We study a variant of the Falconer distance problem for perturbations of the Euclidean and related metrics. We prove that Mattila’s criterion, expressed in terms of circular averages, which would imply the Falconer conjecture, holds on average. We also use a diophantine conversion mechanism to prove that well-distributed case of the Erdos Distance Conjecture holds for almost every appropriate p...

Group decision making is an important part of multiple criteria decision making and the analytic hierarchy process (AHP). The aim of this paper was to compare group AHP methods. Seven simple group AHP aggregation techniques that could be attractive for applications selected from the vast array of group AHP models proposed in the literature were selected for evaluation. We developed three new me...

In this paper we show that the θ-graph with 4 cones has constant stretch factor, i.e., there is a path between any pair of vertices in this graph whose length is at most a constant times the Euclidean distance between that pair of vertices. This is the last θ-graph for which it was not known whether its stretch factor was bounded.

The Gaussian kernel encourages similarity between inputs based on their Euclidean distance. Because we’re not dealing with probabilities which must sum to 1, we can omit the normalization constant found in the Gaussian distribution. But the shape is the same: we strongly encourage similarity among nearby inputs, while as inputs get further away, we encourage similarity by an amount that decreas...

Randomly generated points in IR are connected to their nearest neighbours (Euclidean distance). The resulting connected clusters of points are studied. This paper examines questions related to the collection of clusters formed and to the internal structure of a cluster. In particular, the one-dimensional structure is examined in detail.

This paper presents an efficient algorithm for the classification of features into strong and weak features for every distinct subject to create an intelligent online signature verification system. Whereas Euclidean distance classifier is used for validation processes and low error rates obtained illustrate the feasibility of the algorithm for an online signature verification system. Keywords-S...

In this work we describe a procedure to construct finite signal constellations from lattices associated to rings of algebraic integers and their ideals. The procedure provides a natural way to label the constellation points by elements of a finite field. The labeling is proven to be linear which allows, at the receiver, a fast way to map a constellation point into a field element. The performan...

We present in this paper methods to compute the signed Euclidean distance to surfaces obtained by the intersection (respectively union or difference) of two solids (in two or three dimensions). These implementations can replace min/max or R-functions traditionally used to model set operations used with implicit surfaces.

where Entμ(f ) is the entropy of f with respect to μ (see below). It is well-known that the product measure μ of μ on R then satisfies the preceding inequalities (with the Euclidean length of the gradient of the function f on R) with the same constant C, in particular independent of the dimension n. Let now H be a smooth function on R such that ∫ edμ < ∞. Define Q the probability measure on R w...

The paper investigates some similarity measures in interval bipolar neutrosophic environment for multi-attribute decision making problems. At first, we define Hamming and Euclidean distances measures between interval bipolar neutrosophic sets and establish their basic properties. We also propose two similarity measures based on the Hamming and Euclidean distance functions. Using maximum and min...