The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling J are studied as functions of temperature and J. The two concurrences exhibit a different dependence on J at the ground state, which could be interpreted from the point of view of the correlation functions. The thresho...

This paper presents a multimedia join operator that is carried out through the method of the nearest neighbor search. In contrast to related approaches that utilizes a similarity function to perform a join between two instances of the input tables, we adopt the more flexible and widely used nearest neighbor method. First, we introduce a simple nearest neighbor search algorithm based on an neste...

A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in Euclidean spaces a closed set is Chebyshev if and only if the set is convex. In this paper, from the more general perspective of Bregman distances, we show th...

In this work, one and two-dimensional lattices are studied theoretically by a statistical mechanical approach. The nearest and next-nearest neighbor interactions are both taken into account, and the approximate thermodynamic properties of the lattices are calculated. The results of our calculations show that: (1) even though the next-nearest neighbor interaction may have an insignificant ef...

Change-point analysis is thriving in this Big Data era to address problems arising many fields where massive data sequences are collected study complicated phenomena over time. It plays an important role processing these by segmenting a long sequence into homogeneous parts for follow-up studies. The task requires the method be able process large datasets quickly and deal with various types of c...

This paper provides the first solution to the kinetic reverse k-nearest neighbor (RkNN) problem in R, which is defined as follows: Given a set P of n moving points in arbitrary but fixed dimension d, an integer k, and a query point q / ∈ P at any time t, report all the points p ∈ P for which q is one of the k-nearest neighbors of p.

Using tools from numerical algebraic geometry, we propose a phylogenetic reconstruction algorithm which uses the distance to the nearest point on the phylogenetic model to select the tree of best fit. This method allows for the reconstruction of branch lengths and for hypothesis testing. A data-dependent statistical test identifies correctly reconstructed quartet trees 100% of the time when the...

In this letter, we derive the cumulative density function (CDF) of the nearest neighbor and contact distance distributions of the Matérn cluster process (MCP) in R. These results will be useful in the performance analysis of many realworld wireless networks that exhibit inter-node attraction. Using these results, we concretely demonstrate that the contact distance of the MCP stochastically domi...

This paper presents a simple and effective method for approximate indexing of instances for instance based learning. The method uses an interval tree to determine a good starting search point for the nearest neighbor. The search stops when an early stopping criterion is met. The method proved to be very effective especially when only the first nearest neighbor is required. Keywords—Instance bas...