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Fractal analysis of noise buried time series signals with applications to exoplanet spectroscopy and bio-data

机译:噪声掩埋时间序列信号的分形分析及其在系外行星光谱和生物数据中的应用

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The shape of an exoplanet lightcurve is usually obtained by averaging the noise over multiple datasets. Fractal analysis has been demonstrated to be an effective tool for the detection of exoplanet transits using lightcurves summed over all wavelengths sensitive to the detector (G. Tremberger, Jr et. Al, 2006 Proc SPIE Vol 6265). The detection of spectral features would depend on the extent to which the signal was buried in the noise. Different noise sources would have different fractal characteristics. Also, the signal strength could be discontinuous in time depending on the exoplanet's local atmospheric environment. Such a discontinuity is unlikely to be detected with time integrated data. The lightcurve noise and shape information were characterized with fractal dimension analysis of a noise buried time series signal. Computer simulation revealed that when the noise is three times that of the signal, the fractal algorithm could detect the signal at about the 87% confidence level. Application to noise buried time series datasets (HD 209458b lightcurve, HD 149026b lightcurve) detected discontinuities consistent with the results obtained by averaging datasets. Extension to individual wavelength lightcurves would establish a detection limit for the existence of spectral features at wavelengths important for exoplanet study. Other applications such as pre-implantation genetic screening spectroscopy and spatially varied aneuploidy bio-data could use the same analysis principle as well.
机译:通常通过对多个数据集的噪声求平均来获得系外行星光曲线的形状。分形分析已被证明是使用对探测器灵敏的所有波长求和的光曲线来探测系外行星跃迁的有效工具(G. Tremberger,Jr等人,2006 Proc SPIE Vol 6265)。频谱特征的检测将取决于信号被掩埋在噪声中的程度。不同的噪声源将具有不同的分形特性。同样,信号强度在时间上可能会不连续,这取决于系外行星的当地大气环境。用时间积分数据不太可能检测到这种不连续性。通过对噪声掩埋时间序列信号的分形维数分析来表征光曲线的噪声和形状信息。计算机仿真表明,当噪声是信号的三倍时,分形算法可以在大约87%的置信度下检测到信号。将其应用于噪声掩埋时间序列数据集(HD 209458b光曲线,HD 149026b光曲线)时,发现的不连续性与通过对数据集求平均值所得的结果一致。扩展到单个波长的光曲线将为对系外行星研究重要的波长处的光谱特征的存在建立检测极限。其他应用,例如植入前基因筛选光谱学和空间变化的非整倍性生物数据,也可以使用相同的分析原理。

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