Practical statistical analysis of diffusion tensor images is considered, and we focus primarily on methods that use metrics based on Euclidean distances between powers of diffusion tensors. First we describe a family of anisotropy measures based on a scale invariant power-Euclidean metric, which are useful for visualisation. Some properties of the measures are derived and practical consideratio...

Here shape space is either the manifold of simple closed smooth unparameterized curves in R or is the orbifold of immersions from S to R modulo the group of diffeomorphisms of S. We investige several Riemannian metrics on shape space: L-metrics weighted by expressions in length and curvature. These include a scale invariant metric and a Wasserstein type metric which is sandwiched between two le...

The paper contains some general remarks on the high art of data analysis, some philosophical thoughts about classification, a partial review of outliers and robustness from the point of view of applications, including a discussion of the problem of model choice, and a review of several aspects of robust estimation of covariance matrices, including the pragmatic choice of a weight function based...

The fundamental problem of distance geometry consists in finding a realization of a given weighted graph in a Euclidean space of given dimension, in such a way that vertices are realized as points and edges as straight segments having the same lengths as their given weights. This problem arises in structural proteomics, wireless sensor networks, and clock synchronization protocols to name a few...

We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower bound on Ricci curvature is replaced by the curvature-dimension condition CD(K,N). We show also that for weighted Riemannian manifolds the tria...

‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...

We give a polynomial time, (1+ )-approximation algorithm for the traveling repairman problem (TRP) in the Euclidean plane, on weighted planar graphs, and on weighted trees. This improves on the known quasi-polynomial time approximation schemes for these problems. The algorithm is based on a simple technique that reduces the TRP to what we call the segmented TSP. Here, we are given numbers l1, ....

Dahl, J. 2004. Detection of human-induced stress in streams. Comparison of bioassessment approaches using macroinvertebrates. Doctoral dissertation. ISSN 1401-6230, ISBN 91-576-6716-0. Running water habitats are among the most precious, yet most threatened, ecosystems on earth. Hence, there is a need for reliable methods for detecting the effects of pollution on this valuable commodity. This th...

Wireless Multimedia Sensor Networks (WMSNs) undergo congestion when a link (or a node) becomes overpopulated in terms of incoming packets. In WMSNs this happens especially in upstream nodes where all incoming packets meet and directed to the sink node. Congestion in networks, if not handled properly, might lead to congestion collapse which deteriorates the quality of service (QoS). Therefore, i...