The concepts of regular generalized functions in Gaussian analysis are presented. Spaces of regular generalized functions are characterized and their probabilistic structure is worked out. Finally, these concepts are applied to a nonlinear (Verhulst type) equation. Its solution is shown to be a regular generalized process with martingale property.

The model elimination calculus is a linear, refutationally complete calculus for rst order clause logic. We show how to extend this calculus with a framework for theory reasoning. Theory reasoning means to separate the knowledge of a given domain or theory and treat it by special purpose inference rules. We present two versions of theory model elimination: the one is called total theory model e...

Terrain LOD algorithm is a dynamic and local dough sheet subduction algorithm. On the basis of the research on traditional quadtree algorithm, this paper proposed a new terrain LOD algorithm using quadtree. On deviation computing standard, besides static deviation and view distance, motion vector and observation vector are introduced, which made the result of deviation computing close to the ac...

Fourier-Motzkin variable elimination is introduced as a complete method for deciding linear arithmetic inequalities over R. It is then shown how this method can be extended to also work over Z, giving the Omega Test [2].

A simple but powerful modification of the standard Gaussian distribution is studied. The variables of the rectified Gaussian are constrained to be nonnegative, enabling the use of nonconvex energy functions. Two multimodal examples, the competitive and cooperative distributions, illustrate the representational power of the rectified Gaussian. Since the cooperative distribution can represent the...

In this article we extend and generalize the ideas of two previous articles devoted to linear sensor networks to nonlinear systems. In those previous articles the use of cutsets and a decomposition procedure were proposed and proved efficient to solve large scale linear problems. In this article we show that a similar procedure, now based on a variable elimination scheme, can be also used effic...