Changes in Dimensionality and Fractal Scaling Suggest Soft-Assembled Dynamics in Human EEG

Associations between the resting EEG aperiodic slope and broad domains of cognitive ability

Recent studies suggest that the EEG aperiodic exponent (often represented as a slope in log-log space) is sensitive to individual differences in momentary cognitive skills such as selective attention and information processing speed. However, findings are mixed, and most of the studies have focused on just a narrow range of cognitive domains. This study used an archival dataset to help clarify associations between resting aperiodic features and broad domains of cognitive ability, which vary in their demands on momentary processing. Undergraduates (N = 166) of age 18-52 years completed a resting EEG session as well as a standardized, individually administered assessment of cognitive ability that included measures of processing speed, working memory, and higher-order visuospatial and verbal skills. A subsample (n = 110) also completed a computerized reaction time task with three difficulty levels. Data reduction analyses revealed strong correlations between the aperiodic offset and slope across electrodes, and a single component accounted for ~60% of variance in slopes across the scalp, in both eyes-closed and eyes-open conditions. Structural equation models did not support relations between the slope and specific domains tapping momentary processes. However, secondary analyses indicated that the eyes-open slope was related to higher overall performance, as represented by a single general ability factor. A latent reaction time variable was significantly inversely related to both eyes-closed and eyes-open resting exponents, such that faster reaction times were associated with steeper slopes. These findings support and help clarify the relation of the resting EEG exponent to individual differences in cognitive skills.

Four Methods to Distinguish between Fractal Dimensions in Time Series through Recurrence Quantification Analysis

Fractal properties in time series of human behavior and physiology are quite ubiquitous, and several methods to capture such properties have been proposed in the past decades. Fractal properties are marked by similarities in statistical characteristics over time and space, and it has been suggested that such properties can be well-captured through recurrence quantification analysis. However, no methods to capture fractal fluctuations by means of recurrence-based methods have been developed yet. The present paper takes this suggestion as a point of departure to propose and test several approaches to quantifying fractal fluctuations in synthetic and empirical time-series data using recurrence-based analysis. We show that such measures can be extracted based on recurrence plots, and contrast the different approaches in terms of their accuracy and range of applicability.

NoLiTiA: An Open-Source Toolbox for Non-linear Time Series Analysis

In many scientific fields including neuroscience, climatology or physics, complex relationships can be described most parsimoniously by non-linear mechanics. Despite their relevance, many neuroscientists still apply linear estimates in order to evaluate complex interactions. This is partially due to the lack of a comprehensive compilation of non-linear methods. Available packages mostly specialize in only one aspect of non-linear time-series analysis and most often require some coding proficiency to use. Here, we introduce NoLiTiA, a free open-source MATLAB toolbox for non-linear time series analysis. In comparison to other currently available non-linear packages, NoLiTiA offers (1) an implementation of a broad range of classic and recently developed methods, (2) an implementation of newly proposed spatially and time-resolved recurrence amplitude analysis and (3) an intuitive environment accessible even to users with little coding experience due to a graphical user interface and batch-editor. The core methodology derives from three distinct fields of complex systems theory, including dynamical systems theory, recurrence quantification analysis and information theory. Besides established methodology including estimation of dynamic invariants like Lyapunov exponents and entropy-based measures, such as active information storage, we include recent developments of quantifying time-resolved aperiodic oscillations. In general, the toolbox will make non-linear methods accessible to the broad neuroscientific community engaged in time series processing.

Exploring the reliability and sensitivity of the EEG power spectrum as a biomarker

INTRODUCTION

The slope of the electroencephalography (EEG) power spectrum (also referred to as 1/f noise) is an important consideration when calculating narrow-band power. However, psychophysiological data also suggest this slope is a meaningful signal itself, not merely background activity or noise. We present two different methods for quantifying the slope of the power spectrum and assess their reliability and sensitivity.

METHODS

We used data from N = 60 participants who had EEG collected during rest, a videogame task, and a second period of rest. At all phases of the experiment, we calculated the "spectral slope" (a regression-based method fit to all datapoints) and the "aperiodic slope" (estimated with the fitting oscillations with 1/f algorithm FOOOF). For both methods we assessed: their reliability, their sensitivity to the transition from rest to task, their sensitivity to changes during the videogame task itself, and the agreement between the two measures.

RESULTS

Across resting phases, both spectral and aperiodic slopes showed a high degree of reliability. Both methods also showed a steepening of the power spectrum on-task compared to rest. There was also a high degree of consistency between the two methods in their estimate of the underlying slope, but FOOOF explained more variance in the power spectra across regions and type of activity (rest versus task).

CONCLUSION

The slope of the power spectrum is a highly reliable individual difference and sensitive to within-subject changes across two different methods of estimation. Moving forward, we generally recommend the use of the FOOOF algorithm for its ability to account for narrow-band signals, but these data show how regression-based approaches produce similar estimates of the spectral slope, which may be useful in some applications.

Fractal Analysis of Human Gait Variability via Stride Interval Time Series

Fractal analysis of stride interval time series is a useful tool in human gait research which could be used as a marker for gait adaptability, gait disorder, and fall risk among patients with movement disorders. This study is designed to systematically and comprehensively investigate two practical aspects of fractal analysis which significantly affect the outcome: the series length and the parameters used in the algorithm. The Hurst exponent, scaling exponent, and/or fractal dimension are computed from both simulated and experimental data using three fractal methods, namely detrended fluctuation analysis, box-counting dimension, and Higuchi's fractal dimension. The advantages and drawbacks of each method are discussed, in terms of biases and variability. The results demonstrate that a careful selection of fractal analysis methods and their parameters is required, which is dependent on the aim of study (either analyzing differences between experimental groups or estimating an accurate determination of fractal features). A set of guidelines for the selection of the fractal methods and the length of stride interval time series is provided, along with the optimal parameters for a robust implementation for each method.

The multidimensional brain

Brain activity takes place in three spatial-plus time dimensions. This rather obvious claim has been recently questioned by papers that, taking into account the big data outburst and novel available computational tools, are starting to unveil a more intricate state of affairs. Indeed, various brain activities and their correlated mental functions can be assessed in terms of trajectories embedded in phase spaces of dimensions higher than the canonical ones. In this review, I show how further dimensions may not just represent a convenient methodological tool that allows a better mathematical treatment of otherwise elusive cortical activities, but may also reflect genuine functional or anatomical relationships among real nervous functions. I then describe how to extract hidden multidimensional information from real or artificial neurodata series, and make clear how our mind dilutes, rather than concentrates as currently believed, inputs coming from the environment. Finally, I argue that the principle "the higher the dimension, the greater the information" may explain the occurrence of mental activities and elucidate the mechanisms of human diseases associated with dimensionality reduction.