We develop a theory of isometric subgraphs of hypercubes for which a certain inheritance of isometry plays a crucial role. It is well known that median graphs and closely related graphs embedded in hypercubes bear geometric features that involve realizations by solid cubical complexes or are expressed by Euler-type counting formulae for cubical faces. Such properties can also be established for...

Given a set S of n points in R 2 , the Oja depth of a point is the sum of the areas of all triangles formed by and two elements of S. A point in R 2 with minimum depth is an Oja median. We show how an Oja median may be computed in O(n log 3 n) time. In addition, we present an algorithm for computing the Fermat-Torricelli points of n lines in O(n) time. These points minimize the sum of weighted ...

Utah ranks first in the nation in the number of consumer bankruptcies per household. This study describes 2,567 Chapter 7 and Chapter 13 cases filed in the U.S. Bankruptcy Court for Utah in 1997. Median debt level was $31,981 for Chapter 7 and $41,626 for Chapter 13 cases. While Utah boasts a high proportion of Chapter 13 repayment plans, only 10.8% of these cases were successfully completed. D...

The Planck satellite has recently completed an all-sky galaxy cluster survey exploiting the thermal Sunyaev– Zel’dovich (SZ) effect to locate some of the most massive systems observable. With a median redshift of z 0.22 á ñ = , the clusters found by Planck at z 0.3 > are proving to be exceptionally massive and/or disturbed systems. One notable Planck discovery at z = 0.645, PLCK G147.3-16.6, ha...

Take n > 0 and n + 1 disjoint, bounded intervals I0, . . . , In, possible single points. In [2], motivated by applications in signal processing, it was conjectured that for any numbers a0, . . . , an, there is a unique polynomial of degree n whose median value on Ij equals aj for j = 0, . . . ,n, and this was confirmed for n = 2. We shall verify this conjecture in section 2. Indeed we prove a m...

In rapidly growing urban areas, it is deemed vital to expand (or contract) an existing network of public facilities to meet anticipated changes in the level of demand. We present a multi-period capacitated median model for school network facility location planning that minimizes transportation costs, while functional costs are subject to a budget constraint. The proposed Vintage Flexible Capaci...

The convex ordered median problem is a generalization of the median, the k-centrum or the center problem. The task of the associated inverse problem is to change edge lengths at minimum cost such that a given vertex becomes an optimal solution of the location problem, i.e., an ordered median. It is shown that the problem is NP-hard even if the underlying network is a tree and the ordered median...

Standard median filters preserve abrupt shifts (edges) and remove impulsive noise (outliers) from a constant signal but they deteriorate in trend periods. FIR median hybrid (FMH) filters are more flexible and also preserve shifts, but they are much more vulnerable to outliers. Application of robust regression methods, in particular of the repeated median, has been suggested for removing subsequ...

2 Set up 1 2.1 R code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.1 cclust Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.2 Prediction Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Print Function . . . . . . . . . . . . . . . . . . . . . . . . ...

One of the most widely appreciated problems of contingent valuation is the potential manipulability of the method, thus subjecting it to possible strategic bias. This paper shows that under usual conditions this problem also holds for market-based methods, such as travel cost and hedonic pricing. However, not all formats of these valuation methods are manipulable. This paper finds positive resu...