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Modelling columnarity of pyramidal cells in the human cerebral cortex

By Andreas Dyreborg Christoffersen, Jesper Møller and Heidi Søgaard Christensen
CSGB Research Reports
No. 08, August 2019

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.

Keywords: Cylindrical $K$-function; Determinantal point process; Hierarchical point process model; Line cluster point process; Minicolumn hypothesis

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