Fourier spectrum analysis of the new solar neutrino capture rate data for the Homestake experiment

Haubold, H. J.

doi:10.1016/s0375-9474(97)00268-6

Cited by 5 publications

(8 citation statements)

References 24 publications

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“…If such a variability over time would be discovered, for example, in the Borexino experiment, a mechanism for a chronometer for solar variability could be proposed based on relations between the properties of thermonuclear fusion and g-modes. All the above findings encouraged the conclusion that Fourier and wavelet analysis, which are based upon the analysis of the variance of the respective time series (standard deviation analysis (SDA)) [37,38], should be complemented by the utilization of diffusion entropy analysis (DEA), which measures the scaling of the probability density function (pdf) of the diffusion process generated by the time series, thought of as the physical source of fluctuations [39,40]. For this analysis, we have used the publicly available data of Super-Kamiokande I and Super-Kamiokande II (see Figure 2).…”

Section: Standard Deviation Analysis and Diffusion Entropy Analysismentioning

confidence: 76%

Analysis of Solar Neutrino Data from Super-Kamiokande I and II

Haubold

Mathai

Saxena

2014

Entropy

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Abstract:We are going back to the roots of the original solar neutrino problem: the analysis of data from solar neutrino experiments. The application of standard deviation analysis (SDA) and diffusion entropy analysis (DEA) to the Super-Kamiokande I and II data reveals that they represent a non-Gaussian signal. The Hurst exponent is different from the scaling exponent of the probability density function, and both the Hurst exponent and scaling exponent of the probability density function of the Super-Kamiokande data deviate considerably from the value of 0.5, which indicates that the statistics of the underlying phenomenon is anomalous. To develop a road to the possible interpretation of this finding, we utilize Mathai's pathway model and consider fractional reaction and fractional diffusion as possible explanations of the non-Gaussian content of the Super-Kamiokande data.

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Section: Standard Deviation Analysis and Diffusion Entropy Analysismentioning

confidence: 76%

Analysis of Solar Neutrino Data from Super-Kamiokande I and II

Haubold

Mathai

Saxena

2014

Entropy

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“…This tool performs a localized spectral decomposition of a time series by determining the dominant modes of variability, and how these modes change with time and scale (frequency) (Grossman and Morlet, 1984;Torrence and Compo, 1998). The CWT of a time series f(t) with a dilation a and a translation parameter (time shift) τ, with respect to a wavelet mother function ψ(z), is defined through the integral transform (Haubold, 1998) (1)…”

Section: A) the Continuous Wavelet Spectral Analysismentioning

confidence: 99%

“…Following Foster (1996b) and Haubold (1998), we start by proposing a straightforward, discretized version of (1), viz.…”

Section: B) the Weighted Wavelet Z-transform (Wwz)mentioning

confidence: 99%

“…The number r − 1 (= 2 in this case) describes the degrees of freedom of the power (which is chi-squared distributed), Neff is the effective number of data points, and Sω 2 is the weighted estimated variance of the time series. The last two are defined by Foster (1996b) as (13) (14) where ωα is given by (5) and V f , the weighted variation of the time series f(t), is computed via (15) Finally, the weighted wavelet transform (WWT) is defined by (16) where Vy, the weighted variation of the model function y(t), is calculated in a similar fashion as (15) through the expression (17) For fixed scale factor a and time shift τ, the WWT can be treated as a chi-square statistic with two degrees of freedom and expected value of one (Foster, 1996b;Haubold, 1998). It turns out, however, that the WWT in (16) still has a serious shortcoming: it is very sensitive to the effective number of data Neff, which leads to a shift of the WWT peaks to lower frequencies (at lower frequencies the window is wider, so that more data points can be sampled and Neff becomes larger).…”

Section: B) the Weighted Wavelet Z-transform (Wwz)mentioning

confidence: 99%

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Estimation of the significance of the Foster’s wavelet spectrum by means of a permutation test and its application for paleoclimate records

Polanco-Martínez¹,

Faria²

2018

Bol. geol. min.

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Here we propose a permutation test -a non-parametric computing-intensive test-to evaluate the statistical significance of the Foster's wavelet spectrum by means of Monte Carlo simulations. A procedure (algorithm) is introduced in order to carry out this aim. The Foster's wavelet is an adequate method to cope directly with unevenly spaced paleoclimatic time series. We have conducted time series simulations to study the performance of the Foster's wavelet spectrum and applied the permutation test to localize periodic signals known a priori by randomly increasing the fraction of missing data (from 25% to 75% of the total amount of data of an evenly spaced time series). We found that the periodic signals are progressively lost as larger amounts of data are removed. This loss becomes noticeable at circa 50% of the missing data and gets more evident when 75% of the data is removed. The signal loss is more pronounced in the high-frequency range, due to an intrinsic bias in the wavelet spectrum. Notwithstanding, the Foster's wavelet spectrum and the permutation test succeeded in locating the periodic signals, even with a moderate amount of missing data. Finally, we applied our procedure to the oxygen isotope ratio (δ 18 O) data of the GISP2 deep ice core (Greenland) and we were able to detect the main spectral signature of the unevenly spaced time series of the GISP2 δ 18 O record, i.e., the spectral peak around 1,470 years.

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“…It is developed specifically for unevenly sampled data in the context of observation of variable stars: here, the wavelet is rescaled to satisfy admissibility condition on such irregular sampling. One can for example read the paper of Haubold [12] for an interesting analysis of this method. In this paper, our results will also be compared with those obtained by the WWZ technique.…”

Section: Introductionmentioning

confidence: 99%

Time-Scale and Time-Frequency Analyses of Irregularly Sampled Astronomical Time Series

Thiebaut

Roques

2005

EURASIP J. Adv. Signal Process.

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We evaluate the quality of spectral restoration in the case of irregular sampled signals in astronomy. We study in details a time-scale method leading to a global wavelet spectrum comparable to the Fourier period, and a time-frequency matching pursuit allowing us to identify the frequencies and to control the error propagation. In both cases, the signals are first resampled with a linear interpolation. Both results are compared with those obtained using Lomb's periodogram and using the weighted wavelet -transform developed in astronomy for unevenly sampled variable stars observations. These approaches are applied to simulations and to light variations of four variable stars. This leads to the conclusion that the matching pursuit is more efficient for recovering the spectral contents of a pulsating star, even with a preliminary resampling. In particular, the results are almost independent of the quality of the initial irregular sampling.

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Fourier spectrum analysis of the new solar neutrino capture rate data for the Homestake experiment

Abstract: The paper provides results of the Fourier spectrum analysis of the new Ar-37 production rate data of the Homestake solar neutrino experiment and compares them with results for earlier data, revealing the harmonic content in the Ar-37 production in the Homestake experiment.

Cited by 5 publications

References 24 publications

Analysis of Solar Neutrino Data from Super-Kamiokande I and II

Analysis of Solar Neutrino Data from Super-Kamiokande I and II

Estimation of the significance of the Foster’s wavelet spectrum by means of a permutation test and its application for paleoclimate records

Time-Scale and Time-Frequency Analyses of Irregularly Sampled Astronomical Time Series

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