We calculate the multifractal spectra of heartbeat RR-interval time series (tachograms) of healthy subjects and patients with congestive heart failure (CHF). From these time series, we obtained new subseries of 6 h durations when healthy persons and patients were asleep and awake respectively. For each time series and subseries, we worked out the multifractal spectra with the Chhabra and Jensen method and found that their graphs have different shapes for CHF patients and healthy persons. We suggest to measure two parameters: the curvature around the maximum and the symmetry for all these multifractal spectra graphs, because these parameters were different for healthy and CHF subjects. Multifractal spectra of healthy subjects tend to be right skewed especially when the subjects are asleep and the curvature around the maximum is small compared with the curvature around the maximum of the CHF multifractal spectra; that is, the spectra of patients tend to be more pointed around the maximum. In CHF patients, we also have encountered differences in the curvature of the multifractal spectra depending on their respective New York Heart Association (NYHA) index.

The Olami, Feder and Christensen (OFC) spring-block model has proven to be a powerful tool for analyzing and comparing synthetic and real earthquakes. This work proposes the possible reproduction of Utsu’s law for earthquakes in the OFC model. Based on our previous works, several simulations characterizing real seismic regions were performed. We located the maximum earthquake in these regions and applied Utsu’s formulae to identify a possible aftershock area and made comparisons between synthetic and real earthquakes. The research compares several equations to calculate the aftershock area and proposes a new one with the available data. Subsequently, the team performed new simulations and chose a mainshock to analyze the behavior of the surrounding events, so as to identify whether they could be catalogued as aftershocks and relate them to the aftershock area previously determined using the formula proposed. Additionally, the spatial location of those events was considered in order to classify them as aftershocks. Finally, we plot the epicenters of the mainshock, and the possible aftershocks comprised in the calculated area resembling the original work of Utsu. Having analyzed the results, it is likely to say that Utsu’s law is reproducible using a spring-block model with a self-organized criticality (SOC) model.

We did multifractal analysis of heartbeat interval time series of healthy persons and patients with congestive heart failure (CHF). To analyze circadian rhythm variations we analyzed time series of 24 hours records and segments of six hours when the subject is asleep and segments of six hours when is awake. A decrease in the multifractality degree occurs in the heartbeat interval time series of CHF patients. This multifractality loss is associated with the width reduction of the spectrum and the complexity loss of the signal. Multifractal spectra of healthy persons are right skewed, but the spectra of CHF patients tend to be symmetrical and in some cases are left skewed. To determine the therapy for CHF patients, cardiologists use an index proposed by the NYHA (New York Heart Association). There is a correlation between this index and the multifractal analysis parameters, i.e. while higher is the NYHA index the width of the multifractal spectrum is lower and it is also more symmetrical. In contrast, patients with NYHA index equal to 1 have multifractal parameters similar to those of healthy subjects.

Our study uses multifractal techniques to analyze time series of heart rate variability series (RR time series) during rest and physical activity. Subsets of the RR time series data were extracted for each stage. The multifractal spectra of the RR time series data were constructed using the method developed by Chhabra and Jensen. Then, parameters such as width, symmetry, and curvature of the multifractal spectra were calculated. The multifractal spectra obtained at resting stage were broad, skewed to the right, and they had small curvatures around in the maximum. On the contrary, the subsets of the RR time series obtained during physical activity were narrow, skewed to the left, and showed an increased curvature value around the maximum. In addition, these multifractal spectrum parameters shown significant differences in series of subjects who perform physical activity regularly and sedentary. Furthermore, the results obtained from this study were compared with data from previous works involving patients with congestive heart failure and healthy subjects.

The self-organized critical (SOC) spring-block models are accessible and powerful computational tools for the study of seismic subduction. This work aims to highlight some important findings through an integrative approach of several actual seismic properties, reproduced by using the Olami, Feder, and Christensen (OFC) SOC model and some variations of it. A few interesting updates are also included. These results encompass some properties of the power laws present in the model, such as the Gutenberg-Richter (GR) law, the correlation between the parameters a and b of the linear frequency-magnitude relationship, the stepped plots for cumulative seismicity, and the distribution of the recurrence times of large earthquakes. The spring-block model has been related to other relevant properties of seismic phenomena, such as the fractal distribution of fault sizes, and can be combined with the work of Aki, who established an interesting relationship between the fractal dimension and the b-value of the Gutenberg-Richter relationship. Also included is the work incorporating the idea of asperities, which allowed us to incorporate several inhomogeneous models in the spring-block automaton. Finally, the incorporation of a Ruff-Kanamori-type diagram for synthetic seismicity, which is in reasonable accordance with the original Ruff and Kanamori diagram for real seismicity, is discussed.

The use of the Visibility Graph Algorithm (VGA) has proven to be a valuable tool for analyzing both real and synthetic seismicity series. Specifically, VGA transforms time series into a network representation in which structural properties such as node connectivity, clustering, and community structure can be quantitatively measured, thereby revealing underlying correlations and dynamics that may remain hidden in traditional linear or spectral analyses. The time series transformation into complex networks with VGA provides a new approach to analyze seismic dynamics, allowing scientists to extract trends and behaviors that may not be possible by classical time-series analysis. On the other hand, many studies attempt to find viable trends in order to identify preparation mechanisms prior to a strong earthquake or to analyze the aftershocks. In this work, the seismic activity of Southern California Earthquake was analyzed focusing only on the significant earthquakes. For this purpose, seismic series preceding and following each earthquake were constructed using a windowing method with different overlaps and the slope of the connectivity (k) versus magnitude (M) graph (k-M slope) and the average degree were computed from the mapped complex networks. The results revealed a significant decrease in these parameters after the earthquake, due to the contribution of the aftershocks from the main event. Interestingly, the study was extended to synthetic seismicity series and the same behavior was observed for both k-M slope and average degree. This finding suggests that the spring-block model reproduces a relaxation mechanism following a large-magnitude event like those of real seismic aftershocks. However, this conclusion contrasts with conclusions drawn by other researchers. These results highlight the utility of VGA in studying events that precede and follow major earthquakes. This technique may be used to extract some useful trends in seismicity, which could eventually be employed for a deeper understanding and possible forecasting of seismic behavior.