Discrete dynamical systems serve as useful formal models to study diffusion phenomena in social networks. Motivated by applications in systems biology, several recent papers have studied algorithmic and complexity aspects of diffusion problems for dynamical systems whose underlying graphs are directed, and may contain directed cycles. Such problems can be regarded as reachability problems in the phase space of the corresponding dynamical system. We show that computational intractability results for reachability problems hold even for dynamical systems on directed acyclic graphs (dags). We also show that for dynamical systems on dags where each local function is monotone, the reachability problemmore »can be solved efficiently.« less

Abstract—Networks have entered the mainstream lexicon over the last ten years. This coincides with the pervasive use of networks in a host of disciplines of interest to industry and academia, including biology, neurology, genomics, psychology, social sciences, economics, psychology, and cyber-physical systems and infrastructure. Several dozen journals and conferences regularly contain articles related to networks. Yet, there are no general purpose cyberinfrastructures (CI) that can be used across these varied disciplines and domains. Furthermore, while there are scientific gateways that include some network science capabilities for particular domains (e.g., biochemistry, genetics), there are no general-purpose network-based scientific gateways. In thismore »work, we introduce net.science, a CI for Network Engineering and Science, that is designed to be a community resource. This paper provides an overview of net.science, addressing key requirements and concepts, CI components, the types of applications that our CI will support, and various dimensions of our evaluation process. Index Terms—cyberinfrastructure, network science, net.science« less