**4. Conclusions**

The scaling features of long-range power-law correlations are important markers of the complex dynamics of many real-world systems that can be used to diagnose the state of a system based on experimentally measured datasets. We have discussed a modified approach to the fluctuation analysis of inhomogeneous processes, in which the nonstationarity varies over the entire signal. This approach, EDFA, computes two scaling exponents that quantify power-law correlations and nonstationarity features. To provide a more stable computational procedure and reduce the impact of localized artifacts, we consider the standard deviation of the local RMS fluctuations of the signal profile around the trend, rather than the difference of extreme values. The benefits of the latter procedure are illustrated using simulated datasets.

We then applied this approach to EEG signals in mice to reveal signs of changes in electrical activity of the brain that could be caused by a day's sleep deprivation. These signs can be fairly subtle, in contrast to the effects of prolonged SD, taking into account the significant variability of characteristics during long-term EEG recordings. Using a group of 10 mice, we found quite strong reductions in *α* and *β* scaling exponents in six animals, with only one mouse showing a pronounced opposite effect. In these animals, the *β* exponent provided stronger responses than the *α* exponent of the conventional DFA. Thus, the proposed modified version of the method can be a useful prognostic tool for the evaluation of SD-mediated suppression of the clearance of toxins from the brain that is in accordance with the work [1]. Important open questions that could be further analyzed are the role of SD duration and the factor of age.

**Author Contributions:** Conceptualization, A.N.P. and O.V.S.-G.; methodology, A.N.P.; data curation, A.I.D.; software, O.N.P.; formal analysis, A.I.D., O.N.P.; investigation, A.N.P., O.N.P.; writing original draft preparation, A.N.P. and O.V.S.-G.; writing—review and editing, A.N.P. and O.V.S.-G.; visualization, A.N.P.; supervision, A.N.P. and O.V.S.-G.; project administration, O.V.S.-G.; funding acquisition, O.V.S.-G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the grant of the Government of the Russian Federation No. 075-15-2019-1885 in the part of experimental studies and numerical analysis. A.P. acknowledges the support by the grant of the Russian Science Foundation (Agreement 19-12-00037) in the part of theoretical studies (the development of EDFA method).

**Institutional Review Board Statement:** The study was carried out in accordance with the Guide for the Care and Use of Laboratory Animals (8th ed., The National Academies Press, Washington, 2011), and approved by the Local Bioethics Commission of the Saratov State University (protocol No. 12, 17.02.2020).

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Abbreviations**

The following abbreviations are used in this manuscript:

