  In a seminal paper by von Stein and Sarnthein (2000), it was hypothesized
that "bottom-up" information processing of "content" elicits local, high
frequency (beta-gamma) oscillations, whereas "top-down" processing is
"contextual", characterized by large scale integration spanning distant
cortical regions, and implemented by slower frequency (theta-alpha)
oscillations. This corresponds to a mechanism of cortical information
transactions, where synchronization of beta-gamma oscillations between distant
cortical regions is mediated by widespread theta-alpha oscillations. It is the
aim of this paper to express this hypothesis quantitatively, in terms of a
model that will allow testing this type of information transaction mechanism.
The basic methodology used here corresponds to statistical mediation analysis,
originally developed by (Baron and Kenny 1986). We generalize the classical
mediator model to the case of multivariate complex-valued data, consisting of
the discrete Fourier transform coefficients of signals of electric neuronal
activity, at different frequencies, and at different cortical locations. The
"mediation effect" is quantified here in a novel way, as the product of "dual
frequency RV-coupling coefficients", that were introduced in (Pascual-Marqui et
al 2016, http://arxiv.org/abs/1603.05343). Relevant statistical procedures are
presented for testing the cross-frequency mediation mechanism in general, and
in particular for testing the von Stein & Sarnthein hypothesis.
