Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime,...Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime, a nonlinear method is proposed based on the higher order statistics, on the other aspect, which characterizes the higher order singular spectrum (HOSS) of chaotic signals. All computations are done with Lorenz attractor, Rossler attractor and EEG(electroencephalogram) time series and the comparisions among these results are made. The experimental results show that the Lipschitz exponents and the higher order singular spectra of these signals are significantly different from each other, which indicates these methods are effective for studing the singularity of chaotic signals.展开更多
In order to explore the correlation between the adjacent segments of a long term EEG, an improved principal component analysis(PCA) method based on mutual information algorithm is proposed. A one-dimension EEG time se...In order to explore the correlation between the adjacent segments of a long term EEG, an improved principal component analysis(PCA) method based on mutual information algorithm is proposed. A one-dimension EEG time series is divided equally into many segments, so that each segment can be regarded as an independent variables and multi-segmented EEG can be expressed as a data matrix. Then, we substitute mutual information matrix for covariance matrix in PCA and conduct the relevance analysis of segmented EEG. The experimental results show that the contribution rate of first principal component(FPC) of segmented EEG is more larger than others, which can effectively reflect the difference of epileptic EEG and normal EEG with the change of segment number. In addition, the evolution of FPC conduce to identify the time-segment locations of abnormal dynamic processes of brain activities,these conclusions are helpful for the clinical analysis of EEG.展开更多
In light of the nanostructured surface model, where half-spherical nanoparticles grow out symmetrically from a plane metallic film, the mathematical model for the partial electrical potential around nanospheres is dev...In light of the nanostructured surface model, where half-spherical nanoparticles grow out symmetrically from a plane metallic film, the mathematical model for the partial electrical potential around nanospheres is developed when a uniform external electric field is applied. On the basis of these models, the three-dimensional spatial distribution of the partial electrical potential is obtained and given in the form of a curved surface using a numerical computation method. Our results show that the electrical potential distribution around the nanospheres exhibits an obvious geometrical symmetry. These results could serve as a reference for investigating many abnormal phenomena such as abnormal infrared effects, which are found when CO molecules are adsorbed on the surface of nanostructured transition metals.展开更多
Based on the time-delayed embedding method of phase space reconstruction, a new method to compute the approximate entropy(ApEn) of electroencephalogram (EEG) is proposed. The computational results show that there are ...Based on the time-delayed embedding method of phase space reconstruction, a new method to compute the approximate entropy(ApEn) of electroencephalogram (EEG) is proposed. The computational results show that there are significant differences between epileptic EEG and normal EEG in the approximate entropy with the variance of embedding dimension. This conclusion is helpful to analyze the dynamical behavior of different EEGs by entropy.展开更多
Based on discrete wavelet transform, both relative wavelet energy (RWE) and segment wavelet entropy (SWE) of electroencephalogram (EEG) are defined in this paper. The RWE provides quantitatively the information about ...Based on discrete wavelet transform, both relative wavelet energy (RWE) and segment wavelet entropy (SWE) of electroencephalogram (EEG) are defined in this paper. The RWE provides quantitatively the information about the relative energy associated with different frequency bands present in the EEG. The SWE carries information about the degree of order or disorder associated with different time segment of EEG evolution, which can determine the time-segment localizations of abnormal dynamic processes of brain activity due to the localization characteristics of the wavelet transform. The experimental results show that the RWE and SWE are different between epileptic EEGs and normal EEGs, which demonstrate that the RWE and the SWE are helpful to analyze the dynamic behavior of different EEGs.展开更多
A novel method for detecting the hidden periodicities in EEG is proposed. By using a width-varying window in the time domain, the structure function of EEG time series is defined. It is found that the minima of the st...A novel method for detecting the hidden periodicities in EEG is proposed. By using a width-varying window in the time domain, the structure function of EEG time series is defined. It is found that the minima of the structure function, within a finite window width, can be found regularly, which indicate that there are some certain periodicities associated with EEG time series. Based on the structure function, a further quadratic structure function of EEG time series is defined. By quadratic structure function, it can be seen that the periodicities of EEG become more obvious, moreover, the period of EEG can be determined accurately. These results will be meaningful for studying the neuron activity inside the human brain.展开更多
To effectively suppress white noise and preserve more useful components of electrocardiogram(ECG) signal, a novel de-noising method based on morphological component analysis(MCA) is proposed. MCA is a method which all...To effectively suppress white noise and preserve more useful components of electrocardiogram(ECG) signal, a novel de-noising method based on morphological component analysis(MCA) is proposed. MCA is a method which allows us to separate features contained in an original signal when these features present different morphological aspects. According to the features of ECG, we used the UWT dictionary to sparsely represent mutated component, and used the DCT dictionary to sparsely represent smooth component. The experimental results of the samples choosing from MIT-BIH databases show that the MCA-based method is effective for white noise removal.展开更多
A new wavelet variance analysis method based on window function is proposed to investigate the dynamical features of electroencephalogram(EEG).The exprienmental results show that the wavelet energy of epileptic EEGs a...A new wavelet variance analysis method based on window function is proposed to investigate the dynamical features of electroencephalogram(EEG).The exprienmental results show that the wavelet energy of epileptic EEGs are more discrete than normal EEGs, and the variation of wavelet variance is different between epileptic and normal EEGs with the increase of time-window width. Furthermore, it is found that the wavelet subband entropy (WSE) of the epileptic EEGs are lower than the normal EEGs.展开更多
基金Science Foundation of Educational Commission of Fujian Province of China (Grant NO:JAO04238)
文摘Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime, a nonlinear method is proposed based on the higher order statistics, on the other aspect, which characterizes the higher order singular spectrum (HOSS) of chaotic signals. All computations are done with Lorenz attractor, Rossler attractor and EEG(electroencephalogram) time series and the comparisions among these results are made. The experimental results show that the Lipschitz exponents and the higher order singular spectra of these signals are significantly different from each other, which indicates these methods are effective for studing the singularity of chaotic signals.
