In this paper we analyzed, by the F_DFA root mean square fluctuation (rms) function, the motor/imaginary human activity produced by a 64-channel electroencephalography (EEG). We utilized the Physionet on-line databank, a publicly available database of human EEG signals, as a standardized reference database for this study. Herein, we report the use of detrended fluctuation analysis (DFA) method for EEG analysis. We show that the complex time series of the EEG exhibits characteristic fluctuations depending on the analyzed channel in the scalp-recorded EEG. In order to demonstrate the effectiveness of the proposed technique, we analyzed four distinct channels represented here by F₃32, F₆37 (frontal region of the head) and P₃49, P₆54 (parietal region of the head). We verified that the amplitude of the F_DFA rms function is greater for the frontal channels than for the parietal. To tabulate this information in a better way, we define and calculate the difference between F_DFA (in log scale) for the channels, thus defining a new path for analysis of EEG signals. Finally, related to the studied EEG signals, we obtain the auto-correlation exponent, α_DFA by DFA method, that reveals self-affinity at specific time scale. Our results shows that this strategy can be applied to study the human brain activity in EEG processing.

Climate change is one of the most relevant challenges that the world has to deal with. Studies that aim to understand the behavior of environmental and atmospheric variables and the way they relate to each other can provide helpful insights into how the climate is changing. However, such studies are complex and rarely found in the literature, especially in dealing with data from the Brazilian territory. In this paper, we analyze four environmental and atmospheric variables, namely, wind speed, radiation, temperature, and humidity, measured in 27 Weather Stations (the capital of each of the 26 Brazilian states plus the federal district). We use the detrended fluctuation analysis to evaluate the statistical self-affinity of the time series, as well as the cross-correlation coefficient ρ_DCCA to quantify the long-range cross-correlation between stations, and a network analysis that considers the top 10% ρ_DCCA values to represent the cross-correlations between stations better. The methodology used in this paper represents a step forward in the field of hybrid methodologies, combining time series and network analysis that can be applied to other regions, other environmental variables, and also to other fields of research. The application results are of great importance to better understand the behavior of environmental and atmospheric variables in the Brazilian territory and to provide helpful insights about climate change and renewable energy production.

The control of Levodopa (L-dopa) in Parkinson’s patients receiving chronic deep brain electrical stimulation (with an implant of an electrode into sub-cortical structures) will be studied here. Our main objective is to apply the Detrended Fluctuation Analysis (DFA) method and Shannon Entropy (H) in order to study the speed of tremor recorded in 16 patients with Parkinson’s disease. These Parkinson’s patients were divided into two groups (High Amplitude tremor and Low Amplitude tremor), and basically with two conditions of deep brain stimulation (on–off) and two conditions of L-dopa (on–off). These conditions (on–off) have a clear influence on the \(\alpha _{DFA}\) exponent and the Shannon Entropy respectively. In this sense, the auto-correlation exponent gives us information whether or not there is persistence in the signal produced by the Parkinsonian rest tremor, mainly differentiating those in Low and High Amplitude, or even identifying behavior change with a typical time scale. However, the Shannon Entropy gives us information about the uncertainty in the position of Parkinsonian rest tremor. In this way, a high value of H informs us that we have a high uncertainty in the signal of this tremor. Therefore, by combining these two techniques we have a better view of the (signal/noise) effects of deep brain stimulation and L-dopa (medication) in all patients with Parkinson’s disease, and thus helping to make a better analysis of this health problem, and with the possibility of supplementation in the Unified Parkinson’s Disease Rating Scale and Tremor Rating Scale, identifying fluctuation patterns on different time scales, the nature of the tremor, and its evolution over time.