Statistical Frequency-Dependent Analysis of Trial-to-Trial Variability in Single Time Series by Recurrence Plots

Abstract

For decades, research in neuroscience has supported the hypothesis that brain dynamics exhibits recurrent metastable states connected by transients, which together encode fundamental neural information processing. To understand the system's dynamics it is important to detect such recurrence domains, but it is challenging to extract them from experimental neuroscience datasets due to the large trial-to-trial variability. The proposed methodology extracts recurrent metastable states in univariate time series by transforming datasets into their time-frequency representations and computing recurrence plots based on instantaneous spectral power values in various frequency bands. Additionally, a new statistical inference analysis compares different trial recurrence plots with corresponding surrogates to obtain statistically significant recurrent structures. This combination of methods is validated by applying it to two artificial datasets. In a final study of visually-evoked Local Field Potentials in partially anesthetized ferrets, the methodology is able to reveal recurrence structures of neural responses with trial-to-trial variability. Focusing on different frequency bands, the δ-band activity is much less recurrent than α-band activity. Moreover, α-activity is susceptible to pre-stimuli, while δ-activity is much less sensitive to pre-stimuli. This difference in recurrence structures in different frequency bands indicates diverse underlying information processing steps in the brain.

An Evolutionary Game Theory Model of Spontaneous Brain Functioning

“…The middle inset depicts two areas with non-emulative attitudes. This mechanism, where the two areas converge to different levels of activation, is referred to as bistability, which is a common phenomenon in brain dynamics 52 , 53 . Finally, the lower inset shows an oscillating dynamics obtained when the two areas present different attitudes.…”

A versatile computational algorithm for time-series data analysis and machine-learning models

“…This may limit the identification of recurrent patterns and emergent recurring domains 28 . That is because with thresholding important information related to underlying dynamic processes embedded within the signal may be lost, or spurious patterns introduced with inappropriate thresholding 28,30,31,35 .…”

Sequences by Metastable Attractors: Interweaving Dynamical Systems and Experimental Data

“…T denotes the number of samples and X is a subset of R n . An example might be a multivariate measured signal with dimension n. Note that for univariate time series, X can be reconstructed through phase space embedding [28] or, more recently, through spectral embedding techniques [29,30]. For a given c ∈ N the system's realization (x (c) t ) is a function from the index set T = {t|1 ≤ t ≤ T} into X, i.e., (x (c) t ) ∈ X T .…”