We propose a hardware-assisted visibility ordering algorithm. From a given viewpoint, a (back-to-front) visibility ordering of a set of objects is a partial order on the objects such that if object obstructs object , then precedes in the ordering. Such orderings are useful because they are the building blocks of other rendering algorithms such as direct volume rendering of unstructured grids. T...

The covariance ordering, for discrete and continuous time Markov chains, is defined and studied. This partial ordering gives a necessary and sufficient condition for MCMC estimators to have small asymptotic variance. Connections between this ordering, eigenvalues, and suprema of the spectrum of the Markov transition kernel, are provided. A representation of the asymptotic variance of MCMC estim...

The standard preference ordering on the well-known centering transitions Continue, Retain, Shift is argued to be unmotivated: a partial, context-dependent ordering emerges from the interaction between principles dubbed cohesion (maintaining the same center of attention) and salience (realizing the center of attention as the most prominent NP). A new formulation of Rule 2 of centering theory is ...

It is a challenging task to reason about a dynamically evolving system with events triggering state transitions and uncertainty about the ordering of events. In previous research, uncertainty of the event ordering is mainly modelled by partial orders over the events. In this paper, we investigate uncertainty of the event ordering modelled by time intervals in which the events may occur. Each ev...

Consider the following properties of a binary relation ≤ on a set X: (Reflexivity) For all x ∈ X, x ≤ x. (Anti-Symmetry) For all x, y ∈ X, if x ≤ y and y ≤ x, then x = y. (Transitivity) For all x, y, z ∈ X, if x ≤ y and y ≤ z, then x ≤ z. (Totality) For all x, y ∈ X, either x ≤ y or y ≤ x. A relation which satisfies reflexivity and transitivity is called a quasi-ordering. A relation which satis...

We introduce a description language for specifying partial ordering relations over concept descriptions in description logics, and show how the language can be used in combination with binary trees to efficiently search a database that corresponds to a finite set of concept descriptions. The language consists of a pair of ordering constructors that support a form of exogenous indexing in which ...

In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency were generalized to variable ordering structu...