Networks of noisy oscillators with correlated degree and frequency dispersion

We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase oscillators that represent the node dynamics. Crucially in our work, the variability in the number of connections of the nodes is correlated with the width of the frequency distribution of the oscillators. By numerical simulations on Erdös-Rényi networks, where the frequencies of the oscillators are Gaussian distributed, we make the counterintuitive observation that an increase in the strength of the correlation is accompanied by an increase in the critical coupling strength for the onset of synchronization. We further observe that the critical coupling can solely depend on the average number of connections or even completely lose its dependence on the network connectivity. Only beyond this state, a weighted mean-field approximation breaks down. If noise is present, the correlations have to be stronger to yield similar observations.

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Viewpoint-Based Ambient Occlusion

We've developed a new ambient occlusion technique based on an information-theoretic framework. Essentially, our method computes a weighted visibility from each object polygon to all viewpoints; we then use these visibility values to obtain the information associated with each polygon. So, just as a viewpoint has information about the model's polygons, the polygons gather information on the viewpoints. We therefore have two measures associated with an information channel defined by the set of viewpoints as input and the object's polygons as output, or vice versa. From this polygonal information, we obtain an occlusion map that serves as a classic ambient occlusion technique. Our approach also offers additional applications, including an importance-based viewpoint-selection guide, and a means of enhancing object features and producing nonphotorealistic object visualizations