On Entropy of Probability Integral Transformed Time Series

Breaking Barriers in Emerging Biomedical Applications

The recent global COVID-19 pandemic has revealed that the current healthcare system in modern society can hardly cope with the increased number of patients. Part of the load can be alleviated by incorporating smart healthcare infrastructure in the current system to enable patient’s remote monitoring and personalized treatment. Technological advances in communications and sensing devices have enabled the development of new, portable, and more power-efficient biomedical sensors, as well as innovative healthcare applications. Nevertheless, such applications require reliable, resilient, and secure networks. This paper aims to identify the communication requirements for mass deployment of such smart healthcare sensors by providing the overview of underlying Internet of Things (IoT) technologies. Moreover, it highlights the importance of information theory in understanding the limits and barriers in this emerging field. With this motivation, the paper indicates how data compression and entropy used in security algorithms may pave the way towards mass deployment of such IoT healthcare devices. Future medical practices and paradigms are also discussed.

On Quantization Errors in Approximate and Sample Entropy

Approximate and sample entropies are acclaimed tools for quantifying the regularity and unpredictability of time series. This paper analyses the causes of their inconsistencies. It is shown that the major problem is a coarse quantization of matching probabilities, causing a large error between their estimated and true values. Error distribution is symmetric, so in sample entropy, where matching probabilities are directly summed, errors cancel each other. In approximate entropy, errors are accumulating, as sums involve logarithms of matching probabilities. Increasing the time series length increases the number of quantization levels, and errors in entropy disappear both in approximate and in sample entropies. The distribution of time series also affects the errors. If it is asymmetric, the matching probabilities are asymmetric as well, so the matching probability errors cease to be mutually canceled and cause a persistent entropy error. Despite the accepted opinion, the influence of self-matching is marginal as it just shifts the error distribution along the error axis by the matching probability quant. Artificial lengthening the time series by interpolation, on the other hand, induces large error as interpolated samples are statistically dependent and destroy the level of unpredictability that is inherent to the original signal.

Entropy Analysis of COVID-19 Cardiovascular Signals

The world has faced a coronavirus outbreak, which, in addition to lung complications, has caused other serious problems, including cardiovascular. There is still no explanation for the mechanisms of coronavirus that trigger dysfunction of the cardiac autonomic nervous system (ANS). We believe that the complex mechanisms that change the status of ANS could only be solved by advanced multidimensional analysis of many variables, obtained both from the original cardiovascular signals and from laboratory analysis and detailed patient history. The aim of this paper is to analyze different measures of entropy as potential dimensions of the multidimensional space of cardiovascular data. The measures were applied to heart rate and systolic blood pressure signals collected from 116 patients with COVID-19 and 77 healthy controls. Methods that indicate a statistically significant difference between patients with different levels of infection and healthy controls will be used for further multivariate research. As a result, it was shown that a statistically significant difference between healthy controls and patients with COVID-19 was shown by sample entropy applied to integrated transformed probability signals, common symbolic dynamics entropy, and copula parameters. Statistical significance between serious and mild patients with COVID-19 can only be achieved by cross-entropies of heart rate signals and systolic pressure. This result contributes to the hypothesis that the severity of COVID-19 disease is associated with ANS disorder and encourages further research.