Avoidance problems reconsidered

New problems of pattern avoidance

Multicollinearity Reconsidered

In this paper we intend to improve the explanatory power of regressions when the deletion method is used for the remedy of Multicolinearity. If one deletes the variable (s) that is (are) responsible for Multicolinearity, he loses some information that is not common between the deleted variable (s) and the other remaining variables in the regression. To improve this method, we run the deleted va...

Variational collision avoidance problems on Riemannian manifolds

In this article we introduce a variational approach to collision avoidance of multiple agents evolving on a Riemannian manifold and derive necessary conditions for extremals. The problem consists of finding non-intersecting trajectories of a given number of agents, among a set of admissible curves, to reach a specified configuration, based on minimizing an energy functional that depends on the ...

Reportrapport Declarative Interpretations Reconsidered Declarative Interpretations Reconsidered

Three semantics have been proposed as the most promising candidates for a declarative interpretation for logic programs and pure Prolog programs: the least Herbrand model, the least term model, i.e. the C-semantics, and the S-semantics. Previous results show that a strictly increasing information ordering between these semantics exists for the class of all programs. In particular, the S-semanti...

Nemesis Reconsidered

The hypothesis of a companion object (Nemesis) orbiting the Sun was motivated by the claim of a terrestrial extinction periodicity, thought to be mediated by comet showers. The orbit of a distant companion to the Sun is expected to be perturbed by the Galactic tidal field and encounters with passing stars, which will induce variation in the period. We examine the evidence for the previously pro...