In this paper, we consider the asymptotic behavior of two Teichmüller geodesic rays determined by Jenkins-Strebel differentials, and we obtain a generalization of a theorem by the author in On behavior of pairs of Teichmüller geodesic rays, 2014 . We also consider the infimum of the asymptotic distance up to choice of base points of the rays along the geodesics. We show that the infimum is repr...

An important problem in Bayesian statistics is how the choice of prior distributions influence inferences. One way to study this is to compare values of measures of distance between prior and posterior distributions for different sample sizes and parameter values. The geodesic distance between probability distributions originally proposed by C.R.Rao is one such measure. Using formulae for the g...

We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. A graph Γ = (V,E) with diameter D is distance meanregular when, for given u ∈ V , the averages of the intersection numbers ai(u, v), bi(u, v), and ci(u, v) (defined as usual), computed over all vertices v at distance i = 0, 1, . . . , D from u, do...

In this paper we study the average distance in weighted graphs. More precisely, we consider assignments of families of non-negative weights to the edges. The aim is to maximise (minimise, respectively) the average distance in the resulting weighted graph. Two variants of the problem are considered depending on whether the collection of weights is fixed or not. The main results of this paper are...

Automatic and semi-automatic magnetic resonance angiog-raphy (MRA) segmentation techniques can potentially save radiologists large amounts of time required for manual segmentation and can facilitate further data analysis. The proposed MRA segmentation method uses a mathematical modeling technique which is well-suited to the complicated curve-like structure of blood vessels. We deene the segment...

Abstract. In this paper we construct a graph-based normalisation algorithm for non-linear data analysis. The principle of this algorithm is get, in average, spherical neighborhood with unit ray. In a first paragraph we show why this algorithm can be useful as a preliminary for some neural algorithms as those that need to compute geodesic distance. Then we present the algorithm, its stochastic v...

We present an efficient computational framework for isometry-invariant comparison of smooth surfaces. We formulate the Gromov-Hausdorff distance as a multidimensional scaling (MDS)-like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances ...

We use Lie-theoretic methods to explicitly compute the full spectrum of Laplace--Beltrami operator on homogeneous spheres which occur as geodesic distance in (compact or noncompact) symmetric spaces rank one, and provide a single unified formula for all cases. As an application, we find resonant radii compact case, i.e., where there is bifurcation embedded constant mean curvature spheres, show ...