Modelling columnarity of pyramidal cells in the human cerebral cortex.

For modelling the location of pyramidal cells in the human cerebral cortex we suggest a hierarchical point process in $\mathbb{R}^3$. The model consists first of a generalised shot noise Cox process in the $xy$-plane, providing cylindrical clusters, and next of a Markov random field model on the $z$-axis, providing either repulsion, aggregation, or both within specified areas of interaction. Several cases of these hierarchical point processes are fitted to two pyramidal cell datasets, and of these a model allowing for both repulsion and attraction between the points seem adequate.