27/03/2012, 14:00 — 15:00 — Conference Room, Instituto de Sistemas e Robótica, North Tower, 7th floor, IST
Bernold Fiedler, Free University Berlin
Determining nodes for regulatory networks
We consider systems of differential equations which model complex
regulatory networks by a graph structure of dependencies. We show
that the concepts of informative nodes (Mochizuki) and determining
nodes (Foias, Temam) coincide with the notion of feedback vertex
sets from graph theory. As a result we can determine the long-time
dynamics of the entire network from observations on the feedback
vertex set, only. We present biological examples of gene-regulatory
and signal transduction networks where the required observation set
is much smaller than the entire regulatory network. Since the
mathematical scope of our approach is much broader, however, we
actively seek discussion of regulatory and control aspects in other
networks, for example in electrical engineering, multi-agent
coupling, neural networks, and the like.
All results are joint work with Atsushi Mochizuki (RIKEN, Tokyo).