In this paper we present a production system which acts on xed length vectors of labels Our goal is to automatically generate heuristics to search the state space for shortest paths between states e ciently The heuristic values which guide search in the state space are obtained by searching for the shortest path in an abstract space derived from the de nition of the original space In PSVN a sta...

In this paper we present a production system which acts on xed length vectors of labels. Our goal is to automatically generate heuristics to search the state space for shortest paths between states eeciently. The heuristic values which guide search in the state space are obtained by searching for the shortest path in an abstract space derived from the deenition of the original space. In PSVN, a...

Let G be a directed graph embedded on a surface of genus g with b boundary cycles. We describe an algorithm to compute the shortest non-contractible cycle in G in O((g3 + g b)n log n) time. Our algorithm improves the previous best known time bound of (g + b)O(g+b)n log n for all positive g and b. We also describe an algorithm to compute the shortest non-null-homologous cycle in G in O((g2 + g b...

We extend Penrose’s peeling model for the asymptotic behaviour of solutions to the scalar wave equation at null infinity on asymptotically flat backgrounds, which is well understood for flat space-time, to Schwarzschild and the asymptotically simple space-times of Corvino-Schoen/Chrusciel-Delay. We combine conformal techniques and vector field methods: a naive adaptation of the “Morawetz vector...

In this paper we introduce a reference along a null curve in an n-dimensional Lorentzian space with the minimun number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski space-time and it is called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We characterize the null helices (that is,...

A new strategy to on-line collision-avoidance of the redundant robots with obstacles is presented. The strategy allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effectors trajectory. The effectiveness of the proposed strategy based on null space criteria is discussed by theoretical considerations. The strategy is based on ...

We will present theory that underpins the use of null-space preconditioners, giving eigenvalue bounds that show that the eigenvalues of the preconditioned system are clustered when a good approximation to the null-space matrix can be found. Additionally, we will describe how two of the family of preconditioners, although indefinite and non-symmetric, can be applied with a Krylov method with a s...