The projection median of a finite set of points in R was introduced by Durocher and Kirkpatrick [Computational Geometry: Theory and Applications, Vol. 42 (5), 364–375, 2009]. They proved that the projection median in R provides a better approximation of the 2-dimensional Euclidean median, than the center of mass or the rectilinear median, while maintaining a fixed degree of stability. In this p...

A robust approach for super resolution is presented, which is especially valuable in the presence of outliers. Such outliers may be due to motion erros, inaccurate blur models, noise, moving objects, motion blur etc. This robustness is needed since super-resolution methods are very sensitive to such errors. A robust median estimator is combined in an iterative process to achieve a super resolut...

For i ≥ 0, the i-cube Qi is the graph on 2i vertices representing 0/1 tuples of length i, where two vertices are adjacent whenever the tuples differ in exactly one position. (In particular, Q0 = K1.) Let αi(G) be the number of induced i-cubes of a graph G. Then the cube polynomial c(G,x) of G is introduced as ∑ i≥0 αi(G)x i. It is shown that any function f with two related, natural properties, ...

Starting from individual judgments given as categories (i.e., a profile of partitions on an X item set), we attempt to establish a collective partitioning of the items. For that task, we compare two combinatorial approaches. The first one allows to calculate a consensus partition, namely the median partition of the profile, which is the partition of X whose sum of distances to the individual pa...

Given an m-dimensional compact submanifold M of Euclidean space R, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general R-valued functionals including median location, which is derived from the spatial median. The asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated. Convergence...

The median statistic has recently been discussed by Gott et al. as a more reliable alternative to the standard χ 2 likelihood analysis, in the sense of requiring fewer assumptions about the data and being almost as constraining. We apply this statistic to the currently available combined dataset of 92 distant type Ia supernovae, and also to a mock SNAP-class dataset. We find that the performanc...

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network.

In previous work, we introduced median decompositions of graphs, a generalisation of tree decompositions where a graph can be modelled after any median graph, along with a hierarchy of i-medianwidth parameters (mwi)i≥1 starting from treewidth and converging to the clique number. We introduce another graph parameter based on the concept of median decompositions, to be called i-latticewidth and d...

The distance DG(v) of a vertex v in an undirected graph G is the sum of the distances between v and all other vertices of G. The set of vertices in G with maximum (minimum) distance is the antimedian (median) set of a graph G. In this note we prove that for every connected graph G there exists a graph H such that G is a convex subgraph of H and V (G) is the antimedian set of H . A similar const...

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network.