Dendritic spines, which are small protrusions on the dendrites of a neuron, are of interest in neuroscience as they are related to cognitive processes such as learning and memory. We analyse the distribution of spine locations on six different dendrite trees from mouse neurons using point process theory for linear networks. Besides some possible small-scale repulsion, we find that two of the spine point pattern data sets may be described by inhomogeneous Poisson process models, while the other point pattern data sets exhibit clustering between spines at a larger scale. To model this we propose an inhomogeneous Cox process model constructed by thinning a Poisson process on a linear network with retention probabilities determined by a spatially correlated random field. For model checking we consider network analogues of the empirical $F$-, $G$-, and $J$-functions originally introduced for inhomogeneous point processes on a Euclidean space. The fitted Cox process models seem to not only catch the clustering of spine locations between spines, but also possess a large variance in the number of points for some of the data sets causing large confidence regions for the empirical $F$- and $G$-functions.

树突棘是神经元树突上的小突起，在神经科学中很受关注，因为它们与诸如学习和记忆之类的认知过程有关。我们使用线性网络的点过程理论来分析来自小鼠神经元的六种不同树突树上的脊柱位置分布。除了一些可能的小规模排斥之外，我们发现其中两个脊柱点模式数据集可能由不均匀的Poisson过程模型描述，而其他点模式数据集则显示出较大规模的棘突之间的聚类。为了对此建模，我们提出了一个不均匀的Cox过程模型，该模型通过在线性网络上稀化Poisson过程而构建，其保留概率由空间相关的随机字段确定。对于模型检查，我们考虑经验的网络类似物$F$-， $G$-和 $Ĵ$-最初为欧几里得空间上的不均匀点过程引入的函数。拟合的Cox过程模型似乎不仅捕获了脊椎之间的脊柱位置的聚类，而且对于某些数据集的点数也具有很大的差异，从而导致经验值的较大置信区域$F$-和 $G$-职能。