基金Natural Science Foundatoin of Fujian Province of Chinagrant number:2010J01210,2012J01280
文摘In order to explore the correlation between the adjacent segments of a long term EEG, an improved principal component analysis(PCA) method based on mutual information algorithm is proposed. A one-dimension EEG time series is divided equally into many segments, so that each segment can be regarded as an independent variables and multi-segmented EEG can be expressed as a data matrix. Then, we substitute mutual information matrix for covariance matrix in PCA and conduct the relevance analysis of segmented EEG. The experimental results show that the contribution rate of first principal component(FPC) of segmented EEG is more larger than others, which can effectively reflect the difference of epileptic EEG and normal EEG with the change of segment number. In addition, the evolution of FPC conduce to identify the time-segment locations of abnormal dynamic processes of brain activities,these conclusions are helpful for the clinical analysis of EEG.
基金Project supported by the Natural Science Foundation of Fujian Province,China(Grant No.2010J01210)
文摘In light of the nanostructured surface model, where half-spherical nanoparticles grow out symmetrically from a plane metallic film, the mathematical model for the partial electrical potential around nanospheres is developed when a uniform external electric field is applied. On the basis of these models, the three-dimensional spatial distribution of the partial electrical potential is obtained and given in the form of a curved surface using a numerical computation method. Our results show that the electrical potential distribution around the nanospheres exhibits an obvious geometrical symmetry. These results could serve as a reference for investigating many abnormal phenomena such as abnormal infrared effects, which are found when CO molecules are adsorbed on the surface of nanostructured transition metals.
基金Natural Science Foundation of Fujian Province of China grant number: 2010J01210 and T0750008
文摘Based on the time-delayed embedding method of phase space reconstruction, a new method to compute the approximate entropy(ApEn) of electroencephalogram (EEG) is proposed. The computational results show that there are significant differences between epileptic EEG and normal EEG in the approximate entropy with the variance of embedding dimension. This conclusion is helpful to analyze the dynamical behavior of different EEGs by entropy.
基金GNatural Science Foundatoin of Fujian Province of China grant number: 2010J01210 and T0750008
文摘Based on discrete wavelet transform, both relative wavelet energy (RWE) and segment wavelet entropy (SWE) of electroencephalogram (EEG) are defined in this paper. The RWE provides quantitatively the information about the relative energy associated with different frequency bands present in the EEG. The SWE carries information about the degree of order or disorder associated with different time segment of EEG evolution, which can determine the time-segment localizations of abnormal dynamic processes of brain activity due to the localization characteristics of the wavelet transform. The experimental results show that the RWE and SWE are different between epileptic EEGs and normal EEGs, which demonstrate that the RWE and the SWE are helpful to analyze the dynamic behavior of different EEGs.
基金Natural Science Foundation of Fujian Province of ChinaGrant number:C0710036,T0750008,E0610023
文摘A novel method for detecting the hidden periodicities in EEG is proposed. By using a width-varying window in the time domain, the structure function of EEG time series is defined. It is found that the minima of the structure function, within a finite window width, can be found regularly, which indicate that there are some certain periodicities associated with EEG time series. Based on the structure function, a further quadratic structure function of EEG time series is defined. By quadratic structure function, it can be seen that the periodicities of EEG become more obvious, moreover, the period of EEG can be determined accurately. These results will be meaningful for studying the neuron activity inside the human brain.
基金Natural Science Foundatoin of Fujian Province of Chinagrant number:2012J01280
文摘To effectively suppress white noise and preserve more useful components of electrocardiogram(ECG) signal, a novel de-noising method based on morphological component analysis(MCA) is proposed. MCA is a method which allows us to separate features contained in an original signal when these features present different morphological aspects. According to the features of ECG, we used the UWT dictionary to sparsely represent mutated component, and used the DCT dictionary to sparsely represent smooth component. The experimental results of the samples choosing from MIT-BIH databases show that the MCA-based method is effective for white noise removal.
基金Natural Science Foundatoin of Fujian Province of Chinagrant number:2012J01280
文摘A new wavelet variance analysis method based on window function is proposed to investigate the dynamical features of electroencephalogram(EEG).The exprienmental results show that the wavelet energy of epileptic EEGs are more discrete than normal EEGs, and the variation of wavelet variance is different between epileptic and normal EEGs with the increase of time-window width. Furthermore, it is found that the wavelet subband entropy (WSE) of the epileptic EEGs are lower than the normal EEGs.
