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Gao J.,Guangxi University | Gao J.,PMB Intelligence LLC | Hu J.,Guangxi University | Hu J.,PMB Intelligence LLC
Frontiers in Computational Neuroscience | Year: 2013

Epilepsy is a relatively common brain disorder which may be very debilitating. Currently, determination of epileptic seizures often involves tedious, time-consuming visual inspection of electroencephalography (EEG) data by medical experts. To better monitor seizures and make medications more effective, we propose a recurrence time based approach to characterize brain electrical activity. Recurrence times have a number of distinguished properties that make it very effective for forewarning epileptic seizures as well as studying propagation of seizures: (1) recurrence times amount to periods of periodic signals, (2) recurrence times are closely related to information dimension, Lyapunov exponent, and Kolmogorov entropy of chaotic signals, (3) recurrence times embody Shannon and Renyi entropies of random fields, and (4) recurrence times can readily detect bifurcation-like transitions in dynamical systems. In particular, property (4) dictates that unlike many other non-linear methods, recurrence time method does not require the EEG data be chaotic and/or stationary. Moreover, the method only contains a few parameters that are largely signal-independent, and hence, is very easy to use. The method is also very fast-it is fast enough to on-line process multi-channel EEG data with a typical PC. Therefore, it has the potential to be an excellent candidate for real-time monitoring of epileptic seizures in a clinical setting. © 2013 Gao and Hu.

Gao J.,PMB Intelligence LLC | Hu J.,Affymetrix | Tung W.-W.,Purdue University
Cognitive Neurodynamics | Year: 2011

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. © Springer Science+Business Media B.V. 2011.

Gao J.,PMB Intelligence LLC | Gao J.,Wright State University | Hu J.,Affymetrix | Mao X.,University of Florida | Perc M.,University of Maribor
Journal of the Royal Society Interface | Year: 2012

Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here, we make use of these data by investigating fluctuations in yearly usage frequencies of specific words that describe social and natural phenomena, as derived from books that were published over the course of the past two centuries. We show that the determination of the Hurst parameter by means of fractal analysis provides fundamental insights into the nature of long-range correlations contained in the culturomic trajectories, and by doing so offers new interpretations as to what might be the main driving forces behind the examined phenomena. Quite remarkably, we find that social and natural phenomena are governed by fundamentally different processes. While natural phenomena have properties that are typical for processes with persistent long-range correlations, social phenomena are better described as non-stationary, on-off intermittent or Lévy walk processes. © 2012 The Royal Society.

Tung W.-W.,Purdue University | Gao J.,PMB Intelligence LLC | Hu J.,Affymetrix | Yang L.,University of Florida
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

Detecting chaos and estimating the limit of prediction time in heavy-noise environments is an important and challenging task in many areas of science and engineering. An important first step toward this goal is to reduce noise in the signals. Two major types of methods for reducing noise in chaotic signals are chaos-based approaches and wavelet shrinkage. When noise is strong, chaos-based approaches are not very effective, due to failure to accurately approximate the local chaotic dynamics. Here, we propose a nonlinear adaptive algorithm to recover continuous-time chaotic signals in heavy-noise environments. We show that it is more effective than both chaos-based approaches and wavelet shrinkage. Furthermore, we apply our algorithm to study two important issues in geophysics. One is whether chaos exists in river flow dynamics. The other is the limit of prediction time for the Madden-Julian oscillation (MJO), which is one of the most dominant modes of low-frequency variability in the tropical troposphere and affects a wide range of weather and climate systems. Using the adaptive filter, we show that river flow dynamics can indeed be chaotic. We also show that the MJO is weakly chaotic with the prediction time around 50 days, which is considerably longer than the prediction times determined by other approaches. © 2011 American Physical Society.

Gao J.,PMB Intelligence LLC | Sultan H.,University of Florida | Hu J.,Affymetrix | Tung W.-W.,Purdue University
IEEE Signal Processing Letters | Year: 2010

Time series measured in real world is often nonlinear, even chaotic. To effectively extract desired information from measured time series, it is important to preprocess data to reduce noise. In this Letter, we propose an adaptive denoising algorithm. Using chaotic Lorenz data and calculating root-mean-square-error, Lyapunov exponent, and correlation dimension, we show that our adaptive algorithm more effectively reduces noise in the chaotic Lorenz system than wavelet denoising with three different thresholding choices. We further analyze an electroencephalogram (EEG) signal in sleep apnea and show that the adaptive algorithm again more effectively reduces the Electrocardiogram (ECG) and other types of noise contaminated in EEG than wavelet approaches. © 2009 IEEE.

