相关论文: Nearest Neighbor and Contact Distance Distribution…

Consider a stationary Poisson process in a $d$-dimensional hyperbolic space. For $R>0$ define the point process $\xi_R^{(k)}$ of exceedance heights over a suitable threshold of the hyperbolic volumes of $k$th nearest neighbour balls centred…

We are interested in comparing probability distributions defined on Riemannian manifold. The traditional approach to study a distribution relies on locating its mean point and finding the dispersion about that point. On a general manifold…

Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point…

Nearest-neighbour retrieval is central to classification and explainable-AI pipelines, but current practice relies on hand-tuning feature layers and distance metrics. We propose Targeted Manifold Manipulation-Nearest Neighbour (TMM-NN),…

In this paper, we investigate the cumulative distribution function (CDF) of the aggregate interference in carrier sensing multiple access/collision avoidance (CSMA/CA) networks measured at an arbitrary time and position. We assume that…

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of…

We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero…

Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…

We introduce a novel approach for studying random k-coverage, using Morse theory for the k-nearest neighbor (k-NN) distance function. We prove a sharp phase transition for the number of critical points of the k-NN distance function, from…

In this letter, we consider a 3D molecular communication via diffusion system (MCvDS) with a single point transmitter and multiple fully-absorbing spherical receivers whose centers are distributed as a Poisson point process (PPP) in the…

We use the domination number of a parametrized random digraph family called proportional-edge proximity catch digraphs (PCDs) for testing multivariate spatial point patterns. This digraph family is based on relative positions of data points…

We prove the following three statements: 1) Let $(A, \bar A)$ be a partition of the spherical surface $S^n$ into two measurable sets. Let $st_A$ and $st_{\bar A}$ be their measure density functions of distance. Then $|st_A - st_{\bar A}|$…

Visual defect detection plays an important role in intelligent industry. Patch based methods consider visual images as a collection of image patches according to positions, which have stronger discriminative ability for small defects in…

This paper presents a distributed algorithm to simultaneously compute the diameter, radius and node eccentricity in all nodes of a synchronous network. Such topological information may be useful as input to configure other algorithms.…

We present the Nearest Neighbor Distance (NND) analysis of SDSS DR5 galaxies. We give NND results for observed, mock and random sample, and discuss the differences. We find that the observed sample gives us a significantly stronger…

In directed random graphs, in which edges can be assigned to have one of two directions, or perhaps both, the distance between two vertices $v$ and $v'$ can be computed along paths that are directed from $v$ to $v'$, or along paths that are…

We consider a power-constrained sensor network, consisting of multiple sensor nodes and a fusion center (FC), that is deployed for the purpose of estimating a common random parameter of interest. In contrast to the distributed framework,…

A $k$-nearest neighbor ($k$NN) query determines the $k$ nearest points, using distance metrics, from a specific location. An all $k$-nearest neighbor (A$k$NN) query constitutes a variation of a $k$NN query and retrieves the $k$ nearest…

A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…

In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…