Let XdB be a normal random variable (RV) with mean mXdB and variance σ 2 XdB and let X = 10XdB/10 be the corresponding log-normal RV. (a) Express the mean of X in terms of mXdB and σ 2 XdB . (b) Express the variance of X in terms of mXdB and σ 2 XdB . (c) Express the median of X in terms of mXdB . Based on that, can you now explain why the area mean is sometimes referred to as the median link g...

In phylogenetic analysis, median networks have been proposed as an improvement over tree representations. This paper argues that concept lattices represent a further improvement over median networks because FCA provides a detailed formal description and there are a number of existing software solutions for creating lattices. The purpose of this paper is to raise awareness in the FCA community f...

Applying the recently obtained distributive lattice structure on the set of 1-factors, we show that the resonance graphs of any benzenoid systems G, as well as of general plane (weakly) elementary bipartite graphs, are median graphs and thus extend greatly Klavžar et al.’s result. The n-dimensional vectors of nonnegative integers as a labelling for the 1-factors of G with n inner faces are desc...

We prove that in the case of independent and identically distributed random vectors (Xi, Yi) a class of kernel type M-estimators is universally and strongly consistent for conditional M-functionals. The term universal means that the strong consistency holds for all joint probability distributions of (X, Y ). The conditional M-functional minimizes (2.2) for almost every x. In the case M(y) = |y|...

This paper deals with the existence issue of non-central Wishart distributions which is a research topic initiated by Wishart (1928), and with important contributions by e.g., Lévy (1937), Gindikin (1975), Shanbhag (1988), Peddada & Richards (1991). We present a new method involving the theory of affine Markov processes, which reveals joint necessary conditions on shape and non-centrality param...

In the computer security task of anomaly detection, we wish to measure not only the classiication accuracy of a detector but also the average time to detection. This quantity represents either the average time between false alarms (for a valid user) or the average time until a hostile user is detected. We examine the use of noise suppression lters as componants of a learning classiication syste...

Median graphs are a natural generalisation of trees and hypercubes that are closely related to distributive lattices and graph retracts. In the past decade, they have become of increasing interest to the biological community, where, amongst other things, they are applied to the study of evolutionary relationships within populations. Two simple measures of complexity for a median graph are the n...

We consider maximum b-matching problems where the nodes of the graph represent points in a metric space, and the weight of an edge is the distance between the respective pair of points. We show that if the space is either the rectilinear plane, or the metric space induced by a tree network, then the b-matching problem is the dual of the (single) median location problem with respect to the given...

During the last years, the genomes of more and more species have been sequenced, providing data for phylogenetic reconstruction based on genome rearrangement measures, where the most important distance measures are the reversal distance and the transposition distance. The two main tasks in all phylogenetic reconstruction algorithms is to calculate pairwise distances and to solve the median of t...