论文标题
在集群中心带有孔的母子群集工艺
Matern Cluster Process with Holes at the Cluster Centers
论文作者
论文摘要
受点过程在生物纳米网络中的最新应用的启发，本文提出了Matérn群集过程（MCP）的新型变体，其中距离群集中心一定距离内的点被删除。我们将这个新的过程称为MCP，在集群中心（简而言之MCP-H）带有孔。为了关注三维（3D）空间，我们首先表征给定群集的任意点与原点的条件分布，该距离在该群集的位置，对于MCP和MCP-H的位置。这些分布显示在3D空间中承认非常简单的封闭形式，在简单的二维（2D）情况下，这甚至是不可能的。使用这些分布，对MCP和MCP-H表征了接触距离分布和概率生成功能（PGFL）。
Inspired by recent applications of point processes to biological nanonetworks, this paper presents a novel variant of a Matérn cluster process (MCP) in which the points located within a certain distance from the cluster centers are removed. We term this new process the MCP with holes at the cluster center (MCP-H, in short). Focusing on the three-dimensional (3D) space, we first characterize the conditional distribution of the distance between an arbitrary point of a given cluster to the origin, conditioned on the location of that cluster, for both MCP and MCP-H. These distributions are shown to admit remarkably simple closed forms in the 3D space, which is not even possible in the simpler two-dimensional (2D) case. Using these distributions, the contact distance distribution and the probability generating functional (PGFL) are characterized for both MCP and MCP-H.
