Multiscale Horizontal Visibility Graph Analysis of Higher-Order Moments for Estimating Statistical Dependency

Examining electroencephalogram signatures of people with multiple sclerosis using a nonlinear dynamics approach: a systematic review and bibliographic analysis

Background

Considering that brain activity involves communication between millions of neurons in a complex network, nonlinear analysis is a viable tool for studying electroencephalography (EEG). The main objective of this review was to collate studies that utilized chaotic measures and nonlinear dynamical analysis in EEG of multiple sclerosis (MS) patients and to discuss the contributions of chaos theory techniques to understanding, diagnosing, and treating MS.

Methods

Using the preferred reporting items for systematic reviews and meta-analysis (PRISMA), the databases EbscoHost, IEEE, ProQuest, PubMed, Science Direct, Web of Science, and Google Scholar were searched for publications that applied chaos theory in EEG analysis of MS patients.

Results

A bibliographic analysis was performed using VOSviewer software keyword co-occurrence analysis indicated that MS was the focus of the research and that research on MS diagnosis has shifted from conventional methods, such as magnetic resonance imaging, to EEG techniques in recent years. A total of 17 studies were included in this review. Among the included articles, nine studies examined resting-state, and eight examined task-based conditions.

Conclusion

Although nonlinear EEG analysis of MS is a relatively novel area of research, the findings have been demonstrated to be informative and effective. The most frequently used nonlinear dynamics analyses were fractal dimension, recurrence quantification analysis, mutual information, and coherence. Each analysis selected provided a unique assessment to fulfill the objective of this review. While considering the limitations discussed, there is a promising path forward using nonlinear analyses with MS data.

Multiscale Quantile Correlation Coefficient: Measuring Tail Dependence of Financial Time Series

In the context of the frequent occurrence of extreme events, measuring the tail dependence of financial time series is essential for maintaining the sustainable development of financial markets. In this paper, a multiscale quantile correlation coefficient (MQCC) is proposed to measure the tail dependence of financial time series. The new MQCC method consists of two parts: the multiscale analysis and the correlation analysis. In the multiscale analysis, the coarse graining approach is used to study the financial time series on multiple temporal scales. In the correlation analysis, the quantile correlation coefficient is applied to quantify the correlation strength of different data quantiles, especially regarding the difference and the symmetry of tails. One reason to adopt this method is that the conditional distribution of the explanatory variables can be characterized by the quantile regression, rather than simply by the conditional expectation analysis in the traditional regression. By applying the MQCC method in the financial markets of different regions, many interesting results can be obtained. It is worth noting that there are significant differences in tail dependence between different types of financial markets.