We introduce a scheme of control polygons to design topological skeletons for vector fields of arbitrary topology. Based on this we construct piecewise linear vector fields of exactly the topology specified by the control polygons. This way a controlled construction of vector fields of any topology is possible. Finally we apply this method for topology-preserving compression of vector fields co...

The topological phase factor induced on interfering electrons by external quantum electromagnetic fields has been studied. Two and three electron interference experiments inside distant cavities are considered and the influence of correlated photons on the phase factors is investigated. It is shown that the classical or quantum correlations of the irradiating photons are transferred to the topo...

The self-organizing map (SOM) has been widely used as a software tool for visualization of high-dimensional data. Important SOM features include information compression while trying to preserve topological and metric relationship of the primary data items. The assumption of topological preservation in SOMs is not true for many data mappings involving dimension reduction. With the automation of ...