Approximate Entropy in Canonical and Non-Canonical Fiction

Unravelling COVID-19 waves in Rio de Janeiro city: Qualitative insights from nonlinear dynamic analysis

Since the COVID-19 pandemic was first reported in 2019, it has rapidly spread around the world. Many countries implemented several measures to try to control the virus spreading. The healthcare system and consequently the general quality of life population in the cities have all been significantly impacted by the Coronavirus pandemic. The different waves of contagious were responsible for the increase in the number of cases that, unfortunately, many times lead to death. In this paper, we aim to characterize the dynamics of the six waves of cases and deaths caused by COVID-19 in Rio de Janeiro city using techniques such as the Poincaré plot, approximate entropy, second-order difference plot, and central tendency measures. Our results reveal that by examining the structure and patterns of the time series, using a set of non-linear techniques we can gain a better understanding of the role of multiple waves of COVID-19, also, we can identify underlying dynamics of disease spreading and extract meaningful information about the dynamical behavior of epidemiological time series. Such findings can help to closely approximate the dynamics of virus spread and obtain a correlation between the different stages of the disease, allowing us to identify and categorize the stages due to different virus variants that are reflected in the time series.

Comparative Analysis of Preference in Contemporary and Earlier Texts Using Entropy Measures

Research in computational textual aesthetics has shown that there are textual correlates of preference in prose texts. The present study investigates whether textual correlates of preference vary across different time periods (contemporary texts versus texts from the 19th and early 20th centuries). Preference is operationalized in different ways for the two periods, in terms of canonization for the earlier texts, and through sales figures for the contemporary texts. As potential textual correlates of preference, we measure degrees of (un)predictability in the distributions of two types of low-level observables, parts of speech and sentence length. Specifically, we calculate two entropy measures, Shannon Entropy as a global measure of unpredictability, and Approximate Entropy as a local measure of surprise (unpredictability in a specific context). Preferred texts from both periods (contemporary bestsellers and canonical earlier texts) are characterized by higher degrees of unpredictability. However, unlike canonicity in the earlier texts, sales figures in contemporary texts are reflected in global (text-level) distributions only (as measured with Shannon Entropy), while surprise in local distributions (as measured with Approximate Entropy) does not have an additional discriminating effect. Our findings thus suggest that there are both time-invariant correlates of preference, and period-specific correlates.

Association of heartbeat complexity with survival in advanced non-small cell lung cancer patients

Background

Previous studies have shown that the predictive value of traditional linear (time domain and frequency domain) heart rate variability (HRV) for the survival of patients with advanced non-small cell lung cancer (NSCLC) is controversial. Nonlinear methods, based on the concept of complexity, have been used to evaluate HRV, providing a new means to reveal the physiological and pathological changes in HRV. This study aimed to assess the association between heartbeat complexity and overall survival in patients with advanced NSCLC.

Methods

This study included 78 patients with advanced NSCLC (mean age: 62.0 ± 9.3 years). A 5-min resting electrocardiogram of advanced NSCLC patients was collected to analyze the following HRV parameters: time domain indicators, i.e., standard deviation of the normal-normal intervals (SDNN) and root mean square of successive interval differences (RMSSD); frequency domain indicators, i.e., total power (TP), low frequency power (LF), high frequency power (HF), and the ratio of LF to HF (LF/HF); nonlinear HRV indicators characterizing heartbeat complexity, i.e., approximate entropy (ApEn), sample entropy (SampEn), and recurrence quantification analysis (RQA) indexes: mean diagonal line length (Lmean), maximal diagonal line length (Lmax), recurrence rate (REC), determinism (DET), and shannon entropy (ShanEn).

Results

Univariate analysis revealed that the linear frequency domain parameter HF and nonlinear RQA parameters Lmax, REC, and DET were significantly correlated with the survival of advanced NSCLC patients (all p < 0.05). After adjusting for confounders in the multivariate analysis, HF, REC, and DET were found to be independent prognostic factors for the survival of patients with advanced NSCLC (all p < 0.05).

Conclusion

There was an independent association between heartbeat complexity and survival in advanced NSCLC patients. The nonlinear analysis method based on RQA may provide valuable additional information for the prognostic stratification of patients with advanced NSCLC and may supplement the traditional time domain and frequency domain analysis methods.