Related papers: Nearest-Neighbor and Contact Distance Distribution…
In this letter, we derive the cumulative density function (CDF) of the nearest neighbor and contact distance distributions of the Matern cluster process (MCP) in R2. These results will be useful in the performance analysis of many…
In this letter, we derive the CDF (cumulative distribution function) of $k$th contact distance (CD) and nearest neighbor distance (NND) of the $n$-dimensional ($n$-D) Mat\'ern cluster process (MCP). We present a new approach based on the…
In this paper we present an analytic framework for formulating the statistical distribution of the nearest neighbour distance in hard-core point processes. We apply this framework to Mat\'{e}rn hard-core point process (MHC) to derive the…
In this letter, we derive new lower bounds on the cumulative distribution function (CDF) of the contact distance in the Poisson Hole Process (PHP) for two cases: (i) reference point is selected uniformly at random from $\mathbb{R}^2$…
This letter characterizes the statistics of the contact distance and the nearest neighbor (NN) distance for binomial point processes (BPP) spatially-distributed on spherical surfaces. We consider a setup of $n$ concentric spheres, with each…
In this paper, we consider a Cox point process driven by the Manhattan Poisson line process. We calculate the exact cumulative distribution function (CDF) of the path distance (L1 norm) between a randomly selected intersection and the…
The use of summary statistics beyond the two-point correlation function to analyze the non-Gaussian clustering on small scales is an active field of research in cosmology. In this paper, we explore a set of new summary statistics -- the…
This letter provides exact characterization of the contact and nearest-neighbor distance distributions for the n dimensional (n-D) Matern cluster process (MCP). We also provide novel upper and lower bounds to these distributions in order to…
Cooperation in cellular networks has been recently suggested as a promising scheme to improve system performance. In this work, clusters are formed based on the Mutually Nearest Neighbour relation, which defines which stations cooperate in…
In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson clustered…
Cooperation in cellular networks is a promising scheme to improve system performance. Existing works consider that a user dynamically chooses the stations that cooperate for his/her service, but such assumption often has practical…
Cluster analysis which focuses on the grouping and categorization of similar elements is widely used in various fields of research. Inspired by the phenomenon of atomic fission, a novel density-based clustering algorithm is proposed in this…
Inspired by recent applications of point processes to biological nanonetworks, this paper presents a novel variant of a Mat\'ern cluster process (MCP) in which the points located within a certain distance from the cluster centers are…
Cross-correlations between datasets are used in many different contexts in cosmological analyses. Recently, $k$-Nearest Neighbor Cumulative Distribution Functions ($k{\rm NN}$-${\rm CDF}$) were shown to be sensitive probes of cosmological…
While the Euclidean distance characteristics of the Poisson line Cox process (PLCP) have been investigated in the literature, the analytical characterization of the path distances is still an open problem. In this paper, we solve this…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
We present a comprehensive approach to the modeling, performance analysis, and design of clustered molecular nanonetworks in which nano-machines of different clusters release an appropriate number of molecules to transmit their sensed…
The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are…
This paper introduces a hierarchical clustering algorithm, the Clustroid Hierarchical Nearest Neighbor ($\mathrm{CHN}^2$), designed for datasets with a countably infinite number of points. The method builds clusters across successive levels…
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…