that single-channel EEG analysis, employing the combination of measures, can provide discrimination of depression at the level of multichannel EEG analysis. The performed study shows that there is no single superior measure for detection of depression.

Wake-sleep transition as a noisy bifurcation

A recent physiologically based model of the ascending arousal system is used to analyze the dynamics near the transition from wake to sleep, which corresponds to a saddle-node bifurcation at a critical point. A normal form is derived by approximating the dynamics by those of a particle in a parabolic potential well with dissipation. This mechanical analog is used to calculate the power spectrum of fluctuations in response to a white noise drive, and the scalings of fluctuation variance and spectral width are derived versus distance from the critical point. The predicted scalings are quantitatively confirmed by numerical simulations, which show that the variance increases and the spectrum undergoes critical slowing, both in accord with theory. These signals can thus serve as potential precursors to indicate imminent wake-sleep transition, with potential application to safety-critical occupations in transport, air-traffic control, medicine, and heavy industry.

Separating Fractal and Oscillatory Components in the Power Spectrum of Neurophysiological Signal

Neurophysiological field-potential signals consist of both arrhythmic and rhythmic patterns indicative of the fractal and oscillatory dynamics arising from likely distinct mechanisms. Here, we present a new method, namely the irregular-resampling auto-spectral analysis (IRASA), to separate fractal and oscillatory components in the power spectrum of neurophysiological signal according to their distinct temporal and spectral characteristics. In this method, we irregularly resampled the neural signal by a set of non-integer factors, and statistically summarized the auto-power spectra of the resampled signals to separate the fractal component from the oscillatory component in the frequency domain. We tested this method on simulated data and demonstrated that IRASA could robustly separate the fractal component from the oscillatory component. In addition, applications of IRASA to macaque electrocorticography and human magnetoencephalography data revealed a greater power-law exponent of fractal dynamics during sleep compared to wakefulness. The temporal fluctuation in the broadband power of the fractal component revealed characteristic dynamics within and across the eyes-closed, eyes-open and sleep states. These results demonstrate the efficacy and potential applications of this method in analyzing electrophysiological signatures of large-scale neural circuit activity. We expect that the proposed method or its future variations would potentially allow for more specific characterization of the differential contributions of oscillatory and fractal dynamics to distributed neural processes underlying various brain functions.

A new EEG biomarker of neurobehavioural impairment and sleepiness in sleep apnea patients and controls during extended wakefulness

OBJECTIVE

To explore the use of detrended fluctuation analysis (DFA) scaling exponent of the awake electroencephalogram (EEG) as a new alternative biomarker of neurobehavioural impairment and sleepiness in obstructive sleep apnea (OSA).

METHODS

Eight patients with moderate-severe OSA and nine non-OSA controls underwent a 40-h extended wakefulness challenge with resting awake EEG, neurobehavioural performance (driving simulator and psychomotor vigilance task) and subjective sleepiness recorded every 2-h. The DFA scaling exponent and power spectra of the EEG were calculated at each time point and their correlation with sleepiness and performance were quantified.

RESULTS

DFA scaling exponent and power spectra biomarkers significantly correlated with simultaneously tested performance and self-rated sleepiness across the testing period in OSA patients and controls. Baseline (8am) DFA scaling exponent but not power spectra were markers of impaired simulated driving after 24-h extended wakefulness in OSA (r=0.738, p=0.037). OSA patients had a higher scaling exponent and delta power during wakefulness than controls.

CONCLUSIONS

The DFA scaling exponent of the awake EEG performed as well as conventional power spectra as a marker of impaired performance and sleepiness resulting from sleep loss.

SIGNIFICANCE

DFA may potentially identify patients at risk of neurobehavioural impairment and assess treatment effectiveness.

Multiscale analysis of biological data by scale-dependent lyapunov exponent

Physiological signals often are highly non-stationary (i.e., mean and variance change with time) and multiscaled (i.e., dependent on the spatial or temporal interval lengths). They may exhibit different behaviors, such as non-linearity, sensitive dependence on small disturbances, long memory, and extreme variations. Such data have been accumulating in all areas of health sciences and rapid analysis can serve quality testing, physician assessment, and patient diagnosis. To support patient care, it is very desirable to characterize the different signal behaviors on a wide range of scales simultaneously. The Scale-Dependent Lyapunov Exponent (SDLE) is capable of such a fundamental task. In particular, SDLE can readily characterize all known types of signal data, including deterministic chaos, noisy chaos, random 1/f(α) processes, stochastic limit cycles, among others. SDLE also has some unique capabilities that are not shared by other methods, such as detecting fractal structures from non-stationary data and detecting intermittent chaos. In this article, we describe SDLE in such a way that it can be readily understood and implemented by non-mathematically oriented researchers, develop a SDLE-based consistent, unifying theory for the multiscale analysis, and demonstrate the power of SDLE on analysis of heart-rate variability (HRV) data to detect congestive heart failure and analysis of electroencephalography (EEG) data to detect seizures.

