Connections II
Connections II:  
Fundamentals of Network Science  
1418 August 2006 Pasadena, CA 
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Description
The Connections workshop series pulls together researchers in mathematics, science and engineering who bring together novel ideas and tools from outside their traditional training to influence problems in areas as diverse as networking protocols, systems biology, ecology, geophysics, finance, fluid mechanics, and multiscale physics. An underlying theme of this workshop is to look forward to ways in which future scientists can be educated in mathematical, computational, 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 mathematics, biology, physics, engineering and other disciplines to participate in a 3 day conference exploring the connections between diverse applications and common underlying mathematics, particularly with regard to the role of uncertainty and robustness in complex systems. For the second Connections workshop, we plan to focus on the connections within the mathematics that would form the foundation of a theoretical framework for network science, still motivated by the diverse applications in science and technology that were focus of Connections I.
We are organizing the activities around three main themes (roughly one each day) of Hard Limits, Short Proofs, and Small Models, together with the crosscutting theme of Architecture:
 Hard limits  a major challenge in network science is to understand the fundamental limits on networks due to their components and their interconnection. One challenge is unifying and extending the previously fragmented hard limit theories that arise in thermodynamics, control, communications, and computing, and are often associated with the names Carnot, Bode, Shannon, and Turing. There are encouraging pairwise connections, like the BodeShannon theory developed by Martins et al and others, and this theme will explore the progress and potential for further integration. Also encouraging is the opportunity for overcoming hard limits when new connections are made, such as the relationship between proof complexity and problem fragility.
 Short proofs  in general, overcoming the apparent computational intractability of analysis and design of complex networks is a central challenge, from formal verification of programs and protocols to the robustness analysis of the dynamics of biological networks and advanced technologies. Here the apparent asymmetry between NP/coNP is as significant as that between P/NP, and moving from analysis to synthesis involves higher complexity classes in fundamental ways. Substantial progress has been made recently in creating frameworks to systematically search for short proofs, but the research communities involved and the results are again somewhat fragmented. Fortunately there is also encouraging progress in creating a more unified framework, motivated by new connections within mathematics, the pervasive role of duality, and the concept of "complexity implies fragility" from the first theme.
 Small models  an important route to short proofs is finding small models of complex phenomena through model identification from data, and model reduction. Again, there has been substantial recent progress within relatively fragmented research communities, with encouraging results that suggest the potential for a richer and more unified framework.
 Architecture  a crosscutting theme in the background throughout the workshop will be the challenge of a theory of architecture, as in the claim that "the architecture of the cell and the Internet have enabled their robustness and evolvability." Despite its widespread usage, there is little formalization of the concept and essentially no theory. The existing hard limits theories all assume architectures a priori which are incompatible and incomparable, and thus offer little guidance in the tradeoffs associated with architecture design. Short proofs and small models also arise only in the context of a priori specified proof and modeling architectures. A diverse set of examples of successful and unsuccessful architectures in technology and biology are now available, and motivate the study of a theory. More unified theories of hard limits, short proofs, and small models appear to be essential first steps towards a theory of architecture.
Invited speakers (confirmed)
 Samuel Buss, UC, San Diego
 Mung Chiang, Princeton
 Ali Jadbabaie, Penn
 Neil Gershenfeld, MIT
 Keith Glover, Cambridge
 Bill Helton, UC, San Diego
 Mustafa Khammash, UC, Santa Barbara
 Sanjay Lall, Stanford
 Nuno Martins, U. Maryland
 Antonis Papachristodoulou, Oxford
 Pablo Parrilo, MIT
 Mihai Putinar, UC, Santa Barbara
 Lawrence Saul, UC, San Diego
 Christina Smolke, Caltech
 Lin Xiao, Microsoft Research
Caltech organizers and speakers
 JeanCharles Delvenne, John Doyle, Maryam Fazel, Sichard Murray, Ben Recht, Henrik Sandberg
Agenda
Mon(Tutorial), TueThur (workshop), Fri(Student talks)  
MonThur (workshop)  Daily schedule
 
Monday  Tutorial speaker list
 
Tuesday  Hard Limits
 
Wednesday  Short Proofs
 
Thursday  Small Models
 
Friday  Student talks

Additional Information
The main workshop will be held on 1517 August 2006 in Pasadena, CA, with additional sessions on Monday and Friday for interested participants:
 Monday: tutorial sessions
 Tuesday: Hard Limits
 Wednesday: Short Proofs
 Thursday: Small Models
 Friday: student presentations
 Register to attend
 Participants (restricted page)
The Connections workshop is sponsored by Caltech and the Air Force Office of Scientific Research.