$$p$$-Adic Fractal Strings of Arbitrary Rational Dimensions     and Cantor Strings

Lapidus, Michel L.; Lũ, Hùng; Frankenhuijsen, Machiel van

doi:10.1134/s2070046621030043

Cited by 4 publications

(2 citation statements)

References 34 publications

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“…Modeling in quantum mechanics used p-adic statistics [23]- [25] based on probabilistic calculations when the number of trials is infinitely large. Bernoulli's classical probabilities have been studied by [26].…”

Section: Introductionmentioning

confidence: 99%

Untitled

2023

SIPIJ

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The spectral density of stable signals with p-adic times is already estimated under various conditions. The estimate is made by constructing a periodogram that is subsequently smoothed by a spectral window. It is clear that the convergence rate of this estimator depends on the bandwidth of the spectral window (called the smoothing parameter). This work gives a method to select the smoothing parameter in an optimal way, i.e. the estimator converges to the spectral density with the bestrate.The method is inspired by the cross-validation method, which consists in minimizing the estimate of the integrated square error.

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Section: Introductionmentioning

confidence: 99%

Untitled

2023

SIPIJ

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“…The 2-adic number represents a special case useful for computer design see [22]. The quantum mechanical state has been modeled by using p-adic statistics [23]- [25] focusing on the probabilities when the number of trials is infinitely large. A new asymptotic of Bernoulli's classical probabilities has been demonstrated by [26].…”

Section: Introductionmentioning

confidence: 99%

Smoothing Parameter Selection and Alpha-Stable P-Adic Time Signals

Sabre¹,

Horrigue²

2023

Signal Image Processing and Multimedia

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The estimation of the spectral density of stable p-adic signals is already done. Such estimation is based on smoothing the periodogram by using a spectral window. The convergence rate of this estimator depends on bandwidth of spectral window (called the smoothing parameter). The aim of this work is to give a technique for selecting the optimal parameter, i.e. the parameter that achieves the estimation with the best convergence rate. For that purpose, we were inspired by the cross-validation method of finding the optimal parameter. This method minimizes the integrated square error estimate.

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