Facilitating joint chaos and fractal analysis of biosignals through nonlinear adaptive filtering

Background

Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free.

Methodology/Principal Findings

To facilitate joint chaos and fractal analysis of biosignals, we present an adaptive algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction techniques; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; and (4) offers a new formulation of fractal and multifractal analysis that is better than existing methods when a biosignal contains a strong oscillatory component.

Conclusions

The presented approach is a valuable, versatile tool for the analysis of various types of biological signals. Its effectiveness is demonstrated by offering new important insights into brainwave dynamics and the very high accuracy in automatically detecting epileptic seizures from EEG signals.

Complexity measures of brain wave dynamics

To understand the nature of brain dynamics as well as to develop novel methods for the diagnosis of brain pathologies, recently, a number of complexity measures from information theory, chaos theory, and random fractal theory have been applied to analyze the EEG data. These measures are crucial in quantifying the key notions of neurodynamics, including determinism, stochasticity, causation, and correlations. Finding and understanding the relations among these complexity measures is thus an important issue. However, this is a difficult task, since the foundations of information theory, chaos theory, and random fractal theory are very different. To gain significant insights into this issue, we carry out a comprehensive comparison study of major complexity measures for EEG signals. We find that the variations of commonly used complexity measures with time are either similar or reciprocal. While many of these relations are difficult to explain intuitively, all of them can be readily understood by relating these measures to the values of a multiscale complexity measure, the scale-dependent Lyapunov exponent, at specific scales. We further discuss how better indicators for epileptic seizures can be constructed.

Dynamics of electroencephalogram entropy and pitfalls of scaling detection

In recent studies a number of research groups have determined that human electroencephalograms (EEG) have scaling properties. In particular, a crossover between two regions with different scaling exponents has been reported. Herein we study the time evolution of diffusion entropy to elucidate the scaling of EEG time series. For a cohort of 20 awake healthy volunteers with closed eyes, we find that the diffusion entropy of EEG increments (obtained from EEG waveforms by differencing) exhibits three features: short-time growth, an alpha wave related oscillation whose amplitude gradually decays in time, and asymptotic saturation which is achieved after approximately 1 s. This analysis suggests a linear, stochastic Ornstein-Uhlenbeck Langevin equation with a quasiperiodic forcing (whose frequency and/or amplitude may vary in time) as the model for the underlying dynamics. This model captures the salient properties of EEG dynamics. In particular, both the experimental and simulated EEG time series exhibit short-time scaling which is broken by a strong periodic component, such as alpha waves. The saturation of EEG diffusion entropy precludes the existence of asymptotic scaling. We find that the crossover between two scaling regions seen in detrended fluctuation analysis (DFA) of EEG increments does not originate from the underlying dynamics but is merely an artifact of the algorithm. This artifact is rooted in the failure of the "trend plus signal" paradigm of DFA.

High-frequency Broadband Modulations of Electroencephalographic Spectra

High-frequency cortical potentials in electroencephalographic (EEG) scalp recordings have low amplitudes and may be confounded with scalp muscle activities. EEG data from an eyes-closed emotion imagination task were linearly decomposed using independent component analysis (ICA) into maximally independent component (IC) processes. Joint decomposition of IC log spectrograms into source- and frequency-independent modulator (IM) processes revealed three distinct classes of IMs that separately modulated broadband high-frequency (∼15–200 Hz) power of brain, scalp muscle, and likely ocular motor IC processes. Multi-dimensional scaling revealed significant but spatially complex relationships between mean broadband brain IM effects and the valence of the imagined emotions. Thus, contrary to prevalent assumption, unitary modes of spectral modulation of frequencies encompassing the beta, gamma, and high gamma frequency ranges can be isolated from scalp-recorded EEG data and may be differentially associated with brain sources and cognitive activities.

