For modelling the location of pyramidal cells in the human cerebral cortex we suggest a hierarchical point process in $\mathbb{R}^3$ that exhibits anisotropy in the form of cylinders extending along the $z$-axis. The model consists first of a generalised shot noise Cox process for the $xy$-coordinates, providing cylindrical clusters, and next of a Markov random field model for the $z$-coordinates conditioned on the $xy$-coordinates, 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 final model allowing for both repulsion and attraction between the points seem adequate. We discuss how the final model relates to the so-called minicolumn hypothesis in neuroscience.
翻译:对于模拟人类大脑皮层中金字塔细胞位置的模型,我们建议用$mathbb{R ⁇ 3$来显示一个等级点过程,该过程以圆柱形的形式在 $z$-axis 上展示了异质。该模型首先为 $xy 坐标 提供 圆柱形 圆形 圆球, 下一个 Markov 随机 字段模型, 以 $zy 坐标为条件, 以 $xy$ 坐标为标准, 提供 反向、 聚合或 两者在特定的互动领域 。 这些等级点过程的几例都安装在两个金字塔细胞数据集上, 而这些最后模型允许两个点之间的反光和吸引。 我们讨论最后模型与神经科学中所谓的微型线假设的关系如何。