2019/07/29 by Heidi S. Christensen, Christensen, Heidi S., Jesper Møller +1
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1907.12283
openalex publication_date 2019/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dendritic spines, which are small protrusions on the dendrites of a neuron,\nare of interest in neuroscience as they are related to cognitive processes such\nas learning and memory. We analyse the distribution of spine locations on six\ndifferent dendrite trees from mouse neurons using point process theory for\nlinear networks. Besides some possible small-scale repulsion, we find that\ntwo of the spine point pattern data sets may be described by inhomogeneous\nPoisson process models, while the other point pattern data sets exhibit\nclustering between spines at a larger scale. To model this we propose an\ninhomogeneous Cox process model constructed by thinning a Poisson process on a\nlinear network with retention probabilities determined by a spatially\ncorrelated random field. For model checking we consider network analogues of\nthe empirical F-, G-, and J-functions originally introduced for\ninhomogeneous point processes on a Euclidean space. The fitted Cox process\nmodels seem to catch the clustering of spine locations between spines, but also\nposses a large variance in the number of points for some of the data sets\ncausing large confidence regions for the empirical F- and G-functions.\n