Many phenomena with power laws have been observed in various fields of the natural and social sciences, and these power laws are often interpreted as the macro behaviors of systems that consist of micro units. In this paper, we review some basic mathematical mechanisms that are known to generate power laws. In particular, we focus on stochastic processes including the Yule process and the Simon...

In this paper we establish a Harnack inequality for nonnegative harmonic functions of some discontinuous Markov processes with a diffusion part. AMS 2000 Mathematics Subject Classification: Primary 60J45, 60J75, Secondary 60J25.

In this paper we present examples illustrating five important issues involved in the identification of structural information about social processes using the fragmentary data which is usually available for this purpose. These issues are listed below. (i) It is of considerable importance to use continuous-time models to desi;ribe processes for which there is no substant~ve basis for a choice of...

Today people work together across time, space, cultural and organizational boundaries. To simplify and automate the work, collaboration employs a broad range of tools, such as project management software, groupware, social networking services, or wikis. For a collaboration to be effective, the actions of collaborators need to be properly coordinated, which requires taking into account social, s...

In the proposal the organisers considered that it would be a success if during the week: (a) new simulations are started (b) existing simulations are improved, based on the discussion (c) links between existing models and simulations are identified to design a fabric of simulation models (d) new collaborations are initiated across disciplinary boundaries (e) participants are stimulated to do fu...