Connectionists: dual-frequency coupling coefficient for connectivity analysis

[Roberto D. Pascual-Marqui]

Dear Colleagues,
For those of you interested in this topic, I would like to point your
attention to a recently developed method for connectivity analysis
based on time series of brain activity:
"The dual frequency RV-coupling coefficient: a novel measure for
quantifying cross-frequency information transactions in the brain"
http://arxiv.org/abs/1603.05343
(abstract below)
Cordially,
Roberto

...
Roberto D. Pascual-Marqui, PhD, PD
The KEY Institute for Brain-Mind Research, University of Zurich
Visiting Professor at Neuropsychiatry, Kansai Medical University, Osaka
[www.keyinst.uzh.ch/loreta] [www.researcherid.com/rid/A-2012-2008]
[scholar.google.com/citations?user=pascualmarqui]

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ABSTRACT
Identifying dynamic transactions between brain regions has become
increasingly important. Measurements within and across brain structures,
demonstrating the occurrence of bursts of beta/gamma oscillations only during
one specific phase of each theta/alpha cycle, have motivated the need to
advance beyond linear and stationary time series models. Here we offer a novel
measure, namely, the "dual frequency RV-coupling coefficient", for assessing
different types of frequency-frequency interactions that subserve information
flow in the brain. This is a measure of coherence between two complex-valued
vectors, consisting of the set of Fourier coefficients for two different
frequency bands, within or across two brain regions. RV-coupling is expressed
in terms of instantaneous and lagged components. Furthermore, by using
normalized Fourier coefficients (unit modulus), phase-type couplings can also
be measured. The dual frequency RV-coupling coefficient is based on previous
work: the second order bispectrum, i.e. the dual-frequency coherence (Thomson
1982; Haykin & Thomson 1998); the RV-coefficient (Escoufier 1973); Gorrostieta
et al (2012); and Pascual-Marqui et al (2011). This paper presents the new
measure, and outlines relevant statistical tests. The novel aspects of the
"dual frequency RV-coupling coefficient" are: (1) it can be applied to two
multivariate time series; (2) the method is not limited to single discrete
frequencies, and in addition, the frequency bands are treated by means of
appropriate multivariate statistical methodology; (3) the method makes use of a
novel generalization of the RV-coefficient for complex-valued multivariate
data; (4) real and imaginary covariance contributions to the RV-coherence are
obtained, allowing the definition of a "lagged-coupling" measure that is
minimally affected by the low spatial resolution of estimated cortical electric
neuronal activity.
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