Dynamical behavior of combined detrended cross-correlation analysis methods in random walks and Lévy flights

Min, Seungsik; Shin, Kihong; Baek, Woonhak; Kim, Kyungsik; You, Cheol‐Hwan; Lee, Dong In; Yum, Seong Soo; Kim, Wonheung; Chang, Kae-Sun

doi:10.1016/j.physa.2019.122872

Cited by 3 publications

(1 citation statement)

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“…2d-f. The first PDF is the LF distribution [31]: Equation 1The other PDF is the normal distribution [32]: Equation 2LF and the normal distribution described random walks with different probability distributions. One of the unique properties of the LF model is its slightly larger distribution values in the far right region than the normal distribution has.…”

Section: Lf Fittingmentioning

confidence: 99%

Levy statistics define anxiety and depression in mice subjected to chronic stress

Li¹,

Nie

Zhang³

et al. 2023

Preprint

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Anxiety and depression are considered coping mechanisms organisms adopt in response to external stressors. We employed Levy statistics to investigate the movement patterns of rodent models subjected to stress and compared them to non-stressed controls. Our analysis revealed that stressed mice exhibited heavy-tailed distributions in open fields, consistent with the Levy flights utilized by animal predators in search of scarce food sources. In contrast, non-stressed mice demonstrated a normal distribution of speed. We used the two-dimensional Kolmogorov-Smirnov test to identify significant differences in the γ and μ parameters derived from Levy flight between anxiety, depression, and control mice. Additionally, we employed the support vector machine algorithm to determine the optimal separation of each group. Furthermore, our mathematical model demonstrated the therapeutic effects of fluoxetine. These findings have the potential to contribute to the development of more precise definitions of anxiety and depression, as well as facilitate the evaluation of pharmaceutical developments.

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Section: Lf Fittingmentioning

confidence: 99%