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Effect of Gaussian Noise Amplitude on Translation Error Estimated Using Double-wayland algorithm

Journal of Mathematics and System Science 2012年第8期2卷 482-488页

作者： Kazuki Yoshikawa Hiroki Takada Graduate School of Engineering University of Fukui

The wayland algorithm has been improved in order to evaluate the degree of visible determinism for dynamical systems that generate time series. The objective of this study is to show that the Double-wayland algorithm can distinguish between time series generated by a deterministic process and those generated by a stochastic process. The authors conducted numerical analysis of the van der Pol equation and a stochastic differential equation as a deterministic process and a Ganssian stochastic process, respectively. In case of large S/N ratios, the noise term did not affect the translation error derived from time series data, but affected that from the temporal differences of time series. In case of larger noise amplitudes, the translation error from the differences was calculated to be approximately 1 using the Double-wayland algorithm, and it did not vary in magnitude. Furthermore, the translation error derived from the differenced sequences was considered stable against noise. This novel algorithm was applied to the detection of anomalous signals in some fields of engineering, such as the analysis of railway systems and bio-signals.

关键词： Gaussian white noise wayland algorithm delay time embedding space degree of visible determinism translation error VPE (van der Pol equation) SDE (stochastic differential equation).

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Stochastic Resonance as a Mathematical Model of an Electrogastrogram

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Journal of Physical Science and Application 2012年第6期2卷 186-194页

作者： Matsuura Yasuyuki Miyao Masaru Takada Hiroki Headquarters for Innovative Society-Academia Cooperation University of Fukui Fukui 910-8507 Japan Graduate School of Information Science Nagoya University Nagoya 464-8603 Japan Graduate School of Engineering University of FukuL Fukui 910-8507 Japan

An electrogastrogram （EGG） is a recording of the electrical activity in the stomach, as measured on the abdominal surface. In this study, the goal is to obtain a mathematical model of an EGG; to achieve this, the EGG of 14 subjects （seven males and seven females） will be obtained. Initially, the wayland algorithm to the EGG to measure the degree of determinism is applied. However, it could not be determined whether the EGG could be generated by a chaotic process. In addition, the waveform of the electric potential in the interstitial cells of Cajal is similar to the graphs of the numerical solutions to the Van der Pol equation. Therefore, the Van der Pol equation to a periodic function was added, and random white noise was used to represent the intestinal motility and other biosignals. The EGG and numerical solutions were compared and evaluated on the basis of the translation error （Etrans） in the wayland algorithm and the maximum Lyapunov exponent （2） in Rosenstein＇s algorithm. By projecting the data from an obtained stationary EGG from the subjects, along with the numerical solutions, onto the Etrans-λ plane, the affinity between them was qualitatively evaluated. The EGG was well described by stochastic resonance from the stochastic differential equations.

关键词： Electrogastrography numerical solution wayland algorithm maximum Lyapunov exponent stochastic resonance.

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