A Jones polynomial for braid-like isotopies of oriented links and its categorification

A braid-like isotopy for links in 3-space is an isotopy which uses only those Reidemeister moves which occur in isotopies of braids. We define a refined Jones polynomial and its corresponding Khovanov homology which are, in general, only invariant under braid-like isotopies.Comment: 19 pages, many figure

Track association performance of the best hypotheses search method

Uncontrolled space objects in the geostationary orbit domain are hazardous threats for active satellites. Catalogs need to be build up, in order to protect this precious domain. The Swiss ZimSMART telescope, located in Zimmerwald, regularly scans the geostationary ring in order to provide a homogenous coverage. This surveying technique typically yields short measurement arcs, called tracklets. Each tracklet provides information about the line-of-sight and the rates of change but typically not about the full state of the observed object. Computationally intensive multi-hypothesis filter methods have been developed to associate tracklets with each other. An effective implementation to this approach is presented that uses an optimization algorithm to reduce the number of initial hypotheses. The method is tested with a set of real measurements of the aforementioned telescope