Neuronal information processing is complex and nonlinear at different levels, from the microscopic cellular interactions to the macroscopic interactions between large populations of neurons in, for instance, sensory processing and motor response. This might also be true for the understanding and characterizing of neurological disorders and neurodegenerative diseases, e.g. epilepsy and seizures, tremor, Alzheimer’s and Parkinson’s diseases, considering that brain is a complex nonlinear system.
For decades, linear (functional and effective) connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivity and input-output interconnections in neural systems, from neurophysiological signals - such as electroencephalogram (EEG), magnetoencephalogram (MEG) and fMRI from the brain, electromyogram (EMG) from muscles. Recent studies suggest that these linear methods may only capture a certain amount of neural activities and functional relationships, and therefore may not be able to describe neural behaviors in a precise or complete way. For example, multi-synaptic neural systems, such as the somatosensory system, have been reported highly nonlinear, showing harmonic responses to periodic stimuli. The cross-frequency coupling in the corticothalamic interactions has also been reported when characterizing essential tremor. The nonlinear behavior in neural systems is thought to be associated with various neural functions, including neuronal encoding, neural processing of synaptic inputs, communication between different neuronal populations, and functional integration.
This Research Topic aims to document frontline research in the use of nonlinear dynamic modelling (system identification), nonlinear connectivity or causality analysis, and nonlinear feature extraction techniques to quantitatively study the complex dynamics of neural systems, neuronal information processing, and characterizing and diagnosing neurological disorders. We seek Original Research, Review, Mini-Review, Hypothesis and Theory, Perspective, and Opinion articles that cover, but are not limited to, the following topics:
· Cross-frequency coupling: methodology and applications;
· Nonlinear connectivity analysis and causality analysis: non-parametric methods, kernel methods, dynamic causal modelling, information-theoretical measures (e.g. transfer entropy, mutual information), parametric model-based methods;
· Nonlinear time, frequency, or time-frequency domain signal processing;
· Machine learning and nonlinear feature extraction, using nonlinear dimension reduction, artificial and deep neural networks, clustering, matrix factorization, etc;
· Nonlinear system identification: Volterra series, NARMAX models, neural networks, non-parametric Bayesian models, time-varying system identification;
· Nonlinear dynamics in neural networks;
· Neural information processing;
· Higher-order spectral analysis and nonlinear coherence.
