Consolidating a Link Centered Neural Connectivity Framework with Directed Transfer Function Asymptotics

TL;DR

This paper develops a mathematical framework for analyzing neural connectivity using directed transfer function asymptotics, proposing a link-centered approach that distinguishes direct and indirect influences for clearer neural network interpretation.

Contribution

It introduces a unified derivation of DTF asymptotics and proposes a novel link-centered neural connectivity framework replacing traditional correlation-based concepts.

Findings

Unified mathematical derivation of DTF asymptotics

Introduction of link-centered neural connectivity framework

New concepts of Granger connectivity and influenciability

Abstract

We present a unified mathematical derivation of the asymptotic behaviour of three of the main forms of \textit{directed transfer function} (DTF) complementing recent partial directed coherence (PDC) results \cite{Baccala2013}. Based on these results and numerical examples we argue for a new directed `link' centered neural connectivity framework to replace the widespread correlation based effective/functional network concepts so that directed network influences between structures become classified as to whether links are \textit{active} in a \textit{direct} or in an \textit{indirect} way thereby leading to the new notions of \textit{Granger connectivity} and \textit{Granger influenciability} which are more descriptive than speaking of Granger causality alone.