Evaluation of Directed Causality Measures and Lag Estimations in Multivariate Time-Series

The causality measure of partial mutual information from mixed embedding (PMIME) revisited

The measure of partial mutual information from mixed embedding (PMIME) is an information theory-based measure to accurately identify the direct and directional coupling, termed Granger causality or simply causality, between the observed variables or subsystems of a high-dimensional dynamical and complex system, without any a priori assumptions about the nature of the coupling relationship. In its core, it is a forward selection procedure that aims to iteratively identify the lag-dependence structure of a given observed variable (response) to all the other observed variables (candidate drivers). This model-free approach is capable of detecting nonlinear interactions, abundantly present in real-world complex systems, and it was shown to perform well on multivariate time series of moderately high dimension. However, the PMIME presents some inefficiencies in its performance mainly when applied on strongly stochastic (linear or nonlinear) systems as it may falsely detect non-existent relationships. Moreover, and by construction, the measure cannot extract purely synergetic relationships present in a system. In the current work, the issue of false detections is addressed by introducing an improved resampling significance test and a procedure of rechecking the identified drivers (backward revision). Regarding the inability to detect synergetic relationships, the PMIME is further enhanced by checking pairs as candidate drivers for the response variable after having considered all drivers individually. The effects of these modifications are investigated in a systematic simulation study on properly designed systems involving strong stochasticity, regressor terms with synergetic effects, and a system dimension ranging from 3 to 30. The overall results of the simulations indicate that these modifications indeed improve the performance of PMIME and alleviate to a significant degree the issues of the original algorithm. Guidelines for balancing between accuracy and computational efficiency are also given, particularly relevant for real-world applications. Finally, the measure performance is investigated in the study of futures of various government bonds and stock market indices in the period around COVID-19 pandemic.

Connectivity of neural signals to the primary motor area during preparatory periods for movement following external and internal cues

PURPOSE

We investigated the connectivity of neural signals from movement-related cortical areas to the primary motor area (M1) in the hemisphere contralateral to the movement side during the period of movement-related magnetic fields before movement.

MATERIALS AND METHODS

Participants were 13 healthy adults, and nerual signals were recorded using magnetoencephalography. Spontaneous extension of the right wrist was performed at the participant's own pace and following a visual cue in internal (IC) and external (EC) cue tasks. The connectivity of neural signals to M1 from each movement-related motor area was assessed by Granger causality analysis (GCA). The GCA was performed on the neural activity elicited in a frequency band between 7.8 and 46.9 Hz during the pre-movement periods, which occurred durng the readiness field (RF) and the negative slope prime (NSp). F-values, as connectivity values obtained by GCA, were compared between the EC and IC cue tasks.

RESULTS

For NSp periods, the connectivity of neural signals from the left superior frontal area (SF-L) to M1 was dominant in the IC task, whereas that from the left superior parietal area (SP-L) to M1 was dominant in the EC task. The F value in the GCA from SP-L to M1 was greater in the EC task during RF than in the IC task during equivalent periods.

CONSLUSIONS

In the present study, there were differences in the connectivity of neural signals to M1 between IC and EC tasks. The present results suggested that the pattern of pre-movement neural activity that resulted in a movement was not uniform but differed between movement tasks just before the movement.

Physiological and pathological neuronal connectivity in the living human brain based on intracranial EEG signals: the current state of research

Over the past decades, studies of human brain networks have received growing attention as the assessment and modelling of connectivity in the brain is a topic of high impact with potential application in the understanding of human brain organization under both physiological as well as various pathological conditions. Under specific diagnostic settings, human neuronal signal can be obtained from intracranial EEG (iEEG) recording in epilepsy patients that allows gaining insight into the functional organisation of living human brain. There are two approaches to assess brain connectivity in the iEEG-based signal: evaluation of spontaneous neuronal oscillations during ongoing physiological and pathological brain activity, and analysis of the electrophysiological cortico-cortical neuronal responses, evoked by single pulse electrical stimulation (SPES). Both methods have their own advantages and limitations. The paper outlines available methodological approaches and provides an overview of current findings in studies of physiological and pathological human brain networks, based on intracranial EEG recordings.

Detecting Nonlinear Interactions in Complex Systems: Application in Financial Markets

Emerging or diminishing nonlinear interactions in the evolution of a complex system may signal a possible structural change in its underlying mechanism. This type of structural break may exist in many applications, such as in climate and finance, and standard methods for change-point detection may not be sensitive to it. In this article, we present a novel scheme for detecting structural breaks through the occurrence or vanishing of nonlinear causal relationships in a complex system. A significance resampling test was developed for the null hypothesis (H₀) of no nonlinear causal relationships using (a) an appropriate Gaussian instantaneous transform and vector autoregressive (VAR) process to generate the resampled multivariate time series consistent with H₀; (b) the modelfree Granger causality measure of partial mutual information from mixed embedding (PMIME) to estimate all causal relationships; and (c) a characteristic of the network formed by PMIME as test statistic. The significance test was applied to sliding windows on the observed multivariate time series, and the change from rejection to no-rejection of H₀, or the opposite, signaled a non-trivial change of the underlying dynamics of the observed complex system. Different network indices that capture different characteristics of the PMIME networks were used as test statistics. The test was evaluated on multiple synthetic complex and chaotic systems, as well as on linear and nonlinear stochastic systems, demonstrating that the proposed methodology is capable of detecting nonlinear causality. Furthermore, the scheme was applied to different records of financial indices regarding the global financial crisis of 2008, the two commodity crises of 2014 and 2020, the Brexit referendum of 2016, and the outbreak of COVID-19, accurately identifying the structural breaks at the identified times.

Effective Connectivity in Spinal Cord Injury-Induced Neuropathic Pain

AIM

The aim of this study was to differentiate the effects of spinal cord injury (SCI) and central neuropathic pain (CNP) on effective connectivity during motor imagery of legs, where CNP is typically experienced.

METHODS

Multichannel EEG was recorded during motor imagery of the legs in 3 groups of people: able-bodied (N = 10), SCI with existing CNP (N = 10), and SCI with no CNP (N = 20). The last group was followed up for 6 months to check for the onset of CNP. Source reconstruction was performed to obtain cortical activity in 17 areas spanning sensorimotor regions and pain matrix. Effective connectivity was calculated using the directed transfer function in 4 frequency bands and compared between groups.

RESULTS

A total of 50% of the SCI group with no CNP developed CNP later. Statistically significant differences in effective connectivity were found between all groups. The differences between groups were not dependent on the frequency band. Outflows from the supplementary motor area were greater for the able-bodied group while the outflows from the secondary somatosensory cortex were greater for the SCI groups. The group with existing CNP showed the least differences from the able-bodied group, appearing to reverse the effects of SCI. The connectivities involving the pain matrix were different between able-bodied and SCI groups irrespective of CNP status, indicating their involvement in motor networks generally.

SIGNIFICANCE

The study findings might help guide therapeutic interventions targeted at the brain for CNP alleviation as well as motor recovery post SCI.