We have often observed unexpected state transitions of complex systems. We are thus interested in how to steer a complex system from an unexpected state to a desired state. Here we introduce the concept of transittability of complex networks, and derive a new sufficient and necessary condition for state transittability which can be efficiently verified. We define the steering kernel as a minimal set of steering nodes to which control signals must directly be applied for transition between two specific states of a network, and propose a graph-theoretic algorithm to identify the steering kernel of a network for transition between two specific states. We applied our algorithm to 27 real complex networks, finding that sizes of steering kernels required for transittability are much less than those for complete controllability. Furthermore, applications to regulatory biomolecular networks not only validated our method but also identified the steering kernel for their phenotype transitions.
This course is anchored on the seven main sections associated with the key Economics areas where the complex systems studies approach to economy has been known to have important influence. These sections are: Section I: A Philosophical and Methodological approach to Economy using Complexity Sciences; Section II: The structure of interaction; Section III: Macroeconomics and Growth; Section IV: Financial Markets; Section V: International and Monetary Economy Dynamics; Section VI: Regional Economic Systems; Section VII: Evolutionary Economic Dynamics. Other than discussing the literature, the students will be invited to model, implement and discuss some of the underlying mentioned models using social simulation programming libraries.