Model and empirical study on some collaboration networks

In this paper we present an empirical study of a few practical systems described by cooperation networks, and propose a model to understand the results obtained. We study four non-social systems, which are the Bus Route Networks of Beijing and Yangzhou, the Travel Route Network of China, Huai-Yang recipes of Chinese cooked food, and a social system, which is the Collaboration Network of Hollywood Actors. In order to explain the results related to the degree distribution, act-degree distribution and act-size distribution (especially about the degree distribution, which may be better fitted using a stretched exponential distribution (SED)), we suggest a simple model to show a possible evolutionary mechanism for the emergence of such networks. The analytic and numerical results obtained from the model are in good agreement with the empirical results.     

A note on the kernel of the\bar \partial -Neumann operator on strongly pseudo-convex domains

In this paper, we discuss the relations between a special Heisenberg coordinate system and a normalized Levi metric on strongly pseudo-convex domains in Cⁿ and see how they are related to the -Neumann operator.Work supported by MSRI, Berkeley, California.