Ordinal synchronization: Using ordinal patterns to capture interdependencies between time series

Abstract

We introduce Ordinal Synchronization (OS) as a new measure to quantify synchronization between dynamical systems. OS is calculated from the extraction of the ordinal patterns related to two time series, their transformation into D-dimensional ordinal vectors and the adequate quantification of their alignment. OS provides a fast and robust-to noise tool to assess synchronization without any implicit assumption about the distribution of data sets nor their dynamical properties, capturing in-phase and anti-phase synchronization. Furthermore, varying the length of the ordinal vectors required to compute OS it is possible to detect synchronization at different time scales. We test the performance of OS with data sets coming from unidirectionally coupled electronic Lorenz oscillators and brain imaging datasets obtained from magnetoencephalographic recordings, comparing the performance of OS with other classical metrics that quantify synchronization between dynamical systems.

Neuronal Transmission of Subthreshold Periodic Stimuli Via Symbolic Spike Patterns

“…It would be interesting to compare the results with those obtained with other synchronization quantifiers, such as the phase locking value [ 22 ] or the ordinal synchronization measure that was recently introduced in Ref. [ 23 ]; however, this analysis is left for future work.…”

Dynamics in cortical activity revealed by resting-state MEG rhythms

“…From the perspective of ITQ, they were used to characterize and classify EEG records from control and epileptic patients; [23][24][25][26][27] it has also been applied to differentiate processing information zones for subjects with Alzheimer at several frequency bands, 28 to evidence the irreversibility aspect of EEG at resting-state 29 and epilepsy, 30 to unveil a relationship between the dynamics of electrophysiological signals and the brain network structure, 31 and even to propose a new ordinal-structure methodology to better account for the information transit between brain signals. 32 While the applicability of these methodologies spans over a wide range of neural phenomena, these applications are also of importance when concerning the activation of healthy subjects that are not actively compromised with the sensory or cognitive processes. This fact allows one to contrast results from pathologies or non-resting activities vs a passive null condition also called the Resting-State (RS).…”

Dynamics in cortical activity revealed by resting-state MEG rhythms

“…Brain dynamics characterization has been used to explore the reorganization of networks in mild cognitive impairment 20 ; the modularity of connectivity patterns in epilepsy brain networks and normal subjects 21 ; the effects of memory in brain networks in old and young individuals, the interchange of information between brain hemispheres in resting-state 22 ; the characterization of visuomotor/imaginary movement in EEG 23 ; to name a few. From the perspective of ITQ, they were used to characterize and classify EEG records from control and epileptic patients [24][25][26][27][28] ; it has also been applied to differentiate processing information zones for subjects with Alzheimer at several frequency bands 29 ; to discriminate imagined and non-imagined tasks in motor cortex area and its relation with rhythmic oscillations [30][31][32] ; to evidence the irreversibility aspect of EEG at resting-state 33 and epilepsy 34 ; to unveil a relationship between the dynamics of electrophysiological signals and the brain network structure 35 ; and even to propose a new ordinal-structure methodology to better account for the information transit between brain signals 36 . While the applicability of these methodologies spans over a wide range of neural phenomena, these applications are also of importance when concerning the activation of healthy subjects that are not actively compromised with the sensory or cognitive processes.…”