Ramsey's Theory Meets the Human Brain Connectome.

Ramsey's theory (RAM) from combinatorics and network theory goes looking for regularities and repeated patterns inside structures equipped with nodes and edges. RAM represents the outcome of a dual methodological commitment: by one side a top-down approach evaluates the possible arrangement of specific subgraphs when the number of graph's vertices is already known, by another side a bottom-up approach calculates the possible number of graph's vertices when the arrangement of specific subgraphs is already known. Since natural neural networks are often represented in terms of graphs, we propose to use RAM for the analytical and computational assessment of the human brain connectome, i.e., the distinctive anatomical/functional structure provided with vertices and edges at different coarse-grained scales. We retrospectively examined the literature regarding graph theory in neuroscience, looking for hints that might be related to the RAM framework. At first, we establish that the peculiar network required by RAM, i.e., a graph characterized by every vertex connected with all the others, does exist inside the human brain connectome. Then, we argue that the RAM approach to nervous networks might be able to trace unexpected functional interactions and unexplored motifs shared between different cortical and subcortical subareas. Furthermore, we describe how remarkable RAM outcomes, such as the Ramsey's theorem and the Ramsey's number, might contribute to quantify novel properties of neuronal networks and uncover still unknown anatomical connexions. [ABSTRACT FROM AUTHOR]