Kuznetsov N.,University of Cincinnati | Bonnette S.,University of Cincinnati | Gao J.,PMB Intelligence LLC | Gao J.,Xi'an University of Science and Technology | Riley M.A.,University of Cincinnati
Annals of Biomedical Engineering | Year: 2013

Fractal time series analysis methods are commonly used for analyzing center of pressure (COP) signals with the goal of revealing the underlying neuromuscular processes for upright stance control. The use of fractal methods is often coupled with the assumption that the COP is an instance of fractional Gaussian noise (fGn) or fractional Brownian motion (fBm). Our purpose was to evaluate the applicability of the fGn-fBm framework to the COP in light of several characteristics of COP signals revealed by a new method, adaptive fractal analysis (AFA). AFA quantifies how the variance of the residuals to fits of a globally smooth trend signal scales with the time scale at which the fits are performed. Application of AFA to COP signals revealed that there are potentially three fractal scaling regions in the COP as opposed to one as expected from a pure fGn or fBm process. The scaling region at the fastest scale was anti-persistent and spanned ~30-90 ms, the intermediate was persistent and spanned ~200 ms-1.9 s, and the slowest was anti-persistent and spanned ~5-40 s. The intermediate fractal scaling region was the most clearly defined, but it only contributed around 11% of the total spectral energy of the COP signal, indicating that other features of the COP signal contribute more importantly to the overall dynamics. Also, more than half of the Hurst exponents estimated for the intermediate region were greater than the theoretically expected range [0,1] for fGn-fBm processes. These results suggest the fGn-fBm framework is not appropriate for modeling COP signals. ON-OFF intermittency might provide a better modeling framework for the COP, and multiscale approaches may be more appropriate for analyzing COP data. © 2012 Biomedical Engineering Society.

Gao J.,PMB Intelligence LLC | Gao J.,Wright State University | Hu J.,Affymetrix | Tung W.-W.,Purdue University
PLoS ONE | Year: 2011

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. © 2011 Gao et al.

Zhu H.B.,Ningbo University | Gao J.B.,Guangxi University | Gao J.B.,PMB Intelligence LLC
Physica A: Statistical Mechanics and its Applications | Year: 2014

The fractal behavior of traffic flow is studied by the adaptive fractal analysis method on the basis of the vehicle headway time series, which are obtained from the numerical simulation of the NaSch model. We find that the vehicle headway time series has a fractal behavior that is similar to the standard Brownian motion (BM) over a wide range of scales when the density is low. As the density increases well-defined sharp spectral peaks, corresponding to the stop-and-go waves, appear while the scale range showing BM-like behavior rapidly shrinks. In the high density regime, a new type of fractal behavior with long-range correlations appears, accompanying the worsening of traffic congestions. The underlying dynamics of traffic flow is analyzed, and some meaningful results are obtained. © 2013 Elsevier B.V. All rights reserved.

Gao J.,PMB Intelligence LLC | Gao J.,Wright State University | Hu J.,Affymetrix | Tung W.-W.,Purdue University
Nonlinear Dynamics | Year: 2012

Entropies are among the most popular and promising complexity measures for biological signal analyses. Various types of entropy measures exist, including Shannon entropy, Kolmogorov entropy, approximate entropy (ApEn), sample entropy (SampEn), multiscale entropy (MSE), and so on. A fundamental question is which entropy should be chosen for a specific biological application. To solve this issue, we focus on scaling laws of different entropy measures and introduce an ensemble forecasting framework to find the connections among them. One critical component of the ensemble forecasting framework is the scaledependent Lyapunov exponent (SDLE), whose scaling behavior is found to be the richest among all the entropy measures. In fact, SDLE contains all the essential information of other entropy measures, and can act as a unifying multiscale complexity measure. Furthermore, SDLE has a unique scale separation property to aptly deal with nonstationarity and characterize highdimensional and intermittent chaos. Therefore, SDLE can often be the first choice for exploratory studies in biology. The effectiveness of SDLE and the ensemble forecasting framework is illustrated by considering epileptic seizure detection from EEG. © Springer Science+Business Media B.V. 2011.

Bowers M.C.,Purdue University | Tung W.W.,Purdue University | Gao J.B.,Wright State University | Gao J.B.,PMB Intelligence LLC
Water Resources Research | Year: 2012

Distributional analysis of river discharge time series is an important task in many areas of hydrological engineering, including optimal design of water storage and drainage networks, management of extreme events, risk assessment for water supply, and environmental flow management, among many others. Having diverging moments, heavy-tailed power law distributions have attracted widespread attention, especially for the modeling of the likelihood of extreme events such as floods and droughts. However, straightforward distributional analysis does not connect well with the complicated dynamics of river flows, including fractal and multifractal behavior, chaos-like dynamics, and seasonality. To better reflect river flow dynamics, we propose to carry out distributional analysis of river flow time series according to three "flow seasons": dry, wet, and transitional. We present a concrete statistical procedure to partition river flow data into three such seasons and fit data in these seasons using two types of distributions, power law and lognormal. The latter distribution is a salient property of the cascade multiplicative multifractal model, which is among the best models for turbulence and rainfall. We show that while both power law and lognormal distributions are relevant to dry seasons, river flow data in wet seasons are typically better fitted by lognormal distributions than by power law distributions. © 2012. American Geophysical Union.

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