|Fundamentals of Network Science|
|August 2006 |
The Connections workshop series pulls together researchers mathematics, science and engineering who brought together novel ideas and tools from outside their traditional training to influence problems in areas as diverse as Internet protocols, fluid mechanics, biologic signal transduction, ecology, systems biology, finance, and multiscale physics. 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 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. 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.