The dynamics of EEG entropy

The scaling properties of human EEG have so far been analyzed predominantly in the framework of detrended fluctuation analysis (DFA). In particular, these studies suggested the existence of power-law correlations in EEG. In DFA, EEG time series are tacitly assumed to be made up of fluctuations, whose scaling behavior reflects neurophysiologically important information and polynomial trends. Even though these trends are physiologically irrelevant, they must be eliminated (detrended) to reliably estimate such measures as Hurst exponent or fractal dimension. Here, we employ the diffusion entropy method to study the scaling behavior of EEG. Unlike DFA, this method does not rely on the assumption of trends superposed on EEG fluctuations. We find that the growth of diffusion entropy of EEG increments of awake subjects with closed eyes is arrested only after approximately 0.5 s. We demonstrate that the salient features of diffusion entropy dynamics of EEG, such as the existence of short-term scaling, asymptotic saturation, and alpha wave modulation, may be faithfully reproduced using a dissipative, first-order, stochastic differential equation-an extension of the Langevin equation. The structure of such a model is utterly different from the "noise+trend" paradigm of DFA. Consequently, we argue that the existence of scaling properties for EEG dynamics is an open question that necessitates further studies.

Quantitative study of the sleep onset period via detrended fluctuation analysis: normal vs. narcoleptic subjects

OBJECTIVE

To examine the process of the sleep onset quantitatively and explore differences between narcoleptics and controls during the sleep onset period (SOP).

METHOD

Dynamic detrended fluctuation analysis (DFA) was applied to electroencephalograms recorded during multiple sleep latency tests of 11 drug-free narcoleptic patients (19.3+/-4.4 yrs; 8 males) and 9 healthy controls (23.8+/-6.3 yrs; 6 males). The SOP of each group was estimated by fitting the time courses of the DFA scaling exponents to a parametric curve.

RESULTS

The sequence of DFA exponents showed that electrophysiological brain activity was changing rapidly across the SOP. This transition was also verified by a conventional method (i.e., dynamic spectral analysis). The SOP durations of narcoleptics and controls were estimated as 239+/-25 s and 145+/-20 s, respectively.

CONCLUSIONS

The significantly larger SOP of narcoleptics, compared to controls, is consistent with the wake state of narcolepsy being more susceptible to sleep due to a lower barrier to transitioning to sleep.

SIGNIFICANCE

Our results suggest that electrophysiological signatures of narcolepsy could be quantified by dynamic DFA, so the method may have promise as a potential tool to help the diagnosis of narcolepsy despite the present study's limited sample size.

A study on the possible usefulness of detrended fluctuation analysis of the electroencephalogram background activity in Alzheimer's disease

We studied the EEG background activity of Alzheimer's disease (AD) patients with detrended fluctuation analysis (DFA). DFA provides an estimation of the scaling information and long-range correlations in time series. We recorded the EEG in 11 AD patients and 11 age-matched controls. Our results showed two scaling regions in all subjects' channels (for limited time scales from 0.01 to 0.04 s and from 0.08 to 0.43 s, respectively), with a clear bend when their corresponding slopes (alpha(1) and alpha(2)) were different. No significant differences between groups were found with alpha(1). However, alpha(2) values were significantly lower in control subjects at electrodes T5, T6, and O1 (p < 0.01, Student's t-test). These findings suggest that the scaling behavior of the EEG is sensitive to AD. Although alpha(2) values allowed us to separate AD patients and controls, accuracies were lower than with spectral analysis. However, a forward stepwise linear discriminant analysis with a leave-one-out cross-validation procedure showed that the combined use of DFA and spectral analysis could improve the diagnostic accuracy of each individual technique. Thus, although spectral analysis outperforms DFA, the combined use of both techniques may increase the insight into brain dysfunction in AD.

Influence of filters in the detrended fluctuation analysis of digital electroencephalographic data

The technique named detrended fluctuation analysis (DFA) has been used to reveal the presence of long-range temporal correlations (LRTC) and scaling behavior (SB) in electroencephalographic (EEG) recordings. The occurrence of these phenomena seems to be a salient characteristic of the healthy human brain and alterations in different pathologies has been described. Here we show how the filtering stages implemented in the systems for digital EEG influence the estimation of the DFA parameters used to characterize the brain signals. In consequence, we conclude that it is important to consider these filtering effects before interpreting the results obtained from digital EEG recordings.

Detrended Fluctuation Analysis of EEG as a Measure of Depth of Anesthesia

For several decades, a number of methods have been developed for the noninvasive assessment of the level of consciousness during general anesthesia. In this paper, detrended fluctuation analysis is used to study the scaling behavior of the electroencephalogram as a measure of the level of consciousness. Three indexes are proposed in order to characterize the patient state. Statistical analysis demonstrates that they allow significant discrimination between the awake, sedated and anesthetized states. Two of them present a good correlation with established indexes of depth of anesthesia. The scaling behavior has been found related to the depth of anesthesia and the methodology allows real-time implementation, which enables its application in monitoring devices.

