Reduced System Complexity of Heart Rate Dynamics in Patients with Hyperthyroidism: A Multiscale Entropy Analysis

Studying heart rate dynamics would help understand the effects caused by a hyperkinetic heart in patients with hyperthyroidism. By using a multiscale entropy (MSE) analysis of heart rate dynamics derived from one-channel electrocardiogram recording, we aimed to compare the system complexity of heart rate dynamics between hyperthyroid patients and control subjects. A decreased MSE complexity index (CI) computed from MSE analysis reflects reduced system complexity. Compared with the control subjects (n = 37), the hyperthyroid patients (n = 37) revealed a significant decrease (p < 0.001) in MSE CI (hyperthyroid patients 10.21 ± 0.37 versus control subjects 14.08 ± 0.21), sample entropy for each scale factor (from 1 to 9), and high frequency power (HF) as well as a significant increase (p < 0.001) in low frequency power (LF) in normalized units (LF%) and ratio of LF to HF (LF/HF). In conclusion, besides cardiac autonomic dysfunction, the system complexity of heart rate dynamics is reduced in hyperthyroidism. This finding implies that the adaptability of the heart rate regulating system is impaired in hyperthyroid patients. Additionally, it might explain the exercise intolerance experienced by hyperthyroid patients. In addition, hyperthyroid patients and control subjects could be distinguished by the MSE CI computed from MSE analysis of heart rate dynamics.     

基于多尺度熵的交通流复杂性分析

交通流演化复杂性的研究有助于深刻理解交通系统的内在演化规律,为交通流的预测和控制提供理论依据.多尺度熵方法在生理时间序列和计算机网络流量的分析中得到了广泛的应用.考虑到交通流中的车辆到达和计算机网络中的分组到达具有类似特性,本文以刹车灯模型的车头时距为分析对象,利用多尺度熵方法来分析交通流演化的复杂性.分析结果表明:1)车头时距的复杂性随着时间尺度的增加而降低,反映了交通流的短时间难预测性;2)当时间尺度较小时,车头时距复杂性在自由流时和同步流时差异不大,但是,随着时间尺度的增加,自由流时车头时距的熵值迅速下降,而同步流时车头时距的熵值下降较慢.这一特性对于识别自由流中是否产生了同步流有非常重要的参考价值.本文的研究可以为揭示交通流演化的复杂性提供新的思路和方法.     

Evaluating Temporal Correlations in Time Series Using Permutation Entropy,Ordinal Probabilities and Machine Learning

Time series analysis comprises a wide repertoire of methods for extracting information from data sets. Despite great advances in time series analysis, identifying and quantifying the strength of nonlinear temporal correlations remain a challenge. We have recently proposed a new method based on training a machine learning algorithm to predict the temporal correlation parameter, α, of flicker noise (FN) time series. The algorithm is trained using as input features the probabilities of ordinal patterns computed from FN time series, xαFN(t), generated with different values of α. Then, the ordinal probabilities computed from the time series of interest, x(t), are used as input features to the trained algorithm and that returns a value, αe, that contains meaningful information about the temporal correlations present in x(t). We have also shown that the difference, Ω, of the permutation entropy (PE) of the time series of interest, x(t), and the PE of a FN time series generated with α=αe, xαeFN(t), allows the identification of the underlying determinism in x(t). Here, we apply our methodology to different datasets and analyze how αe and Ω correlate with well-known quantifiers of chaos and complexity. We also discuss the limitations for identifying determinism in highly chaotic time series and in periodic time series contaminated by noise. The open source algorithm is available on Github.     

