This project focuses on one of the most popular models of complex networks, Boolean models, and proposes a new approach based on a process-viewpoint. In contrast to the standard attractor-basin portrait of a discrete dynamical system, the process-viewpoint starts with a single sequence of states and addresses the types of networks that might produce that sequence. The sequence of states, a process, corresponds to a time-course in biological terms and is often the only dynamical data available for real systems. The types of research questions include: what networks produce a given biological process? How do those networks differ and what do they have in common? This project will also consider the space of processes and the types of questions that arise from characterizing the space: Are some processes harder to build networks for? Do some processes need different network properties than others? The approach used is based on mathematical logic and results in a single expression characterizing the space of networks for a given process.
The importance of this research project is threefold. First, the research has the potential of increasing our understanding of complex biological networks, whose functioning is the basis of living systems. Second, the approach might result in a practical algorithm for inferring network structure from the types of data available today; this is significant because the underlying network structure is very difficult to infer with current technologies. The precise network structure and dynamics is essential to understanding how particular reactions within the cell work. Finally, the project will help increase our understanding of complex systems in general. Biocomplexity is merely one type of complexity; to the extent we make headway in building computational tools to help understanding this type of complexity, similar tools are likely to help with other types of complexity. Certainly, this has proved to be the case for other complexity-tools such as small-world networks, scale-free graphs and phase transitions.
