# Connections II

Connections II: |

Fundamentals of Network Science |

August 2006 Pasadena, CA |

In the last five years, the control and dynamical systems (CDS) community has branched out dramatically into application areas that cut across all scientific endeavors. The impact of this work has had an impact affecting areas as diverse as Internet protocols, fluid mechanics, biologic signal transduction, ecology, systems biology, finance, and multiscale physics. Many CDS researchers have brought novel ideas and tools from controls to areas outside their traditional training to influence these diverse fields. But it is increasingly clear that progress in the different domains would be greatly improved by dialog across disciplines: engineers and biologists need to talk to each other, and to theorists who can develop a common foundation. Their communication is hampered first by language barriers, with each area super-specialized in training and research. The communication requires a hard-core re-tooling, a considerable effort to which few scientists are willing and/or able to commit. If an engineer wants to inform biology, time and effort has to be put aside for learning the details and larger structure of biology, a daunting task.

The *Connections* workshop series pulls together people who have
made that commitment at various stages in their careers. An
underlying theme of this workshop is to look forward to ways in which
future scientists can be educated in computation and quantitative
methods, to prepare them to interact broadly from the time they are
students and throughout their academic careers.
The first {\em Connections} workshop, held at Caltech in July 2004,
brought together over 200 researchers in the fields of biology,
mathematics, physics, engineering and other disciplines to participate
in a 3 day conference exploring the the role of uncertainty and
robustness in complex systems. The workshop was structured as a
matrix that brought together researchers from applications in physics,
information and biology to talk about the structure, complex, scale
and design of complex systems. Four speakers in each session were
organized by a moderator who challenged the group before and during
the conference to highlight the common connections in the architecture
and control of diverse complex systems. Each session ended with
biology to highlight the recent application of diverse areas of
controls to biology.

For the second *Connections* workshop, we plan to organize the activities around three main themes (roughly one each day):

- Simple models - one of the key techniques in dealing with complex, network systems is to identify simple models that capture essential phenomena. The CDS community has developed many techniques for doing such modeling, including basic input/output representations for systems and explicit model reduction techniques with undertainty guarantees. Other results include multiscale modeling, learning and ID from data, and model invalidation.

- Short proofs - a key element of any successful theory for large scale networked systems is an understanding of how to generate proofs for complex phenomena. Lots continues to happen around proof automation. It connects with the first thread in that simple models help short proofs. The big win will probably be when model simplification and proof search are coupled through systematic relaxations that exploit symmetries. There are some nice starting points here, and lots of mathematicians are working on aspects of this problem. The tie with 1) is something that is not yet exploited as much as it could be.

- Hard limits - a major challenge in network science is to define the fundmantal limits associated with limits. This thread would be about unifying the previously disconnected hard limits that arise due to thermodynamics, control, communications, and computing. There are now some pairwise connections, like the Bode-Shannon theory developed by Martins, Dahleh, Doyle and others.