Brain Dynamics Altered by Photic Stimulation in Patients with Alzheimer’s Disease and Mild Cognitive Impairment

Individuals with mild cognitive impairment (MCI) are at high risk of developing Alzheimer’s disease (AD). Repetitive photic stimulation (PS) is commonly used in routine electroencephalogram (EEG) examinations for rapid assessment of perceptual functioning. This study aimed to evaluate neural oscillatory responses and nonlinear brain dynamics under the effects of PS in patients with mild AD, moderate AD, severe AD, and MCI, as well as healthy elderly controls (HC). EEG power ratios during PS were estimated as an index of oscillatory responses. Multiscale sample entropy (MSE) was estimated as an index of brain dynamics before, during, and after PS. During PS, EEG harmonic responses were lower and MSE values were higher in the AD subgroups than in HC and MCI groups. PS-induced changes in EEG complexity were less pronounced in the AD subgroups than in HC and MCI groups. Brain dynamics revealed a “transitional change” between MCI and Mild AD. Our findings suggest a deficiency in brain adaptability in AD patients, which hinders their ability to adapt to repetitive perceptual stimulation. This study highlights the importance of combining spectral and nonlinear dynamical analysis when seeking to unravel perceptual functioning and brain adaptability in the various stages of neurodegenerative diseases.     

基于多尺度熵的电力能量流复杂性分析

电力能量流复杂性主要体现于其动态行为的实时性、非线性及不确定性等,网络动力学行为分析是关键.本文在电力系统动力学平衡方程基础上,构建了系统势能与支路势能函数模型;通过提取扰动(或故障)后系统的能量信息,利用多尺度熵对扰动(或故障)后系统能量流演化过程进行了研究.结果表明:1)稳定运行状态下系统复杂度较低,且随着故障持续时间的增加,系统故障后呈现出更高的复杂度;2)不稳定运行状态下,系统在小尺度时间上表现出更强的不确定性,而在大尺度时间上表现出相对更明显的规则性;3)临界稳定运行状态与临界不稳定运行状态下,故障后的系统复杂度在不同时间尺度上呈现出较明显的差异,这对动态过程中临界点的识别有着积极的参考价值.本文研究揭示了电力能量流在物理动态过程中的演化机制,为电力系统动力学行为分析提供了新思路与新方法.     

Neurofeedback Training Based on Motor Imagery Strategies Increases EEG Complexity in Elderly Population

Neurofeedback training (NFT) has shown promising results in recent years as a tool to address the effects of age-related cognitive decline in the elderly. Since previous studies have linked reduced complexity of electroencephalography (EEG) signal to the process of cognitive decline, we propose the use of non-linear methods to characterise changes in EEG complexity induced by NFT. In this study, we analyse the pre- and post-training EEG from 11 elderly subjects who performed an NFT based on motor imagery (MI–NFT). Spectral changes were studied using relative power (RP) from classical frequency bands (delta, theta, alpha, and beta), whilst multiscale entropy (MSE) was applied to assess EEG-induced complexity changes. Furthermore, we analysed the subject’s scores from Luria tests performed before and after MI–NFT. We found that MI–NFT induced a power shift towards rapid frequencies, as well as an increase of EEG complexity in all channels, except for C3. These improvements were most evident in frontal channels. Moreover, results from cognitive tests showed significant enhancement in intellectual and memory functions. Therefore, our findings suggest the usefulness of MI–NFT to improve cognitive functions in the elderly and encourage future studies to use MSE as a metric to characterise EEG changes induced by MI–NFT.     

A Comparative Study of Functional Connectivity Measures for Brain Network Analysis in the Context of AD Detection with EEG

This work addresses brain network analysis considering different clinical severity stages of cognitive dysfunction, based on resting-state electroencephalography (EEG). We use a cohort acquired in real-life clinical conditions, which contains EEG data of subjective cognitive impairment (SCI) patients, mild cognitive impairment (MCI) patients, and Alzheimer’s disease (AD) patients. We propose to exploit an epoch-based entropy measure to quantify the connectivity links in the networks. This entropy measure relies on a refined statistical modeling of EEG signals with Hidden Markov Models, which allow a better estimation of the spatiotemporal characteristics of EEG signals. We also propose to conduct a comparative study by considering three other measures largely used in the literature: phase lag index, coherence, and mutual information. We calculated such measures at different frequency bands and computed different local graph parameters considering different proportional threshold values for a binary network analysis. After applying a feature selection procedure to determine the most relevant features for classification performance with a linear Support Vector Machine algorithm, our study demonstrates the effectiveness of the statistical entropy measure for analyzing the brain network in patients with different stages of cognitive dysfunction.     

