We consider planar upward drawings of directed graphs on arbitrary surfaces where the upward direction is defined by a vector field. This generalizes earlier approaches using surfaces with a fixed embedding in R and introduces new classes of planar upward drawable graphs, where some of them even allow cycles. Our approach leads to a classification of planar upward embeddability. In particular, ...

It is experimentally demonstrated that an arbitrary quantum state of a single spin 1/2, a| upward arrow+b| downward arrow, can be converted into a superposition of the two ferromagnetic states of a spin cluster: a| upward arrow upward arrow... upward arrow upward arrow+b| downward arrow downward arrow... downward arrow downward arrow. The physical system is a cluster of seven dipolar-coupled nu...

A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in software engineering, project management, and visual languages. In this paper we investigate upward planarity test...

hat is upward management? Management is getting things done W through people, and upward management can be defined as getting things done through those who supervise us. This concept has been used effectively by the Japanese. Contrasting management in Japan with that in the United States, a Japanese economist said, Our system is rather like an electric train with each car having its own motor, ...

It is shown that almost every language in ESPACE is very hard to approximate with circuits It follows that P BPP implies that E is a measure subset of ESPACE

In this paper we introduce the quasi-upward planar drawing convention and give a polynomial time algorithm for computing a quasiupward planar drawing with the minimum number of bends within a given planar embedding. Further, we study the problem of computing quasi-upward planar drawings with the minimum number of bends of digraphs considering all the possible planar embeddings. The paper contai...