We derive bivariate exponential distributions using independent auxiliary random variables. We develop separate models for positive and negative correlations between the exponentially distributed variates. To obtain a positive correlation, we define a linear relation between the variates X and Y of the form Y = aX +Z where a is a positive constant and Z is independent of X. To obtain exponentia...

With increased complexity of geometric data, topological models play an increasingly important role beyond boundary representations, assemblies, finite elements, image processing, and other traditional modeling applications. While many graphand indexbased data structures have been proposed, no standard representation has emerged as of now. Furthermore, such representations typically do not deal...

The space ML(F ) of measured geodesic laminations on a given compact closed hyperbolic surface F has a canonical linear structure arising in fact from different sources in 2-dimensional hyperbolic (eartquake theory) or complex projective (grafting) geometry as well in (2 + 1) Lorentzian one (globally hyperbolic spacetimes of constant curvature). We investigate this linear structure, by showing ...

Let V be an n-dimensional vector space over a finite field Fq and P = {1, 2, . . . , n} a poset. We consider on V the poset-metric dP . In this paper, we give a complete description of groups of linear isometries of the metric space (V, dP ), for any poset-metric dP . We show that a linear isometry induces an automorphism of order in poset P , and consequently we show the existence of a pair of...

We describe the algorithms and data structures used for optimizing linear spline approximations of bivariate functions. Our method creates a random initial triangulation of a given data set and then employs a simulated annealing algorithm to improve this initial approximation. In every iteration step, the current approximation is changed in a random but local way, and the distance measure betwe...

This paper continuous the approach of developing an ordertheoretic structure theory of one-dimensional continuum structures as elaborated in [Wi07] (see also [Wi83],[Wi03]). The aim is to extend the order-theoretic structure theory by a meaningful algebraization; for this, we concentrate on the real linear continuum structure with its derived concept lattice which gives rise to the so-called “r...

A dilatation structure encodes the approximate self-similarity of a metric space. A metric space (X, d) which admits a strong dilatation structure (definition 2.2) has a metric tangent space at any point x ∈ X (theorem 4.1), and any such metric tangent space has an algebraic structure of a conical group (theorem 4.2). Particular examples of conical groups are Carnot groups: these are simply con...