Feedback modulates the temporal scale-free dynamics of brain electrical activity in a hypothesis testing task

We used the electroencephalogram (EEG) to investigate whether positive and negative performance feedbacks exert different long-lasting modulations of electrical activity in a reasoning task. Nine college students serially tested hypotheses concerning a hidden rule by judging its presence or absence in triplets of digits, and revised them on the basis of an exogenous performance feedback. The scaling properties of the transition period between feedback and triplet presentation were investigated with detrended fluctuation analysis (DFA). DFA showed temporal scale-free dynamics of EEG activity in both feedback conditions for time scales larger than 150 ms. Furthermore, DFA revealed that negative feedback elicits significantly higher scaling exponents than positive feedback. This effect covers a wide network comprising parieto-occipital and left frontal regions. We thus showed that specific task demands can modify the temporal scale-free dynamics of the ongoing brain activity. Putative neural correlates of these long-lasting feedback-specific modulations are proposed.

Multiscale brain modelling

A central difficulty of brain modelling is to span the range of spatio-temporal scales from synapses to the whole brain. This paper overviews results from a recent model of the generation of brain electrical activity that incorporates both basic microscopic neurophysiology and large-scale brain anatomy to predict brain electrical activity at scales from a few tenths of a millimetre to the whole brain. This model incorporates synaptic and dendritic dynamics, nonlinearity of the firing response, axonal propagation and corticocortical and corticothalamic pathways. Its relatively few parameters measure quantities such as synaptic strengths, corticothalamic delays, synaptic and dendritic time constants, and axonal ranges, and are all constrained by independent physiological measurements. It reproduces quantitative forms of electroencephalograms seen in various states of arousal, evoked response potentials, coherence functions, seizure dynamics and other phenomena. Fitting model predictions to experimental data enables underlying physiological parameters to be inferred, giving a new non-invasive window into brain function that complements slower, but finer-resolution, techniques such as fMRI. Because the parameters measure physiological quantities relating to multiple scales, and probe deep structures such as the thalamus, this will permit the testing of a range of hypotheses about vigilance, cognition, drug action and brain function. In addition, referencing to a standardized database of subjects adds strength and specificity to characterizations obtained.

Electrophysiological measures of acute cerebral ischaemia

A method of EEG analysis is described which provides new insights into EEG pathology in cerebral ischaemia. The method is based on a variant of detrended fluctuation analysis (DFA), which reduces short (10 s) segments of spontaneous EEG time series to two dimensionless scaling exponents. The spatial variability of each exponent is expressed in terms of its statistical moments across EEG channels. Linear discriminant analysis combines the moments into concise indices, which distinguish normal and stroke groups remarkably well. On average over the scalp, stroke patients have larger fluctuations on the longest time scales. This is consistent with the notion of EEG slowing, but extends that notion to a wider range of time scales. The higher moments show that stroke patients have markedly reduced variability over the scalp. This contradicts the notion of a purely focal EEG scalp topography and argues instead for a highly distributed effect. In these indices, subacute patients appear further from normal than acute patients.

Quantifying signals with power-law correlations: a comparative study of detrended fluctuation analysis and detrended moving average techniques

Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals. We systematically study the performance of different variants of the DMA method when applied to artificially generated long-range power-law correlated signals with an a priori known scaling exponent alpha(0) and compare them with the DFA method. We find that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter. Further, we investigate the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent alpha(0) , and how this regime depends on the correlations in the signal. Finally, we develop a three-dimensional representation to determine how the stability of the scaling curves obtained from the DFA and DMA methods depends on the scale of analysis, the order of detrending, and the order of the moving average we use, as well as on the type of correlations in the signal.