An Exploratory Study on the Complexity and Machine Learning Predictability of Stock Market Data

This paper shows if and how the predictability and complexity of stock market data changed over the last half-century and what influence the M1 money supply has. We use three different machine learning algorithms, i.e., a stochastic gradient descent linear regression, a lasso regression, and an XGBoost tree regression, to test the predictability of two stock market indices, the Dow Jones Industrial Average and the NASDAQ (National Association of Securities Dealers Automated Quotations) Composite. In addition, all data under study are discussed in the context of a variety of measures of signal complexity. The results of this complexity analysis are then linked with the machine learning results to discover trends and correlations between predictability and complexity. Our results show a decrease in predictability and an increase in complexity for more recent years. We find a correlation between approximate entropy, sample entropy, and the predictability of the employed machine learning algorithms on the data under study. This link between the predictability of machine learning algorithms and the mentioned entropy measures has not been shown before. It should be considered when analyzing and predicting complex time series data, e.g., stock market data, to e.g., identify regions of increased predictability.     

Working Memory Decline in Alzheimer’s Disease Is Detected by Complexity Analysis of Multimodal EEG-fNIRS

Alzheimer’s disease (AD) is characterized by working memory (WM) failures that can be assessed at early stages through administering clinical tests. Ecological neuroimaging, such as Electroencephalography (EEG) and functional Near Infrared Spectroscopy (fNIRS), may be employed during these tests to support AD early diagnosis within clinical settings. Multimodal EEG-fNIRS could measure brain activity along with neurovascular coupling (NC) and detect their modifications associated with AD. Data analysis procedures based on signal complexity are suitable to estimate electrical and hemodynamic brain activity or their mutual information (NC) during non-structured experimental paradigms. In this study, sample entropy of whole-head EEG and frontal/prefrontal cortex fNIRS was evaluated to assess brain activity in early AD and healthy controls (HC) during WM tasks (i.e., Rey–Osterrieth complex figure and Raven’s progressive matrices). Moreover, conditional entropy between EEG and fNIRS was evaluated as indicative of NC. The findings demonstrated the capability of complexity analysis of multimodal EEG-fNIRS to detect WM decline in AD. Furthermore, a multivariate data-driven analysis, performed on these entropy metrics and based on the General Linear Model, allowed classifying AD and HC with an AUC up to 0.88. EEG-fNIRS may represent a powerful tool for the clinical evaluation of WM decline in early AD.     

Commodity predictability analysis with a permutation information theory approach

It is widely known that commodity markets are not totally efficient. Long-range dependence is present, and thus the celebrated Brownian motion of prices can be considered only as a first approximation. In this work we analyzed the predictability in commodity markets by using a novel approach derived from Information Theory. The complexity-entropy causality plane has been recently shown to be a useful statistical tool to distinguish the stage of stock market development because differences between emergent and developed stock markets can be easily discriminated and visualized with this representation space [L. Zunino, M. Zanin, B.M. Tabak, D.G. Pérez, O.A. Rosso, Complexity-entropy causality plane: a useful approach to quantify the stock market inefficiency, Physica A 389 (2010) 1891-1901]. By estimating the permutation entropy and permutation statistical complexity of twenty basic commodity future markets over a period of around 20 years (1991.01.02-2009.09.01), we can define an associated ranking of efficiency. This ranking is quantifying the presence of patterns and hidden structures in these prime markets. Moreover, the temporal evolution of the commodities in the complexity-entropy causality plane allows us to identify periods of time where the underlying dynamics is more or less predictable.     

Complexity of Fracturing in Terms of Non-Extensive Statistical Physics: From Earthquake Faults to Arctic Sea Ice Fracturing

Fracturing processes within solid Earth materials are inherently a complex phenomenon so that the underlying physics that control fracture initiation and evolution still remain elusive. However, universal scaling relations seem to apply to the collective properties of fracturing phenomena. In this article we present a statistical physics approach to fracturing based on the framework of non-extensive statistical physics (NESP). Fracturing phenomena typically present intermittency, multifractality, long-range correlations and extreme fluctuations, properties that motivate the NESP approach. Initially we provide a brief review of the NESP approach to fracturing and earthquakes and then we analyze stress and stress direction time series within Arctic sea ice. We show that such time series present large fluctuations and probability distributions with “fat” tails, which can exactly be described with the q-Gaussian distribution derived in the framework of NESP. Overall, NESP provide a consistent theoretical framework, based on the principle of entropy, for deriving the collective properties of fracturing phenomena and earthquakes.     

