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A review on HilbertHuang transform: Method and its applications to geophysical studies
 Rev. Geophys
"... [1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the an ..."
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[1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. HilbertHuang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.
Data Dimensionality Estimation Methods: A Survey
 Pattern Recognition
, 2003
"... In this paper, data dimensionality estimation methods are reviewed. The estimation of the dimensionality of a data set is a classical problem of pattern recognition. There are some good reviews [1] in literature but they do not include more recent developments based on fractal techniques and neural ..."
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Cited by 38 (1 self)
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In this paper, data dimensionality estimation methods are reviewed. The estimation of the dimensionality of a data set is a classical problem of pattern recognition. There are some good reviews [1] in literature but they do not include more recent developments based on fractal techniques and neural autoassociators. The aim of this paper is to provide an uptodate survey of the dimensionality estimation methods of a data set, paying special attention to the fractalbased methods.
Analyzing multiple nonlinear time series with extended Granger causality
, 2004
"... Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such relations. In this work we consider nonlinear extensions of G ..."
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Cited by 35 (3 self)
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Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such relations. In this work we consider nonlinear extensions of Granger's idea and refer to the result as extended Granger causality. A simple approach implementing the extended Granger causality is presented and applied to multiple chaotic time series and other types of nonlinear signals. In addition, for situations with three or more time series we propose a conditional extended Granger causality measure that enables us to determine whether the causal relation between two signals is direct or mediated by another process.
a practical approach
, 1991
"... This work is brought to you for free and open access by FIU Digital Commons. It has been accepted for inclusion in Hospitality Review by an ..."
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Cited by 34 (1 self)
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This work is brought to you for free and open access by FIU Digital Commons. It has been accepted for inclusion in Hospitality Review by an
Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection
, 2007
"... Background: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wideranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased “breathiness”. Modelling and surrogat ..."
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Background: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wideranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased “breathiness”. Modelling and surrogate data studies have shown significant nonlinear and nonGaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and nonGaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, nonGaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness. Methods: This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a “hoarseness ” diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices. 1
Spatiotemporal chaos and vacuum fluctuations of quantized fields, World Scientific
, 2002
"... We consider deterministic chaotic models of vacuum fluctuations on a small (quantum gravity) scale. As a suitable smallscale dynamics, nonlinear versions of strings, socalled ‘chaotic strings ’ are introduced. These can be used to provide the ‘noise ’ for second quantization of ordinary strings vi ..."
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Cited by 30 (15 self)
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We consider deterministic chaotic models of vacuum fluctuations on a small (quantum gravity) scale. As a suitable smallscale dynamics, nonlinear versions of strings, socalled ‘chaotic strings ’ are introduced. These can be used to provide the ‘noise ’ for second quantization of ordinary strings via the ParisiWu approach of stochastic quantization. Extensive numerical evidence is presented that the vacuum energy of chaotic strings is minimized for the numerical values of the observed standard model parameters, i.e. in this extended approach to second quantization concrete predictions for vacuum expectations of dilatonlike fields and hence on masses and coupling constants can be given. Lowenergy fermion and boson masses are correctly obtained with a precison of 34 digits, the electroweak and strong coupling strengths with a precison of 45 digits. In particular, the minima of the vacuum energy yield highprecision predictions of the Higgs mass (154 GeV), of the neutrino masses (1.45 · 10 −5 eV, 2.57 ·10 −3 eV, 4.92 ·10 −2 eV) and of the GUT scale (1.73 ·10 16 GeV).The following text is preface, introduction, (detailed) summary, and bibliography
SchulzeBonhage A. How well can epileptic seizures be predicted? An evaluation of a nonlinear method
"... The unpredictability of the occurrence of epileptic seizures contributes to the burden of the disease to a major degree. Thus, various methods have been proposed to predict the onset of seizures based on EEG recordings. A nonlinear feature motivated by the correlation dimension is a seemingly promi ..."
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The unpredictability of the occurrence of epileptic seizures contributes to the burden of the disease to a major degree. Thus, various methods have been proposed to predict the onset of seizures based on EEG recordings. A nonlinear feature motivated by the correlation dimension is a seemingly promising approach. In a previous study this method was reported to identify `preictal dimension drops ' up to 19 min before seizure onset, exceeding the variability of interictal data sets of 30±50 min duration. Here we have investigated the sensitivity and speci®city of this method based on invasive longterm recordings from 21 patients with medically intractable partial epilepsies, who underwent invasive presurgical monitoring. The evaluation of interictal 24h recordings comprising the sleep±wake cycle showed that only one out of 88 seizures was preceded by a signi®cant preictal dimension drop. In a second analysis, the relation between dimension drops within time windows of up to 50 min before seizure onset and interictal periods was investigated. For falseprediction rates below 0.1/h, the sensitivity ranged from 8.3 to 38.3% depending on the prediction window length. Overall, the mean length and amplitude of dimension drops showed no signi®cant differences between interictal and preictal data sets.
Local dynamic stability versus kinematic variability of continuous overground and treadmill walking
 Journal of Biomechanical Engineering
, 2001
"... This study quantified the relationships between local dynamic stability and variability during continuous overground and treadmill walking. Stridetostride standard deviations were computed from temporal and kinematic data. Maximum finitetime Lyapunov exponents were estimated to quantify local dyn ..."
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This study quantified the relationships between local dynamic stability and variability during continuous overground and treadmill walking. Stridetostride standard deviations were computed from temporal and kinematic data. Maximum finitetime Lyapunov exponents were estimated to quantify local dynamic stability. Local stability of gait kinematics was shown to be achieved over multiple consecutive strides. Traditional measures of variability poorly predicted local stability. Treadmill walking was associated with significant changes in both variability and local stability. Thus, motorized treadmills may produce misleading or erroneous results in situations where changes in neuromuscular control are likely to affect the variability and/or stability of locomotion. �DOI: 10.1115/1.1336798� 1
Atomic norm denoising with applications to line spectral estimation ∗
, 2012
"... The subNyquist estimation of line spectra is a classical problem in signal processing, but currently popular subspacebased techniques have few guarantees in the presence of noise and rely on a priori knowledge about system model order. Motivated by recent work on atomic norms in inverse problems, ..."
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The subNyquist estimation of line spectra is a classical problem in signal processing, but currently popular subspacebased techniques have few guarantees in the presence of noise and rely on a priori knowledge about system model order. Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the meansquarederror performance in the presence of noise and without advance knowledge of the model order. We propose an abstract theory of denoising with atomic norms and specialize this theory to provide a convex optimization problem for estimating the frequencies and phases of a mixture of complex exponentials with guaranteed bounds on the meansquared error. We show that the associated convex optimization problem, called Atomic norm Soft Thresholding (AST), can be solved in polynomial time via semidefinite programming. For very large scale problems we provide an alternative, efficient algorithm, called Discretized Atomic norm Soft Thresholding (DAST), based on the Fast Fourier Transform that achieves nearly the same error rate as that guaranteed by the semidefinite programming approach. We compare both AST and DAST with Cadzow’s canonical alternating projection algorithm and demonstrate that AST outperforms DAST which outperforms Cadzow in terms of meansquare reconstruction error over a wide range of signaltonoise ratios. For very large problems DAST is considerably faster than both AST and Cadzow. 1