THE IMPACT OF EARLY LIFE STRESS ON PSYCHOPHYSIOLOGICAL, PERSONALITY AND BEHAVIORAL MEASURES IN 740 NON-CLINICAL SUBJECTS

Early Life Stress (ELS) has been associated with a range of adverse outcomes in adults, including abnormalities in electrical brain activity [1], personality dimensions [40], increased vulnerability to substance abuse and depression [14]. The present study seeks to quantify these proposed effects in a large sample of non-clinical subjects. Data for the study was obtained from The Brain Resource International Database (six laboratories: two in USA, two in Europe, two in Australia). This study analyzed scalp electrophysiological data (EEG eyes open, closed and target auditory oddball data) and personality (NEO-FFI), history of addictive substance use and ELS) data that was acquired from 740 healthy volunteers. The ELS measures were collected via a self-report measure and covered a broad range of events from childhood sexual and physical abuse, to first-hand experience of traumatizing accidents and sustained domestic conflict [41]. Analysis of covariance, controlling for age and gender, compared EEG data from subjects exposed to ELS with those who were unexposed. ELS was associated with significantly decreased power across the EEG spectrum. The between group differences were strongest in the eyes closed paradigm, where subjects who experienced ELS showed significantly reduced beta (F1,405=12.37, p=.000), theta (F1,405=20.48, p=.000), alpha (F1,405=9.65, p=.002) and delta power (F1,450=36.22, p=.000). ELS exposed subjects also showed a significantly higher alpha peak frequency (F1,405=6.39, p=.012) in the eyes closed paradigm. Analysis of covariance on ERP components revealed that subjects who experienced ELS had significantly decreased N2 amplitude (F1,405=7.73, p=.006). Analyses of variance conducted on measures of personality revealed that subjects who experienced ELS had significantly higher levels of neuroticism (F1,264=13.39, p=.000) and openness (F1,264=17.11, p=.000), but lower levels of conscientiousness, than controls (F1,264=4.08, p=.044). The number of ELS events experienced was shown to be a significant predictor of scores on the DASS questionnaire [27], which rates subjects on symptoms of depression (F3,688=16.44, p=.000, R2=.07), anxiety (F3,688=14.32, p=.000, R2=.06) and stress (F3,688=20.02, p=.000, R2=.08). Each additional early life stressor was associated with an increase in these scores independent of age, gender and the type of stressor. Furthermore, the number of ELS experiences among smokers was also found to be a positive predictor of the nicotine dependency score (Faegstrom Test For Nicotine Dependence, [19]) (F3,104=10.99, p=.000, R2=.24), independent of age, gender and type of stressor. In conclusion, we highlight the impact of a history of ELS showed significant effects on brain function (EEG and ERP activity), personality dimensions and nicotine dependence.

Effect of nonlinear filters on detrended fluctuation analysis

When investigating the dynamical properties of complex multiple-component physical and physiological systems, it is often the case that the measurable system's output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms. Instead, the output signal is often a linear or nonlinear function of the quantity of interest. Here, we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal, using the detrended fluctuation analysis (DFA) which has been shown to accurately quantify power-law correlations in nonstationary signals. Specifically, we study the effect of three types of transforms: (i) linear ( y(i) =a x(i) +b) , (ii) nonlinear polynomial ( y(i) =a x(k)(i) ) , and (iii) nonlinear logarithmic [ y(i) =log ( x(i) +Delta) ] filters. We compare the correlation and scaling properties of signals before and after the transform. We find that linear filters do not change the correlation properties, while the effect of nonlinear polynomial and logarithmic filters strongly depends on (a) the strength of correlations in the original signal, (b) the power k of the polynomial filter, and (c) the offset Delta in the logarithmic filter. We further apply the DFA method to investigate the "apparent" scaling of three analytic functions: (i) exponential [exp (+/-x+a) ] , (ii) logarithmic [log (x+a) ] , and (iii) power law [ (x+a)(lambda) ] , which are often encountered as trends in physical and biological processes. While these three functions have different characteristics, we find that there is a broad range of values for parameter a common for all three functions, where the slope of the DFA curves is identical. We further note that the DFA results obtained for a class of other analytic functions can be reduced to these three typical cases. We systematically test the performance of the DFA method when estimating long-range power-law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider.

A method for estimating long-range power law correlations from the electroencephalogram

Recent research has found long-range electroencephalogram (EEG) power law correlations, indicating time scale invariance. However, the EEG is also rather noisy, displaying short-term decorrelation like white noise--i.e., what is scale invariant at one time period may disappear in the next. The paradoxical combination of short-range divergence, but long-range correlations, suggests that any long-range correlations detected in one sample may be spurious, since they could be related to amplitude fluctuations. To overcome this problem, this paper suggests a new technique for analysing EEG signals segmented by zero-crossings, using detrended fluctuation analysis (DFA), evaluated across two time periods (TIME) and different sites (SITE). A mean scaling exponent across all subjects and sites of alpha = 0.67 was observed. MANOVA analysis indicates no significant main effect for TIME or interaction with SITE, suggesting that the zero-crossing method may be successful in determining the fractal nature of EEG dynamics across relatively long time scales.