On the efficiency of sovereign bond markets

The existence of memory in financial time series has been extensively studied for several stock markets around the world by means of different approaches. However, fixed income markets, i.e. those where corporate and sovereign bonds are traded, have been much less studied. We believe that, given the relevance of these markets, not only from the investors’, but also from the issuers’ point of view (government and firms), it is necessary to fill this gap in the literature. In this paper, we study the sovereign market efficiency of thirty bond indices of both developed and emerging countries, using an innovative statistical tool in the financial literature: the complexity-entropy causality plane. This representation space allows us to establish an efficiency ranking of different markets and distinguish different bond market dynamics. We conclude that the classification derived from the complexity-entropy causality plane is consistent with the qualifications assigned by major rating companies to the sovereign instruments. Additionally, we find a correlation between permutation entropy, economic development and market size that could be of interest for policy makers and investors.     

Fractional-calculus analysis of human immunodeficiency virus and CD4+ T-cells with control interventions

It is undeniable that HIV infection has been a censorious public health concern over the past four decades. It is reported that HIV is the main reason for AIDs which has decimated the global population of humans and imposed a significant economic burden on affected areas. Hence, it is significant to study the transmission of HIV viruses in the body of a human host. In this study, we use a fractional framework to organise the intricate interactions of CD4⁺ T-cells and HIV viruses in order to investigate HIV infection with control interventions. We apply the operators of Caputo and Atangana–Baleanu to interrogate the transmission phenomena of HIV viruses. For the analysis of our system, we present the basic concepts of the fractional operators. Numerical schemes are provided to show the solution pathways of the system with the variation of input parameters. Furthermore, the findings emphasise the chaotic and dynamical behaviour of HIV. We run several simulations to visualise the influence of input factors and quantitatively illustrated the dynamics of HIV. Chaos and oscillatory behaviour are intimately linked, and this is owing to the system's nonlinearity. Furthermore, our findings indicate the most important factors for infection control and prevention.     

Testing Jump-Diffusion in Epileptic Brain Dynamics: Impact of Daily Rhythms

Stochastic approaches to complex dynamical systems have recently provided broader insights into spatial-temporal aspects of epileptic brain dynamics. Stochastic qualifiers based on higher-order Kramers-Moyal coefficients derived directly from time series data indicate improved differentiability between physiological and pathophysiological brain dynamics. It remains unclear, however, to what extent stochastic qualifiers of brain dynamics are affected by other endogenous and/or exogenous influencing factors. Addressing this issue, we investigate multi-day, multi-channel electroencephalographic recordings from a subject with epilepsy. We apply a recently proposed criterion to differentiate between Langevin-type and jump-diffusion processes and observe the type of process most qualified to describe brain dynamics to change with time. Stochastic qualifiers of brain dynamics are strongly affected by endogenous and exogenous rhythms acting on various time scales—ranging from hours to days. Such influences would need to be taken into account when constructing evolution equations for the epileptic brain or other complex dynamical systems subject to external forcings.     

Chaos in the solar wind flow near Earth

We have done a time series analysis of daily average data of solar wind velocity, density and temperature at 1 AU measured by ACE spacecraft for a period of nine years. We have used the raw data without filtering to give a faithful representation of the nonlinear behaviour of the solar wind flow which is a novel one. The sensitivity of the results on filtering is highlighted. The attractor dimension is estimated for every parameter of the solar wind and it is found that they differ substantially. Hence a chaotic picture for the problem from different angles have been obtained. The calculated Kolmogorov entropies and Lyapunov exponents are positive showing evidences that the complex solar wind near the Earth is most likely a deterministic chaotic system.