Mixing time trichotomy in regenerating dynamic digraphs

Visualizing Large Dynamic Digraphs

In this paper we investigate the problem of visually representing large dynamic directed graphs with many vertices, edges, and time steps. With this work we do not primarily focus on graph details but more on achieving an overview about long graph sequences with the major focus to be scalable in vertex, edge, and time dimensions. To reach this goal we first map each graph to a bipartite layout ...

TimeRadarTrees: Visualizing Dynamic Compound Digraphs

The evolution of dependencies in information hierarchies can be modeled by sequences of compound digraphs with edge weights. In this paper we present a novel approach to visualize such sequences of graphs. It uses radial tree layout to draw the hierarchy, and circle sectors to represent the temporal change of edges in the digraphs. We have developed several interaction techniques that allow the...

Restricted trichotomy in higher dimensions

I prove, answering a question of Zilber, that if M is an algebraic variety, dimM > 1, and (M, . . .) is a strongly minimal structure with atomic relations definable in the Zariski language on M , then M is locally modular.

Lyapunov Function and Exponential Trichotomy on Time Scales

Dynamic Audio Mixing

3D sound is a powerful technology which allows to give a realistic impression of localization of sound sources. This technology is now mature enough to produce a finegrained spatialization on a set of audio sound sources in real time. However, the are serious limitations in the way this technology is used in current practice. Firstly, composers and sound engineers have great difficulty in maste...