Bringing complexity science to real world: Quantification of stress in humans and systems

Abstract

Analysing real-world data within the context of structural complexity is crucial for accurately revealing the dynamical behavior of systems, ranging from individual (human) to network (economic). Indeed, the so-called "Complexity Loss Theory" establishes that complexity measures are able to provide physically meaningful interpretation of, for example, the occurrence of stress in such systems. This theory states that organisms or systems under constraints, such as ageing illness or more generally loss of degrees of freedom, exhibit lower complexity of their observable responses. To this end, this thesis aims to model/quantify stress levels of two dynamical systems: i) autonomic nervous (in humans), and ii) economic (in financial markets). For human based scenarios, we collected Electrocardiogram (ECG) in two human activities: i) public speaking, and ii) music performance. For the assessment of the structural complexity of systems, stock indices from the four major stock markets in the US were used for studying stress in economic. This thesis introduces a novel framework for analysing physiological stress from heart rate variability (HRV) extracted from the wearable ECG. The framework includes a robust method, established based on the matched filtering method and the Hilbert transform, for detecting R-peaks in noisy ECG. We examine the physiological stress through several standard entropy measures, prior to introducing our novel “Cosine Similarity Entropy” and “Multiscale Cosine Similarity Entropy”. These new entropy measures are derived based on angular distance, Shannon entropy and the coarse-grained scale, and shown to successfully and rigorously quantify structural complexity in systems within the context of self-correlation. The analysis over numerous case studies shows that the proposed framework is capable of detecting loss of degrees of freedom, that is, ‘stress-patterns’ under different stress conditions. Furthermore, we examine economic stress through an enhanced multivariate entropy measure, “Moving-Averaged Multivariate Sample Entropy”, which is established based on a standard multivariate entropy and a novel detrended moving average scale. The MA-MSE makes it possible to capture the periods of financial stress which corresponds to the occurrence of the economic crises correctly. Overall, the novel algorithms in this thesis have resolved several limitations of the existing entropy measures, especially related to short time series, sensitivity to signal amplitudes, and undefined entropy values for data with artefacts. In addition, real world data do not obey any closed-form probability distribution and are often nonstationary, which requires non-parametric entropy estimators suitable for such scenarios - a subject of this thesis.