We present a methodology that detects event aggregation about a mass surface using 3-dimensional study regions with a point pattern and a mass present. The Aggregation about a Mass function determines aggregation, randomness, or repulsion of events with respect to the mass surface. Our method closely resembles Ripley’s K function but is modified to discern the pattern about the mass surface. We briefly state the definition and derivation of Ripley’s K function and explain how the Aggregation about a Mass function is different. We develop the novel function according to the definition: the Aggregation about a Mass function times the intensity is the expected number of events within a distance h of a mass. Special consideration of edge effects is taken in order to make the function invariant to the location of the mass within the study region. Significance of aggregation or repulsion is determined using simulation envelopes. A simulation study is performed to inform researchers how the Aggregation about a Mass function performs under different types of aggregation. Finally, we apply the Aggregation about a Mass function to neuroscience as a novel analysis tool by examining the spatial pattern of neurotransmitter release sites as events about a neuron.

我们提出了一种使用具有点图案和质量存在的 3 维研究区域来检测质量表面的事件聚合的方法。关于质量函数的聚合决定了事件相对于质量表面的聚合、随机性或排斥。我们的方法与 Ripley 的 K 函数非常相似，但经过修改以识别质量表面的模式。我们简要阐述 Ripley 的 K 函数的定义和推导，并解释 Mass 函数的聚合有何不同。我们根据定义开发了这个新函数：质量函数的聚合乘以强度就是质量距离 h 内事件的预期数量。特别考虑了边缘效应，以使函数对于研究区域内质量的位置不变。使用模拟包络线确定聚集或排斥的显着性。进行模拟研究是为了让研究人员了解质量函数的聚合在不同类型的聚合下的表现。最后，我们通过检查神经递质释放位点的空间模式作为神经元的事件，将质量函数的聚合作为一种新颖的分析工具应用于神经科学。