(a) The medians intersect in a point interior to the triangle, called the centroid, which divides each of the medians in the ratio 2 : 1. (b) The medians form a new triangle, called the median triangle. (c) The area of the median triangle is 3/4 of the area of the given triangle in which the medians were constructed. (d) The median triangle of the median triangle is similar to the given triangl...

The present article is a follow-up study of the investigation of labiodentals in German and Dutch by Hamann & Sennema (2005), where we looked at the perception of the Dutch labiodental three-way contrast by German listeners without any knowledge of Dutch and German learners of Dutch. The results of this previous study suggested that the German voiced labiodental fricative /v/ is perceptually cl...

In this paper, we study a prototype learning problem, called Median Point-Set, whose objective is to construct a prototype for a set of given point-sets so as to minimize the total Earth Mover’s Distances (EMD) between the prototype and the point-sets, where EMD between two point-sets is measured under affine transformation. For this problem, we present the first purely geometric approach. Comp...

The maximum asymptotic bias of an estimator is a global robustness measure of the performance of an estimator. The projection median estimator for multivariate location shows a remarkable behavior regarding asymptotic bias. In this paper we consider a modi cation of the projection median estimator which renders an estimate with better bias performance for point mass contaminations (the worst si...

This paper characterizes a mixed strategy Nash equilibrium in a one-dimensional Downsian model of two-candidate elections with a continuous policy space, where candidates are office motivated and one candidate enjoys a nonpolicy advantage over the other candidate. We assume that voters have quadratic preferences over policies and that their ideal points are drawn from a uniform distribution ove...

A large population of voters with single-peaked preferences are partitioned into disjoint constituencies. Collective decisions are taken by their representatives, one from each constituency, according to a weighted voting rule. It is assumed that each representative’s ideal point perfectly matches that of the respective constituency median and that top-tier decisions are in the voting game’s co...

A median (antimedian) of a profile of vertices on a graph G is a vertex that minimizes (maximizes) the sum of the distances to the elements in the profile. The median (antimedian) function has as output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (obnoxious) facility in a network. The median function is well studied. For instance ...

Vector median filtering is a well known technique for reducing noise in color images. These filters are defined on the basis of a suitable distance or similarity measure, being the most common used the Euclidean and City-Block distances. In this paper, a Fuzzy Metric, in the sense of George and Veeramani (1994), is defined and applied to color image filtering by means of a new Vector Median Fil...

This paper characterizes a mixed strategy Nash equilibrium in a one-dimensional Downsian model of two-candidate elections with a continuous policy space, where candidates are office motivated and one candidate enjoys a nonpolicy advantage over the other candidate. We assume that voters have quadratic preferences over policies and that their ideal points are drawn from a uniform distribution ove...

In regression, the desired estimate of y|x is not always given by a conditional mean, although this is most common. Sometimes one wants to obtain a good estimate that satisfies the property that a proportion, τ , of y|x, will be below the estimate. For τ = 0.5 this is an estimate of the median. What might be called median regression, is subsumed under the term quantile regression. We present a ...